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LIBRARY

OF THE

MASSACHUSETTS INSTITUTE
OF TECHNOLOGY

COPY I

EMPIRICAL FOUNDATIONS
OF
ECONOMIC ANALYSIS
83-64
Geoffrey P.E. Clarkson

MASS. INST, TECH.

OCT 30 1964

DEWEY LIBRARY

This essay is a draft for private circulation and comment,
It should not be cited, quoted, or reproduced prior to
publication without the written consent of the author.
The research is supported by a grant from the Sloan
School of Management from the funds provided by the Ford
Foundation and NASA for research in business finance
and organizational decision behavior respectively.

NGv

Dewev

TABLE OF CONTENTS

PAGE

PART ONE: ECONOMICS AND THE STRUCTURE OF A SCIENTIFIC SYSTEM

1. INTRODUCTION 1

2. ON THE STRUCTURES AND CHARACTERISTICS OF A SCIENTIFIC THEORY 12

1. The Structure of a Theory, 13 2. Interpreted Systems
and Empirical Science, 19 3. Testing the Interpreted
Systems, 22 4. Scientific Explanation and Prediction, 26

PART TWO: MATHEMATICAL FOUNDATIONS OF CLASSICAL ANALYSIS

3. CLASSICAL FOUNDATIONS OF ECONOMIC ANALYSIS , . . . 31

1. The Technique of Equilibrium Solutions, 37

2, Comparative Statics and the Displacement of
Equilibrium, 40

4. THE THEORY OF MARKET EQUILIBRIUM ..,,,.. 50

1. Conditions and Postulates of the Theory, 51

2, External Economies and the Slope of the Supply
Function, 57 3. Market Equilibrium, 63 4. Static
and Dynamic Stability of Equilibrium, 70 5. General
Market Equilibrium, 79

5. THE EMPIRICAL CONTENT OF MARKET THEORIES .... o .... . 85

1. Concepts and Condtions, 85 2, Testing and
Theory's Hypotheses, 95

6. AN EMPIRICAL ANALYSIS OF THE CLASSICAL DEDUCTIVE SYSTEM . . 107

1. The Basic Deductive System, 108 2. The General
Deductive System, 112 3. The Market Conditions, 118
4, Equilibrium Analysis and Economic Theory, 120

PART THREE; FOUNDATIONS AND CHARACTERISTICS OF ECONOMETRIC ANALYSIS

7. FOUNDATIONS OF ECONOMETRIC ANALYSIS ............ 128

1. The Basic Postulates, 130 2, Estimating the
Parameters, 136 3. Testing Statistical Hypotheses, 149

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8. SOME PROBLEMS OF APPLICATION 158

1. Lagged Endogenous Variables^ 158 2. Simultaneous
Interdependence, 160 3. The Identification Problem, 164
4, Forecasting, 175 f

9. THE EMPIRICAL CONTENT OF ECONOMETRIC THEORY ......... 180

1. The Initial Conditions, 180 2. Testing Econometric
Hypotheses, 192

10. EXPLANATION AND PREDICTION IN ECONOMETRICS .......... 200

1. Prediction and Empirical Tests, 202 2. Econometric
Forecasts as Predictive Tests,, 204 3, Ceteris Paribus
and Population Stability, 208 4. Micro-Analysis and
Statistical Tests, 212

PART FOUR: BEHAVIORAL FOUNDATIONS OF ECONOMIC ANALYSIS

11. THE ECONOMIST'S PERSPECTIVE , . . . . . . » . . , ...... 221

1. Economic Analysis and the Problem of a River
Process, 225 2, Classical Analysis and Decision
Processes, 238

12. FOUNDATIONS OF BEHAVIORAL THEORY ..o ...... . .... 242

1, A Theory of Individual Decision Behavior, 244

2. Goals and the Structure of Decision Processes, 248

3. On the Explanation of Decision Behavior, 255

4, Towards a General Theory of Decision Behavior, 260

13. SOME PROBLEMS OF APPLICATIONS ...... ,...„.... . 264

1. On the Construction of Decision Theories, 265

2, On Testing Decision Theories, 272 3. The Problem

of Errors, 277 4. Heuristics, Algorithms and Statistical
Tests, 285

14. THEORIES OF ECONOMIC BEHAVIOR--THE CONSUMER AND THE FIRM ... 291

1. On a Theory of Consumer Behavior, 295 2„ On a
Theory of the Firm, 307

PAGE

15. TOWARDS A THEORY OF MARKET BEHAVIOR . . o 318

1. Price Behavior in a Security Market, 321 2. Testing
the Market Processes, 335

16. BEHAVIORAL THEORY, MICRO-ANALYSIS, AND POLICY DECISIONS . . 339

1. Behavioral Theories and Econometrics, 342 2. Time
Series and Behavioral Analysis, 350 3. Behavioral
Theory and Policy Decisions, 354

17. TOWARDS A SCIENCE OF ECONOMICS 359

PART ONE

Economics and the Structure

of a

Scientific System

Chapter 1

INTRODUCTION

Economics is not a well specified discipline. At a general level, it
can be defined as the social science which takes as its subject matter the
behavior of individuals or groups of individuals engaged in the production,
exchange, and consumption of goods and services. The investigation of such
behavior has led some economists to explore the boundaries between economics
and psychology, while others have been concerned with the frontiers conjoining
economics and sociology as well as other social sciences. In brief, the
substance of economics is expanding and the expediency of these alterations
is often a subject of debate. Throughout such vicissitudes the central
objective of economics remains unchanged. It is to describe and explain the
behavior of several types of homoe con omi cs .

This book is concerned with the science of economics. It is not a
treatise on the methods of science. Rather it is an inquiry into the conditions
under which a science of economics can be developed. While much of the economic
literature is devoted to the many aspects of public and private policy decisions,
such prescriptions must ultimately be based upon a knowledge of the relevant
economic behavior. The acquisition of knowledge is the task of science. And
it is toward an examination of this process in economics that this book is
directed.

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The recognition of a specific problem always indicates the beginning of
a scientific venture « Success is achieved when an answer is attained. A
scientific investigation is distinguished by the form of the answer as well
as the type of question to which the venture is addressed. Problems are
raised by posing the question "Why?" and are resolved if the answer is in the
form of an explanation of the "Why?"o To only answer the "What?", "When?",
or "How?" is to evade the primary task of science. The second stage of the
process requires constructing a theory about the events or difficulty in
question 0 The theory must be stated in such a way that it can be employed
as part of the answer to the "Why?"o If the theory is successful in this
regard, ioe, , is able to provide the necessary explanatory link, then this
theory is accepted as part of our empirical knowledge about the phenomena in
question (J

For example, on a cold, rainy day we frequently observe moisture forming
on the inside of automobile windows. The question might well be put;, "Why
does moisture form on the inside of automobile windows under these conditions?"
The answer entails employing our knowledge of the behavior of water vapor in
air to explain the observed moisture. The explanation itself, in outline form,
would consist of the following types of statements; First of all there would
be observations recording that the temperature of the glass in contact with
the coldj, outside air is considerably lower than the temperature of the air
within the automobiles and that the air within the automobile contains water

- 3 -

vapor. Second, there would be the relevant empirical hypotheses which assert
that water vapor in air precipitates as a liquid whenever the air comes in
contact with a surface that is sufficiently cold.

From these statements an explanation of the "Why?" of the moisture on the
window can be constructed, and the general statements or theory within this
explanation are regarded as part of our knowledge about the behavior of water
in air.

In order to provide answers to specific problems the scientific process
leads us to construct theories about particular phenomena. The theories, in
turn, if they survive empirical tests, are then the basis of what constitutes
our empirical knowledge of those particular kinds or classes of events. Con-
sequently, the scientific venture, while principally directed toward providing
answers to specific problems, is at the same time the process by which we
acquire empirical knowledge about specific phenomena.

As economists, therefore, we are faced by a two-fold task: to explain
the occurrence of specific economic phenomena; and at the same time to acquire
and develop a body of empirical knowledge about these economic events. As long
as our theories are responsive to data and can be confuted by experimental
test, then those theories that survive will allow us to perform both of these
tasks.

- 4 -

The heart of the matter is whether the theories of economics are responsive
to data and whether they can be submitted to a process of refutation by em-
pirical test. For if it should be the case that economic theories are stated
in such a way as to preclude their dis confirmation by empirical test, then it
follows that we do not have a basis from which to develop a body of empirical
knowledge of economic events. While such a conclusion may not perturb some
economists, particularly those who are persuaded that a science of human
activity cannot be developed,— it is profoundly disturbing to those who
accept the notion that the principal task of economists is to acquire scientific
knowledge of economic behavior.

Of course, there are many economists who are primarily interested in
deriving normative solutions to the multitude of economic issues which face
nations, communities, firms, and individuals. Such solutions are stated in
terms of what ought to be done under specific circumstances to achieve certain
objectiveSo These prescriptions are not, as a rule, produced from out of
thin air. They are deduced as consequences of particular theoretical frame-
works. If the theory itself is a testable statement of certain economic
processes then such policy conclusions as are derived from it are founded

— A lucid statement of this position is to be found in: Ludwig Von Mises ,
Human Action: A Treatise on Economics , Yale University Press, 1949.

- u -

Of course, there are many economists who are primarily interested in
deriving normative solutions to the multitude of economic issues which face
nations, communities, firms, and individuals. Such solutions are stated in
terms of what ought to be done under specific circumstances to achieve certain
objectives,, These prescriptions are not, as a rule, produced from out of
thin air. They are deduced as consequences of particular theoretical frame-
works. If the theory itself is a testable statement of certain economic
processes then such policy conclusions as are derived from it are founded

— A lucid statement of this position is to be found in: Ludwig Von Mises,
Human Actions A Treatise on Economics , Yale University Press, 1949.

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upon scientific grounds. But if the theory cannot be confuted by empirical
test, there is no possible way by which the stated prescriptions can be
empirically shown to lead to the desired results.

Consider, for example, the case of a gunner in charge of a battery of field
artillery who desires to shell a specific target. From a theory of the be-
havior of projectiles and from a knowledge of the muzzle velocity of the shells
it is possible to compute, under observed wind conditions, the requisite eleva-
tion and bearing. Accordingly, to strike the target the gunner can be instructed
to elevate his guns to such-and-such a position and align them onto a bearing
of so many degrees.

Under certain conditions it is not necessary to start with any theory at
all. If the target is both visible and stationary the gunner can be instructed
to arrive at the correct position for his guns by trial and error. However,
if the target is neither stationary nor directly visible, the only sound way
to proceed is by employing the theory of projectiles in conjunction with
whatever information is available about the target's behavior.

The situation in economics is not entirely dissimilar. If the world
remained the same while experiments were conducted with various economic
policies, it would not be long before a set of normative statements were
developed which could be applied to a large range of problems under specified
conditions. Unfortunately, the economist's world is not nearly so convenient
as the gunner's; it does not remain the same while various policies are tried
out^ Moreover, in most situations of interest it is seldom clear, even after

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the event, why in fact the observed behavior took place as it did. If
economists are to be able to produce normative statements or policy pre-
scriptions on request , these assertions must be directly derivable from the
relevant body of theory. And, what is even more important, if we are to be
capable of demonstrating why the adoption of a specific policy will lead to
the occurrence of a particular outcome or end result , then the theory upon
which the policy is based must be confutable by empirical test. Therefore,
whether one adopts the perspective of the scientist, the advisor, or the
policy maker it is clear that the economist's primary objective is to acquire
a body of empirical knowledge about economic phenomena,

2/
In a recent investigation of the theory of consumer demand— it is shown

that this particular theory cannot be submitted to a process of refutation by

empirical test. That is to say, it is demonstrated that while data can always

be found to support many of the statements in the theory, the theory, including

all propositions derivable from it , does not have sufficient empirical content

to allow it to be confuted by experimental test. Since a theory must be

refutable if it is to serve as part of the explanatory process, it follows

directly that we are unable to employ the theory of consumer demand to explain

consumer behavior. To acquire empirical knowledge about particular events we

2/ ...

— G, P, E, Clarkson, The Theory of Consumer Demand; A Critical Appraisal,

Prentice-Hall, Englewood Cliffs, 1963. "~

- 7 -

must have theories that can withstand empirical tests. Consequently, an
untestable theory of demand does not provide us with a theory with which we
can acquire empirical knowledge about the behavior of consumers.

As scientists and economists we ought to be alarmed by this state of
affairs a If one specific theory places us in a position where we are unable
either to explain the occurrence of economic events or to acquire empirical
knowledge about a particular set of economic phenomena, where are we with
respect to the remainder of microeconomic theory? Is one theory beyond the
pale of empirical science while the rest are able to satisfy scientific
criteria? Or is it the case that the theories of microeconomics are
sufficiently dependent on one another so that if one cannot be confuted then
this dearth of empirical content is passed on to the remaining body of theory?
Alternatively, since all microeconomic theory can be generated from certain
mathematical foundations with the addition of a few behavioral assumptions,
is it the method by which these theories are developed and stated which leads
to their untestable condition?

These are not idle questions o Indeed, it is part of the purpose of this
essay to inquire into the nature of their answers. In particular the second
part of the book is devoted to an examination of the last of these questions.
For if it can be shown that the method by which microeconomic theory is developed
i«eo its mathematical foundations -- leads inevitably to the construction of
of untestable economic theories then such a conclusion will simultaneously
provide answers to the first three questions o

- 8 -

However, in order to be able to discover the answers to these questions
one needs to identify the criteria by which an analysis can be conducted into
the empirical properites of microeconomic theories. Further, it is necessary
to know the criteria by which a theory can be classified as being able to be
refuted by empirical test. While I have no desire to compete with philosophers
of science, the reader and the author must agree, for the duration of the book
at least, on what is meant by each particular term. As a result, it is
necessary to examine, however briefly, the nature of scientific theory as well
as the criteria these theories are expected to meet.

With a description of the analytical tools — the object of the next
chapter — one can then proceed directly to an examination of the mathematical
foundations of microeconomics. If the foundations permit the development of
theories which satisfy the criteria of empirical science, then one can con-
clude that the non-testability of the theory of consumer demand is likely to
be an isolated case in microeconomic theory. If, on the other hand, the
mathematical foundations are such that they inevitably lead to the develop-
ment of economic theories which cannot be confuted by empirical test, then
the theory of consumer behavior is no longer an isolated phenomenon. Indeed,
in this case it is the foundations themselves which are the primary source of
the empirical difficulties.

The second part of this book, therefore, is devoted to the task of examining
the mathematical foundations of microeconomics. Since these foundations do not
by them.selves constitute a theory about observable phenomena, but are rather

- 9 -

the basis from which microeconomic theories are developed, the analysis in
these chapters includes some specific examples of these micro theories.
Accordingly, the object of this inquiry is to examine both the empirical
content of these theories and of the foundations from which they are derived.

For one moment consider one of the possible outcomes of such an inves-
tigation. In particular, what if the analysis demonstrates that microeconomic
theories, by virtue of the manner in which they are derived and expressed,
cannot be subjected to a process of dis confirmation by empirical test? In
this situation it might well be argued that it surely is possible to treat
some microeconomic propositions as independent statements and subject them to
test by themselves. In other words, if microeconomic theories cannot themselves
be subjected to test, can one take individual hypotheses and by a specific
process of parameter estimation independently subject them to empirical tests?

One answer to this query is given by the procedures for measurement and
parameter estimation which are a part of the process called econometric analysis.
If by the application of econometrics either single hypotheses or groups of
such hypotheses can be confuted, then it will no longer matter whether the
classic, mathematically derived, microeconomic theories can be disconfirmed.
For, once one or more hypotheses can be independently subjected to test they
can stand upon their own empirical feet and, as a consequence, are no longer
dependent upon their ancestry.

- 10 -

The question posed by econometrics, which is the subject of the third
part of this essay, is as follows: are econometric methods sufficient to per-
mit the disconfirmation of economic hypotheses by empirical test? If the answer
is in the affirmative the search for the foundations of a science of economics
is at an end. Once hypotheses exist that can survive a direct confrontation
with empirical tests these very propositions become the comer stone upon
which testable theories can be built =>

But if, as the analysis in the third segment of the book shows, current
econometrics methods are not sufficient to permit the disconfirmation of
econometric hypotheses then it is necessary to search among more recent pro-
posals in behavioral theory for the possible existence of the required empirical
foundations o Accordingly, the final part of the book is devoted to an analysis
of recent attempts to reconstruct economic theory on behavioral grounds.

The main task facing economists is to acquire empirical knowledge of
economic phenomena. In order to succeed in this endeavor it must be possible
to develop testable theories of economic processes. Although this entire book
is devoted to a search for the requisite empirical foundations, it is not until
the final chapters that specific grounds are described upon which a science of
economics can be built. This, of course, is not to say that these foundations
are the only possible ones capable of performing in the required manner. Clearly,
after one solution to a problem is presented other more efficient or elegant
ones may rapidly follow. The point to note, however, is that by themselves

- 11 -

neither the classic, mathematical formulations nor those derived from econo-
metrics can stand by themselves as bases from which refutable propositions
can be derivedo

To demonstrate the validity of this last assertion it is necessary, as has
already been noted, to take a brief foray into the nature and characteristics
of scientific theories. While such a discussion may appear superfluous to
the reader, in my opinion it is essential to the progress and force of this
indagation to clarify beforehand the terms, concepts and analytical framework
that is to be used.

t Chapter 2

ON THE STRUCTURE AND CHARACTERISTICS OF SCIENTIFIC THEORY

Everyone who has ever tried to devise an answer to the question, "Why
does (did) such-and-such an event occur?" has been in the position of trying
to construct a sequence of steps which leads in a logical fashion from some
starting point to the event in question,, Frequently, if the event is of
sufficient interest some of the individual steps in this process will be
stated as specific hypotheses or propositions about the behavior of the events
under consideration o These hypotheses will refer to certain properties or
characteristics of these events. And when such a collection of propositions
forms a coherent whole they are referred to collectively as a theory.

Not all such theories, whatever language they are stated in, are adjudged
to be a part of science. Indeed, the problem of what distinguishes scientific
theories from other forms of theory has been an issue of central concern to
philosophers of science for a large number of years,— Accordingly it is not
altogether surprising to discover that there are a number of issues upon which
philosophers continue to disagree. As a result, it is clearly not possible to

"" An excellent and comprehensive statement of the views of a specific
group of philosophers of science is to be found in: 0, Neurath, R, Camap,
and Ci Morris, (eds,), International Encyclopedia of Unified Science,
University of Chicago Press, Vols, I and II, 1955,

- 13 -

assert that there is only one acceptable point of view or one set of
criteria. But, on the other hand, in order to perform a theoretical
analysis such as is proposed in this book a single, analytical frame-
work is required. To satisfy this acquirement as well as to circumvent
a number of the thorny, undecided issues, I have resolved the problem
by accepting and now presenting what appears to me to represent a
consensus of philosophic opinion.

2/
1. The Structure of a Theory—

A theory may be considered as a set of propositions which are
expressed in terms of a particular vocabulary. The vocabulary of the
theory in turn consists of two sets of terms. The first set contains
all the logical terms, e.g. is, not, or, implies, if and only if, etc.
which the theory contains. The other set consists of the extra logical
terms, some ef which may or may not refer directly to observables. In
either case the extra logical terms of the vocabulary can usually be
divided into two classes s those for which no definition is specified
within the theory--the so-called primitive terms j and those which are
defined in terms of the primitive and/or other concepts in the
vocabulary. In a similar manner the propositions of a theory can also
be divided into two classes: The first class contains those sentences

— A lucid exposition of the structure and characteristics of
scientific theory is to be found ins R.B, Braithwaite, Scientific
Explanation, Cambridge University Press, London, 1953, Chapter 2.

-14 -

which are primitive or basic to the development of the theory. These
sentences are frequently called the postulates or axioms of the theory. The
second class consists of those sentences which are derived by the rules
of logical inference from the conjunction of the defined terms and the
postulates. While this manner of representing the structure of a theory
is in some what formal terms it provides a convenient schema by which
they may be described. Hence, when referring to a theory we can conceive
of it as consisting first of all of its primitive terms and its primitive
propositions or postulates. From the primitive terms the remainder of the
vocabulary can be developed by the definitional rules contained in the
theory. From the concatentation of the complete vocabulary and the
postulates the entire theory can be developed by the selective applica-
tion of the cannons of deductive logic.

Viewed in this manner, a theory is a deductive system. Once the
primitive terms and postulates are specified the derivation of further
propositions or theorems can be carried out solely by the application
of the relevant rules of inference. At no time during this deductive
process is it necessary to refer to the meaning of the sentences being
derived. As long as their derivation follows the requisite logical rules
within a specified deductive framework their validity as sentences within

the theory is not dependent on any meaning which might be ascribed to them.

3/
For example^ consider a single deductive system- which contains one

— I am indebted for this example to H. Hochberg^ "Axiomatic Systems,

Formalization, and Scientific Theories^" in L. Gross ^ Symposium on

Sociological Theory ^ Row, Peterson and Co.^ pp. 407-436.

- 15-

priraitive term and four primitive sentences or postulates;

The primitive term in this system is 'point'. The postulates are:

P-1: Every line has at least two points as members

P-2: There are at least two lines

P-3: Two lines do not have two points in common

P-4: For any two points there is a line that they are both
members of.

The one defined term in these postulates is 'line', and it is defined

in terms of 'point' as follows;

D-1: 'line' for 'class of points"

Given the vocabulary and the postulates we can now derive further

propostions within this deductive system as follows;

Step 1: There are two lines--call them A and B By P-2

Step 2: A has two points^ a^ and a- 5 By P-1

B has two points, b^ and b „ . and Step 1

Step 3: At most one point of A can be identical with By P-3 and

one point of Bo Hence there are three points. Step 2.

As a result of this sequence of inferences we can now add the following

proposition or theorem to our system;

T-1; There are at least three points.

Clearly, we can proceed to add further propositions in a similar

manner. We can begin with T-1 and by the application of P-4 and the

definition of a 'line' arrive at the proposition T-2; There are at least

three lines. Throughout this process no reference has been made to the

empirical meaning of T-1 and T-2 or P-1, P-2, P-3.9 P-4 and such reference

is quite unnecessary when we are examining the theory as a deductive system.

-16 -

For example, we could have replaced 'point' and 'line' by the Greek letters
'E' and 'a' so that the definition and postulates would now read:

D'-l: 'a' for 'class of E'

P'-l: Every A has at least two E as members.

p'-2: There are at least two A.

P'-3: Two A do not have two E in common,

P'-4: For any two E there is a A that they are both members of.
Clearly, substituting Greek letters for the terms 'point' and 'line'
is not going to affect our ability to deduce T'-l: There are at least
three E, or T'-2: There are at least three A. Nor would the deductions
be affected if the logical words in the postulates were replaced by other
formal symbols. In fact, if this were done the result would be a

deductive system of the type logicians prefer to deal witho A system

4/
of this sort is called an uninterpreted calculus or deductive system.—

The point to note is that the process of deductive inference is
governed by a specific set of rules which makes no reference to what the
propositions themselves refer to. In order to determine what is meant
by a specific postulate or proposition within a deductive system an
additional procedure is employed.

To explicate this procedure suppose that L, M, N, 0, are the names
of propositions in a calculus where this calculus consists of simple
English sentences. Then, if P, Q, R, S are variables in the language
used to talk about the calculus (the metalanguage), these variables can

— The properties of a number of such calculi are examined in detail
in: A. Church, Introduction to Mathematical Logic, Princeton University
Press, Vol, 1, 1956.

17 -

denote any of the sentences in the deductive system. For example, if the
calculus consists of sentences like 'this object is made of iron' and
'this object expands when heated' their names are L and M respectively;
but in the metalanguage they are referred to as the variables P and £.

To complete the procedure for determining what is meant by such
statements in a calculus, an interpretation must be given to the logical
terms that are employed to link individual sentences together to form
new propositions. For example, if a logical connective is represented
in the metalanguage by '-»" then the problem to be resolved is to decide
on a procedure for determining what is being asserted by the statement
'this object is made of iron' '-»' 'this object expands when heated'.

The resolution proceeds in the following way. Each statement
within the calculus can be assigned a truth value--i.e. P must either
have the value 'true' or 'false'. At the same time each logical
connective must have an associated truth table, where the truth table
specifies the truth value of a statement given the different possible
combinations of the truth values of its component parts. To
illustrate this point the truth tables for two connectives '-*' and
•~' are shown in Tables (I) and (II),

Table (I) Table (II)

P Q P -* Q

K 1 1

F F T

p ~p

I I
F T

-18 -

From Table (I) it is clear that the meaning of the symbol '-»'
corresponds to the meaning usually accorded to the English words
'if... then' or 'implies', and from Table (II) the meaning of the symbol
'~' corresponds to the accepted usage of the word 'not'. But the
point to note is that no matter what the truth values are of the component
parts, the truth table for the relevant connective defines the truth
value for the entire statement.

Consider, for example, the statement P -»• ^ where the truth value of
P is 'true* and the value of ^ is 'false'. Manifestly the value of
P ^ Q is 'false'. Further, this is the only ordering of the truth
values of P and £ which will result in the statement P -► 2. having
the value 'false,'

Within any calculus there are some statements which have the
value 'true' for all truth values of their component parts. Such
propositions are called tautologies and are usually described as being

logically true. If all propositions within a deductive system

5/
are tautologies then this is called a 'pure'— or uninterpreted

deductive system. On the other hand, if the truth values of some

sentences depend not only upon the values of the logical connectives

but also upon whether its components parts are supported by the available

empirical evidence, the calculus is described as an applied or

interpreted deductive system.

— The concepts of 'pure' and 'applied' deductive systems are discussed
in greater detail in; R.B, Braithwaite, Scientific Explanation, op. cit.,
Chapter 2,

-19 -

<■

2. Interpreted Systems and Empirical Science

A deductive system can function as a theory in empirical science only
if some of the extra logical terms within the system are given an
empirical interpretation. Such an interpretation can be provided by a
set of sentences which relate certain terms in the deductive system to
specific observational terms. When a deductive system has been
sufficiently interpreted such that some of its deduced hypotheses can
be directly submitted to empirical test^ then such a system can be
classified as a scientific theory. The theory itself may, on being
subjected to test, be refuted or it may survive each test to which it
is put. The point to note^ however^ is that until a theory contains
some hypotheses which can be directly submitted to empirical test, the
theory is not sufficiently interpreted to be classified as a scientific
theory.

Consider for a moment the pure deductive system represented in
the earlier example. In order to turn this system into a testable
theory suitable interpretations need to be provided for the symbols
'Z' and 'a'. If one chooses the language of physics as the basis
upon which to interpret these signs, then '£% the only undefined concept,
could be interpreted in terms of the intersection of two find hairs or
in terms of the intersection of two specific rays of light. In either
event, once a suitable interpretation for '£' is selected one then has
an interpretation for 'a" , since 'a' is defined solely in terms of 'Z'.
In this particular simple example a suitable interpretation of 'Z'

-20 -

is sufficient to provide a physical interpretation of the entire deductive
system. Accordingly^ it is now possible to inquire into the empirical
relevance of this system. Indeed, one can directly investigate whether
as a matter of empirical fact 'there are at least three points j' and
whether 'there are at least three lines „° In the same manner it is
possible to submit, in this particular example, the remainder of the
deducible hypotheses to a direct confrontation with empirical evidence.

Clearly I could have chosen a slightly different example. I could
have selected for the postulates the axioms for what is usually called
Euclidean Geometry. If this deductive system is provided with a
suitable physical interpretion one could again subject a number of the
inferred hypotheses of this theory to empirical test. For once one
has ascribed a physical interpretation to the terms 'angle' and 'degree'
one can then test the hypothesis that 'the sum of the three angles in
any triangle is one hundred and eighty degrees."

In performing such a test on an applied deductive system it may
well happen that the evidence confutes the hypothesis. If this occurs
then it readily follows that under this particular interpretation,
for exaiqjle, it is a matter of empirical fact that 'the sum of the three
angles in any triangle is not one hundred and eighty degrees.' While this
may well appear as an obvious conclusion it must not be forgotten that
within the pure deductive system this hypothesis remains a valid statement.
What has happened is that by placing a particular physical interpretation
on the system part of this theory has been shown to be empirically false
with respect to that specific interpretation.

- 21 -

Now consider agaln^ for a moment^ the pure deductive system. Also
suppose that I have a theory which is a physical interpretation of this
system. Suppose further that both the deductive system and its physical
interpretation are well developed^ and that the theory has been submitted
to and survived a number of empirical tests. Then, within the context
of its physical interpretation the theory would be a corroborated theory
of empirical science, I now devise a second physical interpretation
for the basic deductive system where I ascribe new empirical meanings
to the terms of the original system. Given the new interpretation I
can now develop this new theory by taking advantage of all the
hypotheses (or theorems) that have already been proved in the original
deductive system. Strictly by placing the new interpretations upon
the symbols contained in the original hypotheses it is possible to
write down at once many of the hypotheses of my new theory. Whether
these hypotheses will be corroborated or refuted is a matter for
experiment and test. But the point to note is that because the second
theory is a new interpretation of a basic system^ one which has
already been successfully interpreted into a tested theory^ the
theorems of the basic system can be immediately accepted as part of
the new theory.

For exait^le^ if the basic system is a pure deductive system of
geometry, and if the postulates of the new theory are particular
hypotheses of physics, then if it can be shown that these postulates
are simply a specific interpretation of the pure geometry, all the
theorems of this geometry become, once suitably interpreted,

- 22 -

hypotheses of the new physical theory.—'

3. Testing the Interpreted Systems

Once we have an interpreted deductive system or theory we are then in a
position to inquire how and under what conditions we are able to submit this
theory to empirical test,— The first and most obvious requirement is that
if none of the theory's hypotheses (these include all hypotheses that are
deducible within the confines of the deductive system) are stated solely
in terms of observables j, then none of the hypotheses can be directly
confuted by empirical test.

The significance of this rather obvious requirement is due to the way
in which meaning is given to propositions (hypotheses) stated in their
normal^ conditional form (see )<> As was noted above a

conditional statement can only be shown to be false if there is evidence
affirming the truth of the antecedent clause. If it is not possible to
observe whether 'p' is true, then to find evidence supporting the whole
statement 'p ■* Q' does not allow us to infer anything about the truth value

—'A penetrating discussion of this point is to be found in: CoG. Hempel,
"Geometry and Empirical Science/' American Mathematical Monthly, Volo 52,
1945. (Reprinted in: H, Feigl and W. Sellars, (eds) Readings in
Philisophical Analysis, Appleton-Century-Craf ts, New York^ 1949, pp. 238-249.

- An excellent history of the criteria of empirical validity is to
be found in: C.G. Hempel , "Problems and Changes in Empirical Criterion
of Meaning," Revue Internationale de Philosophie. Vol. 11, 1950.
(Reprinted in: L. Linsky, (ed) , Semantics and the Philosophy of
Language , University of Illinois Press, Urbana^ 1952, pp. 163-185.

- 23 -

of the clause 'P' . Since the proposition 'P -♦ £' can have the value 'true'
when both 'P' and '£' are false, it follows that we must have some knowledge
concerning the empirical truth value of 'P' before it is pertinent to subject
the hypothesis 'P -► £' to an empirical test.

If none of the theory's hypotheses are stated in terms of observables
then the theory cannot provide us with a proposition within which one can
determine the empirical truth value of the antecedent clause. Under this
condition it is not possible to test for the empirical truth value of any
of the theory's propositions. Consequently^ the theory cannot be refuted
by empirical test. If a theory only contains hypotheses which cannot be
refuted then the theory itself is not saying anything about the world of
empirical science. For once a theory makes an empirical claim then it
is at the same time denying the opposite of that which it claims. If it
is not possible to refute any of a theory's hypotheses then the theory
is not denying anything. Accordingly, it is equally obvious that under
these conditions the theory cannot be making any positive, empirical
claims. Hence if a theory--that is, any of its hypotheses--cannot be
refuted by empirical test then the theory cannot be considered a part
of en5)irical science.

For a theory to be a part of empirical science at least one of its
hypotheses must be stated in terms of observables. Assuming, for the moment,
that we are considering such a theory. Let us now examine the different
ways in which It can be submitted to empirical test. Since a theory consists
of certain basic postulates, some defintions, some hypotheses and some
interpretive rules we can imagine conducting our empirical tests upon the

- 24 -

postulates as well as the hypotheses. l£ the interpretive rules are such
that the postulates themselves can be directly submitted to test then
these tests can be performed independently from the theory for which they
are the deductive base. If these postulates survive such tests then not
only can they be considered as empirical hypotheses but they also serve
as a strong empirical base for the resulting theory.

For example, consider an entire theory as consisting of a long
sequence (conjunction) of conditional statements. Then the postulates
are the initial statements in a number of sequences, where these series
of statements are a part of the entire sequence of propositions
representing the theory. Since the postulates are empirical hypotheses
they provide the empirical truth value for the antecedent clause in each
of the sequences of which they are the initial clause. In sequences
where they are employed in other steps in the deductive process they
again perform the function of imparting an empirical truth value to
that part of the sequence. Consequently^ a number of hypotheses can be
identified for which the empirical truth value of the antecedent clause
can be inferred. Manifestly, with such hypotheses, as long as the
consequent refers to observables the hypothesis itself can be submitted
to empirical test.

Since all theories do not contain basic postulates which are by
themselves empirical hypotheses it is necessary to consider the conditions
under which the remaining classes of theories can be submitted to
empirical test. Clearly, if the postulates cannot be tested directly it
must be possible to deduce some hypotheses which can be submitted to test.

- 25 -

Such hypotheses, as we have seen, must be stated in terms of observables.
And if they are corroborated by such tests as they are exposed to then
these hypotheses in turn provide the empirical support for the hypotheses
from which they were inferred.

It should be noted, as well, that to be able to test a general
hypothesis it must be possible to deduce from it a singular instance
against which the experimental data are to be applied. One cannot test
a general hypothesis or law by employing general data. The best that
can be done is to repeatedly test the general law by subjecting further
specific instances of it to experimental test.

An obvious example of this process can be found if by examining the
general law which asserts , that : every body near the earth that is
freely falling towards the earth falls with an acceleration of 32
feet per second per second. To test the empirical validity of this
law one cannot employ general data about every free falling body
near the earth's surface. To test it at all one must deduce from the

general law the singular statement that: a body starting from rest and

2
freely falling towards the earth falls 16£ feet in t^ seconds. By

specifying some initial conditions--namely, that _t shall have the value

of one second, ---the directly testable statement is inferred thatt a

body starting from rest and freely falling towards the earth falls 16

feet in one second. This, and numerous other such singular instances

of the general law^ can be subjected to the process of refutation by

empirical test. And so long as the evidence does not confute these

statements the general law is accepted as an empirical hypothesis which

has yet to be disconf irmed.

- 26 -
4, Scientific Explanations and predictions—'

Once we have a testable theory of some particular class of phemonema
we are then in a position to inquire how to employ this theory to
establish explanations of the occurrence of those events. To explain
the occurrence of a specific event part or all of the theory is employed
in the following manner:

The theory itself provides the hypotheses and delineates the
initial conditions that must be taken into account if the event is to be
explained. The underlying deductive system provides the rules of
inference by which^ from the conjunction of the Initial conditions and
the relevant hypotheses^ we deduce the occurrence of the event in
question, Hence^ an explanation is established by deducing the
occurrence of an event from the conjunction of the theory's hypotheses
and a specific set of observable initial conditions.

— The term "scientific explanation" has no honorific connotations.

It is used to distinguish the type of explanation discussed in this

book from teleological , as well as other types of explanation found

in discussions of the explanatory process. Accordingly throughout

this essay the terms "scientific explanation" and "explanation" are

used synonymously.

One further item concerns the type of explanatory process discussed
in this section. The following pages are concerned with a brief
description of what is called the deductive-nomological schema. Later
in this essay probabilistic explanations and predictions will be considered.
For a detailed exposition of the explanatory process sees C.G. Hempel
and P. Oppenheim, "The Logic of Explanation," Philosophy of Science^ Vol. 15,
1948, (Reprinted in H. Feigl and M. Brodbeck, (eds) , Readings in the
Philosophy of Science, Appleton-Century-Craf ts , 1953, pp. 319-352.

- 27 -

We have already seen that for a theory to be a part of empirical
science it must contain at least one hypothesis that can be submitted to
empirical test. But before a theory can be employed to establish a
scientific explanation it must contain at least one hypothesis that has
survived a number of empirical tests. It is not sufficient that at
least one hypothesis is refutable, it must have been demonstrated to
be able to withstand empirical tests.

Given that the theory contains at least one general, empirical
hypothesis the other main requirement for an explanation is that the
statements describing the initial conditions be empirically true. If
we are to deduce the occurrence of an event from the conjunction of a
set of hypotheses and initial conditions then just as at least one
hypothesis must have been submitted to empirical test so the initial
conditions must also be empirically true if the explanation itself is
to be empirically true.

The same conditions^ of course^ must be met if we are to establish
a scientific prediction of the occurrence of a particular event. These
requirements must be met for the same reasons as were put forward when
the process was described by which a hypothesis or theory is submitted to
empirical test. If the initial conditions are not known to be empirically
true^ and if at least one hypothesis within the theory has not survived
a number of empirical tests ^ then to employ such a theory to predict the
occurrence of an event is an empirically meaningless affair.

Frequently, the predictions of a theory are employed as a way of
submitting the theory to empirical test. If by this process a correct

- 28 -

prediction is produced then before it is scientifically meaningful as
evidence of the theory's eiq>irical validity, it must be shown that the
theory contains at least one empirical hypothesis and that the initial
conditions were empirically true. Otherwise we are in the position which
can be represented by the case where we are dealing with the conditional
statement 'P -♦ Q' and where we do not know the empirical truth value of
'P'. If 'P' is false then 'P -► (^' is true whether '£' is true or not.
Hence^ solely by correctly predicting and observing the occurrence of 'Q'
we have not learned anything about the empirical truth value either
of 'P -» Q' or 'P"o But if from empirical observation 'P' is true then
to correctly predict and observe ''^' permits us to corroborate °P -* Q' „
Hence, a prediction has the same logical form as an explanation and must
meet the same requirements if it is to be classified as a part of
empirical science.

Summary

Having examined the logical structure of a theory^ the conditions
under which it can be subjected to empirical test, and the manner in
which it can be employed to establish scientific explanations and
predictions it will aid the analysis in the following pages if author
and reader are both quite clear on what it is that a theory is expected
to do„ In particular, what characteristics or properties are expected

of a theory of economics? A comprehensive answer to this question is

9/
given by Quine— c, and by a direct interpretation the following statement

— Williard Van Orman Quine, From a Logical Point of View^ Harvard

University Press, 1953j, pp. 53-54o

- 29 -

describes what we might expect from a theory in microeconomics o

One begins by describing the desired class of significant sequences of
observed behavior to which the theory refers, as the class K, Class K is
itself the culmination of four classes, H, 1^ J, K, of observable statements
of economic behavior. These classes are of increasing size and are
described as follows; H is the class of observed sequences of behavior,
excluding any which are ruled inappropriate in the sense of being beyond
the scope or domain of the theory. For example^ if the theory is concerned
with the production and distribution process of the firm, the observed
behavior of consumers might be ruled as being beyond the domain of the
theory. Similarly, statements of observed behavior belonging to other
subject matter such as physiology or biology, would also be ruled as
inappropriate to H. 1 is the class of all such observed sequences of
economic behavior and all that will ever be professionally observed,
excluding again those which are ruled inappropriate. Hence, for class
I the theory of the production and distribution process of a firm would
include all professionally observed sequences of behavior relating to
the production and distribution process of the firm. J is the class
of all observable sequences of economic behavior ever occurring, now
or in the past or the future^ whether professionally observed or not,
excluding once again, only those sequences which are ruled to be
inappropriate. K^ finally, is the infinite class of all those sequences
of behavior, excluding the inappropriate ones as usual, which could
be observed. Hence, K is the class which the theorist would like to
approximate in his formal reconstruction, where K is more inclusive
then J, notwithstanding H and lo From this description it can be seen

- 30 -

that the class of statements contained in H constitutes at best the growing
record. Class J on the other hand includes statements that go beyond any
record even though these statements still have a certain common sense
reality. However^ very little can be said about the reality of the state-
ments included in K because of the word 'tould' ^ .

A theory that is constructed by making observations within H can and,
as a rule^ is tested by applying it to other sequences of observed behavior
in H. If the theory survives in H and is not confuted by any part of it^
then it is within the class of I that disconf irmation or continued
corroboration must come« Although the theory may be presumed to hold
in J and K^ science is restricted to testing its theories against observable
sequences of behavior. Consequently^, a theory can only be subjected to
test within H and J, As a result, no matter what our feelings are toward
the "eternal truths" embodied in any particular theory, the domain of
observable events over which we may speak of a theory holding--i„eo not
having been disconf irmed--is in practice delimited by the classes H and !_,

As scientists we are committed to the working hypothesis that although
our theories may be false in J we can only talk about their empirical
validity within H and I^, Thus^ if a theory is to be empirically testable^ and
if it is to explain and predict the occurrence of specific events, then we
can conceive of its function as that of being able, in principle^ to generate
all of the relevant, observable sequences of behavior included in H and I^,
It is in carrying out this investigation--namely, of seeing whether the
sequences of behavior generated by the theory conform with those contained in
H and l--that we in fact submit the theory to test and determine whether it can
be accepted as empirically confirmed.

PART TWO

Mathematical Foundations
of
Classical Analysis

Chapter 3^
CLASSICAL FOUNDATIONS OF ECONOMIC ANALYSIS-

In order to be able to understand the way in which economic theory
has been and currently still is developed it is necessary to examine the
basic deductive system from which the theory is derived, as well as the
empirical interpretation that is placed upon the terms once the theory
is constructed. This chapter is concerned with an investigation of the
former--i.e. the mathematical basis of microeconomic theory- -leaving
for later chapters the task of examining the rules by which these theories
are empirically interpreted.

To help focus attention on the significant properties of the
mathematical foundations consider the following simple example of the way
in which an answer is produced to a specific economic question. The
problem is to determine what the effect will be on the output of a firm
if a tax on output is imposed. To answer this question we need to know
the relation between a tax on output and the firm's output itself. That
is to say^ if such a tax is levied will the firm increase or decrease its
output? Or if such a tax is already in effect and is further increased will
output increase or decrease. The answer to these questions is provided
in the following ways

First consider a firm for which the demand curve for its goods and

— This chapter is primarily based upon P.A. Samuelson's classic book.
Foundations of Economic Analysis, Harvard University Press, 1947, Further,
in order to facilitate reference to this excellent analysis of the
mathematical foundations, the notation employed in this chapter is kept
the same wherever possible.

-32-

services is known. For simplicity take the case where the firm produces

only one item. Then our knowledge of the demand curve will tell us the

quantity of items the firm will produce at various market prices. To proceed

with the analysis we also need to known the relation between the total

production cost for the firm and its output--the production cost schedule.

Given that these two main items are known we can then state that the

total profit for the firm for any particular price for its product is

the difference between its total revenue and Its total costs

If X represents the quantity sold,

p(x) represents the market price for this quantity

C(x) represents the lowest total product cost at which each
output is produced

n represents total profit.

then

n = X p(x) - c(x)

Now if a tax of t dollars is imposed on each unit of output x, then the
total tax payment is given by _tx„ Thus, after such a tax is imposed the
firm's total profit is:

n = x p(x) - C(x) ' tx (3ol)

Suchj, then^ is the general form of the effect of a tax on output upon
the profit of the firm. But, before this statement asserts anything about
the firm's behavior in response to this tax it must be possible to write
down the relations assumed under the terms x p(x) and C(x) , Further we must

be able to produce the requisite initial conditions, ioe, in this case a

' o

specific tax rate of, say, t_ dollars per unit. Once the tax rate is given

then the output of the firm at this tax rate, x_, can be represented by;

-33 -

x° = g(t°) (3.2)

where the relation g(t ) represents that specific set of parameter values
in the equations representing xp(x) and C(x) which will yield an output
of x_ for a tax per unit of (t ).

For any particular collection of equations representing xp(x) and
C(x) there are a variety of different sets of parameter values which will
yield an output x_ for an initial condition of t . Each of these
different sets of parameter values represents a solution to the total
system of equations » Since there can be as many possible solutions
the (sets of parameter values) as there are equations in the theory some
restrictions must be introduced if we are to have a unique solution to
the problem^ If such restrictions are not imposed, then each real
solution provides a separate answer each of which is as valid as any
other. Accordingly^ without a rule for selecting among solutions
we would be unable to arrive at a single answer to the original
question.

To generate a unique solution it is assumed that the firm will
select for the given tax rate t_ the particular output which will
maximize its profit (net revenue). By introducing this assumption
the possible set of different solutions are restricted to exactly that
one set which will satisfy this maximum or equilibrium restriction.
The answer is arrived at by applying the conditions for this equilibrium
to the theory of the firm's behavior represented by (3,1),

The equilibrium conditions for a regular maximum of profit with
respect to the output under a specific tax rate are

- 34-

^M"", *^) ^ 0 (3.3)

^ n(x. t) < Q (3,4)

The first condition (3.3) states that for the firm to be maximizing
net reserve it must be at a point such that the slope of the function
depicting profit against output is equal to zero. While condition (3,4)
insures that we do have a maximum by excluding the cases of being at a

minimum or a saddle point.

2/
Applying condition (3.3)— to the original equation (3.1) the first

restriction is written as

1^ [xp(x) - C(x) - tx] = 0

Hence

^ [xp(x) - C(x)]- t = 0

t = I- [xp(x) - C(x)] (3.5)

By solving equation (3,5) we determine its roots. By taking the
second differential of (3,5) with respect to x we can ascertain whether
the solutions developed for (3,5) represent the position of a maximum
or not. If condition (3,4) is satisfied for all relevant values of x
and t^ then we have determined the equilibrium quantity x that corresponds
to the tax rate t_.

In equation (3,2) it was noted that for a specific sec of parameter

-By applying conditions (3,3) and (3.4) to equation (3.1) we are
implicitly assuming that all the function represented in (3.1) contain
continuous first and second derivatives everywhere over the relevant
domain.

- 35-

values in the functions xp(x) and C(x) a tax rate t^ yields an output x°.
In equation (3.5) the same result is described in a more general form.
In (3.5) it is clear that for each value of _t there will be a set of
parameter values for the functions on the right hand side^ and that
this set of values will be the equilibrium solution for those specific
values of t^.

Once the firm's output for each tax rate is determined (as long
as the firm continues to maximize its profit) the next step is to
discover how the values of the equilibrium output behave with respect
to changes in the tax rate. Presumably^ this question can be answered
by solving equation (3.5) and working out numerical answers for
different values of t^. To perform these calculations the relations
represented by xp(x) and C(x) must be specified for a particular firm.
Further^ these relations must be stated in a form that is suitable .
to analytic or numerical analysis. Given that the requisite knowledge
is available explicit numerical solutions can be calculated and the
results plotted. Accordingly^ one can graphically determine the rate
at which the equilibrium output alters with respect to changes in the tax.

However^ from our knowledge of the equilibrium conditions we can
also analytically derive some conclusions about the rate of change of
output. Since we have already deduced that the equilibrium output for
each value of the tax rate Is given by

t = ^ [xp(x) - C(x)] (3.5)

we can differentiate (3.5) with respect to £ to arrive at the following
rate of change as follows:

-36-

where x° and t^ denotes that we are differentiating with respect to

equilibrium values.

Carrying out the differentiation this equation is reduced to

1 = (|f)° {-\ [x°p(x°) - C(x)]3 (3.6)

From (3.6) it follows that the equilibrium rate of change of output with
respect to t^ is given by

,ax o 1

(3t> - .2

^ [x°p(x°)-C(x°)3

ax2
But we also know from the previous analysis of equation (3,5) that for all

relevant values of x and t^

^ [x°p(x°) - C(x°)3 <0l/
Hence it follows that

(||,° < 0
which states that as long as the firm is maximizing its net revenue both
before and after the tax on output is applied then as the tax rate is
increased (decreased) the output will decrease (increase). Without
specifying in complete detail the functions represented by xp(x) and C(x)
it is not possible to determine the specific rate at which output will

— This being a sufficient condition to assure a relative maximum^

see relation (3.4),

-37 -
increase or decrease. But without employing such detail we can determine^
under the equilibrium restriction, the direction of this rate of change.

In this example two basic analytic techniques are employed that
characterize a large part of the mathematical foundations of microeconomics.
But in order to derive a clearer understanding of exactly what they entail
for economic analysis we need to examine them in additional detail.

1. The Technique of Equilibrium Solutions

In the example of the tax on a firm's output it was assumed that
we knew the demand and production cost schedules for a firm. While these
relations were represented by two terms , xp(x) and C(x) , this system of
functions were neither specified nor examined in any detail. To do so let
us take the general case where the economic system, including the demand

and production cost schedules^, can be described by n variables (x,^X2,o.,,x )

<
and ro parameters (a, ..ao .■><><>« jiQt ) where m - n„ It is assumed that these

n variables and m parameters are contained in n independent and consistent

functional relations.

In the tax example we supposed that we knew the demand and production
cost schedules for the firm. Accordingly we were supposing that we could
write down in complete detail the specific equations^ variables and
parameters which pertained to that firm.

In general terms the total system of functional relations can be
written in the following way:

■38

f (x ,X2, • • • >x ,ct, ,Q!2^ • • • ^Q^j-) = ^
2

*• \^i ^ x^ ^ O O « ^^_ ^Ct-1 ^Qf^ ^ O O O ^Q!„/ — ^

(3.7)

where each relation is represented as being a function of all n variables and m
parameters. Of course,, in any particular case the values of many of the
parameters for each relation would be equal to zero. But when considering
the general case it is useful to express the system as noted in (3.7),

Given n independent and consistent functional relations there are in
general n possible sets of solutions. In other words^ it is possible that
there are n different sets of values of the parameters (a, ^.a^ ^ • • » ^o; ) which
correspond to n different values of the variables (x^^X2,o..,x )^ each set
of values representing one solution to the functional relations.

In the tax exan^le the possible set of solutions were reduced to a
single one by imposing the conditions for equilibrium (3,3) and (3,4) upon
the system. The addition of these conditions determined a unique value for

the variable x which corresponded to a given value of t^„ These two values

o o
are labelled x and t . For the general case we can employ the same

notation and represent the equilibrium solution for the system by that set
of values for the variables (x? ,x„^ , , , ,x ) which correspond to the given
values of the parameters (a?.,a°^ , ■> , ^0;°) . The equilibrium values of x^^ are
thus a function of some specific parameter values (aj^ 5^2 .' ° » ° 'Q^m^ " "^^^^
relation can be expressed as;

X? = gi(a° a° „o.,a°) (i=l,2,,,,,n) (3.8)

1 k i.' m

-39-

which clearly corresponds to relation (3.2),

In order to discover the equilibrium values x. in the general case the
procedure is to impose a set of initial conditions (choose a set of parameter
values) and to constrain the possible set of solutions by employing the
first and second order conditions: For the general case these constraints are
represented by:

Ajj f (Xj^^x2^ o » o ,x^,afj^^a!2j o • » ^QCjjj) ~ ^ (3 •9)

^2 ^

Sx.

If (3olO) is satisfied for the relevant parameter values then the solution
to the system of relations represented by (3=9) is the unique set given

by (3.8)^ i.e.

o _ i^ o o O /• 1 9

X. — g t.QIi ^QJo ii ° " ° .'Ctjj,^ (^i— i J,/ J, o « o ^n}

Consequently, for any given case if we are able to completely specify the
relations contained in (3,7) j, then by selecting the initial conditions and
by imposing (3,9) and (3«10) we are able to arrive at the unique solution
represented by (3<,8)„ Further, by solving for the relations expressed in
(3.8) we can then determine the equilibrium values for all the variables
of the system that correspond to this particular set of parameter values.

In the problem on the effect of a tax on the output of a firm the
equilibrium solution for the tax rate jt is given by;

^ = >Z [^P(^) " C(x)3

o o

For an initial value of t_ there corresponds an unique value of x given by x .

This value can be precisely computed if the relations represented by xp(x) and

C(x) are known. In this specific case it should be noted that the equilibrium

- 40 -

conditions correspond to the behavioral postulate that firms behave so as to
maximize their net revenue. Accordingly, given this postulate we are able
to Infer that the firm In question is operating at a point of maximum net
revenue which in turn permits the deduction of the relation between the tax
rate and output as noted above.

Returning to the general case it is clear that if the economic system
under investigation can be represented by n independent and consistent
functional relations consisting of n variables and m parameters, then an
unique solution to this system can always be determined if and only if
the conditions for equilibrium representing some behavioral postulates about
the system are imposed.

2. Comparative Statics and the Displacement of Equilibrium

Once we know the relations governing a specific economic system we can^
with the aid of a maximizing or similar equilibrium postulate^ determine
its equilibrium solution. In most practical applications^ however^ a
variety of difficulties are encountered. The first and most obvious
obstacle is that it is not always possible to state the precise set of
relations of which the system under investigation is composed. While
we may be able to note its general form as well as some of the variables that
must be included, we are frequently unable to specify for a particular case
the empirical relations that constitute the system, A second difficulty is
raised by the parameter values themselves. Not all the variables in these
economic relations refer to items that can be directly observed. As a result,
a number of parameters do not refer to observational items. But to generate

- 41 -

a specific, equilibrium solution the initial values of the parameters must be
specified. Consequentlyj, within any particular application it may not be
possible to derive a solution which is stated entirely in terms of
observableso

If specific equilibrium solutions could always be generated for each
economic application, then it would always be possible to plot the way in
which a variable of interest altered given certain changes in the initial
conditions. In the tax example this would mean that if one were able to
completely specify the solution of t=^ [xp(x)-C(x) ] , one would then be able
to plot the different values of x that would correspond to a variety of
assumed tax rates. Once this was accomplished, and as long as the system
of relations continued to represent the economic system in question, then
one would be in a position to state^ for example, exactly how the
equilibrium output of this firm would respond to alterations in such a
tax rate.

Unfortunately, we are not always going to be able to derive specific
equilibrium solutions for which the results may be plotted by varying the
initial conditions. At the same time, for a variety of reasons, we still
would like to know something about the responses of the particular economic
system to selected changes in the initial conditions. As a result an
additional technique is required, known as comparative statics , which allows
us to determine the directional change of individual variables in response
to a selected change m the initial conditions.

The method of comparative statics proceeds by subjecting the equilibrium
solution to shifts in its parameter values. These shifts are then en^loyed to

- 42 -

determine the slope or directional change of selected variables. The entire

analysis is conducted under equilibrium restrictions so that these conditions

can be employed to help derive the unique solution to the new system. More

specifically, suppose that we wish to determine the rates of change of some

or all of the variables within the economic system with respect to a change

in the initial value of, say^ gi<. To effect such an analysis we proceed

in the following way:

We begin, of course, with the current equilibrium solution to the

system. That is to say, we already have the initial conditions given by

the parameter values (a?^a^ » • • » 9Ct°) with the corresponding set of variables

(x, .x„,...,x ). At the same time we have the system of relations at their
^ 1^ 2' ' n'

equilibrium values given by

i/OO OOO O, p. f s ^ o r,\

as well as the solution to this system given by

O i/ O O On /,• 1 -> „\

X. = g {a, ,ar, i " -> )0c ) (i=i,^, o. o,n;

X i Z" m

We now want to determine the rate of change of the variables with

respect to a, » To accomplish this we take the first derivative of the

variables in the relations f (x. ,x „ 5X° ,0!, ,a_ , o . . ,a ) with respect to

12 • n 1 2 m

a, 5 while at the same time holding the values of all the other parameters
constant. By taking the partial derivative of each relation with respect
to a, and holding all other parameter values constant we generate a system
of n relations as follows;

- 43 -

ax O ax O 1 ^''n ° 1

2 ax o 2 ^""2 ° 2 ^""n ° 2

(3.11)

a o V V

ax, o ax^ o ax

f n^ 1) ^ f n 2^ n n ^ .^ n

x/^^ x2-aa^^ x^^^^ a^

where the symbols

-i af o o o o o o.

X ~ ax ^^■\)^2^°°'^^n^^l^'^2^°'°'^m
J J
and

i _ af o o o o o o.

a ~ a^ \'^-j^>^2' ° ° ° ^^n'^l''^2^ ° ° ° ^'^m

and where within each relation all the remaining variables and parameters are
kept constant.

These relations while formidable in appearance correspond directly to
the single relation given by (3o6). In that case the term

f "■ = f ^ = -^ [x°p(x)-C(x)], while the term f^^ = f J = ^ [t] = lo After
performing the partial differentiation of x with respect to t_ we were left
with the expression

(|7)° i^ [x°P(x°)-C(x°)]} = 1 ,

^^ ax^

To solve this equation in terms of the desired rate of change, (^) , the
second order condition for equilibrium was employed to show that the value of
-^ [x°p(x°) - C(x°)] < 0 .

ax^

Thus 5 we could immediately conclude that the value of (^) was also less than
zero.

- 44 -

In the general case we proceed towards a solution with respect to the

^x. o
desired rates of change (^ — ) in a similar way.

^1
If we examine the relations expressed in (3.11) more closely we see that

the f are all constant terms and that the f represent the coefficients
-a, ^ -X. '^

1 dx o J

of the n variables (t— ) o Accordingly^ (3.11) is a system of n linear
equations in n unknowns.

The solution for such a system of linear equations for the non-singular

case is readily represented in matrix terms;—'

OX o A 1=1 a, —is
/ Ss _ _' si 1

^^^ - lAf- m

^^S— X^Z, « o o y^)

(3,12)

where A = f

£ X o o e £

'^l ^^2 ''n

.22 2

f f ... f

^1 ^2 "^n

f " f " ... f "
12 n

and where A. represents the cofactor of the element of the ith row and the

—is ^ —

sth column.

jx o

In order to solve for the exact values of (Tr~) it is necessary to

know all the values of all the f terras appearing in (3.11). But all we

j Sx o

primarily interested in knowing is the algebraic sign of the (T~~) terms.

Consequently, although we do not need to know the exact values of the f

—This procedure is examined in more detail in Appendix A.

- 45 -

terms, we do need to know their algebraic sign.

To evaluate (3.12) in terms of its signs it must be possible to determine
the sign of |a| and A^g.

The value of |a| is given by the product of nl terms, each of which is
the product of n elements. If we are to be able to deduce the sign of JAJ
we clearly need to know the signs of the n! . terms. Further to know,
unambiguously, the signs of the nl. terms we need to know the signs of the
individual n elements which comprise these terms. Since these individual
elements are the signs of the f^^'s we seem to be caught in an unpleasant
position. For by this analysis it appears that we must know the direction
of the rates of change before we are able to solve for them. Clearly,
this does not constitute a solution to the problem. And In order to effect
a solution a slightly different direction approach is required.

A solution is achieved by placing a number of restrictions upon the way

Sx o
s
in which the signs of the unknowns, (^r~) , are allowed to shift with

respect to changes in selected parameter values. The first restriction

requires that cases only be considered where one parameter is allowed to

shift at one time. The second condition requires that this change in the

parameter may only alter one of the equilibrium relations as are represented

in (3.11). By requiring that a change in the i^th parameter must leave all

others but the i^th equation unchanged, the rate of change of the Lth variable

to the remaining parameters must be equal to zero. Under these conditions

it is possible to arrive at a criterion with which we can ascertain the

direction of the rate of change of the J^th variable in response to a shift

^x. o
in the i^th parameter--i.e, the sign of ('^T") is determinable.

- 46-

The criterion is derived from the first and second order conditions for

an equilibrium and is given by the following statement;—'

Sx o
f i-^) > 0 (3.13)

This criterion states that under equilibrium conditions the rate of change
of the i^th variable with respect to a shift in the i^th parameter is of the
same sign as f , where

- ,_5_. . S_. ^.oo ooo o.

x.a. " ^bxJ^'^oT^ t(Xj^^x2,,..,x^,aj.,a2^°'"^°^n''
11 i 1

If the shift in the equilibrium equation is in the same direction as an

Sx. o
increase in x, , then £ is positive. Under this condition (■rr-) is also

i i i

clearly positive. Similarly if the shift in the equilibrium equation is

in the opposite direction to an increase in x. , then both f and
^ -1^ -x.a.

dx. o 11

(■sr— i^) are negative.

To illustrate the application of this criterion let us reconsider the
example discussed earlier in this chapter. Once again the object is to
discover the direction of the rate of change of the equilibrium output of
a firm with respect to a shift in the tax rate. We have already seen that the
net profit of the firm with a tax imposed upon its output is given by (3.1) or:

n = xp(x) - C(x) - tx
Now if the firm is operating so as to maximize its net revenue than the
equilibrium criterion states that the direction of the rate of change of

—'The steps of the proof leading up to the statement of this criterion
are given in Math Appendix,

- 47 -

output, X, with respect to a shift in Jt is determined by (3.13). In this
case the criterion is expressed by

where

fxt = <lr>d> " = (|e)d)t(^P(^) - C(x) - t(x)] .

Taking the two partial differentials of n with respect to x and t we have in

successive stages; first

th.„ ^ = -1.

Substituting the value of f into (3.14) we have

-xt

ax °

From which it follows that (^) < 0, which states that the equilibrium output
of the firm will move in the opposite direction to a shift in the tax rate.

Summary

The purpose of this chapter has been to examine the basic deductive
system that underlies microeconomic theory. While one particular economic
example was employed to briefly illustrate the application of this deductive
framework to a specific problem, the principal concern has been to inquire
into the basic components of this deductive apparatus. As a result of this
investigation it is clear that the basic components of the mathematical
foundations are as follows?

- 48 -

(1) If we are able to represent the economic system under investigation by
n independent and consistent relations consisting of n variables or unknowns,
then a unique solution to the values of these variables can be determined, only
if we in^ose the first and second order conditions for equilibrium upon the
system. By the imposition of these equilibrium conditions we also require
that the n independent and consistent relations have continuous first and
second derivatives everywhere over the relevant domain, (As a matter of fact

certain analytic techniques allow us to be able to include relations which have

6/
selected types of discontinuities,— but aside from these specific exceptions

the relations must have continuous first and second order derivatives.)

(2) Given that we can derive the equilibrium solution to our economic
system we are then in a position to determine the direction in which specific
equilibrium variables will shift in response to certain changes in specific
parameter values. To be able to determine these directional shifts in the
variables we need to restrict our attention to the particular case where an
alteration in a single parameter affects the value of only one equilibrium
variable. In other words to find the direction of the rate of change of one
equilibrium variable with respect to a change in one parameter, all other
variables and parameters must be treated as constants.

Stated in terms of the analytical framework presented in the previous
chapter the deductive system can be represented in the following way: The
basic postulates are the behavioral assumptions which are represented by the
two equilibrium constraints (3.9) and (3,10) „ The hypotheses of the system

— See P. A. Samuelson, op, cit. , pp. 70-73,

- 49 -

are the set of n independent and consistent relations which are represented
by (3,7). The logical rules of inference are those which pertain to the
differential and integral calculus for the sinqile reason that this is the
calculus that is employed to express and manipulate the system's hypotheses.
As expressed, for example, by the three sets of relations (3.7), (3.9), and
(3.10) the deductive system can be called pure. Such a system becomes empirical
significant when some or all of its terms are related to observational terms.
Accordingly, in order to begin the exploration of the way in which these
basic components are employed in the statement and development of economic
theory the next chapter is devoted to an examination of the microeconomic
theory of market equilibrium.

Chapter 4
THE THEORY OF MARKET EQUILIBRIUM

The theory of market equilibrium is a theory of the behavior of firms and
consumers in the market place. The theory itself is stated in mathematical
form and as a result the behavior of firms and consumers is represented by
mathematical relations « Whether these relations can be sufficiently
interpreted such that they themselves, or consequences deducible from them,
can be confuted by empirical test is a question to be examined in later
chapters. For the moment it is the process by which such a theory is
developed that is of primary interest. Accordingly, this chapter is concerned
with an examination of the specific application of the economic deductive
system which leads to the microeconomic theory of market equilibrium.

The theory to be examined refers to a perfectly competitive commodity
market. Although there are a number of theories which refer to specific,
different types of markets,, e.g. monopoly, monopsony, duopoly, oligopoly, to mention
but a few of the possible cases, each is developed by a similar application
of the rules and constraints of the economic deductive system to a specific
set of initial postulates. Hence, the selection of the perfectly competitive
market for examination in no way restricts the scope or relevance of the
analysis of the process by which a theory of market equilibrium is developed.

The object of a theory of market equilibrium is to describe the
mechanisms which determine the quantities bought and sold^ as well as the
prices at which these transactions take place. The market consists of
consumers and firms, and the combination of all their purchases and sales
constitutes the total volume of transactions. While the consumer may be the

-51 -

buyer and the firm the seller in a market for one particular kind or class
of goods^ e.g. automobiles^ the firm is the buyer and the consumer is the
seller in the market for the consumer's labor. In a number of markets firms
are both buyers and sellers ^ such as in the case of mining companies that
produce and distribute various ores to manufacturing conpanies who purchase
the ores. In all of these cases it is the interaction between buyer and seller
that is of principal interest and to which the market theory is primarily
addressed,

1. Conditions and Postulates of the Theory

A commodity market is classified as perfectly competitive if the
following conditions are satisfied: (1) the firms operating within this
particular market all produce a specific type of commodity such that the
product of one firm is indistinguishable to the consumer from that of any
of the other firms 5 (2) the consumers of this market are such that they all
appear identical to the sellers so that there are no special advantages to
be gained or losses to be incurred by selling to one consumer rather than
another^ (3) the number of consumers and firms is sufficiently large so
that the purchases or sales of each specific unit is small in relation to the
total volume of transactions within the market j (4) information on prices
and quantities offered within the market is such that both consumers and firms
have perfect knowledge of the current prices and bidss (5) there is no
restriction on participating in the market-=i,eo both consumers and firms
are free to enter and leave the market at any time.

-52 -

The first condition requires all firms within the market to be producing
a homogeneous product. If brand names, special promotional schemes, trade-
marks, and other means for identifying products exist then the market does
not satisfy this condition. The object of the condition is to identify a
market in which consumers have no criterion other than price with which to
distinguish the product of one firm against that of another. The second
condition is a complement to the first in that it requires the consumers of
this market to be indistinguishable from one another with respect to the
sellers. As a result firms within this market have no criterion other than
price by which they decide to sell their produce to one consumer rather
then another.

The third condition requires that the number of consumers and firms be
sufficiently large so that the purchases or sales of any one individual
are not large enough to significantly affect the market price. Accordingly,
both consumers and producers perceive the prevailing price for a particular
commodity as the only one available and make their decisions to buy or sell
on the basis of this price alone.

The fourth and fifth conditions ensure that both producers and consumers
are fully aware of the current prices and bids for the commodities in question.
If this information is such that the consumer or the producer decides to
withdraw from the market then there is no restriction associated with
this decision. As a result neither consumers nor producers can buy or sell
except at the prevailing price^ and the market is determined to be perfectly
competitive if these conditions are satisfied by both buyers and sellers.

- 53-

The first main hypothesis of the theory is that a consumer's demand for

a specific product in the market is a function of the price of the product, the

prices of all other products within the market, and his income. Consider the

ith consumer and the 2th commodity. Then this hypothesis can be stated as

follows:

2ij = ^ij^Pl^Pz^'-^Pm^yi^ (i=l,2,,..,n) ( j=l,2, . . . ,m) (4.1)

where D represents the ith consumers demand for the ith commodity,
-ij

(p p . ..,p ) the prices of the m commodities in the market, and ^ and

i^th consumer's income.

If we are concerned solely with the market for a particular commodity,

say 1^., then we are interested in the behavior of the demand for Q- with

respect to a change in its prices £., From the previous chapter it is clear

that in order to determine the rate of change of one variable with respect to

a shift in a single parameter value one can only do so if all other variables

and parameters are treated as constants. Thus, to determine the rate of change

of the ith consumer's demand for Q. with respect to a shift in p. all other
— —J *-J

prices and quantities must be treated as constants. Consequently, the demand
for ^., although still depending upon the prices of the other commodities and
the consumer's income, becomes a function of £. alone, i.e.;

Dij=Dij(£j) •
Since the i^th consumer within a competitive market is indistinguishable
from any other consumer with respect to a seller the demand for £. for all
consumers is solely a function of the price of this commodity. Further, since
there are n consumers each of which demands a certain amount of Q . at a

-54 -

specific price £,, the total market demand for 2.4 is given by the sum of the
individual quantities demanded:

°j = i?l^ij<Pj) =Dj(£j)
or by dropping the product subscript

D = Ji D.(p) = D(p) (4.2)

where (2) is derived by holding all other prices and the incomes of all n
consumers constant.

For example, consider a market which only contains two commodities
Q, and Qo— . If the i^th consumer spends all his income on these two
commodities then his expenditure can be represented by:

^i = Pl^l +P2^2 ^""'^^

where £, and £ are the prices and q^^ and £„ at* the amounts purchased of £,

and £2 respectively. Under equilibrium conditions the quantity demanded by

the ith consumer for each item is directly deduced as:
— o ■' o

^il = ^1 = ^ ""' °i2 = ^2 = ^ (^•^)

— While a two commodity market may appear somewhat unrealistic to the
reader, realism can be introduced by considering one of these items as a
composite commodity defined in the Hicksian sense. Under this definition
Q2 , for example, includes all other commodities including savings so that
the total amount spent on £1 and £2 represents the consumer's total income
for the period. For further discussion of this point see: J.R. Hicks,
A Revision of Demand Theory, Clarendon Press, Oxford, 1956j and G.P.E.
Clarkson, op. cit., Chapter 3.

- 55-

where C, and C- are constants and where D^^ and D^2 can be seen to be

monotonically decreasing functions of price.—' By summing over all consumers

in the market the result is a market demand curve for each commodity, i.e.:

^1 = Ql = C^ °2 = <52 = C^ <^-^)

where Y° is the total equilibrium level of income for the n consumers. Since
(4.4) is derived by holding income and the other price constant, the relations
in (4.4) are clearly a function of the single price, £j^ or 2^' Similarly the
aggregate demand functions of (4.5) are also monotonically decreasing functions
of one price alone.

The second main hypothesis of the market theory is that the function which
represents the amount a firm will produce of a particular item depends solely
upon the market price for this item. Under the equilibrium postulates a firm
produces at the point where marginal cost equals market price. Thus, the supply
function of the firm is identical to a portion of the function representing the
marginal cost curve of the firm for that item. Under conditions described as
the "short-run", where each firm may vary output but is unable to vary the size
of its plant, the relevant segment is that portion of the marginal cost curve
which lies above the firm's average variable cost curve.

—'To demonstrate that demand curves are monotonically decreasing functions

of price under certain general conditions it is necessary to take into account

the Slutsky relation incorporating the income and substitution effects. This

relation is derived ins E.E. Slutsky, "On the Theory of the Budget of the

Consumer," Giornale degli Economisti, Vol. 51, July, 1951, pp. 1-26. (Reprinted

in, American Economic Association, Readings in Price Theory, Irwin, Homewood,

Illinois, 1952, pp. 27-56. For an excellent presentation of the proof of the

monotonicity of demand curves sees J.M. Henderson and R.E. Quandt, Microeconomic

Theory, McGraw-Hill, New York, 1958, Chapter 2.

- 56-
Since the marginal cost curve measures the quantity a firm will supply of a
particular item over a range of market prices^ the short-run marginal cost
curve is a function of output and price. Hence, the relevant portion of the
£th firm's marginal cost curve for a single item can be represented by:

MC^ = ^±i^i) (4.6)

where MC. is the first derivative of the i^th firm's total cost of producing the

3/
item taken with respect to the output.—' Under the short-run condition the

supply function for the i^th firm is obtained by applying the first order

condition for equilibrium and by solving for £. . From the first order

condition the relation p=MC. is inferred. And by solving for q. in terms of

a supply function S^. we get;

S^ = S.(p) for all £ that lie above the minimum point on the

average variable cost curve

(4.7)
S^ = 0 for all £ that are below the minimum point on the

average variable cost curve.

The aggregate supply function for commodity Q is obtained in the same
manner as the aggregate demand function. All prices and costs of other
commodities are held constant so that the sum of the n individual supply
function represents the aggregate:

S = ill S^(p) = S(p) (4.8)

By applying the second order conditions for equilibrium it can be shown that in

— If the i^th firm cost function for item ££ is represented by

C=<I)(qi)+b5 i<,e. a function of the level of output plus the cost of fixed
inputs^ ^"^i^^i ='^'^^^ since b is a constant.

- 57-

most normal—' circumstances the rate of change of output with respect to changes

in price is positive. Further that the £th firm's supply function is a

monotonically increasing function with respect to price. Thus, due to the

process by which it is derived, the aggregate supply function is also a

monotonically increasing function.

Under conditions described as the "long-run" the firm is regarded as

being able to adjust the values of all variables. In the long-run, then, the

supply function is identical with that portion of the marginal cost curve

which lies above the firm's average cost curve. The long-run supply function

is derived under the same conditions as above and for the i^th firm it can be

represented by:

S^ = Sj^(p) (i=l,2,,..,n)

Consequently, the long-run, aggregate supply function is given by:

S = J^ S.(p) = S(p) (i=l,2,...,n) (4.9)

2. External Economies and the Slope of the Supply Function

In the preceding analysis it is noted that in most normal circumstances
the supply function can be shown to have a positive slope. As part of the
hypothesis about the supply function the firm's costs are assumed to be solely
a function of its output. Earlier the i^th firm's cost function for a
specific item was represented by:

—See: J.M. Henderson and R.E. Quandt, op. cit., p. 90.

-58 -

C = 4>(q) + b (A. 10)

where b represents the fixed costs and £(£) the variable costs associated with a
particular level of output. In this case, the function £(£) reflects the labor,
material, and other costs which vary with the output level. If all these items
do not depend upon the level of output or behavior of any other firm, then
the supply function for the i^th firm can be shown to have a positive slope.

However, it frequently happens that a firm's total costs do depend upon
the output of other firms. Other firms may develop new methods of production
which allow them to increase output as well as reduce price. If the i^th firm
employs these items within its manufacturing process its cost function will
reflect the lower input costs. Similarly if new industries arise which use
many of the same raw materials as firm i^, the enlarged demand for these inputs
may raise their market price. Accordingly, the increased costs will be
reflected in the i^th firm's cost function. As a result there are two possible
cases where the cost function of firm i^ is affected by the output levels of
other firms. The first is where an expansion of, say, the j^th firm's output
lowers the total cost function of the i^th firm--a situation where external
economies are realized. The second distinct possibility is when the expansion
of the 2th firm's output raises the total cost function of the i^th firm--a
situation where external diseconomies are realized.—

—'A clear discussion of the classical problem posed by external economies and
diseconomies is presented in: J.E. Meade, "External Economies and Diseconomies
in a Competitive Situation," Economic Journal, Vol. LXII, March, 1952, pp. 54-67.
For an excellent analysis of the various welfare solutions that are possible under
these circumstances see: O.A. Davis and A. Whinston, "Externalities, Welfare,
and the Theory of Games," Journal of Political Economy, Vol. IXX, June, 1962,
pp. 241-262,

- 39 -

In order to inspect the e££ect external economies and diseconomies have
upon the slope of the supply function it is necessary to represent the £th
firm's cost function as dependent upon the output levels of all n firms:

Ci = <i>^i<lj^,<l2' '">%'> ii=l,2,...,n)

where £. is the output of the ^th firm. At the same time the profit of the ith
firm is the difference between the total revenue derived from the sale of
commodity £. and the cost of producing this output C^. If the market price
for q. is given by £, then the ^th firm's profit is

"i = Pli ■ ^i (i=l,2,...,n) (4.11)

For the n firms in this commodity market there are n functions represented by
(4.11). In order to discover the equilibrium solution we proceed as outlined
in the previous chapter. First we apply the first order condition which in
this case requires that we differentiate H. with respect to £. and set this
partial differential equal to zero. In order to take the partial differential
of n^ with respect to £. it must not be forgotten that at the same time the values
of all other variables are held constant. Proceeding with this application of
partial differentials to the system of functions in (4.11) we have:

^ = P-^ = P-%<^l'^2---^n> =°

(4.12)

n ^n ^n

By imposing the second order conditions that

bh.

2^ (^l,<l2>'-->%'> > 0 ^°^ *11 (i=l,2,...,n)

upon the system of relations in (A. 12) the unique, equilibrium solution to this
set of functions is generated in terms of q.. By writing these solutions in
terms of S instead of £ the following system of solutions results:
Si = Sj(p)

S2 = S2(P)

S = S (p)

(4.13)

Now, if the slopes of Si,S9,...,S are known then it is possible to infer the
slope of the aggregate supply function

S = Ji S^(p) = S(p) .
But each firm bases its output decision upon the relevant portion of its own
marginal cost function. Hence, each firm, for example the i^th firm, observes the
equilibrium output values of all the other firms (qi ^q2^ • • • ^qh^'li ^ • • • >^ ) ^^^
selects that value of ^. for his own output which satisfies his own
equilibrium relation:

1 1.00 o o o. „

1 1

Similarly, the equilibrium value of £? may affect the output decisions of other

entrepreneurs. Hence, while the supply functions (4.13) state that, after all

these adjustments are made, the equilibrium outputs are a function of price they

do not include a reference as to the sign of their respective slopes.

To determine the slopes of the respective supply functions one either needs

to know the signs of all the coefficients in (4.12) or one must apply the methods

- 61 -

of comparative statics. In the latter case one would apply the schema outlined

In the previous chapter and by a suitable application of restrictions Infer

the directions of the rates of change of the various quantities to their

respective prices. Of course, this analysis can only be carried out if the

equilibrium solutions to the system of relations in (4.12) are known. But

presuming that these relations have been solved then this solution can be

employed as the initial conditions in order to proceed step by step to the

resolution of the signs of the Individual rates of change. If each of the

supply functions S^. has a slope with the same sign, then the aggregate

function S will also have the same sign. But if not all S. are either
— —1

positive or negative then without knowing the relative magnitude of each
component we are still unable to determine the sign of S.

In the former case, however, we know the signs of all the coefficients
in (4.12). If we represent the cost functions of the n firms in the following
way

^1 = ^1^1 -^^2^2 + ••• -^-^In^n

S = *21^1 ■^*22'l2 -^ ••• +^2n^n

• « • •

2 2 2

C = a , q, + a -q + ... + a q
n nl^l n2^2 nn^n

then the coefficients, whose signs we know, are represented by a, , ,a ^ ,a, ^ . . . a .

—11'— 12'— 13' '— nn

If the market can be characterized entirely in terms of external economies -- 1. e. ,
an expansion in the output of each firm lowers the total cost function of at
least one other firm--then all a. . for (i^j) must be negative. At the same time,
of course, we need to know the signs of the remaining a^^. when (l=j). If they

- 62 -
are all of one sign, say positive, then we can proceed to a unique solution in

the following way. From (4.12) the equilibrium relations are given by:

a^ = P ■ '*ii^i =

■r — = p - 2a„„Q„ = 0
bq^ ^ 22^2

•r — = p - 2a q =0
da nn^n

Solving these equations into the form given in (4.13) one gets:
'^ ^ 2*11

n 2a

where the aggregate supply function is

^ = i?i^i = 2 (ir- + ir-^---+r-) <^-i^>

11 22 nn
If, as supposed, all ±^if (i=j)^ are positive then it is clear that the slope of

(4.14) is also positive. Similarly, if all a.., (i=j), are negative then the

slope of (4,14) is negative. But, if not all of the a. ., (i=l), are either

positive or negative then once again we need to know the relative magnitude of

each a. ., (i=j)^ before the slope of the resulting aggregate supply function

can be determined.

- 63 -

3. Market Equilibrium

The equilibrium of a commodity market is realized when the quantity demanded
through the aggregate demand function is equal to the quantity supplied through
the aggregate supply function. Since both functions are stated in terms of the
market price for a particular commodity, one condition for equilibrium is
realized if one price prevails for that commodity throughout the market.
Consequently, for market equilibrium of a particular commodity,

D(p) = S(p) (4.15)

Under short-run conditions sellers can vary output but not their plant and
equipment. Hence, if under these conditions (4.15) does not hold for some
price 2. - R^ > then either buyers wish to purchase more of the commodity than
is available at £ or sellers wish to sell more than is being purchased at this
price. If such an event occurs then various efforts can be expected to be
made to alter the price £^ so that both buyers and sellers are making consistent
demands upon each other.

For example, suppose the production facilities of each supplier are such
that the requisite quantity of the commodity in question can be produced in a
very short period of time. Further, suppose that buyers and sellers enter the
market for the purpose of making contracts to buy and sell certain quantities
at specific prices. If these contracts are such that they entitle both
parties to recontract if either or both parties are able to find more
favorable offers, then the process of contracting and recontracting will not
cease until each buyer and supplier is completely satisfied. If an auctioneer
records the price and quantity of each contract as it is made so that all
participants are aware of all bids and offers, then because of the equilibrium
conditions imposed upon both buyers and sellers the contracting process will

- 64 -

proceed in one of two possible ways.

If the price of the initial contract, £, , is such that buyers are unwilling
to purchase at this price all the items that suppliers indicate they are willing
to supply, some suppliers will attempt to recontract at a lower price, £„. Once
£„ is announced by the auctioneer all contracts at £^ are renegotiated and
suppliers will soon see whether they are able to sell all that they are willing
to supply at the new price. If they are unable to do so recontracting will
take place at a yet lower price, £„. This process continues until such time
when the contract price is just sufficient to allow the suppliers to sell all
the items they are willing to produce at this price. Such a price is, of
course, the equilibrium price, £ . Once all contracts are made at this price,
suppliers produce the required output and both consumers and sellers are
satisfied.

If, however, the initial contract price, £,, is such that consumers are
willing to contract for more items than the suppliers are willing to produce
at this price, then the recontracting process works in the opposite direction.
Now, it is some of the consumers who offer a higher price, p„, which then
becomes the price at which new contracts are made. At £_ suppliers are willing
to increase the amount they are willing to produce. If this amount is not
sufficient to satisfy the consumers demands recontracting continues until the
auctioneer announces a price, £°, at which both consumers and suppliers are
satisfied.

Despite the restrictive nature of this example it is clear that the
equilibrium conditions imply that the market for a particular commodity, in the
short-run, is in equilibrium if and only if there is one price which
simultaneously satisfies both consumers and producers. Consequently, within any

- 65 -

particular market the equilibrium price is determined by solving the demand and
supply functions (4.2) and (4.8) under the constraint D(p) = S(p).

For long-run equilibrium each producer may alter his output as well as
his plant and equipment. At the same time his supply function is now
equivalent to that portion of his marginal cost curve which is above his long-
run, average cost curve. Consequently, for a market in which there are a
specific number of firms the equilibrium price for this market will be given
by the intersection of the aggregate, long-run supply and demand functions,

i.e., D(p) = S(p).

In this case, however, we must take into account the amount of profit each
firm is making at the equilibrium price. Since we started with a specific number
of firms the equilibrium price may be such as to allow some or all of these
firms to receive more than the minimum returns necessary to them to remain in
business. If such is the situation then new firms will be enticed to enter
this market. At some market price, £j , the profits accruing to an efficient
firm will be such that new firms will enter this market. Once this occurs the
aggregate supply function will be increased. As a result, the market price, £„,
necessary to clear this larger amount will be lower than £, . As long as new
producers enter the market the recontracting process will permit the price to
fall until a point is reached where excess or above normal profits can no longer
be earned. At this point long-run demand equals long-run supply and excess
profits are zero. Hence, for long-run equilibrium in a single commodity market
there are two conditions which must be satisfied;

D(P) = S(p)
and

- 66 -
n = p ill q^ - ill C^ = 0 (4.16)

Substituting Eq. = S and $.(q.) for C^ (4.16) becomes

n = pS - Ji *i(<li) = 0
But if there are n firms in the industry each producing £. , the total cost for the

i^th firm of producing q., if all firms have identical cost functions, can be

S S

represented by ^. (— ) . Substituting £.(-) for 0. (q.) we get:

n = pS - E$ . (-) =0

n = pS - n(D^(|) = 0 (4.17)

Consequently, by applying the equilibrium conditions (4.15) and (4.17) to the
long-run supply and demand functions we can not only determine the equilibrium
price for a particular commodity, but also the number of firms in the industry,
as long as all these firms have identical cost functions.

A. An Example—

In the preceding discussion it is implicitly supposed that consumers and
producers are sufficiently near to each other so that no reference is made to
transportation or other types of marketing costs. In many markets, however,
consumers and producers are not spatially near one another and some producers have
to ship their products greater distances than others. If such a market is to be
in equilibrium only one price may prevail. As a result, since some firms have
greater transportation costs than others, this difference in costs must affect

—'This example is taken from J.M. Henderson and R.E. Quandt, op. cit..

pp. 101-104.

-67 -

the amount they are willing to supply. To explore the manner in which firms

within such a market behave--city markets for dairy products are representative

examples--we apply the equilibrium analysis in the following way.

First we need to include the transportational costs in the total cost

function of the representative firm:

C. = *.(q.) + b. + a.q, (^.18)

X 11 1 1 i

where $.(q.) and b. represent, as before, the variable and fixed cost components,

and where a. is the cost per unit of £. for transporting it from the firm to the

city market. The profit for the i^th firm is given by:

n = pq^ - ^^i\) - b^ - a^q^ (4.19)

By applying the first order conditions for equilibrium to (4.19) we have:

an. ps

T^ = P - ^ <I>.(q.) - a. = 0
Bq. oq. i^^i' 1

^ a>^(q^) = p - a^ (4.20)

Accordingly, to be operating at equilibrium output (4.20) states that the
firm should equate the marginal cost of production to the market price minus
the transportation cost. If each of the n firms in the industry has the same
production cost function ^j(q£) but has a different transportation cost a.f then
the marginal cost of production will differ for each firm. Thus, for a
specific equilibrium price, £°, each firm will be willing to supply a different
amount. In the short-run, the market will be in equilibrium when the total
supply equals the total demand.

To make the example more specific let us suppose that the firms supplying
commodity £ to a market can be divided into two classes: those whose

- 68 -

transportation costs are 10 dollars a unit and those whose costs are 13
dollars a unit. There are one hundred firms which are evenly divided between

the two classes. If all firms have the same production cost functions, £{(^-)^

2
then the total costs for the respresentative firms, where *. (q^) = 0.5q. +a.q-^

are given by:

2 2

Cj^ = 0.5qj^ + lOqj^ C2 = .05q2 + 13 q^^

where the subscripts 1 and 2 represent firms of the two classes. Applying the
first order conditions for equilibrium we get from (4.19) and (4.20):
qj^ = P - 10 q^ = p - 13

The supply functions for these firms are derived in the same manner as

(4.7) by substituting £. and q . , and remembering that £. = 0 for all points on

the marginal cost curve which lie below the minimum point on the average variable

cost curve. Under these conditions the representative supply functions are:

S^ = 0 if 0 < p < 10

S = p - 10 if 10 < p

(4.21)
$2=0 if 0 < p < 13

$2 = P - 13 if 13 < p

Hence, firms in the first class will not supply any output if the price is less
than 10 dollars, while the second class of firms will not supply any output if
the price is less then 13 dollars a unit.

The aggregate supply function is derived as in (4.8). Since there are one
hundred firms this function is given by the following relations:

S = 0

0 < p < 10

S = 50(p-10) = 50p - 500

10 < p < 13

S = 50(p-10) + 50(p-13)

= lOOp - 1150

13 < p

To solve for the equilibrium price level we need to know the aggregate demand
function. Suppose this function can be represented by

D = 30p + 250 .
Then the equilibrium price is determined by setting £ == D, or:

lOOp - 1150 = 30p + 250

p = 20

and

S = D = 850

From (4.21) each firm in class 1 sells 10 units while each firm in class 2

sells 7. From the profit relations^

% = pq^ - Cj(q^) n2 = pq2 - C2(q2)

we can determine that each firm in class 1 makes a profit of 50 dollars while
each firm in class 2 makes a profit of 20 dollars. In the short-run this result
constitutes an equilibrium position.

For a long-run equilibrium, however^ we need to impose the additional
constraint that profits must be equal to zero. In this particular example
long-run equilibrium could be achieved in a variety of ways. One way would
be for new firms to enter the geographical location of the class 1 firms until
such time as the price per unit falls below 13 dollars. At this point the firms
in class 2 would no longer produce and the market would be con^osed solely
of class 1 firms. Another possibility would be for the owners of the land

- 70 -

nearer the market to charge a higher rent than that being charged the class 2
firms. As new firms enter the market, to take advantage of the higher
profits of the class 1 location, rents would rise until such time as they made
the net profit from the two locations the same. While neither of these
processes need necessarily lead the market to a point of zero profits, some
combiuacion of these and other similar processes must take place if the
market is to reach a long-run equilibrium position.

4. Static and Dynamic Stability of Equilibrium

The previous section is concerned with the process by which equilibrium,
both short and long-run, is attained. In describing the process, however, it
was noted that the opening price on any market need not be the equilibrium
price. Further, once equilibrium is reached a shift in consumer preferences
or a shift in the supply curve, caused by some technological or other change,
can alter the equilibrium. Since there are a variety of factors which can
disturb the equilibrating process two possibilities are evident? the first is
that the disturbing factors may prevent an equilibrium from ever being
attained^ the second is that once it is arrived at the equilibrium point may
not be a stable one. If an equilibrium is stable then the market will return
to equilibrium no matter what disturbance has affected it. But, if an
equilibrium is unstable then the market will not return to equilibrium once it
has reached and been disturbed from this equilibrium point. Consequently, it
is necessary to inquire into the properties of equilibrium points, both in
static and dynamic cases, so as to be able to distinguish those that are
stable from those that are not.

- 7L -
A. The Static Conditions

In the last section it is shown that a market equilibrium for a particular
commodity can be achieved if after each set of contracts are made both buyers
and suppliers can recontract if and when more favorable opportunities become
available. If the initial price is such that consumers are willing to contract
for more of the commodity than the sellers are willing to supply at that price,
the price is increased by some consumers to enable them to increase their
purchases. Under a static analysis there is no concern over the path
described by this process over time. Instead we merely wish to know the
direction of each change or adjustment, and whether this is toward or away
from the equilibrium point.

In order to be able to examine the adjustment process it is necessary to
introduce the notion of excess demand at a particular price. If the price
prevailing at any instant in a market is not equal to the equilibrium price then
there is excess demand at that price. If the prevailing price is above (below)
the equilibrium point the excess demand is negative (positive). In figure 1
there is a negative excess demand at price £2, and a positive excess demand at
price £j , Due to the condition for market equilibrium, e.g., D(p) = S(p), there
clearly cannot be any excess demand at price £ . Consequently the excess
demand at any price £ can be represented by:

p
p.

Figure 1
dE(p)

72 -

E(p) = D(p) - S(p) (4.22)
Suppose, for the moment, that there is
excess demand in the market under
consideration, then the question to be
answered concerns the direction of the rate
of change of E(p) with respect to changes
in £. If the price is at £, and shifts
toward £° then, because E(p) decreases with

this shift in £, ""^'T' < 0, If the price shifts from £„ towards £ then, for the

same reason, ^^^^ < 0. Hence, as long as the rate of change of E(p) with
'dp ~

respect to change in the market price is negative the market is moving toward
an equilibrium.

To ensure that this condition is met an additional constraint, or postulate,
is imposed upon the behavior of the consumers in the market. This constraint,
which is known as the Walrasian stability condition, requires buyers to raise
their bids if excess demand is positive and sellers to lower their prices if it
is negative. If buyers and sellers behave in such a manner so as to satisfy this
condition then as long as a shift in price reduces the excess demand the market
is stable. The Walrasian stability condition is given by:

So far the stabilizing process has been regarded as one which is solely a
function of shifts in the market price. However, in the analysis of market
equilibrium suppliers may respond to shifts in prices by raising or lowering
the amount they are willing to supply. As a result, we must inquire into the
conditions under which these shifts in the amount supplied affect the stability
of the market.

- 73 -

To isolate the effects of the shifts on the supply side the notion of an
excess demand price is introduced. If at any point of time in a particular
market there is a difference between the price consumers are willing to pay and
the price sellers are asking for a specific quantity of a commodity then this
difference is the excess demand price.

An excess demand price can occur in the following way. If we take the

aggregate demand and supply functions, D(p) and £(p) , and restate them in terms

of the quantity (not price) required for market equilibrium, the equilibrium

condition is D=£=q. At equilibrium there is one price, £ , at which consumers will

purchase this equilibrium quantity £ , But, at any point other than at £° , there

is a price, £ , at which suppliers are willing to sell this quantity. At the

same time there is also a price, £,, at which consumers are willing to buy such

a quantity. At all points other than at equilibrium the supply price, n, is

not equal to the demand price, p^. To determine these prices for a specific market

one solves the aggregate demand and supply functions in terms of p and p^ as

follows:

P^ = D"^(q)

P3 = S"^(q)

where D and S are the inverses of the aggregate demand and supply functions.—

Once the demand and supply prices are known, the excess demand price is given by

the difference between the two, or;

E(q) = Pj - Pg = D"\q) - S'^(q) (4.24)

— If for the relation y=f (x) there is a solution it can be written as

x=f~^(y), where f~^ is what is called the inverse of f(x). For further discussion

see Appendix A.

^2 ^

Figure 2

The stability of the market depends^
then on the direction of the rate of
change of E(q) with respect to a
shift in £. If for a certain market
the quantity to be supplied is
represented by £ , in Figure 2, the
demand and supply prices are given by
D, and £ . If the quantity supplied

shifts from £^ toward £ then we are interested in the directional shift E(q) .
Since in this instance, E(q) will decrease as £ shifts toward £°j, ,^'^ < 0.
Similarly, if the quantity supplied is represented by £„ and then shifts toward
q , , ^ < 0. Accordingly, the market will approach a stable equilibrium as
long as the rate of change of the excess demand price is negative with respect
to changes in the quantity supplied. To ensure that this condition is satisfied
producers must be willing to increase output if E(q) > 0, e„go, such as when
q^ represents the amount they are currently supplying. At the same time they
must also be willing to decrease output if E(q) < 0--epg., when at a position
represented by £ This requirement on the behavior of producers is known as
the Marshallian stability condition. Consequently, the market is in stable
equilibrium in the Marshallian sense if

^ = Ji »"'(') - ^ ="'<'> < ° <*•")

If the aggregate demand function has a negative slope and the aggregate
supply function has a positive slope both conditions, (4,23) and (4.25), are
satisfied. Manifestly, under these conditions the market is stable from both
points of view. However, if external economics or diseconomies are present

- 75 -

within the market the supply function may have a negative slope. Under this
eventuality both equilibrium conditions cannot be simultaneously satisfied.

To show that such is the case divide both sides of (4.25) by
[^ D-^(q)] . [As-l(q)] to get

But

35 s-'(')

' s-^,)

^ ■>"'«.)

< 0

(4.26)

=d^^(P>

d n-1, , dq
di° <^>

D(P)

(4.27)

By substituting these values into (4.26) we get;

^S(p) -^D(p)<0
But the Walrasian stability condition (4,23) states that:

^D(p) -^S(p)<0

Clearly both cannot be satisfied at one time. Thus^ if the equilibrium is stable
in the Walrasian sense it is unstable in the Marshallian^ and vice versa.

For example^ consider the situation represented in Figure 3, At price^ £ ,

the amount demanded equals the
amount supplied^ £ , and the market is
in equilibrium. But, if a disturbance
occurs and the price temporarily
shifts to £- there will be a positive
excess demanded represented by AB.
q Under the Walrasian conditions buyers
will tend to raise their prices and
Figure 3 the excess demand will be reduced.

q° q,

- 76 -

Concurrently, however, suppliers are willing to produce q^ at £ which implies a
positive, excess demand price represented by AC. As a result, under the
Marshallian conditions, producers will tend to increase the supply. If the
supply increases consumers will be unsuccessful in their attempts to reduce
the excess demand by raising the price, and the actual price and quantity will
move away from the equilibrium point.

B. The Dynamic Conditions

In the dynamic case we are interested in examining the time path of the
process by which equilibrium is reached. If we revert to the example where
consumers contract with suppliers at one price and then recontract at a new price
the minute a more favorable contract can be made, we are now interested in
path these successive prices describe over time. This recontracting process
is dynamically stable if, over time, the price approaches the equilibrium
price. It is dynamically unstable if the direction in which the prices change
is away from the equilibrium price. Stated in this manner dynamic stability
has been defined in a Walrasian sense. Clearly, it is also possible to examine
the path described by the recontracted quantities. If these approach the
equilibrium quantity over time then the market will be dynamically stable in
the Marshalliam sense.

To explore the conditions under which an equilibrium is dynamically stable

the Walrasian position is adopted here. Accordingly, the analysis is based upon

a study of the effects of excess demand upon price.— As has already been

— The same analysis can be applied under Marshallian conditions but is

omitted here for brevity.

- 77 -
pointed out consumers respond to an excess demand by raising the price. If each
price change is considered to take place within a discrete interval of time,
this process can be represented by:

a E(Pt.i) = Pt - Pt-l ^""'^^^

where a is a positive constant, £ the price at period t, and £^_j^ the price at
the period before t_. While there are numerous different relations which will
express a similar type of behavior, (4.28) states that a positive excess demand
in period t-1 will induce a price increase in period t^. Suppose for the moment
that the aggregate demand and supply functions are known and that they can be
represented by the relations:

D^ = b p^ + c (4.29)

S = d p^ + e (4.30)

t t

Then from relation (4.22) excess demand in period t-1 is:

E(t-l) = (b p^.^ + c) - (d p^_^ + E) = (b-d)p^.j^ + c - e (4.31)

By substituting this result into (4.28) we get:

a[(b-d)p , + c - e] = p - p..,

^ ^ c t i (4.32)

[1 + a(b-d)]p^_^ + a(c-e) = p^
which represents the behavior of the price, £, as it shifts from one period to

the next.

At equilibrium the aggregate demand equals the aggregate supply, and excess
demand is equal to zero. Therefore, by setting D =S in (4.29) and (4.30) we can
solve for the equilibrium price £^=£ as follows:

From (4o32) we know the path that the market prices will describe (as
long as the relation (4.31) is satisfied by the market). And from (4.33) we

- 78 -

know the value of the equilibrium price, £ , in terms of the constants in the

aggregate demand and supply functions (4.29) and (4.30). What has yet to be

determined is whether and under what conditions d will approach £ as time
increases.

To be able to answer these questions it is necessary to solve the relation

(4,32) in terms of £ . But, to solve this first order difference equation we

9/
need to know the initial value of £ at t=0— . Suppose for the moment that

£=£, at t=0, then the solution of (4,32) in terms of £ is given by:

Pt = (Pi "Sf> t^ +a(b-d)]'^ +£lf (4.34)

Since the last term in (4.34) is the value of the equilibrium price,
the equilibrium is dynamically stable if p -► -r-r as t^ increases. This will
occur--i.e. £ will converge directly to £ if

0 < 1 + a(b-d) < 1 (4.35)

Now, if the aggregate demand function has a negative slope, b < 0, and if the
aggregate supply function has a positive slope, d > 0, then under these two
conditions b < d which is sufficient to ensure that, 1 + a(b-d) < 1. For the
left hand side of (4.35) to hold

^ < d^ C4,36)

where a measures in these relations the degree to which buyers and sellers adjust
their bids in the presence of excess demand.

If the aggregate supply function has a negative slope the equilibrium will
be dynamically stable as long as b^ < d. For since r is the slope of the demand
function (4.29) and — is the slope of the supply function (4.30), the equilibrium

— See math Appendix for solution procedure.

- 79-

is dynamically stable as long as r- > -r* —

Oscillations around the equilibrium level are introduced if condition
(4.35) is not satisfied and, 1 + a(b-d) < 0. This can occur if both a < 0 and
b-d < 0, and a is sufficiently large to make 1 + a(b-d) < 0. If the values of
a, b, and d are such that -1 < 1 + a(b-d) < 0 the equilibrium is dynamically
stable and the price converges to £ with decreasing oscillations. But,
if 1 + a(b-d) < -1 then the oscillations about £° will increase with time
and the market will be dynamically unstable.

Dynamic stability in a market in^lies, of course, that the market is stable
under static conditions. The converse, however, does not follow. Thus, a
market which satisfies the Walrasian or Marshallian conditions for static
stability may at the same time be dynamically unstable. Consequently, when
analysing the equilibrium position of a particular market great care must be
taken to identify both the type of analysis relevant to the investigation as
well as the behavioral conditions which are supposed to control the equilibrating
process.

5. General Market Equilibrium

So far the analysis has been concerned with the processes by which
equilibrium is attained in a single commodity market. In order to focus on
these processes the analysis excluded any interactions between the markets for
different commodities. As a result, the quantities of other goods bought and

— It should not be forgotten that this analysis is dealing with the
Walrasian stability conditions. Under Marshallian conditions this would be
an unstable equilibrium.

- 80 -

sold at their respective prices are treated as parameters when the
equilibrium price and quantity within a single market is being determined.
If we were faced with the task of finding the equilibrium positions of n
different markets, one way to proceed would be to treat each market as a separate
entity. Under this arrangement each factor and its price would be a variable
in the analysis of its own market^, while it would be considered as a parameter in
the analysis of the remaining n-1 markets. Proceeding in this manner it is then
possible to determine n separate equilibrium values of prices and quantities
for the n markets.

But to determine the price for Q. in the analysis of the market for £.
the analysis supposes that we already know the prices of all the other
commodities (Q, ,Q-j , . . . ,Q. ,Q • , . . . ,Q ). Hence, whether we actually know these
prices or not, the method of analysis requires that we assign them particular
values. Since all markets are interrelated, the only condition under which it
is possible to derive the correct equilibrium point for market ^. is when
the equilibrium values for the remaining n-1 commodity markets are already
determined. Otherwise one is in the position of deriving an equilibrium
position for market g. which depends on the prices of the other commodities
at a time when these prices are not the equilibrium values.

Since the demand for each commodity depends on the prices of all other
commodities and the total income of all consumers, these variables cannot be
treated as parameters if we wish to determine the equilibrium position in all
markets. For exanple, in the analysis of consumer demand some commodities are

- 81 -

identified in terms of the consumer's behavior as substitutes or complements of
each other.— One commodity is called a substitute for another commodity if
the quantity demanded of the first commodity increases as the price of the
second increases. However, if the quantity demanded of the first commodity
falls as the price of the second rises then these commodities are called
complements of each other. Similar relations hold between the factors used
by producers as inputs to the production process. Consequently, if we are
interested in simultaneously determining the equilibrium values for all
markets, these relations must be taken into account. One way of ensuring
that these conditions are met is to treat the functions representing all
products and prices as a complete system whose simultaneous solution provides
the consistent set of equilibrium values we are after.

While it will not serve the purpose of this book to delve into the analysis
of general market equilibrium in too great detail, a brief analysis of one
example will permit an examination of how the conditions of a single market
equilibrium are applied to the case where many markets are dealt with at one

time. To keep the analysis as simple as possible the exan^jle is used of the

12/
case of a general exchange economy. —

In a general exchange economy each consumer enters the market with a

certain amount or stock of one or more of the total number of available

commodities. Let £^. represent the amount of commodity ^ held by the i^th

11/

— 'See, for example, the discussion on substitutes and complements in:

G.P.E. Clarkson, op. cit., Chapters 213.

12/

— 'For a more detailed discussion of multi-market equilibrium, to which

this section is indebted, see: J.M, Henderson and R.E. Quandt, op. cit. , Chapter 5.

- 82.

consumer when he enters the market. Since each consumer is free to buy and sell

at the market price^ after an exchange has taken place the i^th consumer's holding

of £. can be represented by £ . . . Accordingly, the i^th consumer's excess demand

for £. is represented by E . . where:

iij =aij - SiJ (j=l,2,...,m) (4.37)

If excess demand is positive it means that his consumption of (^. exceeded his
initial holdings £ . . • Similarly, if excess demand is negative it implies that
the i^th consumer did not need all of his £, . and was able to exchange some of
his holdings for other commodities. Since the consumer's income is equal to the
value of his initial holdings^ and since the consumer cannot exceed his income,
the value of his purchases and sales must equal his income. By representing the
consumer's utility function in terms of the quantities of the commodities he
consumes, his utility function can be restated as a function of his excess demands
and initial holdings in keeping with (4.37). Concurrently, the consumer's
behavior in the market is bounded by equilibrium conditions which require that the
net value of his excess demands must be equal to zero. If we are dealing with a
market containing m commodities, the i^th consumer's utility function can then be
solved under the first and second order conditions. The solution yields the
function

hi - \j<»i'P2'-'P„) a:l;2;:::;») <'^-^^>

which states that the i^th consumer's excess demands depend upon the prices of all
other commodities. As long as his initial holdings of commodity £. is greater than
zero his excess demand for ^. may be positive or negative depending upon the
prevailing prices. Nevertheless, under equilibrium conditions his net excess
demands for £. must be equal to zero.

- 83 -
An aggregate excess demand function for a particular commodity is constructed
in the usual way by adding together the individual excess demand functions for the
n consumers. For ^. the aggregate excess demand function would be

^j =iiliij<PpP2'---Pm> ^""'^^^

From (4.39) the partial equilibrium price of ^. can be determined by setting the
other (m-1) prices equal to a set of fixed values. Having determined the partial
equilibrium price £? it can be substituted back into the individual excess demand
functions (4.38) to find out the purchases and sales each consumer made under
these conditions.

The problem, however, is to determine the simultaneous equilibrium of all m
markets. The equilibrium condition is that excess demand in all markets must

equal zero:

E.(p^,P2,...,pJ = 0 (j=l,2,...,m) (4.40)

This condition represents a system of m equations in m variables. If all m
equations are independent and consistent then it is possible to determine the

absolute values of the ra variables or prices. But, the system of equations

13/
represented by (4.40) has only (m-1) independent equations. — Consequently, it

is not possible to solve directly for the equilibrium prices. Instead one solves for

the equilibrium set of price or exchange ratios. This solution is derived by

taking the price of one of the commodities (usually called the numeraire) and

13/

— For a proof of this assertion see: J.M. Henderson and R.E. Quandt,

op. cit. , p. 132.

- 84 -

14/

dividing the prices of the remaining (m-1) items by this price. — As a result

the number of unknown price ratios is reduced to (m-1) , a solution for which is
provided by the (m-1) independent equations.

For example^ if we select the price of the mth commodity, p , as the base
price or numeraire, the excess demand functions at equilibrium become: :

^AE.l>R2'"''^m-l>^'> = ° (j=l,2,...,m) (4.41)

P P P

'^m ^m '^m

where the variables are the exchange ratios of the m commodities relative to the

price of Q . The solution of (4.41) provides the equilibrium price or exchange

ratios. Accordingly, substituting these values back into the individual excess

demand functions the specific purchases and sales of each individual can be

determined.

Given the equilibrium position of a particular general market case we might

now wish to examine the conditions under which such an equilibrium is statically

as well as dynamically stable. The analysis proceeds in a manner analogous to

that of the case of a single market. But now it is necessary to consider the

effect that disturbances in one commodity market have on the remaining markets.

In brief, stability in the static case is achieved if the total rate of change of

dE.
excess demand with respect to price, i.e. -r-^ (j=l,2, , . ,,m) , is negative for all

possible combinations of prices. Dynamic stability requires an analysis of this

time paths of all the price movements over time. To effect such an analysis one

needs to know the exact relations governing the price adjustments over time. If

all prices always approach their equilibrium values then, of course, the market is

dynamically stable.

14/

— This manipulation is possible because demand functions are homogeneous

of degree zero.

chapter 5

THE EMPIRICAL CONTENT OF MARKET THEORIES

A testable theory, as noted in Chapter 2, can be considered as an
empirically interpreted deductive system. The basis of this system consists
of primitive terms and a set of independent and consistent postulates. From
this basis the remainder of the system is developed by the application of the
formal definitions and the logical rules of deductive inference. Accordingly
the theory itself consists of the conjunction of this basis and all the
propositions or hypotheses that can be deduced from it. To determine whether
a particular theory meets the criteria of a formal deductive system one can
examine the structure of the theory independently of any meanings assigned to
its coDq)onent parts. But, in order to assess the empirical content of a theory
it is the interpretive rules that are the object of the investigation since it
is assumed that the deductive system already satisfies the deductive criteria.
In the following analysis, therefore, no questions are raised as to the
independence of the basic postulates, the consistency or completeness of the
system, or whether any logical errors have made in the deduction of the theory's
hypothesis. What will be examined is the extent to which the concepts and
hypotheses of the market theories are related to observable phenomena.

1. Concepts and Conditions

If the concepts of a theory are devoid of empirical content then the
hypotheses of which they are a part cannot be submitted to empirical test. While
this may appear to be an unnecessarily obvious statement it emphasized the fact
that the empirical content of a theory resides mainly in its concepts.

- 86-

Consequently, even though the explanatory and predictive force of a concept can
only be determined within the context of the relevant hypothesis or theory, its
empirical content can be separately examined.—

A. The Concept of Demand

2/
The first principal hypothesis of the theory of market behavior— is that a

consumer's purchases of a specific item are determined by a function which is
stated in terms of the price of that item, the prices of all other available
products, and his income. This function is called the demand function. For a
particular commodity, £., and for a specific consumer, i, the function is
represented by the relation;

Dij = D^j (.Pi>P2>°"'Py"°}^ta'^i'> (j=l,2,...,m) (5.1)

where (p, ,p„, , . . ,p . , . . . ,p ) are the prices of the m commodities, and ^. is the
ith consumer's income. If we are solely interested in the rate of change of the
ith consumer's demand to a change in the price of Q. then, as noted in the
previous chapter, the demand function becomes a function of p. alone, i.e.
D . . = D. .(£•). But what is the empirical interpretation of this concept and this
relation? Clearly, in its general form, (5.1), there is no obvious connection
between this function and observable phenomena. While the £'s represent prices

— For a detailed exposition of the problems associated with the empirical
analysis of concepts in science see: C.G. Hempel, "The Fundamentals of Concept
Formation in Empirical Science," International Encyclopedia of Unified Science,
University of Chicago Press, Chicago, Vol. II, Chapter 7, 1955,

—'This postulate is not just employed in the theory of a single commodity

market. It is employed in a number of different market theories.

-87 -

and V represents income (5.1) does not specify directly the manner in which
these variables are related. Consequently, in order to assess the empirical
relevance of the concept of demand it is necessary to examine the basis from
which this concept or function is derived. To facilitate this analysis
attention will temporarily be restricted to the case where the consumer is
confronted with a market that contains only two commodities.

The concept of demand emanates from an analysis of the choice behavior of
an individual consumer during a specific interval of time. In a two commodity
market the consumer's total purchases are a direct summation of the amount he

spends on each of the two items. If one of the available commodities

3/
represents the consumer's stock of money,—' then his total income for the period

is equal to his total purchases, i.e. y=p.q, + P2q2° ^^^ purchasing specific

quantities of Q, and ^o ^^^ consumer derives a certain utility which is

represented by the function U=f(q^,q2). Since any combination of Q^ and Q2

will satisfy this function the equilibrium postulates are imposed upon the

consumer's behavior to ensure that an unique selection is made. If a

consumer's utility function is represented by the specific relation U=q, q^

his purchases at equilibrium are determined in the following way:

Since the consumer's total income is given by, y=p, q, + P2q2> ^^^ ^^^

utility from these purchases by, U=q^ q2, one can form with the aid of the

Lagrangian multiplier K a new expression which states that the consumer's

utility is now given by: W=q,q2 + X(y-p, q, -P2q2) • To find the equilibrium

position of this utility function one applies the first order conditions as

-See pp. 54-55, Chapter 4,

-88 -

follows: By taking partial differentials with respect to q , q and \,
respectively and setting them equal to zero we get:

1^ - qj - P2 X = 0 (5.2)

^ = y - p^q^ - P2q2 = o

4/
Solving these equations for q and a— two expressions result which relate £

and q„ to their respective prices and the consumer's income:

"1=2^ "2=2^ (^-S)

Hence, under the condition that the consumer is maximizing his utility function
during this period of time, the quantities of ^. and ^2 he will purchase are
strictly a function of his income and the price of the relevant item.—

The concept of demand is introduced by defining it to be equivalent to the
quantity purchased of a particular commodity by a specific consumer at
equilibrium. Accordingly, in this example, the demand for ^^ is equal to the
consumer's income divided by twice the market price of this commodity. Further,
because the demand for £, and ^.o is solely a function of its price, a shift in
the price will immediately alter the quantity demanded. To be more precise,
the specific demand functions in this example allow us to conclude that an

— It is assumed here that the second order condition for a maximum is

also satisfied.

—Note that (5,3) is a specific case of the general relation (4,4).

-89 -

increase (decrease) in price will be followed by a decrease (increase) in the
quantity demanded. As long as the demand functions are stated in this form it
is clear that there is an inverse relation between market price and the quantity
demanded.

Since a consumer's total income is assumed to be constant throughout the
period in which these purchase decisions are made it is also apparent that the
demand for ^^ or Q^ is homogeneous of degree zero. That is to say, if both
prices and income were simultaneously reduced or increased by a similar
percentage of their respective values, the quantity demanded would remain the
same. Thus, as long as the consumer's income remains constant the demand function
is a monotonically decreasing function of price. It represents the quantity a
consumer will purchase of a specific commodity at the equilibrium point of his
utility function.

Since the aggregate demand for a particular commodity is constructed by a
summation of the quantity demanded by each individual, the aggregate demand function
represents the total market purchases of a commodity only as long as each
consumer is operating at his equilibrium point. If, for a particular period of
time, the income of each consumer is constant, and if during this same period
each consumer maximizes his utility function, then the aggregate demand function
will also be a monotonically decreasing function of price alone.

It should be noted, however, that the decreasing monotonicity of the demand
function depends upon the consumer's reaction to a price shift. If the price of
Qi falls the effect on the consumer's purchases can be broken down into two
components s the substitution and the income effect. To begin with, a drop in the
price of g^, makes this commodity a better purchase relative to £2* Accordingly,

as long as the consumer's utility function remains unchanged his purchases of Q,
will increase. Thus, a fall in the price of ^, will induce the consumer to sub-
stitute more of ^, for ^ . But, at the same time the fall in the price of £
increases the consumer's total income, i.e. it increases the total amount of
commodities the consumer can purchase.

For example, before the price of ^ is altered the consumer's total income
is given by, y=p,q^ + P-^q^. If the consumer is maximizing his utility his
position on his utility curve is at the point of tangency between it and his
income line. In Figure 1 this point is represented by A where Ua represents his
current level of utility and Y-Y his income line. When the price of Q^ falls the
demand for ^, increases « And if the consumer remains on the same utility function

the increase in consumption of g can
be represented by point B. But, unless
the consumer purchases a sufficiently
large amount of Q so that the amount

he now spends on Q, is equal to the
original amount spent on Qi,i.e., £13,1,
he will also be able to purchase more of
£p . This extra quantity that he can
Figure 1 purchase of ^ represents the effect the

price change has on his real income. If due to the decrease in price the consumer
decides to consume at point C it is clear that not only has he been able to shift
to a higher level of utility, U, , with a corresponding shift in his income line
Y-Y' , but this shift has allowed him to consume more of both Qi and Q .

- 91-

However, it is not always the case that the consumer will purchase more of both
2, and 2o« If Si i^ *" inferior good then a decrease in its price will not lead
to an increase in its consumption. On the contrary, in this case the income
effect will dominate the substitution effect and the consumer will spend the extra
amount on ^-^ Accordingly if after a fall in the price of a particular commodity
the income effect is sufficient to offset the substitution effect the demand
function for that commodity cannot be represented as a monotonically decreasing
function of price. If all consumers behave in this fashion with respect to this
specific commodity then the aggregate demand function can no longer be represented
as having a negative slope. Moreover, if a particular item is an inferior good
only to a certain number of the consumers in the market, then to determine the slope
of the aggregate demand function it is necessary to know the relative magnitude of
the total substitution and income effects. Since the substitution effect always
increases the demand for a commodity it is only the presence of a large and
positive income effect which will allow the fall in a price to effectively
decrease the demand for that commodity.—

B. The Concept of Supply

The second main hypothesis of the theory of market behavior states that the
amount of a specific item which a firm will produce is a function of the market
price alone. The supply function itself is derived by defining it to be identical
to the relevant portion of the firm's marginal cost curve. Under short-run

— For a more detailed description of the theory of consumer behavior see:

PoA. Samuelson, Foundations of Economic Analysis, Harvard University Press,

1947, Chapter 5| and G.P.E. Clarkson, op. cit., Chapter 3.

- 92-

conditions the supply function is defined as that, part of the marginal cost
curve which lies above the firm's average variable cost curve. Under long-run
conditions it is identical to the segment of the marginal cost curve that lies
above the average cost curve. As a result, to assess the empirical relevance
of the supply function one must in turn inspect the basis from which the marginal
cost curve is developed. Cost function is developed from a knowledge of the
firm's production function, a function which relates the cost of the variable and
fixed inputs to the production process, and a function which describes the way
in which the inputs should be increased if the firm's output is to be expanded at
a minimum of cost. By combining these three functions a single relation is
produced which is an explicit function of the levels of output and the amount of
fixed cost. This is the total cost function and it represents the minimum cost
at which each level of output can be produced by this particular firm. Once the
firm's cost function is determined the marginal cost function is derived by taking
the first derivative of the cost function with respect to output. Since the cost
relation is a function of variable and fixed costs, the marginal cost relation is
a function of variable cost alone.

For example, if the total cost relation of a particular firm for a product
^ can be represented by C = <l>(q) + b, where b represents the fixed cost associated
with producing q, then the marginal cost of producing £ is given bys

^ C = ^ .(q) (5.4)

where $(q) represents the variable costs associated with different levels of output.
Since the cost relation, C, gives the minimum cost at which each level of output
can be produced^ the marginal cost curve gives the minimum, additional, variable
cost incurred at each level of output.

- 93-

Now the supply function is identical to that part of the marginal cost curve
which lies above the average variable cost function in the short-run and the average
cost function in the long-run. Hence to determine the beginning of the supply
function--that is, the point below which the firm will not produce any output--
one needs to locate the intersection of the average variable and long-run average
cost functions with the marginal cost function. Since the average variable cost
function is given by ^' it is easy to determine the point of intersection between
it and the marginal cost function given by (5.4). The intersection takes place at
the minimum point of the average variable cost function. In the same manner it
can be shown that in the long-run when all costs are variable costs the intersection
takes place at the minimum point of the average cost function.

Once the beginning of the supply curve is determined its only remaining
important characteristic is its slope. To determine the slope of the supply curve
we need to identify the slope of the marginal cost curve. This is accomplished
in the following way- Consider a firm which is selling its output, q, at the
current market price, £. The firm's revenue is given by the quantity sold
multiplied by the price. Profit is the difference between the revenue and the
cost of production. Hence, the firm's profit can be represented by:

n = pq - 1>(q) - b ■ ■ (5.5)

To determine the output the firm will produce the first-order condition is
applied--i.e. , that profit must be at a maximum--and the first derivative of
profit is taken with respect to output.

- 94 -

35 = P - ^ *«" - 0 - <=•«

p = 4- *(<l) = Marginal Cost (5.7)

Consequently, the firm produces at the point where marginal cost equals the market

price. To find the slope of the marginal cost curve the second-order for a maximum

d^n
is applied, i.e., — r < 0, to obtain;

dq^
2 2

^ = ~^ <i'(q) < 0 (5.8)

dq dq
Hence, the slope of the marginal cost curve which is given by, ^ [^ *(q)] > 0^
is greater than zero. Accordingly, the supply function for a particular firm has
a positive slope and is a monotonically increasing function of price alone. Since,
the aggregate supply function for a market is a direct summation of the individual
functions, the aggregate supply function has the same characteristics as long as
all firms have positively sloped supply functions.

As has already been noted, there is one situation--i,e. where external

economics or diseconomies occur--in which the aggregate supply function may be

8 /
negatively sloped,— This is the case where the cost function of each firm is

no longer independent of the output levels of other firms but is instead

dependent upon such outputs. If these dependencies are such that the relevant

portion of the firm's marginal cost curve becomes negatively sloped then the

supply function will also have a negative slope. As a result, unless the supply

— Note the similarity between (5.5) and (5.6), and their general formulation

in (4,11) and (4.12),

8 /

—'See section 2 Chapter 4,

- 95 -

function of each firm has the same slope, or unless the relative magnitude of
the respective slopes is known, it is no longer possible to determine the slope
of the aggregate supply function.

C. The Concept of Equilibrium

A market is at equilibrium if the aggregate amount demanded equals the
aggregate amount supplied. If the market is at equilibrium then there is only
one price for each product in the market. Each consumer is at equilibrium if
with each set of purchases he is maximizing his utility function. Similarly
each producer is at equilibrium if his output is such that he is operating at
the point where his marginal cost function equals the market price. If the
market conditions are such that there are no external economics or diseconomies,
and if the income effect of price changes can be ignored, then from a knowledge
of producers' cost functions and consumers' demand functions the equilibrium
price at which each commodity will be bought and sold can be determined.
Further from a knowledge of the slopes of the aggregate supply and demand
functions it is possible to determine whether the equilibrium is stable or not.
Moreover from the equilibrium positions of consumers and producers the theory
provides a set of relations which must hold if market equilibrium is to be
attained. Consequently, under the full set of equilibrium conditions the theory
of market behavior provides a set of hypotheses with which all market
transactions and behavior can be determined,

2. Testing the Theory's Hypotheses

In order to submit a theory to empirical test there must be at least one
hypotheses^ or consequence of a hypothesis, that under appropriate initial

- 96 -

conditions refers directly to observable phenomena. If the theory does not contain
such a hypotheses then, as noted in Chapter 2, the theory cannot be employed to
explain or predict the occurrence of observable events. Thus, while the theory
may remain as an interesting deductive system, it is not possible to consider it
as a part of empirical science.

Since we, as economists, are interested in being able to employ the theory
of market equilibrium to explain and predict market behavior we must first make
sure that the theory contains at least one testable hypotheses. If the theory
contains such a testable hypothesis then we can proceed to employ market data to
check, test, and amend the theory. However, if the theory does not contain a
testable hypothesis then we cannot employ it an empirical theory and must classify
it as an uninterpreted deductive system.

To subject the theory or any of its hypotheses to empirical test presents
the experimenter with several problems. The first main obstacle is the manner
in which the theory is to be considered. If the theory is to be tested directly
against observed market behavior then it is necessary to determine, before a test
is conducted, that the initial conditions are all satisfied.

For example, to be able to test any of the hypotheses concerning consumer
behavior one must first determine that each consumer is maximizing his utility
function. Unless this condition is satisfied it is not possible to test these
hypotheses. For the theory does not hold except under equilibrium conditions.
Consequently, the first task is to examine the behavior of certain consumers and
ascertain whether they are behaving so as to maximize their utility functions. To
carry out such an investigation requires one to be able to identify a consumer's
utility surface and simultaneously determine whether he is situated at the
maximum point on this surface. Since it is not possible to employ one set of

- 97 -

observations to simultaneously determine both the utility surface and whether the
consumer is at a maximum of utility, the best that can be done is to take
observations at succeeding intervals of time. But the minute the observations are
extended over several time periods a further complication is introduced.

The consumer's utility function, and consequently his demand function as well,
is defined only over a single interval of time. For tastes and income must be
held constant to permit the hypotheses about consumer behavior to be inferred.
Accordingly, the theory allows the consumer to shift to a new equilibrium position
at the beginning of each interval of time. Hence, unless one has a method
whereby one can determine that tastes and income have not changed between intervals
one cannot employ the data from two different periods of time to substantiate
one utility surface. Clearly, if the constancy of tastes and preferences were
separately measurable for a consumer over time, then one could employ this
knowledge to establish the hypotheses governing his choice behavior. But, the
theory requires that tastes remain constant within each interval without
providing a basis from which this condition can be tested. Thus, it is manifestly
not possible to determine from one set of observations whether this condition has
been fulfilled.

Unless this condition can be independently established the hypotheses about
consumer behavior cannot be submitted to test. That this conclusion must hold
follows directly from the earlier analysis of the conditions under which a
hypothesis or theory can be tested. If the initial conditions under which the
theory is supposed to hold are represented by, £, and the relevant hypotheses by,
Q, then the theory can be represented by the conditional statement, if P then ^,
i.e, P ^ 2^0 To subject this relation to test it must be possible to disconfirm it.

- 98 -

The only condition und«r which this is so is when there is evidence supporting
the propositions included in P. If the empirical truth value of P is unknown it
is not possible to determine the empirical truth value of the relation £ -♦ Q.
While evidence supporting §. "lay or if*y riot be easy to find, such evidence cannot
by itself corroborate the entire relation. Consequently, before it even makes
sense to inquire whether a particular set of consumers are maximizing their
utility it must first be possible to measure, by an independent set of tests,
the constancy of their preferences.

At the same time consider the problem of testing for the slope of the
aggregate demand function. The theory asserts that the aggregate demand function
will have a negative slope if consumers are maximizing their utility functions,
if the substitution effect is always greater than the income effect, and if we
are not dealing with commodities, such as a number of luxury items, for which the
individual demand functions are positively sloped. Under these conditions the
aggregate demand function will have a negative slope. Manifestly, to test this
hypothesis one must first be able to empirically determine whether in a particular
market situation these conditions are satisfied. As long as the commodities are
superior goods the substitution effect will be sufficiently larger than the
income effect to satisfy this requirement. But how does one identify, prior to
and independently of a particular investigation, which goods for a specific set of
consumers are superior? If there were a set of tests which were always able to
identify inferior goods relative to a particular group of consumers the first of
these three conditions could be established. But the theory does not provide a
mechanism for establishing such a set of tests. The only way the theory can be
used to classify commodities is to observe, in a particular instance, whether the

- 99 -

demand function after a price change for an individual or group of consumers is
positively or negatively sloped. The same comments hold for the third condition.
For the theory does not provide any method for independently establishing the
slope of the demand function for cases when it is not negatively sloped. Since
the impossibility of testing the second condition has already been discussed it is
clear that it is not possible to independently determine whether these conditions

are fulfilled. To be unable to empirically establish the initial conditions

9/
implies, of course, that one cannot submit the hypotheses to empirical test,—

If the initial conditions on the demand side of the theory perhaps cannot be
empirically established perhaps it is possible to do so on the supply side. For
example, in order to test the hypothesis that the supply function of a particular
firm is positively sloped all one needs to be able to do is to determine the slope
of the firm's marginal cost function. The marginal cost function is directly
derived from the firm's total cost function. Thus, the first problem is to
empirically establish the nature of this function for the firm in question. But,
to determine the total cost function of a firm it is not sufficient merely to
discover a relation which yields the total cost to the firm of producing a certain
output.

The total cost function of the theory defines a relation between the cost of
inputs and outputs such that this is the minimum cost at which such an output can
be produced by this firm. As is noted above, the cost function is derived from
the firm's production function, its minimum cost relation, and a function specifying

— A more detailed analysis of the empirical content of the classical theory

of consumer demand is to be found in; CP.E. Clarkson, op. cit,, Chapters 4, 5,
and 6.

-100 -

the manner in which inputs should be increased if output is increased so as to
remain at a minimum of cost. Manifestly, if a firm's cost function is to be
en^Jloyed as the basis for the supply function, one must first make sure that the
firm is producing at a point of minimum cost. But how does one ensure that this
condition is satisfied? Further, not only is it necessary to determine that the
firm is operating at a point of minimum cost, but it must also be shown that it
has set its level of output such that marginal cost equals price. If this latter
condition is not satisfied, then for obvious reasons it is not possible to inspect
the properties of the supply function.

In an empirical investigation of a firm's behavior one can readily examine,
for a particular period of time, the cost of its inputs, the current level of
fixed cost, the amount of output product , as well as the price per unit received
for this output. Clearly, this examination can be carried out in great detail
so as to develop an accurate picture of the cost structure of the firm. But, this
is not enoughl Along with these data it must also be possible to tell whether
the firm's production process is such that it is operating at a point of minimum
cost. While observations can provide data on current costs they cannot at the
same time provide any information on whether this is a minimum level or not. To
determine whether the firm is at a minimum one would need to be able to assess
all the possible ways of combining the inputs to achieve the same level of output.
But the actual observations cannot yield this information at the same time as they
are depicting the firm's current behavior. Once again a separate and independent
means is required for checking the empirical truth value of these initial conditions,

Similar difficulties are encountered if one is dealing with aggregate data
and wish to test the hypothesis that the aggregate supply function has a positive
slope. In this case, in addition to the initial conditions which pertain to the

-lOi -

determination of an individual supply function, it must be possible to identify
whether external economies or diseconomies exist in the market. Unless one can
determine when, for example, external economies are present prior to and
independently of an inspection of the slope of a supply function, then it is not
possible to conduct any empirically meaningful tests on the slope of an aggregate
supply function.

For example, consider the analysis of the effect of externalities upon the
slope of the supply function discussed in the previous chapter. Here the analysis
began by supposing that one could write down the profit functions for all n firms
in the market. These functions are represented by:

n. = pq. - C^ (i = l,2,...,n)— ^ (5.9)

where C. represents the total cost function of the i^th firm which is dependent upon
the level of output of all other firms, i.e. C, =<!'. (q, ,q2, . . . ,q ). An equilibrium
solution for this market is described by taking the partial differentials of
each firm's profit function with respect to the commodity it produces, setting
these relations equal to zero and solving for the set of equilibrium outputs,
£. . The supply functions are derived from the equilibrium solution. If their
slopes are known the slope of the aggregate function can be deduced. But, due
to the presence of externalities one can only determine the slope of an individual
supply function if one already knows the signs of all the coefficients in its cost
function. It is not sufficient to know that each firm is maximizing its net
revenue. It must also be possible to ascertain the effect of each firm's output
decision on that of every other firm. Since the cost function of a firm is

10/

— 'See (4.11) and the accompanying discussion in Chapter 4.

- 102-

empirically non-determinable when externalities are absent, the same reasons
preclude the measurement of the values of the relevant coefficients when
externalities are present.

In the analysis of externalities in Chapter 4 it is noted that if the values of
the coefficients are not known in the individual cost functions, then the theory
still permits one to solve for the slopes of the supply functions by an
application of the technique of comparative statics. — To employ this method
of analysis one must first derive the equilibrium solution for the total market.
Employing this solution as the initial conditions a new set of relations are
introduced by taking the partial differentials of the equilibrium relations with
respect to the outputs of the individual firms. The process of partial
differentiation requires, of course, all other parameters and variables to be
treated as constants. Accordingly, the rates of change that are derived by this
method only hold under conditions where all other factors can be shown to have
remained constant. Further, comparative statics requires the initial conditions
to be the equilibrium solution of the market. Therefore, since it is not possible
to empirically determine when the market is at equilibrium it follows that it
is also not possible to test for the empirical significance of the rates of change
generated by this method.

In the previous sentence it is asserted that it is not possible to determine
when a market is at equilibrium. While I have demonstrated that it is not possible
to submit the hypotheses of the theory of market behavior to a process of
refutation by empirical test, it may well be claimed by some that they can at least
tell when a market is in equilibrium. After all, a market is in equilibrium when

— ^See pp. 59-62.

-103 -

aggregate demand equals aggregate supply. And it follows that this condition is
met when there is only one price for each commodity on the market. Consequently,
all that needs to be done, it might be argued, is to find a market in which one
price has prevailed for each commodity over some reasonable interval of time and
this will be an example of a commodity market in competitive equilibrium.
Unfortunately, however, it is not legitimate to infer from the observation of one
price, during a reasonable interval of time, to the presence of an equilibrium
position in the market. The market may have only one price for each commodity
for a large number of reasons, e.g., a variety of collusive business practices, or
government intervention in pricing decisions, but only one of them ensures that
the market is at the theoretical equilibrium. This is, of course, the requirement
that each firm is maximizing his net revenue and each consumer is maximizing his
utility function. Since it is not possible to determine by observation when this
requirement is met, it is clearly not possible to test whether the one price
per commodity prevailing in the market is an indication of equilibrium or not.
If an empirical investigation cannot be establish when a market is in equilibrium

then none of the hypotheses which employ market equilibrium as an initial condition

12/
can be confuted by empirical test. —

Consider, for example, the case of the spatially distributed firms dealing

13/
in dairy products which is examined in some detail in the last chapter. — In

this case there are two sets of firms. The first set are nearer the central

12/

— The problem of testing for the empirical validity of equilibrium conditions

is further discussed in the next chapter and again in Chapter 11, A detailed
examination of this issue with respect to decision behavior of individuals and
groups is presented in: G.P.E. Clarkson, op. cit., Chapter 5.

13/

— See pp. 66-70,

-104 -

market and have a transportation cost of a,=10 dollars per unit. While the second
set incur transportation costs of 00=13 dollars per unit. Aside from this
difference all firms are supposed to have identical cost functions. If all firms
have identical cost functions then it follows that they must have identical
production functions^ cost relations, and expansion functions. Now it is clear
that one can examine the cost structure of each firm and determine the process
by which it transforms inputs into outputs. But even if under the most detailed
scrutiny^ each firm has identical production processess and cost structures,
one is still unable to empirically ascertain whether this cost structure represents
the minimum attainable. While the presumptive evidence might be strongly in
favor of such a conclusion, thi'.re is no independent measure by which its
empirical validity can be determined. Unless this cost function represents the
minimum attainable with the current technology then the first condition for a
market equilibrium has not been met.

Continuing with the example, the next step in the analysis is to derive the
supply function for each class of firms. This is accomplished by finding that
output which maximizes their net profit. By applying the first-order condition
for equilibrium to the profit function and solving for the quantity produced one
can analytically specify the supply function for each class of firm. However,
to subject the results of this analysis to empirica] test one must once again be
able to demonstrate that the initial conditions are empirically true. This
implies establishing the fact that these firms are operating at a position of
maximum net revenue. But, even to observe that all firms within each class are
producing the same output is not sufficient evidence to guarantee they are
maximizing their net revenue. While such behavior would clearly be consistent
with the theory, it cannot be eiq>loyed to corroborate the theory's conclusions.

-105 -
To do so requires an independent check on the empirical validity of the initial
conditions. Moreover, to determine that the initial conditions are satisfied
requires an independent measure of when a firm is operating at a maximum of net
revenue. Since the theory does not provide the interpretive rules whereby such
measurements can be made it is manifestly not possible to subject these hypotheses
to test.

Summary and Conclusions

In the first part of this chapter the conditions under which the concepts of
demand, supply, and market equilibrium are derived and employed are inspected in
some detail. The theoretical basis of each concept is examined as well as the
criteria by which it is possible to measure such observable attributes as slope,
output, and price. At the same time it is noted that to subject a theory or any
of its hypotheses to empirical test the initial conditions must be shown to be
empirically true.

The remainder of the chapter is then devoted to an analysis of some of the main
hypotheses of the theory of market equilibrium. The object of this examination
is to discover whether the theory contains any hypotheses which can be subjected to
test. In carrying out this investigation it is shown that all the theory's
hypotheses have at least one equilibrium requirement as part of their initial
conditions. Further, it is demonstrated that within the context of the theory it
is not possible in any specific case to empirically determine whether such
equilibrium conditions are satisfied. If the initial conditions cannot be shown
to hold the hypothesis cannot be subjected to test. It follows, therefore, that
none of the theory's hypotheses can be subjected to a process of refutation by

-106 -

empirical test. Consequently, one is forced to conclude that the theory of market
equilibrium is devoid of empirical content. It can make no claim to refer to
observable phenomena. This is a strong and serious conclusion, and the next
chapter is devoted to examining the implications of this result for classical
theories of microeconomic behavior.

chapter 6
AN EMPIRICAL ANALYSIS OF THE CUSSICAL DEDUCTIVE SYSTEM

In order to explain or predict the occurrence of an ecpnomic event it is
necessary to have an economic theory that can satisfy the following two
conditions: (i) the theory must contain at least one hypothesis which can be
directly submitted to empirical testj (ii) such hypotheses must have been
submitted to and have survived at least one test. The theory of market
equilibrium, however, is unable to satisfy the first requirement. Accordingly,
it is clear that it is not possible to employ this theory to explain or predict
the occurrence of the market phenomena to which it refers. This is an important
conclusion. It not only in^ilies that the theory is empirically vacuous, but it
also suggests that the obstacle to empirical interpretation lies within the
deductive system from which the theory is developed. If this latter inference
is correct, then all theories which are based upon that same deductive system
will encounter similar empirical difficulties. That is to say, if the absence of
enqjirical content can be shown to be a result of the way in which classical
theories of economics are developed then it follows that none of these theories
will contain empirical hypotheses which refer to observable economic behavior. If
such is the case then none of these theories can be employed to explain or predict
the occurrence of economic events. The seriousness of this corollary warrants
a detailed investigation of its validity, and this chapter is devoted to such an
examination.

- 108 -

1 . The Basic Deductive System

In Chapter 3 the examination of the classical foundations of economic analysis
began with an example of how a firm's reaction to a tax upon its output is
determined. By an application of basic deductive system it is shown that there
is a negative relation between the rate of change of the firm's output and the
tax rate--i.e. if the tax rate is increased the firm's output will decrease and
vice versa. Since it is perfectly clear that one can observe both an increase
in a firm's taxes as well as a decrease in its level of output this instance
appears to present a counter example to the argument of the previous chapter.
Consequently, it is reasonable to begin the investigation of the classical
deductive system by a re-examination of the empirical content of this example.

In this case a firm is considered for which it is supposed that the demand
curve for its output, xp(x) is already known. To simplify the analysis the firm
produced only one item, X. (If a firm was selected which produced many items then
the firm's demand curve would have to be defined in terms of all such items.)
Furthermore it is supposed that there is sufficient information on the firm's
production process so that we knew the relation between the total production cost
for the firm and its output, C(x) is also known. With these two functions it is
then possible to specify the profit function for the firm, in the normal manner,
as the difference between its total revenue and the total cost of producing a
certain output at a specific price;
n = xp(x) - C(x)

A tax on output is then imposed upon the firm and is included as a further item in
the profit function:

n = xp(x) - C(x) - t(x) (6.1)

- 109 -

In order to determine the effect of the tax rate on output one first has to

derive the expression which specifies the equilibrium relation between output and

the tax rate. To generate the equilibrium solution the first-order condition for
a maximum with respect to output is applied to (6.1) which yields:

t =^ [xp(x) - C(x)] (6.2)

To ensure that this is a position of maximum net revenue the second-order condition

for a maximum must also be satisfied, i.e.;

>2
-2- [xp(x) - C(x)] < 0 (6.3)

Sx^
But before it is empirically meaningful to apply these equilibrium conditions
to (6.1) production cost function, C(x) , represents for this firm the lowest
total production cost at which each level of output is produced. Unless the cost
function has this property it makes no sense to apply the equilibrium conditions
and solve for the equilibrium level of output with respect to the tax rate as in
(6.2). Moreover, unless the demand function, xp(x) , can be shown to represent
the demand at various prices for this firm's product it makes no empirical sense
to construct the profit function (6,1) in this manner.

In the previous chapter it is argued that by taking observations at any one
point in time it is not possible to determine whether a firm is operating at a
point of minimum cost. If several observations are taken over succeeding intervals
of time at varying levels of output then it is necessary to be able to measure
the minimum production cost at each of these output levels. A minimum can only
be ascertained if all possible combinations of inputs and their respective costs
are measured against a specific level of output. Further, the production cost
function represents the locus of these minimum points as output is varied. Thus,

- 110 -

to determine the production cost function one needs to be able to observe and
ascertain whether or not the firm is always operating at a minimum of cost. Since
at any given point in time the theory does not provide us with sufficient
interpretive rules to allow us to measure whether the firm is at a minimum of cost,
it is manifestly not possible to empirically determine the locus of a series of
such points. If the function, C(x) is not empirically specified, then it is not
possible to specify the profit relation given in (6.1). Consequently, for any
particular firm it follows that one is unable to demonstrate that the function
represented by (6,2) is the actual equilibrium solution.

To ensure the presence of a maximum the second-order condition, (6.3), must be
satisfied. But, this requires an empirical knowledge of the functions xp(x) and
C(x) such their second partial derivatives can be evaluated with respect to output.
If it is not possible to empirically determine the minimum production cost
function of a firm it is certainly not feasible to evaluate its second partial
derivative with respect to output.

In Chapter 3 the second condition is employed to infer the direction of the

ax °

equilibrium rate of change of output with respect to the tax rate, (rrr) •
Unfortunately, one cannot determine for a specific firm whether the second-order
condition is empirically satisfied. Consequently, the derivation of the rate of
change output with respect to a change in the tax rate results in a situation
where once again it is not possible to determine if the initial conditions are
empirically true.

It could be argued, however, that the equilibrium method of solution only
directly applies to the case of an ideal firm, market, or consumer, as the case
may be. In this the respect the above example would yield the direction of the

- Ill -

equilibrium rate of change of output with respect to the tax rate for an ideal
firm that operated at the relevant equilibrium position. Further, it would be
pointed out that most of the theories in the physical sciences are formulated in
this manner in that they only refer to specific, ideal cases. For instance, the
theory about the behavior of gases states that the pressure of a gas is a function
of its temperature and volume. This theory is defined and the function's
parameters are specified in terms of an ideal gas--namelyj a specific type of gas
which has a number of idealized properties. To relate such an ideal theory to
specific, observable cases interpretive rules are provided which permit the
experimenter to empirically establish the presence or absence of the requisite
initial conditions. Since the initial conditions can be observed and the relevant
pressure, temperature, and volume can be measured, the theory itself can be
submitted to test in a variety of specific cases,— Accordingly, if one is to
treat economic theory in a similar manner the theory itself must provide
sufficient interpretive rules to permit part or all of the theory to be confronted
by empirical test.

The analysis in the last chapter argues, in effect, that economic theory does
not contain such interpretive rules. That is to say, it is demonstrated that the
deductive system underlying economic theory is such that all hypotheses require

— For an extensive analysis of the uses and misuses of the concept of "ideal"
type, case, and theory in empirical science see- E. Nagel and Carl G. Hempel,
"Symposium: Problems of Concept and Theory Formation in the Social Sciences,"
Science, Language, and Human Rights, American Philosophical Association, Eastern
Division, University of Pittsburgh Press, Philadelphia, 1952, Vol. I, pp. 43-86.
(Reprinted as; E. Nagel, Problems of Concept and Theory Formation in the Social
Sciences," and C.G. Hempel, "Typological Methods in the Social Sciences," in
M. Natanson, (ed). Philosophy of the Social Sciences, Random House, New York, 1963,
pp, 189-209, and pp. 210-230, respectively^

- 112 -

some equilibrium conditions to be met as part of their initial conditions. Since
economic theory does not provide any interpretive rules by which these initial
conditions can be observed it is concluded that it is not possible to subject the
theory to en^irical test. In order to subject both this claim and its corollary
to a more detailed scrutiny it is necessary to re-examine the deductive system
upon which all classical economic theory is based.

2. The General Deductive System

In the general case the economic system is represented by n functional
relations each of which contains n variables and m parameters. If each functional
relation is represented by the notations

^ v'^l J 2 ) ° ' ' )^r\ ''-''1 f^J .»">•" ''^m ~

then the total system of functions is represented by;

t ^Xt ^x„ , o . . >x ^q;^ ^QJo ) " " ' .''-I'rYl' ~ yi— 1 ^ ^ ,s • « • .» ^/ Co .H-}

If this system is to represent the basis of a deductive system then the n relations
in (6.4) must be independent of each other as well as consistent with each other.
While both these conditions must be satisfied by any specific application^ neither
depend upon the empirical content of the system. Consequently, for the purposes

of this analysis the process by which one determines whether these criteria are

met will be ignored. Instead suppose that they are in fact satisfied.—

The basis of the economic system, then, is represented by (6.4). The

— The criteria of independence and consistency in deductive systems, i.e.

calculi, are discussed in detail in; A. Church, op. cit. , Chapter 1.

- 113 -

equilibrium solution is derived by applying the following constraints: First, a
set of initial conditions are chosen--namely, a specific set of values are given to
the parameters (an ^cto ' * • * ^^ ^ ^°^ each of the n functional relations. Second, the
first-order condition

■^ f^ i>i^, yi^, ... ,x^,a^,a2, '" ,ci J = 0 (6.5)

is imposed and a further set of n relations represented by (6 .5) are generated.
Since the equilibrium point represents a maximum the third step consists of
examining whether the second-order condition

— 2 ^ i^i.f^2> " ° '^n'^^l^^^Z' ' " ^°^va^ "^ ° (6.6)

dx.

is satisfied for all n relations in (6,5). If each of these conditions is imposed

and if each is satisfied then the equilibrium solution to (6.4) is given by a set

of n values of the variables x. , These values are stated in terms of the initial
— —X

values given to the parameters (a, ^ao j> • ° « .^Qt ) and can be represented in functional

form as:

o i, o o 0\ /• 1 o \3/ ,, _.

X. = g (a, .?a2 J , o , ,a ) (1=1^2,, ,.^n)— (6.7)

By this deductive process a specific set of values are arrived at for the
variables x, in terms of the initial values given to the parameters
(oCt }(Xy } . . . }0C ), Now, if within the context of a particular case^ it were possible
to observe and test the relations given in (6.5) it would imply that it was also
possible to observe and record the appropriate initial values of the parameters.

— Relations (6,5), (6,6), and (6o7) are, of course, identical to (3.9), (3.10),

and (3o8) respectively.

- 114 -

Under such conditions it might then be possible to observe some of the values of
the X. and as a consequence test whether the system under consideration is at
equilibrium.

In a specific application of this deductive process to an economic system
empirical difficulties are encountered at all three stages. To begin with the
functions represented by (6.5) are themselves equilibrium relations. In the
example mentioned in this chapter they would represent the production and cost
functions of n firms whose output was or is to be taxed. Indeed, the relevant
production and cost functions are those which specify the relation between inputs
and output such that the output is being produced at a minimum of cost. In the
case of a consumer the functions in (6.5) represent the relevant demand relations.
These relations are also equilibrium functions and depend upon the continued
maximization by each consumer of his utility function. Since, the relations in
(6.5) are equilibrium relations this implies that the initial parameter values
(cx^jOCyf'sOt^) ai^e also equilibrium values. Accordingly, to empirically determine
their values one would need to go back a step and inspect the process by which
they were generated. Such an analysis, however, leads to exactly the same position
as was examined in the last chapter. There it was noted that it was not possible
to employ the results of a single empirical investigation to determine whether a
firm was employing a minimum cost and production schedule or whether a consumer was
maximizing his utility. Thus, as one cannot submit the process by which the
equilibrium parameters are generated to test, it is clear that there is not an
empirical process by which one can establish the initial values (a, ^a^ ,...., a )•
Without such a process it is not possible to empirically determine which parameter
values satisfy the first of the three constraints.

- 115 -

The third constraint given by (6.6) poses another serious obstacle. If
one is unable to empirically establish the equilibrium values of (a-, ,a^ , > " ,0C )
how can one possibly confute whether the second-order partial differential
equations have values less than zero? Since not all relations one might care
to write down will satisfy (6.4) j, and since one is unable to ascertain the
relevant parameter values, it follows that one is also unable to determine for
any specific case whether (6.6) is satisfied or not.

The same remarks apply with equal force to the second constraint represented

by (6.5) as well as to the solution to these relations given by (7). If the

values of (a, >Q;„ , . . . ,ct ) cannot be empirically established how is one to test
12 m

for the equilibrium values of the variables, x. = g (a, ,(Xy , . . . ,cc )? Manifestly,
one is in the same position as before where the inability to establish the
initial conditions precludes the possibility of being able to subject the result-
ing relations to empirical test.

In order to circumvent the full force of these obstacles to empirical
interpretation a method was devised which permits the determination of the
directional change of individual variables in response to selected changes in
the initial conditions. This method of comparative statics begins, as already
described, by first assuming that it is possible to solve for the equilibrium
solution given by (6.7). Once the relations in (6.7) are known selected shifts

O O Os

'l ''^2 ' ° ' ° •''^m

in the values of (ai >Q:^ , . . . ,a„) are made so as to determine the effect these

shifts have upon the direction of the rate of change of certain variables. The
deductive process proceeds by taking the first partial derivative of the
equilibrium relations f (x ,X2 .,..., x ,a-, ;a2 .» • • • .'Ct ) with respect to one of the

- 116 -

parameter values, say a,. The result of this operation is a system of n partial
differential relations where all parameters and variables except the ones being
differentiated, are treated as constants. This system of relations is represented

by:

Sx^ o . 3x„ o . dx o

f^ (_Jl) + f^ (_£) + ... + f^ ( ".) = -f^ (6.8)

^1^1 ^2^1 ''n ^ ^1

where

£i _ ^f o o o o o o.

X. ~ 'STT ^\>^2'°"'\'^l''^2'°"'°^m^
J J
and

r:l df c ° o o o o.

Since all other variables and parameters are treated as constants, during the process

of partial dif f entiation, all the f terms represent coefficients of the variables
5x. o 1

(^— ) <, Hence, as noted in Chapter 3, (6o8) represents a system of n linear

equations in n unknowns. The unknowns in turn represent the equilibrium rates of

change with respect to the shift in the value of the parameter a, .

The desired result is to be able to determine the sign of each of the variables
dx. o
(^— -) = In other words ^ the procedure is designed to ascertain the sign of the

coefficients given by

i
fi- _ of /• ° ° o o o o
X ~ Av v^i >^2 ■> ° " ' ■'^n''^l ■''^2 ' ° ° ° •''^m
J J

The analytical process by which these results are derived is described in Chapter 3
and need not be repeated here,—' except to note that the resolution of the signs

-'see pp. 40-47,

- 117 -

requires the application of a number of further conditions. These constraints make
use of the equilibrium conditions as well as the special requirement that a shift
in one parameter may only affect one of the relations in (6.8). The principal
result of this analysis is a criterion function with which one is able to determine

ax.

the sign of the variables (^T") • This criterion function is given by

11 1
where

xa " ^"b^^^^^ f(Xi,X2,...,x^,ct^,a2,...,ajjj) (i=l ,2, .. , ,n)
i i i i

Disregarding, for the moment, the special conditions under which this criterion is

developed one can now inspect it to see whether it permits the direction of these

rates of change to be empirically established. If one is to be able to test the

result of an application of this criterion one must be able to specify the function

o o o o o o
represented by, f (xi jXj, , . . ,x ^ai .,aj, ,, . o . ,a ). But this is the equilibrium

relation derived from the solution of (6,5). But, one cannot empirically establish

the solution to (6,5). Hence, it is hard to know how to establish the empirical

relevance of the criterion in (6,9). Indeed, to determine the empirical content

of (6.9) it is necessary to be able to demonstrate the empirical relevance of the

other special conditions. That is to say^, it must be defended upon observational

grounds that not only is it possible to treat a shift in one parameter at a time,

but it is also possible to show that the effects of this shift are restricted to

one of the equilibrium relations. Moreover, the theory does not permit the empirical

specification of the equilibrium relations, let alone their initial conditions.

Thus, the empirical relevance of these constraints is meagre to the vanishing

point.

- 118 -

Since the technique of comparative statics is based upon the equilibrium
solution to the original set of relations (6,4) all hypotheses which are deduced
by this technique have some equilibrium values as their initial conditions. It
follows, therefore, that all propositions or hypotheses produced by this deductive
system have as a part of their initial conditions some unobservable equilibrium
values .

To subject an hypothesis to test it must be possible to observe the
occurrence of its initial conditions. To be a part of empirical science a theory
must contain at least one hypothesis that can be submitted to the process of
refutation by empirical test. But the deductive system of classical economics
by relying upon equilibrium constraints precludes the possibility of generating
testable hypotheses. Consequently, it is the deductive system itself which
confers the empirical vacuity upon the hypotheses and theory of classical
economics.

3, The Market Conditions

So far the analysis of the deductive system has not included the
empirical conditions delimiting the type of market under which these theories
are supposed to hold. Clearly before a market theory could be submitted to
test one would need to be able to show that the requisite initial conditions
were satisfied by the specific market under investigation. For example, if
one were testing the theory of market behavior under perfect competition one
would need to empirically establish whether: (i) All firms within the market
are producing a homogeneous product. A market for dairy products is a
reasonable example of such a market and was employed in Chapter 4. But, if
brand names and other promotional schemes are employed in the market such that

- 119 -

the consumer's decision process is no longer solely a function of the product's
price, then such a market fails to satisfy this condition, (ii) All consumers
are indistinguishable from each other from the seller's point of view. If
firm's have no other basis than the market price with which to decide who is
to buy their product, then this requirement is also satisfied, (iii) The
number of consumers and producers is sufficiently large so that the decisions
of any one member of the market are not large enough to significantly alter
the market price« If one buyer or seller is observed to be in a position to
set his own price independently of the prevailing market price, then such an
action would indicate that the market is not in a state of perfect competition,
(iv) All consumers and producers are aware of current prices and bids for all
the commodities in the market, (v) All consumers and producers are free to
enter or leave the market as they see fit„ There are no restrictions such
as membership fees inposed upon this decision. If all these conditions are
satisfied by a specific market under investigation then one would be entitled
to apply the perfectly competitive market theory. Similarly, if these
conditions were violated, but the market was such that it satisfied the
requirements of another market type, i.e„ monopoly, duopoly, oligopoly,
oligopsony, etc, then the appropriate market theory could be employed.
However, each of these market theories is developed from the same
basic deductive system. Hence, each theory is con^osed of propositions
or hypotheses that require certain equilibrium conditions to be met as
part of their initial conditions. Since the presence of equilibrium
conditions within each theory is not dependent on the type of market under
consideration, the market conditions become empirically relevant only if

- 120 -

the theories themselves contain hypotheses which can be subjected to test. But,
the ubiquitous equilibrium conditions prevent these hypotheses from being
submitted to test. Therefore, even though each market theory can only be
empirically investigated if certain market conditions are satisfied, their
inherent untestability is a consequence of the deductive system from which
they are developed. Accordingly, the analysis and conclusions of this and
the previous chapter apply to all theories developed in this manner.
Moreover, until such time as testable theories of market behavior are
constructed there is no need to investigate the empirical validity of the
criteria which delimit particular market types.

4. Equilibrium Analysis and Economic Theory

The fundamental problem facing economists is to acquire a body of
empirical knowledge about economic phenomena. Once this knowledge Is
acquired it can be used for whatever purposes economists or other social
scientists have in mind. How such knowledge should be employed is not in
question here. The primary object of the analysis has been the acquisitive
process itself. In particular, the theories of classical economics have
been examined to determine whether they permit the development of a set of
testable theories of economic behavior. Without such theories there is no
basis from which to develop empirical knowledge about economic events.

In the preceding sections economic theories of market behavior as well
as their basic deductive system have been submitted to an extensive
examination. The object has been to discover whether these theories can be
submitted to test. The analysis has led to the conclusion that the classical

- 121 -

deductive system is such that it leads to the construction of theories which
cannot be subjected to a process of refutation by empirical test. If a theory
cannot be tested, it cannot be employed as the basis for acquiring empirical
knowledge. Hence, we, as economists, are apparently in a position where it
is not possible to employ classical economic theory as a basis from which to
generate empirical knowledge of economic phenomena.

This is a strong as well as unfortunate conclusion. It implies that
classical economic theory is empirically vacuous. It also states that
classical theory cannot be employed to generate empirically significant
explanations and predictions of economic events. Clearly, however, this
theory was intended to provide economists with the ability to make
empirically meaningful assertions about the relations among certain economic
variables. Unfortunately, these intentions have not been translated by the
method of equilibrium analysis into a body of testable theory. Since the
primary objective remains unchanged- -namely, to develop testable theories
of economic behavior--it is necessary to delimit the conditions which if
satisfied would provide classical economic theory with the requisite empirical
content. To describe these requirements one needs Co return for a moment
to a general statement of what it is that one expects from a testable theory
of economics.

In the second chapter the characteristics of such an economic theory are
described by a statement of the classes of observable behavior that one
expects it to encompass, H is the class of observed sequences of economic
behavior whether in the part or the present that belong within the theory's
domain, I^ is the class of all such observed sequences which includes those
in H as well as all which will ever be professionally observed. If a theory

- 122 -

is testable within H then it is also testable within I^. Whether it is
empirically true or false can only be determined by actual tests. But, if
theories are to have empirical significance then they imist, in principle,
have the ability to generate all of the relevant, observable sequences of
behavior contained in H or I^.

Classical economics contains theories that are stated in terms of
equilibrium relations. Hence, if the class of observable sequences of economic
behavior only includes behavior that is at equilibrium, then these theories
are compatible with the behavior included in H or I^. Unfortunately, economic
theory does not provide sufficient interpretive rules to permit either the
identification of sequences of equilibrium behavior or the testing of the
relations in which these sequences occur. As a result, it is not possible
to empirically establish whether H or I^ solely consist of sequences of
equilibrium behavior. If one can neither establish nor refute a claim it
has no empirical force. Consequently, the only conclusion to be drawn
is that while H or !_ may include observable sequences of behavior at
equilibrium such sequences do not exhaust the entire collection of

observable behavior contained in H or I^o

5/
Consider, for a moment, an example— of such a state of affairs.

Suppose the classes H and 1 consist of the observable sequences of behavior

of a liquid in a specific container. If the container is always at rest

then we could readily develop a theory which would account for the behavior

— I am indebted for this example to H.A. Simon, "Theories of Decision-
Making in Economics and Behavioral Science," American Economic Review,
Vol. 49, June, 1959, pp. 253-283,

- 123 -

recorded in H or I. Indeed, the theory could consist of a hypothesis which
related the equilibrium position of the liquid's center of gravity to the
gravitational forces acting upon it. In particular, the hypothesis could
state that the liquid would minimize the height of its center of gravity.
Accompanied by a statement of the initial conditions--in this case, the
internal structure of the container--the equilibrium point is uniquely
determined. Consequently, the theory is able to generate the observations
contained in H or I^.

If the container is not at rest, and if H and I^ still include all the
liquid's observable behavior then the theory is no longer capable of
generating these sequences of behavior^ Clearly, if the container never
comes to rest then the theory cannot, without further elaboration, generate
any of the observed sequences of the liquid's behavior. If the theory does
not contain interpretive rules with which we can determine when the liquid
is in equilibrium, then we will be unable to test any of the theory's
conclusions.

To describe and explain the behavior of this liquid we would need to
know the processes by which it adapted itself to such changes in its
environment as are brought about by the movement of the container. Once
these processes are known and stated in a testable form then we can employ
them to generate the behavior recorded in H or I^.

In a similar manner equilibrium analysis provides us with theories
which describe the end state of an equilibrating process. If the economic
world remained at rest, and if the theory contained interpretive rules
which permitted the observation of equilibrium points, then we could employ

- 124 -

classical equilibrium analysis to generate the observable, economic
equilibrium states. Unfortunately, none of these conditions are met either
by the classical theory or by the data which represent the observables noted
in H or I^.

To be able to describe and explain obser ble economic behavior we
need to know the processes by which economic units whether individuals,
firms, industries, or markets respond to their changing environment. To
acquire a knowledge of these processes implies the existence of a theory
or collection of theories which contain testable hypotheses abov t them.
Such hypotheses must contain observable initial conditions. And if they
are to permit the occurrence of economic events to be explained some
of these hypotheses must be able to withstand and survive empirical tests.

In defence of classical theory it might be argued, that if the processes
which guide the behavior of economic units are discovered then the
equilibrium positions will turn out to be particular stages in the total
sequence of observable behavior. Accordingly, while classical theory
might not be able to generate all of the behavior contained in H and I^
it would be able to account for some. To argue in this fashion, however, is
to overlook the fact that classical theory does not provide the criteria
with which equilibria can be recognized. If the occurrence of equilibria
cannot be detected then one cannot argue that one stage of a particular
process represents an equilibrium point. Moreover, until such criteria
are established it does not even make empirical sense to argue that
equilibria occur at all. Further, a knowledge of the processes which determine
the behavior of economic units does not imply that one will be able to

- 125 -

discover the equilibrium points of classical economic analysis. On the
contrary, while a knowledge of the relevant processes would permit the
generation of all the statements in H and I^, it might also lead to the
conclusion that classical equilibria, if empirically recognizable, do not
exist as members of the total sequence of observable economic behavior.

Summary

At the beginning of this chapter it is noted that in order to explain
the occurrence of an event a theory must contain at least one hypothesis
which has survived empirical test. It is an obvious corollary of this
statement that to meet this criterion the theory must contain at least
one testable hypothesis. Since it was shown in some detail that the
theory of market equilibrium did not contain such an hypothesis, the query
was raised whether any of the theories of classical economics could
satisfy this corollary.

To contain a testable hypothesis a theory must be stated in such a
manner that the initial conditions of at least one hypothesis refer to
observables. If all hypotheses of a theory contain as part of their initial
conditions some terms which do not refer to observables then none of them can
be submitted to test.

Classical economic theory is developed from a single deductive system.
This deductive system employs a process of equilibrium analysis as the basis
for generating economic theory. An analysis of this deductive system
demonstrated that for every theory developed in this manner each of its
hypotheses contained at least one equilibrium constraint as part of its
initial conditions. Since the theories themselves do not provide criteria

- 126 -

by which these conditions can be empirically established, the equilibrium
constraints do not refer to observables. Moreover, as none of the hypotheses
have observable initial conditions, none of them can be submitted to empirical
test. Therefore, it follows that none of these theories can be employed to
explain or predict the occurrence of economic events.

The primary obstacle to empirical interpretation lies in the concept of
an equilibrium. If a system is at rest or reaches a position of rest within
a short interval of time, the end state may usefully be described as an
equilibrium position. However, for systems that do not meet these conditions,
the notion of an end state has less and less relevance the longer the time
interval between states of rest. In observable economic systems the classical
theories do not provide criteria with which it is possible to ascertain the
presence of a state of rest. As a result, the classical economic conception
of equilibrium has no empirical meaning within the context of observable
economic behavior. If the concept of equilibrium is en^irically vacuous then
all theories based upon this concept must be vacuous as well.

In order to be able to describe and explain observable sequences of economic
behavior one needs to be able to discover the processes by which the individual
economic units respond to their changing environment. Once testable theories
of these processes exist then it will be possible to proceed with the task of
acquiring empirical knowledge about economic phenomena. Until such testable
hypotheses are discovered no progress can be made. For although the object
is to acquire knowledge, a necessary condition for such knowledge is the presence
of testable hypotheses. Since classical equilibrium theory contains no such
hypotheses it is necessary to continue the search by inspecting the hypotheses

- 127 -

and deductive system of otherbodies of economic theory. In this regard the

next part of the book is devoted to an examination of the hypotheses and theories

which result from econometric analysis.

PART THREE

Foundations and Characterists
of
Econometric Analysis

Chapter 7
FOUNDATIONS OF ECONOMETRIC ANALYSIS

The theory of econometrics is to a. large extent the theory of how to
measure certain types of economic relations. While the subject of measurement
is not sufficient by itself to differentiate econometrics from other parts
of economics^ the special techniques econometric ians employ serve as the
theoretical basis for their empirical investigations. One part of the
econometrician's task is to observe actual economic data and measure the
interactions among specific economic variables. The measuring procedures are
a direct application of the theory of econometrics. The specific economic
variables and their hypothesized relations to one another are derived in part
from econometrics and in part from classical economic theory. Although the
source of these relations is an important part of any econometric investiga-
tion, their structure is a consequence of the theory itself and not of the
specific application.

Consider^ for example^ the following relation which represents a
specific demand function.

y=a + Pp+U|. (7.1)

where ^ is the quantity demanded, £ is the prevailing price^ a and £ are
parameters, and u is a random variable. The econometrician's task consists
of first specifying that the relation (7.1) represents a certain demand
function--i„e. J, the first step is to express the economic hypothesis or
relation in a particular mathematical form. The next step is to employ such
data as are available to derive estimates of the values of the parameters
a and £, and of the error termu. . With these estimates the relation in (7.1)

- 129 -

can now be confronted by additional data to determine^ by means of certain
statistical criteria, its "goodness-of-f it." If the goodness-of-f it is
satisfactory the relation is then used as a vehicle for generating limited
predictions about the future course of the relevant variables.

From this example, it is clear that the major part of the econometrician's
job is encompassed by the first three stages; specifying the relations,
estimating their parameters, and testing the degree to which the hypothesized
relations fit the data. While the process of prediction is certainly valuable
and important, it cannot be employed if the first three stages have not been
successfully conpleted. As a result, an examination of the foundations of
econometrics is primarily an analysis of the deductive system employed
in the processes of specification, estimation, and testing.

If econometrics is to provide economists with the ability to establish
testable theories of economic behavior, then its deductive system must permit
the statement of hypotheses which can be subjected to test. If testable
hypotheses can be generated by this approach then they can be examined to
determine if any of them can survive the appropriate tests. Once tested
relations are established we are at the beginnings of a science of economics.
For with empirically tested hypotheses we can establish explanations and
predictions of the relevant economic events.

The analysis of classical economics led to the conclusion that testable
hypotheses were not a product of such a deductive system. It is the purpose
of the following pages to discover whether econometrics is in the same class
as classical economics, or whether its deductive system permits the develop-
ment of a testable body of economic hypotheses. In order to clarify some of •

- 130 -

the basic concepts of this deductive system the analysis begins with an
examination of its fundamental assunqjtions or postulates.

1. The Basic Postulates

The first assumption of econometrics is that all hypotheses are to be
stated in stochastic form. In the example above an error term u is included
in the demand relation. This error term represents a random variable which
is generated from a specific distribution with a known mean. The value of
this error term varies from one interval of time to the next. Hence^ a
stochastic relation like (7.1) no longer states that the demand ^ is exactly
equal to a constant a plus a constant ^ times price £, as in the case of
classical theory. With the addition of the error term the deterministic
relation is changed into an inexact specification of demand.

If one merely wished to construct an inexact relation there are many
ways in which this could be accomplished. One could argue that the relation,
X = a + P p J is only a rough approximation to the actual relation governing
consumer demand. At the same time one could claim that no matter how carefully
data were collected these data would always contain errors.— Similarly^
one could assert that no matter how many equations and variables were employed
and despite the care with which the parameter values were estimated, the
theories would never be better than inexact statements of hypothesized economic

— An excellent analysis of errors in economic data is to be found in;

0. Morgenstern, On the Accuracy of Economic Observations, Second Edition,
revised, Princeton University Press, Princeton, 1963.

- 131 -

relations. As a result, the equations could have errors in specification
(an incomplete set of variables are selected), errors in measurement, or be
subject to a variety of unspecified disturbances. To reduce this complexity
of errors to manageable proportions, econometric theory assumes that measure-
ment can be accomplished without error. If there are no errors in measure-
ment, then a mis-specification of an hypothesis can be determined by
testing its goodness-of-f it. Thus, all errors are categorized under the
heading of random disturbances and are collected in the error term, u. Since
the variables themselves are no longer supposed to be subject to variation,
the relations are made stochastic by the addition of this error term.

There are many reasons for the addition of an error term into the

II
structure of all econometric hypotheses— . But perhaps the fundamental

justification lies in the statistical methods employed to estimate parameter

values. If an equation contains a random variable as an error term--i.e,

if we are dealing with stochastic relations--and if this random variable has

certain well defined properties, then these properties delimit a particular

class of estimating procedures. Since the process of parameter estimation

depends upon the stochastic assumptions, different assumptions about the

behavior of u entail different estimation techniques. The point to note,

however, is that estimation procedures depend upon the stochastic assumptions.

And since econometricians employ a specific set of estimation techniques these

procedures imply that econometric hypotheses must contain error terms with certain

specific characteristics.

— A list of such reasons is provided in; S, Valavanis, Econometrics ,

McGraw-Hill, New York, 1959, pp. 5-6.

- 132 -
A. The Error Term

The characteristics of an error term are a consequence of the assumptions
that are made about its behavior. While a number of different assumptions can
be and are employed in a variety of econometric studies the set to be examined
are those which are most generally used.

The first assumption is that for every value of t^ Uf. ^^ * random variable.
A random variable can be discrete or continuous, but in each case it must
take on each of its several values with a definite probability. In
mathematical terms this assumption is stated as follows;

If p(u) is defined for all values of u such that
p(u)du = 1

/■

u
or

E p(u) = 1
u

where ^ £ P £ ■'■

then u^ is a random variable for all values of t«

In equation (7.1) this assumption states that at each period of time the
value of u is determined by its own density function. In other words ^ while
the value of u may change from period to period the actual value is determined
by its propability of occurrence which is defined by its density or probability
function. If this density function is unknown, then the propabilities with
which u takes on specific values are also unknown. Further, it is not possible
to analytically determine any of its characteristics, i.e. its expected value,
variance, and higher -moments. Hence, if one is to be able to specify the
properties of u^^ its density function as well as the values of certain of its
moments must be known.

- 133 -

The second assumption concerns the density function and states that u
is normally distributed. Mathematically this assumption is expressed by

where -co < u < »
and where E[u] represents the mean and a_ the standard deviation of the density
function. Having specified the density function one now needs to know what
values to associate with its mean and variance.

The third assumption is that the expected value of u is equal to zero--i.e,

-00 for all t.

Combining (7,3) with (7.2) the density function of u can be rewritten as

To be able to estimate the value of u at any particular period of time
and to relate this value to one derived during another time interval, it is
necessary to know that the variance of u 's density function is not changing
over time. Hence, the fourth assumption states that p(u) has a finite

variance which is constant over time, i.e. the second moment about the mean,

2
a y is constant over time and finite;

2 2 2

2
and 0 < a < «

2 r 2

where a^ = / (u^. - E[u^]) p(u)du

- 134 -

One consequence of the last three assumptions is that the value of the error
term for any particular period is derived by a random selection from a normal
distribution with zero mean and constant variance. Each value of u does not
depend on any of its preceding or succeeding values. Each is independent- of
each other and depends solely on the particular normal distribution from which
it is derived. As a result^ there are two further assumptions implicit in this
characterization of the error term.

The fifth assumption is^ as has just been noted, that specific values of u^^
are independent of each other^ i.e. are not correlated to one another.
Mathematically this statement is represented by the condition:
E[u^, u^_.] = 0

where t may take on all possible values and ij^O

Concurrently, if all values of u are to be independent of each other, they
must also be independent variable contained in the relevant hypotheses. For
relation (7,1) this last assumption states that the covariance of u and £ must
be equal to zero, i.e. u is independent of £ if
Cov(Uj., p^_.) . 0^^^ p^__ = 0

for all £ and all i

These assumptions delimiting the properties of the error term are stated
for the case where a theory consists of one equation. But, not all theories
are quite so simple and econometricians frequently deal with theories containing
several equations. Since each relation contains an error term these assumptions
need to be interpreted to include this general case.

Suppose for the moment that we are dealing with the general case where
there are n relations containing n variables. Since each relation is stochastic,

- 135 -

each relation has an error term. For the n relations there will be n such error
terms which can be represented by a vector U(t) = (u (t), U2(t) , , . . ^u^(t)) .

If n=l, the first assumption requires that u(t) be a random variable. If
n^l, all u.(t), (j=rl,2, . . . ,n) are random variables. Hence, the vector U(t) is
also a random variable.

The second assumption is generalized by requiring the error terms
(u, (t)^U2(t) , . . . ,u (t)) to be jointly normally distributed.

Similarly if for n=l^ E[u(t)] = 0, then the means of all the error terms
are equal to zero. Consequently, the vector given by E[U(t)] is a vector of
zeros, i.e. E[U(t)] = (0,0,,„,,0). This has the same meaning as the statement
that the joint normal distribution has a mean equal to zero.

If the joint normal distribution is to have a constant variance then the
covariances of the respective errors must not vary with time, i,e.
Cov(u,(t),u (t)) = cr.j^(t) = constant for all _t

If each of the values of the n error terms is to be independent of all of
its other values then for each relation
E[Uj(t),Uj(t-i)] = 0

for all values of _t where ij^O and j = (lj,2, . . . j,n)

Similarly^ if the vector U(t) is to be independent of the values of any of
the variables in the n relations, the covariances between each error term and
the independent variables in its equation must also be equal to zero.

Earlier it is noted that estimation procedures depend upon the stochastic
assumptions. Having described the assumptions concerning the behavior of the
error term it is now sensible to examine the statistical procedures employed in
the estimation of the parameters of these stochastic relations.

- 136 -
2. Estimating the Parameters
A. Single Equation Models

In order to estimate the parameters of a particular hypotheses it is
necessary to have an estimating criterion function. While a number of such
functions can be generated and used^ the principal criterion employed in
econometrics is the maximum likelihood criterion.

All estimating functions produce estimates which have somewhat different

properties. But very few are able to generate estimates that are unbiassed^

consistent^ sufficient, and efficient— , In most normal situations the

maximum likelihood criterion produces estimates with these characteristics. As
a result of these as well as other convenient properties the majority of
estimates in econometrics are maximum likelihood estimates.

To explicate the notion of a maximum of likelihood consider a simple

4/
estimation problem- , Suppose we are faced with an urn in which there are a

number of red and white balls. Suppose further that we know there are twice

as many of one color as of the other^ but we do not know which color is the

more numerous. If we draw a sample of n balls from the urn with replacement

we know that the distribution of the number of white balls in the urn is given

by the binomial

t(X5 p) = p q

Further, we know that the probability of drawing a white ball is either 1/3 or

—'A definition of these terms is given in the mathematical Appendix B.

—This example is adapted froms A.M. Mood and F.A. Graybill, Introduction

to the Theory of Statistics., McGraw-Hill , New York, Second Edition, 1963, p. 179,

- 137 -

2/3. The problem is to estimate the value of £ from the particular colors of
the balls in a specific sample. If the sample consists of four balls^ then the
total number of possible outcomes is given by:

no.

of white (x)

f(x,l/3)

16/81

32/81

24/81

8/81

1/81

f(x,2/3)

1/81

8/81

24/81

32/81

16/81

Consequently^ if only one of the balls in the sample is white the estimate of
£=1/3 would be chosen^ since the probability of 32/81 is greater than that of 8/81,
Similarly if the sample contained three white balls our estimate of £ would
be 2/3.

For the procedure to provide a good estimate of £ it is clearly necessary
that the sample represent the distribution of balls in the urn. If we draw a
sample with no white balls when there are twice as many white as red, the sample
would lead to an er»"oneous estimate of £„ The maximum likelihood procedure
assumes that the sample is representative of the population. Hence, in this
example^ for every value of x it selects the value of £ so that

f(x5 p) > f(xs p")
where p represents the maximum likelihood estimate, and p' the alternative value.
To generalize this result to the case where an estimate is required of the
value of an unknown parameter u from a random sample of size n the procedure is
as follows. The sample values Xi ^2i? :> " • ° ^2i define a sample density
f (x, ,X2^ . . . ,x J u) . The maximum likelihood estimate of u is the number u^ if it
exists, such that the value of

t (x, ^X- 5 o o . jX s u^ > t (X. ,x„ , , « . ,x J u 5

where u' is any other possible value of u.

- 138 -

In order to find a. particular maximum likelihood estimate it is necessary
to construct the likelihood function and then find its maximum point. The
likelihood function is derived from the sample density. A sample value from a
population of known density provides us with the sample density for that value.

For exan^le^ two white balls in a sample of five drawn from the urn gives a

/5 \ 2 3
sample density of f (2j p) = / j p (1-p) , where f (Zj p) is the likelihood

function in this case. If p could take on all possible values, i.e. 0 < p < 1,

then to find the value of £ which maximizes the likelihood function one would

differentiate f (2j p) with respect to £, set the resulting equation equal to

zero, and solve for £. The solution is £, the maximum likelihood estimate of £.

In general, if 2ii ^iS?-' • • " '^ ^^^ sample values and f(x ,x„,,.,^x , u) is the

n
sample density, then the function .En f(x.j u) is the likelihood function of u

for the particular sample values (x. ,x-;, , . . , ^x ), Since .II-, f (x. j u) has its

n
maximum at the same point as the function, log .n f(x.j u) , and because the

logarithm of the likelihood function is usually easier to deal with, it is

customary to find the maximum of the logarithm of the likelihood function.—

To apply this procedure to an econometric relation consider the demand

relation, y =a + P p + u „ By a suitable transposition of terms this equation

becomes

"t = ^t " ^ - P Pt • (7-5)

According to the sixth assumption about the error term, u must not be

directly dependent upon any of the independent (exogenous) variables. From

(7.5) it is clear that, while Cov(u , Pj-_i) may be equal to zero, the value of u^^

— For a more detailed presentation of the maximum likelihood technique see:
A.M. Wood and F.A. Graybill^ op, cit. , Chapter 8.

- 139 -

is a function of the observed values of ^ and £ as well as of the unknown

values of a ^^'^ £•

The problem is to derive maximum likelihood estimates of a and £. It is
assumed^ as in the urn example, that the sample data are representative of
the population. Hence, one begins by observing a sample of values of ^ and £
at a particular time _t. To construct the likelihood function one needs to know
the sample distribution of u. But the assumption about the error terms is
that the u's are normally distributed with zero mean and constant variance.
As the sample is assumed to be representative of the population, the sample
distribution of u is the normal distribution with zero mean and fixed variance.
Consequently, the likelihood function is a function of the values of u which
correspond to the observed sample values of ^ and £. Denoting the likelihood
function by the letter L a sample of size n gives the likelihood function:

L = f(u^,u2,...,u^)
where the particular values of u. (i.-l,2 , . . . ,n) are a function of the n pairs
of observations on y and £, To maximize L one has to find those values of a
and Q which make L as large as possible.

Each sample value of u is normally distributed. Thus, the distribution of
n sample values is a multivariate normal. The multivariate normal relates to the
univariate normal distribution in the following way. The univariate normal is
customarily written as in (7.2):

i(U-E[u] 2
1 2^ a ^

72n 0
Hov/ever^ in order to point out the relation between the univariate and the

multivariate normal, the univariate distribution can be stated as

- 140

P(u)

1 - i J

y2n a

(7.6)

ere la I represents the determinant of covariances of u. and u., and

' u . u . ' —1 —J

-1

1- J

(a ) represents the inverse of the covariance of u. and u.. In the case

u . u . ~J- ~J

1 J
of one variable the value of la,, I is the same as the value of o . For the

i J
determinant only contains this element. Similarly for the univariate normal

(a ) is equal to (a )

^ u u u'

i J

To derive the multivariate normal one must designate the n variables. Let

Ui,Uo,,..,u be n variables which have a joint normal distribution. Then, as

noted above^ these variables can be represented by the vector U = (u u^ ,,..., ,u )

In a similar fashion the expected values of these variables can be represented

by the vector E[u3 = (E[u-, ] ,E[u„ ] , . . , ^E[u ]). For n variables the matrix of

covariances is given by:

uu"

"i"i

u u,
n 1

"l"2

"2"2

a,, ..<
u u„
n 2

u,u
i n

u„u
2 n

u u
n n

(7.7)

Hence the value of j a

UUl
-1

is the determinental value of the matrix given in (7.7)^
and the value of (cr,,,,) ^ is the value of the inverse of (7.7).

Employing this notation the multivariate normal is given by

4{(U-E[U])(a„„)"^U-E[U])3

P(U) = (/7-) (/T=^) e ^

'UU^

(7.8)

Returning to the estimation problem one can now write the likelihood
function for a sample of n values of the u's as.

141

n
2

In' ^/\a

-) e

-1.

1 - 1 i 4{(U-E[U])(a ) "(U-E[U])3

(7.9)

uu'

However, the third assumption about the error term states that the expected
value of each u is zero, i.e. E[U] = (0,0,. ..,0). Therefore, (7.9) becomes

L = (o-) (77 — r) e

(7.10)

Further the fifth assumption states that the covariances between each error

term and each independer.t variable is zero, i.e. a =0 for i^j. Consequently,

"i"j
the matrix a is given by

^uu=

"l"l

"2^2

0
0

u u
n n

(7.11)

0 0

Thus, the value of the determinant |o.jj.| is the product (a ) (o ) . . , (a ).

11 2 2 n n

But, by the fourth assumption a =a „ =...=a . Hence, the value of
' '^ u,u u^u u u '

112 2 n n

I ajjjjj =(a^^^^)n or (a^^) . Similarly, the value of the inverse (cr,...) is given by
the inverse {^^^ " or (a^j) . Accordingly, (7.10) can be simplified to

n _n _j^r,w ^-l.

2 T -¥(u(^,) u}
L = (2n) ^ (a ) ^ e "
u

(7.12)
Taking the logarithm of the likelihood function (7.12) the function becomes

log L = -H log 2n - \ log

1 / v-1 n .?

2 ""& ^" ■J ^"S 0., - t <.<^..-' ,-?^M 1-.. (7.13)

To find the maximum of a function one takes the partial derivatives with
respect to the unknown variables, sets the resulting equations equal to zero, and

- 142 -

solves for the unknown values.— In equation (7.13) the unknowns are a and the
u.. But, u.=y.-a-p p{. Substituting this value for u. into (7.13) the logarithm
of the likelihood function is given by:

log L = - I log 2it - I log a^ - i (a^)"^ Ji (y^'OC-^ P^)^ (7.14)

The unknowns are now a, ^^ and a , since ^, and p. are the observed sample
values. By taking partial differentials of (7.14) with respect to a, ^, and a
and by setting the resulting equations equal to zero one generates three
equations in three unknowns

Jl (y^-a-p p.) - 0

•ll (y.-a-p Pi)p. = 0 (7.15)

\ ill (^i-^-P Pi)^ = ^u

Solving the equations in (7.15) in terms of the three unknowns a. £, and a

— u

produces the maximum likelihood estimates which are designated by a, ^^ and £ .

While the equation used in this example contains only one independent
variable_, £ , the procedure for deriving maximum likelihood estimates is the same
for equations with n independent variables. For example, if the demand for a
particular commodity can be represented as a function of the prices of n other
commodities, then this hypothesis is represented by:

y = Q: + pj^p^ + P2P2 + "•• + PnPn ■•" "t
The error term is still a function of these n+1 variables, i.e. u=y-ci-p p^-p p -.,

P p and the covariance of ij with each of these variables must be equal to zero.

— Likelihood functions do not have a minimum, hence it is not necessary

to apply the second order condition for a maximum.

- 143 -

Accordingly, the likelihood function is formed in the manner described above and

the partial differential equations are solved in the standard fashion for the

A A ^ A A
maximum likelihood estimates cc, pi ^Po^ • • • ^Pn^ ° •

It should be noted that when the parameter values of a single equation

are estimated the maximum likelihood estimates are equivalent to the estimates

derived by the method of least squares. That is to say, the equations in

(7,15) are identical to the estimating equations generated by the least squares

approach. However, as soon as the parameters of more than one equation are

being simultaneously estimated the equivalence between least squares and maximum

likelihood estimates no longer holds.

B. Several Equations Models

In order to examine the case where the econometric theory consists of
several equations, consider the general model which <;ontains the following n
equations:

^1 + "12^2 + • • • + Q^lk^k + Pll^l + Pl2^2 + • • • + Pim^n, = ^

^^21^1 + y2 + »•• +^2),y\, + Pzi^l + ^22^2 + ••• + Pzm^m = "^

(7.16)

^kl^l +«k2y2 + ••• + Vk + Pkl^l + Pk2^2 + ••• + Pkm^m = "k
In (7.16) the y's represent the dependent (endogenous) variables, the £'s the
independent (exogenous) variables, the a's the coefficients of the endogenous
variables, the ^'s the coefficients of the exogenous variables, and the u's
are the error terms. To estimate the a's and £'s by the maximum likelihood approach
it is necessary to be sure that the error terms of one equation are not correlated
with the error term of any other equation, ---i.e. the Cov(u.,u.)=0 for i^j.

- 144 -

Earlier, when the case of several observations on one equation was considered it

was noted that the covariance between the several values of the one error term

had to be equal to zero. With more than one equation there are a number of

different error terms. As a result, in order to ensure that the value of each

error term is independent of the value of any other error term, the covariance

between any two error terms must also be equal to zero.

Two further points need to be mentioned about the system of equations in

(7,16), The first is that none of these equations may represent an economic

or accounting identity. One obvious example of an economic identity is the

equation

c(t) + s(t) = y(t) (7,17)

where y(t) represents income, c(t) consumption, and s(t) savings. While the model
(system of equations) might contain a function relating consumption to income,
e,g, c(t)=a+py(t)+v(t) , the presence of the strict identity violates the require-
ment that the value of u(t) be uncorrelated with the values of the independent
variable y(t) , For g and £ are constants and c(t) and s(t) are the dependent
variables. Hence, under this arrangement u(t) determines the value of y(t) .
Accordingly, the presence of identities in a system such as (7,16) violates the
requirement that the covariance between the error term and the independent
variables must be zero.

The second point to note in (7.16) is that the equations are written without
a constant term and with parameters g. .=1 for i= j , The constant term can be
included by letting the final independent variable, £j_. be equal to 1 . In this
case its parameter £- represents the constant term. Concurrently, it is possible
to reduce the number of parameters by dividing each equation by one of its
coeff icients--namely, g^^^ where i=j.

- 145

To form the likelihood function of this system of equations it is convenient
to make use of some simplifying notation. If the endogenous variables are
separated from the exogenous in equation (7.16) the coefficients of these variables
can be represented by two matrices:

^12 ••• ^Ik

«kl ^k2

Pll Pl2 ••• Plm
21 ^22 •

P9i P99 ••• P2m

kl ''k2

Further, if the matrix of endogenous variables is represented by Y and the
corresponding matrix of exogenous variables by Z^, then the equations in (7.16)
can be written in the simplified matrix form

AY + BZ = U (7.18)

where U is the vector of error terms

In order to estimate the values of the coefficients in A and B a sample
of observations is needed for each of the rows of the matrices Y and Z. Suppose
that the samples are all of the same size with each containing n observations.
The likelihood function of the sample can then be written as:

N
2

(7.19)

km I

Except for the addition of the term |j| , this relation has exactly the same form
as the likelihood function in (7.10). In (7.10) the term, Oj.„, represents the
diagonal matrix of covariances given in (7.11). In (7.19) the term, 5j^^, represents
the matrix of covariances given by Cov(u. ,u .) . But as is noted above Cov(u.,u.)=0

- 146 -
for all i^j. Therefore, 5, , is also a diagonal matrix of covariances, with |6

km'

-1

representing its determinantal value, and [6, ] its inverse.

The term J is the determinant of the Jacobian matrix.— When one is
dealing with a single linear equation the value of |j| is 1, and it can be ignored
as in (7,10). However, when the model contains two or more equations the matrix
of these partial derivatives must be included.

To evaluate | j| two conditions must be met. The first is that there must be
a one-to-one functional relation between the error terms and the dependent
variables. If the relation is one-to-many then the Jacobian is undefined. Since
J is a matrix of partial differentials, e,g. Su/Sy^ the functions must also be
continuous with first derivatives defined over the relevant domain. For |j| to
have a unique value J must be non-singular. Hence, the second condition is that
|j| can only be evaluated if there are as many u's as there are ^'s.

If these conditions are met and if the model can be represented by a set of
linear equations as in (7.16) then the matrix of partial derivatives given by J
is the matrix of coefficients of the ^'s, i.e.

J =

^21 ^

= A

^'kl '^k2 °°' ^

Accordingly, the likelihood function for the equations in (7.16) is given by:

. ,1 J u," , 1 } -i^nil^n ^\j\^
L = (^) A (TT— r) e

'ir

(7.20)

'kml

It follows, then that the logarithm of the likelihood function can be represented
by:

— Jacobians are discussed in greater detail in; L,R. Klein, Textbook of
Econometrics, Row, Peterson and Company, Evanston, 1953, pp. 32-38.

- 147 -

log L = -| log 2n + N log |A| -| log |5j^^| -i J^ U^ [^km^'^UA (7.21)

Now (7.18) states that^ U = AY + BZ. Thus, to find the maximum likelihood
estimates of the a's, £.'s, and the covariances (u.^ u.) for i=j, one substitutes^
U = AY + BZ, into (7.21) to get the likelihood function in the same form as
(7.14), i.e.

log L = -| log 2Tt + N log |A| - - log |5j^^|

(7,22)

- i nil (AY4«Z)^ [s^J-l (AY-fBZ);

To derive the system of estimating equations analogous to (7,15) one takes the
partial differentials of (7,22) with respect to the a's, £'s, and o 's and sets
the resulting relations equal to zero. The simultaneous solution of these
equations generates the maximum likelihood estimates, a's, £'s, and a's.

Since the a's, ^'s, and £'s are a consequence of the simultaneous solution

'=12-

of the estimating equations each estimate, say aio, depends on the values of the

remaining parameters. That is to say, the estimates of the g"s for one equation
depend on the values for the a's and ^'s of another equation j and the estimates
of the ct's depend on one another as well as the estimates of the a's and £'s
of another equation.

When dealing with a single equation model it was noted that the method of
least squares produced exactly the same estimating equations as the maximum
likelihood approach. In this situation, both methods are equally appropriate
for estimating the parameters of a single equation. However, the moment models
are entertained which contain several equations the standard least squares approach
can no longer be employed. The reason for this is quite simple. If the method
of least squares is employed to estimate the parameters in (7,16) each equation

- 148 -

is treated as though it were independent of the remainder. Such a procedure
ensures that the values of the parameters of one equation do not affect those

of another.

For example, by using the least squares approach the covariances a of
each equation would be estimated without reference either to the remaining
covariances or to the values of the a's and ^'s of the other equations.
Similarly, the term |j|=|a| would be excluded from the estimating equations.
As a result, by applying the method of least squares to a model containing
several equations estimates would be generated that are completely at variance
with the maximum likelihood estimates. Since the maximum likelihood criterion
usually provides estimates which have the desirable characteristics of
unbiassedness, consistency, sufficiency and efficiency, least squares is clearly
inappropriate except in the case where the parameters of a single equation are
being estimated.

The correct procedure is to employ the function given in (7.22) to generate
the estimation equations. This process, however, involves a large amount of
computation. To reduce the computations various special techniques are employed.
Because the method of least squares is not a viable alternative, a number of
approximations to maximum likelihood have evolved. Among these the techniques
of limited information, instrumental variables, and Theil's method of reduced
forms are frequently used,—' The object of these methods is to approximate the

— For a detailed discussion of these techniques see: S. Valavanis, op.cit. ,

Chapters 7, 8, and 9.

- 149 -

maximum likelihood estimates without going through the elaborate analysis
required by the solution of the equations derived from (7.22). While such
techniques are important to the practicing econometrician they can be disregarded
here as this analysis is concerned with the foundations of measurement in
econometrics not with various computational procedures.

3. Testing Statistical Hypotheses—

A statistical hypothesis is a statement about the probability density

function (frequency function) of a random variable. Since all econometric

hypotheses contain a random variable with an assumed density function, all such

statements are statistical hypotheses. In order to submit such hypotheses to

empirical test a procedure is required which permits the decision to be made

whether to accept or reject a particular hypothesis.

Suppose for the moment that one is Interested in the specific hypothesis

y(t) = a + p P(t) + u(t) (7.23)

where u(t) Is normally distributed with zero mean and constant variance. To

estimate the values of a and £ one takes a sample of observations on y(t) and p(t)

and proceeds, in this case by either least squares or maximum likelihood, to

generate the estimates a, P^ and a. These estimates are based on a single, specific

set of observations. Hence, without the introduction of additional criteria, it

is not possible to assess the reliability of these estimates. For example, assume

in the context of a particular set of data that the values of the estimates are

given by: a=l.-?.. p-2.31 and a=3.40. If these values are substituted directly

— An extensive discussion of the problems surrounding statistical testing is

to be found in; C.W. Churchman, Theory of Experimental Inference, Macmillian,
New York, 1948.

- 150 -

into (7.23) a specific application of the hypothesis to a particular set of data
is produced. But without estimating the reliability of these estimated values
it is not possible to determine whether to accept or reject (7.23) as a statement
of the functional relation governing y(t) and p(t) .

In order to assess the statistical reliability of an estimate one needs to
examine its possible range of variation. Parameter estimates are based on finite
samples. Also each sample generates a different value for the parameter being
estimated. As a result^ each estimate contains a certain error which is ascribed
to the sampling process. If the sample was infinite and included all possible
observations on the relevant variables^ the estimated value would equal the true
parameter value. But^ all econometric samples are finite. Thus^ the first task
is to estimate the size of the sampling error.

One such measure is provided by computing the variance of the parameter estimate,

A A

If ^ is the maximum likelihood estimate of £, then £ is a function of the sample

observations and is itself a random variable. The variance of a random variable

is the expected value of the square of the difference between the random variable

and its expected value. Accordingly^ the variance of ^ is given by;

o^ = E[p - E[p]] (7.24)

But £ is an unbiassed estimate of ^, That is to say^ if a series of random

samples were drawn and an estimate of £ were computed from each a distribution

of values of £'s would result. Since £ is unbiassed the mean of this distribution

of £ s would approach the true value of £. In the limit as the number of samples
increased to infinity, E[pj=p, where the individual values of £ are dispersed about
this mean with a variance given by (7,24). Because E[p]=p, (7.24) can be rewritten

as?

- 151 -

al = E[p-p]^ (7.25)

when the sample estimates of £ are normally distributed one can expect approximately

95% of any set of values, £. , (1=1,2, .„. ,n) to lie between the two limits

p - 2a^ and p + 2a^
P P

In econometrics it is usual only to have a single sample and as a result a
single estimate of £. If the sample size is sufficiently large (n > 30), and £
can be assumed to be normally distributed, then the 95% confidence interval for

A A

the estimate is provided by the limits, p - 2a and p + 2a . If the sample size is

P ^

samller than 30 the limits are formed by using the t^ distribution e.g. p - t ^.^o

.05 p

and p + t „i-cT. 5 where the value of t ,, ^ is found from tables of the t
.UjA — .ud —

P 10/

distribution at this level of significance and the relevant sample size. — To

construct and employ these confidence intervals £ must be normally distributed.

In (7.23) the distribution of the values of £. is a function of the sample
observations of ^. j and the distribution of the £. is a linear function of the
values of ^. . In turn, ^. is a linear function of the values of the random
variable u . . And u, is normally distributed with zero mean and constant variance.

Hence both ^. and £. are normally distributed and it is legitimate to employ
the particular confidence intervals noted above.

Applying these results to the example at the beginning of this section it
is now possible to estimate the reliability of the parameter estimates. All that
is required is to compute the standard error of each estimate, i.e. a , c , and
cr , and employ the appropriate confidence limits. For example, the standard

— A
0

— The properties of these and other sample distributions are discussed in:
A.M. Mood and F.A. Graybill, op. cit. , Chapter 10.

152 -

error for, a, in (7.23) is given by the formula

(7.26)
P /ill <Pi-P)"

2
where £ is the variance of u, £. the sample values of the exogenous variable £,

and p the mean of these sample values. Now the variance of u is an unknown

quantity which has a calculated estimate^ £ . Substituting £ for a in (7.26)

one arrives at a formula which provides the sample estimate of the standard

11/
error. —

/^2

^A = fn — (7-27)

P \/iSl (Pi-P>'

From (7.27) one can directly compute the confidence limits which for n > 30 and

. ^

a 95% level of confidence are p + 2a^,

P
Having defined a measure of reliability it is now possible to return to the

problem of describing a procedure by which one can decide v'rether to accept or

reject a particular hypothesis. The theory of hypothesis testing is customarily

phrased in terms of a choice between two alternative hypotheses: the null

hypothesis, H , and some alternative hypothesis H^ . In the above example, the

null hypothesis could be that the true value of £ = 1.5, i.e.

H ; 3=1.5
o ^

The alternative hypothesis could be that ^ has another specific value or just
Hj ^ 2^ 1,5

11/

— This formula as well as the formula for the general case is derived in;

LoR. Klein, op. cit. , pp. 134-137.

- 153 -
To be able to decide whether to accept H a critical or rejection region for the

—O JO

values of £ must be defined. If the observed (estimated) value of £ falls within
this critical region H is rejected. Otherwise it is accepted. The normal
procedure is to set the acceptance region so that it includes 957„ of the area of
the function defined by H . By doing so one incurs the chance of committing a
Type I error 5% of the time. That is to say, 57o of the time it is possible to
reject H when it is in fact true. Similarly, there is a certain chance, the
Type II error, that H will be accepted when it is false. One cannot avoid making
these errors. Consequently, to select the best of a set of alternative tests,

one chooses that test which for a specified Type I error has the smallest Type II

12/
error. —

In order to clarify this procedure consider once again the example mentioned

at the beginning of this section. Suppose that a sample of forty observations

are taken and that the estimate for p is given by p = 2.31 (see above). The null

hypothesis is H : £ = 1.5, The Type I error is set at 57o, i.e. (a 957o level

of confidence is adopted) and the test can now be stated as follows: If the value

of £ -= 1.5 is contained in the interval p ± 1.96 o^ accept H ; otherwise reject

2
H^. On the other hand, if the true variance of £, £„, were known then the test

could be rephrased to read; Accept H if the observed value of £ lies in the

interval p ± 1.96 a„j otherwise reject H .

P ' o

In econometric work one does not and cannot know the true value of £ or any
of the other parameters. At the same tim.e the sample data are employed to generate

12/

— This comparison of alternative tests is conducted by an analysis of their

power functions. See: P,G. Hoel , Introduction to Mathematical Statistics, Wiley,
New York, Third Edition, 1962, pp, 54-56.

- 154 -

maximum likelihood estimates for all parameters. Consequently, it is not possible
to set up and test a null hypothesis of the type described above where specific
values are tested against other alternatives. The only null hypothesis it is
possible to subject to test is that the true value of the parameter is zero, i.e.

H^: P = 0

where the alternative hypothesis is H ° Pi^O. Given the estimates £ and a^ one

P
can determine for a particular level of confidence, say Type I error of 5%,

f^ A

whether the interval p ± 1.96 o. includes ^=0. In other words it is possible

P
to conduct a test to determine whether the true parameter value, ^, can be accepted

as being equal to zero. Manifestly, if H is accepted then it is necessary

to accept the corollary-namely, the variable associated with ^ can be deleted

from the hypothesis.

Even though the null hypothesis, H : P=0, is not rejected by a particular

sample estimate, ^, it should not be forgotten that the acceptance of H does not

rule out the possibility that the data may be consistent with a number of other

hypotheses. Indeed, a test of this null hypothesis, within the context of a

specific hypothesis and sample data, can only provide information about the

probability of the sample estimates coming from a population with a true parameter

value equal to zero. For example, if the estimate of the parameter's sample

error is large relative to the estimate of the parameter itself the interval

A A

P ± 1.96 a may well include the point, £=0. Under such circumstances a test of

P
the hypothesis, H : P=0^ will lead to the acceptance of the null hypothesis.

A /\

For if p = 1.4 and a^ = 0.8 the interval would be given by (-0.17 to 2.97) which

is clearly consistent with the null hypothesis. At the same time, it is also

consistent with a large number of other hypotheses including the hypothesis that

- 155 -

the true value of ^ is greater than one. Unfortunately, in econometric work it is
not possible to determine the true value of £. It is therefore not possible to
subject the sample estimates to other more revealing tests.

With regard to statistical tests one further point is worth noting. In the
beginning of this chapter the assumptions underlying the error term u were discussed.
These assumptions state in part that u is a random variable with a normal distribu-
tion which has a mean equal to zero and a constant variance. Within the context
of a particular hypothesis, e.g. y = a + a, z + a^z^ + u, the assumptions about
the mean and variance of u can be subjected to test. By rearranging the
hypothesis u can be shown as a function of the remaining variables:
u = y - a^ - a^z^ - a^z^ .

The null hypothesis is that u is normally distributed with mean equal to zero i.e.

^ 2

1 -z^-rn

H : 0=0
o

To subject this hypothesis to test one would derive the sample estimate u, construct
the confidence interval, and examine whether 6_ = E[u] = 0 is contained within this
interval. In order to test whether the variance of u is constant it would be
necessary to generate at least two sample estimates of a . The test would then
consist of an attempt to determine whether these estimates were consistent with
the hypothesis that they came from two normal populations with the same variance.
While this test employs the F distribution instead of the normal or t^ distribution
as above, the procedure is quite straight forward and the null hypothesis is either
accepted or rejected as before. In a similar manner it is also possible, although

- 156 -
somewhat more complicated, to test the remainder of the statistical assumptions
about u. Hence, although statistical tests on the individual parameter values
of a particular hypothesis are frequently inconclusive it is possible to subject
the assumptions about the error term to a number of statistical tests.

Chapter 8

SOME PROBLEMS OF APPLICATION

The previous chapter is concerned with the basic assumptions and measurement
techniques that delimit the foundations of econometric analysis. To keep the
analysis within reasonable bounds of simplicity, examples of models and
statistical hypotheses were employed which were linear in parameters as well
as variables. Frequently, however, the econometrician is required to use more
complex forms in the statement of his hypotheses. While no attempt will be made
to investigate all such deviations from strictly linear models, the purpose
of this chapter is to explore some of the problems that confront the economist
when he tries to apply these statistical methods to the estimation of a variety
of economic relations.

1 , Lagged Endogenous Variables

In econometrics it often happens that one wants to represent the behavior
of a system where the values of certain variables in the current period depend
directly on their values in the previous period. For instance, from studies
of the behavior of consumers it may appear that total consumption in one period
is a function of consumption in the previous period. Such behavior could also
be expressed by a function which noted that the proportion of income spent
on consumption in a specific period depends directly on the proportion of
income consumed in the previous period. Many theories describing the cyclic
behavior of certain aggregate economic variables also have this property.—

— '^See, for example, the well known models of economic growth and trade
cycles: R,F. Harrod, Essay in Dynamic Theory," Economic Journal , Vol, 49,
1939, pp. 14-33j E. Domar, "Capital Expansion, Rate of Growth and Employment,"
Econometrica, Vol. 14, 1946, pp, 137-147; and N, Kaldor, "A Model of the Trade
Cycle," Economic Journal, Vol. 50, 1940, pp. 78-93. Both the Harrod-Domar and
the Kaldor snodels are discussed in soma detail in: L.R. Klein, An Introduction
to Econometrics, Prentice-Hall, Englewood Cliffs, 1962, Chapter 5.

- 159 -

initial value of ^(t) is known and is a constant, i.e. if y(o) = C, then the
maximum likelihood estimate of £ is given by

ill ^-i

Usually maximum likelihood estimates are unbiassed. In this case, however, the
estimate of £ is biassed where the extent of the bias is a function of the sample
size and the initial value C. For small samples the bias can be quite large
(approximately 25%) and even though an increase in the sample size reduces the
bias it cannot be eliminated completely. At the same time, it should not be
forgotten that to be able to judge the reliability of a particular estimate it
must be unbiassed. Hence, a procedure which generates a biassed estimate of ^
cannot be employed if we are to be able to subject the resulting relation to test.

To obtain an unbiassed estimate of £ it is necessary to limit the sample
size to one item. If one begins at the time period, t=0, and the value of
^(o)=C then the value of the relation is given by, y(l)=p C + u(t). Under these
conditions an unbiassed estimate of £ is given by the degenerate least squares
estimate.

P = ^ (8.4)

Consequently, the general form of the estimating equation is given by

For example, if relation (8.2) refers to the consumption behavior of one individual
then it is possible to derive an unbiassed (though inefficient) estimate of the
parameter £. As long as the values of ^(t-1) and ^(t) can be observed one can
derive such an estimate. But, If (8.2) refers to the aggregate behavior of a
group of consumers, then before (8.4) or (8„5) can be employed to estimate £ one

- 160 -

has to be able to show that the amount consumed by all of these consumers during
period (t-1) is the same. In other words, if during period (t-1) all consumers
under investigation can be shown to have consumed exactly ^(t-1) dollars worth
of commodities each, then £ can be estimated by waiting until the next period,
observing for one consumer the value of j^(t), and computing £ according to (8.5)—',

Manifestly, if it were possible to control the initial conditions so that
one was always assured of the initial equality of the ^(t-l)'s, then one could
average the individual estimates, ^. , and derive an unbiassed and efficient
estimate of £. Unfortunately, economists working with aggregate data, such as
time series, are not able to inspect or control the initial conditions. Further,
when working with time series data too short a time interval can produce strong
dependencies in the values of several variables between one period and the next.
As a result, the presence of lagged endogenous variables (auto regressiveness)

can severely restrict the ability to derive unbiassed estimates of a model's

4/
parameters.—

2, Simultaneous Interdependence

In section 2.B of the previous chapter the problem was discussed of
simultaneously estimating the parameters of several equations. It was noted
that a maximum likelihood function can be formed and employed to produce the

—For further discussion see: S. Valavanis, op. cit., pp. 57-61.

—For detailed studies of the effects of autoregression in major economic

models see; G.H. Orcutt, "A Study of the Autoregressive Nature of the Time
Series Used for Tinbergen's Model of the Economic System of the United States
1919-1932," Journal of the Royal Statistical Society, sec. B, Vol. 10, 1948,
pp. 1-53 J and A.J. Gartaganis, "Autoregression in the United States Economy,
1870-1929," Econometrics, Vol, 22, April 1954, pp. 228-243.

- 158 -

which can be represented in its simplest form by the relation

y(t) = a + P^ZjCt) + p2Z2(t) + ... + Pm^mCt) + u(t) (8.1)

where some of the z.(t) are lagged values of y(t) , e.g. Zj^(t)=7j(y^_j) , 22(t) =
7 (y 2)^ etc. Since y(t) represents the endogenous variable in this relation,
then z., z and any of the other £'s which are lagged values of y(t) must also be
endogenous variables. For if none of the £'s are lagged values of y(t) then y(t)
is the only variable dependent on the value of u(t) . But once some of the £'s
are lagged values of y(t) then these values are necessarily correlated with
some past values of u(t) . Accordingly, the lagged variables cannot be independent

of the error term, and one of the statistical assumptions about the error term is

2/
violated, i.e. Cov[u(t), z, .v]^0 for all t and all i^.— The assumptions

concerning the error term are employed because once satisfied they permit the

techniques of maximum likelihood and least squares (if appropriate) to be used

to estimate the unknown parameter values. If one of these assumptions no longer

holds then it is reasonable to expect certain difficulties in applying these

estimating techniques.

To illustrate the difficulties consider the simple relation

y(t) = p y(t-l) +u(t) (8.2)

In this case ^(t) as well as ^(t-1) are correlated with the values of the error

term u(t) and u(t-l) respectively. Such a situation does not satisfy the

independence requirement on the error term. In order to estimate the value of £

it is necessary to take a sample of values of both j^(t) and ^(t-1). If the

—'See Chapter 7, p. 134.

- 161 -
maximum likelihood estimates of the parameters in the general system given by

^1 ■" ^12^2 "- '" ^ °=lkyk + Pll^l + Pl2^2 + ••••*■ Plm^n. = "l

"21^1 + yz + ••• +<^2kyk + P21^1 + ^22^2 ^ ••• + P2m"n. = "2

(8.6)

^kl^l + «k2y2 + ••• + yk "*" Pkl^l + Pk2"2 + ••• + Pkm^m = "k

Further, it was pointed out that the value of each parameter depended upon the

values of some parameters in the remaining equations. Thus, if each equation

were treated as an independent unit and the parameters were estimated by least

squares, then the resulting estimates would be at variance with those generated

by maximizing likelihood function. Because the maximum likelihood estimates

are unbiassed, the least squares estimates would clearly be biassed and hence

of limited value.

Consider the more usual case where the basic model consists of equations

including error terms, as well as one or two economic identities. Earlier

it was pointed out that if the parameters of an identity are to be estimated

it must be transposed into a normal statistical hypothesis.— For example, if

the basic model were given by:

y(t) = a + p 2,(t) + u(t)

(8.7)
y(t) + Z2(t) = z^(t)

the second relation would have to be translated into a statistical hypothesis
before estimation procedures could begin. One way of performing this

-^See pp. 143-144.

- 162 -

transposition is to substitute [(y(t) + Z2(t)] for £ (t) in the first equation,
and [a + 3 z, (t) + u(t)] for ^(t) in the second to get

y(t) = a + p[y(t) + z^ct)] + u(t)
z^(t) = z^Ct) + [a + p z^(t) + u(t)]

Simplifying these relations we have

(8.8)

^(•^> =T?p +I^"2('^> +T^^

Notice, that both relations are now statistical hypotheses with £2('-) being the

u(t)
only exogenous variable. The error term is given by -rZo which has the same

properties as u(t) except for a shift in its variance. Further, each relation

is now independent of the other, i.e. each has a single dependent variable

and the same independent variable. Thus, the parameters of each equation can

be estimated independently of each other. For a single, linear equation the

technique of least squares produces estimates that are identical to maximum

likelihood estimates. Consequently, if the parameters of (8.8) are denoted

by a' - a/l-p, £,' - p/l-p, and £' = 1/1-p the parameters of the following

two relations can be estimated by least squares:

y(t) = a' + Pi zit) +j^^

^ ^ ^ (8.9)

z^(t) =a' +p' z^Ct) +f^^

Once the estimates of a's, £' and £' are obtained one can immediately compute the

Ai , ^ . A, a ^. P , ^ , 1

estimates a and p, since a = JTS' > Pi = TTS'-' ^ ^2 "^ T^ '

In order to transpose (8.7) into (8.9) and to estimate the new parameters
by least squares three conditions must be met. The first is that the relation
between the dependent and independent variables has to be one-to-one. A

- 163 -

2
many-to-one relation, e.g. y(t) = a + P^z (t) + p^z^Ct) + u(t), allows z (t) to

have two values for every value of ^(t). Unless the ^'s and the £, 's are equally

6/
numerous— the Jacobian is undefined and neither least squares nor maximum

likelihood methods can directly be applied. The second condition is that the

system of equations must form a set of independent statistical hypotheses. If

the first equation in (8.9) contained the variable, £i(t)> or if the second

equation contained the variable, ^(t), or if both conditions were true (8.9)

would no longer consist of two independent relations. Accordingly, least squares

would be inappropriate and the parameters would have to be estimated by the

maximum likelihood approach.

If the first two conditions are satisfied but the parameters g' , £i^3o;...,3'

are such that they do not uniquely define the original parameters a, £i ^£.2 ■» * * * '£. '

then these equations cannot be estimated either by least squares or maximum

likelihood methods. Hence, the third condition requires that the estimates of

the new parameters to uniquely determine the estimates of the parameters in the

original equations. For example, suppose the original equations are such that

some of the transposed parameters are given by:

Pi = Pi + p-

(8.10)

P2 = P2 "^ ^3

0 =^2+^2
0 := P2 + Pi

From (7.10) it is clear that there are two possible estimates of £ i.e.

^ A, , A A ,

P2 =^ ~^i s"a P2 = ~^2° ^^ ^^ ^ situation it is not possible to estimate the
values of the parameters. In order to do so the original relations must be altered

-See Chapter 7, Sec, 2,B,

- 164 -

in such a way that the ambiguity disappears. The problem of ambiguity or non-
uniqueness of the parameters is part of a general class of difficulties which
unless resolved completely obstructs the process of estimation. These
difficulties are encompassed by what is called the identification problem. And
it is toward an examination of this class of problems that the next section is
directed.

3. The Identification Problem-

As long as the econometric model consists of a single equation, with one
dependent variable represented as a linear function of the parameters of the
exogenous variables, the estimation of these parameters is quite straight
forward. The minute the model is enlarged to include more than one equation the
parameters can be estimated only if these equations are fully identified. A
model of two equations, each of which contains one endogenous and two exogenous
variables, is fully identified if neither of the two relations, or any two
relations which can be derived from them, look alike from a statistical point.

That is to say, if each of the two relations is logically independent of the

8 /
other— then the system itself is identified. In a similar manner^ if the

number of equations is increased to n, the model is identified if and only if.

— An excellent discussion of the identification problem is provided by:
T.C. Koopmans, "Identification Problems in Economic Model Construction," in
W.C. Hood and T.C. Koopmans (eds) , Studies in Econometric Method, Cowles
Commission Monograph, No. 14, Wiley, New York, 1953, pp. 27-48.

— Two axioms, postulates or hypotheses,, are independent of each other

if neither can be derived from the other. (See Chapter 2, fn,4).

- 165 -

all the model's functional relations are independent of each other.

Consider, for example, a model which states that the quantity demanded of
a certain class of items is a function of its price, that the quantity supplied
is a function of the market price, and that market equilibrium occurs when the
quantity demanded equals the quantity supplied. If ^ represents quantity and
z represents price, this model can be expressed by:
y^(t) = aj^ + (3^ z(t) + u^(t)

yg(t) = a2 + P2 ^^"^ "^ ''2^''^ ^^'^^^

where the subscripts d and s refer to the demand and supply relations respectively.

For (8.11) to be identified the three relations must be independent of each

other. But if the third equation is substituted into the first, (8.11) is

transposed into the following system of two relations;

y,-x(t) = a, + p, z(t) + u,(t) - u (t)
(S) L i i J (8,12)

J'gCt) = a2 + p2 ^^^'^ "^ "2^^^
If Ui(t), H.o(t)^ ii-i^^) represented observables these two equations would not
be statistically identical. However, the u's represent non-observable, random
disturbances. Thus, the term, u (t) - u (t), is also a random variable and is
not statistically distinguishable from the term u„(t). As a result, if one
collected a sample of data and tried to estimate the parameter values, a, and
£ , there would be no statistical way of determining which estimate belonged
to which parameter. Since these two relations are statistically indistinguishable
the system in (8.11) is not identified.

In order to delimit the necessary and sufficient conditions for
identification in econometric models consider the general case:

- 166 -

^1 + Pll^l + Pl2"2 + Pl3"3 + Pl4^ = "l

72+0=23^3+^21^1 +P24^ = "2 ^^-^^^

^31^1 + ^3 -^ P31^ + ^32^2 + ^33^3 + ^34^4 = "3
where the y's represent endogenous variables, the £'s exogenous variables , and the
parameters a and £ fixed constants. The system (8.13) is identified if the three
equations are independent of each other. If the three equations are independent
then there is a unique triplet of values (v, ,^2^Z'^) which is the solution to
this system.

The necessary and sufficient condition for a unique solution is that the
matrix of coefficients of the endogenous variables ^ be non-singular. This matrix
is given by the row and column array of a. -'s. The matrix of a's, the A

matrix, is non-singular if it is a square array of terms which has a non-zero

9/
determinental value.— If any row in the A matrix can be shown to be a linear

combination of the terms of any other row, then the value of the determinant

of A is zero and matrix A is singular. Consequently, if the relations in (8.13)

are such that the coefficients of the dependent variables form a non-singular

matrix, then a unique solution is assured and the system is identified.

One way of investigating the properties of the A matrix, and hence whether a

specific set of hypotheses is identified, is to rewrite the equations in terras

of the dependent variables (as in (8.8) and (8.9) above). — For example, the set

of relations in (8.13) can be rewritten by a process of appropriate substitutions

— See Appendix.

— 1 am indebted for this approach to: S. Valavanis, op. cit . , Chapter 6.

- 167 -
into the following form:

^1 = ''11^1 + ''12^2 + ''13^3 •*■ ''14% + ^1

^2 = ''21^ + ''22'2 + ''23^3 + ^24% + ^2 ^^'^''^

^3 = ^31^1 "^ ''32^2 + ^33^3 + ''34% + ^3
where the 2's represent the coefficients which result from this transformation and
the v's the random disturbances. Both the 2's and the v's are linear combinations
of the original coefficients and disturbances in (8.13) »

To compute the values of the y's one begins with the relations in (8.13)
where from the first equation it can be seen that

^'l = -Pll^l ■ ^12^2 - P 13% - Pl4% +^

From (8.14)

^1 = ''11% + ''12% + ''13% + ''14% + "1
Hence it follows that

-Pll = ''11
■P12 = ''12

'^is ~ ''13

■Pl4 = ^14
By substituting the value for ^^ from (8ol4) into the third equation of (8.13)
we have

^3 = ■'^31^''ll% + ''12% + ''13% + ''14%> - ^31% " ^32% " ^33%

- ^34% + "3

^3 ^ ■^^3l''ll + ^31^% " ^"31^12 "■ P32>% " («3l''l3 + ^33^%

- (a3^7i4 + P34)24 + U3

- 168 -
From (8.14)

^3 = ''3l"l + ^'32^2 + ''33^3 + ^34^ •*■ ^3
Consequently the values of £ are given by:

""^31 " ^3l''ll "^ ''31

JJ. i^ j^ (8.16)

"P33 = '^Sl^'U "•" ^"33
"P34 = ^31^4 + ^34
Similarly by substituting the value for y_ from (8.14) into the second equation

of (8.13) we get

^2 = ■^23(''3l"l + ^32^2 ^ ^'33^3 + ^34"4> ' ^21^1 " ^24^ + "2

^2 = -(^23^31 + P21>^1 " °^23^32"2 " a=23''33"3 ^ ^^23^34 + P24^"4 "^ "^

From (8.14)

^2 = ^21^ + ^22^2 + ''23^3 + ''23^ "" ^2
Accordingly, the remaining values of ^ are given by

■■^21 " "^23^31 "*■ ^21

° = ^^23^32 "*" ^^22
0 = a23733 + 723

(8.17)

"^24 '^23''34 "^ ''24
Having determined the values of the £'s in terms of the parameters a and 2
it is now possible to assess whether each relation in the original system (8,13)
is identified. From (8,15) it is clear that there is a one-to-one relation
between these £'s and j's. So that a knowledge of the values of--i,e. estimates
of--^ 2i 1 ^ Zi - ? Zi T ^""^ 214' uniquely determines the values of £•■ , > £19; £.10 ^^'^
p^-,,. Accordingly, these four parameters (j^i •, .'Pi 2.»£l3.s£i a) ^^^ exactly identified.

- 169 -

In (8.16), however, there are four equations in five unknowns. That is to say,
estimates of the values of 2^^ 1^2' ^W ^lh> ^ZV ^ZV -2^33 ^"^ -2^34 "^^^ '^°'^
permit the values of the unknowns £31:, ^32* .^33^ -2-34 ^^^ —Zl '■° ^^ determined.
The system of equations is underdetermined, and as a result the parameters

•2-31' ^32' •^33' ^34 ^""^ -31 ^^^ underidentif ied.

The equations in (8.17) present yet another problem. Here the two middle
relations state that the value of ^2^ is determined in two different ways, i.e.

^^23 = "''22/^32 ^"*^ ^23 .= "''23/''33

Unless it is specified that the value of >„„ = Jj'x ^'^'^ ^-jo ^ ^33 ^'^ ^^ clear that
the equations in (8.17) over-determine the value of g,^. Ay a result the parameter
q; is over-identified.

In the previous section it was noted that the equations of a system in the
form of (8.14) can be independently estimated by least squares if three
conditions are satisfied. The first condition requires a one-to-one correspondence
between the endogenous and exogenous variables. The second states that the
equations must be statistically independent of each other. And the third requires
that the parameters of (8.14) uniquely define the parameters of the original
system (8,13). If these conditions are met then it is possible to derive least
squares estimates of the 2!^° Once the j^ s are estimated it follows that one
can immediately specify the maximum likelihood estimates of the g's and the £'s.
But, from the analysis of the relations between the parameters of (8.13) and
(8,14) it is clear that the system in (8.13) does not meet all of these
conditions. In particular, the relations in (8,16) and (8,17) demonstrate
that some of the parameters e.g., ^■:^-j .3_o9 v^-o «^oa ^ and g.,-, are underidentif ied
v;hile g^^ is overidentif ied , Therefore, it is not possible to take the system

- 170 -

of equations in (8.14) and from least squares estimates of these parameters derive
estimates for the parameters of the original system in (8.13).

To estimate the parameters of (8.13) the equations must be identified.
Although there are several techniques by which an unidentified system can be
transformed so that it is fully identified, there are two general rules by which
the identification of individual equations can be determined. The first is a
necessary condition for identification while the second is both necessary
and sufficient.

The first rule is concerned with the statistical independence of each
equation. If all the equations of a particular model are of the endogenous
and exogenous variables of the system then these equations are not going to be
statistically independent. If each equation has a certain number of the total
set of variables absent from it then it is possible that these equations are
independent of each other. Consequently, to determine the identif iability of
an equation it is the variables that are absent from it which become the
critical factor. Accordingly, it is not surprising that the first, necessary
condition is stated in terms of the variables which are absent from a particular
equation: If an equation is to be exactly identified it is necessary that the
number of variables absent from it be equal to the number of dependent variables
minus one.

Employing the customary econometric notation a variable present in a
specific equation is labelled with an asterisk^ while a variable of the system
that is absent from this equation is denoted by two asterisks. Hence, the first
equation of (8.13) can be written;

- 171 -
* Vf* ** * * * *

y^+y2 +73 + Pn-i + Pi2^2 + Pl3"3 + Pi4^ = "i <«-i3>

Since there are three endogenous variables in (8.13) the necessary condition
for the identif lability of this equation is that (8,18) must contain two, double
asterisk variables. In fact (8.18) meets this condition. Using the same
notation the second and third equations of (8.13) are given by:

******* Vf

^31^1 -^ ^2 + ^3 •*■ ^31^ + P32^2 ' ^33^3 + ^34^ = ^3 ^^-2°)

In (8.19) there are three, double asterisk variables. But, to satisfy the
necessary condition there should only be two variables absent from it.
Similarly, (8.20) also fails to satisfy the necessary condition as it contains
only one, double asterisk variable.

One way of altering (8.19) and (8,20) to meet this requirement is to add or
subtract the appropriate number of variables by setting the relevant parameters
to non-zero values. In (8.19) variables z_. and £„ are absent and hence their
parameter values were originally specified to be equal to zero. If this decision
is changed and either z_ or £„ is given a non-zero parameter value, e.g. £
or £-,3 are included in (8.19), then (8,19) will satisfy the necessary condition
for identification. In the same fashion, (8.20) will satisfy this requirement
if one of the parameters, a , £ , R , £ £ , are declared to be equal to
zero. Such adjustments obviously change the original set of hypotheses in
(8,13), But without making these alternations the system is unidentified
and as a result it is not possible to estimate and test the original hypotheses
recorded in (8,13).

172

The second rule approaches the problem of identification from the relations
between the parameters of (8.13) and (8.14) « As has already been noted, if
the parameters of (8.14) uniquely determine the parameters of (8,13), then the
original system of equations is identified. In all other cases, i.e. if the
parameters of (8.14) over- or under-determine the parameters of (8.13), the
system is over- or under-identified. Manifestly, the unique determination
of the parameters of (8.13) is a function of the presence or absence of the
appropriate parameters in the equations of (8.13) itself. Consequently, once
again the criterion which governs identification is stated in terms of those
parameters which are absent from a particular equation: If an equation is to
be identified it is both necessary and sufficient that the matrix of parameters

■it*

C (which is formed by deleting the columns from the two matrices A and B
which correspond to the variables present in the relevant equation) has the
rank equal to the number of endogenous variables minus one.

In (8,13) the matrix C represents the total matrix of parameter values, e.g.

0^2

0=31

23 '^21

12
0

^32

'13
0

'14

'24

'34

_**

Consider the first equation. To form the matrix C one deletes from C all
columns which correspond to variables in this equation, i,e, one deletes all
columns in which there are non-zero entries in the first row of C, For the
first equation of (8,13), C, is given by:

0 0

- 173

h3]

Similarly for the second equation;

0 0 0

P33_

And for the third equation of (8.13)

°'31 ^32

_**

idc

The rule states that (8.13) is identified if each of the matrices, C^ ,
£2 , and C„ , has a rank equal to the number of endogenous variables minus
one. In this case, the rank must be equal to 2, A matrix has rank £ if at
least one of the matrix's sub-matrices is a square array, r x r, which has a
non-zero determinant, and if all remaining square sub-matrices of higher order
have determinantal values equal to zero.

r example, C^ is a 2x3 matrix. The largest square array is 2 x 2»

*Vc

In C, there are three such sub-matrices

0 0

1 a

23
1

The first two have a determinantal value equal to zero. But the last has a

non-zero determinant. Hence, the rank of C, is 2, and the first equation

is identified. Cy is a square 3x3 array whose determinantal value is zero.

■"it

However, C is composed of nine sub-ma.trices of order 2x2, including

which has a non-zero determinant. Hence, C^ also has a rank equal

a^3 P32

2. C3 , on the other hand, is a 1 x 3 matrix. Its only type of square

174 -

sub-matrix is a 1 x 1 matrix which precludes C- from having a rank equal to 2.
As a result, by this criterion the first two equations are identified, while the
third is not. Consequently, the system given in (8.13) is unidentified.
In order to satisfy the first criterion, a necessary condition for
identification, one solution was to add one variable to the second equation
and delete one from the third. One such possible arrangement is given by

+ p^^z^ + p^2^2 + Pl3"3 + Pl4^ = "l
^2 + ^23^3 + P2l"l + ^22^2

+ P24^4 = "2

(8.21)

^31^1

^3 + ^31^

+ P

+ P^/,^A = ".

33 3 '"34 4

_**

From (8,21) the C matrices are now given by

**
^1

^23

Pl3

°=31

P33

■k-k
£3

Pl2~

P22

Since C is unaffected by the alternations in (8.21) it still has a rank equal
to 2. The addition and subtraction of parameters has affected C„ and C_ , and
it can readily be shown that these two matrices also have a rank equal to 2,
Because the second criterion has been satisfied one can conclude that the adjust-
ments made to meet the first requirement are in this case sufficient to

guarantee the identif iability of the new system given in (8.21).

- 175 -

This is not to say that any alteration which satisfies the first require-
ment will automatically meet the second. Nor is it being suggested that the
only solution is to add and delete the appropriate parameters from the system.
Clearly, there are a number of possible ways by which the system in (8.13) can
be altered so that its equations are identified. One alternative, noted in
the discussion of the relations in (8.17) , is to set some of the parameters in
the reduced form (8.14) equal to each other. But whatever adjustment is chosen
in the initial specification of the system's hypotheses, if the system fails
to satisfy either of these two criteria then its parameters can be estimated
as the equations are unidentified.

4, Forecasting

Once a model has been estimated from the data of a particular time period
it is frequently employed to generate forecasts for the next or later time
periods. To examine the way in which the estimated relations can be used to
forecast or predict^ consider the sinqjle linear relation;

y(t) = a + p z(t) + u(t) (8.22)

This equation is identified since it is linear in both parameters and variables
and since there is a one-to-one relation between the enogenous and exogenous
variables. To estimate the parameters, gc and ^, a san^le of data on y(t) and
z(t) is collected and the maximum likelihood estimates are generated by solving
the estimating equations:

ill (y. - a - p z.) = 0

ill (y^ - a - p z.)z. = 0 (8.23)

k ill (yi - a ■ P \)^ = o^

- 176 -

From the solution of these relations the estimated equation for the particular
time period under consideration is given by:

y(t) = a + P z(t) (8.24)

Note that the estimated relation (8.24) no longer contains an error term. This
is due to the fact that the expected value of the error term, u(t) , is zero.
Further, the solution of the relations in (8.23) provides an estimate of the

standard error a . The standard error can be used to determine estimates of

— u

the standard error of the parameter estimates a and a . — Once these two

a p
estimates are formed, it is then possible to construct confidence intervals

about the parameter estimates and adjudge their reliability.

In order to forecast the value of 2 for the next time interval, t+1 , all
that is required is to insert in (8.24) the observed value for z(t+l) and compute
the value of ^ (t+1) . This procedure assumes^ of course, that there have been
no significant structural changes and that the estimates gc and £ form a valid
basis for the forecast. If certain changes are observed during the interval,
t+1, such that (8,22) is no longer appropriate, then it is clear that (8.24)
cannot be used for forecasting. In this case a new hypothesis would have to be
constructed and its parameters estimated. If this process were carried out
during the period t+1 then the new estimated relation could be employed to forecast
the values of the relevant variables in t+2. However, for the purposes of this
discussion assume that significant changes have not occurred and that (8.24)
is an appropriate forecast relation.

Even though (8.24) is of the simplest possible form it has forecasting
characteristics in common with the most complex models. In particular, by
employing (8.24) or any other estimated relation to forecast variable values

11/

— For details of this procedure see Chapter 7, p. 152.

- 177 -

point forecasts are generated. For instance, in period t+1 (8,24) provides the

F F

point forecast of ^ (t+1). By itself the point forecast ^ (t+1) can be compared

to the observed value of ^ in the period t+1. But without specifying some

interval about ^ (t+1) such a direct comparison does not provide much

F
information. Since ^(t) and £(t) are random variables, 2 (t+1) and ^(t+l) are

also random varibles. Hence to compare, i.e. test for equility, the values of

two random variables one needs to be able to assess whether the value of one,

F
say y(t+l), falls within some expected interval about the other, ^^ (t+1).

When dealing with point estimates of parameter values it is possible to construct

a confidence interval about these estimates and employ this interval as the

12/
basis for testing certain null hypotheses. — Accordingly, to be able to

submit the point forecasts to a similar testing procedure an interval about

the forecasted values must be defined.

The theory of measuring the reliability of point forecasts is relevant

to the case where the endogenous variable is a linear function of the exogenous

variables. If the endogenous variable is normally distributed with a true

2
mean of y^ and a true variance of £ , tolerance limits are formed by adding

and subtracting from the mean, y., a specific multiple K of the standard

deviation, £, In other words, if n and £ are the true mean and variance of

the distribution, the tolerance limits for a value of the endogenous variable

ars given by

Hy ± K ay (8.25)

where K is a parameter and depends on the sample size and the proportion of

12/

— 'See Chapter 7, pp. 150-151,

- 178 -

13/

values of ^ to be included in the interval. —

Tolerance limits are not the same as confidence limits. A confidence limit
for the mean, e.g. x ± 1.96a, states that 95% of the time we expect the true
population mean to lie between the limits x - 1.96a and x + 1.96a, where x
represents the sample mean. A 95% tolerance limit on the other hand, states that
we expect 95% of the sample values of the endogenous variable to include a
proportion P of the values in its distribution. That is to say, the endogenous
variable has a distribution (assumed to be normal in this case) from which each
sample value, ^(t), is derived. For a given level of confidence, say 95%, the
tolerance interval delimits the minimum proportion of these sample values that
we can expect to be included within the limits. Further by increasing the value
of K the probability that the tolerance interval contains at least P of the
population can be made to be as close to 1 as desired.

In normal circumstances the true mean and variance of the distribution of
the endogenous variable are not known. Accordingly, to construct a tolerance

interval it is necessary to employ sample estimates. The sample estimate of

F
the mean is given for (8.24) by the forecast value of ^, i.e. iz-t+l)' '^^^

estimate of the variance can be computed from the previously generated maximum
likelihood estimates so that the tolerance interval is given by;

^(t+D^^'^F <«-^^>

^(t+1)

13/

— Values of K for normal distributions with constant mean are given in

tables by A.H. Bowker , "Tolerance Limits for Normal Distributions," in

C. Eisenhart, M. Hastay, and W.A. Wallis, (eds) , Techniques of Statistical

Analysis, McGraw-Hill, 1947, pp. 102-107.

- 179 -

p
Consequently, (8.26) defines a range of values of Xrt+l') within which at least

a proportion P of the non-sampled observations are expected to fall with a certain

probability. As noted above, the value of K depends on the proportion P of

future observations which are to lie in this interval, the probability with which

this is to occur, and on the size of the sample. Hence, for a specific sample

size, for assigned values of P, and for the probability of this occurring, say

p
957o of the time, K is determined and an interval for X/'f-j.i\ ^^ specified.,

So far the reliability of a forecast has been considered for a single linear

equation like (8.22). In order to examine the case of a model with several

linear equations, consider the identified system given in (8.21). As mentioned

above, estimates of the parameters of this system can be derived directly by

the maximum likelihood method. However, it is also possible to transpose (8.21)

into the reduced form;

^1 = ''11^ + ^12^2 + ''13^3 + ^14^4 + ^1

^2 = ''21^1 + ^'22^2 ■*■ ^23^ + ^24^ + ^2 ^^'^^^

^3 = ^31^1 + ^32^2 "^ ^33^3 + ^34^ + ^3
and estimate the new parameters, 2- • .» t)y least squares. Since all the equations
of (8.27) represent one endogenous variable as a linear function of exogenous
variables, and since each of these equations is independent of each other, the
relations in (8.27) are in the appropriate form for forecasting. To construct
tolerance intervals for the endogenous variables it is .necessary to compute the
appropriate sample variances and covariances. Once these values are determined,

however, the forecasting procedures are the same as for the case of the single

14/
equation model outlined above. —

14/

— For further detail in forecasting technique see; L.R. Klein, A Textbook

of Econometrics, op. cit., pp. 249-276.

Chapter 9

THE EMPIRICAL CONTENT OF ECONOMETRIC THEORY

We^ as economists, require testable theories of economic behavior. Without
such theories economics as a discipline can never provide scientific explanations
or predictions of the many important and interesting, observable economic
phenomena. In the examination of classical economic theory it was noted that
the testability of a theory depends on the empirical content and testability
of the theory's hypotheses. In brief, a theory can be corroborated by test
if and only if at least one of its constituent hypotheses can be subjected
to a process of refutation by empirical test. To submit a single hypothesis
to test it must be possible to observe that the initial conditions are
empirically true. In Chapters 5 and 6 all hypotheses within classical economic
theory were shown to contain unobservable equilibrium conditions as a part
of their initial conditions. As a result,, none of these hypotheses can be
confuted by empirical test. The object of this chapter is to examine the
empirical content^ and as a consequence the testability^ of econometric
hypotheses. The primary goal, of course^ is to discover a set of economic
hypotheses that can be subjected to a process of refutation by empirical test.

1. The Initial Conditions

A. The Error Term

In order to test an econometric hypothesis it must be possible to ascertain
that the relevant initial conditions are empirically true. Since all
econometric hypotheses are stochastic, the initial conditions which must be
empirically established are those concerned with the error term. In Chapter 1 ,

- 181 -

one particular set of assumptions surrounding the error term are discussed.
Estimating procedures are a function of the assumptions about the error term.
Also the most common estimation criterion is that of maximum likelihood. Hence,
these assumptions about the error term, while not universally employed by
econometrians , are those which are most commonly used. Accordingly, although a
different set of assumptions would require a separate analysis of their empirical
content, the method by which their content would be determined would be similar
to that which is described below.

To facilitate the analysis, consider the error term within the context
of a specific demand function;

y(t) =0= + ^ P(t) +"(t) (^•^>

where ^ is the quantity of a certain commodity that is demanded during period

t, p, . is the prevailing market price, a and ^ are the parameters to be

estimated, and u, , is the value of the error term for this period. Now the
-(t)

error term is assumed to be a random variable, so that its value at each period
of time is a function of its probability density function. Thus, the particular
value of u during period £, i.e. u is determined by the probability of
this value occurring, which in turn is defined by the density function which
describes the total population of the values of u. This population of values
of u is assumed to be normally distributed with a mean of zero. Accordingly,
if a large sample of values of u were collected one would expect these
individual values to describe the outlines of a normal population with zero
mean. The assumption of the normal distribution is clearly one of the basic
postulates about the error term. Thus, it is pertinent to inquire whether
this assumption can be checked.

- 182 -

The answer, of course, is obvious to anyone familiar with the application
of statistics to problems of this sort. But, the more interesting point
concerns the data that must be collected if this assumption is to be tested.
At present the analysis is concerned with (9.1), a simple, linear hypothesis
about the demand for a particular commodity with a given time period, t^. In
order to test the postulate of normality of the error term one can proceed in
a number of directions. The value of u, , is the result of a particular
sample of data on x.( t\ ^""^ £ctV '^° determine the distribution from which
u^ s is derived one needs a sample of values of U/f.-). For a sufficiently

large number of samples of values of U/^n it is immediately known that the

mean of these samples is normally distributed.—' The problem here, however,

is to determine the distribution of the underlying and unobservable population
from which these values are derived. That is to say, it is necessary to test
the postulate on the basis of actual sample values and not sample means. In
fact, there are a number of ways in which this postulate can be check.ed„ One
such method is to employ the Kolmogorov-Smirnov statistic. Under the null
hypothesis that the population is normally distributed with mean zero it is
possible to determine the cumulative distribution of the sample values themselves
and test directly the null hypothesis. Another approach is to use the Chi-

Square statistic to test the expected frequencies under the same null

hypothesis against the observed frequencies from the sample values.— What-
ever the method it is clear that a sample of values of ii/,.\ is required.

—This result is a consequence of the Central Limit Theorem, see: A.M.

Mood and F.A. Graybill^ op. cit. , pp. 149-153

—'For other methods see any advanced tex
and F.A. Graybill, op. cit.; or P.G. Hoel, op. cit

—'For other methods see any advanced text on statistics, e.g. A.M. Mood

- 183 -

These values must be collected during period t. Although the minimum sample
size varies with the statistic employed, each testing procedure requires a
number of estimates of (9.1) to be generated within the relevant time period.

The next assumption about the error term is that the density function does

t change with time. That is to say, during period t the value of u. . comes

— ~i.t;

2
from a normal population with a mean of zero and a specific variance n . If

2
the density function does not vary with time, then the variance £ must

remain constant over time. Consequently, one is now concerned with testing

for the observed sample values of u over several intervals of time. To

determine whether the true population variance remains constant over time,

it is once again necessary to adopt the null hypothesis that it does and to

test against this null hypothesis with the sample data. To perform this

test a sample of values of u are drawn for a number of time intervals. The

sample variances are computed and are used to derive a value for the

likelihood ratio X. Since -2 log :v is approximately distributed as the

Chi-Square the value of this statistic, for the relevant degrees of freedom

and level of confidence, is compared with that derived from the logarithm

3/
of the likelihood ratio.—'

Notive once again that the test requires a sample of values of the

error term to be gathered for each time interval. Since these data have to

be collected to test for the constancy of the true variance over time, it is

clear that the same data can be employed to determine whether the true

— For a complete statement of this test see; A.M. Mood and F.A. Graybill,

op. cit., pp. 284-290; and P.G. Hoel, op. cit., pp. 225-228.

- 184 -

population density function is normal with a zero mean.

If each of the sample values of u.^v is generated from a random sample
of the total population of ^'s and £'s, then each value of u^^x is a random
variable. Concurrently, because the values of u. , are arrived at by independent
random san^les, the sample values of u^^x will normally be statistically
independent of each other. The only time when this result will not occur is
when the value of u.. v is directly related to the value of the independent
variable, 2.(t\° Hence, in the case of the simple linear relation (9.1) it
is sufficient to test the fifth and sixth assumptions by only submitting the

sixth to an en^irical check.

4/
The sixth assumption requires the covariance of u. , and 2.(r\ ^° ^^ zero,—

where the covariance is the first product moment of the observed values about

their means, i.e.

00 00

Cov(u, p) = E[u-E[u]3[p-E[p]] =f J u(p-E[p]) f(u, P)dP(t)du^j.^

"CO "00

Since the joint density of u and £, f(u, p) may well be unknown, the test can
be conducted by computing the correlation coefficient between the sample
values of u,^. and p, .. It must not be forgotten that the sixth assumption
requires that Cov(u. x, P/j._i\) = 0 for all t and all i^. Consequently, over
the relevant number of time periods all correlation coefficients have to be
shown to be statistically indistinguishable from zero.

So far the discussion has been concerned with describing the procedures
by which one can determine whether the initial conditions implied by the error

-See Chapter 7, p, 134.

- 185 -

term U(f.\ in (9.1) are empirically true or false within the context of a
particular case. It follows from this analysis that sufficient statistics
exist to permit such testing to take place. As a result, the initial conditions
surrounding the error term can indeed be put to statistical test. Whether they
are in fact satisfied for a specific relation and by a particular set of data
is not of interest here. The point to note is that these conditions can be
put to statistical test.

The minute one progresses from a single to a many equation model the testing
of the assumptions about the error terms becomes somewhat more complex. Instead
of dealing with a single error term, one is now concerned with a vector of
error terms. Instead of a univariate normal distribution with zero mean, the
underlying population is assumed to be a multivariate, or a jointly normal,
distribution with a mean of zero. If the multivariate normal is to have a
constant variance over successive intervals of time, then the covariances
between the respective individual error terms must be constant over time. In
an analogous manner the fifth and sixth assumptions require that both the
covariances between the error terms and the values of the independent variables
be equal to zero.

While the statistical tests are somewhat complicated by the introduction
of the multivariate normal, the complications do not preclude the possibility
of conducting them. Clearly, the introduction of a many equation model
increases both the problem of data collection as well as that of computation.
Indeed, if the number of equations is large enough these practical problems
may well prevent the testing from taking place. The problem, however, is not
whether these tests can in fact be carried out in every imaginable case. This

- 186 -

is not an important point. The question at issue is whether it is possible given
as much time^ computational facilities^ and data as needed to empirically
establish within the context of a particular case the presence or absence of
these six initial conditions. If these conditions are shown to be statistically
true, the one can proceed to test the empirical relevance of the hypothesis
or model itself. If the conditions are, within the context of a specific case,
statistically false then there is no need to proceed any further. In either
event, however, there is no question that there are explicit procedures for
ascertaining the statistical truth or falseness of these initial conditions.
Consequently, whether these conditions apply to each and every case or not, it
is possible to submit them to empirical scrutiny--that is, the initial conditions
are members of the class of observable items.

B . The Remaining Conditions

One point which has not yet received proper attention concerns the source
or origin of econometric hypotheses. If each time an hypothesis or model is
developed it is constructed de novo then the total number of initial conditions
are circumscribed and are defined by the hypothesis or model itself. On the
other hand, if the hypothesis is suggested by, or is a product of, some prior
theoretical framework then it may well occur that parts of this theory are
reflected as conditions surrounding the hypothesis. In such a case these
conditions then become a part of the initial conditions which must be observed
before the hypothesis can be submitted to test.

Consider, for example, the demand relation noted in the previous section

y(t) =^ + P P(t) +"(t) (9-1)

- 187 -

Where does this hypothesis come from? And what additional conditions accompany

it?

Demand curves are, as has already been shown,— derived from an analysis of
the choice behavior of consumers under equilibrium conditions. If the consumer
maximizes his utility function subject to his budget constraint, the demand
relation is a direct consequent of this theory of choice. Further, this relation
between the price of a commodity and the quantity purchased only refers to
those cases where the consumer's taste, income, as well as the prices of related
goods, and other environmental factors are both given and unchanging. Not only
must all equilibrium conditions be satisfied before the relation can be deduced,
but all relevant variables in the environment must remain the same if the
relation is to hold at all.

It does not follow that the conditions surrounding the demand relation in
classical theory need to be a part of the econometric formulation. Manifestly,
the relation (9.1) can be the plain, explicit statement that the quantity
purchased of a certain commodity is related to its market price during a
specific time interval in the stated manner. Further, that this relation is
based upon repeated observations of the behavior of the price and quantity
purchased of this commodity. That is to say, over a certain interval of time
a sample of values have been observed and recorded and (9.1) represents
the best fitting, stochastic relation as in Figure 1. In this case there is
no reference to the theory of consumer choice, to the equilibrium conditions, or

— See Chapters 4 and 5, sections 1 and l.A respectively.

Price

Quantity
FIGURE 1

- 188 -

to other environmental factors. The
relation is based on actual occurrences
and the parameters^ a and £, are estimated
from these sample values. If as in Figure 1
the relation has a negative slope, i.e. ^
has a negative value, then this is a fact

about this sample of values and not a
consequent of a theory of consumer behavior.
This is an important point and one to which reference will be made again
in the discussion on testing econometric hypotheses. For, if the relation is
derived from classical theory, and if the econometric statement of its is merely
one way of placing it into testable form, then the initial conditions must
include the unobservable equilibrium conditions as well as the ceteris paribus
clause. If these are a part of the initial conditions, then the hypotheses
cannot be submitted to test. For, although it is possible to statistically
test the assumed properties of the error term, it is not possible to show that
the equilibrium conditions are satisfied.

An example of this point is offered in a recent discussion of the Cobb-

6/
Douglas production function.— The Cobb-Douglas function is given by

P = b L^ C^-^ i/
where P represents output, L labor input, C capital input, and b^ and k are

(9.2)

- H.A. Simon and F.L. Levy, "A Note on the Cobb-Douglas Function," Review
of Economic Studies, Vol. XXX, June 1963, pp. 93-94.

-In keeping "vith these author's presentation the error term is ignored.

- 189 -

parameters of the relation. This equation is a part of the classical theory of
production where the partial derivative of output with respect to labor input,
■^, is the marginal productivity of labor, and where the parameter k represents
labor's fraction of total output. Setting the marginal productivity equal to
the competitive wage, the result is the relation:

Sl L

^ = i ? (9.3)

where for a given period of time -r^ is a constant.

A number of empirical tests have been conducted to measure the value of k. One
set of tests were concerned with fitting (9.2) directly to sample data on the
values of P, L, and C. A second sample of data was then employed to derive a
value of k from a direct assessment of labor's share of total income. These two
values of k were observed to be in fair agreement with one another. Consequently,
it was inferred that this test corroborated the assumptions underlying (9.2).
Simon and Levy suggest^ however^ that approximately the same values of k
will be obtained if the production function is given by the simple linear

relation

P = a L + d C (9.4)

where a and d are parameters representing the average wage and yield on capital

respectively. Labor's fraction of output (income) is intrduced as

K-' ^
^ = P

By dealing with average values of output and labor input, P and L, the value of

K is given by

K = a i (9.5)

- 190 -

The issue at hand is not which of these two relations, (9.2) or (9.4), is
the "right" one. Rather the point revolves around the question of what it means
to have the values of K be approximately the same in both of these cases. That
is to say, does the fact that the fitted value of K, from (9.2), agrees with
the observed value of K corroborate the underlying hypothesis and assumptions
of (9.2)? The answer, of course, is no. If the assumptions and initial
conditions are enumerated, and observed to be empirically true during the period
in which the data are collected, then the evidence on K would indeed serve to
support these assumptions. But in fact, some of these initial conditions are
the ubiquitous, unobservable equilibrium conditions. Accordingly, no claim
can be made that the evidence on K corroborates these unobservable assumptions.

At the risk of exhausting the reader's patience this argument can be
further clarified if the logical notation introduced in Chapter 2 is employed.
Let ^ represent the general theory of production with its concomitant equilibrium
conditions, R the Cobb-Douglas production function in the form of (9.2)^ and S
the consequent of R which is the relation denoted by (9.3). If the production
function is considered a part of the classical theory of production then the
chain of inference is represented by the proposition 2. -* R -♦ S^» The data from
the statistical tests refer to the value of K, i.e. the proposition S. The
inference which is usually, but erroneously drawn, is that the evidence
supporting S^ in turn supports R which in turn serves as indirect support for
the theory embodied in Q. But, as has been noted before, the only way in
which evidence for S_ can be used to corroborate R is if we have independent
evidence supporting either Q or R. In the above formulation Q and hence R
contain a number of unobservable initial conditions. Since the presence of

- 191 -

these conditions precludes the possibility of directly testing the propositions
in Q and R, the evidence supporting £ cannot be employed to support the
proposition Q -♦ R -* £•

Clearly, the Cobb-Douglas function R can be taken by itself, without any
of its usual theoretical underpinnings ^ and put forward as an observed statistical
regularity. That is to say, R can be proposed as an hypothesis standing by itself
and can be fitted to the appropriate data. Under these conditions the general
proposition would now be restricted to R — S^. To corroborate this proposition
one would still need two sets of data, one supporting R and one supporting S^.
But, as R has been detached from its unobservable antecedents, such support is
no longer theoretically impossible.

The same comments, of course, apply to the Simon-Levy proposition which can
be represented by R' -► S_ where R' is the hypothesis given by (9.4). Since the
same data support the consequent S^ in both cases, an independent set of data
would have to be found which supported r' before the proposition R' -* S^ could
be said to be empirically confirmed.

Nothing, so far, has been mentioned about how one might subject propositions
like R -* S^ or R' -* S_ to the requisite empirical tests. This topic will be
discussed next. At present my concern is to point out the fact that as long
as econometric hypotheses are considered as consequents of general economic
theory, such as Q ^ R -» S_;) then the presence of equilibrium conditions will
preclude the possibility of ever subjecting these hypotheses to empirical test.
On the other hand, if econometric hypotheses are viewed as standing by themselves
for empirical appraisal then, whatever their actual or theoretical origins, it
is at least possible to observe the relevant initial conditions preparatory

- 192 -

to conducting empirical tests. In this respect an hypothesis' origins are
irrelevant, and the important questions which remain--can this hypothesis be
tested? is this hypothesis enpirically true?--can now be investigated.

2. Testing Econometric Hypotheses

In order to submit any hypothesis to a process of refutation by empirical
test it is necessary to have a procedure which will identify those data that
will disconfirm the hypothesis. The process of testing is, in fact, a process
fo searching for negative results. Unless the testing procedure delimits
those data which are to be considered instances of disconf irmation, the testing
process cannot be carried out. The growth of a body of scientific theory is
predicated upon the detection of erroneous hypotheses. And unless it is
possible to identify the disconf irming instances it is not possible to
detect the errors. Consequently, when examining a testing procedure the
principal item to look for is the process by which an hypothesis is rejected.
If it is not possible to reject certain hypotheses then it is not possible to
decide whether they are empirically true or false. Thus, in this examination
of econometric hypotheses the object is to investigate the procedures, if any,
by which this class of propositions can be rejected by empirical test.

To clarify the difficulties which surround the testing of econometric
hypothesis it is easiest to begin by examining the general problem of testing
statistical hypotheses. As noted in Chapter 7 a statistical hypothesis is a
statement about the probability density function of a random variable. The
density function of a random variable refers to the assumed or actual density
function which characterizes the population of which the variable is a member.

- 193 -

When a sample of observations is taken it is drawn from this population. And if
the test is concerned with determining the actual density function describing
this population, it is the sample data that are used to perform the test.

In the simple example employed to illustrate the principle of maximum
likelihood there was an urn which contained a population of red and white balls.
We happen to know that this population is characterized by the binomial
distribution. But if we were presented with this urn without knowing the
distribution of balls inside it we could determine its density function by a
number of methods each of which relies on our ability to draw repeated samples
from the urn. If the population of the urn were large enough the sampling could
be conducted without replacement. For the size of the population would
prevent the withdrawal of the individual samples from distorting its actual
density function.

Suppose, for example, that we have an urn which is filled with a large

number of colored balls. In all, there are four different colors red, green,

white and black. The population of this urn is generated by a particular

biological process about which we have a theory. One of the hypotheses of this ,

theory concerns the frequency of occurrence of the phenomena we have called

colored balls. Under appropriate conditions this hypothesis states that the

different colors are present in the population in the ratios 9 ,! 3 :

red green

3 u-^ t lui 1 • We are unable to observe and count the actual frequencies
whxte black ^

in the population,, but the population is large enough so that we can sample
without replacement.

In order to test this hypothesis we draw a number of samples from the
population and record the total number of occurrences of each of the colored balls,

. - 194 -

From the theory, the hypothesis states that the probabilities of occurrence are

Pred=^/^^' Pgreen=3/16, P„hite=2/1^' Pblack=l/^^- ^^" ^^"P^" "^'^ P""^^*^" '^"
observed frequencies of their occurrence which can be directly compared to the

theoretical by multiplying the theoretical probabilities by the total sample

size as shovm below.

240

244

Red Green White Black
Observed Frequencies

Theoretical Frequencies

Total Sample Size = 343 Observations

To test the null hypothesis we employ the Chi-Square statistic. Computing its

2
value from these data the result is x = 3.9. In this case there are three

degrees of freedom, and if the rejection region is set at 5% the critical value

2
of the statistic is given by JL = 7.8. Since the confuted is less than the

critical value we do not reject the null hypothesis. Clearly, if the computed

had exceeded the critical value we would have rejected the hypothesis.

The process of accepting or rejecting an hypothesis by con^aring a

computed to a critical value is based upon the notion of a confidence interval

and the critical region from which these intervals are built. A critical region

of 5% implies that under the assumption the null hypothesis is true the computed

value will lie within this region 57„ of the time. Thus, a critical region like

a confidence interval rests on the tacit assumption that the experiment can

be repeated a large number of times. To repeat an experiment the population

from which the samples are drawn must remain unchanged. In actual practice

minor changes can take place in a population without significantly affecting

the testing procedure. But as long as the major factors are known and

- 195 -

controllable^ repeated sampling can be employed to test hypotheses about the
nature of the underlying population.

While this simple example and the ancillary comments are undoubtedly obvious
to the reader their full force does not seem to be appreciated by practicing
econometricians . For econometric hypotheses differ in several important
respects from the one employed above. To begin with econometric hypotheses
are stated in terms of endogenous and exogenous variables, and parameters. In
the above example the theory about the biological process asserted the existence
of a particular ratio of probabilities of occurrence. These probabilities are
the counterparts to the parameters in an econometric hypothesis. Hence, one
would expect to be able to determine the "actual" value of the econometric

parameters in the same way that the actual values of the probabilities were

8 /
ascertained. To determine the "true"— parameter values of a population density,

it is necessary to have a stable population--namely, one from which repeated

samples can be drawn. Unfortunately, the population of economic variables is

quite unlike that of the urn. Not only does one not have any assurance that

the population remains the same from one time period to the next, but one is

also unable to control the principal factors effecting such changes. Consequently,

samples drawn at different periods of time cannot be shown to come from the

same theoretical urn and little can be done to alleviate this problem.

Another significant difference between the exemplar and an econometric

hypothesis occurs in the manner in which the sample data are normally employed.

8 /

— That we can never know the exact values of the population's parameters,

goes without saying. But, as long as the population density remains unchanged

we can come as close to the true value as we have the time and the patience

to sample.

- 196 -

In econometrics the sample data are used to estimate the parameter values. By
calculating the standard errors of the estimates^ confidence intervals can be
constructed to adjudge the estimators' reliability. The notion of a confidence
interval, however, depends on the assumption that the same population can be
repeatedly sampled. Since this condition does not strictly apply to econometric
investigations this measure of an estimate's reliability is only relevant in

a loose and qualitative way. When dealing with the urn it is possible to test

9/
the observed sample estimates against the known (and knowable— ) population

parameters. To do so the null hypothesis is constructed from the actual

population values and the sample estimates are employed to reject or not reject

H . For an econometric hypothesis, however, what is the null hypothesis? Since

the actual parameter values are not ascertainable against what set of values

is it possible to test?

An immediate answer is to employ the null hypothesis where the parameter

values are set equal to zero. For example, if one collected data to estimate

the values of the parameters in (9.1) the relevant null hypothesis would be:

H^: a = 0 p = 0

As noted in Chapter 7, from the standard errors of the sample estimates a and

a one can set up a confidence interval for a and £. If these intervals

P A A

include a = 0 and p = 0, then according to normal procedure one is not able
to reject the null hypothesis. However, since it is not possible to conduct
repeated samples there does not appear to be any reasons why this test is

— The population's parameters are knowable in the sense that it is in

principle possible to ascertain their values to whatever degree of accuracy
one cares to chose.

- 197 -

appropriate in the first place. Even though the sample size may be increased to
enhance the statistical significance of the results, the inability to repeatedly
sample from the same population reduces the rigor of the test.

In order to circumvent this obstacle one would have to know (have a testable
and tested theory of) the process by which the elements of the population are
generated. In the case of the urn a biological theory containing both testable
and tested hypotheses accounts for the process by which the relevant ratios
are derived. While this theory may eventually be replaced by another, at the
present moment it asserts that the generating process is of a certain type with
specific, identifiable and testable characteristics. Consequently, even though
various factors may affect this process from time to time, the effect these
influences have on the characteristics of the population can be evaluated from
a knowledge of the generating process. In econometrics the process or processes
by which the members of a specific population are generated are unknown--i.e.
econometrics does not contain tested theories of these processes. Manifestly,
it is this lack of knowledge of the process which prevents one from being able
to demonstrate that it is possible to repeatedly sample from the same
population.

Summary and Conclusion

At the beginning of this chapter the empirical content of the initial
conditions surrounding the error term was examined. As any competent statistician
would readily avow, there are a number of statistical tests with which it is
possible to determine the presence or absence, in any particular case, of the
five basic assumptions. These tests depend, like all statistical tests, on the
presumption that the population being sampled from remains unchanged throughout

- 198 -

the sampling process. Further, the method of constructing the null hypothesis
and employing sample data to confute or support it can only yield statistically
and hence empirically significant results if the null hypothesis concerning the
unchanging population is supported by test. To conduct such tests it is
necessary either to know the process by which the population is generated or to
be able to independently measure the population's relevant characteristics.
Since it is not possible to independently measure the "true" values of an
econometric population's characteristics, it follows that to employ statistical
tests the process by which these populations are generated must be knov,;n. To
be required to have a knowledge of the process is another way of saying that
one needs to have a testable and tested theory of the process. If such a theory
is to be stated in econometric (stochastic) terms one will again require some
further independent means for checking on the population's stability.

It appears, therefore, that the testing of econometric hypotheses is caught
in a moderately vicious circle. In order to ascertain whether the initial
conditions of the error term are satisfied a knowledge of the stability of the
relevant characteristics of the population is required. Similarly, if one is
to adjudge the reliability of parameter estimates, the basis of this measure
lies in the assumed ability to repeatedly sample from the same population.
Moreover, it is not possible to test the estimated hypothesis against such
simple null hypotheses as, H ° a ^ 0, p = 0, unless the stability of the
population can be empirically established.

One way of answering this problem would be to appeal to classical economic
theory as the theory about the process by which the econometric populations
are generated. If this body of theory, or any of its principal hypotheses, could
be corroborated by empirical test then these hypotheses could be employed as the

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basis from which the independent checks on the population could be carried out.
But, to invoke the hypotheses of classical economic theory is to require one to
be able to en^iirically identify the presence or absence of the relevant
equilibrium conditions. Since this body of theory does not contain sufficient
interpretive rules to allow the initial equilibrium conditions to be empirically
investigated, it is not possible to confute these hypotheses by empirical test.
To be unable to test these hypotheses is to render them incapable of performing
the requisite service. As a result, a knowledge of the relevant processes
cannot be acquired by appealing to classical equilibrium theory. To do so is
to ensure that the resulting econometric theory is completely untestable.

A second approach to a solution would be to adopt a somewhat pragmatic
approach to econometric theory itself. If all econometric hypotheses and
models are considered by themselves as statements about the behavior of certain
economic variables, then the empirical corroboration of these propositions
rests upon two possible grounds. The first, concerns the empirical basis for
the statistical tests that are employed. This basis principally requires the
population from which the samples are drawn to remain stable throughout the
testing process. But econometric theory does not contain the requisite
theoretical statements and interpretive rules by which this stability can be
empirically ascertained. Consequently, there is no way by which the suppositions
entailed in the first approach can be supported by empirical test. If neither
the hypothesis nor its sample estimates can be tested on direct statistical
grounds, there is only one other possible source of evidential support--namely,
the use of forecasts or predictions as the basis for empirical tests. It is
toward an examination of this approach to empirical corroboration of econometric
hypotheses that the next chapter is devoted.

Chapter 10

Explanation and Prediction in Econometrics

To establish an explanation for the occurrence of an event it is necessary
to be able to deduce the phenomena from the conjunction of the theory's hypotheses
and the relevant initial conditions. Further, the initial conditions must be
empirically true and the theory itself must contain at least one hypothesis
that survived empirical tests.

In the previous chapter the empirical content of econometric hypotheses
was explored with special attention being paid to their initial conditions.
If, as I have argued is the case, the presence or absence of an hypothesis'
initial conditions cannot be established by statistical test then one of
the basic requirements for a scientific explanation is not satisfied. Since
all econometric hypotheses contain error terms and since, without a measure of
the population's stability, neither the conditions surrounding the error term
nor the reliability of the parameter estimates can be assessed, econometric
hypotheses cannot be employed to establish explanations of economic events.
Consequently, the question immediately arises as to whether predictions
generated by these hypotheses can be employed as a means for subjecting them
to test.

For example, consider the simple demand relation used in the previous chapter.

One way to test this hypothesis., it might be argued, is to collect a set of data
during period t^ en the quantity demanded of a certain commodity, X/■^^.' ^^'^ °^
the market price at which these transactions were carried out, £/•,_•>• If these
data were divided into two lots, one lot could be used to develop the estimates

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for a B and u, .. From these data the estimated relation would be developed
-' ^ -(t)

as well as the standard errors of these estimates. The next step would be to
employ the second set of data to test the estimated relation (10.2). This test
could be conducted in a number of ways^ one of which would be as follows: Take
relation (10.1) and use the new data to estimate the parameters once again. The
result is a new set of estimates which can be represented by

y(t) = S^ +'p^ p(t) +u^(t) (10.3)

To test (10.3) against (10,2). adopt the estimates a. P., and u(t) as the values
for the null hypothesis. By employing the standard errors and sample size
associated with (10.3) one can^ for a specific size of Type I error^ develop
the required confidence intervals about a,, p,j, and u,(t), and determine whether
the null hypothesis is to be rejected or not. The procedure is based on the
prediction that the relation estimated from the first set of data will hold for
the second set as well. Clearly^ if the total pool of data is large enough
it can be broken up into a number of subsets, and several of these tests can be
conducted.

For a test to have empirical significance it must be possible for the data
to disconfirm the stated hypothesis. Hence, if these checks on the estimated
relation (10.2) are to serve as legitimate tests it must be possible to reject
the null hypothesis. But what conditions must be met if it is to be possible to
reject the null hypothesis? As in the case of any empirical test on a specific
hypothesis it must be possible to empirically identify the presence of the
initial conditions „ It has already been shown^ however, that one cannot establish
the initial conditions surrounding the error term as empirically true. Even

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though these tests may well produce supporting evidence for the null hypothesis
given by (10.2) none of these tests can serve to disconfirm it. Accordingly,
this application of (10.2) as a predictive device within period, _t, does not
provide a method for testing the basic hypothesis given in (10.1).

Since the first approach is not successful, a second attempt at a solution
is offered by employing the estimated relation of period t to predict the price
and quantity relation to be observed in the following period. That is to say,
if the data from period _t are employed to generate estimates for (10 .1) the
estimated hypothesis can then be used to predict or forecast the relation which
occurs in period t+1. If the data from t4l support the estimate based on
period t, this result is said to confirm the basic hypothesis given by (10,1).
In order to examine the merits of this claim it is necessary to review briefly
the conditions under which a prediction can be employed to test a particular
hypothesis.

1. Prediction and Empirical Tests

The structure of a scientific prediction is similar to that of an
explanation. In the case of a deterministic (non-statistical) hypothesis a
prediction can be used as a test of the hypothesis if the same three conditions
are met;-' First, the predicted event must belong to the class of observables.
Second, the theory or hypothesis must be open to rejection by empirical test.
Third, for the second condition to be satisfied the relevant initial conditions

-See Chapter 2, pp. 26-28.

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must be empirically true. Hence, if an hypothesis is represented by K, and the

deduced or predicted relation is represented by S, the structure of the prediction

is given by the proposition R -* S^. As has already been noted, evidence

supporting S can be counted as confirming R -* S if there is independent evidence

r
supporting R. Part of such evidence is data demonstrating the presence of the

relevant initial conditions. If R is a consequence of the theory Q, then some

of the initial conditions may also be a consequent of Q. But if R is considered

by itself, the specification of R Implies that certain initial conditions be

satisfied. As long as these initial conditions can be subjected to empirical

test, then the proposition R -» S can indeed be confirmed or disconfirmed by

the evidence pertaining to S^.

However, when dealing with a statistical hypothesis the problem becomes
slightly more complex. Consider, for example, a statistical hypothesis which
relates the occurrence of two propertiss of certain events by a specific
probability. Suppose the probability that an occurrence of M(x.) will also be
an occurrence of N(x,) is given by r_ (where £ is the long-run frequency of all
M(x.)'s being N(x,)''s), then the hypothesis can be stated in the standard form:
for all X., p[M(xp, N(x.)] = r.

Given such an hypothesis how does one subject it to test? To begin with
it is perfectly clear that^ even though the relevant initial conditions can
be shown to be satisfied and that M and N are observable attributes of x. ,
one contrary instance is not sufficient to reject the hypothesis. For whatever
the value of r_, say £ = .95. there are bound to be instances where an occurrence
of M(x.) is not also an occurrence of N(x.). Indeed, one would expect this to
happen l-ry,, of the time. Thus, to disconfirm such an hypothesis it must be

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possible to estimate from the test data whether the observed frequency is

2/
significantly different from the hypothesized value, r.-

To determine the statistical significance of the observed frequency a null

hypothesis is set up which employs the hypothesized r. By using the appropriate

statistical test and accepting a specific Type I error one can then ascertain

whether the null hypothesis is to be rejected or not. The basic assumption

underlying this procedure is that this test can be repeated a large number of

times. If a Type I error of 5% is accepted one is essentially stating that one

expects to reject the null hypothesis 5% of the time when it is in fact correct.

In the same respect, the Type II error states the percentage of the time one

expects to accept the null hypothesis (i.e. not reject it) when it is in fact

false. None of these percentages have any statistical meaning unless it is

possible to repeat the test. To repeat the test it must be possible to

repeatedly sample from the same population. And, as noted above, this condition

requires the services of some device or theory which enables one to measure or

account for the stability of the population. Therefore^ to be able to employ

a prediction as a test of a statistical hypothesis it must be possible to repeat

the test. If this condition cannot be met then the result of a test cannot be

employed to confirm or disconfirm the hypothesis.

2, Econometric Forecasts as Predictive Tests
To help determine whether forecafts can be employed as a means for subjecting

— A detailed analysis of the problems posed by the use of statistical

hypotheses in explanation and prediction can be found in: C.B, Hempel ,
"Deductive-Nomological vs. Statistical Explanation," in H. Feigl,,et al , (eds),
Minnesota Studies in the Philosophy of Science, Vol, III^ University of
Minnesota Press^ Minneapolis, 1962^ pp. 98-169.

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econometric hypotheses to test, a brief examination of the forecasting procedure
is in order. To generate a forecasting relation one begins with the basic
hypothesis and estimates the relevant parameters from a sample of data from,
say, period t. The result, with the error term deleted, is the forecast relation:

The error term is ignored because even though a particular set of data may produce
an error estimate, such as u.j.s in (10.2) or (10,3), the expected value of u^^^
is assumed to be zero. Once (10.4) is developed for forecast for period t+1,
y^(t)^ is generated by substituting into (10.4) the observed value for £(t+l).
This method of producing forecasts is employed whether the theory is given by
the simple relation (10.1) or is represented by a many equation model. Consequently,
the question that is being raised can be simply stated as follows: Under what
conditions can the forecast value ^ (t+1) be used as an empirical test of the
original hypothesis Y ,j^y- a + P p,^.. + "/,-\?

From the discussion in the previous section it is clear that a single
negative instance is not sufficient to disconfirm the hypothesis. For even though
the error term has ostensibla disappeared, (10,4) is still a statistical relation

and can only be confuted by appropriate statistical test. Hence^ to compute

p
2 (t+1) and then to compare it to the observed value of ^ in period t+1 is not

sufficient by itself. To adjudge the empirical significance of this comparison

it is necessary to examine the statistical test by which these two values can be

related.

The standard econometric procedure is to construct an interval about

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F 3/

^ (t+1) and then examine whether the observed value falls within this interval.—

The interval represents the null hypothesis and is given by:

y^(t+l) ± K^ _ (10.5)

y^.t+1)

where the value of K depends on the size of the san^le and the percentage of values
of y(t+l) to be included in the interval.

The interval (10.5) is a tolerance interval not a confidence interval. And
the difference between the two is readily apparent once one examines them a little
more closely, A confidence limit or interval for the sample mean of a normal
population is of the form^ x ± KS , where x is the sample mean, K the number of
standard deviations (defined by the size of the Type I error), and S_ is the sample
standard deviation (error) . Moreover, confidence limits are computed in such a
way that they will include the actual mean of the population distribution in a
fraction 2^ where j, = 1-Type 1 error, of the total set of samples which are
gathered. Tolerance intervals, on the other hand, while of the same form, i.e.
X ± YS_, are computed so that within the fraction ^ of the samples they will include
at least a fraction P of the items in the distribution.

For example, for a normal population the confidence interval ^ ± 1,96a
includes 957o of the population. The tolerance interval x ± KS, for the same
population, however, is computed so that in a large series of samples the
fraction j_ of the intervals will include at least P of the population. If the
population remains unchanged and if one is free to gather numerous samples, then 2
becomes the measure of the degree of confidence with which the tolerance interval
can be said to include at least P of the population.

—The procedure is described more fully in Chapter 8, sec, 4,

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Returning to the econometric relation it is clear that since y/j^\ and 2.(t)

p
are random variables it follows that ^ (t+1) is also a random variable. If

u^ s is normally distributed then ^ and hence ^ (t+1) are normally distributed.

p
Further, since ^ (t+1) is a random variable it also follows that the estimate

of the sample standard deviation (error), £ , is a random variable.

y (t+1) p

Consequently, for each specific sample the variables ^ (t+1) and a will

y (t+1)

have different values. Accordingly, the tolerance interval will vary
from sample to sample. While this result does not constitute a special problem
it must be possible to repeatedly sample from the sample population before the
tolerance interval can be employed as the null hypothesis. For, if there is
complete freedom in sampling the value of K (which depends on the sample size)
can be chosen so that the probability, j.) that the interval will include at
least P^ of the population is as close to 1^ as is desired.

The problem in econometrics is aside from specific sampling difficulties,
whether the population remains unchanged. If one is dealing with stable
populations then the reliability of the forecast can be assessed by the tolerance
interval. But, once it is not possible to adjudge the population's stability,
other than by finding out that the forecasted value is in error, then it is no
longer possible to employ tolerance intervals to test the forecast relation.

In the previous chapter the problem of testing the initial conditions was
examined. Here it was demonstrated that the initial conditions could be
empirically checked if and only if the population from which the samples were
drawn remained unchanged throughout the sampling process. Further inspection
of econometric hypothesis revealed the fact that they do not contain sufficient
interpretive rules to permit independent checks on the population's stability

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to be made. As a result^ it was concluded that it was not possible to empirically
test for the presence or absence of the error term's initial conditions. If
econometric hypotheses do not contain sufficient interpretive rules to permit
the determination of a population's stability this absence of rules also
precludes the possibility of submitting the forecasting relation to test. For
consider once again the nature of the predictive test. From an estimated equation,
such as (10,4), one derives the forecast ^ (t+l)« By sampling in period (t+1)
one computes the observed value of \;(t+l). Either ^(t+l) falls within the
tolerance interval about ^ (t+1) or it does not. But in either event this
result cannot serve to confirm or disconfirm (10.4). In order for the evidence
to support or deny the forecast relation it must be demonstrated that tha
population from which the samples were drawn has remained unchanged. Manifestly,
such a demonstration is not possible within the bounds of econometrics.

The same argument applies to the case when ^(t+1) falls outside of the
tolerance interval. For without independent knowledge of the behavior of the
population this result may well have occurred because of some shift in the
population. Such changes are customarily referred to as structural shifts. In
the event that they occur the econometrian has no recourse except to re-estimate
his original relation and hope there will be no more shifts the next time a
forecast is made. While such procedures may well serve the pragmatic test of
"usefulness" they are not sufficient to perm.it the establishment of testable
econometric theories or hypotheses,

3. Ceteris Paribus and Population Stability

Part of the inability to test econometric hypotheses stems from the implicit
use of the ceteris paribus clause. For, if while the sampling and computations

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necessary to check on the forecasted values are being carried out everything else
remains unchanged then the testing of econometric hypotheses becomes a practical
possibility. Since econometrics does not contain a sufficient set of rules to
permit the items in the ceteris paribus clause to be checked one alternative is
to examine the effects of ignoring these items on the behavior of a dynamic
system. That is to say, if it can be shown that the position of the hypothesized
system in period (t+i) will be approximately the same whether the items in the
ceteris paribus clause are taken into account or not then, according to this view,
there are grounds for Ignoring the factors covered by the clause. This approach
is based upon two related theorems— which deal with the problems of analyzing
and testing the empirical validity of a dynamic system whose variables are in turn
related to other variables not explicitly included in the systera--these variables
are either assumed to be constant or are merely placed in the general repository,
the ceteris paribus clause.—

In order to explicate this position it is necessary to introduce the concepts
of completely decomposable and decomposable systems. A set of relations, theory,
or system is completely decomposable if the values of their variables are only a
function of past or present values of the same set of variables. Thus^ a closed

- H.A. Simon and A. Ando , "Aggregation of Variables in Dynamic Systems/'
Econometrica, Vol. 29, April 1961, pp. 111-138; and A. Ando and F.M. Fisher,
"Near-Decomposability, Partition and Aggregation, and the Relevance of Stability
Discussions," International Economic Review, Vol. IV, January 1963, pp. 53-67.
(Both of these articles are reprinted in A. Ando, F.M. Fisher, and H.A. Simon,
Essays on the Struc::ure of Social Science Models, M.I.T. Press, Cambridge, 1963,
pp. 64-91 and pp. 92-106 respectively.)

— A mors detailed discussion of the problem and the results so far obtained

to vfhich this section is to be found in„ F.M. Fisher and A. Ando, "Two Theorems
on Ceteris Paribus in the Analysis of Dynamic Systems," American Political Science
Review, Vol, 56, March 1962, pp. 108-113. (Reprinted in Ando, Fisher, Simon,
OD. cit.j pp. 1.07-112.

- 210 -

system (one in which all factors are accounted for) is a completely decomposable

system. A decomposable system, on the other hand, is one in which outside

factors affect the behavior of the system while the system cannot affect the values

of these outside variables. In other words, if a given system is influenced

by certain, specified external factors (e.g. exogenous variables) but the system

itself is unable to affect the values of these variables, and if these external

factors are the only external influences on the system, then the system is called

decomposable.

Since neither completely decomposable nor just plain decomposable systems
occur with any apparent frequency in economics the two theorems deal with
situations which are close approximations to these ideal states. The first, the
Simon-Ando theorem, is concerned with systems that are approximately (nearly)
completely decomposable--the variables within the system do depend on past values
of some outside variables but the dependencies are quite weak in comparison
to the internal relations. Given such a system (theory) the theorem asserts that
either in the long- or short-run if these external dependencies are ignored the
results obtained by treating the system as completely decomposable will be
approximately valid. Accordingly^ if the external dependencies are relatively
weak, the relative behavior of the system treated in isolation will not differ
substantially from the behavior the system would have produced if the external
factors were taken into account.

The second, Ando-Fisher theorem^ states that a similar result holds for
systems which are approximately decomposable. That is to say, for systems in
which the external dependencies are all one-way and are too large to ignore,
the relative behavior both in the long- and the short-run of the system treated

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in isolation will not differ substantially from that which the system would have
generated if these dependencies were incorporated into the system. "Thus the
economist who takes tastes and technology as influencing but uninfluenced by
economic variables will f ind--provided that such an assumption is nearly correct--
that his results will be approximately valid in all respects in the short run
and that even in the long run, when the full effects of feedbacks in the causal

structure are felt, the internal , relative behavior of the variables he studies

6/
will be approximately the same."—

To agree, however, that a particular econometric theory can be said to be

nearly completely decomposable or only nearly decomposable does not alter the

basic obstacles which confront any attempt to submit the theory to empirical test.

In either case the temporary exclusion of the contents of the ceteris paribus

clause does not bring one any closer to being able to measure the stability of

the underlying population. What these theorems permit one to do is to break

down some rather large system^ such as a whole economy, into a number of

relatively independent parts. This is an important step in the analysis of complex

systems. But such an advance does not obviate the necessity for being able to

7/
independently assess the characteristics of the underlying population.— Even

though these two theorems permit the econometric theory to exclude those variables

in the ceteris paribus clause the statistical form of the theory remains

— A. Ando and F.M. Fisher, in A. Ando, P.M. Fisher and H.A. Simon, op. cit.,

p. 109.

— For further discussion see: F.M. Fisher, A Priori Information and Time
Series Analysis; Essays in Economic Theory and Measurement, North Holland
Publishing Company, Amsterdam, 1962.

- 212 -

unchanged. Indeed, if econometric theories are to be corroborable by empirical
test the basic requirements for the statistical tests must be empirically
satisfied. Consequently, until it can be demonstrated that it is possible to
repeatedly sample from the sample population the statistical tests are devoid of
empirical significance.

4. Micro-Analysis and Statistical Tests

The principal obstacles confronting the testing of econometric hypotheses

also appear to encompass the detailed, micro analytic investigations currently

8/
being carried out under the aegis of the Social Systems Research Institute.—

The long-range objective of this research is to build a realistic dynamic model

of the United States Economy. To construct such a model the economy is

represented as consisting of a number of major components each of which is

composed of a large number of microcomponents. Accordingly, the behavior of the

economy is hypothesized to result in part from the interactions of the

microcomponents within each of the major segments, where the components "include

markets, goods, and microconyonents such as individuals and families imbedded

vjithin regional household sectors and firms imbedded within industries,"—

One of the basic types of components is a "decision unit" and these interact
vjith each other by means of components representing "markets." To complete the
interaction between decision units and markets a third type of component is
employed which is designated "goods." This last type of component includes all

— For a recent statement of the approach, objectives, and general conceptual
framev7ork of this research see: Guy H. Orcutt, "Microanalytic Models of the 'United
States Economy: Need and Development," American Economic Review, Vol. LII, May
1962, pp. 229-240.

— Guy H. Orcutt, op. cit. , p. 231.

- 213 -

items which are exchanged, produced or consumed by the decision units. Components
are described by their input, output and status variables. If the inputs are
viewed for the moment as exogenous variables then the behavior of the component
is determined by the relations that link the exogenous variables to the status
variables which in turn generate the values of the output variables. Each decision
unit has a number of outputs some of which become the inputs to the market
components which in turn distribute these items, as outputs of the markets, on to
other decision units. Since the output of one component frequently is the input
of another the principal function of these inputs (output) is to update the
values of the appropriate status variable and by means of the behavioral relations
generate new values for the outputs.

If the interactions between the major components is slight these parts of the
model could be viewed as nearly completely decomposable. As a result, they could
be analyzed and investigated independently of the rest of the system. If within
each of the major components, the interactions between decision units, markets,
and goods are such that the causal relations — can be specified, then it may
well occur that some of these components can be described as nearly decomposable.
Under this condition such components may also be treated as relatively independent
units.

In order to examine the problems posed by subjecting such a model to
empirical test it is perhaps easiest to first consider one of the nearly

10/

— The meaning of this use of "causality" is presented and employed in:

H.A. Simon, "Causal Ordering and Identif lability," W.C. Hood and T.C. Koopmans,

(eds) , Studies in Econometric Method, Cowles Commission Monograph No. 14,

Chapter 3, Wiley, 1933. (Reprinted in H.A. Simon, Models of Man, Chapter 1,

Wiley, 1957, and in A. Ando, F.M. Fisher, and H.A. Simon, Chapter 1, op. cit.)

- 214 -

decomposable microcomponents . Whether a particular model contains nearly
decomposable units or not is immaterial to the problem at hand. For if it is
not possible to confute a relatively isolated component it will not be possible
to subject larger portions, up to and including the entire model, to a process
of refutation by empirical test.

Consider, then, an approximately or nearly decomposable microcomponent.
This component has certain variables which function as inputs, some which are
categorized as outputs, as well as its internal status variables. — The relations
which link the inputs to the status variables to the outputs are stochastic.
Thus, once a set of inputs are specified these relations specify the probabilities
of the occurrence of the outputs. Since the relations are stochastic the
problems of submitting them to empirical test are the same as are discussed
above--to wit, it must be possible to empirically identify the relevant initial
conditions as well as those conditions surrounding the statistical tests. Unless
these constraints are satisfied the tests are empirically meaningless.

An example of such a model is provided by recent investigations of some

12/
aspects of consumer behavior. — While the model does not represent the finished

product of this research and is still undergoing modification it will aid the

discussion to have a specific case to examine. The model is concerned with the

— The component will be nearly decomposable if most of the inputs for
period t_ are the outputs of period t-1.

12/

— A.S. Goldberger and M.L. Lee, "Toward A Microanalytic Model of the

Household Sector," American Economic Review, Vol. LII, May 1962, pp. 241-251.

- 215 -

demographic and economic behavior of household units and is based upon data
collected by the Surveys of Consumer Finance of the Survey Research Center. The
relations (operating characteristics) are stochastic and contain the probabilities
of the occurrence of the relevant outputs. These probabilities as well as the
parameter values are estimated from the survey data and are tested in the usual
way for statistical significance. In the model reported in this study there are
23 dependent variables: "total income, home ownership (probability and value
of owned home) ^ monthly rent^ expenditures on additions and repairs to house
(probability and amount^ car ownership (probability), new car ownership
(probability), multiple car ownership (probability), purchase of car in prior
year (probability, total price, and net outlay) , purchase of new car in prior
year (probability), purchase of household durables in prior year (probability
and amount), mortgage indebtedness (probability, amount, and monthly payment),
non-car installment indebtedness (probability, amount, and monthly payment),

and debt incurred in connection with purchase of car in prior year (probability

13/
and amount)," — The value of each variable, as mentioned above, is estimated

by least squares regression from the survey data. And the results are reported

along with a notation as to their statistical significance.

While the sample size (3,000 units for each year) and the number of variables

considered are considerably larger and the level of detail conspicuously more

14/
microscopic than most econometric studies, — the obstacles to submitting this

model to empirical test have not been altered or overcome. This is not to say

13/

— A.S. Goldberger and M.L. Lee, op. cit . , p. 244.

14/

— The earliest and most complete microanalytic model is presented in

considerable detail in; G.H. Orcutt, M. Greenberger, J. Korbel , and A.M. Rivlin,

Microanalysis of Socioeconomic Systems; A Simulation Study, Harper and Row

Company, New York, 1961.

- 216 -

that if 27 variables were considered instead of 23 the results would not differ
from the above. Nor am I suggesting that it is not possible to discard certain
variables when it turns out that they have non-significant coefficients. For the
difficulty lies not in our ability to regress or manipulate variables and data.
The problem is whether such models can ever be disconfirmed by empirical test.
As has been noted above the answer to this question is to be found within
the statistical tests that are employed. All statistical tests require specific
initial conditions to be satisfied. And all statistical tests assume that
repeated samples can be drawn from, the same population. In the casa where
controlled experiments are performed, statistically significant differences
between two populations are determined by maintaining a "control" group as well
as a "test" group throughout the experiment. In the case of the household model,
however, how is one to determine the stability of the underlying population?
The data are drawn from sample surveys which are in turn based on detailed
interviews of household behavior. If a relation is estimated from the data of
one year and then employed to forecast some variable values in the next year hovj
are negative results to be interpreted? Clearly, a shift in the population could
account for such a result just as readily as an error in the initial specification
of the relation. Further, if the model cannot be considered to be approximately
decomposable the negative result could perhaps be attributed to a shift in one of
the exogenous factors. If the process by which households made the decisions
relevant to the above model were understood, and if it were also possible to test
for the constancy of this process, then It would begin to be possible to determine
the stability of the population from, which the samples are drawn. But, until the
stability of the population can be independently measured it is not possible to

- 217 -

disconfirm either this model or any similar microanalytic model by the application
of statistical tests.

Summary and Conclusions

At the beginning of the chapter it was suggested that it might be possible
to test econometric hypotheses by employing them to generate forecasts or
predictions for forthcoming periods. If the forecasts could be compared with
the actual outcome it was hoped that this comparison would serve as the empirical
basis for the test. For such a test to have empirical significance, however, it
must be possible to disconfirm the hypothesis from v;7hich the forecast was deduced.
With econometric relations this implies that it must be possible to rejecr the
null hypothesis. But to reject the null hypothesis two conditions must be
satisfied. The first,, which is derived from the standard requirements of an
empirical test, requires that the initial conditions surrounding the error term
be empirically true. The second, which follov7S from the basic nature of all
statistical tests, requires that it must be possible to draw repeated samples
from the same population. Only if a test can be repeated under the same relevant
conditions does it make statistical sense to employ confidence intervals and
other measures to determine the rejection <x non-rejection of the null hypothesis.

In a particular test a specific hypothesis the forecasted value is generated
and compared to the observed outcome. For the comparison of these values to reject
the hypothesis it must be possible to exclude all other sources of error. If
the initial conditions are satisfied and if the population from which the sample
values are drawn is the same in both cases, and if it is possible to repeat the
test any number of times, then a negative result can serve to disconfirm the

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hypothesis. Once the characteristics of a population are empirically
deterninable then it is possible to test for the presence of the initial
conditions as well as for the stability throughout the testing process of the
underlying population. Even though the testing of forecasts requires the use of
tolerance intervals, if the above factors are empirically determinable,
econometric hypotheses can be submitted to test.

KovjGvcr, econometric hypotheses are concerned withtlie characteristics of
certain populations. Indeed, they are no more than hypothesized relations among
selected characteristics of certain underlying populations. Further, these
hypotheses are not concerned with the processes by which the populations are
generated. As a result, econometric hypotheses do not contain the requisite
interpretive rules for ascertaining the true values of the population's parameters.
Since a shift in the population (structural shift) cannot be determined prior to
and independently of a specific test of a particular hypothesis it is not possible
to use the results of a test to disconfirm the hypothesis.

The same conclusion holds even for the cases of nearly completely
decomposable or nearly decomposable models. For, although in these cases the
sources of error are greatly reduced--one Is now entitled to ignore the factors
in the ceteris paribus clause--it is nevertheless still not possible to disconfirra
the model or hypothesis. To do so requires a knowledge of the underlying
population and the process by which it changes over time. Consequently, even
v;hen dealing with completely decomposable models econometrics does not provide
the requisite interpretive rules. Similarly, in microanalytic models where
the hypotheses may relate to individual units such as households and the sample
sizes are noticeably increased, the fundamental obstacles to empirical testing
still have not been removed.

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If we cannot disconfirm a hypothesis it is not possible to employ it to
establish a scientific explanation or prediction of an economic event. Since
we cannot disconfirm econometric hypotheses it follows that we, as economists,
are completely unable to explain or predict the occurrence of economic events.
While this conclusion may neither surprise nor upset some economists it does
reflect rather strikingly upon the state of economics as a scientific enterprise.
For, since we are unable to submit our hypotheses to disconf irm.ation by empirical
test, economics cannot be a part of empirical science. It follows, therefore,
that none of the conclusions, policies and prescriptions derived from either
classical or econometric theory rest upon a testable and tested empirical base.

To me this is an alarming conclusion and one to which a considerable amount
of serious thought should be given. If a body of economic knowledge is to be
developed it is necessary to have economic hypotheses that can be submitted to
empirical test. Since the equilibrium conditions of classical theory appear to
be empirically intractable there is little to be gained by searching for a
solution in this direction. In econometrics the empirical obstacle is the
inability to employ econometric hypotheses to measure directly a population's
characteristics. Unless this difficulty can be circumvented econometrics cannot
serve as the method for developing testable hypotheses or theories.

In order to rescue econometrics from beyond the pale of empirical science
it is clearly necessary to be able to understand the decision processes which
govern the behavior of economic units, whether they be individuals, households,
markets or firms. Such an understanding would have to imply that a knowledge
of the decision processes themselves is sufficient to provide the requisite
measures on a population's characteristics and stability. That is to say, for

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this understanding to perform the required service a knowledge of the relevant
decision processes must lead to empirical measures of a population's stability.
Since empirical knowledge is a consequent of testable theory, the acquisition
of knowledge about decision processes entails the development of testable
theories about such processes. Moreover, once theories are constructed which
describe and explain the decision behavior of economic units, these theories
may well provide a new basis from which to infer the structure and content of
testable econometric hypotheses. While this line of reasoning may strike
the reader as a trifle fanciful the remaining chapters are devoted to a
detailed exploration of the empirical and practical possibilities of developing
a science of economics in this manner.

PART FOUR

Behavioral Foundations
of
Economic Analysis

Chapter 11
THE ECONOMIST'S PERSPECTIVE

The fundamental problem facing economists is to acquire a body of
empirical knowledge about economic phenomena. Whether such knowledge ^ once
garnered, is used to explain the occurrence of particular economic events or
is employed as the basis of public or private policy formulations is not
at issue here. For before, knowledge can be used to explain events or to
solve problems it must be acquired. And so far the analysis has been solely
devoted to the acquisitive process which is a consequence of both classical
and econometric theories of economics.

In order to develop a body of knowledge about particular observable
events it is first necessary to have one or more empirical hypotheses
about the phenomena in question. If these hypotheses survive a number of
tests then they themselves constitute the basis for empirical knowledge
of this class or these classes of events. Concurrently, such hypotheses
also permit one to establish explanations and predictions of the occurrences
of the phenomena with which they are concerned.

In the previous two parts of the book the body of economic theory
that has been developed both from classical and econometric foundations
is examined in some detail. The object of the inquiry is to discover whether
either or both of these collections of theory can serve as the basis for
a corpus of empirical knowledge of economic phenomena. For a theory to
serve this important function at least one of its constituent hypotheses
must be confutable by empirical test. But the analysis demonstrates that
both the classical and the econometric foundations are such that they preclude
the possibility of submitting either type of hypothesis to empirical test.
In the former case it is the nonobservable, equilibruim conditions which
constitute the empirical stumbling block. While with econometric hypotheses

222 -

it is the intractable behavior of the population distribution which prevents
statistically significant tests from being performed. As a result^ neither
class of theory can^ in its present state^ provide the theoretical basis
for a body of empirical knowledge of economic events.

Given such a conclusion it might well be in order to ask whether in
fact we^ as economists, need testable theories. After all, since neither
classical nor econometric theories can be refuted by test, economists have
survived remarkably well without the benefits such theories are supposed
to provide. To answer this query it is necessary to examine the types of
problems to which economic theory in it current condition is applied. For
econom/cs is a sufficiently established discipline to suggest that some
problems must form reasonably appropriate bases for economic investigation.

One major class of problems to which economic theory has always been
applied is the entire range of normative questions and issues. What should
be done in such a situation if we wish to maximize (or minimize) some
criterion function? What, given certain social and political values, should
the best national policy be toward the problems of taxation, unemployment,
social welfare, tariffs, money supply, etc. In all of these questions
economic theory is used to provide the basis for a "rational" answer. As
such the specific set of hypotheses that are employed are used as the in-
struments — with which a solution is generated. Since the desired solution
is generated. Since the desired solution is normative, a close correspondence

between theory and observed behavior is frequently considered to be

2/
unnecessary." For the solution is a proposal for what ought to be done.

i' This approach to the justification of a theory is admirably presented
by K. R. Popper: "Three Views Concerning Human Knowledge," Conjectures and
Refutations , Chapter 3, 1963.

2/ . '

— See for example; La Von Mises, _0£. c 1 1 ;..

- 223

Indeed^ if current behavior is at variance with the proposed then this is
just further evidence why a particular solution should be adopted.

In keeping with this prescript Ive function of economic theory it is also
argued that it is not necessary to completely understand the behavior of
economic actors or units for the purpose of developing rules or policies
by which they should behave. Accordingly^ economists should restrict
themselves to finding normative solutions to all economic problems, so

that once they are discovered all that need be done is to get the people

3/
involved to follow the prescribed policies.— Indeed, if governments and

individuals would only follow the economist's prescriptions and behave

according to all the rules, then there would be no need to be concerned

over the question whether these theories were testable or not. For in this

case the theories would govern economic behavior.

Unfortunately, either governments or individuals are not sufficiently

amenable to the economist's persuasion or they are unable to sort their way

through the conflicting policies with which they are presented. In either

event while economists generate normative theories wLth their concomitant

"rational" solutions the procession of economic events proceeds unexplained.

If we were uninterested in the actual economic events themselves this state

of affairs would cause little or no concern. But clearly the converse is

the case. It is the actual events which affect our lives and create the

problems which economic theory is supposed to be able to resolve. And since

the theories of economics cannot be refuted by empirical test we as economists

and private individuals are left with an unbridged gulf between the economic

— For an interesting discussion of this issue see; C. W. Churchman,

Prediction and Optimal Decision, Prentice-Hall, Englewood Cliffs, N. J., 1961,

- 224 -

events of daily life and policies we are supposed to follow.

While I have no wish to suggest that the formulation of public and
private policy is not one of the prime functions of the economist I am willing
to argue that this important activity has been approached from the wrong
direction. By basing policies on untestable theories there is no possible
way of detecting error. Since it sometimes occurs that policy prescriptions
are not mutually consistent on what basis is a choice to be made? If economic
theory were based on testable theories the answer to such a question would
be clear. That is to say ^ the procedure for arriving at an answer would be
given by the theories themselves--submit the conflicting hypotheses to test
and see which of them survives or corresponds more closely to the relevant
data. Even though such a procedure may not immediately resolve all ambiguities ^
e.g., the long struggle between the proponents of the wave and corpuscular
theories of light, it is the only process by which the conflict can be
empirically resolved other than that of resorting to professional fiat.

Further, since science can only progress through the detection of error--
progress comes from adopting and creating new theories to account for the
inconsistencies and errors in the old--to be deprived of. this corrective
process is to forever abandon economics to the tyranny of rhetoric and the
defense of established positions. Under these conditions criticism on
empirical grounds cannot play its vital role.

To avoid this situation, as well as to be in the position where policy
formulations can be based on observed behavior, a body of theory must be
developed that can be submitted to empirical test. This is not to say that
all classical and econometric theory need be immediately scrapped. Rather,
the point is that unless and until they can be transposed into empirically
testable states, they cannot serve as the basis for a science of economics.

225

If we are unable to directly employ the results of classical and modern
economic thought^ how then are we to proceed? And upon what basis and in
what direction are we to look for testable hypotheses? While the answers
to both these questions may not be immediately obvious, their outlines are
explored in the remainder of this chapter.

1 . Economic Analysis and the Problem of a River Process it'

Consider, for a moment, the problem of understanding the behavior
of an object which is freely floating on the surface of a river. The river
in question empties into a tidal basin where the tides are sufficiently
large to affect the river's rate of flow. In fact, at particular periods
during the tidal cycle the river, to an observer on its bank, appears to
flow in an upstream direction. We, as observers, newly arrived on the scene,
are unaware of the tidal properties of the river, and observing the progress
of the previously mentioned object feel stimulated to develop a theory to
account for its behavior. In keeping with our classical training we immediately
perceive the floating object as part of an equilibrium system. We observe a
wind as well as the movement of the water and are content to hypothesize
that the behavior of the object is determined by the resultant of these
two forces .

Gradually, as we stand there congratulating ourselves on our undoubted
perspicacity, the object ceases to continue in its "normal" direction.
We note that the wind has not perceptibly altered and are moderately puzzled.
At this point the object begins to move in the opposite direction and lacking
any knowledge about the behavior of the river itself one of us is led to
construct the following theory: "Consider the object, if you will
pardon the anthropomorphism, as having an overt desire to prolong its stay

— The example used .in. this section is. directly indebted to; W. Van Orman
Quine From a Logical Point of View, op . cit . , Chapter 4

- 226 -

on the river. Since the river must eventually empty into some larger body of
water, the object can only prolong its stay if it propels itself
against the current. Having only a certain amount of energy at its disposal
at any one time it has to decide how to consume this energy to its best
advantage. If we posit the existence of a utility surface then it rapidly
becomes clear how we are to understand its behavior. For surely^ the only
rational thing for the object to do is to maximize its utility function
subject to its energy constraint."

When questioned on how we might employ this theory to predict the yet
unobserved behavior of the object the reply was immediate. "First we must
observe the choices made by the object in each j^eriod of time. Since
it has many alternatives facing it at each instant^ the action it takes is
clearly that which it perf ers . Second^ we need a measure of the amount of
energy that can be expended per period. Then, since we have the utility
surface and the energy constraint we can deduce certain characteristics of
its behavior. For example, it will proceed from one equilibruim position
to another. And if these equilibria are stable it will remain there until
either the wind shifts or some other factor disturbs it. At which point it
will strive to return to a new equilibruim position. If you want to deduce
further characteristics of its behavior employ the method of comparative
statics and determine the directions of the appropriate rates of change."

At this juncture, another member of our company, while agreeing with the
theory as stated, proposed a more direct method by which we could predict
the future behavior of this object. "Since the object's behavior is in
part determined by the river's current and the prevailing wind we should
set up a relation including these components and estimate the relevant

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parameters by taking a sample of observations. In particular, the dominant
direction of the wind should be noted so that the net effect of the wind
in this direction can be represented by an error term. Then^ if we also
measure the distance of the object traverses in a given time interval and intro-
duce an unknown variable to represent the river's speedy we can estimate the
value of this unknown by standard econometric methods. Once we have an
estimate of the river's speed then, in conjunction with the estimate of the
utility surface and the object's desire to maximize same subject to its
energy constraint, we can predict for a specific interval of time the future
course of the object's progress."

While this example may appear quite fanciful to some readers, let us
stop for a minute to examine the position into which we have been led by
both of these methods of analysis.

To begin with it should not be forgotten that the problem is to account
for the seemingly "odd" behavior of the floating object. The classical
approach considers behavior in terms of equilibrium positions. Thus
all movement is either toward or away from such equilibria. Concurrently^
the equilibria are end points or states of momentary rest, especially if they
are stabel^ and behavior is viewed as a process of proceeding from one
end state to the next. To account for the object's progress on the river
the classical observer was led to represent its behavior in terms of these
equilibria. As a result, the observed behavior was "seen" in these terms
and constructs were developed to accommodate this view. Moreover^ all
behavior exhibited by the object supports this position^ since none can
confound it .

But what have we learned about the object's behavior? Since the theory
cannot be refuted the scientist must reply, "Not a thingi Because, you

- 228 -

have been looking at the wrong sorts of things.—' To focus your attention
on equilibrium positions is to put yourself in the same situation as Heracleitus^
who long ago complained that he could not bathe in the same river twice because
new waters were forever flowing by. What Heracleitus apparently noticed was
that he could only bathe at any one instant of time in one stage of the river.
At a second moment he could bathe in another river stage but it could not be
the same river stage as that in which he had previously been immersed.

"Equilibria are very similar to river stages. No two equilibria can be
the same, and each marks another stage in the object's progress over time. To
focus on equilibria is to focus on behavior stages. Behavior is a process
through time and behavior stages represented by equilibria are at best its
mementary parts. But. and here is the point you seem to have
missed, to identify the river bathed in the first time with river bathed in
once again is precisely what determines the subject matter to be a river process
and not a river stage. In other words, by seeing observed behavior in terms
of behavior stages you should have been led to study the behavior process not
the behavior stages. For to confine your investigations to behavior stages
(equilibria) is to forever restrict yourselves to studying things that never
remain the same. Science seeks to discover empirical regularities so it is
somewhat awkward to be looking for testable relations where none can be found.

"Those of us who labor in the natural sciences are admittedly blessed
with the opportunity of conducting controlled experiments when we are confronted
with behavior we do not understand. But take your object floating out there

— For further discussion of this point see: ibid . pp. 65-68.

- 229 -

on the river. Under the circumstances we cannot very well experiment with it
so how should we proceed? To understand its behavior we need to know, as
you have already correctly pointed out^ something about the forces that
impinge upon it. In this case we would like to know the forces acting on the
object from the water and from the wind. But more than that we need to know
something about the behavior processes of the object itself. If ^ as you have
suggested^ it is animate^ we need to know the process by which it reacts to water
and wind. If it is inanimate it behavior is solely the result of the external
forces acting upon it. In either event it avails us not to whit to view
the observed behavior as anything but the resultant of the interaction of
a number of specifiable forces and processes. To hypothesize that the observed
behavior is the resultant of an equilibrating process^ so that all we can see
are the equilibrium stages is. unless we have by other means acquired a
knowledge of the processes themselves, to place ourselves in the unenviable
position of never being acquainted with more than the equilibrium stages
themselves. While we may describe these stages in ever increasing detail_,
because each one differs from the next, we will never find the empirical
regularities we would so much like to find.

"You must forgive me for carrying on at such length and for bringing up
the point I should like to mention next.— But, you see, in the natural
sciences we were straightened out on this point quite some time ago. In the
very early days of science, Aristotle, if I am correct, thought that all bodies
were supposed to want to come to rest. That is to say^ all bodies had a natural

— This part is indebted to the excellent history of science presented by
Herbert Butterfield. The Origins of Modern Science, C. Bell and Sons^ London, 1957.

- 230 -

place on which or in which they were supposed to want to rest. For example,
all heavy terrestial bodies were believed to have a natural motion towards the
center of the universe. And as the center of the universe was believed to be the
earth, all such bodies had a natural motion toward the center of the earth. The
behavior of objects, then, was viewed as comprising successive stages toward
a natural end state or equilibrium stage. Any movement away from a state of
rest implied the existence of a motivating force or "mover." As such this was
a theory of rest or end states. Consequently, it was motion, not rest, which
attracted attention and required an explanation.

"For example, if a body was observed in motion it was assumed that there
was a mover actually in contact with it, giving to the object the motion that
was observed. Only when the mover ceased to operate could the body come to
rest, fall straight to the ground, and arrive at an end state. When you
suppose that the object on the river is proceeding from one equilibrium to the
next you have also assumed the existence of a mover. In this case you gave a
name to the mover and described it as a process of maximization of utility
subject to an energy constraint. Clearly your theories about the behavior
of consumers, firms and the economic system as a whole are also built in this
fashion. But do you really mean to argue that the economy is seeking an end
stage or equilibrium point so that once there, if no longer disturbed, it
would remain forever in one place?

"Or consider the other side of the same argument. If a body's motion is
due solely to the presence of a mover, then, since there is almost always some
external resistance to a body's motion, the speed of a body must be proportional
to the force being exerted by the mover. If the external resistance is reduced
and all other facts remain unchanged, the speed of the body will increase.

- 231 -

Following this line of reasoning to its conclusion we see^ as Aristotelians thought^
that the speed of bodies in a vacuum (zero resistance) must be infinite.
Since they found this an absurd conclusion they rejected the notion of a vacuum,
claiming that such a thing could not exist. In a similar manner what happens to
an economy, a firm^ or a consumer if the frictional forces or resistances to
its behavior are reduced? Does the speed of their motion increase in inverse
proportion to the resistive forces? Will an economy grow at an ever increasing
rate if the frictional forces are reduced? Will the object on the river suddenly
start moving at an infinite rate if all frictional forces between it and its
environment are eliminated? Does an object freely falling in an approximate
vacuum fall with an approximately infinite velocity?

"The answer, in the last case, is obvious for we have certain theories
and empirical laws to account for the behavior of freely falling bodies. In
particular we have the classical approximation of this behavior--that under

normal conditions in vacuo the acceleration of a freely falling body near

2
the earth's surface is given by _d_£ = 32 feet per second. Once again you

dt2
may well retort that this is a well known empirical regularity which was arrived

at by controlled experimentation. But that. I am sorry to say is not really

the point. The point is that as long as motion was the phenomenon to be

explained, and the end state or equilibrium position the natural place of

rest, no on could have observed or discovered this law of behavior.

"It was not until the middle of the seventeenth century that the conceptual

framework was sufficiently altered to permit the observation and discovery of

such physical regularities. If my memory does not fail, it was Galileo who

first realized that motion was not the important thing to explain. Rather it

was the change in any particular set of behavior which required the explanation.

As you undoubtedly recall, he altered the Aristotelian conception of inertia

- 232 -

so that now a body would either remain at rest or in a uniform motion in any
particular direction until some outside force changed that motion. No
longer was an object seeking an equilibrium position and once there remaining
in a state of rest. Now all objects were either at rest or in a uniform motion
and any changes in these motions were the factors to explain.

"The consequences of this view have had, as you are well aware, a profound
effect on the course of the physical sciences. And, I am willing to argue, the
same would be true of your investigations if only this conception of behavior
were taken seriously. For consider once again the object you observed floating
in one direction at a fairly steady speed. This motion caused you no surprise
as we are all accustomed to seeing objects floating on rivers at moderately
constant velocities. But the minute the object's motion changed direction
your attention was caught and you began to hypothesize an equilibrium system
to account for its behavior. By focusing on equilibria your attention shifted
from the original item which caught your notice--the change in direction to
a theory which would account for the "mover". Without a mover, an equilibrium
approach which seeks to define the end states does not make much sense.
Accordingly, the theory you were led to construct was primarily a theory of the
mover. And since this kind of mover is not the sort of thing you ought to be
looking for, is it any wonder that the result of such an inquiry is an untestable
theory of the object's behavior?

"While you may still object to this analysis of your theoretical procedures
consider the further difficulties you are led to by the econometric approach.
Once again the econometrician is inclined to perceive the object's behavior in
terms of movers and equilibria. So much so in fact, that if you inspect a
normal econometric model you will find that many of the model's variables
come directly from the classical equilibrium conceptual scheme. I refer, of course.

- 233 -
to such variables as the marginal rates of substitution between one variable and
another J the marginal propensities to behave in certain ways^ and the many other
remaining examples of this type. By including these variables within the econo;-
metric relations to be estimated you are in effect trying to estimate the
various hypothesized characteristics of the mover or movers in question. Since
no two equilibrium positions can be the same, no two sets of observations can
be guaranteed to be samples from the same population. Not to mention the external
forces acting on the object which you either classify as exogenous variables
or lump together in the error term.

"In order to develop testable regularities in this fashion you have to
know something about the behavior of the population from which you are
drawing your samples. For unless you can be sure that the samples come from
the sample population it is not possible to submit such relations to test.
By focusing your attention on the mover you are unable to learn anything about
the population. And once again you are left in the most unsatisfactory position
of being unable to empirically test your hypothesized relations.

"For example^ consider once again the object floating on the river and the
method you proposed for discovering the relation which governs the object's
behavior. If I remember correctly, one of you suggested setting up an
expression which included the distance travelled by the object during a given
interval of time, time itself, the unknown speed of the river ^ and an error term
which expressed the net effect of the wind upon the object. Assuming, at
this point, that the object is an animate one you then suggested taking an
observation on the distance travelled during the specified interval and using
this as your estimate of the object's progress over the assumed constant
river speed. As should be apparent by now, this is a procedure for trying to
estimate the characteristics of the object's mover. Since the object's behavior

- 234 -

with respect to you standing on the bank did not remain constant over time
(it was the change in behavior that caught your attention)^ how can; you
possibly hope to estimate the parameters of a regularity from observations
that are constantly varying? The only way you can do this is by knowing
the process that governs the river's speed. And since^ in this case, the tidal
effect violates your constancy requirement we are at an apparent dead end.

"Even if the object is inanimate the problem viewed in this fashion is
really no different. For how are you going to reconcile the estimate of the
river's speed from one instant of time from that derived at some later period?
It does not help that these estimates are all derived by maximum likelihood
techniques and that each is an unbiased and consistent estimate. If the speed
of the river is changing from sample to sample the estimates are all being

based, on different underlying populations. Accordingly what is really at the
heart of the problem, is that you are unable to tell from your estimates
alone whether the underlying population has remained the same or not. Indeed,
until by some independent check you can be sure of this point it is not
mathematically legitimate to employ the appropriate statistical tests.

"Clearly, if you could control the river's progress so that you were assured
of its constancy, your methods would produce reliable results. But, unfortunately,
you can no more control the river's speed than you can the behavior of the
consumers, firms and whole economies which are the more usual subjects of your
investigations. Moreover, in these latter cases the behavior patterns are
vastly more complex than that of the object floating on the river. If your
method of approach cannot lead you to testable relations about this object's

behavior how can it possibly succeed when faced with behaviors that are many
times more complex?

- 235 -

"The answer^ if indeed there is an answer^ must lie in an under-
standing of the processes that govern the behavior under investigation.
To understand the process it appears to be necessary to recognize that
neither motion nor rest themselves are the prime objects for inquiry.
Rather^ it is change in motion which should act as the focus of attention.
If all objects^ whether inanimate or not are perceived as continuing in
a state of uniform motion or that of rest until disturbed by an external
force, the key to the understanding of the object's behavior lies in
discovering the processes which govern the interaction between the object's
motion and the disturbing force.

"For example, to understand the behavior of the floating object we
need to know both the process that governs its motion as well as the processes
by which it interacts with its environment. If the object is inanimate
we would all agree that it will continue in a uniform motion downstream
until disturbed by wind or contrary river current. Given this conceptual
framework, the change in the object's behavior would lead us at once to
conjecture some shift in the behavior of the river or the wind. If the
wind is observed to be much the same as before we would immediately be
led to suspect some shift in the river's motion. Even though we were
unaware of the tidal effect we would, without much mental agitation have
assumed that some such activity was disturbing the river's flow. Further,
if we were sufficiently curious, we could readily corroborate this assumption.

"Given this orderly procession from conjecture to observation, why
should we behave differently when the object is no longer inanimate?
Admittedly, inanimate objects are easier to handle as one can concentrate
almost exclusively on the external forces. But the only additional problem
posed by the animate is that we have to understand their internal decision

- 236 -

processes. That is to say^ with the animate we have to understand both the
internal decision process as well as the processes which govern the interaction
between it and its environment. However^ by employing the natural sciences
as our guide the task should not be as awesome as it may appear. For,
under the general hypothesis that all bodies continue in uniform motion
until disturbed by an external force^ our primary concern is to explain
changes in behavior. From an analysis of change we are led to construct
hypotheses about the interaction between the environment and the object's
decision process. And from an analysis of these processes, if successful,
we are led to an explanation of the change.

"Consider, for a moment, how we might proceed by this approach to
develop a testable theory to explain the behavior of a consumer, a firm,
or an economy. First of all we acknowledge the assumption that we expect
the decision behavior of the subject (the consumer, the firm or the
economy) to remain unchanged until acted upon by some external force..
Such changes in behavior may take place for a variety of reasons, but note
that our basic hypothesis leads us to focus on change itself as the
event to be explained. To explain this type of event we first need to
know a certain amount about the decision process of the subject under con-
sideration. Once we are able to describe and explain such processes we
will also be able to identify the external factors that can alter the
subject's behavior. For a change in some external factor which is not
a part of the subject's decision processes can not very well affect its
decision behavior. Consequently, a knowledge of the subject's decison
processes will provide us with ability to identify the most likely to the

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external influences.—' A knowledge of the object's behavior with respect
to its environment suggested the presence of a reverse or tidal current.
Similarly J a knowledge of the normal decision behavior of a consumer would
suggest the principal factors which would induce him to alter this behavior.
While the external events may remain beyond either our own or the consumer's
control , a knowledge of his decision processes will lead to hypotheses
about the interactive or adaptive process. Once this latter process is
sufficiently explored the observed changes can now be explained.

"One further comment and then I will stop. Observe what has been
gained by this approach. Firsts unless your subjects are more recalcitrant
than I can imagine, you should begin to discover testable relations
governing specific classes of decision behavior. Second, once the first
of these has been proposed and tested you will be in a position to
employ other observed behavior to test, amend, and generate further empirical
hypotheses. At this point you should be in a position to explain the
decision behavior of certain individual subjects as well as perhaps that
of certain classes of subjects. That is to say, your empirical hypotheses
should already have a modest generality.

"Having progressed this far with your empirical knowledge of decision
processes it may well be possible to begin employing some of your more
established economic techniques. For, if you can specify the principal
components of the decision processes of a particular class of economic
actors you will have at the same time identified the major external variables

— Since we are only concerned with decision processes the possible list
of external factors such as directly affect the physiology of the organism
itself, such as death, cripling disease, etc., are specifically excluded
from consideration.

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which can affect the behavior of these actors. From a knowledge of the
decision process it is possible to detect when this process changes.
Since it was the lact of knowledge about such processes upon which your
econometric method foundered, it may well be possible to link these two
approaches together. In other words, a knowledge of the decision process
may provide the measure that is needed to guage the stability of the
econometric population. Once the population's stability can be assured,
then econometric relations can be submitted to test. Whether a knowledge
of decision processes will provide all the information you need to measure
a specific population's stability is a question for you to answer. But
the possibility of such a solution should not be overlooked. And in my
opinion it would appear to warrant a rather searching examination. At
the very least.> this whole approach will generate testable hypotheses
about economic decision behavior, and with luck it will provide the basis
for an empirical science of economic behavior."

2 . Classical Analysis and Decision Processes

From the foregoing it is apparent that we, as economists, need to
search for testable economic relations which describe the changes in a
particular actor's or system's decision behavior or motion. Since
physical laws do not state that "A will be followed by B" there is no
reason to suggest that economic laws should be framed in this manner
either. Rather, like physical laws, we need to develop relations which
will tell us how an actor's or a system's behavior is changing at each
moment of time, not where the system or actor will be at some future moment.

In this respect, it would appear that the classical economic framework
is unsuited to such a task. For the concepts of equilibrium and stability
are concepts of states of rest--they describe the points to which the

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system may arrive at some future moment^ but hot how or why the behavior
is changing from moment to moment # Since the classical approach is most

readily represented by its deductive system the abandonment of these

8/
classical concepts entails a departure from this particular deductive system.—'

That this conclusion follows directly from the analysis is readily
seen if one considers once again the effect of a conceptual framework upon
theoretical development. For it could well be argued that it is the
mathematics of the classical system which leads to hypotheses concerning
equilibria and which stimulates the discussion of stability conditions^
the convexity of sets, and the most suitable axioms for a theory of
choice .

If we are to shift our attention from end states to processes, then
we need a conceptual framework as well as a deductive system which will
lead us to focus on these processes. Further we require a theoretical
system in which both the economic decision behavior of individuals and
groups can be explained. If such a theoretical system is to generate
testable hypotheses of lasting significance it must allow for the variety
of observable differences in individual behavior. Further, the theoretical
schema should be such that the decision processes themselves can be expressed
in a variety of content languages where each of these descriptions has the
same classes of observable phenomena.

For example, if we are describing the decision processes of an in-
dividual we need a language that will accommodate such psychological
characteristics as are involved in human learning; while if we are discussing

The mathematical system is described in some detail in Chapter 3.

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a larger economic system it may be more convenient to talk about different
types of adaptive processes. As long as these processes are described
in such a way that they can be tested against the same classes of data
then hypotheses tested in one context can be related to those of another.

One possible approach to this general task would be to assume that each
individual economic actor^ whether individual or firm behaves according to
its own, "rational" or "irrational" decision process. If each process
is unique unto itself then the only way we can begin to understand the
interactions among these processes is by positing the existence of some
simple decision rules to account for some of the aggregate characteristics
of the observed behavior. Such a procedure, however^ will lead us
right back to the classical position since the class of maximizing decision
rules are precisely of this type.

Another^ and if it is corroborated by empirical test, more powerful
approach is to postulate that there is an invariance in the decision
processes of various classes of economic actors. If a theoretical state-
ment of these invariances is possible^ then any one individual's decision
processes are explainable by the combination of the invariant process and
a specific set of parameters and processes that are particular to the
individual^ where these latter parameters and processes are directly
related to observables or have operational forms of measurement. If it ie
possible to describe an invariant structure for individual decision
processes^ then the next step is to identify an invariant structure for
the decision behavior of groups or organizations by developing a set of
correspondences between the structure of individual and group processes.
With such a theory^ individual as well as group (firm^ organization^ and
market) behavior would be explained on the basis of a set of invariant
decision structures with the addition of a specific sets of observable

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parameters and decision processes.

In order to construct such a theory the several components must be
empirically specified. That is to say ^ the invariant structures must be
identified and defined, and it must be demonstrated that these structures
are sufficient to generate a wide variety of observed behavior. Moreover,
to account for a particular stream of individual behavior techniques need
to be developed which permit the specification of those parameters and
processes which must be included in the statement of the individual's
decision process. Once these structures and processes have been described
they must then be submitted to empirical test. For this approach, like
any other in science, can only be justified by its ability to lead to
the development of theories which can withstand a process of refutation
by empirical test. Consequently, it is toward a detailed examination of
the empirical as well as the economic relevance of this conceptual
framework that the remainder of this book is directed.

Chapter 12
FOUNDATIONS OF BEHAVIORAL THEORY

The discussion in the previous chapter argues that in order to
construct testable theories of economic behavior it is first necessary
to understand and to be able to explain the decision behavior of economic
actors. While classicists and econometricians can undoubtedly agree with
this statement, it has been demonstrated that their theories cannot be
employed to establish the necessary explanations. One of their principal
failings is that these theories cannot be submitted to test independently
of specific economic contexts. Accordingly, if a new body of theory is
to be constructed which can be corroborated by empirical test the implica-
tion is that it must be formulated in such a way so that at least some of
its hypotheses are independent of a particular economic context. That
is to say, if economics is to rest on a testable theory of economic
processes, hypotheses about these processes must be corroborable by
direct reference to a wide variety of observable behavior. In brief, a
theory of economic processes is needed which is capable of satisfying
several requirements. First of all, it must enable one to account for
observed decision behavior occurring at a particular time and under
specific conditions. Concurrently, it m«st allow one to be able to
explain the decision behavior of individ^ials as well as groups of organiza-
tions. For if the behavior of firms or groups of consumers is to be
explained, a theory is required which encompasses the decision behavior
of such collections of individuals.

An understanding of economic decision processes appears to be the
principal requirement to be satisfied if a science of economics is to be
developed. Given this basic position, it follows that the search for

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such a foundation should be conducted amongst the recent researches in
behavioral and psychological theories of decision-making behavior.—'
Eventh'ooagh these theories are not all concerned with the same economic
phenomena, they all employ a basic set of hypotheses which posit the
existence of certain empirical regularities in the decision processes of
economic actors. These hypothesized regularities are in turn derived
from various researches in the simulation of individual decision

behavior.—' Accordingly, before one can accept behavioral theories as a
possible basis for a science of economics it is necessary to be sure that
the principal hypotheses of the underlying theory of individual behavior
are both capable of test and have been corroborated by a number of tests.

\_l That this is not a novel suggestion is evinced by the fact that
several economists, for example, A. Papandreou, "Some Basic Problems in
the Theory of the Firm," in B. F. Haley, (ed.), Survey of Contemporary
Economics , Irwin, Homewood, Vol. 2,, 1952, pp. 183-219; and E. Grunberg,
"Notes on the Verif lability of Economic Laws/' Philosophy of Science.
Vol. 24, 1957, pp. 337-348, have pointed out both the desirability and
the possibility of reducing economic theory to psychological or behavioral
terms .

The most notable of the early researches in behavioral theories as
well as a detailed presentation of a behavioral theory of the firm are
to be found in: R. M. Cyert and J. G. March, A Behavioral Theory of the
Firm, Prentice-Hall, Englewood Cliffs, 1963.

Ij For a survey of research on simulation see the papers presented
by G. H. Orcutt, M. Shubik, and G. P. E. Clarkson and H. A. Simon in
"Simulation: A Symposium," American Economic Review, Vol. 50, Dec. 1960,
pp. 894-932. For a more extensive analysis of the problems of simulating
human decision-making behavior see the papers included in: Bi A.
Feigenbaum and J. Feldman, (eds). Computers and Thought, McGraw-Hill, 19d3,
Part 2, "Simulation of Cognitive Processes, pp. 2o9-38o.

244 -

1, A Theory of Individual Decision Behavior—'

The theory upon which the above noted theories of economic decision

processes are based was developed to account for the problem solving

behavior of individual subjects as they performed a number of specified

tasks.— The purpose of the theory is to explain the process of human

problem solving by identifying the classes of decision processes which are

employed by humans while deriving the solutions to a range of different

problems. Questions about problem solving behavior could, no doubt, be

answered at several levels and in varying amounts of detail. This theory

seeks to explain such behavior in terms of a set of basic information

processes. These processes are partially defined by the theory's main

postulates which state that for each problem solver there exists:

"(1) A control system consisting of a number of memories which
contain ayrmbolized information and are interconnected by
various ordering relations...

(2) A number of primitive information processes which operate on
the information in the memories,...

(3) A perfectly definite set of rules for combining these processes
into whole programs of processing. . ."5./

3_/ This section is principally indebted to G. P. E. Clarkson and
W. F. Pounds, "Theory and Method in the Exploration of Human Decision
Behavior ,('^J Industrial Management Review, Vol. 5, Fall, 1963, pp. 17-27.

4/ The earliest statement of the theory is to be found in: A. Newell,
J. C. Shaw, and H. A. Simon, "Elements of a Theory of Human Problem Solving,"
Psychological Review, Vol. 65, 1958, pp. 151-166. A more recent statement,
which includes some of the empirical investigation of the theory, is
presented ini H« A. Simon and K. Kotovsky, "Human Acquisition of Concepts
for Sequential Patterns/' Psychological Review, Vol. 70, 1963, pp. 534-546.

5_/ A. Newell, J. C. Shaw, and H. A, Simon, ibid . , p. 151.

- 245 -

From these postulates it is clear the theory assumes that decision
processes can be isolated as well as identified. Indeed, the theory also
assumes that they can be represented by a series of straight-forward
mechanical processes. In other words, the theory posits that decision
processes consist of certain specific components, e.g. the memory, the
basic information processes, and the rules for combining these processes
into whole programs of information processing, which in turn are composed
of collections of simple, describable mechanisms.

In order to clarify the empirical meaning of these postulates consider

the following application of the theory of human problem solving to the

6 /
decision processes of an investor of trust funds in a bank.—' This

theory of investment behavior was developed to account for the portfolio

selection process of a particular trust investor. The basic postulates

state that the trust investor has:

(1) A memory which contains information associated with the general

economy, industries, and individual companies. The information is

ordered in associated lists. Although all investors may not

associate a particular company with a given industry, the process of

classification by industry is the primary basis for listing companies

in the memory. The information related to each company may also

vary among investors, but each company is represented as having

a list of attributes with their values stored in the memory, e.g.

growth rates of sales and earnings, price earnings ratio,

dividend rate, etc.

6_/ For a complete statement of the theory see: G. P. E. Clarkson,
Portfolio Selection: A Simulation of Trust Investment, Prentice-Hall,
Englewood Cliffs, 1962.

- 246 -

(2) Basic information processes which perform the tasks of searching
the lists of information in the memory, selecting those items which
have the required attributes, regrouping the selected pieces of
information into new lists, and performing algebraic operations when
necessary,

(3) A set of rules or criteria which determine the decision-making
process by denoting the order and manner in which each information
process is to be employed. This set of rules constitutes the
structure of the investor's portfolio decision process.

As a further application of the basic postulates consider the theory
of human problem solving which has been proposed under the name of
General Problem Solver.—^ The object of this theory is to explain the
problem solving behavior of individuals when they are involved in the
solution of tasks for which means-ends analysis is an appropriate method
of attack. In order to operate within the context of a particular problem
situation the basic postulates of the theory require the following
information to be provided:

For the memory:

"(1) A vocabulary, for talking about the task environment,
containing terms like: object, operation, difference, feature..

l_l A. Newell, J. C. Shaw, and H. A. Simon, "Report on a General
Problem Solving Program for a Computer," Proceedings of the lAternational
Conference on Information Processing, UNESC, Paris, 1959, (Reprinted in
Computers and Automation, Vol. 8, 1959).

- 247 -

(2) A vocabulary, dealing with the organization of the problem

solving processes, containing terms like: goal type, method,

evaluation "

For the decision processes:

"(3) A set of programs defining the terms of the problem

solving vocabulary by terms in the vocabulary for describing

the task environment.

(4) A set of programs (correlative definitions) applying the

terms of the task - environment vocabulary to a particular

environment , . . "£.'
Within the context of a particular subject area, e.g. chess, symbolic
logic, or trigonometry, GPS is a theory of human problem solvipg which
essentially consists of a collection of general rules and detailed tech-
niques for generating problem solutions. Because these processing rules
are largely independent of the subject matter of a particular problem,
e.g. capturing a bishop, proving a theorePi, or proving an identity, GPS
is more than a theory of one individual's decision processes. It is in
fact the beginnings of a general theory which when suitably interpreted
is sufficient to account for the decision behavior of a number of
individuals .— '

8/ A. Newell, J. C. Shaw, and H. A. Simon, Op. cit., (Computers
and Automation), pp. 11-12.

9_/ A discussion of the conditions under which these theories are
subjected to test and an examination of the evidence currently available
is left until later.

- 248 -

As can be seen from these two examples the theory of human problem

solving asserts that the decision processes of individuals can be
analyzed and described in terms of information processes. When these
operations are collected into a set of statements which describe the
behavior of the individual or individuals under investigation, such state-
ments become a theory of the decision-making process. That such a set of
rules can be considered to be a theory is evinced by the requirement that
it must be possible to deduce unequivocally the externally observable
behavior which will be generated by it. To ensure the satisfaction of
this condition, the theory is translated into a formal language (in this
case a suitable computer language, about which more will be said below) and
the logical consequences are derived by performing each operation according
to the specified rules.

2. Goals and the Structure of Decision Processes
From this discussion of the basic postulates and assumptions of
the theory of human problem solving it is now possible to examine the
manner in which observed behavior is to be classified and structured.
According to the theory all decision behavior can be analyzed and described
by a set of processing rules operating on a specific collection of informa-
tion which is available to the decision-maker. This information is
available to the individual either in his memory or in his environment.
But before the theory can be usefully applied to a particular situation
it is necessary to be able to isolate and identify the principal decision
processes as well as the structure by which they are related.

Most theories of human behavior include a reference to the purpose
or goal toward which, it is argued, the behavior is directed. In classical
economic theory the goal of the consumer is to maximize his utility
(expected) subject to his budget constraint. Similarly, the goal of the

- 249 -

firm is to maximize net revenue, or in the case of a recent proposal the
goal is to maximize net sales subject to a profit constraint.—' While
disputes may arise over which goal the behavior is supposed to serve—',
most theories reflect the general belief that behavior can be usefully
described in these terms.

Under the theory of human problem solving a specific stream of observed
behavior is described and explained by identifying a particular set of
decision rules as well as the information upon which they operate. Within
the context of this theory an external goal or purpose is not relevant to
the understanding of the behavior. For the behavior of a set of mechanisms
operating in a particular environment determines the consequences oi: final
output. Behavior is generated by specific processes operating on items
obtained from the memory or the environment and is not a function of
external goals.

To help clarify the point consider the following examples of "goal
directed" behavior. To begin with consider an inanimate torpedo. Suppose
for the moment that it has been constructed in such a way that its steering
mechanism is directly connected to an electronic mechanism which is
sensitive to certain vibrations in the water. Under normal conditions
this electronic mechanism will process the incoming vibrations and alter

10 / W. J. Baumol, Business Behavior, Value and Growth, Macmilla^,
New York, 1959.

11/ For example, consider the list of different goals to which
individuals are posited as striving towards in gaming and bargaining
situations, e.g., R. D. Luce and H. Raiffa, Games and Decision, Wiley,
New York, 1957; R. D. Luce, Individual Choice Behavior, Wiley, New York,
1959; and T. C. Schelling, The Strategy of Conflict, Harvard University
Press, Cambridge, l':)oO.

- 250 -

the direction of the torpedo in conformity with these signals. If we, as
observers, witnessed this torpedo intercept a moving object on the water,
we might describe it as a homing torpedo but we would be most unlikely to
ascribe to it the goal or purpose of destroying particular types of
floating objects. The behavior of the torpedo at any instant is completely
described by a knowledge of its control process and the incoming signals.
While the torpedo may or may not eventually strike a floating object, the
inclusion of this result of its behavior is not relevant to the explanation
of its behavior when it is still some distance from the object.

As a second, and animate example, consider the problem of describing
the behavior of an investor who is selecting a portfolio for a client.
One of the first ttems to be determined is the investment policy for this
account. Once the policy is selected, it can be applied to a suitable
list of securities in order to determine which securities are to be
included in the portfolio. If the policy is "growth" then a decision
process is needed which will select a particular set of growth stocks
from the total list of such stocks which are available at the time. We,
again as observers of this process, might describe this selection process
as one which seeks to select a growth portfolio or one which has growth
as its goal . But, in fact, the actual growth rate of the resulting port-
folio is largely independent of the process by which it is selected. As
a result, the term "growth" is really the name for the process which acts
as the selection mechanism. This is not to say that the investor could
not have a "target" rate of growth, say ten per cent per year. If at the
end of a year the portfolio has not grown in value by this amount such a
failure may well trigger off a re-examination of the existing portfolio.
However, even though this target rate of growth may be viewed by an
outsider as a goal to which the investor is striving, it is on closer

- 251 -

inspection no more than a control device--one which under certain conditions

activates certain other processes, such as searching for other

. . 12/
securities .±=-'

A third example of the manner in which the theory of problem solving
employs the term goal is given by GPS itself. GPS, as mentioned above,
is a theory of problem solving which encompasses problems to which means-ends
analysis is appropriate. Hence, GPS is able to work on problems which can
be formulated in terms of objects and operators. An operator is a decision
process or a process for developing a decision process which can be
applied to certain objects to produce different objects. An object is
described by its features and one of the commonest features that dis-
tinguish pairs of objects is the differences between them. In order to
address itself to a specific problem GPS employs three types of goals:
A Transform goal, a Reduce Difference goal, and an Apply Operator goal.
To each of these goals is associated one or more methods for achieving it.
Consequently, when a goal is activated the relevant methods for accomplish-
ing this goal are brought out from the memory and tried. For example, one
method of changing the object a_ into the object b is to note the difference
between them d and by activating the Reduce Difference goal try to find a
method which when applied will reduce differences of this sort. If a
method is found it is applied by the Apply Operator goal.

12/ For an excellent analysis of goals and their effect upon
decision behavior see: W- F. Pounds, "A Study of Problem Solving
Control," unpublished Ph. D. dissertation, Carnegie Institute of Tech-
nology, 1964; available in mimeograph. School of Manjagement, Working
Paper 33-63, Massachusetts Institute of Technology,

- 252 -

Once again, it is clear that the term goal refers to the name of a
decision process and not to some result or consequent which is external
to the decision process. Accordingly, this approach to decision behavior
argues that to understand decision behavior only requires one to discover
the decision processes which determine the observed behavior. This is not
to say that humans do not "have purposes" which affect their behavior,
such as wanting to get married, desiring great wealth, prestige, or a
happy life. On the contrary, these objectives or targets frequently
occur in conversations and no doubt influence the motivations and
emotions of many individuals. However, in order to describe and explain
an observed stream of problem solving behavior it is not necessary to know
the source of inspiration, frustration, or motivation; it is sufficient
to be able to describe the processes and the concomitant information which
determine the observed behavior. To command someone "to do better" is
the height of futility unless that person has or is able to acquire a
set of decision processes which will lead him to produce the desired
results. Behavior is determined by decision processes and to stipulate
an objective without providing the requisite decision rules and control
processes is not the way to produce the required behavior.

Decision processes which select or operate on the information in the
memory or environment are represented, under this theory of decision
behavior, by nets. A net is an associated list of tests or filters through
which the information passes. Each test or item in the net is the name
of another process, and the behavior of the entire process is the result
of the net operating upon the information that passes through it.

For example, in the theory of investment behavior the decision
processes or discrimination net which selects the individual securities
for a specific portfolio is represented by a collection of tests through

- 253 -

which a security must pass if it is to be accepted. Each of these tests
may be simple or complex, but the discrimination net itself will only
contain their names and the order in which they are associated to one
another. In the following net, which is part of the Growth Portfolio

discrimination net, T1-T9 represent a particular sequence of tests that

13/
are applied in turn to an appropriate list of securities. —

Yes (t1

Dictionary

Tl - Mean growth in price (past) c! 20%

T3 - Mean growth in earnings per share (past)

T4 - Mean growth in sales past

T5 - Forecasted growth in earnings per
share (1 year)

T6 - Forecasted growth in sales (1 year)

T7 - Mean growth in cash flow per share
(past)

T8 - Mean growth in profit margin (past)

T9 - (y) on Relative Value List

B - "Below" average for industry

'^B - "Not Below" average for industry

R -- Reject.

FIGURE 1

In this net processing begins with the test named T_l. If a security passes
this test, T6 is applied. From T3^ the security will either be processed

13/ For complete description of this net and the way in which it is
employed see: G. P. E. Clarkson, Portfolio Selection, Op. Git . , Chapter 4,

- 254 -

by T4 or T5^ depending on the outcome at T^. Aside from Tl, the outcome of
each test depends on the relative characteristics of each security.
Further, the tests are arranged in hierarchies so that if a specific
security is "below average" with respect to the characteristic examined by
T5 it must pass through T6_, T]_, and T8 if it is not to be rejected and is
to return to 19 and the remainder of the net.

A further example of this structure of decision processes is provided
by employing a maze as a representation of the problem solving process. A
maze is an hierarchical structure of paths, (See Figure 2) some elements
of which belong to the set of "correct paths"--i . e , , they lead to the
solution of the problem. The maze can be represented as consisting of all
the possible paths which could have been taken. — Or the maze can

FIGURE 2

SOLUTION

14/ In this case the maze is analogous to the nation of a game tree
used in game theory and statistical decision theory, see: R. D. Luce
and H. Raiffa, o£. cit . ; and H. Raiffa and R. Schlaifer, Applied Statistical
Decision Theory, Wiley, New York, 1954.

255

represent that set of paths taken by a single individual to reach a particular
solution, as in the investment example above.—' Under this interpretation
all problem solving behavior can be represented by a sequential list of
operations. Since discrimination nets have the required associative and
hierarchical structure, all decision processes can be represented by
discrimination nets. Consequently, in order to be able to empirically identify
a specific decision process it is necessary to know the contents of the
tests or processes as well as the way in which they are intercomsetJlied in
the net. Once these items are known the behavior of the decision process
is fully determined. For by hypothesis, the generated behavior is the result
of the decision process acting on the information stored in the memory or
the environment. As a result, the key to the explanation of observed
decision behavior lies in the ability to isolate and identify the contents
of discrimination nets, and, as a consequent, the information required by
these nets.

3. On the Explanation of Decision Behavior—'
In the preceding sections it has been suggested that the theory of
problem solving behavior is sufficient to provide the empirical foundations
for the explanation of observai decision behavior. Since all theories claim

15/ For a more detailed discussion of the maze as a prepresentation
of the problem solving process see: A. Newell, J. C. Shaw, and H. A. Simon,
"The Processes of Creative Thinking." in H. E. Gruber, G. Terrell, and
M. Wertheimer, (eds . ) , Contemporary Approaches to Creative Thinking,
Atherton Press, New York, 1962, pp. 63-119.

16/- This section is in part drawn from, G. P. E. Clarkson,
"Verification and the Function of Laws in Micro-Economics," Industrial
Management Review, Vol. 4, Fall, 1962, pp. 41-58 and from The Theory of
Consumer Demand, op. cit . , Chapter 7.

- 256 -

to be able to explain something and, as has already been shown, not all
theories do so, it is appropriate to re-examine briefly what is meant by
the word "explain,"

To establish a scientific explanation (6dr the occurrence of an event,
three conditions must be satisfied. — ' The first is that the occurrence
of the event must be deducible as a direct consequence from the conjunction
of the theory and the appropriate initial conditions. For this condition
to be satisfied the theoretical system must conform to the general rules
of logic which govern the formation and manipulation of deductive systems.
Theories which are stated in verbal or mathematical form can meet these
conditions just as well as theories stated in terms of a computer program.

In ail cases the theory can be constructed so that the process of deductive

IP /
inference will conform to the general rules governing deductive systems.— i^'

The second condition is that the theory itself must contain at least
one general hypothesis or law which has been confronted with and survived a
process of refutation by empirical test. Accordingly, at least one of the
theory's hypotheses must be stated in such a manner that it can be
corroborated by empirical test. The third condition requires the state-
ments describing the initial conditions to be empirically true.

If the theory of human problem solving is to provide the empirical
foundations for testable theories of decision behavior, then 'the explanations
provided by such theories must satisfy these three conditions. From the
previous sections it is clear that an explanation of observed behavior is
achieved by applying the hypothesized decision processes to the information

17/ For a further discussion of scientific explanations see Chapter 2,
and the references cited there.

18/ These rules are described and detailed references are provided
in Chapter 2.

- 257 -

(initial conditions) contained in the memory or the environment. If the
generated behavior matches the observed (in a manner to be discussed in
the next chapter) then that set of observed behavior is said to have been
explained.

In order to determine whether such explanations satisfy the three
criteria consider the following example of an explanation of an economic
event that is proposed by the theory of trust investment mentioned above.
The event to be explained is the selection of a portfolio of securities by
a particular trust investor for a specific trust account. To establish the
explanation of this event the theory requires the initial and boundary
conditions to include: Data on the historical, current and expected values
of relevant financial attributes, e.g. price, yield, earnings per share,
profit margin, growth rates of price, sales, and earnings, etc. for a
specified list of securities; data on the historical, current and expected
values of specific industrial and economic indicators; and certain data
on the particular trust account in question. The hypotheses of the theory
are concerned with the trust investor's decision process. They posit that
the decision process can be represented by: (i) a memory which contains
the data noted above listed in a particular form; (ii) a set of procedures
which allow the data in the memory to be searched, manipulated, and desired
items selected for further processing; and (iii) a set of decision rules
that determine the decision-making process by stipulating when and where
each decision process is to be° carried out. These hypotheses include
statements about the structure of the memory and of the individual
decision processes, the way in which expectations are formulated, and the
sequence in which the various decision processes are applied.—' In

19/ It should not be forgotten that these hypotheses are stated in
sufficient detail to permit their programming and testing on a digital computer,

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brief, the hypotheses define both the structure and the order of the
decision processes. When they are employed in conjunction with the initial
and boundary conditions the decision processes select a specific portfolio.
Accordingly, the explanation of the selection of a particular portfolio
is established by applying the decision procedures given by the theory to
the data of the security market and the specific trust account in question.

Since the statements describing the initial and boundary conditions
refer exclusively to observables the third criterion is manifestly satisfied,
Moreover, the theory itself is translatable into an unambiguous computer
program. Thus, as long as the computer language contains all the requisite
properties of a formal language, the deductive system (the computer program)
satisfies the first condition. Hence, in order to determine whether this
explanation can be considered to be "scientific" all that is necessary is
to show that the theory contains at least one general hypothesis which is
both refutable and not yet confuted by empirical test.

To demonstrate that this criterion is satisfied all one need do is
submit the theory of trust investment to a number of empirical tests. If
the three postulates of the theory of human problem solving are taken as
exemplars of the general hypotheses for the theory of trust investment,
then a successful series of empirical tests on these hypotheses will
constitute evidence for their empirical validity. Indeed, since the
initial conditions are all observable, all such tests constitute potential
d is confirmation.

For example, the theory of trust investment was constructed by
incorporating into its hypotheses such decision processes as were observed
(and inferred.) from the trust investor's behavior. To test the theory's
ability to reproduce the decision behavior the initial conditions were
specified by providing the requisite data of the security markets and of

- 239 -

some specific trust accounts for a particular time period. The theory was
then required to generate portfolios for these trust accounts. The
specific portfolios, however, only constitute the end product of the
investor's decision process. Consequently, the theory was also subjected
to a set of tests which compared the behavior generated by its hypotheses
with the recorded decision behavior of the trust investor.

Although it is of some interest to be able to explain and predict the
actual portfolio selections of a specific trust investor, there are pre-
sumably a variety of theories which will accomplish this result. What is
of much greater importance, is the fact that in a number of actual tests
the theory's decision behavior compared favorably with that of the trust
investor--i.e. it appeared even on close inspection, that the theory was
employing similar decision procedures and was arriving at the same results
for substantially the same reasons as the particular investor under investi-
gation. By comparing the behavior generated by each of the theory's major
hypotheses directly with the observed it is possible to submit the theory's
decision processes to a process of refutation by empirical test. Manifestly,
this testing procedure can be repeated. Also the hypothesized processes
can be compared with observed behavior to whatever level of detail is
appropriate or desired. As a result, while the theory of trust investment
may or may not have been adequately confirmed, it is demonstrably possible
to corroborate its principal hypotheses ..^ii'

20/ The actual procedures by which such hypotheses can be submitted
to test are discussed in the next chapter. For a detailed presentation of
the results of the direct tests of the investment theory's hypotheses see:
G. P. E. Clarkson, Portfolio Selection, op. cit . , Chapter 7.

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4. Towards a General Theory of Decision Behavior

Once it is possible to corroborate hypotheses about decision processes
within a given economic context the next important step is to determine
whether some of them can also be subjected to test independently from their
application in, say, the theory of 'portfolio selection. For, although
individual economic decision processes are of interest by themselves, one
cannot establish the empirical validity of a general theory of decision
processes unless it is possible to subject some of the hypotheses to test
independently of a specific economic context.

Behavioral theories, just as theories of individual decision behavior,
are concerned with explaining various aspects of human decision-making
behavior. All of these theories contain hypotheses which make definite
assertions about the structure and ordering of the relevant decision
processes. Since each of these theories deals with various aspects of
observed decision behavior it is manifestly both possible and practicable
to study human decision-making behavior in a diver's (non-economic) number
of contexts. For example, the decision behavior of individuals engaged in
the solution of problems in geometry, logic or chess could be used as the
framework within which to test the empirical validity of many of the
hypothesized decision processes .■=^' It is not being suggested that all

21/ Indeed, the basic hypotheses employed in the theory of trust
investment were derived from researches in individual decision behavior
which used the problems of geometry, logic and chess as their sources of
empirical evidence. See for example: A. Newell, J. C, Shaw, and H. A.
Simon, "Empirical Explorations of the Logic Theory Machine," Proceedings
of the Western Joint Computer Conference, February, 1957, pp. 218-230, and
"Chess-Playing Programs and the Problem of Complexity," IBM Journal of
Research and Development, October, 1958, pp. 320-335; and H. L. Gelenter,
J. R. Hansen, and D. W. Loveland, "Empirical Explorations of che Geometry
Theorem Machine," Proceedings of the Western Joint Computer Conference, 1960,
pp. 143-159. (All three articles are treprinted m E. A. Feigenbaum and J. Feidman
(^ds.) Computers and Automation dp. cit., pp. 109-133, 39-70, 153-163 respectively.)

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hypotheses of a single theory, say the theory of trust investment, can
be tested independently from its economic context. Certainly, some- of them,
e.g. the criteria by which companies are listed in the memory, the order
in which the testing and processing of the individual securities, etc.,
are performed will be peculiar to the specific economic context. What is
being asserted is that there are a certain number of invariances among the
decision processes of different problem solvers, and that it is possible
to test for their empirical truth value in a variety of empirical
contexts .

Consider, in this respect, the theory of human problem solving. It
contains three postulates which assert the existence in a human decision-
maker of a memory, some primitive information processes, and an hierarchy
of decision rules. The theory of trust investment, like the General
Problem Solver, turns these postulates into testable hypotheses by specifying
in detail the content and structure of the memory, the information processes,
and the content and order of the decision rules. If it were not possible
to specify how to characterize and empirically interpret these processes,
then it would not be possible to directly adapt these postulates into a
testable theory of individual behavior. Moreover, unless invariances,
like the structure of the contents in memory and the structure of the
decision processes themselves, exist among decision-makers it is not
possible to construct theories of decision behavior in this manner.

Implicit in this last statement is the postulate that invariances exist
among the decision processes of different problem solvers. Indeed, it is
being posited that these invariances not only exist but they can also be
isolated, identified and empirically confirmed. As evidence for this
postulate consider the number of theories of human decision behavior which

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are directly derived from the theory of human problem solving. — ' While
it is not being suggested that this postulate can be accepted as a well
tested empirical regularity, it is clear that it has been subjected to a
number of empirical tests. Further, and what is perhaps more important,
it is in principle possible to submit such hypotheses to test and the
references to the literature point to examples where such a program is
already being carried out.

In order to demonstrate the empirical possibility of developing
testable theories of decision behavior, it is sufficient to show that it
is possible to implement such a testing procedure. For, if the appropriate
tests are performed and some of the hypotheses are not disconf irmed, then
these relations will have become the independently tested empirical
regularities which will constitute the empirical foundations. Once a set
of empirical regularities is established then all hypotheses that can be
deduced from them either alone or in conjunction with other postulates
become in turn capable of being, at least indirectly, confirmed or dis-
conf irmed by empirical test. Consequently, when a particular theory, say
the theory of trust investment, is employed in the explanation of a
specific economic event, the independent testability of its principal
hypotheses ensures that a scientific explanation has been established.

Concurrently, once some hypotheses about decision behavior have been
established as empirical regularities the prediction of the occurrence of an

22/ For examples of these theories see;, E, A. Feigenbaum, "The Simula-
tion of Verbal Learning Behavior," Proceedings of the Western Joint Computer
Conference, May, 19d1, pp. 121-132; J. Feldman, "Simulation of Behavior in
the Binary Choice Experiment," Proceedings of the Western Joint Computer
Conference, May, 1961, pp. 133-144; (Both of these papers are reprinted in
E. A. Feigenbaum and J. Feldman (eds.) o£. cit . , -pp. 297-309, 329-346
respectively) ;R. K. Lindsay, "Inferential Memory as the Basis of Machines which
Understand Natural Language," in E. A. Feigenbaum and J, Feldman, og^. cit . ,
pp. 217-233; and A. Newell and H. A. Simon, "GPS, A Program that Simulates Human
Thought," in E. A. Feigenbaum and J. Feldman, o£, cit . , pp. 279-293.

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event can also be employed as the basis from which to test part or all of
the hypotheses in a theory. For example, the trust investment theory was
subjected to test by requiring it to predict, under different market
conditions, the investor's portfolio selections. In this case, the theory's
portfolios can be used to determine whether the theory's decision processes
are sufficient to reflect the changing economic conditions in the securities
which are selected. If the predicted portfolios compare favorably with
the investor's under one set of conditions but not under another, then it

would follow that the decision processes were not sufficient to permit the

23/
theory to adapt its selections to the prevailing market conditions. —

Therefore, to the extent that empirical regularities of decision-making
behavior can be established it is then possible to develop general theories
of decision behavior which can explain and predict the observed behavior
of a variety of economic actors.

23/ The evidence on this point is presented in ibid. , Chapter 6

Chapter 13
Some Problems of Application

Imagine, for the moment, that ve, you and I dear reader, wish to develop
a theory to explain a particular sequence of observed behavior. The behavior
in question is of such frequent occurrence that a theory which is sufficient to
explain it will considerably improve our understanding of the behavior of the
economic factors involved. Moreover, for purposes of social welfare we should
like to be able to exercise some degree of control over this form of economic
behavior. As a result, an understanding of the decision processes involved is
clearly of great importance to us. For, once we have a theory which can explain
the observed behavior, we will also have an empirical basis from which to discuss
and experiment with alternative methods of control.

From the previous two chapters we are convinced that the theory must accoiont
for the economic decision processes of the individuals involved. Since no other
alternatives seem to be available it appears that we should construct our theory
upon the foundations provided by the theory of human decision behavior. That is
to say, if our appreciation of the situation is correct what we need to do is
take the general theory of decision behavior as our theoretical base and by adding
the appropriate information and decision rules develop a testable theory of the
behavior in question. Because all decision processes can be represented by ordered
structures of information processes our task is quite straight forward — it is to
isolate and identify both the requisite information and decision processes. Once
OUT hypotheses are formulated and the theory is constructed the next step is to
subject the theory to empirical test. If the theory survives the test or tests
our task is complete. For with this theory we can now explain the behavior which
stimulated our interest and this theoretical activity. Manifestly, the principal

265

components of such an endeavor consist of first developing the individual
hypotheses and then submitting these hypotheses to a process of refutation
by empirical test. This chapter is directed toward an examination of both of
these processes.

1/
1. On the Construction of Decision Theories

The theory of human problem solving posits the existence of a memory, a set
of information processes, and a program of processing rules. Thus, if theories
of decision behavior are to be based upon this foundation then behavioral
theories must include these three postulates as part of the total set of hypotheses.
Further, in order to construct a theory to explain a particular set of behavior
it is necessary to specify the empirical interpretation of these postulates in
complete detail. It is not sufficient, for exanrple, to postulate that the
economic factor in question has a memory. For just any memory will not serve
the purpose at hand. Before the postulate about the structure of memory has
empirical meaning the interpretive rules must specify both its content and the
order in which the items are associated to one another.

In the theory of trust investment the postulate about the structure of the
memory is given empirical meaning by a number of interpretive rules. First, since
the theory deals with that part of the investor's memory relevant to the port-
folio selection process, the primary criterion by which conrpanies are listed in
memory is noted. Once the companies are specified as being ordered by industry
the appropriate attributes of each conrpany as well as their values need to be
discovered. These attitudes and values are associated by a particular memory

l/Thls section is in part indebted to G. P. E. Clarkson and W. F. Pounds, op. cit

- 266

structure to each of the corapariies that are being considered. Since the theory
also includes information on industry as well as general economy indicators,
these items must also be related by a specific structure to the information
already placed in memory. In the trust investment case the detailed information
is drawn from observations on one individual. However, the general requirement
for the specificity of the contents of memory must be satisfied whether the
theory concerns the behavior of one or many individuals. For the contents of
the memory and the relevant items in the environment (which can frequently be
represented as a part of the memory) constitute the initial conditions. Unless,
the initial conditions of a theory are both specifiable and empirically
observable it is not possible to submit the theory to empirical test. Consequently,
the identification of the struct\n-e and contents of memory is the first important
step in the construction of a theory of decision behavior.

The second main hypothesis asserts the existence of a set of primitive
information processes which operate on the information already located in the
memory. While there are undoubtedly a number of ways in which these information

processes could be specified the representation employed by this theory is defined

3/
by the language that is used--. IPL V is a formal language which satisfies the

syntactical rules governing languages in deductive systems. Accordingly, a

theory stated in this language is able to satisfy the formal requirements of a

• 2/For detailed investigations of memory structures see: E.A. Feigenbaum,
op. cit. and R. K. Lindsay, op. cit.

3/This language is presented in complete detail in A. Newell, (ed)
Information Processing Language V Manual, Prentice-Hall, Englewood Cliffs, New
Jersey, I96I.

- 267 -

deductive system and can constitute the language for a scientific theory.
The language itself is composed of a set of basic information processes and a
number of interpretive rules for executing the information processes. The
information processes, denoted by the prefix J, are in tixrn based upon an
hypothesized structure of the memory. As a result, these processes are
principally concerned with finding^ deleting, adding, re-ordering, and manipulat-
ing the items associated in list structures of the memory. These specific
processes are the empirical interpretations of the general class of primitive
information processes. Even though it is not asserted that they represent
a complete set of such processes, to employ this language is to adopt the
hypothesis that these processes are sufficient for the pujrpose at hand. That
is to say, in order to empirically specify a theory's hypothesized decision
processes this language provides a sufficient set of primitive information
processes so that either by themselves or in appropriate combinations they are
the requisite interpretive rules. Without such a set of interpretive rules
hypotheses about decision processes vould be devoid of empirical content. Despite
the fact that these primitive processes could be specified in a number of different

languages, the actual existence of IPL V provides the necessary assurance that

"~~ 5/

hypothesized decision processes can be empirically interpreted.

The third postulate claims that observable decision behavior is a

consequence of a set of rules or decision processes which combine the primitive

4/For further discussion of these requirements see Chapter 2, sec. 1 and the
references cited there particularly: G.P.E. Clarkson, The Theory of Consumer
Demand, op. cit. Ch. 2.

5/A number of these points are discussed with reference to particular examples
of human decision processes in: H. A. Simon and K. Kotovsky, op. cit.

268 -

information processes into vhole programs of processing. As has already been
noted, a theory of decision behavior is a statement of the ordered structure of
decision rules which describe the decision behavior under investigation.
Consequently, in order to construct a theory of a particular stream of decision
behavior, it is necessary to isolate and identify the decision rules which
guide and constitute the decision-making process.

For example, consider once again the portfolio selection process of a trust
investor. Since it is hypothesized, that all decision behavior can be analyzed
in terms of a set of decision routines which act upon a set of information
contained in the memory, (the memory being the general repository of all pertinent
information including that supplied by the environment) this theory represents
the investment process as consisting of three major segments: (a) processes
concerned with the analysis and selection of, from an initial set of stocks, a
list of securities which are ciirrently suitable for purchasingj (b) processes
which determine the investment policy appropriate for each account; (c) processes
which perform the actual selection of the individual securities for the portfolio
for each account.

In accordance with the first postulate the information in the memory consists
of ordered lists of data on specific economy and industry variables as well as
data for a ten-year period on the relevant attributes of the total set of
companies (eighty in this case) and their securities o Section (a) of the theory
contains decision processes which employ these data to create various ratios
and indices by which it will be possible for other processes to judge the relative
performance and relative value of one company's stock against another. Data on

- 269

expectations are also included and are reduced by additional processes so that
patterns can be found and recognized. A pattern recognizing process is then
employed to create a list of stocks suitable for current acquisition. This list
is derived from the original set of securities and its contents depend directly
on the outputs of the relative performance, relative value^ and expectational
processes.

Section (b) of the theory consists of a set of decision processes vhich
formulate an investment policy for each account. The investment policy is
derived by processing certain data taken from the bank's records and the legal
instrument setting up the trust account as well as data on specific attributes
of the client or the trust account. The principal hypothesis of this decision
process is a discrimination net vhich associates certain patterns of attributes
and their values with specific investment policies.

In section (c) the portfolios are chosen by applying the selection processes
associated with each investment policy to the list of securities generated by
section (a). Concurrently, decision procedures are employed which determine how
many shares to purchase of each security that is selected as well as how to ensure
that the portfolio is appropriately diversified. The end result is a portfolio
of securities for a specific trust account where the theory specifies the name
of each security, the number of shares to purchase, the price per share at that
time, and the total amount to be expended for each security.

From this brief description it is apparent that this is a moderately large
and complex theory of decision behavior. In order to develop the three hypotheses

6/ These processes are represented by discrimination nets^, an example of which
is given in Chapter 12, p. 253.

- 270 -

of the theory of human decision-making behavior were empirically interpreted by
adding the appropriate information and decision rules. Each decision process
was constructed by observing and reviewing in detail a particular investor's
decision behavior. Consequently^, to construct such a theory it is inrportant to
know how to discover^ collect and fit into the general structure the requisite
information and decision rules. This may sound like a formidable task, but the
general theory provides the structure with which the data are to be sorted and
arranged as well as an outline which guides the observational process. Accordingly^
even though the identification of the components of specific decision process
requires careful observation^ the task is made quite practicable by knowing what
to look for.

Within this framework the task of constructing a theory to account for a
particular sequence of observed behavior becomes a problem of uncovering the
principal decision rules employed by the decision-maker. To obtain these data a
variety of interview and observational techniques can be employed. The following
list is merely an outline of some methods that have been used to advantage:

a) Interview

One method of discovering the components of an individual's decision
process is by the question and answer approach of a normal interview. If the
decision process in question is one which is frequently employed by the individual,
questions about the procedure followed, the records consulted^ the information
that is processed, and the output can provide a rough outline of the more important
parts of the decision process. Interviews are frequently more rewarding if there
is one person to ask the questions while another takes notes. But, it must not be

- 271 -

overlooked that this approach in effect asks an individual to describe and in
part justify why he behaves as he does. To the extent that many people are
unable to describe in detail by what process they reached a particular decision
the information gathered in this manner must be regarded with some caution,
b) Protocols of Decision Behavior

A more reliable guide to the identification of decision processes is by
taking protocols of an individual's decision behavior. A protocol is a tape
recorded transcript of the verbalized thoughts and actions of a subject who has
been instructed to think or problem solve aloud- Consequently^ the transcipt is
a record of the subject's thought processes while he is engaged in making a
decision. Since a protocol is a detailed description of what a person does

while problem solving it avoids some of the difficulties inherent in the inter-

1/
view and questionnaire techniques.

c j Constrained Problem Solving Interviews

A variant on the interview approach is to ask the subject to write out

a decision process which he is willing to defend as being able to accomplish the

task at hand. By requesting him to write out the decision processes and then

7/ "Thinking aloud is just as truly behavior as is circling the correct answer
on a paper-and-pencil test. What we infer from it about other processes going on
inside the subject (or the machine) is, of course, another question. In the case
of the machine, the problem is simpler than in the case of the human, for we can
determine exactly the correspondence between the internal processes and what the
machine prints out," Ac Newell, J. C. Shaw, and H. A. Simon, "Elements of a Theory
of Human Problem Solving, " op. cit., p. I56.

The relevance of protocol data for testing pvirposes is discussed later in this
chapter o

8/For examples of the application of this technique see: W. F. Pounds, op, cit.

272 -

posing such questions as "but what happens if ", he may be led to

expand and alter what he had previously written down. Such modifications
provide useful information on what are the important items in the decision
process. Additional data can be obtained if it is possible to get the
subject to employ his written decision routine to make one or more actual
decisions. If, after observing the behavior of his own routine he is
satisfied with its behavior, then this is a good basis from which to develop
specific hypotheses concerning his decision behavior.

Throughout the data gathering process checks must be made to ensure
that the relevant parts of the decision process are being identified. One
way of checking initial hypotheses is to construct simple nets and decision
rules. By applying these rules to the appropriate data one can readily
determine whether they are going to be sufficient to reproduce the observations
recorded, for example, in the protocols. If a record of past decisions is
available hypotheses can be tested against these data as well. The object of
this testing is, to identify the principal decision processes and data inputs
which must be included if the observed behavior is to be explained. The
construction of such a theory is, however, only the first part of the total
process. Once a theory is built it must be tested. And the remainder of this
chapter is devoted to an examination of this stage of the experimental procediire.

2. On Testing Decision Theories
One theory is a "model" of another theory only if their postulates and

hypotheses are structurally similar. Hence, a particular application of a

9/For a stimulating as well as intensive examination of the relation between
models and theories see: M. Brodbeck,' "Models, Meaning and Theories, " in L. Gross,
(ed) Symposium on Sociological Theory, Row, Peterson and Co., 1958, pp. 373-^03.

- 273 -

theory to a specific set of decision processes is a model of those processes.
For example, when the general theory of problem solving behavior is employed
to develop a theory of investment behavior, this application is a model of
the general theory. Similarly, when a theory of trust investment is applied
to a particular individual, the theory of the specific investor is a model
of the investment theory. Moreover, as it is usually difficult to find general
data against which to test general theories, theories are customarily submitted
to empirical test by testing specific models against particular collections
of data. In short, the process of testing a theory is in actuality a process
of submitting a particular model of this theory to specific tests.

In order to examine the testing procedure, assume for the moment that one
has at hand a theory of a particular set of decision behavior. Manifestly,
the testing procedure for such a theory must take into account the fact that
it is necessary to be able to check the final output as well as the decision
processes by which the output was produced. Accordingly, the first step is
to construct a specific model of the theory by specifying, where necessary,
the particular parameter values (initial conditions) and decision rules that
pertain to the context in which the theory is to be tested. Next, the model,
i.e. the statements and decision rules which describe the behavior under
investigation, and the statements containing the appropriate initial conditions
are translated into a suitable computer language--e.g. Information Processing
Language V. The computer is then activated and, as in the more familiar case
of scientific theories^, the logical consequences are derived by performing the
individual operations according to the specified rules. Finally, to conduct

- 274 -

the test the behavior generated by the model is compared to the observed
behavior of the individual or individuals under investigation. When the model
yields results that are consistent with the observed^ the theory is said to be
sufficient to account for the recorded decision behavior.

Given such a model it is now possible to examine a number of problems that
are raised by this testing procedure. To begin with what criteria are to be
employed to discriminate between models that successfully reproduce observed
behavior and those that do not? One answer is to accept the model as being
corroborated when the results generated by it are consistent with those obtained
from human decision-makers. In other words, accept the model, and hence the
theory^ when it is sufficient to account for observed decision behavior.
Such an answer^ however, does not provide an operational criterion for
distinguishing when the results are to be considered "consistent." Unfortunately,
there is no one criterion which can directly perform this service. As in any
branch of empirical science it is not possible to "prove" that a theory or model
is "empirically true." The best that can ever be said for a theory is that it
has not yet been disconfirmed by empirical test. Accordingly^ one cannot prove
that a model of certain decision processes is empirically true. The best that
can be done is to submit these models to more and more stringent tests in order
to eliminate those hypotheses, and consequently theories, that are demonstrably
false.

One testing procedure that meets this latter requirement is the adaption

- 275 -

of Turing's Test — proposed by Newell and Simon. — Turing was concerned with
creating a test which would determine whether a machine could think. He called
his test an imitation game and it proceeds as follows:

The game is played by three contestants--a machine^, a human and an
interrogator--and there are two channels of communication (say teletypes) which
link the interrogator, separately to the human and the machine. The object
of the game for the interrogator is to specify the identity of the two players.
Active questioning by the interrogator is allowed, and the machine's task is
to delude the interrogator while the human is supposed to want co do his best to
reveal his "true" identity. The interrogator succeeds and the machine is
declared unable to "think," if on a given number of trials he correctly
identifies the players on a better than chance basis.

The adaption of Turing's Test to the problem of discriminating between the
output of a specific model and the decision behavior of the human proceeds
in a similar way: Data are gathered on the decision behavior of one or more
subjects by making protocols or other records of the decision processes. The
output generated by the model is also collected and can now be directly compared
with the recorded human behavior. This comparison can be carried out at many
levels of detail. The only restriction is the level of detail provided by the
data on the human's decision processes. When the model produces behavior that
meets the criterion of Turing's Test the model is sufficient to account for the

— A.M. Turing^ "Can a Machine Think?" Mind, Vol. 59, October, 1950^
pp. 433-460, (Reprinted in E.A, Feigenbaum and J. Feldman, op. cit . j, pp. 11-35),

— A. Newell and H,A, Simon, "The Simulation of Human Thought," in W. Dennis,
(ed) , Current Trends in Psychological Theory, University of Pittsburgh Press,
1961, pp. 152-179.

- 276 -

decision-making behavior under investigation. This test can be applied to the
output of the model as a whole as well as to the behavior of the individual
decision processes. In the former case the test might be considered to be quite
weak since there are presumably a variety of models that will yield a specified
output. But^ by carrying the matching process down to the level of the
individual decision processes the tests become more and more discriminating. In
brief, the strength of the test can be determined by the experimenters and our
confidence in the empirical validity of the model is manifestly a function of
the level of detail at which this testing procedure is carried out.

For example^ in order to determine the trust investment model's ability
to reproduce the portfolio selection process of the trust investor, one set
of tests consisted of comparing against each other four specific portfolios
chosen both by the model and the investor for the same accounts during the
first and third quarters of I960. To achieve a perfect score, the model not
only had to select the correct number of securities for each portfolio^ but
it also had to choose the same stocks and the same number of shares of each
security as was purchased by the trust investor. As can be seen from the

two examples in Figure 1, the similarity between the two sets of portfolios

12/

is quite striking. —

Since there are no doubt a variety of models that could generate the
same portfolios, the next series of tests are concerned with determining

12/

— For a detailed presentation and analysis of these portfolios see:

G.P.E. Clarkson, Portfolio Selection, op. cit. , Chapter 6.

- 277 -

whether the model's decision processes are consistent with the trust investor's.
To conduct this test a record of the model's decision behavior was made which
was then compared to the statements recorded in the investor's protocols. For
the model to pass these tests its behavior has to be sufficiently similar to
the trust investor's so that a close inspection of the two streams of behavior
do not provide a basis for deciding which is produced by the investor and which
by the model. While these tests did not unequivocally confirm the model as
well as its individual decision processes, the evidence is such that it supports

the hypothesis that the model, and hence the theory, is sufficient to account

13/

for a considerable portion of the trust investment process, —

It is apparent, from this discussion, that theories of decision behavior can
be subjected to a series of empirical tests. Moreover^ these tests can be applied
to the theory as a whole as well as to the theory's individual hypotheses. As
a result, Turing's Test is a powerful method for determining the empirical
validity of theories whose object is to explain human decision-inaking behavior.

3. The Problem of Errors

Unfortunately, the discriminatory power of these tests is somewhat impaired
by the absence of suitable measures for assessing the "type" and "degree" of
a model's failure. That is to say, although some models may account for
observed behavior. with great accuracy, others will not be so successful. Hence,
the question immediately arises of how to classify, identify and measure the

13/

— The evidence and the tests are presented in detail in: lb id . , Chapter 7,

278 -

FIGURE 1

Account 1^ Selected January 8^ 1960

Investment Policy: High growth with little concern for dividend income,

total funds: $22,000

MODEL'S PORTFOLIO

INVESTOR'S PORTFOLIO

Stock

Price

Total

Stock

Price

Total

General American Trans-
port Company

$ 70

4,200

Corning Glass

$145

4,350

Dow Chemical

4.950

Dow Chemical

4,900

IBM

440

4,400

IBM

4^0

4,400

Merck and Company

^,740

Merck and Company

4,000

Owens Corning

Fiberglas
ESTIMATED Yield 1.

.6%

88 3,960
$22,250

Owens Corning

Fiberglas
ESTIMATED Yield

.6%

4,450
$22,100

Account 2, Selected June 10, I960

Investment Policy: High income with possibility of price appreciation,

total funds: $37,500

MODEL'S PORTFOLIO

100 American Can Company

100 Continential Insurance

100 Equitable Gas Company

100 Duguesne Light Company

100 Libbey Owens Ford

100 International Harvester

100 Philadelphia Electric

100 Phillips Petroleum

100 Socony Mobil

ESTIMATED Yield 4„87o

Price

Total

$3,700

100

5. ,100

100

3,600

100

2,400

100

5,000

100

4,400

4,900

100

4,300

100

3,700

100

INVESTOR'S PORTFOLIO

Price Total

American Can Co. 38 $3,800

Continential Ins, 51 5,100

Equitable Gas Co, 35 3,500

General Public

Utility 24

Libbey Ownes Ford 51

National Lead 91

Philadelphia Elec, 49

Phillips Petroleum 43

Socony Mobil

$37,100

,400

,100

,550

,900

,300

,600

F.STTMATF.S Yield 4 , 6?„ $37,250

- 279 -

types of "errors" such models must contain. One answer is to postulate that
all errors are due to an incorrect specification of the model's decision
processes. If this rule is taken as the principal criterion then whenever

errors occur this is a signal to go back and retest the appropriate parts of

14/
the model until such time as its output can account for the observed. —

Such a rule^ despite its apparent simplicity^ does not provide a complete

answer to the problem. If all errors in the model's behavior are considered

as errors in its decision processes then theorists will be motivated to include

as many hypotheses and parameters as are necessary to produce the desired

stream of behavior. Consequently, models will tend to contain an abundance

of free parameters and general rules about parsimony will tend to be ignored.

This is not to say that as these models are subjected to an increasing number

of empirical tests ^ excess parameters will not be deleted where possible. Rather,

it is being suggested that unless some measures are developed which permit

the determination of the degree to which a model fails a particular test^ the

tendency will be to construct models which have a large number of free parameters

and as a result are capable of being "fitted" to a wide range of observed

behavior. The problem is clearly one of how to distinguish between models

which are in some reasonable sense empirically "true" from those which are

corroborated simply because they contain so many free parameters that they can

be fitted to the available data. Turing's Test is a method for discriminating

14/

— For a further discussion of the error problem see; Part 2, "Simulation

of Cognitive Processes" in E.A. Fergenbaum and J. Feldman, op. cit.

- 280 -

between those models which can and those which cannot produce behavior that
is indistinguishable from its human counterpart. But of the set of models which
pass this test, how is one to avoid accepting as empirically confirmed models
which have passed the test for essentially trivial reasons? In effect, the answer
to this question is no different for models of decision processes than it is
for other models in empirical science. In the physical sciences it is never
possible to tell whether a particular theory or its model is en^irically true.
The best that can ever be said is that so far it has not been disconfirmed
by all of the tests to which it has been submitted. Thus, until such time as
a theory is disconfirmed or replaced by one which is more comprehensive, the
theory must be accepted as it stand3--an empirically testable theory of a
particular set of behavior.

To illustrate these remarks consider for a moment the task of deciding
whether a specific model of the theory of problem solving encompassed by the
General Problem Solver is to be consider corroborated or confuted by a particular
test. The model in question was constructed to account for the behavior of
certain subjects when they were engaged in the solution of a set of problems
m symbolic logic. After providing the model with the requisite vocabulary,
a set of definitions sufficient to allow it to consider problems in symbolic
logic, and the initial conditions, i.e. the axioms of the system and the theorems
to be proved, the model was instructed to develop the required proofs.^
Concurrently, protocols were taken of the decision processes of a number of

15/

— See Chapter 12, p. 246-47 and the references for the principal

hypotheses of GPS .

- 281 -

students. Their task being to construct proofs for the same theorems. To test
the model the output of the model's processes is compared with the recorded behavior
of the subjects. Such a comparison is provided by the following excerpts from
the decision behavior of a student and the model^ when they were considering the

problem of transforming the statement R
Model's Behavior

1. L^: (Q P) • R

2 . L : R • (~ P =J Q)

3. Goal 0: Transform L, and L

—1 -o

4. Match gives position difference
(A P)

5. Goal 1: Reduce A P between L, and L

— 1 -o

6. Search list of rules

7. Goal 2: Apply R to L

(~ P 3 Q) into the statement (Q P) • R

Student's Protocol

(Expression to be obtained) —

(Expression given at start)

(Goal set by experimenter)

I'm looking at the idea of
reversing these twc things now,

(Thinking about reversing what?)

The R's „ . , .

16/

8,
9.

10.

Match; R. applicable

Test rule functions:
reduces A p

no others

11 o Set to execute R when analysis

complete

-1

Then I'd have a similar group at
the beginning but that seems to be,

I could easily leave something
like that to the end, then
I'll

■k -k ic

it ir *

— For a detailed discussion of the model and this test see; A. Newell
and H.A. Simon, "The Simulation of Human Thought," op. cit . , pp. 155-176.

— Statements in parentheses are experimenter's statements and explanatory
statementSo All other statements are the subject's.

282

Model's Behavior

23. Goal 7: Apply R^ to right L,

24. Match: R- not applicable

25. Goal 8: Apply R, to L,

26.

28.

Match: R, not applicable

Test rule functions;
doesn't reduce A p

.18/

Student's Protocol

Well.... then I look down at Rule 3

and that doesn't look any too
practical

Now 4 looks interesting

Its got three parts similar to
that. . .and. . .there are dots so
that connective. . .seems to work
easily enough,

but there's no switching of order .

•k it ic

•k -k -k

33.
34.
35.
36.

37,

38,
39.

40.
41.

Search rules again, but don't

reject»without attacking subproblem

Goal 14: Apply R, to right L,

Match: R. fails, right
right L, has r> (A c)

Test rule functions: reduces A P,

no others

Set to execute R^ , if applicable

I need that P and Q changes so,

Goal 15: Reduce A £ between right
L, and R

Search list of rules, for rule

I've got a horseshoe there.

That doesn't seem practical any
place through here.

I'm looking for a way now, to get
rid of that horseshoe.

with ri that reduces A c

18/
function.

But the subject mistakenly thinks R, is applicable; therefore tests its

283

Model's Behavior

42. Goal 16: Apply R^ to right L

43. Match: R, applicable

Student's Protocol

Ah... here it is, Rule 6.

* *

■k -k it

67.

Match: L, identical with L
—4 — o

And. . .that's it. — '

19/

Given this evidence is it possible tc decide whether the model has been
confirmed or disconfirmed by this test? Manifestly, this is a difficult
question to answer directly. For in a number of ways the decision processes
of the model closely parallel those of the student. Yet there are cases,
notably line 26, where the student errs and unnecessarily proceeds to test the
function. Also the model examines the applicability of all the rules, while
the student provides evidence of only examining the first few. This is not to say-
that the model's decision behavior does not come close to matching the student's.
especially if one imagines the model generating grammaclcal sentences instead
of chopped up statements. But since a method has not yet been devised for
measuring the difference between these two streams of verbal behavior it is not
possible in this case to directly answer the question: how close is close
enough? If a technique were available for measuring the difference between two
sets of verbal behavior^ then it would be possible to inspect these models for
excess parameters. For, if. the "goodness of performance" is measurable, empirical

19/

— A complete listing of these statements from which these are taken is

given in Ibid. , pp. 171-173.

- 284 -

explorations of the model will permit the identification of those parameters and
processes which can be deleted without lowering the level of performance
below some acceptable standard. Such is the case, if the model produces an
output which is amenable to numerical analysis.

For example, if a theory is concerned with the pricing process within a
firm, part of a particular model's output will be a collection of items to each
of which is attached a specific price. The actual prices set for the items can
be readily observed and the differences between these two sets of prices noted.
For a given level of predictive success, say 907o, the model can now be

experimented with to see which set of processes and parameters can be deleted

20/
so that its ability to predict the actual prices never falls below 90%. —

Consequently, as long as it is possible to measure a model's predictive success,

and as long as it is possible to agree on the significance of specific levels

of success, then empirical explorations can be conducted so that excess parameters

and processes are deleted and parsimony preserved.

The essence of this testing procedure is to employ predictions to confute

or corroborate a theory's hypotheses. One striking way to accomplish same

would be to infer from an existing model one or more propositions about decision

behavior which have not yet been put to test. If they are not disconfirmed then

20 /

— It should be noted that a theory has already been constructed to account

for pricing decisions in a department store. Further, in the tests that have

been conducted, a particular model predicts correct prices, including special

sale prices and mark-downs, approximately 95% of the time. While tests have not

been conducted to determine the number, if any., of excess parameters and processes,

this model meets the conditions required for such empirical explorations. The

model is described and the data are presented in; R.M. Cyert and J.G, March,

A Behavioral Theory of the Firm, Prentice-Hall, Englewood Cliffs^ 1963, Chapter 7.

- 285 -

such evidence would provide strong support for the original hypotheses. Such
tests can serve as corroborative evidence because the model's hypotheses can
also be subjected to test. If this were not the case^ then theories of decision
behavior would no more be a part of empirical science than those of econometrics
or classical economics.

4, Heuristics, Algorithms and Statistical Tests

So far the discussion has focused on the problems raised by subjecting theories
of decision processes to Turing's Test. While it has been noted that this test
can be applied in varying strengths it has also been pointed out that when comparing
two sets of verbal behavior it is not yet possible to reliably measure the degree
of difference or error between them. Despite the absence of such a measure
it is still possible to distinguish between models which are sufficient to
account for observed behavior and those that are not. Accordingly, even though
this difference is not expressible as a numerical function of specific variables,
these models can be subjected to a series of empirical tests.

It is important to remember that the testing procedure can be applied to
the model's decision processes and that the limit of detail at which this testing
can take place is defined by the level of detail recorded in the protocols. By
emphasizing the fact that the decision processes can be submitted to test a
criterion is provided for identifying the types of decision processes that are
appropriate for any specific model. In particular, it provides a criterion
by i^hich the appropriateness of heuristic or algorithmic decision rules can be
decided.

To illustrate this point consider for a moment the decision processes
which are employed to select portfolios in the investment model. These processes

- 286 -

are stated in the form of heuristics--!. e. , they describe the search and selection
procedures which delimit the available alternatives. The restricted set of
alternatives in turn provides the basis for the final selection. A selection
is made by choosing the first security that passes the relevant criteria from
each of a number of industry lists. Thus, selections are made sequentially,
and many securities, although quite suited for the particular portfolio, may never
even be brought up for consideration. On the other hand, if a set of
algorithmic decision rules were employed, e.g. choose only those securities
which optimize some criterion function where the process of optimization was
specified in complete detail, the behavior generated by such processes would be
quite different from that of the investment model. Since the decision behavior
generated by both these types of decision rules can be compared with behavior
recorded in protocols, it is clear that on this basis it is possible to reject
those processes that are inconsistent with the observed behavior.

For example, assume for the moment that one wants to test the hypothesis that
the trust investor employs algorithmic decision rules. Further, assume that

these rules take the form of some optimizing routine, e.g. choose those securities

21/
which subject to certain constraints maximize expected returns. — With such a

decision rule it is clear that the model will examine all of the relevant

alternatives before selecting its portfolio--an optimizing decision rule implies

that ail alternatives are to be examined before a choice is made. Accordingly,

21/

— For an excellent exposition of such a position see: H.A. Latane,

"The Rationality Model in Organizational Decision-Making," in H.J. Leavitt, (ed) ,

The Social Science of Organization, Prentice-Hall, Inc., Englswood Cliffs, 1963,

pp. 85-136.

- 287 -

this pattern of search and selection behavior can be contrasted with the
observed, and consistencies as well as inconsistencies noted. Also, if an
algorithm of this sort is employed, processing time should be roughly equivalent
for each security examined. For, given the decision rules and the appropriate
data, there is no reason to suppose it will take longer to evaluate the expected
returns of one security rather than another. But human processing time can also
be observed. And if, as was the case in the investment study, some securities
are accepted or rejected quite rapidly while others are processed for longer
periods, then this evidence would tend to confute what might be called the
algorithmic hypothesis. When the decision processes themselves are subjected
to a process of refutation by empirical test, the debate over heuristic vs.
algorithmic decision rules rapidly disappears. For it is highly unlikely that
two such different types of processes could generate identical s'treams of

decision behavior. The problem of choice is simply resolved by selecting the

22/
one that most closely accounts for observed data. — -

When carrying out such a series of tests it has already been mentioned that

if the model's predictive success can be adequately measured, then excess free

parameters can be isolated and deleted by repeated empirical explorations. The

point to note in this respect is that statistical tests are unfortunately of

slight value in helping to isolate the surplus or excess free parameters. If these

models were stated in terms of standard difference, differential, or stochastic

22/

— For a stimulating example of the power of a specific set of heuristic

decision rules to reproduce the search and selection procedures of grandmaster

and expert chess players see; H.A. Sinran and P. A. Simon, "Trial and Error

Search in Solving Difficult Problems: Evidence from the Game of Chess,"

Behavioral Science, Vol. 7, October, 1962, pp. 425-429.

- 288 -

equations with a limited number of independent variables^ then the problem of

excess parameters could be answered within the confines of the identification

23/
problem. — But decision theories are stated in terms of programs of processing

rules which are not amenable to a similar mathematical analysis. Despite the

fact that the problem could be considered in an analagous manner the standard

mathematical methods of solution are no longer applicable.

For example^ consider the problem of estimating the statistical significance
of each parameter in a small set of decision processes. Assume for the moment
that these processes describe a sequential selection procedure which consists
of fifteen different items. Also assume that a statistical test is to be
employed^ say an analysis of variance test, which will permit the delineation
of those parameters that play a statistically significant role in accounting
for the observed data. In order to conduct this test two items must be known
or be capable of being estimated; the density function of the population
from which the data is to be drawn, and the sample size required for statistically
significant results to be produced.

Taking these points in reverse order it is clear that if samples of twenty
will generate significant results, and if each of the fifteen items were employed
each time the decision process were used, then twenty experiments would provide
the requisite data. But it frequently happens that not all decision points are
evoked each time a decision process is employed. If it takes on the average
twenty-five applications of the selection process to ensure that each item has been

23/

— See Chapter 8, section 3 for a discussion of this subject.

- 289 -

evoked at least once^ then it will take approximately five hundred experiments to
generate samples of at least twenty observations for each parameter. Further,
if the selection process itself is not employed each time this part of the model
is subjected to empirical test (e.g. if the process in question is an infrequently
used sub-routine), the number of experiments required has now increased to a
very large and impractical number. — This, however, is a practical difficulty
which can no doubt in many cases be met by practical expedients. The principal
obstacle lies in estimating the characteristics of the population from which the

data are drawn. In an artificial case the data can be selected from nearly

25/
normalized populations. — But when dealing with theories that are intended to

account for observed behavior the data are provided by environment. And as noted

above, the empirical determination of population density functions is not

26/
without its difficulties. —

From this brief example it is clear that it simple not feasible to employ

standard techniques to examine the sample distributions and to evaluate the

statistical significance of each item in a theory of decision behavior. This is

not to suggest that the task of eliminating excess parameters is, for all

practical purposes, hopeless. Rather, the problem must be approached in. the same

24/

— For an excellent example of the problems posed by the m.easurement of the

statistical significance of specific parameters in a behaving system see:
C.P. Bonini, Simulation of Information and Decision Systems in the Firm, Prentice-
Hall, Englewood Cliffs, 1963, Chapters 7 and 8.

25/

— See for example: M.A. Geisler, "The Sizes of Simulation Samples Required

to Compute Certain Inventory Characteristics with Stated Precision and Confidence,"

Management Science, Vol. 10, January, 1964, pp. 261-286.

—'See the discussions of this point in Chapters 9 and 10, sections 2,
and 2 and 3 respectively.

- 290 -

spirit as is the development and testing of theories in any branch of science.
There theoretical speculations are controlled and refined by direct confrontation
with empirical observation. Therefore^ although the primary goal may be to
simplify and increase the power of our theories, progress can only be achieved
by the diligent application of empirical test.

Chapter 14

THEORIES OF ECONOMIC BEHAVIOR - THE CONSUMER AND THE FIRM

In the previous two chapters the discussion is directed toward an
examination of the task of developing theories of individual decision behavior.
While some of the evidence cited both in the text and the references is concerned
with economic decision processes, it is clear from the remainder that the empiri-
cal content of these theories of decision-making behavior resides in the ability
to test their hypotheses against a diversity of observable behavior. Our primary
interest as economists, however, is to be able to explain and predict the
behavior of aggregates of individuals and not just the behavior of the individuals
themselves. This is not to say that theories of individual behavior are of
little concern to economists. Rather, our interests will be best served if it is
possible to develop testable theories with which the behavior of collections of
individuals, such as consumers, as well as groups or organizations of individuals,
such as firms can be explained. Moreover, to fully analyze the behavior of an
economy it is also necessary to be able to explain the interactions among indivi-
duals, and among individuals and firms such as takes place in various markets.
In order to develop such theories it is clear that the first task is to isolate
and identify a set of testable relations which can serve as the empirical base
for these theoretical structures.

- 292

One method of approach is to start with a theory of organizational or firm
behavior from which it is possible to deduce testable hypotheses of decision
behavior. If the inferred relations are in fact corroborated, then they would
constitute the beginnings of scientific theory of organizational or firm decision-
making behavior. Manifestly this is, in outline form, the general procedure
which guided the development of the classical theory of the firm. It is also
apparent from the analysis in Part II that the classic approach is not able to
produce the desired, testable hypotheses. However, the existence of a behavioral
theory of the firm- -- a theory of firm behavior based upon observations of
organizational decision processes -- lends support to this general strategy.
If it is to succeed, it must be possible to deduce the required empirical rela-
tions as well as demonstrate that they are able to survive repeated tests. Yet
even if by employing this theory it were possible to establish a set of empirical
relations about firm behavior, only one part of the total task would have been
accomplished. This is not to suggest that to have constructed a testable theory
of firm behavior would not be an important accomplishment. But it would only
enable one to account for one of the three classes of behavior noted in the pre-
ceding paragraph.

- R. M. Cyert and J. G. March, A Behavioral Theory of the Firm, op. cit,

293

A second, a ideally more complete, solution can perhaps be found by beginning
with theories of individual, economic decision-making behavior. Such theories
must be capable of scoring repeated empirical tests, and, as already noted,
are to be based on a wide variety of observable decision behavior. The second
step is to employ the theories of individual behavior as the empirical basis for

theories of organizational or firm behavior. In effect, 1 am proposing that a

2/
resolution of the theoretical and empirical obstacles can be found by "reducing"—

existing theories of organizational and firm behavior to testable theories of

individual decision behavior.

For this reduction process to succeed it implies that the theories of
individual, economic decision behavior must be constructed in such a fashion
that they are sufficient to account for individual as well as group behavior. In
order for this result to occur two conditions must be satisfied. The first is
that the laws or hypotheses of group or organizational theories must be deduc-
tible from the theories of individual behavior. If a theory of organizational or

— For an excellent discussion of the process of reduction in empirical

science see: E. Nagel, The Structure of Science, Harcourt, Brace and World,

New York, 1961, Ch. 11; and P. Oppenheim and H. Putnam, "Unity of Science as a

Working Hypothesis," in H. Feigl, et al. (eds.), Minnesota Studies in the

Philosophy of Science, University of Minnesota Press, Vol. II, 1958, pp. 3-36.

This argument, with respect to the development of a testable theory of
consumer behavior, is presented in greater detail in: G. P. E. Clarkson, The
Theory of Consumer Demand , op . cit . , Ch . 7 .

294

firm behavior contains terms and expressions which do not appear in the relevant
theory of individual behavior then it is not possible to immediately meet the
first criterion. In this case various assumptions or further hypotheses must be
introduced to link the terms in the theory of individual behavior to the terms
and relations contained in the orgainzational theory. For example, if hypotheses
about the role of goals and the resolution of conflict in the structure of
organizational decision processes are to be inferred, then the theory accounting
for individual behavior must either already contain these terms and expressions
or further postulates must be introduced to permit the derivation to take place.

The second main condition is that the basic postulates or hypotheses of the

3/
individual theory must be both testable and reasonably well confirmed— by the

available evidence. The purpose of this criterion is to ensure that essentially

trivial reduction theories are not constructed. It would not be an important

scientific accomplishment merely to develop a set of hypotheses about individual

behavior from which theories of firm and organizational behavior could be deduced.

if these theories could not be subjected to empirical test. Hence, before a

theory of individual behavior can be accepted as a possible basis for this

— The condition of being "reasonably well confirmed" is admittedly vague.

But the problems involved in determining a degree of confirmation go beyond the
scope of our analysis. For a detailed and lucid presentation of one interpreta-
tion of the meaning of "degree of confirmation" see: R. Carnap, Logical Foundation
of Probability, University of Chicago Press, Chicago, 1950, and "Statistical and
Inductive Probability," in E. H. Madded, (ed.), The Structure of Scientific
Thought . Houghton Mifflin, Boston, 1960, pp. 269-279. For a different interpre-
tation see: K. R. Popper, Conjectures and Refutations, Reutledge and Kegan Paul,
London, 1963, especially Chs. 3, 10 and 11.

- 295 -

scientific venture it must be demonstrated that its hypotheses are both capable
of test and have already survived a number of such tests.

In the preceding two chapters a theory is presented which meets these
formal requirements- -i.e . , the theory contains testable hypotheses and the avail-
able evidence demonstrates that some of these hypotheses have survived a number
of tests. Since the formal criteria are satisfied the task that has yet to be
completed is to develop the economic theories of firms, consumers and markets
that are consistent with this approach. Accordingly, the remainder of this
chapter and the whole of the next are devoted to an examination of the methods
by which the required theories can be developed.

4/
1 . On a Theory of Consumer Behavior—

In order to explain the decision behavior of consumers a theory is needed
which can be employed to account for the observable diversity of decisions made
by individual consumers. While some economists may be particularly interested
in consumer decisions with respect to purchases of durables, others are interested
in the processes which determine the purchases of comestibles, clothing, enter-
tainment, etc. Concurrently, there are still other investigators who are concerned

-'This section is indebted to: G. P. E. Clarkson, The Theory of Consumer
Demand: A Critical Appraisal, op. cit., Ch. 8.

- 297 -

with the processes by which specific types, makes or brands of articles are
purchased within a given category. If a theory is to explain consumer behavior,
it must be possible to adapt it to each of these varying circumstances. That
is to say, it must be constructed in such a fashion so that with the addition
of the appropriate information and interpretive rules it can be applied with
equal success to each of these specific decision situations.

To develop such a theory there are two possible strategies which might be
adopted. The first would be to inspect in detail the decision processes of a
number of consumers for each of the major commodity categories. From such obser-
vations theories of these specific decision processes would be constructed so
that the observed behavior of these consumers could be explained. Once the
theories had survived a number of tests the theories themselves would be examined
in order to detect the general characteristics that they had in common. From
such general characteristics a general theory of consumer behavior would evolve
which in turn, with suitable amendations, could be applied to explain specific
sets of behavior.

A second method of approach would be to begin with the general postulate
of the invariance of the structure of decision processes among decision-makers.
This postulate states that the structure of decision processes is the same for
all decision-makers. Thus, the structure of a general theory of consumer behavior
can be directly inferred from the structure of the theory of individual decision
behavior. A general structure, however, cannot serve directly as a testable

- 298 -

theory of a particular set of behavior. In order to function in this manner
the general structure has to be conjoined with the appropriate detail on the
relevant decision processes. In effect, this would entail adding to the general
structure the requisite detailed processes and their concomitant data, the latter
being developed by an empirical analysis of consumer decision behavior.

Both of these strategies clearly require a detailed study of consumer
decision behavior. At the same time, they are based on the general premise
that the object of this theoretical exercise should be a general theory of
consumer behavior which can be adapted to the explanation of specific events
by the inclusion of certain data and decision rules. That is to say, if a
general theory of consumer behavior is to be developed it can be considered as
an "ideal" theory, where the additional data and decision processes are the
interpretive rules which permit the ideal theory to be related to and to explain
the behavior of a particular consumer,—

To illustrate this general approach consider once again the general theory
of human problem solving, GPS. This theory essentially consists of two separate
components. The first is a set of general hypotheses about the structure and
content of problem solving decision processes. These hypotheses include such
items as general methods for solving problems, the basic decision processes

— It should be noted that the natural sciences frequently use this
technique of formulating theories to account for "ideal" cases. Almost all
the well-known physical laws, e.g., the gas and gravitational theories, are
formulated in this manner; and as long as a set of interpretive rules exist
these theories can be tested against actual observations. See, for example,
the excellent discussions of this point in: E. Nagel, "Problems of Concept
and Theory Formation in the Social Sciences," op. cit.; and C.G. Hempel,
"Typological Methods in the Social Sciences," op. cit. For further examples
see: J.W.N. Watkins, "Ideal Types and Historical Explanation," in H. Feigl
and M. Brodbeck, op. cit., pp. 723-743.

- 299 -

available to the theory and the structure of the memory. For the theory to
be applied to a specific situation the data and decision rules pertinent to
the second component must be added. These items consist of the vocabulary,
special definitions, and other data necessary to interpret the specific problem
situation for the theory.— As a result, GPS is a general or ideal theory of
human problem solving which must be conjoined with the appropriate interpretive
rules before it can be employed to explain the decision behavior of an individual
problem solver.

In a similar manner, therefore, a theory of consumer behavior would consist
of general hypotheses about consumer decision processes, basic informative
processes, and the structure of memory which when appropriately interpreted
would be sufficient to explain observable behavior. To develop such a theory
it is clearly necessary to construct both components, i.e. the ideal theory,
and the interpretive rules. The former can in part be derived from the theory
of individual behavior. But the remainder of the general theory as well as the
interpretive rules can only be developed from a detailed inspection of consumer
behavior. While a general theory could apply to the behavior of one or more
consumers, to be able to test the theory the interpretive rules must specify
whether it is the behavior of a single consumer or groups of consumers that is
to be explained. To test a theory specif ic, data must be employed. Accordingly,
if the behavior of groups of consumers is to be explained the interpretive rules

-See Chapter 12, pp. 246-247.

/ ■'

- 300 -

nvust pertain to the decision processes of such aggregates. Similarly, if it is
an individual's behavior that is under investigation, the interpretive rules
need only pertain to this specific consumer. Hence, as already noted, although
the structure of the general theory can be derived from the theory of decision
behavior, it is only by empirical exploration of consumer behavior that the
detailed specification of this structure and the interpretive rules can be
determined.

To illustrate these remarks consider the general characteristics of
consumer behavior that would need to be included if the theory were to account
for observable decision behavior. Since each consumer has a certain level
of income a decision process is required which will allocate this income over
the various classes of commodities. While consumers may differ in the proportions
of their income which they allocate to each set of commodities, this allocative
process is common to all consumers. Further, within any particular social
and economic stratum regularities may appear among the specific proportions
selected by these consumers. Such regularities, if they are confirmed by
empirical research, can also be inspected for the rate at which they change
over time. If, as the evidence appears to indicate,— the allocative process
is reasonably stable these results would immediately lead to a specification of
one part of the allocative decision process. Such a process is summarized by

— Much of the evidence from recent research on consumer behavior is
reviewed in R. Ferber, "Research on Household Behavior," American Economic
Review, Vol. 52, March 1962, pp. 19-63.

- 301 -

the following three postulates: (i) Each consumer decides over a given interval

of time on the proportion of his total income to be spent on each category of

8/
commodities;— (ii) this decision procedure remains constant over time, as

long as total income does not vary significantly; and (iii) the proportions

of total income a consumer allocates to each category are closely approximated

by the proportions allocated to these same commodity classes by those consumers

who within a given geographic location are in the same social and economic

position.

With these three postulates it is clearly possible to begin to observe
the allocative decision procedures of individuals as well as groups of consumers.
If the theory is to account for an individual's allocations the actual proportions
employed by this individual must be observed and entered as specific parameter
values. Similarly, if the theory is to explain a group's allocative procedure
only the group's proportions need be observed. Accordingly, given these three
postulates, and assuming for the moment that they are supported by empirical
test, it is clear that the observed proportions constitute the requisite inter-
pretive rules.

Once a consumer chooses to spend a certain proportion of his income on a
particular commodity category, say food, he is then faced with the problem of
deciding how to allocate these funds among the possible types of comestibles.

— It should be noted that the notion of such an allocative process is

not a novel idea. For a theoretical, formulation within classic utility
analysis see: R.H. Strotz, "The Empirical Implications of a Utility Tree,"
Econometrica, Vol. 25, 1957, pp. 269-280; and I.F. Pearce, "An Exact Method
of Consumer Demand Analysis," Econometrica, Vol, 29, October, 1961,
pp. 499-516.

- 302 -

To understand this decision process^ it is necessary to examine the decision
procedures that govern the expenditure of these funds. Similarly, if the theory
is to account for all expenditures, then the decision processes relevant to each
commodity category must also be determined. Such a theory would be somewhat large
and complex. Moreover, if all processes have to be empirically checked against
the behavior of each consumer, the task of constructing the desired body of theory
would be very demanding. However, if there are some similarities among the
decision processes relevant to each commodity category, then the problem of
developing a theory of consumer behavior may not be as formidable as previously
expected.

For example, as noted above, the General Problem Solver principally consists
of a set of hypotheses which describe the processes by which humans solve
certain types of problems. These hypotheses contain no references to the subject
matter of any specific problem. Consequently, when the theory is employed to
account for the behavior of individuals proving theorems in symbolic logic
the theory has to be interpreted by providing it with the requisite vocabulary,
axioms, and rules of inference. Similar interpretive rules must be provided
if the theory is to account for the behavior of subjects proving theorems in
geometry, deciding on moves in chess, or tackling other problems which are
consistent with the means-ends analysis of the theory. As a result, if a
single theory is to encompass the decision processes of individuals as well
as groups of consumers, and if at the same time it is to reflect the principal
characteristics of th» general theory of human problem solving, it is evident
that a substantial proportion of its hypotheses are to be stated in such a way
that they are independent of the particulars relevant to a specific commodity

- 303 -

category. This implies that the decisions processes sufficient to account for,
say, the allocative decisions within one class of commodities are also sufficient
to account for the allocation of funds within any of the remaining categories.
In brief, such a theory assumes that consumers employ largely similar sets
of decision processes to solve all of their allocation and purchasing decisions.

A. Some Possible Processes and Interpretive Rules

In order to guide the development of some of the principal decision
processes as well as their respective interpretive rules the basic requirements
of a theory of consumer behavior can be stated as follows; (i) the principal
decision processes are to consist of a single set which can be applied to the
allocation of funds among commodity categories as well as to the selection of
individual items within any specific category; (ii) these decision processes
are to be constructed so that they are independent of the subject matter of
any one class of commodities j and (iii) for each category of commodities some
specific decision processes are required so that the processes in (i) can be
applied to the particular decisions that occur within each of the individual
categories. Given these requirements, it is now possible to examine some of
the decision processes that, subject to corroboration by actual investigations,
could be constructed to be largely independent of the particular contents of
any single class of commodities. Concurrently, once these processes are
specified, it is then possible to note the interpretive rules that must be
provided if the resulting theory is to account for the observed behavior of
individuals or collections of individual consumers.

- 304 -

The first decision procedure that could be constructed in this manner is
the process by which a consumer decides how to pay for a particular purchase.
While, at first sight, this may not appear to be a particularly important process,
its function would be to determine whether the item under consideration is to be
paid for by cash or cash equivalents, or by a set of monthly payments, A general
process of this sort could be constructed to encompass such decisions as;
(i) Whether to rent or puchase housing accommodation. For if the decision is to
purchase a house, the decision process would include the size of the mortgage,
interest and tax payments that could be afforded. As a result, it would also
include the decision on the price that a consumer would be willing to pay for his
housing. (ii) Whether to purchase other durables for cash or by accepting
credit to spread the payments over a period of time. Since a separate process
allocates the total funds to the separate categories, this decision process would
also include a mechanism for specifying the upper limit of these periodic payments
for each category. (iii) The remaining rent or buy decision that a consumer
has to make from time to time.

Even though the explanation of each of these decisions may require a separate
process, they all have certain elements in common--namely, whether there already
are allocated funds available to cover the intended purchase or, if not, whether
by accepting credit the periodic payments are low enough to permit them to be
paid for out of the available funds for that class of commodities. Manifestly,
this process can be constructed so that it is independent of the commodity category,
and where its object is to determine within the amount of funds allocated
to each category how a particular purchase is to be financed. While this second
allocative process may differ in detail among individuals it would be a postulate

- 305 -

of this theory that its principal components could be represented by a single set
of decision processes.

In order to subject such a process to empirical test it is necessary to
provide some interpretive rules. Sine the "buy-now-pay-later" decision rule
is dependent on the process which allocates funds to the separate categories,
both processes must be given an empirical interpretation before tests can be
conducted. For the first decision process the interpretive rules, as noted above,
are readily identifiable. All that is needed is to observe the proportions of
total income a consumer or group of consumers allocate to each commodity category.
Clearly, this process would account for the observed allocations up until that
moment when the proportions were altered. In order to accommodate such
observable changes a set of adaptive mechanisms would have to be included which
would allow these proportions to change as total income rose or fell.— Once this
process is empirically determined it is then necessary to examine this second
allocative procedure--i,e. , the process by which the funds per category are
spent. The object, of course, is to empirically determine the parameters, e.g.,
the interest rate, the amount of credit already outstanding, the cost of the item,
etc., as well as the specific processes which are sufficient to account for this
part of the consumer's decision process.

— Two such adaptive mechanisms are suggested by the "permanent income

hypotheses" of M. Friedman, A Theory of the Consumption Function, National
Bureau of Economic Research, Princeton, 1957, and the "permanent wealth,"
hypothesis of F. Modigliani and A. Ando, "The 'Permanent Income' and the
'Life Cycle' Hypotheses of Saving Behavior," in I. Friend and R. Jones
(eds.). Proceedings of the Conference on Consumption and Saving, University
of Pennsylvania, Vol. II, 1960, pp. 49-174.

- 305 -

of this theory that its principal components could be represented by a single set
of decision processes.

observable changes a set of adaptive mechanisms would have to be included which

9/
would allow these proportions to change as total income rose or fell.— Once this

process is empirically determined it is then necessary to examine this second

allocative procedure--i,e. , the process by which the funds per category are

spent. The object, of course, is to empirically determine the parameters, e.g.,

the interest rate, the amount of credit already outstanding, the cost of the item,

etc., as well as the specific processes which are sufficient to account for this

part of the consumer's decision process.

— Two such adaptive mechanisms are suggested by the "permanent income

hypotheses" of M. Friedman, A Theory of the Consumption Function, National

Bureau of Economic Research, Princeton, 1957, and the "permanent wealth,"

hypothesis of F. Modigliani and A. Ando, "The 'Permanent Income' and the

'Life Cycle' Hypotheses of Saving Behavior," in I. Friend and R. Jones

(eds.). Proceedings of the Conference on Consumption and Saving, University

of Pennsylvania, Vol. II, 1960, pp. 49-174.

- 306 -

In a similar manner processes could be developed which would account for
the resolution of conflicts or mis-allocations of funds among the categories^
the process by which expectations about future prices^ product developments and
other variables affect current behavior^ and the actual selection procedures
that permit a consumer to chose within a given category one set of commodities
from those available at the time. Each of these processes would consist of a
basic set of decision procedures — which would need to be empirically interpreted
to account for a specific set of observed behavior.

For example, with respect to the first of these processes^ the funds avail-
able for expenditure within a category at a particular time may not be
sufficient to cover either the proposed purchase or the payments already
incurred. One method or resolving such conflicts is by a process which
prohibits further purchases in this category until further funds are allocated.
Another possibility is a decision rule which permits the interchange of unspent
monies between one category and another. In either event it is the task of
empirical research to discover which, if either, of these processes is consistent
with observed behavior.

The point to notice, however, is not whether any one or all of the decision
processes outlined above do represent the actual decision procedures employed
by consumers. But rather that it is possible to postulate the existence of
such processes and then carry out the empirical investigations necessary to

— For further discussion of these hypothesized processes see: G.P.E.
Clarkson, The Theory of Consumer Demand, op. cit.. Chapter 8,

- 307 -

to corroborate or confute them. Consequently, although the development and
specification of the requisite hypotheses and interpretive rules can only be
accomplished by empirical research, the research already completed on individual
decision of behavior provides a sound, empirical foundation upon which to build
a testable theory of consumer behavior.

2, On a Theory of the Firm

To construct a theory of consumer behavior which would be sufficient to
account for the behavior of individuals as well as groups of consumers a
postulate is employed which asserts the existence of invariances in the structure
of decision processes among decision-makers. While this postulate is sufficient
to permit the development of theories dealing with individual behavior, a theory
of organizational or firm behavior needs to account for the interactions among
individuals as well as the behavior of the individuals themselves. Earlier
it was pointed out that one method of developing a testable theory of firm
behavior would be to reduce current theories of organizational and firm behavior
to the theory of individual decision behavior. The advantage of such an approach
is clear, in that the reduction process would enable the theory of individual
behavior to serve as the empirical foundation for theories dealing with
organizational behavior. That is to say, if such a reduction can be established
then some hypotheses about organizational behavior can be tested by direct
reference to individual behavior. Manifestly, many hypotheses concerning the
behavior of a firm will relate to the firm's decision problems. Yet, if an
empirical link can be established between the behavior of a firm and that of
the individuals of which it is composed, then the empirical research on individual

- 308 -

behavior can be used to test, augment, and interpret hypotheses about the firm's
decision making process.

To effect this reduction between existing theories of organizational and
firm behavior a second postulate is required--namely, a postulate which asserts
the existence of invariances between the structure of individual and organizational
decision processes. The basis of this postulate resides in inductive and empirical
grounds. It cannot be proved as a theorem. Indeed, the only grounds upon which
it can be supported, other than by direct empirical test, is its consistency
with the theory of individual decision-making behavior. Essentially, this is
nothing more than an appeal to parsimony as a rule of procedure and a
supposition that this is the appropriate way in which Occam's razor ought to
be applied.

The empirical value of the postulate lies in the ability it provides to
interpret theories of organizational behavior on the basis of the empirical
theories of individual behavior. While its value to research can only be deter-
mined by empirical test, it should not be overlooked that the empirical basis
for such a postulate is in part already emerging. Consider, for example, a set

of hypotheses that are taken from a general theory of planning and innovation

. ^. 11/
in organizations. —

(1) "Those variables that are largely within the control of

the problem-solving individual or organizational unit

— J.G. March and H.A. Simon, Organizations, Wiley, New York, 1958,

pp. 170-180.

- 309 -

will be considered first."

(2) "If a satisfactory program is not discovered by these
means attention will be directed to changing other
variables that are not under the direct control of the
problem solvers."

(3) "If a satisfactory program is still not evolved, attention
will be turned to the criteria that the program must
satisfy, and an effort will be made to relax these criteria
so that a satisfactory program can be found„"

(4) "In the search for possible courses of action, alternatives
will be tested sequentially."

Without further elaboration and specification of the empirical meaning of these
variables as well as the conditions under which the hypotheses apply it would
not be possible to submit them directly to empirical test. However, if the
second postulate of invariance is accepted temporarily, (a postulate that is
manifestly implicit in the hypotheses quoted above) these hypotheses no longer
remain in an uninterpreted state. For if this postulate is employed the variables
can be immediately specified and the interpretive rules determined by an empirical
investigation of these hypotheses among individual decision-makers.

For instance, since a theory of individual decision behavior can be
subjected to a process of refutation by empirical test, it must be possible
to determine the empirical validity of the following hypotheses concerning
individual behavior:

- 310 -

(1) Within a given problem context individuals will select
those parts of the problem to be worked on first that
are within their ability to control.

(2) If a solution cannot be reached in this manner^ an
individual will then direct his attention to the
remaining parts of the problem that are not under his
control.

(3) If a solution is still not attained, attention will be
directed to the criteria that the solution must satisfy^,
and an attempt will be made to relax these criteria so
that a satisfactory solution can be found,

(4) In the search for a solution, alternatives will be
examined sequentially.

That these hypotheses can be subjected to test is clear. That they will in fact

12/
be corroborated can only be determined by conducting such tests, — What is more

important, however, is that whether they turn out to be empirically true or false,

a procedure exists for determining their empirical validity.

As a further illustration of this method of interpreting theories about

organizational behavior, consider the recently proposed behavioral theory of

13/

— Evidence strongly suggesting their empirical validity can be found in

the empirical exploration of the game of chess. See, for example, the behavior
described in: A, Newell, J.C. Shaw, and H.A. Simon, "Chess-Playing Programs
and the Problem of Complexity," op. cit , , and H.A. Simon and P.A. Simon,
op. cit.

- 311 -

13/

the firm. — The basic framework of this theory consists of a set of variable

classes and a set of relational concepts. The chief postulate is that the firm
can be represented by a set of decision-making processes^ and the analysis of
these decision processes is to be carried out in terms of the variable classes
and the relation concepts.

Firms, under this theory, have goals as well as expectations and have to make
choices among various alternatives. Goals are represented as the names of a
collection of independent variables. Attached to each of these goals is an
attribute known as the level-of -aspiration with respect to that goal. Aspiration
levels are single valued entities which are either satisfied or unsatisfied by
the operating behavior of the firm. For example, a firm could be represented as
having specific goals with respect to total sales, market share, profit, production
rate as well as a variety of other variables dealing with other aspects of the
organization. To each of these goals v/ould be associated a level-of-aspiration,
which in the case of sales, market share, profit and production rate could be
represented numerically. While the aspiration levels themselves depend on past
experience, as well as on a number of other factors, at any one moment of time
they are either being satisfied or not. And it is the lack of satisfaction or
violation of an aspiration level which is the hypothesized mechanism by which
attention is directed to the various goals.

13/

— RoM. Cyert and J.G, March, A Behavioral Theory of the Firm, op. cit.,

see especially Chapter 6,

- 312 -

Goals are set by the firm independently of each other. During any one period
of time they need neither be consistent nor compatible with one another. As a
result, the organization requires some procedures whereby conflict between
goals and their concomitant behavioral routines can be resolved. The behavioral
theory of the firm posits that an organization divides its total decision-making
process into subsections ; and then assigns these separate segments to individual
units within the firm. By this postulate of local rationality the total decision
problem is broken down into a number of independent parts, the responsibility
of each of which residing in a single, organizational subunit. In addition,
the theory postulates that each decision unit employs a set of decision rules
which are again based on the notion of acceptable levels of performance. Since
the failure to satisfy a goal is the process by which attention is directed by
the organization to a problem area, there is no reason to suppose that several
goals will not require attention at any one item. In order to take care of such
situations the theory postulates that the organizations will attend to these
goals sequentially. Conflict between two inconsistent goals is thereby avoided.
For if each problem is viewed in relative isolation, and if problems are only
attended to one at a time, then conflict between two separate problems will occur
infrequently since the two situations are not dealt with simultaneously.

For example, consider a firm which is encountering difficulties in meeting
the fluctuating demands of its customers as well as the production problems
associated with producing this varying output. If both problems were evoked
and dealt with simultaneously, there would be an obvious source of conflict
between those who wanted to satisfy the customers and those who wanted to smooth
out the production process. But, if problems are attended to sequentially the

- 313 -

task of satisfying the customers will be dealt with at one time and the task of
smoothing production at another. Similarly^ if the problems are dealt with by
separate subunits of the organization inconsistencies between the proposed
solutions will go unnotices. As a result^ the inherent conflict in many
situations is largely resolved by decision procedures which preclude its
recognition.

Organizational expectations are included as consequence of processes which
make inferences from information available at the time. These processes are
represented by a number of pattern-recognition processes and simple procedures
of extrapolation. Also^ their behavior depends upon the way in which information
is collected and processes by the firm. Accordingly^ the theory includes
the three postulates on information securing or search activity. The first states
that a search for information is only initiated after a problem has arisen. Such
search activity is classified under the general rubric of "problemistic search."
In the words of the authors, "In a general way^ problemistic search can he
distinguished from the former because it has a goal^, from the latter because

it is interested in understanding only insofar as such understanding contributes

14/
to control," — As a result^ it is postulated that all search activity is motivated

by the existence of specific problems and is directed toward obtaining acceptable

solutions to them.

14/

— R.M. Cyert and J.G, March, ibid, , p, 121,

- 314 -

Since search activity could be conducted in a number of ways^ the next
postulate states that the search for information and alternatives will begin in
the neighborhood of the problem itself and in the neighborhood of the current
alternative^ if there is one. Essentially, this postulate argues that search
activity will first be initiated by the subunit within which the problem
originated. If this process is unsuccessful and if the pressure to reach a
solution is sufficiently great^ the search process will become more complex
as different subunits of the organization enter into this decision activity. One
consequence of the second postulate is that the actual search procedures used
by any specific unit of the organization will be biassed by the way in which this
unit views the environment. For instance, if the sales department is engaged
in search activity, it will view both its problem and the possible alternatives
in terms of items directly connected with selling activity. Similarly a
production unit will see the solution of its problems in terms of such items
as workforce, production rate, inventory costs, etc. This is not to say that
an adequate solution will not be found by such approaches. Rather, such
behavior has been observed on a number of occasions — and forms the basis of
the third postulate which states that all search activity is biassed in a
manner similar to that mentioned above.

The problem posed by having to choose between available alternatives,
the third of the principal components of the theory, is in part accounted for
by the hypotheses noted above. If goals are independent and are attended to

15/

— See for example: D,C, Dearborn and H.A. Simon, "Selective Perception:

A Note on the Departmental Identifications of Executives," Sociometry , Vol. 21,
1958, pp. 140-144.

- 315 -

sequentially, if acceptable-level decision rules are eraployedj and if alternatives
are only sought when the need arises, the problem of choice is resolved down to
the point where the subunit involved accepts the first one that satisfies its
requirements. In other words, search is terminated and a solution is adopted as
soon as one alternative appears to satisfy the goal's aspiration level.

One part of the organization's choice problem, however, concerns the way in
which it contends with the element of uncertainty which is a part of all its
decision-making. In this theory of organizational behavior firms are represented
as trying to avoid dealing with such uncertainty. In order to do so they are
hypothesized as employing decision rules which anticipate and respond only to

events in the short-run. Further, by actively searching for ways of reducing
uncertainty, e.g., industry trade practices, standard operating procedures, long
run purchase and sale contracts, (price stabilization, etc.) a firm can rely
upon its short-run decision rules as sufficient for the task at hand.

While this discussion has only rioted some of the more important hypothesis
it is clear, at this level of description, that the theory is stated in far too
general terms to be directly submitted to empirical test. To test the theory,

both the variables and concepts as well as the hypothesized decision rules must

Ifi/
be empirically interpreted and specified in all the requisite detail. — Moreover,

in order to subject the hypotheses to test large-scale experiments on, and detail

observation of, a firm's decision processes are required. Although the detailed

— Two actual models of this theory, a specific price and output model
and a general model of price and output, are described in ibid., Chapters 7 and 8,

- 316 -

model of a department store's pricing behavior evinces the practicality of
conducting such tests — ' , the ability to test some of these hypotheses against
individual behavior^ provided by the second postulate of invariance^ substantially
reduces the experimental problem.

To illustrate these remarks consider the process by which firms are postulated
to direct and control their attention and problem solving behavior. First of all^
the organization is represented as having a number of independent goals. These
goals are established by different subunits and to each goal there is associated
an attribute called a level of aspiration. A problem situation occurs when the
results of the firm's activity fail to satisfy one or more of these goals. That
is to say, a problem is defined by a failure of the level of aspiration
associated with a particular goal to be reached. Once this occurs a search for
a solution is initiated and is only termnated when the level of aspiration is
satisfied. Accordingly,- one of the basic hypotheses being employed is that
failure to meet some specified target (aspiration level) is the mechanism by
which problems are defined and problem-solving activity is controlled. In brief,
this theory posits that problem-solving activity is directly controlled by the
satisfaction or the lack of satisfaction of the levels of aspiration attached
to the respective goals. One consequent of this hypothesis is the statement
that if all goals are at one time simultaneously satisfied then no problem-solving
activity should be observed. Another is that, if more than one goal is
simultaneously unsatisfied, a mechanism must be introduced which accounts for the

17/, . c . .
— See previous footnote.

- 317 -

order in which these problems are dealt with. The theory posits that they will
be considered sequentially, but if one is to explain a particular set of behavior
it will also be necessary to be able to account for the particular sequence
which is observed. Now both the firm and its subunits are composed of
individuals. Also it is the individuals themselves who carry out the problem-
solving activity. Thus by the second postulate of invariance these two
inferences can be tested by a direct examination of individual behavior. More-
over, an empirical investigation has already been undertaken to determine the

process which controls the allocation of problem-solving behavior--i.eo ^ the

18/

process that directs an individual's attention from one problem to the next. —

That is to say, an experimental situation was designed to test the propostions:
(1) that problem-solving will take place when an aspiration level is
unsatisf ied--i,e. , when some goal has not been attained, and (2) that in the
absence of failure there will be no problem-solving activity. This study was
concerned with individual decision behavior, and aside from testing these two

propositions its object was to develop a theory to explain the problem-solving

19/

control process. —

In brief, the results are quite clear and strongly negate, for individual
decision behavior, both of these propositions. When all goals are satisfied subjects
do not desist from problem-solving. Further, an aspiration level does not need
to be violated before problem-solving begins. When a subject's behavior is

18/

— W.F. Founds, "A Study of Problem-Solving Control," op. cit.

19/

— Some aspects of this study are further discussed in the next chapter.

- 318 -

analyzed in terms of his decision processes it spears that problem-solving
is a continuous activity. Consequently, the key to the explanation of the
behavior lies in discovering the processes which allocate problem-solving
activity from one problem to the next. Whether this allocative process can
be reconciled with a level-of-aspiration representation is not at issue here.
The importance of these experimental results pertain to the development of
testable theories. Indeed, these experiments demonstrate it is practicably
possible to test hypotheses about organizational decision behavior by
experimental investigation of individual behavior. Obviously, not all
hypotheses about organizational behavior can be tested in this manner. But
as long as some are suited to this approach, and as long as the results from
such tests are directly applicable to theories of organizational behavior,
then theories of firm behavior are assured of a strong empirical foundation.

Chapter 15
TOWARDS A THEORY OF MARKET BEHAVIOR

Under classic conditions a market is analyzed in terms of demand and
supply schedules and their intersection at equilibrium. White it is hard
to imagine a market which does not consist of at least one buyer and one
seller, it is evident that the notion of an equilibrium is extraneous to
an analysis of decision behavior. Since the interactions that take place
in a market are the result of the decision processes of both buyer
and seller, it would seem reasonable to hypothesize that market behavior
can be explained by an understanding of the separate decision processes
and the ways in which they interact.

In the preceding chapter a set of procedures were described by
which theories can be constructed to explain the decision-making
processes of both consumers and firms „ Such theories represent the
decision-maker as having a set of decision processes which act upon
and react to information which is already available to him in his
memory or is made available by his environment „ All behavior, under
this theoretical framework, is a consequence of some describable
decision process acting upon some ascertainable set of information.
Concurrently, it has been argued that the decision behavior of
individuals, as well as collections of individuals, and organizations
or groups of individuals can be represented in a similar fashion. That
is to say, whether one is dealing with one or many individuals acting
by themselves or in groups, the resulting decision behavior can be
described by a set of decision processes acting upon the relevant
information. Since both individuals and firms frequently buy and sell

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commodities through the medium of a market the behavior of the market must be
a direct consequence of the individual decision processes.

Usually it is the variation in the price and the quantity supplied and
purchased that constitutes what is known as a market's behavior. At any one
period of time only one prices is in effect for each item. But over time
these prices change, and it is this change in price that constitutes the
market's behavior. At the same time, it is the change in price that must
be explained if one is to be able to explain and predict the behavior of one
or more markets.

In many markets the price per item is part of the information required
by the individual or firm in order to decide on the quantity to buy or sell.
As such the price is part of the decision-maker's initial conditions prior
to making a decision. While the price may well change over time, the price
at the moment is the item which is processed by that decision-maker. In
these cases, the price is not subject to direct negotiation between buyer and
seller. The buyer (seller) can decide to buy (sell) more or less of a
particular item at the stated price but there is no opportunity to revise the
price while this decision is being made,

A consumer in a department store, supermarket, or any other retail
establishment is an exemplar of such activity. All items have a stated price

— Clearly the price for any one item can differ for wholesale and retail
sales as well as for wholesale or retail purchases. But at any one period of
time there is only one of each of these prices in effect in a specific market,

- 320 -
and the consumer's problem is to decide how much of each, if any, to purchase.
In order to explain the consumer's behavior, all one needs to know are the
prevailing prices and his decision processes. It is not necessary to know
anything about the mechanism by which these particular prices are set. In
some situations it may be necessary to know something about the recent
history of the prices of these items, e.g., are they special sales prices?
Even in this event, however, to explain the consumer's behavior it is quite
unnecessary to know why the prices have changed.

On the seller's side of the market an example is provided by decision
processes which account for the setting of prices in a department store.
Again, at each moment of time there is only one price attached to each item
in the store. And it is up to the price setter to decide whether to alter
these prices or not. Such alternations, however, do not take place from
instant to instant. They are based on a set of decision rules which are
activated by certain events--notably , the recent history of sales, the level
of inventories, the change in seasons, the approach of holidays, etc. All
this information constitutes part of the initial conditions for the price
setting decision process. Although, prices do change over time, the prices
at any one period of time are explained solely by means of this process and

not by a process which incorporates the customer's immediate reaction to these

2/
prices .—

In brief, under these conditions a classical market, with its own

mechanisms for setting and adjusting prices, does not exist. Prices are set

— For a detailed model of the price setting decision process m a

department store, which has survived empirical tests, see: R.M. Cyert and
J.G. March, op. cit. , Chapter 7.

- 321 -

by one set of decision processes and purchase decisions are determined by
another set. At no one point in time do these processes directly interact.
That is to say, the department store or supermarket is perhaps a convenient
place for consumers to examine the available goods and for merchants to
display their wares. But within these shops all purchases and sales are
conducted at set prices and there is no opportunity for the classic
balancing of prices and quantity to be carried out from one moment to the
next. To understand the behavior of the buyer or seller, therefore, it is
sufficient to know the decision processes by which each decides how much
of each item to buy or what price per item to change. Moreover, procedures
have already been outlined by which theories of such behavior can be
constructed and tested. Consequently, to account for this class of market
behavior it is not necessary to develop a further set or body of theory.
Manifestly, it is sufficient to be able to explain the behavior of the
individual participants,

1. Price Behavior in a Security Market

There are other types of markets, however, in which buyer and seller come
together and by their interaction directly establish a price and the quantity
to be purchased. One such case is provided by the various security markets.
In this instance the commodity in question, whether it be a bond, a stock,
or a future, is known to both buyer and seller, and it is through their
interaction that purchase and sales agreements are made. Since it is the
fluctuation in the prices that is one of the chief characteristics of these
markets, it is here if anywhere that a theory of market behavior is needed.
Indeed, if it is the function of a theory of market behavior to explain, among

- 322 -

other items, the movement in prices, then the price fluctuations of the security
markets are prime candidates for explanation by such a theory.

It is my position that in order to explain the behavior of security prices
a theory of market behavior, as such, is not required. For even in this
situation the behavior of the prices is a direct consequence of the decision
processes of the individuals concerned, and no additional mechanism or theory
is required to account for this behavior. Although classical theory employs
a supply-equal-to-demand relation to establish an equilibrium market price,
it is my assertion that not only is such a mechanism untestable and hence
empirically vacuous, but it is also completely unnecessary. In brief, I am
suggesting that the behavior of prices can be explained without reference
to an equilibrating process. And further, that market behavior is strictly
determined by the decision processes of the individual participants.

While this is hardly a novel conclusion, in that it is a somewhat obvious
statement of the case, it implies for any specific market that one needs to
know in detail the decision processes of all participants. If the behavior
of certain commodity prices is being examined the number of such participants
could be very large indeed. In addition if one has to be able to describe each
of these decision processes the explanation of the behavior of the prices will
indeed be a formidable and wearisome task. Security markets like other types
of markets, are not composed of a collection of individuals indiscriminately
competing for the opportunity to buy and sell. On the contrary, the process by
which orders to buy and sell are executed is governed by certain institutional
constraints, and the participants in the market can be classified into different
categories. For example, actual transactions are usually conducted through

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official agents^ such as brokers and traders, and the participants can be

categorized as to whether they represent investment societies^ banks,

2/
insurance companies, pension funds, or private individuals.— Now, if

the traders in a particular market behave according to a specific set of

decision rules, then, and this is clearly a testable proposition, it is

possible to describe the decision processes which determine their decision

behavior. Similarly, if each category of investors behaves in recognizably

different ways, such discrepancies must be a result of differences in their

decision processes. Accordingly, if within each category decision behavior

is sufficiently similar, then a set of decision rules can be described which

will represent the decision-making procedures of each class of Investors,

Under these assumptions, all of which can be analyzed for their empirical

validity, the problem of explaining price behavior becomes relatively simple

and straightforward. For the prevailing price at any one moment will be a

direct consequent of the trader's and the remaining, appropriate decision

processes.

A, The Trader

In order to illustrate these remarks consider a recent investigation

3/
into the decision processes of the over-the-counter trader.— In the over-
the-counter market--a market which accounts for approximately three-fourths

— While this is hardly an exhaustive set of categories, the participants

in any market can be classified into observable sets of different types of
investors ,

- R,A, Jenkins, "Professional Trader Price Quoting in the Over-the-Counter

Stock Market," unpublished Master's thesis. School of Management, Massachusetts
Institute of Technology, 1964.

- 324 -

of the gross value of all security sales in the United States--the trader is
responsible for quoting specific prices on all stocks in which he trades. Each
trader maintains an interest in a particular set of securities, usually

between 15 and 20 stocks^ and in response to an inquiry will quote either

4/
a selling (asked) or buying (bid) price on any one of these securities,—

Since the trader's price at a particular moment of time can be the market

price--if a transaction is consummated, this price is the market price at

this moment--one has to be able to explain the trader's price setting process

if the behavior of prices over time is to be explained.

The trader is undoubtedly influenced by many different items of information.
For instance a single trader has access to a number of sources of information,
e.g., the Dow Jones ticker, the Dow Jones broad tape, the daily publication
of the National Quotation Bureau which gives for each security the trader
and the prices at the middle of the preceding day, as well as telephone
conversations with other trades and stock brokers. Nonetheless, all trading
activity is carried on over a telephone in very brief intervals of time.
Accordingly, at any one moment a trader can be asked over the telephone for
the price on a particular security. He responds, as a rule, with the bid
and asked prices on a hundred-share lot. If this price is accepted, a
transaction has been made and the trader has either sold or bought a number
of hundred-share lots.

It should be noted that the trader only deals with stock brokers or
other traders. Under no circumstances is it possible for a private individual

— The difference between the asked and bid prices on a security is

what is known as the spread.

325

or institution to deal with a trader directly. The stock broker takes orders
from private or institutional investors and then telephones a trader to
ascertain price. Since the broker charges a fee for this service, the price
to the ultimate purchaser differs somewhat from the price set by the trader.
Moreover, it follows from this outline of the procedure that when a trader
receives a telephone call he knows that the broker has an order to buy or sell.
Thus, whether there will be an immediate transaction or not depends entirely
upon the broker's reaction to the trader's quoted price. Since the broker
can telephone any of the traders who are known to have an interest in this
particular security, he is not dependent upon a single quote from one trader.
However, as soon as the broker accepts a price that is the price at which the
transaction is made, and consequently it is the market price in the particular
security at that instant of time.

Before examining the trader's pricing decision process in detail it is
pertinent to consider his possible alternative strategies. One alternative
is for the trader to deliberately maintain either a net long or net short
position in a particular security. In a rising market the value of his
inventory will increase, and as a result he would want to have a net long
position. Conversely, in a falling market a profit can be made by buying
back stock at a lower value than that which he sold it for. Accordingly, he
would want to maintain a net short position. While during certain periods of
time traders may actively seek to maintain long or short positions— the

— The most notable period when these strategies were actively pursued

was in the latter part of the 1920 's, see: I. Friend, et. al , The Over-the
Counter Securitieis Markets, McGraw-Hill, New York, 1958.

- 326 -

current strategy is to make a profit by trading on the difference between the
bid and asked prices. Although traders may make a certain amount of profit
by taking advantage of a position they find themselves in, the principal
monetary return comes from buying at his bid price and selling at the asked
price. As a result, in order to be successful the trader must maintain this
spread between prices such that when combined with the volume of trading an
adequate level of compensation is assured.

B. The Pricing Decision

Given this brief description of the trader's function in the over-the-
counter market, it is now relevant to examine the pricing or quoting decision
process itself. A decision is required of a trader each time a broker
telephones to ask for a price. Since the trader must reply virtually
immediately, one would not expect the pricing process to be unduly complex.
According to the study mentioned above—' the basic components of the pricing
process can be represented as follows;

Interest of
Inquirer

Estimate of
Street Prices

Desired Direction
of Position Change

Desired Price in
Relation to Street

Trader's
Quote

Figure 1

— R.A. Jenkins, op. cit.

- 327 -

While each of these components is a result of the influence of a number of other
factors,— the final decision process which takes place at the end of a
telephone can be represented by the interaction of these four items. For example,
a trader alters his quote depending upon the characteristics of the inquirer.
Such factors as whether the inquirer is a buyer or seller, whether the
orders from this person are usually large or small and whether he is a
friendly— competitor or not affect the quote in a manner to be outlined below.

At the same time the trader knows whether he wants to increase or decrease
his current long or short position in a particular stock. For at all times
the trader knows his current position as well as his estimate of the position
he would like to have. Since traders normally have a maximum amount of money
that they can invest in any one security, their general impressions and
attitudes toward the market, constrained by this limit, are what identify
the position he would currently like to be in. Any discrepancy between the
desired and actual position provides what has been labelled the desired
direction of position change.

The estimate of the street or current market price is derived by the simple
process of listening to the reply on the telephone. If the trader's quote
is accepted then he is either right on or a little low (on asked price), right
on or a little above (on bid price) the current market. Conversely, if no
transaction is effected, his asked price is a bit high and his bid price is a

— For a full description of the decision process see ibid , Chapter 3.

— A friendly competitior is one who does not take advantage of a bargain

or poor quote.

- 328 -

bit low. If, for some reason, the stock has not been traded for awhile, an
individual trader can obtain an estimate of the current price by telephoning
a competitor. But if the stock is being actively traded, each trader will
have a fairly accurate estimate of the current market price. Given this
estimate and any desired change in position, the quoted price can be directly

determined.

While the actual increments, e.g., 1/8, 1/4, 1/8, etc., may vary with
different securities- the price setting decision process can be represented
by the following table:

Inquirer and

Desired Direction
of Position Change

Desired Price Relation To Street

His Interest

Bid Price

Asked Price

Retail

Buyer

longer
indifferent
shorter

1/8 above street

equal street

1/4 below street

1/4 to 1/2 above street
1/8 above street
equal street

Retail
Seller

longer
indifferent
shorter

equal street

1/8 below street

1/4 to 1/2 below
street

1/4 above street

equal street

1/8 below street

Friendly
Competitor

(Interest
unknown)

longer

indifferent
shorter

equal street

equal street
1/8 below street

1/8 above street

equal street
equal street

Enemy
Competitor

(Interest
unknown)

longer

indifferent
shorter

much lower
than street

much higher
than street

Table 1

— See ibid. Chapters 3 and 4 for a detailed discussion of the variation
in spread.

- 329 -

This table describes the components of the price quoting decision process
in sufficient detail to permit some of the processes to be subjected to test.
Further, from the evidence presented in the study, these decision processes
are sufficient to account for a substantial proportion of the observed
changes in traders' prices for a number of securities. — Consequently, it
can be accepted, for the moment, as a detailed representation of the price
setting decision process.

Of particular interest in this decision procedure is the mechanism by
which a price is changed. If the trader quotes a price which does not result
in a transaction, no change is made in the price. But, if a transaction is
effected--i.e. , the broker accepts the trader's price--then the trader's price
will change in the direction specified by the process outlined above. As
a result, price changes are for the most part a consequence of a
transaction being consummated and are seldom altered to effect a transaction.
Thus, prices respond to the occurrence of transactions--and are in effect
determined by these contracts.

Lest the reader feel that somehow the price setting process could not be
as simple as portrayed above, or that it would be more likely for the trader
to change his price in order to get transactions, it is worth noting that the
process outlined above apparently reflects a decision procedure which is used
by many people when placed in roughly the same situation. That is to say,
when faced with the task of bidding for contracts in an experimental market

— See ibid. Chapters 4 and 5,

- 330 -

most subjects employ decision procedures which are strikingly similar to those
used by the over-the-counter trader. This observation is one result of the
experimental study of problem solving control mentioned earlier in this book, —
The experiment itself consists of placing a subject in a situation where he
has to announce bids in two markets siraultaneouslyo The subject states his
bids in monetary terms, and the experimenter by consulting a specific list
of random numbers determines whether these bids "win" or "lose." A bid "wins"
when it is below the experimenter's number, and "loses" when it is equal to
or above. There is a fixed cost associated with each trial and the subject is
restricted to making at most one new bid on each trial. Hence^ on each trial
the subject has to decide which market to leave alone and which bid to alter
if at all. A subject's earnings are a direct function of the contracts he
wins over a given number of trials.

In this experiment a subject's behavior is a record of bids or prices on
two markets. These prices change ever timeo Hence, an explanation of this
behavior consists of an explanation of the changes in the respective prices.
Since subjects have no direct knowledge about the list of numbers employed by
the experimenter their behavior is clearly a function of how they decide to
respond to their record of wins and losses as it unfolds. While many of the
subjects who participated in this experiment employed slightly different
decision procedures, there is one principal set of processes that characterizes
and accounts for a large proportion of the observed behavior. This process
is expressed by the following table;

— See W,Fo Pounds, op, cit„, Chapters 4 and 5,

- 331

WIN

LOSE

WIN ^^^^^ ^^^ ^°^^'^
of the two bids

Lower the
losing bid

LOSE ^'"'^ ^^*
losing bid

Lower the higher
of the two bidSc

Table 2

Although this set of processes does not include the amount to alter the
price by^ nor a procedure for deciding what to do in the event both markets
have won or lost and both bids are the same, it does contain the principal
components of most subjects' price setting procedures. The principal
characteristic of the process, aside from its simplicity and symmetry ;, is
that new bids are made in response to contracts made or lost. Prices are
lowered when losses occur and are raised or held the same when contracts
are won.

The significant point is^ of course, that it would be perfectly simple
to choose prices according to some sampling or other statistical procedure.
To employ a notion of sampling one would note the frequency of wins and losses
at various prices in each of the markets and choose that price which appeared
to yield the desired earnings. In fact, despite the statistical training
of many of the subjects^ very few chose to behave in this or any other
fashion. As a result^ it appears that when little or nothing is directly known
about the behavior of the environment, processes are frequently employed
which respond to rather than anticipate the occurrences of the relevant events.
This is not to suggest that the subjects in this experiment are all fledgeling
traders, not is it being suggested that the two situations are the same. But
the similarity in characteristics of the traders' and subjects' decision

- 332 -

processes is too striking to ignore. And since the simplicity of the traders'
pricing decision process is reflected in the bidding process of the subjects,
the empirical validity of the trader's price setting process has received a
certain measure of independent empirical support,

C. The Broker

In the over-the-counter market the function of the broker is to accept
orders from customers and by talking directly with the traders negotiate
the transactions. Clearly, the broker does not have to accept the first
price he receives over the telephone. But if he frequently deals with a
particular set of traders he in turn will have an estimate of the relation
between their prices and the prices of other traders, i.e. the street. What
the broker does not know is the trader's desired direction of position
change, and hence whether his price is di^liberately slightly above or below
the street price. The broker's task is to find a favorable price for his
customer, and if he believes he can do better by trying another trader all
he has to do is pick up the telephone and find outo

One of the factors which influences the trader's price, not noted above,
is the activity or volume of purchases or sales in a particular security.
Each trader has a ceiling on the amount of money he can commit to a single
stock, which given the prevailing price places a limit on the number of shares
of this stock that he can hold. Now, if the traders in Stock A are known to
be holding approximately 500 shares each, and the broker receives an order
to buy 4,000 shares, he is clearly placed in a bit of a dilemma. Since no one
trader can fill his order, he must buy (or sell) from a number of traders.
News of this activity in Stock A will spread to competing traders fairly

- 333 -

rapidly. Consequently^ the broker can expect the price to rise (fall) as he
proceeds from one trader to the next. Thus^ a broker faced with a large

order for a particular security is unlikely to be able to negotiate the entire

• 1 .12/
transaction at a single price, —

D. The Investors

The investor, whether he represents himself or an institution, constitutes
the origin of the orders which the broker receives. While each investor may
feel that he analyzes the market and its securities by an unique method, there
are similarities among these methods of approach. In fact, it has already
been suggested that investors can probably be placed in a modest number of
categories where these categories are defined in terms of the methods of analysis
and selection employed. In order to identify these categories it is necessary
to examine the portfolio selection processes of a number of types of investors.

For example, the portfolio selection process of investors of trust
funds for banks has already, in part^ been examined. This process consists of
a particular set of decision processes which are described in terms of certain
discrimination nets. These nets contain a collection of specific tests which

in turn refer to those attributes of securities which are considered important

13/

for trust investment purposes. While the theory of trust investment — cannot

as yet claim to represent the portfolio selection process of all trust investors,

14/
it would not be a difficult task to conduct the requisite tests. — If these

12/

— 'Throughout this discussion the possibility of the broker carrying an

inventory of securities of his own has been ignored,

13/

— G.P.E. Clarkson, Portfolio Selection, op. cit.

14/
— In fact, part of this testing process is already being conducted on the

trust investment process of banks in Massachusetts. See: W. Mihaltse,

" "j unpublished Master's thesis^

School of Management, Massachusetts. Institute of Technology, 1964.

334

tests corroborate the theory, then this particular set of decision processes would
represent in detail the procedures by which investors of trust funds select
securities for their portfolios. Once these procedures are known the only
other items of information required are the amount of funds available for
investment classified by the types of portfolios desired, e.g. growth, income,
etc. By an application of the decision process to current market data specific
portfolios of securities are generated. These portfolios represent the orders
which are given to the broker by the investor. As a result, it is these
portfolio decisions which constitute the origin of the broker's orders.

It is worth noting that portfolio decisions are relatively insensitive
to the exact prices prevailing in the market at the time the portfolios are
selected. Since the actual price for a particular order is only determined
after the broker has received it and has contracted with a trader, the investor
must select his portfolios on the basis of some previous prices. While these
prices may closely approximate the actual prices paid after the broker has
completed his transaction, nevertheless, portfolio decisions are clearly made
without an exact knowledge of the price per security that will be paid.

Due to various legal constraints investors of trust funds are not
allowed to purchase securities on the over-the-counter market. Hence, with
respect to this market a knowledge of the trust investment process does not
provide the basis for one category of investors. However, since it is possible
to describe the portfolio procedures of trust investors there is no reason
to suppose that the investment behavior of other institutional investors who
do participate in the over-the-counter market cannot be described in a similar
manner. Further, the theory of decision behavior outlined in previous chapters

- 335 -

provides the theoretical schema by which these investment processes can be
described and the particular selections explained. Consequently, since a
theory of each class of investors can be constructed and tested, it is clearly
possible to describe the processes by which the orders received by brokers
are generated,

2. Testing the Market Processes

2 ,

In the case under consideration the market for securities consists of
the interactions of brokers and traders. If the traders' decision process is
accepted, for the moment, as it is given above, and if a simple decision process
was constructed to account for broker behavior, the behavior of prices would
be determined by these two processes. That is to say, if one is not concerned
about explaining the flow of buy and sell orders to the broker, all that is
required is the sequence of orders plus the two decision procedures. With the
orders as part of the initial conditions, the behavior of the relevant prices
will be a result of the interaction of the broker's order contracting process
and the trader's price setting process.

Manifestly, it is possible to examine the simple case where there is only
one trader who holds an inventory in a particular stock. Since this condition
is likely to occur only when there is little interest and activity in a
security, the number of brokers who receive orders for this stock will be
quite limited. Hence, the behavior of the price of this security will be a
direct consequence of a few brokers interacting with one trader. Given such
a situation, it is neither difficult nor laborious to determine the particular
decision processes employed by each of the participants. Once these processes

- 336 -

are described, with the brokers' orders forming a part of the initial conditions,
the behavior of the price of this particular security can be immediately
explained. For the interaction of these decision processes, if they are each
able to account for their respective decision behavior, will generate a
sequence of price movements which should be identical to the observed.

In order to test the accuracy with which this model of market behavior
reproduces the observed movements in price, it is only necessary to set up a
criterion of success and failure and compare the two time series. Such a
comparison can be conducted upon the actual prices themselves, as well as on
whether the model produces a set of prices that move at each decision point
in the same direction as the observed. Once measures of success and failure
are def ined--i.e. , underwhat conditions the model's price is to be considered
the same as the actual--the model's level of success can be measured by the
frequency with which it accounts for the observed price change. Since each of
the individual decision processes can be independently subjected to test, the
model as a whole can be satisfactorily tested on its ability to reproduce the
observed time series by determining its relative frequency of success.

In a situation where there is more than one trader who holds an inventory
in a particular security the model would become correspondingly more complex.
For once there are several traders as well as a number of brokers there may
be more than once price prevailing at any one point in time. Each broker
agrees to a transaction when he thinks he has secured a favorable price. But
each broker does not canvass all traders before making a decision. In addition,
more than one broker may be interested in a certain security at one period of

- 337 -

time. Therefore, it is possible for there to be slightly different prices
prevailing at one instant of time.

In order to reproduce these detailed events the model would have to
include the individual decision processes of each participant. To empirically
determine these separate processes would be a time consuming task. But if a
complete explanation of a certain stream of price behavior is desired the
separate decision processes must be taken into account.

However, if an explanation of each movement in price is not required and
if the behavior under investigation is concerned only with some of the more
aggregate characteristics of the price changes over an interval of time,
e.g., direction of change from beginning to end of interval, incremental
change, etc., then a simplified model would suffice. Such a model could perhaps
consist of a generalized broker's decision process interacting with a generalized
price quoting process. Whether such a model would produce the desired
behavior is open to empirical investigation. But since each of the individual
processes can also be independently subjected to empirical test, the eiipirical
validity of the entire model is not solely dependent upon the general
characteristics of the generated time series being similar to the observed.
Consequently, it would appear that it is quite possible to develop a general
model of price behavior without too much difficulty.

The point to note is that none of these models require an equilibrating
mechanism. Each is based solely upon the interaction of independent decision
processes. Thus, although their empirical validity has yet to be demonstrated^
the research described above is in my opinion sufficient to indicate the
theoretical and empirical merit of this approach. Accordingly, while only one

- 338 -

type of market has been examined in any detail it appears that all market
behavior can be explained by theories which include the decision processes
of the individual participants and which do not incorporate the classic
equilibrating hypothesis.

chapter 16
BEHAVIORAL THEORY, MICROANALYSIS AND POLICY DECISIONS

In the latter part of Chapter 10 it is noted that the only condition
under which it is possible to test econometric hypotheses is when these exists
an independent method of measuring the population's stability. Within the
confines of econometrics itself it is not possible to determine whether each
sample comes from the same underlying population--i„eo whether the population's
characteristics remain stable over the period in which the samples are drawn.
Accordingly, unless the behavior of the population can be separately determined
and the constancy of its relevant characteristics ascertained, econometric
hypotheses cannot be submitted to a process of refutation by empirical test.

The previous four chapters, however, have been concerned with describing
and examining a theory as well as an experimental method by which the behavior
of an individual, a class of individuals, and a group or organization of
individuals can be explained. While a general theory of economic decision
processes has yet to be fully developed, the basic theory of decision-making
behavior provides the structure around which such a theory can be constructed.
Further, the various models of this theory which have already been successfully
submitted to test demonstrate the empirical testability of these behavioral theories,
That is to say, the evidence strongly supports the proposition that testable
theories can indeed be constructed which are able to describe and explain the
economic decision behavior of individuals whether acting singly or in groups.

If the proposition is accepted the question then arises as to whether
these behavioral theories can serve as the independent measure of a specific
population's characteristics and stability. For example, if a theory is

340

developed which explains a particular sequence of economic decision-making
behavior, then this theory can be employed to determine the point at which
this decision behavior begins to change. Such a point occurs the minute the
theory is no longer able to describe and explain the observed behavior. In
other words, if a theory of a certain decision process has survived a number
of tests and has already been shown to be sufficient to account for this behavior,
then as soon as the theory can no longer account for the behavior, the inference
can be drawn that the economic decision process has altered in some way.
Accordingly, up until the moment that the theory can no longer account for the
observed behavior, the theory itself provides a means for determining both the
constancy and the characteristics of the decision process.

Behavioral theories represent economic decision processes. Since their
hypotheses can be subjected to test, the constancy of specific decision
process is assured by the ability to detect change. Once a theory fails to
explain, a change can be presumed to have occurred and the constancy of the
decision processes is placed in doubt. But until this moment arrives the theory
itself describes the relevant decision process, and is a direct and independent
neasure of their stability over time.

Once a theory fails to explain the occurrence of a specific event, its
hypotheses are re-examined in order to detect the source of the error. If after
further tests and analysis the theory is once again sufficient to account for
the relevant decision behavior, then the alterations in the theory represent
the changes that are presumed to have taken place in the observed decision
behavior. Accordingly, not only can a behavioral theory represent the actual
decision processes at one period of time, but as it is amended it can also account

- 341 -

for new observations. Consequently, the amendations are a record of the changes
that are occurring in the relevant decision behavior.

Since a behavioral theory describes observed decision behavior in terms
of decision processes and their attributes or component parts, behavioral
theories also provide a description of the characteristics of decision processes.
As a result, any alterations to a theory must be reflected in the hypothesized
processes and their attributes which in turn alter the characteristics of the
decision-making process. While some changes may verge on the insignificant,
others may considerably affect the resulting decision behavior. In either event,
however, the existence of a testable theory of this decision behavior provides
both an indicator of change as well as a method whereby the extent of the change
can be assessed. Consequently, it appears that behavioral theories can indeed
serve as an independent measure of the constancy as well as the alterations in
specific economic decision processes.

For example, consider the decision behavior of an investor of trust funds.
It is clear from foregoing chapters that a theory can be developed which describes
such an economic decision process in considerable detail. Further, such theories
can be submitted to test and on the basis of such tests can be classified as
being sufficient to account for a particular sequence of portfolio selections.
As long as the theory continues to survive empirical tests, its hypotheses
consist of a precise specification of the factors that are considered as well as
the order in which they are related in the selection of securities for particular
portfolios. Accordingly, both the discrimination nets and the remaining
processes represent the attributes and character'stics of the portfolio selection
process. If a change occurs such that some of these hypotheses--notably , the

- 342 -

respective discrimination nets--need to be amended^ then the extent of the change
in the observed behavior can be measured by the number and type of alterations
made in the theory's hypotheses. In addition, the new theory now serves as
the basis from which further changes in the observed behavior can be detected,
analyzed and assessed. Therefore, a theory of the decision processes of trust
investors provides the requisite hypotheses and observable initial conditions
to establish explanations of the behavior of this class of economic actors.

1 . Behavioral Theories and Econometrics

Since behavioral theories are a direct representation of economic decision
processes the next point to examine is the relation between econometric and
behavioral hypotheses. For if behavioral theories are to be employed an
independent measure of economic decision behavior these must be a direct
connection between these two types of theories if this measure is to perform
the required task. That is to say, unless econometric hypotheses refer to the
same attributes and characteristics of the observed behavior as the corresponding
behavioral theories, the existence of testable theories of economic decision
processes will not enable econometric hypotheses to be submitted to test.

Traditionally econometric hypotheses are formulated by reference to the
theories and hypotheses of classical economics. Accordingly, econometric
hypothesffi usually contain concepts and terms which correspond directly with
the terms and concepts employed by classic economics.— Since the theories from

— For specific examples and further detail see the econometric models
described in Part III.

- 343 -

which these concepts are taken cannot be subjected to test it is highly

questionable whether many of these terms are themselves subject to empirical

analysis.— In addition, it is apparent from the analysis in Part IH that

even if some or all of the terms in an econometric theory refer directly to
observables the empirical validity of the theory cannot be assessed due to the
lack of appropriate measures on the underlying population. Thus, although the
objective is to transform econometric hypotheses in to a state of empirical
testability, it appears that in order to accomplish this task the method by
which such hypotheses are formulated must also undergo a change.

One possible method of approach is to construct econometric hypotheses on
the basis of the corresponding behavioral theory. Behavioral hypotheses are
deterministric statements which represent the conqjonents of the relevant
economic decision-making process. Econometric hypotheses, however, are
stochastic propositions which usually consist of a linear relation among the
appropriate variables. To formulate an econometric theory on the basis of a
behavioral clearly requires, among other things, that determinate relations
be converted into a statistical framework. If the resulting econometric theory
were to be used to explain the behavior of a single economic actor, there would
be little reason to justify such a transposition. For if the observed behavior
can be accounted for by a deterministic theory the dictates of parsimony would
preclude the addition of unnecessary statistical factors. But, if the

— For a detailed examination of the empirical content of the concepts

employed in the classical theories of utility and demand see: G.P.E. Clarkson,
Theory of Demand, op. cit. , Chapter 4.

- 344

econometric theory were to be employed to account for the aggregate behavior of
a class of economic actors^ the transposition to statistical hypotheses may
indeed simplify the resulting theory.

In order to construct such econometric hypotheses it would be necessary
to begin with a tested theory of the decision behavior under consideration.
One of the principal features of decision-making theories is the discrimination
nets with which the relevant information from the memory and the environment
is processedo These discrimination nets are composed of a series of tests
or operations. Since these tests or operations are represented in the nets
by their names it is clearly possible to identify one variable with each of
these items. A particular discrimination net would then be represented in
econometric terms by a list of variables. If the discrimination net in
question were a simple sequence of tests, it could then be represented by a
linear relation of the respective variables. Consequently, a statistical
hypothesis could be constructed by forming a linear relation of the variables
in the discrimination net with the addition of an error term.

For example, consider the following discrimination net which is composed of
eight tests or operations.

A^ ^

- 345 -

If each item is represented by a different variable the discrimination net
could be transposed into the following econometric hypotheses:

^1 "^ ^1^1 "^ "^3^3 "*" ^^5^5 "^ ^6^6 "*" ^7^7 "*" "l
y^ = + P2X2 + P^x^ + p^xg + P3X3 + U2

For in this case the cells marked A and A are not reached unless each of the
respective tests is passed successfully.

Suppose for the moment that this discrimination net represents a particular
segment of a specific economic decision process. Suppose further that by the
addition of the requisite information (initial conditions and interpretive
rules) this net is corroborated by empirical test--i.e,, it is sufficient to
account for the observed behavior of a number of individuals. As such the net
is a general theory of this particular sequence of decision-making behavior.
The net is tested by applying it to the observed behavior of single behavior
of single individuals, Thus^ even though it is possible to employ this net
to explain the behavior of a number of individual decision-makers the net
itself is not constructed to be tested against aggregate measures of such
behavior. Manifestly, it is to account for these aggregate measures that the
econometric hypotheses are to be employed. That is to say, by transposing
the discrimination net into the corresponding econometic relations
hypotheses are established which are suitably constructed for testing against
aggregate data. For data can now be collected on the decision behavior of this
class of economic actors and the coefficients can be estimated by the customary
statistical procedures.

- 346 -

Once these relations are established with the appropriate values for their
coefficients and error terms they can then be employed to explain or predict
other collections of similar aggregate data. For, by constructing these
statistical relations from the tested hypotheses of behavioral theories a
method is provided for measuring the stability and characteristics of the under-
lying population. As long as the behavioral theory is continually subjected
to and survives empirical tests ^ the behavior of the total population can be
assumed to remain unchanged. Consequently, all samples drawn during this
period come from the same population, and the basic requirement of statistical
testing is satisfied. If during a sequence of tests the behavioral theory
fails and has to be amended in order to continue to account for the observed
behavior, then such changes as are made must be reflected in the corresponding
econometric relations. Once some tests are deleted while others are added to
form new discrimination nets, the same alterations must be made to the respective
variables. For, it is only as long as the two sets of theories remain
structurally similar that the empirical testability of the econometric relations
can be assured.

In order to illustrate this method of procedure in more detail consider the

microanalytic model of the household sector referred to toward the end of

3/
Chapter 10, As noted above— this model is concerned with the demographic

and economic behavior of household units. In particular stochastic relations

are derived which represent what are called the operating characteristics of

— See Chapter 10^ section 4.

- 347 -

the household. These relations are developed from sample survey data and refer
to the probabilities of the behavior of some 23 dependent variables. The
behavior under investigation is that of household spending on certain durable
goods.—' Although the data are based on 3,000 units for each year, this
microanalytic model is confronted with the same empirical obstacles as any other
set of econometric relations. For unless it is possible to independently
determine the stability and characteristics of such household behavior, it
is not possible to subject these relations to a process of disconf irmation
by empirical test.

To transpose this microanalytic model into an empirically testable state,
according to the proposed procedure given above, it is first necessary to
develop a behavioral theory of this household behavior. Since the microanalytic
model is concerned with purchases of certain durable goods, it follows that
a behavioral theory must be constructed which can account for the decision-making
process of households with respect to home ownership, nronthly rent, car
ownership, purchases of household durables, etc. In brief, a theory is
required which describes and explains this segment of consumer behavior.

In Chapter 14 an outline of such a theory is described. It will be recalled
that the proposed theory of consumer behavior contained a number of basic sets
of decision processes. The first of these is a decision procedure for allocating
the consumer's (or in this case the household's) total income among the various

A list of the variables appears on page 215.

- 348 -

categories of commodities^ such as housing^ food, clothes, entertainment, etc.
The theory assumed that the proportion of total income allocated to each of these
categories would remain fairly stable over time, and would also correspond to
the purchasing behavior of other consumers in the same social and economic
class. While evidence was not presented to support these propositions it is
clear that they can readily be submitted to empirical test.

The next set of decision processes are concerned with the procedures by
which the funds assigned to each commodity category are allocated over the
actual items purchased. In particular these processes were postulated to
include: a decision procedure which determines whether purchases are to be
made by cash or cash equivalents or by a series of periodic payments j decision
rules which describe the processes by which the consumer (household) selects
one set of commodities, within a particular category, from the available
alternatives; decision processes that permit the theory to adjust its selection
behavior in accordance with certain expectations about the future behavior
of prices and other variables that are considered important; and a procedure
for resolving such conflicts as might arise among the primary allocation of
funds to the respective categories.

Manifestly, a theory can be constructed which accounts for the decision-
making processes of households. If one is solely concerned with expenditures
on durable goods, the theory can be restricted to such commodity categories.
The point to note, however, is that once such a theory has been developed and
tested its decision processes will provide the basis for the desired
microanalytic model. For, while such a behavioral theory may appear to the
reader as somewhat complex, it should not be forgotten that its decision processes

- 349 -
are represented by discrimination nets. And, as is argued above, the components
of discrimination nets can be classified as variables which can then be composed
into the appropriate econometric relations. Consequently, once a testable theory
of household decision behavior with respect to durable purchases is constructed
a microanalytic model can be developed which is similar in attributes and
characteristics to the behavioral theory. As long as the behavioral theory
continues to account for observed behavior the resulting microanalytic model
can be employed to explain and predict. For, once again a knowledge of the
population's decision processes provides a direct measure of the stability and
characteristics of these decision procedures. Also, the similarity in structure
between the behavioral and microanalytic relations permits the behavioral theory
to serve as a direct measure of the microanalytic model's population--a measure
which is vitally required if statistical tests are to have any empirical
significance.

Since the microanalytic approach is designed to be able to employ the data
from sample surveys and other interview techniques , there does not appear to be
any reason why such data cannot still be employed to estimate the relations of
the revised models. The only difference would be that instead of basing the
econometric relations upon the survey data--i.e, constructing relations from
the data reported in these surveys--the microanalytic models would now be
developed from the behavioral theory. As a result, the survey data would be used
to estimate the already specified relations. Once this is accomplished further
data can now be explained or predicted in the normal fashion.

One possible consequence of this approach to microanalytic model
construction is that these revised models may well contain variables for which

- 350 -

sample data has not yet been collected. While the occurrence of such an event
would delay the process of submitting the model to empirical test it could
hardly be classified as a serious obstacle to the whole endeavor. The remedy,
of course, is to commence a survey which will yield the appropriate data. More-
over, as there is little to be gained by the indiscriminate gathering of data
such a theoretical focus would provide a much needed structure to the data
collection process.

2. Time Series and Behavioral Analysis

Another way in which behavioral theories can be employed to further
econometric theory is in the statistical analysis of the behavior of time.
One class of time series that have received a considerable amount of attention
is the set which reflects the movement of security prices over time. The object
of many investigations has been to determine whether the movement in prices
follows some detectable pattern or whether such price behavior is
Indistinguishable from that which characterizes Brownian motion or a random
v;alk.— Recently, results have been published which suggest that although
the behavior of stock prices does not appear to be consistent with a pure
random walk, stock price behavior is consistent with the hypothesis that prices

— Some recent examples of this endeavor are to be found in; M.F.M. Osborne,
"Brownian Motion in the Stock Market," Operations Research, Vol. 7, March-
April, 1959, pp. 145-173; H. Working, "Note on the Correlation of First
Differences of Averages in a Random Chain," Econometrica, Vol, 28, October, 1960,
pp. 916-918; and H. Houthakker, "Systematic and Random Elements in Short Term
Price Movements," American Economic Review, Vol. 51, May, 1961, pp. 164-172,
(The Osborne and Working papers are reprinted in; P.H. Cootner, ed., The
Random Character of Stock Market Prices, M.I.T. Press, Cambridge^ 1964,
pp. 100-128, and 129-121, respectively.)

- 351 -

move in a random fashion between certain limits or reflecting barriers. While
these barriers do not remain constant over time, the shifts are what indicate
a trend, the movement within the barriers is indistinguishable from that of a
random walk.- Of course, if stock prices follow some discernible pattern then
once this behavior is known to at least one individual his monetary reward
would no doubt justly compensate the effort involved in reaching this discovery.
However, it is presumed that the behavior of stock prices is not being examined
solely for pecuniary motives, and that the fundamental objective of these
investigations is to be able to explain the behavior of such time series by
means of the appropriate statistical analysis.

The change in prices over time is a consequence of the interaction between
broker and trader--i.e. by studying such time series one is investigating the
final result of a set of market processes. While statistical investigations
may well lead to stimulating results, it would appear to me that a good deal more
could be learned about the relevance of certain characteristics of these time
series by examining the processes by which they are generated. For, by an
analysis of the price setting process and the sequence in which orders are placed
it may well be possible to identify the principal factors which affect the move-
ment of prices over time.

In the previous chapter a theory of the decision-making process of the over-
the-counter security market is discussed. In the simplest case the time series

- See the results and analysis cited in: S. Alexander, "Price Movements in
Speculative Markets: Trends or Random Walks," Industrial Management Review, Vol. 2,
May, 1961, pp. 7-26j and P.H. Cootner, "Stock Prices: Random vs Systematic
Changes," Industrial Management Review, Vol. 3, May, 1962, pp, 24-45. (Reprinted
in: P.H. Cootner, op. cit., pp, 199-218, and 231-252, respectively.)

- 352 -

of the prices for one security is a direct result of the interaction between
the trader's price-setting process and the broker's order-placing process. Since
both of these processes can be described in detail, it is clearly possible to
construct a specific model of this market behavior. If the model is provided with
the requisite information the final result of its behavior will be a series of
prices. This sequence of prices will, if the model has been properly
constructed, correspond to an actual, observable time series--namely , the actual
market prices for this security during the interval in question. Since the
generated sequence of prices is a perfectly respectable time series it can be
submitted to the same statistical tests as are employed in the above mentioned
investigations of stock prices. But, and this is what appears to be the
important point, whatever the outcome or inferences that are drawn from such
statistical analyses, the model provides the mechanisms by which these statistical
characteristics are produced. Indeed, if it can be shown that certain decision
processes, on the part of both broker and trader, lead invariably to the
generation of time series with particular statistical characteristics, then a
basis would have been established from which decision processes might be
inferred from statistical characteristics. If, as may well be the case, different
sets of decision processes lead to time series with significantly different
statistical characteristics, then these characteristics with their corresponding
decision processes can be grouped into separate classes.

While these suppositions may appear somewhat idealistic, and may well be
rejected out of hand as requiring far too much effort to investigate, permit me
to remind the reader that they are perfectly straightforward propositions which
can readily be subjected to empirical analysis. Further, whether they turn out

- 353 -

to be corroborated or not the process of subjecting them to test would not be
as involved as it may at first seem. For once a theory of the market process
is developed its behavior can be assessed under a variety of initial conditions
and environments. If the time series so produced vary significantly in their
characteristics, then it would appear that these characteristics can be classified
by decision process as well as environmental conditions. Concurrently, by
examining the decision processes governing the setting of prices in several
markets it would also be possible, given some differences in these processes,
to identify the effect these differences have on the behavior of prices over
time. In short, such an investigation would lead to a more detailed understanding
of market behavior as well as an explication of the origins of specific time
series and their statistical characteristics.

Even though this book is primarily concerned with the development of an
empirical science of economics, consider for a moment one application to which
such knowledge of market processes could be put. Suppose that you are asked
by some organization such as the Security and Exchanges Commission to give your
considered opinion on the way in which the trading in securities on the major
exchanges should be managed. Their concern is not so much with the administration
and policing of their regulations. Rather they are concerned with the behavior
of security prices 'and request you to consider the problem of how to secure
an orderly market in such prices.

One way of describing the properties of an orderly market is in terms of
the characteristics of the time series of its prices. If certain classes of time
series are considered satisfactory by the commissioners the answer to their
problem lies in prescribing the set of decision processes which will produce such a
time series. While further investigations of market processes would undoubtedly

354 -

lead to amendments and refinements in the recommendations, the process by
which such knowledge is acquired would remain the same as outlined above.
Consequently, even though some might still be tempted to say that they had
found the "best" way, the ability to empirically evaluate alternative proposals
would enable "better" procedures to be discovered and adopted.

3 . Behavioral Theory and Policy Decisions—

Historically, one of the principal concerns of economists has been^ and will
no doubt remain so in the future^ to employ economic theory with its
concomittant analytical tests to develop and prescribe policies for the many
important public and private economic decision problens. Whether the problems
concern the national welfare or pertain to private and individual enterprise,
economists have always responded to policy problems v;ith recommendations as
to the most appropriate policies to be adopted in each of the problem areas.
These policies are based either upon classical or econometric analysis.
Accordingly, if the analysis contained within the second and third parts of this
book is correct^ it follows that such recommendations have been based upon
empirically untestable theories. Indeed, while specific policy decisicr.s viay
or may not have proved useful at the time, none of these decisions were based
upon an empirically tested theory of the economic decision process under
consideration.

— This section is indebted to: G.P.E. Clarkson, "Interactions of Economic
Theory and Operations Research," in A.R. Oxenfeldt, (ed) „ Models of Markets,
Columbia University Press, New York, 1963, pp. 339-361.

- 355 -

The existence of a method by which testable theories of economic processes
can be constructed profoundly alters the task of formulating policy decisions.
For^ once a theory is established which describes and explains the economic
behavior in question this theory is the basis upon which policy decisions
ought to be made. Empirical knowledge of the relevant decision processes
leads immediately to a knowledge of the principal factors which affect the
decision behavior. Experimental investigations of these processes will provide
a knowledge of the changes in the decision behavior which correspond to certain
selected alterations in the environment or within the decision processes
themselves. Manifestly^, such a body of knowledge constitutes a sound empirical
base upon which to construct policy decisions.

To illustrate the effect testable theories may have upon well known
policy decisions consider the traditional conception of how industrial
pricing policies ought to be regulated. Classical theory^ as noted in Part II,
asserts that competitive pricing is the most efficient method of keeping the
prices of finished products^ e.g., consumer prices^ as low as possible.
Accordingly, when competitive pricing appears to have vanished and one or
two companies are observed to dominate an industry;, antitrust measures are

invoked with the avowed intent of restoring competitive pricing to that

8/
particular market. But if, as investigations of business behavior suggest,—

the pricing decision is only one of a firm's decision problems, then to increase

— For further discussion of this point see: R,M, Cyert and J.G. March,

op. cit, , Chapter 6j and H.A, Simon, "New Developments in the Theory of the

Firm," American Economic Review, Vol, 52, May, 1962, pp, 1-15,

- 356 -

the number of firms in the market may not have the desired effect. For unless
it can be shown that the number of firms in the industry is an integral part
of the pricing decision process, it does not make much sense to invoke anti-
trust measures whose purpose is to increase the number of competing firms.
For example, it has been observed in a number of cases that increases in

internal administrative costs frequently lead large firms to centralize their

decision-making processes.— In effect, these firms are led to replace

internal pricing mechanisms with central planning. Departments no longer
maintain their own profit and loss figures, but work instead from allocated
budgets and set prices. A further stimulant to centralized decision-making
is provided by the high-speed computer and management information and control
systems; and it is clear that many firms are making use of this data-processing
capability. If prices and budgets of large corporations are set by a central
plan, this plan will not be sensitive to changes in the external environment.
For the vast amount of coordination required by centralized decision-making
precludes the possibility of these decision processes being too sensitive
to external disturbances. Consequently, once prices within an industry are
judged by some regulatory body to be too high and antitrust measures are
invoked, then for these measures to be effective they must somehow directly
affect some of the principal components of the centralized pricing process.
Unfortunately, not enough is yet known about planning and pricing decision

— For example see: J.G. March and H.A, Simon, Organizations . Wiley,

New York, 1958, Chapter 7; and II. A, Simon, The New Science of Management Decision,
Harper and Brothers, New York, 1960, Chapter 5.

- 357 -

processes to suggest effective procedures for inducing the desired change. But
the evidence is sufficient to call into question many of the traditional beliefs
about the efficacy of antitrust measures in controlling prices.

As a further example of how policy conclusions may have to revised consider
the traditional conception of a firm's reaction to various tax policies. In
particular what is the effect of levying a lump-sura or poll tax on a corporation's
prices? As noted in Chapter 3 the assessment of a poll tax is supposed to be
one of the most effective ways of imposing a tax upon a corporation without
having the cost of this tax passed on to the consumer. The conclusion is based
upon the classical assertion (derived as equation

on page ) that changes in fixed costs are to be ignored when making pricing
and output decisions. Observations of business behavior do not support this
assertion. On the contrary firms have been observed to raise prices to compf.nsate
for increases in overhead costs. — The answer to the question resides in the
corporation's decision processes that determine pricing decisions. If overhead
costs are included in this decision process then prices will reflect any increases
in fixed costs such as a poll tax.

The point to note in this respect is that It is possible to investigate and
determine a firm's pricing policy. In other words ^ It is no longer either
necessary or prudent to rely upon traditional conceptions of firm behavior
with the attendant policy prescriptions. For if the classical conclusion on

— See, for example: W.J. Baumol^ Business Behavior, Value and Growth,
Macmlllian^ New York, 1959, p. 78.

- 358 -

poll taxes is in error^ and if its conclusions about the means to achieve
competitive pricing are open to serious question, the only way in which these
issues can be resolved is by empirical investigations of the decisions processes
involved. To examine and develop testable theories about economic behavior is
not by itself a method for resolving policy disputes. But, it is the only method
by which differences of opinion can be compared upon the common ground of
empirically valid results. Consequently, if decision processes are to be
understood, and if this knowledge is to be used to assist in public and
private decision procedures, a considerable effort must be devoted to empirical
research. Such research should focus on the economic decision-making processes
of individuals and organizations. In addition, these investigations can be
carried out in a reasonably systematic way, due to the empirical testability
of behavioral hypotheses.

At present, the only impediment to the development of a body of tested
hypotheses is a lack of reliable data on individual and organizational decision
behavior. This scarcity is not a result of a paucity of ways for collecting
it. On the contrary, intensive interviews, detailed observations, and the
techniques previously mentioned in the analysis of decision-making behavior
are all useful methods for gathering and sorting data. Therefore, since the
number of untested hypotheses far exceeds the available data it is toward this
endeavor that the emphasis on economic research should be placed.

Chapter 17
TOWARDS A SCIENCE OF ECONOMICS

The primary objective of science is to explain the occurrence of divers
iihenomena. To carry out this endeavor theories are required which can survive
repeated empirical tests. Once developed, such theories perform two vital
functions: they provide the theoretical link in the explanatory process; and
they are the basis from which empirical knowledge of the phenomena is derived.
Without testable theories one can neither explain the occurrence of events
nor acquire knowledge about their behavior. In brief, empirical theories
are a prerequisite of science.

To be a part of empirical science economics, like any other discipline,
must contain theories which can be subjected to the process of disconf irmation
by empirical test. Economics as a subject of social study has had a long and
distinguished history. As a science, however, it has barely reached the
stage of a neophyte. For whether one examines its theoretical statements
in the classical or econometric forms, testable hypotheses of economic behavior
are no where to be found. Neither of these bodies of theory can be used to
explain the occurrence of economic events nor can they be used, in their
current formulations, as a basis for the acquisition of empirical knowledge.
That this assertion is correct can be seen from the analysis presented in
the second and third parts of this book.

Classical mathematical theory fails to produce testable hypotheses
because the deductive system ensures that each and every hypothesis contains
at least one non-observable equilibrium condition as part of its initial
conditions. To submit a hypothesis to an empirically meaningful test, all
the relevant initial conditions must be observed, at the onset of the test.

- 360 -
to be empirically true. The presence of equilibria in the initial conditions

violates this requirement. For classical theory provides no interpretive
rules by which the presence or absence of equilibria can be empirically
established. To base a deductive system and^ as a consequence, the develop-
ment of a body of economic theory on the concept of equilibrium can be
scientifically successful only if the occurrence of equilibria is readily
measurable. However, not only are economic equilibria unobservable, but
there is also every reason to believe that no two such points are the
same. To construct hypotheses which deal with unobservables makes the
task of empirical interpretation difficult enough. To search for general
propositions which relate events whose observable characteristics are
always changing is to confront the development of a science with insuperable
obstacles. In brief, the theories and hypotheses of classical mathematical
economics cannot be disconfirmed by empirical test. Consequently, all
propositions which are based upon this system, while perhaps being engaging
vehicles for after the fact rationalizations, are not a part of empirical
science.

In response to this assertion critics may well argue that to be a science
is not the whole purpose of economics. Further that classical theory provides
an excellent framework with which to analyse and interpret the many important
and pressing problems of national and daily economic life. In these
situations one frequently wants to know how to act, what to do, or what
policy to prescribe. All of these decisions can be taken, so the critics
might assert, without any reference to a scientific theory. The principal
task is a normative one. If policy prescriptions are carried out in detail,
these prescriptions will describe behavior and there is no need to be concerned
with explaining previous behavior.

- 361 -

Such a position, however, places the economist in a most unenviable
situation. For as long as economic theories are not responsive to data how
is one to tell which of a number of competing propositions or prescriptions
to follow? Moreover, without the benefit of empirical criticism the
acceptance and rejection of theories is based upon their conformity with
established positions. In addition, if hypotheses cannot be submitted to
test, then it is not possible to develop policy recommendations in the
standard engineering way--i.e., to discover by diligent experimental
investigation tested methods of achieving the desired results.

Similar difficulties are encountered with econometric theories. In
this case it is not the presence of unobservable initial conditions which
precludes submitting these hypotheses to empirical test. On the contrary,
econometric hypotheses are usually stated so that all variables represent
entities which can be directly observed and measured. The empirical
obstacles are a consequence of the basic requirements for all statistical
tests--i<,e. , to perform empirically significant statistical tests it
must be possible to repeatedly draw samples from the same population.

Econometric hypotheses are stochastic relations. As such their components
represent random variables whose populations have certain density functions.
' If the "true" characteristics of these populations were known, then
statistical tests could be conducted to determine whether particular
sample values came from these density functions or not. In actual fact,
however, the "true" values are unknown, and sample values are used to
calculate parameter estimates. While parameters can be estimated from
sample values, the empirical truth or falsity of an estimated relation

- 362 -

can only be determined if it is possible to draw repeated samples from the
same population. If this condition cannot be ensured, then such tests as
are performed have no empirical significance.

In econometrics the estimated relations are usually tested by the
generation of forecasts for the next period. This test on the theory's
predictive power is empirically meaningful if and only if the population
from which the samples are drawn has remained constant over time. Unfor-
tunately, econometric theory is unable to guarantee that this condition
is satisfied. For the only evidence it can produce is whether the forecast
is confirmed or not. Clearly, correct or erroneous forecasts can occur
for a number of trivial as well as important reasons. The problem is
that the occurrence of either does not provide any evidence on the
required constancy of the underlying population. Unless and until
the stability of such populations can be empirically established it is
not possible to subject econometric hypotheses to a process of disconfirma-
tion by empirical test.

This book is concerned with the development of an empirical science
of economics. Since neither classical nor econometric theory can satisfy
the basic requirements of science, it is necessary to examine recent
behavioral formulations to discover whether these theories can provide the
requisite empirical foundations.

Behavioral theories represent the decision behavior of a variety of
economic actors, A basic premise of these theories is that behavior is a
ccnsequence of specific decision processes acting upon the information

- 363

available at the time. The information itself may reside in the actor's memory
or it may be a product of the environment. In either event such information
is describable and refers to observable entities. Hence, it satisfies
the condition that the initial conditions be empirically determinable.

The empirical validity of the hypothesized decision processes is less
easy to establish. None the less, the procedures by which decision
processes are inferred and tested are such as to permit these theories
to be confuted by empirical test. As evidence for this statement there
are a number of models of economic decision-making behavior which have
survived a variety of empirical tests. These tests corroborate both
the models themselves as well as the theory of human decision behavior from
which they are derived. As a result^ behavioral theories can be constructed
which satisfy all of the requirements of empirical science.

For behavioral theories to serve as the empirical foundations of
economic analysis decision models must be constructed to account for the
variety of observable economic behavior. Given such a statement it
would appear that a model is required for each behaving unit in the economy.
To develop same would clearly be an impractical as well as an exhausting
undertaking. Fortunately, it is also unnecessary as the theory of human
decision behavior permits the identification of classes of decision
behavior which can be encompassed by separate behavioral models.

However^ to be able to explain the behavior of a specific class of
coasuiners or firms is not sufficient to satisfy all economists. For there
are many who are interested in resolving problems with national or
international domains or reference. To develop a science of economics

- 364 -
which can be used by all economists entails the construction of a body of
propositions which refer to large aggregates of individual units as well
as to the units themselves. Traditionally, econometrics is used when dealing
with highly aggregated models while classical economic models are
employed when one is working with the individual units. Since neither of
these systems can provide testable theories a new approach is required--
one which resolves the empirical obstacles while concurrently presenting
economists with the desired theoretical tools.

The solution proposed in this book is as follows: Behavioral theories
should replace classical theories in all situations where microeconomic
analysis is to be employed. With behavioral theories observed decision
behavior can be described in detail and explained. The theory's testability
permits the economist to acquire empirical knowledge of the behaving
units in addition to endowing him with the capability of exploring the
consequences of specific policies by experimental investigation.

One further consequence of behavioral theories is that they provide a
direct measure of the characteristics of a population's decision processes.
That is to say, the minute a model can no longer explain observed
behavior techniques are available with which the alterations in the decision
processes can be isolated and identified. Such shifts in behavior can
be assessed for their effect on the original theory, and by the application
of a new set of tests the amended theory can be corroborated or disconf irmed.
Clearly, this procedure enables one to detect change and hence measure
the stability of specific decision processes. Consequently, behavioral

- 365 -

theories provide a measure on the constancy of decision processes over time
with respect to single economic units or collections of such units.

This is the measure that econometric theory lacks. In addition, most
econometric theories contain variables which are derived from classical
economic theory. Hence, econometric theories, in their current formulations,
do not refer to the same processes and variables as are being measured by
behavioral theories. If the latter are to serve as the requisite measure of a
population's stability over time, the econometric relations must refer to
the same processess. The answer is to construct econometric hypotheses in
terms of the variables that appear in the discrimination nets of behavioral
theories. As long as the process models continue to survive empirical
tests, the concomittant econometric relations can be subjected to empirical
test. For under these conditions, the stability of the population is assured
and the standard statistical test have empirical significance.

The proposal of a solution does not end the matter. For if the major
interests of the economist are to be served a large amount of empirical
work must be done. In particular, the foundations of behavioral theories
must be investigated in greater detail, more models must be constructed and
tested in order to develop general theories of specific economic decision
processes, and the first of a series of behavioral-econometric theories must
be developed and submitted to empirical test. Despite the magnitude of the
task, the actual emergence of a science of economics should be by itself
a sufficient reward.

9»--2.3f

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