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ECONOMIC CYCLES: THEIR LAW
AND CAUSE

THE MACMILLAN COMPANV

NEW YORK • BOSTON • CHICAGO • DALLAS
ATLANTA • SAN FRANCISCO

MACMILLAN & CO.. Limiteo

LONDON ■ BOMBAY • CALCUTTA
MELBOURNE

THE MACMILLAN CO. OF CANADA. Ltd.

TORONTO

ECONOMIC CYCLES: THEIR
LAW AIVD CAUSE

BY
HENRY LUDWELL MOORE

PROFESSOR OF POLITICAL ECONOMY IN COLUMBIA UNIVERSITY
AUTHOR OF " LAWS OF WAGES "

" Nous croyons en effet, pour notre part, que
pour avancer vraiment dans la connaissance
4conomique, il faut s'attaquer directement et
d'abord, a des variations, c'est-a-dire a la forme
dynamique des ph6nomenes, par la voic ex-
perimentale." FR.-VNgois Simiand.

Nruj f nrk

THE MACMILLAN COMPANY

1914

All rights reserved

COPTRIOHT, 1914

By the MACMILLAN COMPANY
Published December, 1914.

TO

JANE MOORE

A CRITIC WHO NEVER DISHEARTENS
A CO-WORKER WHO KEEPS THE FAITH

CONTENTS

CHAPTER I
Introduction 1

CHAPTER II

CYCLES OF RAINFALL

The Use of Fourier's Theorem 6

Periodogram of Rainfall 14

The Equation to the Rainfall Curve 21

Rainfall in the Corn Belt 26

CHAPTER III

RAINFALL AND THE CROPS

The Secular Trend in the Yield of the Croi)s 35

Critical Periods of Growth 41

Cycles in the Yield of the Representative Crops and the

Corresponding Cycles of Rainfall 44

Cycles in the Index of Crop Fluctuations and in the Corre-
sponding Index of Mean Effective Rainfall 49

CHAPTER IV

THE LAW OF DEMAND

The Tlicory of Demand 02

Statistical Laws of Demand GO

The Prediction of Prices 77

Elasticity of Demand 82

vii

viii Contents

CHAPTER V

THE .MECHANISM OF CYCLES

The Pri(;es of Agriculturul Conunoditios Correlated with the

Yield of the Several Crops 94

Rising and Falling Prices as Related to Yield-Price Curves . 100

The "N'olunie of the Crops and the Activity of Industry . . 108

A New Type of Demand Curves 110

The Fundamental, Persistent Cause of Economic Cycles . . 116

CHAPTER VI

SUMMARY AND CONCLUSIONS 135

ECONOMIC CYCLES: THEIR LAW
AND CAUSE

CHAPTER I
INTRODUCTION

There is a considerable unanimity of opinion among
experts that, from the purely economic point of view,
the most general and characteristic phenomenon of a
changing society is the ebb and flow of economic life,
the alternation of energetic, buoyant activity with a
spiritless, depressed and uncertain drifting. During the
creative period of the rhythmic change each factor in
production receives an augmenting income, and the
mutual adjustment of interests in the productive
process is brought about in a natural w^ay, primarily
through the operation of competitive law. The period
of decline in the cycle presents a sharply contrasted
aspect of industry. With the organization of capital
and labor at first unchanged, the amount of the product
falls; each of the interested factors seeks at least to
retain its absolute share of the product; friction and
strife ensue with a threatening of the disruption of
industry. What is the cause of this alternation of
periods of activity and depression? What is its law?
These are the fundamental problems of economic
dynamics the solution of which is offered in this Essay.

Political Economy began to make progress in a
rational way when the Physiocrats put forth their
doctrine of the dependence of all forms of economic life

1

2 Economic Cycles: Their Lmv and Cause

upon agriculture. Another momentous step was taken
in the direction of theoretical development when the
English economists formulated the law of diminishing
returns in agriculture and traced its all-pervasive
influence in the production and distribution of the
product of industry. The desideratum of economic
dynamics at the present time is the discovery of a law
that shall be to a changing society what the law of
diminishing returns in agriculture is to a society in a
comparatively static condition.

The full truth in the old Physiocratic doctrine has
not been exploited. The Department of Agriculture
of the United States reaffirms the central idea of the
doctrine in its motto: ''Agriculture is the Foundation
of Manufacture and Commerce," and in the spirit of
this motto it publishes invaluable statistical data.

It is proverbial that the farmer is at the mercy of the
weather. If it be true that the explanation of economic
cycles is to be found in the law of supply of agricultural
products, it is surely wise in a study of rhythmic eco-
nomic changes to inquire whether the law of the chang-
ing supply of raw material is not associated with a law of
changing weather. Is there a well-defined law of chang-
ing weather?

Supposing that it is possible to discover that the
weather passes through cycles of definite periods and
definite amplitudes, it will then be necessary to show
how the crops are affected by the weather and how the
cycles of the weather are reproduced in cycles of the
yield of the principal crops.

Introduction 3

Wlien the changes in the physical yield of the crops
are shown to be dependent upon changes in the weather,
the next stage in the investigation is to connect the
yield with its value, and this brings one face to face
with another unsolved problem in theoretical economics.
The most recent phase of economic theory opens with a
description of the ''law of demand," which from the
time of Cournot, Dupuit, and Gossen has been assumed
in all theoretical discussions, but there has been no
method for finding the statistical equation to the law.
It will be necessary to overcome the difficulties of this
problem before a solution can be offered of the more
fundamental inquiry as to the law and cause of cycles in
economic phenomena.

When the physical yield of the crops has, on the one
hand, been related to the cycles of the weather and, on
the other, to the prices of the respective crops, it will
then be possible to take the final step and to show how
the cycles in the physical yield of the crops produce the
cycles in the activity of industry and the cycles of
general prices, and how, finally, the law of the cycles of
the crops is the law of Economic Cycles.

CHAPTER II

CYCLES OF RAINFALL

"The first thing that in my opinion ought to be done towards
making the observations useful for scientific purposes is to perform
that kind of more perfect averaging which is afforded by the har-
monic analysis. There is a certain amount of averaging done, but
that is chiefly daily averages, with monthly averages, and yearly
averages; but the more perfect averaging of the harmonic analysis
would give the level of the variation of the phenomenon."

— Lord Kelvin, in his testimony before the Meteorological Com-
mittee of the Royal Society, 1876.

From the point of view of the relation of changing
weather to the varying fruitfulness of agriculture, the
most important factors that are usually included in
the term, weather, are temperature and rainfall. We
begin our investigation with this common belief and
inquire, in this chapter, whether the varying amount
of annual rainfall is subject to any simple law.

In order to carry forward the inquiry as to the exist-
ence of a law of annual rainfall an analysis must be
made of a long record of precipitation. Our choice of
a record is limited by two conditions: First, our object
in investigating the periodicity of rainfall is the hope
of throwing light upon the periodicity in the yield of
the crops, and this expectation obviously makes it
desirable that the record of rainfall shall be as repre-
sentative as possible of the conditions of precipitation

4

Cycles of Rainfall 5

in our leading crop area; secondly, as the existing
meteorological records are of unequal lengths and of
varying reliability, it is necessary to take the best long
records that can be found within the limits of the crop
area.

The principal region of grain production in the United
States is in the Mississippi Valley, but the meteoro-
logical records of the Middle West do not extend through
a long period of time. In order to achieve the two ends
of having a long record of precipitation and of having
the record typical of the conditions in the grain area,
the device has been adopted of investigating rainfall in
the Ohio Valley — which affords the longest record ob-
tainable in the neighborhood of the central Mississippi
region — and of showing that the rainfall of our lead-
ing grain state, Illinois, follows the same law as the
rainfall of the Ohio Valley.

The stations in the Ohio Valley with long rainfall
records are Marietta, Portsmouth, and Cincinnati.
Their mean annual rainfall since 1839 is given in
Table I ^ of the Appendix to this chapter. The graph
of the course of rainfall in the Ohio Valley since 1839
is traced with other graphs on Figures 4, 5, and 6. The
problem that must now be faced is the question as to
whether the sequence of annual rainfall in the Ohio
Valley follows a simple law, and if so, to give a quanti-
tative formulation of the law.

1 The data were taken from Bulletin W of the Weather Bureau of
the United States and from the Annual Reports of the Chief of the
Weather Bureau.

6 Ecojiomic Cycles: Their Law and Cause

The Use of Fourier^ s Theorem

A preliminary examination of the rainfall data of the
Ohio Valley leads to the conclusion that there is prob-
ably no secular trend to the data, that is to say, there
is probably no tendency of the rainfall to increase con-
tinuously or to decrease continuously with the flow of
time. It is true that when the amount of rainfall is
correlated with time, the coefficient of correlation is
r = — .227 ± .075, where the coefficient is three times its
probable error and is therefore suggestive of a decrease
in the amount of rainfall with the flow of time. More-
over, if a straight line is fitted to the data, the indicated
annual decrease in the rainfall is seven hundredths of
an inch. But these facts are no justification for hold-
ing to a secular decrease in the amount of annual
rainfall. For, in the first place, if there are cycles in
the amount of the rainfall, the low degree of the ob-
served correlation might be due to the data of rainfall
including incomplete cycles; in the second place, the
record is drawn from only three stations and because
of the limited number of stations might give an acciden-
tal, low degree of correlation between amount of rain-
fall and time; and in the third place, improvements
in the method of taking the observations might have
introduced changes that would account for the ob-
served small annual decrease in the amount of rain-
fall. In view of these considerations, it is probably
best to proceed with our problem on the assumption
that there is no secular trend in the amount of annual

Cycles of Rainfall 7

rainfall. If this assumption is true, it follows that, in
all probability, the course of rainfall in the Ohio Valley,
is cyclical, or a combination of cycles.

In an inductive treatment of any form of rhythmic
or cyclical change it is necessary that the method
adopted shall satisfy two conditions: (1) It shall be
consistent with recognized mathematical processes;
(2) It shall afford means of testing the degree of proba-
bility that the results are not chance phenomena.
Unless the method rests clearly upon an approved
mathematical process, it is scarcely possible to say
whether the attained results may not be entirely formal ;
and unless the findings are tested for the degree of their
probability, there is no assurance that the adduced
cycle may not be a chance occurrence. The literature
in which rhythmic phenomena are treated in a statis-
tical way teems with fallacies and uncertainties that
illustrate the need of observing the above conditions;
for the method frequently adopted of smoothing the
data is so arbitrary that one is at a loss to know whether,
after all, the alleged periodicity may not, in fact, be due
to the process of smoothing; and, in addition, one is
left in doubt as to whether an indefinite number of
cycles other than the particular one adduced might not,
with equal or greater probability, be obtained from the
same data.

The method that was employed to reach the results
of this chapter rests upon the analysis invented by
Joseph Fourier,^ which is called, in English treatises,

' The most philosophic exposition of Fourier's tlieoreni is in

8 Economic Cycles: Their Law and Cause

harmonic analysis. The perfection of the method
whereby the findings may be subjected to the test of
probabiUty is the work of Professor Arthur Schuster ^
of Manchester.

We may begin the presentation of the method with a
definition of a series of terms that constantly recur in

the treatment of periodic phe-
nomena. Figure 1 will facili-
tate the exposition by affording
a graphic description of the
terms dealt with.

Suppose that the pomt Q
moves uniformly in the circle
of Figure 1 , that is to say, sup-
'^^^^ ■ pose that the point Q describes

equal arcs in equal times and, therefore, proportional
arcs in different times. Then, if the measurements of
the arcs of the circle are made from the point A and
the reckoning of time is begam when Q is at E, the
angle A O E w> called the angle at epoch, or simply

Fourier's own work: Theorie analytique de la chaleur. In Freeman's
English translation the treatment is found on pp. 137-212.

^ The fundamental memoirs of Professor Schuster are

"On the Investigation of Hidden Periodicities wdth Application
to a Supposed 26 Day Period of Meteorological Phenomena."
Terrestrial Magnetism for March, 1898.

"The Periodogram of Magnetic DecUnation as obtained from the
records of the Greenwich Observatory during the j-ears 1871-1895."
Cambridge Philosophical Society Transactions, Vol. 18, 1899.

"On the Periodicity of Sunspots." Philosophical Transactions of
the Royal Society of London, A, Vol. 206, 1906.

"The Periodogi'am and its Oi)tical Analog}'." Proceedings of
the Royal Society of Lo'ni!<))t, A, 'N'oL 77, 1906.

Cycles of Rainfall 9

the epoch of the uniform circular motion. The
radius of the circle is the amplitude of the motion;
the time of going once around the circle is the
period of the motion; the ratio of A Q to the
circumference of the circle is the phase of the mo-
tion.

If from each position of Q a perpendicular is dropped
upon the diameter of the circle, G H, the foot of the
perpendicular will describe a simple harmonic motion.
The amplitude of the simple harmonic motion is one-
half of the range of the motion, that is, one-half of G H,
or the radius of the circle. The period of the siinple
harmonic motion is the interval between the passing
of the point P twice through the same position in the
same du-ection. The distance of the point P from the
middle of its range, 0, is a simple harmonic function
of the time, 0 P =y =asm {nt-\-e), where a is the radius
of the cii'cle — or the amplitude of the simple harmonic
motion — e is the angle of epoch, and n is the angle de-
scribed by the moving point Q in the unit of time. The
period of the simple harmonic motion is, in the above

27r , . nt -\- e

case, — . Its phase is —^ — .

11 ^ 27r

Figure 2 presents a graph of simple harmonic mo-
tion. As in Figure 1, the point Q moves uniformly in
the circle ; the point P performs sunple harmonic motion
according to the formula y=a sin {nt-\-e), where a is
the amplitude of the motion, or radius of the circle, e
is the angle of the epoch, namely, A 0 E, and n is the
arc described by Q in the unit of time. If time is meas-

10

Economic Cycles: Their Law and Cause

ured upon the line B C, the sinuous curve of Figure 2
is the graph of the function, y ^asin {nt-\-e).

Figure 2.

The importance of simple harmonic functions in
the study of periodic phenomena grows out of the fact
that any periodic curve however complex ^ can be ex-
pressed mathematically by a series of simple harmonic
functions. By the help of Fourier's analysis a periodic
function may be put in the form

(1) ?/ =^o + cti COS kt + tto cos 2 H + as cos Zkt-k- . . .
+ 6i sin ki + 62 sin 2 kt + 63 sin 3 A;i + . . .

If in (1), we put,

ai = Ai sin e^; a^ = A^ sin e.,; a^ = A^ sin e^', &c.,
hi = Ay cos Ci; 62 = ^2 cos e,; 63 = A3 cos 63; &c.,

We get,

(2) ?/ = Ao +Ai sin (/c/ + ^i) + A., sin (2 kt + 63)
4- A3 sin (3A:^ + e3) + . . .

where y is expressed as a series of sines. In a similar

manner, equation (1) may be expressed as a series of

cosines,

1 The few exceptions to the general rule are discussed in the
mathematical texts that develop Fourier's theorem.

Cycles of Rainfall 1 1

(3) y = Ao + Bi cos (kt - c i) + ^2 cos (2 kt-e^)

+ B^ cos (3 A-f - e 3) + . . .

In the use of Fourier's theorem for the purpose of
analyzmg periodic phenomena, we follow a process
analogous to the use of Taylor's theorem in the simpler
demonstrations of mathematical economics. By far
the greater part of Cournot's pioneer treatise and of
subsequent work of his school is based upon the as-
sumption that, if the economic function under investi-
gation is y=f{x), then fix +h) may be expanded by
Taylor's theorem, and the first terms of the series may
be used as an approximation to the form of /(x). Simi-
larly, in our use of Fourier's series, the attention will be
focussed upon a few harmonics as a first approximation
to the solution of the problem in hand of expressing
in mathematical form the periodicity of annual rainfall.

Assuming that any periodic function may be ex-
pressed as a Fourier series, the problem is presented of
determining the values of the coefficients. The series,
as we know, is of the form

y = / (0 = Ao + Qi COS kt + a.2 COS 2 kt+ . . .
+ bi sin kt + bo sin 2 kt+ ...

What are the values of the first term and of the co-
efficients of the sines and cosines? In order to deduce
the necessary values, we shall have need of the follow-
ing lemma:

If 7n and n are two unequal integers and k is put equal
to -ji^, then

12 Economic Cycles: Their Law and Cause

I cos mkt cos nkt di = 0,

/T
sin mkt sin nkt dt = 0,

o

/T
sin 7/2.A-^ cos nkt dt =0.

o

The lemma may be proved to be true by evaluating the
three integrals according to the usual methods. The
first integral, for example, becomes

COS mkt cos nkt dt = \ j | cos (m—n) kt +cos (m+n) kt\dt

o o

rsin (m-n) kt sin (m + n) ktV^
^ V 2 (m-w) k ^ 2 {m + n) k L

But fc = -^, and, consequently, I cos mkt cos nkt dt = 0.

o

With the aid of this lemma we may proceed to evalu-
ate the coefficients in Fourier's series. If we integrate
the series between the Umits o and T, we get,

f (t) dt = A^ I dt + Qi j COS ktdt + bi j sin kt dt+ .. .

o o o o

But all of the terms except the first on the right-hand
side of the equation will vanish, and consequently

/T
/ (0 dt

j''f{t)dt= A, j^dt = A,T, or A,= ^-^

o * o

Since / f(i)dt is the area of the original curve for one

o

whole period T, the constant term in Fourier's series is
equal to the value of the mean ordinate of the original
curve.

Cycles of Rainfall 13

To determine the value of Oi, multiply throughout
by cos kt and integrate between Umits o and T.

/ {t) COS kt dt = Ao I cos kt dt + a^ j cos^ A;^ di

o o o

sin A*^ cos kt dt + . . .

o

/ (0 COS kt dt = tti I C0S2 kt dt, since / cos kt dt and

o o o

/T
sin A-< cos kt dt are both equal to zero and all the other

o

terms on the right-hand side of the equation, according
to our lemma, disappear. But

T'' ,.j. pi + cos 2 A-^,^ , r, sin2A-n^ T

o o

and as a result, we have ^t

/ / (/) cos kt dt

fli 2 = / f ^^^ ^^^ ^^ ^^' or Qj = 2 ^

o

Therefore oi is equal to twice the mean value of the
product /(O cos kt.

In a similar manner the value of any other coefficient
may be determined. Take, for example, b„. Multiply
throughout by sin 7ikt and integrate between o and T,

n. , . ■ , , , H- ,.j. , r^ l-cos2nA;< J,
I / (0 sin nkt dt = bn I sm^ nkt dt = b„ j ^ ^^ =

o o o

, f.r, sin 2 nkiy I T

/T
. Therefore 6„

14 Economic Cycles: Their Law and Cause

is equal to twice the mean value of the product
f{t) sin nkt.

Having found the algebraic values of the coefficients
in Fourier's series, we may now proceed to determine
their statistical equivalents in the case of annual rainfall.

The Periodograin of Rainfall

If the length of a cycle of rainfall were known before-
hand, the preceding exposition of Fourier's theorem
would suffice to determine, from the data of precipita-
tion, the amplitudes and phases of the harmonic con-
stituents of the Fourier series descriptive of the rainfall
cycle. But in the problem before us of analyzing the
rainfall data of the Ohio Valley, we do not know whether
there are many cycles or only one cycle or, indeed,
whether there are any cycles at all. And there is no
short method of solving the problem.

Suppose, for example, it were assumed from a priori
considerations that the amount of rainfall is affected
by sunspots, and, as sunspots are known to occur in
periods of about eleven years, suppose it should be in-
ferred that the annual rainfall will likewise show a period
of eleven years. If the rainfall data of the Ohio Valley
are examined for an eleven years period, it will be found
that the data yield a definite amphtude and a definite
phase for a cycle of eleven years, but this fact is no
warrant for holding that there is a true rainfall period of
eleven years. Every other grouping of the seventy-two
years record will likewise show a definite amplitude

Cycles of Rainfall 15

and a definite phase. The questions that one is in-
terested to have answered are: (1) What is the law of
the distribution of Fourier coefficients when the data
are analyzed for all possible periods; and (2) how may
the true cycles be separated from the accidental,
spurious cycles that are obtained when the data are
exhaustively analyzed?

In Figure 3 the results of a detailed, laborious ex-
amination of the data of annual rainfall in the Ohio
Valley are presented in graphic form. On the axis of
abscissas are measured, within assigned limits, the
possible lengths of cycles in the 72 years of rainfall.
By extending the calculations to 36 years, we obtain
for the assumed periods a record of possible recur-
rences varying from 2, in case of the period of 36
years, to 24, in case of the period of 3 years. On the
axis of ordinates are measured the squares of the co-
efficients of the first harmonic in tlie Fourier series
corresponding to the lengths of periods recorded on
the axis of abscissas. The numerical values of these
squares are given in the fourth and eighth columns of
Table II in the Appendix to this chapter. The method
of deriving the values may be illustrated by taking the
cycle of 8 years. Suppose, as a first approximation,
that the equation to Fourier's series is put in the alge-
braic form

y = F(t) = Ao + ai cos kt + bi sin kt'^=AQ+]Ai^sm(kt + e).

Then the corresponding arithmetical values derived
from the Ohio rainfall data are

16

Economic Cycles: Their Law and Cause

■//Pju/p^jo satfoui ui 3pn4iic/uje at^j. jo a^enbc

Cycles of Rainfall 17

y = F{t) = 41.19-3.13 cos g- ^ + 2.69 sin -g- i

= 41.19+4.13 sin (^ t + 310° 41').

The values of the terms a\, 6;, A\ are respectively
(3.1339)-, (2.6938)-, (4.1325)-, and these values are
given in the proper columns of Table II in the Ap-
pendix. In Figure 3, the values of A"^ for the several
periods are measured on the axis of ordinates.

An examination of Figure 3 will illustrate the truth of
a statement advanced a moment ago. It is clear from
the course of the periodograph ^ that if one were to
take any period at random between the hmits of 3
years and 36 years, he would in every case obtain a
finite value for the amphtude of the selected cycle ; and
if, by chance, selection should fall upon, say, 18, or 21, or
29, or 36 years, an argument might be made with some
degree of plausibility that a real cycle had been dis-
covered. But, in truth, the real significance of no one
cycle taken at random can be judged apart from its
place in the distribution of all the cycles that can be
derived from the data.

This last point is of fundamental importance. The
only object of investigating cycles of rainfall or cycles of
economic phenomena is that the knowledge of the

1 The terms periodograph and periodogram were coined by Pro-
fessor Schuster.

The periodograph is the cur\-e tracing the values of A-; the
periodogram is the surface between the periodograph and tlie base
line giving the lengths of the periods. Schuster: "The Period-
ogram of Magnetic Declination," p. 108.

18 Economic Cycles: Their Law and Cause

constant recurrence of the cycles may place one in a
position to foresee and utilize the dependent phenomena.
But the control of phenomena dependent upon a cycle
presupposes that the cycle is itself a real phenomenon
with a natural cause, and that consequently it persists
with an increase in the number of observations. If,
however, an apparent cycle of any length taken at
random is obtained from the given data, one would
surely misspend his time if he were to set about the
search for its cause, and were to derive conclusions based
upon the hypothesis of the persistence of the cause.
The cycles due to formal, accidental causes must be
discriminated from the cycles with natural causes.

The separation of true cycles from spurious or
accidental cycles is facihtated by the periodogram ^ of
observations. If, following Professor Schuster, we call
the square of the amplitude of any given period the
"intensity" of the period, then it may be said that the
probability of the reality of a period is dependent upon
the ratio of its intensity to the mean intensity of the
periodogram. Or, again following Professor Schuster,
if we call the mean intensity of the periodogram the
''expectancy," then the reality of a period is dependent
upon the ratio of its intensity to the expectancy of the
periodogram. For instance, if in case of a given period
the ratio of intensity to expectancy is, say, 3 to 1, then
in about one case in twenty we should expect to obtain
by chance a greater amphtude than the amplitude of
the particular period in question. If, on the other hand,
1 See the preceding note.

Cycles of Rainfall 19

the ratio were say, 7 to 1, a greater ratio would not
occur by chance once in a thousand times. ^

With these facts in mind, let us again examine Fig-
ure 3. It is clear that the principal periods needing
attention are those respectively of 8, 29, 33, 36 years.
In case of the 8 year cycle there can be very little
doubt as to the existence of a true periodicity approx-
imating 8 years in length. The ratio of the square of
its amplitude to the mean square amplitude of the
periodogram is 6.71 to 1. We may accordingly accept
with considerable confidence the existence of a natural
period of rainfall in the Ohio Valley approximating
8 years in length.

The cycle of 33 years, inasmuch as the ratio of the
square of its amplitude to the mean square amplitude
of the periodogram is 3.27 to 1 is in all probability a
true cycle. The doubt that exists is due to the smallness
of the ratio and the few recurrences — only two - —

1 Schuster: "The Periodogram of Magnetic Dechnation," pp. 124-
125.

2 Those who deprecate the use of such meager data should con-
sider well the testimony of Lord Kehdn before the Meteorological
Committee of the Royal Society, 1876.

Question 1710. "The sum which parhament will give for this
purpose being a limited sum, do you think that it would be well to
reduce the number of observations in order to have more money to
spend upon the reduction of observations? / think at all events tintil
one eleven yearn period, the sun spot period, is completed, it would be
ivrong to reduce the number of observations."

Question 1735. "Supposing that you had one of these analyses
calculated for a period of 11 years, would each year's observations
and still more each period of 11 j^ears observations, require to be
introduced into this analysis so that you would have an analysis of
22 years, and an analysis of 33 years, and so on from time to time,

20 Eco7iomic Cycles: Their Law and Cause

that our data afford. A greater confidence in the exist-
ence of a real period of 33 years is given by the fact that
Briickner ^ claims to have found a true period of about
35 years in an examination of a vast mass of rainfall
material all over the world. Accordingly, the existence
in the Ohio Valley of a real 33 years period of rainfall we
shall assume to be very probable.

The other two periods of 29 years and 36 years are
not easily disposed of. But in the first place, the ratios
of the squares of the respective amphtudes to the mean
square amplitude of the periodogram are not such as to
justify the acceptance, with any degree of confidence, of
the existence of true cycles of 29 years and 36 years.
In the second place, they are both so close to the period
of 33 years as to cause a doubt as to whether they may
not be spurious periods that are likely to appear in the
neighborhood of a real period.^

Considering the short range of our data it would not
be properly cautious to press the point of the existence
of any definite real cycle. But this much is certain:
If there are true cycles in the data of the 72 years of
rainfall in the Ohio Valley, there is far greater prob-
abihty that two cycles are those of 8 years and 33
years than of any other round numbers between 3 and

or, being done, would it be done once for all? / cannot say whether
anything with reference to Terrestrial Meteorology is done once for all.
I think probably the work will never be done."

1 Edward Bruckner: Kliniaschwankungen seit 1700. Bruckner's
period fluctuates greatly in length and has an average value of 35
years.

2 Schuster: "The Periodogram of Magnetic Declination," p. 130.

Cycles of Rainfall 21

36 years. Moreover, the periods of 8 years and 33
years afford the most probable basis derivable from the
data upon which to reason both as to the future course
of rainfall in the Ohio Valley and as to the course of the
phenomena dependent upon rainfall.

Assuming, then, that for the purpose in hand, the 33
years and 8 years periods are the most probable and
valuable, we turn to the consideration of the equation
to the graph giving the course of rainfall in the Ohio
Valley.

The Equation to the Rainfall Curve

It will be helpful to approach the algebraic descrip-
tion of the cyclical movement of rainfall in the Ohio
Valley, by observing how we obtain an increasingly
accurate account of the actual rainfall by superposing
the constituent cycles. We shall use, as an index of the
relative fit of the several curves, the root-mean-square
deviation of the observations from each curve.

If, as a preliminary step, the raw data of the course
of annual rainfall are examined, it is found that the
mean annual rainfall in the Ohio Valley is 41.19 inches,
and the root-mean-square deviation about the mean is
/S = 6.70 inches.

If the long 33 years cycle is considered by itself, it
appears that the root-mean-square deviation about the
33 years curve is >S = 6.39 inches. The graph of the
33 years cycle is given in Figure 4. Its equation is

y = 41.19 + 2.88 sin (^ t + 328° 7'V

22 Economic Cycles: Their Law and Cause

Cycles of Rainfall 23

the origin being at 1839. This curve traces in bold
outline the general course of ramfall. It gives the
ground-swell of the rainfall movement.

If the 8 years cycle is superposed upon the 33 years
cycle, the root-mean-square deviation about the curve
becomes S = 5.66 inches. The graph of the combination
of these two curves is traced in Figure 5. Its equation is

1/ = 41.19 + 2.88 sin (1^^ + 328° 7') +4.13 sin (I'i + SIOMI'),

the origin being at 1839. A point of interest with regard
to the flow of the curve is the rapidity with which it
rises from the least minimum to the greatest maximum,
and the slowness with which it then descends to the
subsequent least minimum.

If the 8 years cycle and its semiharmonic of 4 years
are combined with the 33 years cycle and its semi-
harmonic of 16.5 years, the root-mean-square deviation
about the compound curve becomes *S=5.29 inches.
The graph of the curve is given in Figure 6. Its equa-
tion is

7/ =4 1.19 + 2.88 sin (1^ i + 328° 7') + 2.25 sin (';*^^ + 27 P 42')

+ 4.13 sin/^ t+3l0° 41') + 2.14 sin/^ t + 180° 28') ,

the origin being at 1839. In this closer approximation
the characteristic rapid rise to a general maximum and
slow fall to a general minimum is reproduced. Another
characteristic is the longer interval that the curve

24

Economic Cycles: Their Law and Cause

siL/ou: ui iiejuipj /enuu\/

Cycles of Rainfall

25

tiL/iui ui ijefuipj ienuu\/

26 Economic Cycles: Their Law and Cause

lingers at the minima and the short period during which
it flows in the neighborhood of the maxima.^

Rainfall in the Corn Belt
Thus far we have dealt with the law of rainfall only
in the Ohio Valley. The object in taking the Ohio
data, rather than the data of a state more representa-
tive of the leading cereal area, was to make an investiga-
tion of a longer meteorological record than is afforded
by the data of the central Mississippi Valley. But our
purpose in dealing with meteorological records at all is
to show the dependence of crops upon the cyclical
movement of the elements of the weather. We must,
therefore, prove that the cycles of rainfall which we have

1 1 should like to make clear the method I have followed in the
derivation of the equations to the cun'es. My object was to obtain
a summaiy description of the general course of rainfall in order that
I might discover, later on, whether the characteristic general fea-
tures of the movement of rainfall are reproduced in the changing
yield per acre of the crops. As a first step I tried to detect the real
cycles in rainfall and I believe I have sho^\^l that, if the 72 years
record is sufficiently long to reveal the true cycles, then the most
probable lengths of the cycles are, in round numbers, 33 years and
8 years respectively. With so short a range of data I regarded it as
useless to attempt to calculate the lengtlis of the periods to a greater
degree of precision. I next had to derive the equations to the curves
showing the characteristic general course of rainfall, and it seemed
to me that, for this purpose, the method described in the text for
evaluating the coefficients in a Fourier series might properly be
used. If the 33 years cycle were taken as the fundamental cycle,
then the 8 years cycle would be approximately the fourth harmonic
in the series, and the 4 j^ears cycle would be the eighth harmonic.

The arithmetical process for computing the coefficients is indi-
cated by Professor Schuster in Hidden Periodicities, pp. 13, 14 and is
briefly described by Professor Perry in an article on "Harmonic
Analysis" in The Electrician, for February 5, 1892.

Cycles of Rainfall 27

discovered for the Ohio Valley are likewise the cycles
that exist in the heart of the grain producing area.

.■Vmong the states of the Middle West, Illinois is
probably the most highly representative of American
cereal production. It produces the largest crop of
corn/ which is the leading American cereal, and it
ranks second in the production of oats. Most of the
other cereals that are produced in the upper Mississippi
Valley are likewise cultivated with success in Illinois.
Another fact that makes Illinois a desirable state for
our purpose is that its meteorological records are fairly
long and are obtainable from so many stations as to be
representative of the weather conditions in the entire
state. This last fact is all-important if the statistics
for crop production of the whole state are to be con-
sidered in relation to the weather cycles of the state.

In Table III of the Appendix to this chapter the
record of the annual rainfall in Illinois is given for a
period of 41 years.'- The ideal direct method with

1 This statement was accurate when it was first \\Titten. But in
1912 Iowa gained by a narrow margin the first place among the corn
producing states.

2 The raw data were taken from Bulletin W of the Weather Bu-
reau of the United States and from the Annual Reports of the Chief
of the Weather Bureau. The stations used in computing the mean
annual rainfall were: — In Northern lUinois: Aurora, Cambridge,
Chicago, Tiskilwa, Galva, Kishwaukee, Ottawa, Winnebago, and
Henry. In Central Illinois: Charleston, Carlinville, Coatsburg,
Decatur, Griggsville, Knoxville, Havana, LaHarpe, Pana, Peoria,
and 8j)ringfield. In Southern Illinois: Cairo, Cobden, Carlyle,
Golconda, Flora, Greenville, McLeansboro, Mascoutah, Mt.
Carmcl, and Palestine.

All of these stations do not present full records for the 41 years.

28 Economic Cycles: Their Law and Cause

reference to these data would be to compute the
periodogram in the same manner in which it was com-
puted in the case of the Ohio Valley data, and then com-
pare the periodograms. But this method has not been
followed. A less direct, and far less laborious, process
has been adopted. We know from the Ohio data that
there are two cycles of rainfall, a 33 years cycle and an 8
years cycle, and we know, furthermore, that when the
curve for rainfall in the Ohio Valley is computed for the
33 years and 8 years periods and their semiharmonics, a
good fit to the data is obtained. The questions that are
asked with reference to the Illinois data are these:
If we assume the existence of a 33 years period and an
8 years period in the Illinois rainfall data, will the
rainfall curve fit the Illinois data as well as the Ohio
curve fits the Ohio data? Will the Illinois curve re-
produce the characteristic features of the Ohio curve?
A presumption in favor of an affirmative answer to
these questions is suggested by the fact that the correla-
tion between the annual rainfall in the Ohio Valley and
the annual rainfall in the state of Illinois is r=6.00.
The graph of the curve of rainfall in Illinois is given
in Figure 7. Its equation is

2/ =38.53 +3.03 sin /|| ^+325° 35'^ + 1.87 sin (^^ ^+ 194° 55')

+3.05 sin (^ ^ +241° 52') + 1 . 12 sin /^ f +232° 26') ,

the origin being at 1870. The root-mean-square devia-

but in no year were fewer than seven records obtainable while for a
large proportion of the years the thirty records were complete.

Cycles of Rainfall

29

+

+

+

a]

194°
rigin

+ o

t>-

■^ 1 CO

+

sai^oui ui iiBj-UiPJ jDnuuY

30 Economic Cycles: Their Lmv and Cause

tion of the observations from this curve is S =4.20. In
case of the Ohio curve the root-mean-square deviation
was 5=5.29. But this is a better relative fit for the
lUinois curve than we have a right to claim, because in
Ohio the mean annual rainfall is 41.19, while in Illinois
the mean is 38.53. If we express the relative scatter of
the observations about the curve as the ratio of the
root-mean-square deviation of the observations to the
mean rainfall, we get for Ohio and Illinois, respectively,
5^ = . 128;. SI = .109.

In Figure 8, the Ohio curve for 1870-1910 is placed
upon the same chart as the Illinois curve for the same
flow of time, and the degree of correspondence of the
two curves is seen to be so close that, with due allowance
for the difference in their mean annual rainfall, they
seem to be almost congruent.

We may say, therefore, that the two curves fit their
respective data equally well.

Our problem has now received its solution. Annual
rainfall in the chief grain-producing area of the United
States has no secular trend, but its mean course is the
resultant of causes producing two cycles of 33 years
and 8 years respectively. The manner in which these
cycles of rainfall produce a rhythmical expansion and
contraction in the yield of the crops we shall examine in
the next chapter.

Cycles of Rainfall

31

Tai^Dui ui IIPJ.UIPJ jpnuu^

32

Economic Cycles: Their Law and Cause

APPENDIX

TABLE I. — Annual Rainfall in the Ohio Valley
Stations: Cincinnati, Portsmouth, Marietta

Year

Rainfall in \
Inches

Year

Rainfall in
Inches

Year

Rainf.vll in
Inches

1839

29.92

1863

37.95

1887

38.00

1840

42.84

1864

36.68

1888

46.19

1841

43.94

1865

48.93

1889

37.06

1842

41.89

1866

47.37

1890

55.43

1843

48.20

1867

40.72

1891

40.68

1844

37.95

1868

46.87

1892

36.96

1845

40.11

1869

41.29

1893

40.80

1846

48.39

1870

37.46

1894

31.07

1847

55.26

1871

29.91

1895

29.05

1848

44.97

1872

32.90

1896

39.22

1849

46.37

1873

45.18

1897

44.80

1850

54.77

1874

38.48

1898

45.04

1851

32.54

1875

44.78

1899

40.46

1852

46.73

1876

47.34

1900

* 33.60

1853

35.67

1877

34.69

1901

31.78

1854

40.30

1878

36.35

1902

39.53

1855

47.89

1879

39.22

1903

37.98

1856

28.98

1880

49.94

1904

28.24

1857

37.95

1881

41.60

1905

42.81

1858

55.48

1882

56.10

1906

41.95

1859

46.68

1883

49.25

1907

46.68

1860

36.00

1884

40.05

1908

33.29

1861

43.81

1885

37.63

1909

41.40

1862

40.26

1886

39.61

1910

36.20

Cycles of Rainfall

33

TABLE II. — The Periodogram of Rainfall in the Ohio

Valley

y = F(t) = Ao + ai cos kt + bi sin kt = Ao -{- Ay sin (kt -f- e)

Length

OF

Period

IN Years

o-

6^

a2+62=A2

Length
OF Pe-
riod IN
Years

a2

6-

a^+b-=A-

3

1.2628

2.4821

3.7449

21

.0046

4.4260

4.4306

4

.0003

4.5689

4.5692

22

.2454

2 . 4237

2.6691

5

.0897

.4520

.5417

23

.8471

.8714

1.7185

6

.2220

. 1403

.3623

24

.3551

.0678

.4229

7

2.1838

3.7869

5.9707

25

.2755

. 1327

.4082

8

9.8215

7.2563

17.0778

26

.0566

.0002

.0568

9

.0327

.3120

.3447

27

.9692

.0019

.9711

10

.5978

.0190

.6168

28

.6227

.0300

.6527

11

1.0756

.6791

1.7547

29

4.2657

1.1153

5.3S10

12

.4371

.1143

.5514

30

.6464

.4767

1 . 1231

13

.0044

.0007

.0051

31

.6112

.5923

1.2035

14

.1078

.1670

.2748

32

.5776

1.1168

1.6944

15

. 1874

.0863

.2737

33

2.3199

5.9974

8.3173

16

.7691

.0424

.8115

34

.2017

1.76.52

1.9669

17

.9795

.0626

1.0421

35

.0456

1.7914

1.8370

18

2.9332

.9270

3.8602

36

.0036

6.8567

6.8603

19
20

1.4777
.0294

1 . 9422
1.5961

3.4199
1.6255

Mea

n value

of A' = 2.5459

34

Economic Cycles: Their Law and Cause

TABLE III. — Annual Rainfall in Illinois

Year

Rainfall in Inches

Year

Rainfall in Inches

1870

29.65

1891

34.11

1871

36.53

1892

44.17

1872

33.98

1893

35.89

1873

41.62

1894

28.99

1874

32.91

1895

32.92

1875

40.34

1896

38.27

1876

45.50

1897

37.44

1877

42.76

1898

49.09

1878

37.61

1899

34.95

1879

36.10

1900

36.19

1880

42.31

1901

27.17

1881

42.32

1902

42 . 65

1882

49.04

1903

35.97

1883

47.81

1904

39.33

1884

45.83

1905

37.33

1885

40.80

1906

38.10

1886

36.16

1907

40.61

1887

33.40

1908

36 . 76

1888

39.41

1909

44.74

1889

36.27

1910

34.34

1890

40.34

Mean

38.53

CHAPTER III

RAINFALL AND THE CROPS

"It is mere weather . . . doing and undoing without end."

— William James.

In the preceding chapter the course of annual rainfall
in the great cereal-producing area of the United States
has been shown to move in cycles: There is a ground-
swell of thirty-three years in length upon which cycles
of eight years in duration are superposed. Our object
in studying the rhythmic changes in the volume of rain-
fall was to bring these changes into relation with the
variations in the yield per acre of the crops, and in the
present chapter we shall be able to i-ealize our purpose.
The actual course of the varying yield per acre of the
crops will be shown to have both a secular and a cyclical
movement; these two movements will be separated for
representative crops; and the cyclical movements will
be shown to be dependent upon the cyclical movements
in the weather represented by the cycles of rainfall.

The Secular Trend in the Yield of the Crops

The state of Illinois was chosen in the preceding
chapter to illustrate the general conditions of rainfall
in the Corn Belt of the Middle West, and we shall now
examine the statistics of the yield of its most important
crops.

35

Acreage

Value of Crop

10,658,000

$174,791,000

4,220,000

54,818,000

2,512,000

41,152,000

1,183,000

8,641,000

137,000

8,302,000

57,000

952,000

48,000

538,000

4,000

70,000

900

62,000

36 Economic Cycles: Their Law and Cause

According to the Yearbook of the Department of
Agriculture for 1912, we find the acreage and value of
the leading Illinois crops as they are given in the
subjoined Table:

Acreage and Value of Crops in Illinois, 1912

Crop

(1) Corn

(2) Oats

(3) Hay

(4) Wheat

(5) Potatoes

(6) Barley

(7) Rye

(8) Buckwheat

(9) Tobacco

It is clear, from this Table, that five crops — corn, oats,
hay, wheat, and potatoes — make up the bulk of the
crops of lUinois, and one could not go far wrong if he
based his generalizations as to the conditions of agricul-
ture in the state upon these five crops. But for the
purposes we have in view, in this and other chapters, it
is not possible to utilize the statistics of wheat produc-
tion because both spring and winter wheat are grown in
the state, and the statistics of their relative yield and
price are not given in the published material for the
long record covered in our investigation. Accordingly,
the crops that have been actually used in our inquiry
are corn, oats, hay, and potatoes. These crops total
93.13 per cent, of the crop acreage and 96.45 per cent, of
the crop value as these quantities are given in the'above
Table.

Rainfall and the Crops 37

As the yield per acre of the various crops may show a
secular as well as a complex cyclical change, it will be
necessary, before their cyclical elements can be brought
into relation with the corresponding cyclical changes of
rainfall, to eliminate from the recorded course of the
yield per acre of the several crops the element of change
that is secular in character.

The method that has been adopted here to effect the
elimination of the secular change is simple, but to secure
a first approximation, it is adequate. For a period of
time covered by the statistics, a change is regarded as a
secular change if, for the period of time taken as a
whole, the yield per acre of the crop shows a tendency
either to increase or to decrease. In order to determine
whether there is a secular change in the yield per acre,
for a certain period of time, the yield data are correlated
with time, and the existence or non-existence of a
secular change is inferred from the relative magnitudes
of the coefficient of correlation and its probable error.
If there be a secular change, the calculation of the
coefficient of correlation of the yield with time is then a
first-step toward the elimination of the secular element
by means of a regression equation in which the co-
efficient of correlation is a factor.

The method may be illustrated by taking the history
of the yield per acre of corn. In Figure 9 the actual
yield per acre in Illinois is plotted for the period 1870-
1910. The straight fine showing the secular trend of the
yield is the graph of the regression equation between
the yield per acre and time. The correlation of the

38 Economic Cycles: Their Law and Cause

3JOQ j^cf u^ooj.o sf9i^sng

Rainfall and the Crops 39

yield per acre and time is r = .382 ± .090, and the regres-
sion equation is, ?/ = .204x +26.93, where y= yield per
acre, a: = time, and the origin is at 1870. The secular
trend is eliminated by means of the facts summarized
in the regression equation: Beginning with the year
1870, as many times .204 are subtracted from the
jdeld per acre for the several years, as the respective
years differ from 1870. For example, the yield for the
year 1872 was 39.8 bushels per acre; consequently the
reduced yield for that year was 39.8-2(.204) =39.8-
.408 =39.39. Figure 10 traces the yield per acre of corn
freed from the secular trend.

Of the four leading crops of Illinois that form the
basis of our investigation, only two, corn and potatoes,
show a significant ^ tendency to secular change. The
correlation between the yield per acre and time is,
for hay, r = .013 ±.105 and, for oats, r = .043 ±.105;
consequently the figures for the yield per acre of these
two crops have not been reduced. In the case of
potatoes, r = .122 ±.104, and the regression equation
is 1/ = .233^+70.51, where the origin is at 1870. The
figures for the actual yield per acre and the reduced
yield per acre for corn and potatoes, as well as the
figures for the yield of hay and of oats, are given - in
Table I of the Appendix to this chapter.

1 The indicated secular trend in potatoes is not significant in
the mathematical sense, because the probable error of the coefficient
of correlation is nearly as large as the coefficient itself. I have
nevertheless eliminated the indicated secular trend before using the
data.

2 The raw data were taken from BuUelins 56, 58, 62, 63 of the

40

Economic Cycles: Their Law and Cause

1 1 1 1 1

"^^.^^

,--'

/

-

------lll-

-

\__

^__

,r-

^^-''

-

/

-

-

.2

-

_,

__,^^ — """

V

-

^^

-~~.

-

_,

^

N

X^

a * , '■

1

, ,. 1 1

1 1 1

_ CO _a;

■<2vjp -/^</ ujoo JO sidLjsng

Rainfall and the Crops 41

Critical Periods Of Growth

If the rhythmical changes in rainfall are to give the
clue to the changes in the yield of the crops, the varia-
tions in the rainfall must be closely related with the
variations in the yield of the crops. But different crops
have different times of planting and of harvesting,
different periods of growth, and different requirements
of moisture at the various stages of growth. The direct
Way to find whether the course of rainfall determines
the course of the varying yield of the crops is first to
ascertain the critical season for every crop ; and then to
compare the course of the yield of each crop with the
course of the rainfall of its critical season.

The method of discovering the critical period of a.
crop may be illustrated in the treatment of corn. In
Table II of the Appendix to this chapter, the mean ^
monthly rainfall for Illinois is tabulated for seven
months, March, April, May, June, July, August, and
September. Table I of the Appendix records the data

Bureau of Statistics of tlie United States Department of Agriculture
and from recent Yearbooks of the United States Department of
Agriculture.

1 The raw data were taken froni Bulletin W of the Weather
Bureau of the United States and from the Annual Reports of the
Chief of the Weather Bureau. The stations used in computing the
mean monthly rainfall were, in Northern Illinois: Aurora, Cam-
bridge, Chicago, Tiskilwa, Galva, Kishwaukee, Ottawa, Winnebago
and Henry. In Central Illinois: Charleston, Carlinville, Coatsburg,
Decatur, Griggsville, Knoxville, Havana, LaHar])e, Pana, Peoria
and S])ringfield. In Southern Illinois: Cairo, Cobden, Carlyle,
Golconda, Flora, Greenville, McLeansboro, JMascoutah, Mt.
Carmel and Palestine.

42 Economic Cycles: Their Law and Cause

referring to the yield per acre of the several crops after
the secular trends have been eliminated. These two
Tables furnish the statistical material for ascertaining
the critical periods of the respective crops. The facts
as to the times of planting and harvesting may be
obtained from an article in the Yearbook of the United
States Department of Agriculture, 1910, pp. 488-494,
on ''Seedtime and Harvest: Average Dates of Planting
and Harvesting in the United States." The method of
detecting the period of critical relation between yield
and rainfall consists in ascertaining, for each crop, the
month or combination of months, within the interval
between planting and harvesting,^ whose rainfall gives
the highest correlation with the ultimate yield per
acre of the crop. The time for planting corn in Ilhnois,
according to the official publication cited above, begins
about April 30, it is general about May 13, and it ends
about June 2. The average time for harvesting, accord-
ing to the same publication, begins about September 26,
is general by October 29, and ends about December 10.
The correlation between the yield of corn per acre
(secular trend eliminated), and the rainfall for June is,
r = .069; for July, r = .496; for August, r = .293; for
September, r = .087 ; for July and August combined,
r = .589. The critical period of growth for corn has,
therefore, been assumed to be the interval of two
months — July and August.^

1 For some purposes it would be desirable to test the correlation
beyond these limits.

2 Of course all possible combinations of months have not been

Rainfall and the Crops 43

The critical periods for the other crops are, for oats —
May, June, July, r = .290; for hay — March, April,
May, June, r = .620; for potatoes — July and August,
r = .666. The critical season for corn, as we found a
while ago, is July and August, r = .589.

The high correlation between the yield of the crops
and the rainfall of their respective critical seasons
promises well for the theory as to the relation of the
cycles of rainfall and cycles of crops. In the last chapter
we found that by examining the periodogram of annual
rainfall in the Ohio Valley, cycles of eight years and of
thirty-three years were discovered; and that by taking
periods of thirty-three years and eight years with their
semiharmonics, a good fit to the annual rainfall curve
was obtained. It was then shown that the annual rain-
fall in Illinois is correlated with the annual rainfall
in the Ohio Valley, the correlation coefficient being
r - .600. Upon the basis of this relatively high correla-
tion, it was assumed that the annual rainfall in Ilhnois
passed through similar cycles to the rainfall in the
Ohio Valley, and we found that this assumption was
justified by the facts inasmuch as the harmonic analysis
applied in the same way to the Ilhnois data afforded as
good a fit as when it was apphed to the data of the
Ohio Valley. Since in two of the four representative
crops the correlation between the yield and the rainfall

exhausted in the above case, nor have we made any attempt to
place the critical period for a smaller interval of time than a month.
If for any other period a closer relation could be found than r = .589,
the conclusions that we draw from our investigation would only be
strengthened.

44 Economic Cycles: Their Law and Cause

of the critical season of growth is greater than the
correlation between the annual rainfall in Illinois and
the annual rainfall in the Ohio Valley, there would
seem to be excellent ground for beheving that the cycles
of the yield of the crops would flow congruently with
the cycles of rainfall during their respective critical
periods.

Cycles in the Yield of the Representative Crops and the
Corresponding Cycles of Rainfall

The method of bringing the cycles of rainfall for the
critical period of growth of the several crops into rela-
tion with the cycles of the respective crops is similar to
the method that was employed in passing from the
cycles of annual rainfall in the Ohio Valley to the
corresponding cycles in the state of IlUnois. The
laborious but direct way of treating the problem would
be to compute the periodogram of rainfall for the
critical period of growth of each crop, and then to com-
pare the results with the corresponding periodograms of
the respective crops. It may be that this laborious
process may eventually have to be followed. The
process that has been adopted in the present investiga-
tion makes several assumptions which it is highly
desirable to have clear in mind. It is assumed

(1) That the course of the annual rainfall is the mean

course of the rainfall of the parts of the year

and that, consequently, by computing the

: : periodogram of annual rainfall, we obtain a

general type of curve for describing not only

Rainfall and the Crops 45

the annual rainfall but also the rainfall of
any considerable part of the year. Or, more
concretely, that the annual rainfall and the
rainfall of any considerable part of the year
may be described by an equation of the form

+ «i sin l-^t + rjA + a^^ sin (^y ^ + ■»?•.) ,

where the constants in the series may be differ-
ent for the several parts of the year,

(2) That where the correlation between the yield per

acre of a particular crop and the rainfall of its
critical season is high, the same general type
of equation will fit both groups of data, the
data of rainfall and the data of the yield per
acre of the crops.

(3) That both of the i^receding assumptions are

greatly fortified if the compound curves de-
duced from the actual data of rainfall and
yield satisfy a reasonable test of fit to the data.

The working out of the consequences of these as-
sumptions is exliibited in Figures 11, 12, 13, and the
equations descriptive of the several curves appear on
the corresponding Figures.

To measure the degree of fit of the curves to their
respective data, we shall employ a coefficient K, which
may be described as the ratio of the arithmetical sum
of the deviations of the observations from the curve

46

Economic Cycles: Their Law and Cause

Bushels o-f pofafoes per acre

'^FO^ny pup ^/"P 'sSLjOui ui npjuie^

Rainfall and the Crops

47

Tons of hdy per acre

■9unp'/p(^'ludY'LiDjei^'saLfOui ui //P/i^'Py

48

Economic Cycles: Their Law and Cause

Bushels of corn per acre.

.fcn^n^ pup //np's^Lfjui ui HPjuiey

Rainfall and the Crops 49

divided by the area included between the curve and the
straight Hne indicating the mean value of the observa-
tions. In the equation to the compound cycle describ-
ing the typical curve with which we shall have to deal,
the first term gives the mean value of the observations,
and the remaining four harmonic terms trace the area
about the horizontal line drawn at a distance from the
base line equal to the mean value of the observations.
The reason for adopting this complex coefficient K is
that the curves whose relative degrees of fit are in
question apply to qualitatively different things. From
the method of calculating K, it follows that the smaller
the value of K, the better is the degree of fit of the curve
to the observations.

Passing now to the calculations referring to the
representative crops, we find,

For potatoes, the correlation of the yield per acre
with the rainfall of its critical period — July and Au-
gust— is r = .666. The measure of the fit of the com-
pound cycle of thirty-three years and eight years with
their semiharmonics is, in case of the yield per acre,
K = 1.97, and in case of the rainfall of the critical period
of growth, K = 1.30.

For hay, the correlation of the yield per acre with
the rainfall of its critical period — March, April, May,
June — is r = .620. The measure of the fit of the com-
pound cycle to the data is, in case of the yield per acre,
K = 1.57, and in case of the rainfall of the critical season,

For corn, the correlation of the yield per acre with

50 Economic Cycles: Their Law and Cause

the rainfall of the critical season — July and August —
is r = .589. The measure of the fit of the compound
cycle to the data is, for the yield per acre, K = \.52,
and, for the rainfall of the critical season, K = 1 .30.

For oats, the computation of the equation has not
been carried out because no critical period of growth
could be found in which the correlation between yield
and rainfall was higher than r = .3. The correlations
were, for March, r = — .181; for April, r = — .147; for
May, r = 120; for June, r = .297; for July, r = .140; for
May, June, and July, r = .290.

Referring now to the Figures 11, 12, 13 and to the
calculations that have just been reviewed, we observe
that the compound cycles of yield per acre and of the
rainfall of the critical seasons flow almost congruently,
and that the compound cycle of thirty-three years
and eight years with their semiharmonics fits the yield
data nearly as well as it fits the rainfall data.

Cycles in the Index of Crop Fluctuations and in the Cor-
respondirig Index of Mean Effective Rainfall

Does the cyclical movement of rainfall give a rhyth-
mic movement to the fluctuations in the yield of the
crops taken all together? The preceding section has
treated the relation of the yield of the separate crops
to the rainfall of their respective critical seasons; we
now inquire whether the yield of all of the crops taken
together shows a tendency to conform to the cycUcal
movement of rainfall. In order to answer this question
two preUminary steps must be taken: (1) A method

Rainfall and the Crops 51

must be devised for measuring the fluctuation in the
yield of the crops when the crops are taken all together;
and (2) a method must be devised for combining the
rainfall of the critical periods of the growth of the
several crops. These two steps we shall now consider.
In regard to the first of these desiderata, it is clear
that the measure of the fluctuation of crops taken as a
whole should be based upon the best measure of the
fluctuation of the yield of the crops taken singly. More-
over, there is a general agreement that the standard
deviation of a frequency scheme is a good measure of
the scatter of the observations about their mean value.
A natural step, therefore, would be to assume that if
the observations form a series in time, a good rela-
tive measure of their fluctuations at different epochs is
afforded by the ratio of the deviations of the observa-
tions from their mean divided by the standard devia-
tion. For example, the mean yield of oats in Illinois,
for the period 1870 to 1910, was 31.4 bushels per acre,
and the standard deviation of the yield for the same
period of time was cr = 5.2 bushels. The yield per acre
for the year 1910 was 38.0 bushels. If A be taken to rep-
resent the deviation of the yield of any year from the
mean yield of the whole period, then the A for 1910 was
38.0-31.4=6.6, and the fluctuation for 1910 was

- = -^ = 1.27. Similarly, for the year 1908, when the
o- 5.2

A
yield was 23.0 bushels, the fluctuation was, - = - l.()2.

It happens that in the case of oats, there is no secular
trend to the yield, but when the secular trend exists.

52 Economic Cycles: Their Law and Cause

it must be eliminated before the fluctuation is com-
puted.

In Table III of the Appendix to this chapter the
fluctuation for each of the forty-one years 1870-1910
is given for corn, oats, hay, and potatoes. By taking
the algebraic sum of the fluctuations for all the crops
for any given year and dividing by four — the number of
the crops — a measure of the fluctuation of the crops
taken all together is obtained. This measure we shall
refer to as the index of the fluctuation of crops. The
index for each of the years 1870-1910 is recorded in the
last column of Table III.

The index of crop fluctuation computed in the man-
ner that has just been described is regarded as a more
accurate measure of the fluctuation of crops than
would be obtained from an index formed by taking as
the fluctuation for each year, in case of each crop, the
ratio of the deviation from the mean divided by the
mean. If the crops differ in their coefficients of varia-
tion, that is to say, if the ratio ^j, where M is the mean

yield and cr is the standard deviation, is not the same
for all crops, then the crop with the largest coefficient of
variation would receive the largest weight in the general
index. The coefficients of variation for the crops in

our Table are, for corn, ^^;f~-- =.217; for oats, ^~~ =

2b. 93 .31.44

.104; for hay, j^ = .137; for potatoes, ^||^ = ..330. If

the usual method of forming index numbers were em-
ployed in this case to measure crop fluctuations, the

Rainfall and the Crops 53

several crops would, in consequence of their different
variabilities, receive disproportionate weights. The
method of calculating the index which we have em-
ployed obviates this difficulty.

Having now obtained an index of the fluctuation of
crops, we next consider the method of combining the rain-
fall of the critical periods of growth for the several crops.
The method will be clear if we bear in mind that the
critical period of growth of a crop is the combination of
months whose rainfall gives the highest correlation with
the yield. The mean effective monthly rainfall for the
critical period of a crop is the total rainfall of the critical
period of growth divided by the number of months mak-
ing up the critical period. In case of hay, for example,
the critical period of growth is March, April, May,
June. The mean effective rainfall for any given year
would be the total rainfall for the four months, March,
April, May, June, divided by the number of the months.
If the mean effective monthly rainfall for the several
crops is summed for each year and divided by the num-
ber of crops, a measure is obtained of the mean effective
monthly rainfall for the crops taken all together. In
Table IV of the Appendix to this chapter the mean
effective rainfall of the several crops, and of the crops
taken all together, is tabulated for each of the years
1870-1910.

We have now an index of the fluctuation of crops and
an index of the mean effective rainfall of the critical
periods of the crops. The correlation between the
two series is r = .584. In Figure 14 are traced the graphs

54

Economic Cycles: Their Law and Cause

Index of flu cfua tion of crops.

/lPj.uiej /(jLi4.uouj 3ai4.03jI^s ups^a^

Rainfall and the Crops 55

of the compound cycles that describe the two series,
each graph consisting of two cycles and their semi-
harmonics, a thirty-three years cycle describing the
ground-swell and the smaller cycle of eight years sum-
marizing the minor cyclical movements. The measure
of the degree of fit to the observations is, in case of the
yield curve, K =2.46, and in case of the rainfall curve,
K = 1.68. The yield curve reproduces the general
characteristic features of the rainfall curve.

Our findings with reference to the crops taken to-
gether are similar to what we discovered in case of the
single crops: The yield per acre and the rainfall of the
critical season are highly correlated; the rhythmical
movements of the yield and of the effective rainfall
may be accurately described by a compound cycle of
thirty-three years and eight years with their semi-
harmonics; and the yield curve reproduces the general
characteristics of the curve of effective rainfall.

Passing now to a summary of the contents of this
chapter, we may collect our results in a series of prop-
ositions.

(1) The yield per acre of the four representative

crops, corn, hay, oats, and potatoes is associ-
ated with the amount of the rainfall of their
respective critical periods of growth. In
three out of the four cases the degree of cor-
relation lies between r = .589 and r = .666.

(2) The rhythmical changes in the yield per acre of

the crops and in the rainfall of the respective

56 Economic Cycles: Their Law and Cause

critical seasons may both be accurately de-
scribed by a compound cycle composed of a
thirty-three years cycle with its semihar-
monic, which summarizes the ground-swell of
the movement, and a superposed cycle of eight
years with its semiharmonic, describing the
shorter rhythmical movements.

(3) In three of the four representative crops, the

compound cycles summarizing the changes in
the rainfall of the critical periods of growth
and the changes in the yield per acre of the
crops are so nearly congruent that, consider-
ing the high correlation of the yield with the
rainfall, one may conclude, with a high degree
of probability, that the rhythmical movement
in the weather conditions represented by
rainfall is the cause of the cycles of the crops.

(4) The index of the fluctuation of the crops taken

together, and the index representative of the
mean effective rainfall during the critical
seasons are highly correlated, r = .584.

(5) The rhythmical changes in the index of the

fluctuation of the crops and in the index of
the mean effective rainfall are accurately
described by a compound cycle which is made
up of a thirty-three years cycle and an eight
years cycle with their semiharmonics, and
these two compound curves are, in their gen-
eral characteristics, much alike.

(6) The investigation of the crops taken singly and

Rainfall and the Crops 57

taken together leads to the general conclu-
sions :

(a) that there is a rhythmical movement
in both the yield of the crops and in the
rainfall of the critical periods which is
summarized in a compound cycle, in
which the constituent elements are a
ground-swell of thirty-three years and
its semiharmonic, and a shorter super-
posed cycle of eight years with its
semiharmonic ;

(b) that the cyclical movement in the
weather conditions represented by rain-
fall is the fundamental, persistent cause
of the cycles of the crops.

APPENDIX

TABLE I. — The Crops op Illinois

Year

Yield Per Acre of
Corn, in Bushels

Yield Per Acre of
Potatoes, in Bushels

Yield Per

Acre of

Hav, in

Tons

Ton = 2000

lbs.

Yield Per
Acre of
Oats, in
Bushels

Actual
Yield

Reduced
Yield

Actual
Yield

Reduced

YiEID

1870

35.2

35.2

81

81.0

1.18

26.0

1871

38.3

38.1

61

60.8

1.31

33.1

1872

39.8

39.4

75

74.5

1.35

36.6

1873

21.0

20.4

40

39.3

1.25

30.0

1874

18.0

17.2

55

54.1

1.20

17,5

1875

34.3

33.3

128

126.8

1.37

33.0

1876

25.0

23.8

75

73.6

1.40

20.0

• 1877

29.0

27.6

93

91.4

1.60

37.0

1878

27.1

25,5

67

65.1

1.49

35.9

1879

35.0

33.2

88

85.9

1.21

32.0

1880

27.2

25.2

75

72.7

1.45

31.8

1881

19.4

17.2

48

45.4

1.30

33.4

1882

23.0

20.6

85

81.8

1.25

40.7

1883

25.0

22.4

92

89.0

1.45

36.1

1884

30.0

27.1

79

75.7

1.40

32.8

1885

31.4

28.3

87

83.5

1.30

32.8

1886

24.5

21.2

67

63.3

1.34

31.8

1887

19.2

15.7

33

29.0

.80

29.5

1888

35.7

32.0

80

75.8

1.40

35. S

1889

32.3

28.4

99

94.6

1.39

37.5

1890

26.2

22. 1

30

25.3

1.30

21.0

1891

33.5

29.2

92

87.1

1.25

34,0

1892

26.2

21.7

52

46.9

1.25

26.3

1893

25.7

21.0

53

47.6

1.21

27.2

1894

28.8

23.9

50

44.4

1.14

36.1

1895

37.4

32.3

77

71.2

.66

24.4

1896

40.5

35.2

97

90.9

1.38

28.0

1897

32.5

27.0

38

31.7

1.29

32.0

1898

30.0

24.3

70

63.5

1.56

29.0

1899

36.0

30.1

96

89.2

1.29

38.0

1900

37.0

30.9

90

83.0

1.27

38.0

1901

21.4

15.1

35

27.8

1.08

28.2

1902

38.7

32.2

118

110.5

1.50

37.7

1903

32.2

25.5

72

64.3

1.54

26.6

1904

36 . 5

29.6

108

100.1

1.36

32.0

1905

39.8

32.7

75

66.8

1.35

35.5

1906

30.1

28.8

97

88.6

.98

29.5

1907

36.0

28.4

87

78.4

1.40

24.5

1908

31.6

23.8

71

62.2

1.53

23.0

1909

35.9

27.9

91

81.9

1.45

36.6

1910

39.1

30.9

75

65.7

1.33

38.0

58

Rainfall and the Crops

59

TABLE II. — Mean Monthly Rainfall in Illinois

Mean Monthly R

AINFALL

Year

March

April

Mat

June

July

August

Septem-
ber

1870

3.92

1.43

1.64

1.93

2.85

3,95

3.69

1871

3.31

2.47

3.06

4.00

3.11

3.50

1.22

1872

2.59

3.39

3.60

5.68

5.00

3,65

4.29

1873

1.75

4.98

4.87

2.18

3.99

1.77

3.19

1874

2.39

3.50

2.25

3.45

2.06

4,28

3.95

1875

2.83

2.60

4.57

5.36

9.37

1,96

4,60

1876

5.13

3.38

4.68

5.53

4.91

3,83

4.33

1877

4.02

3.53

3.13

7.39

3,27

2.78

2.29

1878

3.04

4.66

5.04

2.72

3.83

4.10

1.61

1879

2.59

2.42

2.10

4,33

3.44

4.89

1.48

1880

3.31

4.29

5.93

3.53

3.10

3.65

3.59

1881

3.16

2.18

2.26

5.93

2.58

0.84

4.04

1882

4.00

4.00

6.60

6.61

3.46

4.65

2.08

1883

1.81

4.16

5.38

5.51

4.86

1.86

0.88

1884

3.31

3,36

4.40

5.13

4.09

2.40

4.80

1885

0.53

4.13

3.03

5.63

2.80

5.06

5.67

1886

3.02

3.60

4.07

4.42

1.15

3.86

4.81

1887

2.37

2.46

2.90

1.94

2.40

2.46

3.25

1888

4.09

1.94

5.18

4.80

3.83

4.31

1.46

1889

1.62

2.00

5,11

5.35

4.45

1.22

3.78

1890

4.34

3.75

3.86

4.58

2.03

2.96

3.04

1891

3.43

2,91

2.19

4.11

1.88

4,71

1.02

1892

2.17

6.43

8,06

5.77

3.71

3.03

2.01

1893

3.31

7.64

4.24

3.51

2.20

0.96

3.09

1894

2.98

2.73

3.29

2.31

1.58

1.74

4.53

1895

1.72

2,17

2.34

2.68

6.01

2.76

3,00

1896

1.90

2.84

6.09

4.14

6.17

2.95

5 , 79

1897

6.22

4.53

1.94

4.28

3.59

1.19

0.99

1898

7.70

3.47

6.26

4.71

2.84

4.70

5 . 07

1899

3.19

1.64

6.41

3.00

3,42

2.70

2,23

1900

2.12

1.64

4.51

4.31

4.15

3,72

3,59

1901

3.80

1.84

1.86

3,55

2,63

1,91

1,97

1902

3.64

2.55

3.78

7.77

4,78

4.67

4.24

1903

3.23

4.51

3.25

3.03

3.41

4.58

3.85

1904

6.41

3.76

3.29

3.28

5.23

4.25

5.43

1905

2.32

3.88

4.27

3.69

4.78

3.41

2.89

1906

4.09

2.09

2.39

3.08

2.58

4,15

5.15

1907

3.26

2.89

3.95

4.17

5.39

5 , 56

2.38

1908

3.21

4.59

8.07

3.14

3.32

2 , 39

1.41

1909

2.62

5.94

4.23

4.04

4 , 96

2,12

4.25

1910

0.32

3,66

5.04

2,62

4.72

2.51

4.61

60

Economic Cycles: Their Law and Cause

TABLE III. — Index of Fluctuation of Crops. A = Devia-
tion FROM THE Mean after the Secular Trend has been
Eliminated, cr = Standard Deviation

Corn

Oats

Hay

Pota-

Sum op

Sum of

Index

1 of

Year

A

A

A

toes
A

Positive

Negative

Differ-

: Fluct-

—

—

—

Fluctua-

Fluctu-a-

ence

uation

cr

cr

(T

<r

tions

TIONS

OF

Crops

1870

1.43

—1.04

— .72

.45

1.88

1.76

+ .12

+ .03

1871

1.93

.33

.00

— .42

2.26

.42

+ 1.84

+ .46

1872

2.16

1.00

.22

.17

3.55

.00

+3.55

+ .89

1873

—1.12

— .27

— .33

—1.34

.00

3.06

—3.06

— .76

1874

—1.67

—2.67

— .61

— .70

.00

5.65

—5.65

—1.41

1875

1.10

.31

.33

2.42

4.16

.00

+4.16

+ 1.04

1876

— .67

—2.19

.50

.13

.63

2.86

—2.23

— .56

1877

.12

1.08

1.61

.90

3,71

.00

+3.71

+ .93

1878

— .24

.87

1.00

— .23

1,87

.47

+ 1.40

+ .35

1879

1.09

.12

— .56

.66

1.87

.56

+ 1.31

+ .33

1880

— .29

.08

.78

.09

.95

.29

+ .66

+ .16

1881

—1.69

.38

— .06

—1.08

.38

2.83

—2.45

— .61

1882

—1.09

1,79

— .33

.48

2.27

1.42

+ .85

+ .21

1883

— .78

.90

.78

.79

2.47

.78

+ 1.69

+ .42

1884

.03

.27

.50

.22

1.02

.00

+ 1.02

+ .25

1885

.24

.27

— .06

.56

1.07

.06

+ 1.01

+ .25

1886

— .98

.08

.17

— .31

.25

1.29

—1.04

— .26

1887

—1.93

— .37

—2.83

—1.78

.00

6.91

—6.91

—1.73

1888

.88

.85

.50

.23

2.46

.00

+2.46

+ .61

1889

.26

1.17

.44

1.03

2,90

.00

+2.90

+ .72

1890

—1.00

—2.00

— .06

—1.94

.00

5.00

—5.00

—1.25

1891

.40

.50

— .33

.71

1.61

.33

+ 1.28

+ .32

1892

— .90

— .98

— .33

—1.01

.00

3.22

—3.22

— .80

1893

—1.02

— .81

— .56

— .98

.00

3.37

—3.37

— .84

1894

— .52

.90

— .94

—1.12

.90

2.58

—1.68

— .42

1895

.93

—1.35

—3.61

.03

.96

4.96

—4.00

—1.00

1896

1.43

— .65

.39

.88

2,70

.65

+2.05

+ .51

1897

.02

.12

— .11

—1.67

,14

1.78

—1.64

— .41

1898

— .45

— .46

1.39

— .30

1.39

1.21

+ .18

+ .05

1899

.55

1.27

— .11

.80

2,62

.11

+2.51

+ .63

1900

.69

1.27

— ■ .22

.54

2.50

.22

+2.28

+ .57

1901

—2.03

— .62

— 1.2S

—1.83

.00

5 , 76

—5.76

—1.44

1902

.91

1.21

1.00

1,72

4.90

,00

+4.90

+ 1.22

1903

— .24

— .92

1.28

— .27

1.28

1,43

— .15

— .04

1901

.47

.12

.2'^

1,27

2.14

.00

+2.14

+ .54

1905

1.00

.79

.22

— .16

2.01

.16

+ 1.85

+ .46

1903

.31

— .37

—1.83

.78

1.09

2,20

—1.11

— .28

1907

.26

—1.33

.50

.34

1.10

1,33

— .23

— .06

1908

— .53

—1.62

1.22

— .36

1.22

2,51

—1,29

— .32

1909

.17

1.00

.78

.49

2.44

.00

+2,44

+ .61

1910

.69

1.27

.11

— .21

2.07

.21

+ 1.86

+ .46

Rainfall and the Crops

61

TABLE IV. — Mean Effective Monthly Rainfall in Illinois

!

Mean Effective Monthly Rainfall

Mean
Effective
Monthly
Rainfall
for Crops

Year

For
Corn

For
Oats

For
Hay

For
Potatoes

Sum of
Preceding
Columns

1870

3.40

2.14

2.23

3.40

11.17

2.79

1871

3.30

3.39

3.21

3.30

13.20

3.30

1872

4.33

4.76

3.81

4.33

17.23

4.31

1873

2.88

3.68

3.45

2.SS

12.89

3.22

1874

3.17

2.59

2.90

3.17

11.83

2.98

1875

5.66

6.43

3.84

5.66

21.59

5.40

1876

4.37

5.04

4.68

4.37

18.46

4.61

1877

3.02

4.60

4.52

3.02

15.16

3.79

1878

3.96

3.86

3.86

3.96

15.64

3.91

1879

4.16

3.29

2.86

4.16

14.47

3.62

ISSO

3.37

4.19

4.26

3.37

15.^9

3.80

1881

1.71

3.58

3.38

1.71

10.3.^

2.59

1882

4.05

5.56

5.30

4.05

18.96

4.74

1883

3.36

5.25

4.20

3.36

16.17

4.04

1884

3.25

4.54

4.05

3.25

15.09

3.77

1885

3.93

3.82

3.33

3.93

15.01

3.75

1886

2.51

3.21

3.78

2.51

12.01

3.00

1887

2.43

2.41

2.42

2.43

9.69

2.42

1888

4.07

4.60

4.00

4.07

16.74

4.18

1889

2.84

4.97

3.52

2.84

14.17

3.54

1890

2.50

3.49

4.13

2.50

12.62

3.15

1891

3.29

2,73

3.16

3.29

12.47

3.12

1892

3.37

5. 85

5.61

3.37

18.20

4.55

1893

1.58

3.32

4.67

1.58

11.15

2.79

1894

1.66

2.39

2.83

1.66

8.54

2.14

1895

4.38

3.68

2.23

4.38

14.67

3.67

1896

4.56

5.47

3.74

4.56

18.33

4.58

1897

2.39

3.27

4.24

2.39

12.29

3.07

1898

3.77

4 . 60

5.53

3.77

17.67

4.42

1899

3.06

4.2S

3.56

3.06

13.96

3.49

1900

3.93

4.32

3.15

3.93

15.33

3.83

1901

2.27

2.68

2.76

2.27

9.98

2.50

1902

4.72

5.44

4.43

4.72

19.31

4.83

1903

4.00

3.23

3.50

4.00

14.73

3.68

1904

4.74

3.93

4.18

4.74

17.59

4.40

1905

4.09

4.25

3.54

4.09

15.97

3.99

1906

3.36

2.68

2.91

3.36

12.31

3.08

1907

5.47

4.50

3.57

5.47

19.01

4.75

1908

2.85

4.84

4.75

2.85

15.29

3.82

1909

3.54

4.41

4.22

3.54

15.71

3.93

1910

3.61

4.13

2.91

3.61

14.26

3.56

CHAPTER IV

THE LAW OF DEMAND

Kann man nicht die Nachfragefunktion genauer feststellen, so
genau, dass wiv nicht bloss ein eindeutiges, sondern ein konkretes
Resultat gewinnen? Ich glaube die Antwort zu horen: Welch'
ein phantastisches Unterfangen-Unberechenbarkeit der wirtschaft-
lichen Vorgange — steter Wechsel — u. s. w!

Joseph Schumpeter.

Questions affecting for the most part the supply of
commodities have thus far been the object of our in-
vestigation, but the inquiry as to the cause and law of
economic cycles must extend to a consideration of
cycles of values and prices. Since the rhythmical
variation in the supply of crops produces its effect upon
crop prices in accordance with the laws of demand for
the several crops, the obvious first and necessary step
in bringing the results of the preceding chapters to bear
upon the question of the cause and law of economic
cycles is to solve the problem of the relation between
the variations in the supply of the several crops and
the resulting variations in their respective prices. It
is required to derive from existing data the concrete
laws of demand for the representative crops.

The Theory of Demand

The mathematical treatment of the theory of demand
furnishes two doctrines that are of importance in our

62

The Law of Demmid

63

Figure 15. The law of demand.

subsequent work : The doctrine of the uniformity of the
demand function and the doctrine of the elasticity of
demand. The exposition of these two doctrines will be
faciUtated by reference to Figure 15, in which, accord-
ing to the usual practice, quantities of commodity are
measured upon the axis
of abscissas, and the cor-
responding prices per
unit, upon the axis of
ordinates.

The doctrine of the
uniformity of the demand
function, which is trace-
able to Cournot,^ but is
especially stressed by
Professor Mar.shall, has been put in these words:
"There is then one general laiv of demand viz., that
the greater the amount to be sold, the smaller will
be the price at which it will find purchasers ; or, in other
words, that the amount demanded increases with a
fall in price and diminishes with a rise in price." Re-

1 Cournot: Recherches sur les principes mathematiqties de la theorie
des richesses, §§21, 22. Assuming that the relation between price
and the amount demanded is represented by F(p), he says, p. 54:
"Si la fonction F(p) est continue, elle jouira dc la propri^t6 conmiune
a toutes les fonctions de cette nature, et sur laquellc reposent tant
d'appHcations important es de I'analyse mathematique: les varia-
tions de la demande seront sensiblement proportionelles aux varia-
tions du prix, tant que celles-ci seront de petites fractions du prix
originaire. D'ailleurs, ces variations seront de signes contraires,
c'est-5,-dire qu'k une augmentation de prix correspondra une dimi-
nution de la demande."

64 Economic Cycles: Their Law and Cause

f erring to Figure 15, this statement means tliat if at
any point in the demand curve DD', say the point P,
a straight hue is drawn tangent to the curve, then the
trigonometric tangent of the angle which the hne makes
with the positive direction of the axis of x, is negative.
In Professor Marshall's words: "The one universal
rule to which the demand curve conforms is that it is
inclined negatively throughout the whole of its length."^
As we proceed we shall find that the law of demand for
some commodities does indeed conform to the type of
curve which has just been described, but it will be a part
of the work of the next chapter to show that the doc-
trine of the uniformity of the demand function is an
idol of the static state — of the method of costeris
-paribus — which has stood in the way of the successful
treatment of concrete dynamic problems.

Assuming that the law of demand for a given com-
modity is represented by the descending curve DD' in
Figure 15, the elasticity of demand for the commodity
when OM units ai'e bought is measured by the ratio

7) l7 "^ PM "^h^^ ^^ ^^ ^^y> ^^^ general terms, if the price
of the commodity undergoes a small change, the amount
of the commodity that is demanded likewise undergoes
a small change, and the degree of the elasticity of de-
mand for the commodity, in the given state of the mar-
ket, is measured by the ratio of the relative change in

' Marshall: Priiiciples of Economics, 4th edit., pp. 174, 174 note 2.
In the subsequent reasoning we shall call this tyj^e of dcn^and
curve the negative type.

The Laiv of Demand 65

the amount demanded to the small relative change in
the price. Or, more definitely, if "a fall of 1 per cent.
in price would cause an increase of 2 per cent, in the
amount demanded, the elasticity of demand would be
two;" if "a fall of 1 per cent, in price would cause an
increase of /g per cent, in the amount demanded, the
elasticity of demand would be one-third; and so on." ^
It will be observed that the theory of elasticity of
demand in this classical form is presented from the
point of view of infinitesimal changes in the two va-
riables — , price and commodity demanded. It gives
the degree of elasticity of demand for a point in time,
for a given state of the market assuming all other
things to remain the same ; and for this reason it may be
said to treat of elasticity of demand from a statical
point of view. But this is not its most serious limitation.
It postulates a knowledge of the demand curve, and
while it gives an exposition of the method by which the
degree of elasticity of demand might be determined
provided the demand curve were known, there have
been grave doubts as to whether the practical difficulty
of deriving the demand curve would ever be overcome.

The problem before us is to derive the demand curve
from statistics; to measure the degree in which it is an
accurate description of the changes of actual industry;
and to give the numerical coefficients of elasticity of
demand for typical commodities.

1 Marshall: Principles of Economics, 4th edit., pp. 177-178,
note.

66 Economic Cycles: Their Law and Cause

Statistical Laws of Demand

Two fundamental defects in the current theoretical
method of treating economic questions are exemplified
in the case of the theory of demand: first, the assump-
tion is made that all other things being equal (the old
cceteris paribus), an increase in the supply of the com-
modity will lead to a corresponding fall in the price;
secondly, it is assumed that the concrete problem of
the relation of price and supply of commodity will be
simplified by attacking first the constituent elements
of the question rather than by attacking directly the
problem in its full concreteness. Neither assumption
is satisfactory nor indeed admissible. The "other
things" that are supposed to remain equal are seldom
mentioned and are never completely enumerated; and
consequently the assumption that, other unmentioned
and unenumerated factors remaining constant, the law
of demand will be of a certain type, is really tantamount
to saying that under conditions which are unanalyzed
and unknown, the law of demand will take the supposed
definite form. The burden of proof is upon anyone
using this method to show that the assumption does not
at least involve a physical impossibility.

The second of the above two assumptions is not more
satisfactory than the first. It reproduces the defects
of the first assumption with others superadded. The
movement of prices results from changes in many
factors: According to the statical method, the method
of cceteris paribus, the proper course to follow in the

The Law of Demand 67

explanation of the phenomenon is to investigate in
turn, theoretically, the effect upon price of each factor,
ccBteris paribus, and then finally to make a synthesis!
But if in case of the relation of each factor to price the
assumption cceteris paribus involves large and at least
questionable hypotheses, does one not completely lose
himself in a maze of implicit hypotheses when he speaks
of a final synthesis of the several effects? We shall not
adopt this bewildering method, but shall follow the
opposite course and attack the problem of the relation
of prices and supply in its full concreteness.

The fruitfulness of the statistical theory of correlation
stands in significant contrast to the vast barrenness of
the method that has just been described, and the two
methods follow opposed courses in dealing with a
problem of multiple effects. Take, for example, the
question of the effects of weather upon crops. What a
useless bit of speculation it would be to try to solve, in a
hypothetical way, the question as to the effect of rain-
fall upon the crops, other unenumerated elements of
weather remaining constant? The question as to the
effect of temperature, cceteris paribus? How, finally,
would a synthesis be made of the several individual
effects? The statistical method of multiple correlation
formulates no such vain questions. It inquires, di-
rectly, what is the relation between crop and rainfall,
not cceteris paribus, but other things changing accord-
ing to their natural order; what is the relation between
crop and temperature, other things conforming to the
observed changes in temperature; and, finally, what is

68 Economic Cycles: Their Law and Cause

the relation between crop and rainfall for constant
values of temperature? The problem of the effects of
the constituent factors is solved only after the more
general problem has received its solution. This method
offers promise of an answer to the question as to the
relation between the effective demand price and the
supply of the commodity.

The chief difficulties in the computation of statistical
laws of demand are due to changes that occur in the
market during the period to which the statistics of
prices and of quantities of commodities refer. In order
that the statistical laws of demand shall have sufficient
validity to serve as prediction formulae, the observations
must be numerous ; and in order to obtain the requisite
number of observations, a considerable period must be
covered. This usually means that, during the interval
surveyed in the statistical series, important changes
occur in the condition of the market. But in case
of staple commodities, such as the agricultural products
with which we shall have to deal, the effects of those
changes in the condition of the market that obscure the
relation between prices and amounts of commodity may
be largely eliminated. As far as the law of demand is
concerned, the principal dynamic effects that need to
be considered are changes in the volume of the com-
modity that arise from the increasing population, and
changes in the level of prices which are the combined
result of causes specifically responsible for price cycles
and of causes that produce a secular trend in prices.

The Law of Dernand 69

The effects of these two fundamental changes may be
eliminated approximately by a single statistical device,
namely, by deducing the law of demand from a gen-
eralized treatment of the elasticity of demand.

The degree of elasticity of demand, according to the
classic formula, is measured by the ratio of the relative
change in the amount of the commodity that is bought
to the relative change in the price per unit of the com-
modity. Suppose, now, that instead of restricting
this conception to infinitesimal changes in price and in
amount of commodity, we extend it to the finite changes
that actually occur in the market. Then, the relative
change in the amount of commodity that is bought
may be correlated with the relative change in the
corresponding price, and the resulting appropriate
regression equation will give the statistical law of
demand for the coimnodity. By taking the relative
change in the amount of the commodity that is de-
manded, instead of the absolute quantities, the effects
of increasing population are approximately eliminated;
and by taking the relative change in the corresponding
prices instead of the corresponding absolute prices, the
errors due to a fluctuating general price level are par-
tially removed. If the observations should cover the
period of a major cycle of prices, and the commodity
under investigation should be a staple commodity such
as the representative agricultural products with which
we shall have to deal, the above method of deriving the
demand curve will give an extremely accurate formula
sunmiarizing the relation between variations in price

70 Economic Cycles: Their Law and Cause

and variations in the amount of the commodity that is
demanded.

The method may be illustrated by deriving the law of
demand for corn. In Table I of the Appendix to this
chapter are recorded, for the period of 1866-1911, in the
United States, the quantities of corn annually pro-
duced, the corresponding prices per bushel, the relative
changes in the quantity produced and the relative
changes in the price per bushel. If the correlation of
the relative change in the amount of corn that is pro-
duced and the relative change in the corresponding
price per bushel of corn is assumed to be hnear, the
coefficient of correlation is r = — .789, and the equation
of regression is ?/ = —.8896.x +7.79, the origin being at
{o,o). (See Figure 16.)

In Tables ^ II, III, IV, of the Appendix to this
chapter, similar data are given for hay, oats, and
potatoes. The coefficients of correlation are, for
hay, r = —.715; for oats, r = —.722; and for potatoes,
r = —.856. The regression equations are,

for hay, 7/ = — .7643x+3.61;
for oats, ?/ = — 1.0455a: +6. 93;
for potatoes, ^ = —1.2194.T + 15.75;

the origin in all cases being at {o^o).

The high coefficients of correlation that have just

been given were obtained on the assumption that the

correlation between relative change in amount de-

1 The data of the Tables I, II, III, IV were taken from the Year-
hook of the Department of Agriculture of the United States, for
1911.

The Law of Demand

71

Percentage chantie in the production of corn.

Figure 16. The law of demand for corn.
y = -.8896x + 7.79, origin at (0, 0).

72 Economic Cycles: Their Law and Cause

manded and relative change in price is linear. We shall
see later on that the two variables are even more
intimately associated than would be suggested by the
high coefficients of correlation. Just now we wish to
know the form of the law of demand when the restric-
tion involved in the assumption of linearity of regres-
sion is removed. What will be the statistical laws of
demand for the representative commodities corn, hay,
oats, and potatoes, if the regression of relative change in
price upon relative change in quantity of commodity is
assumed to be skew and of the type y =a-\-hx-{-cxr-\-dx^1
The question is answered by fitting, according to the
Method of Least Squares, the equation y =a+hx-\-cx'^-\r
dx^ to the data of Tables I, II, III, IV of the Appendix
to this chapter. The results of the computations are
exhibited in Figures 17, 18, 19, 20 of the text.

The statistical laws of demand for the commodities
corn, hay, oats, and potatoes present the fundamental
characteristic which, in the classical treatment of de-
mand, has been assumed to belong to all demand
curves, namely, they are all negatively inclined ; that is
to say, speaking from the point of view of average
results, ''the greater the amount to be sold, the smaller
will be the price at which it will find purchasers, or, in
other words, . . . the amount demanded increases
with a fall in price and diminishes with a rise in price." ^

1 Marshall: Principles of Economics, 4th edit., p. 174. In case of
the law of demand for hay, there is a slight upward turn at the ex-
tremity of the curve. This is due to one extreme observation, and
the variation is not a significant exception to the above general rule.

The Law of Demand

73

Percenfade chande in the production of corn.

Figure 17. The law of demand for corn.
1/ = .94 — 1.0899a; + .0239 1.t 2 — .000234x3, origin at (0, 0).

74

Economic Cycles: Their Law and Cause

1-4S

\-"

K

V-

h/\

\

>v. N

\

^\

V

1

i

\

^\

s;

\\

N

^

A

\\

/\

% -IS

'^

V\

^

^^

)

-15

-35
-AS

Percenfade chande in the production of hay.

Figure 18. The law of demand for hay.
y = 4.17 — .9460x — .00770x2 + .OOOSSox', origin at (0, 0).

The Law of Demand

75

^

1.

"^vr — =^,

Percentage chande in the production O'F oats.

Figure 19. The law of demand for oats.
y = 8.22 — 1.1904X — .00663a:» + .000273x3, origin at (0, 0).

76

Economic Cycles: Their Law and Cause

^^s

V

>>

^"

V

\

\

'

\k

f\

1

1

\

V

\.

^

^^ — s,

^^

K,

\

Percenfade chende in 'the production of potatoes.

Figure 20. The law of demand for potatoes.
y = 1.77 — 1.5062X + .02489x2— .000197x^ origin at (0, 0).

The Law of Demand 77

But unlike the classical theory of demand which was
limited to the simple enunciation of this one character-
istic, coeteris paribus, the statistical laws that have just
been derived apply to the average changes that society
is actually undergoing. They summarize the changes
in prices that are to be expected from changes in the
supply of the commodity, thus enabUng one to predict
the probable variation in price that will follow upon an
assigned variation in the amount of the commodity.
They exhibit the connection of probable results not
only in a qualitative but also in a quantitative form.

The Prediction of Prices

It has been said that the statistical laws of demand
enable the economist to predict the probable variation
in price that will follow upon an assigned variation in
the quantity of commodity that is to be sold. How
accurate are the results of prediction that are based
upon the statistical law of demand?

The accuracy of the prediction in the case of any
given commodity will vary according to the degree of
fit of the type of curve that is assumed to represent the
relation between the relative change in price and the
relative change in the quantity of the commodity. If,
for example, the commodity in question is corn in the
United States, and the type of demand curve is assumed
to be Unear, then, according to the results in foregoing
pages, the correlation between the two variables is
r=— .789, and the regression equation is y= — .8896x
+7.79, the origin being at {o,o). (Figure 16 will facili-

78 Economic Cycles: Their Law and Cause

tate the discussion of the case.) By means of this law
of demand it is possible to predict the probable change
in the price that will follow upon a given change in
the quantity to be sold. In 1911, in the United States,
the quantity of corn produced was 2,531,488,000
bushels, and the mean farm price on December 1, 1911
was 61.8 cents. In 1912 the quantity of corn produced
was 3,124,746,000 bushels ; what, then, was the probable
price of corn on December 1, 1912? The percentage
change in the quantity produced was 23.44. Sub-
stitute this value for x in the formula for the law of
demand y= — .8896a; +7.79, and solve for the value
oiy. It is found that the probable change in price would
be a fall of 13.06 per cent., which, since the price in
1911 was 61.8 cents, would give 52.7 cents as the prob-
able price for December 1, 1912, whereas the actual
price was 48.7 cents.

According to the theory of linear correlation, the
accuracy of the regression equation as a prediction
formula is measured by S = ^y^ 1 — r-, where r is
the coefficient of correlation between the variables,
^y is the standard deviation of the variable y about
its mean value, and S is the root-mean-square devia-
tion of the actual observations about the regression
line; or, in other words, *S- is the mean value of the
mean-square deviations about the regression line, of
the observations in the several arrays of ?/'s. From
the Table of the Probability Integral it is known
that in a symmetrical distribution of observations
about their mean value, 68 per cent, of all the observa-

The Law of Demand 79

tions fall within ± the root-mean-square deviation of
the observations from their mean value; 95 per cent.,
between ± twice the root-mean-square deviation; and
99.7 per cent, between =*= three times the root-mean-
square deviation. It is therefore possible, by means
of the Probability Integral, to affix the degree of prob-
ability that a deviation shall fall within any given
multiples or submultiples of the root-mean-square
deviation. In case of the use of the Unear law of de-
mand for corn in the United States as a prediction
formula, the root-mean-square deviation of the ob-
servations about the demand curve was S =^y^l—r'^ =
15.92 per cent. That is to say, if we assume the law of
demand that was based upon observations from 1866
to 1911 to hold in 1912, then it is 95 to 5, or 19 to 1, that
the percentage variation in the actual price for 1912
from the percentage variation as calculated from the
law of demand will be between ^ 2 (15.92), or 31.84
per cent. The calculated percentage change in the
price for 1912 was a fall of 13.06 per cent.; the actual
fall was 21,20 per cent., giving a difference of 7.14 per
cent.

The precision with which the linear law of demand
may be used for the prediction of the price of corn in
the United States justifies the belief that for some pur-
poses it is unnecessary to seek a greater degree of
accuracy than is afforded by the simple linear laws.
But it is well to be able to reach the maximum degree
of precision, and for this reason we have fitted, to the
data of the Tables in the Appendix, the more complex

80

Economic Cycles: Their Law and Cause

curves y =a-\-bx-\-cx~+dx^, the graphs of which, in case
of the representative commodities corn, hay, oats, and
potatoes, are given in Figures 17, 18, 19, 20. What is
the gain in precision when tlie more complex curve is
substituted for the simple straight line? The scatter
of the observations about the straight Hne of regression
was measured, a while ago, by taking the root-mean-
square deviation of the observations about the hne,
that is, by using S = o'yVl—r'^. In order to compare
with this result the distribution of the observations
about the more complex curve, y =a-\-hx-\-cx^-\-dx^,
the distribution about the latter curve will likewise be
measured by the root-mean-square deviation of the
observations. In the little table given below, the
measures of scatter of the observations for the two
types of demand curves are presented in a form that
will make comparison easy.

Scatter of Observations About the Law of Demand
Root-Mean-Square Deviation of Observations

Crops

When the regres-
sion is linear

When the regres-
sion is skew

Corn

Hay

Oats

Potatoes

15 . 92 per cent.
9.53 " "
16.02 " "
21.29 " "

7 . 36 per cent.
4.65 " "
10.17 " "
9.94 " ''

It is clear that in all cases a gain in precision is ob-
tained by using the more complex curve.

Before leaving this topic a remark should be made

The Law of Demand 81

that has a bearing upon the a priori theory of demand.
In treatises on pure economics, particularly in those in
which mathematical analysis is employed, the masters
of the a priori method point out what they regard as
the extreme difficulty of the actual problem of the rela-
tion of price to quantity of commodity — a difficulty
growing out of the interrelation of the many factors in
the problem. If, to limit the illustration to a simple
case, one wishes to know how the price of corn is re-
lated to the quantity of corn that is produced, he is
told that the problem is inextricably complex: If there
is a deficiency in corn, then hay, or potatoes, or oats,
or all three may be substituted in part for corn, and con-
sequently the variation in the price of corn that fol-
lows upon a deficiency of corn cannot be traced with-
out knowing in what degree, when the price of corn
varies, hay, oats, and potatoes are used as substitutes.
But this is not all. The degree in which hay, oats, and
potatoes are substituted for corn is dependent not only
upon the price of corn but also on their own several
prices, and these latter prices are, in turn, dependent
upon the supply and price of corn! This statement of
the problem, complex as it appears, is unduly simpli-
fied; and it is presented not in order to ridicule the work
of the masters who have elaborated the method of
stating the problem in the form of simultaneous equa-
tions, but to show how hopelessly remote from reality
is the very best theoretical treatment of the problem
of the relation of price to the quantity of commodity,
and to suggest, from the results of the preceding pages

82 Economic Cycles: Their Law and Cause

of this chapter, how imaginary, theoretical difficulties
are dispelled by solving real problems.

Of course it is theoretically possible when there is a
deficiency in the production of corn, that oats, hay, and
potatoes may be substituted in part for corn, but in-
stead of conjuring up these and other possibilities that
are never tested, would it not be wise to ascertain first
just how closely is the variation in the price of corn
related to the variation in its own supply? When the
statistical investigation is made and it is found that
the correlation coefficient is r = — .789, and that when
a skew relation is assumed instead of the usual linear
relation, the connection between the variables is still
closer, one sees very clearly, if our illustration is a
typical case, that for most of the problems of actual
life, it is unnecessary to face the complex possible in-
terrelation of phenomena contemplated in the theoret-
ical treatment. For the sake of economy of time and
of talent, theoretical and statistical work should go
hand in hand. Even the complex theoretical problem
that has just been sketched may be tested as to its
hypotheses and conclusion by the statistical method
of multiple correlation.

Elasticity of Demand

The coefficient of the elasticity of demand for a
commodity has been described as the ratio of the rela-
tive change in the quantity of the commodity demanded
to the relative change in the price, when the relative
changes are infinitesimal. Starting with this descrip-

The Law of Demand 83

tion, we are able, by means of the laws of demand for

the several commodities, to measure their respective

degrees of elasticity of demand. It will be recalled that,

in the form in which the laws of demand have been

presented in preceding pages, the variable x has been

taken to represent the relative change in the quantity

of the commodity, and the variable y, the corresponding

relative change in the price. The coefficient of the

dx
elasticity of demand, therefore, is equal to -t- when x is

zero. All that is needed to obtain the measure of the
degree of elasticity of demand is to differentiate y with
respect to x in the equation to the law of demand,
place x = zero, and then take the reciprocal of the result.
The method may be illustrated in case of the four
representative commodities, corn, hay, oats, and pota-
toes. The law of demand for corn — see Figure 17 — is

y = .94- 1.0899X + .02391a:2- .000234a:'

Therefore, ^ = - 1.0899 + 2(.02391).c-3(.000234)x2
ax

When a: = 0, ^ = -1.0899, ^ =- r74^ = --92
dx dy 1.0899

and consequently the coefficient of the elasticity of

demand for corn is — .92. Since the law of demand for

hay is

y = 4. 17-.946:r -.0077x2 + .000385a:'

-^ = —.946 when x = zero,
dx

and the coefficient of elasticity of demand is — 1.06.
For similar reasons the degrees of elasticity of demand

84 Economic Cycles: Their Law and Cause

for oats and for potatoes are respectively, — .84 and
—.66.

In obtaining these numerical values for the coefficient
of elasticity, the laws of demand for the respective
crops have been assumed to be parabolas of the third
order. If the linear laws of demand had been taken for
the purpose, the coefficients of elasticity would have
been different. For example, the law of demand

for corn — see Figure 16— is ?/ =— .8896.T + 7.79 which

dii dx

would give -t-= — .8896, or t^=— 1.12, whereas the

coefficient was — .92 in case of the more complex curve.
This discrepancy between the results when different
types of curves are used for the demand curve shows the
need of care in drawing conclusions that are based upon
numerical values of the coefficient of elasticity. The
discrepancy does not invalidate the method. When
different measures of degrees of elasticity are afforded
by different types of curves, there is a perfectly satis-
factory criterion which makes it possible to decide
between different coefficients of elasticity: The coeffi-
cient is to be preferred which is deduced from the de-
mand curve that fits the data with the highest degree of
probability. The demand curve that fits best the data
affords the best measure of the degree of elasticity of
demand.

The conclusions of this chapter may be briefly sum-
marized. In the closing quarter of the last century
great hopes were entertained by economists with
regard to the capacity of economics to be made an

The Law of Demand 85

''exact science." According to the view of the foremost
theorists, the development of the doctrines of utiUty
and value had laid the foundation of scientific economics
in exact concepts, and it would soon be possible to
erect upon the new foundation a firm structure of
interrelated parts which, in definiteness and cogency,
would be suggestive of the severe beauty of the
mathematico-physical sciences. But this expectation
has not been realized. On the contrary, faith in the
possibility of an adequate ''exact" treatment of the
science has progressively diminished, and interest in
economic theory m general has decidedly lost ground.
There must have been somethmg fundamentally wrong
with the traditional handlmg of the subject, for cer-
tainly it must be admitted that the parts of a science
most worthy of study are precisely those parts which are
concerned with the general and the universal. Why,
then, should there have been the gradual dissipation of
interest in theoretical economics?

The explanation is found in the prejudiced point of
view from which economists regarded the possibilities of
the science and in the radically wrong method which
they pursued. It was assumed gratuitously that
economics was to be modeled on the simpler mathe-
matical, physical sciences, and this assumption created
a prejudice at the outset both in selecting the data to be
investigated and in conceiving of the types of laws that
were to be the object of research. Economics was
to be a "calculus of pleasure and pain," a "mechanics of
utility," a "social mechanics," a ^^ physique sociale."

86 Economic Cycles: Their Law and Cause

The biased point of view implied in these descriptions
led to an undue stressing of those aspects of the science
which seemed to bear out the pretentious metaphors.
One would naturally suppose from this manner of
conceiving the science that the economic theorists
would at once have entered upon their task with the
methods that had proved themselves useful in the
physical sciences. But this they did not do. They
seemed to identify the method of physical sciences with
experimentation, and since, as they held, scientific
experimentation is impossible in social life, a special
method had to be devised. The invention was a dis-
guised form of the classical cceteris paribus, the method
of the static state.

The point of view that has been exemplified in this
chapter is that the facts in their full concreteness must
never be lost from sight ; that the laws which are sought
are of necessity, at first, proximate laws, laws that
obtain in full empirical reality, and are means of arriv-
ing at laws of larger generality; that the method to be
followed is the method which makes progress from the
data to generalization by a progressive synthesis —
the method of statistics.^

1 With regard to the methodology of the social sciences, the
writings of Cournot are always hclj^ful. The following quotatipn
is taken from a treatise published thirteen years after his epoch
making Recherches sur les principes matMmatiques de la theorie des
richesses.

Si nous restons dans I'ordre des causes secondaires et des faits
observables, le seul auquel la science puisse atteindre, la theorie
math^matique du hasard . . . nous apparait comme I'apphcation
la plus vaste de la science des nombres, et celle qui justifie le mieux

The Law of Demand 87

Starting with this point of view and pursuing the
method that has just been described, we have attacked
the old problem of the form of the law of demand. We
have obtained the concrete laws of demand for repre-
sentative commodities, have affixed the degree of preci-
sion with which the laws may be used as formulae for
predicting prices, and have measured the elasticity of
demand for the respective commodities.

In all likelihood it will be said that what we have
achieved is not exactly what the partisans of the method
of cceteris paribus proposed. To this criticism we reply
that their immediate problem of the relation of price and
quantity of commodity, cceteris paribus, was vaguely
conceived and actually abandoned by those who sought
to give it definiteness, as being incapable of concrete

I'adage: Mundum regunt numeri. En cffet, quoiqu'en aient pens6
certains philosophes, rien ne nous autorise a croire qu'on puisse
rendre raison de tous les phenomencs avcc les notions d'etenduc, de
temps, de mouvement, en un mot, avec les seules notions des grand-
eurs continues sur lesquelles portent les mesures et les calculs du
g^ometre. Les actes des etres vivants, intelligents et moraux ne
s'expliquent nuUement, dans I'etat de nos connaissances, et 11 y a
de bonnes raisons de croire qu'ils ne s'expliqueront jamais par la
mecanique et la geom^trie. lis ne tombent done point, ]!ar le cote
g^om^trique ou mecanique dans le domaine des nombres, niais ils
s'y retrouvcnt places, en tant que les notions de combinaison et de
chance, de cause et de hasard, sont superieures, dans I'ordre des
abstractions, S, la geometric et k la mecanique, et s'appliquent aux
ph^nomenes de la nature vivante comme k ceux que produisent les
forces qui sollicitent la mati^rc inorganiquc; aux actes r^flechis des
6tres libres, comme aux determinations fatales de I'app^tit et de
I'instinct.

Essai sur les fondements de nns connaissances et sur les caracteres
de la critique philosophiqne, vol. 1, pp. 64-65.

88 Economic Cyces: Th eir Law and Cause

solution; that when the problem is clearly stated, it
admits of solution by means of a method which we have
indicated, the method of multiple correlation; and that
what we have achieved is the solution of their ultimate
problem of the relation of price and quantity of com-
modity in a dynamic society.

.\PPENDIX

TABLE I. — The Production and the Price of Corn in the
United States

Average

Production of

Farm Price

Percentage

Percentage

Year

Corn in Thou-

Per Bushel

Change in

Change in

sands OF Bushels

December 1,
IN Cents

Production

Price

1866

867,946

47.4

1867

768,320

57.0

—11.48

+ 19.41

1868

906,527

46.8

+ 17.99

—17.89

1869

874,320

59.8

— 3.55

+27.78

1870

1,094,255

49.4

+25.15

—17.39

1871

991,898

43.4

— 9.35

—12.15

1872

1,092,719

35.3

+ 10.17

—18.66

1873

932,274

44.2

—14.68

+25.21

1874

850,148

58.4

— 8.81

+32.13

1875

1,321,069

36.7

+55.39

—37.16

1876

1,283,828

34.0

— 2.82

— 7.36

1877

1,342,558

34.8

+ 4.57

+ 2.35

1878

1,388,219

31.7

+ 3.40

— 8.91

1879

1,547,902

37.5

+ 11.50

+ 18.30

1880

1,717,435

39.6

+ 10.95

+ 5.60

1881

1,194,916

63.6

—30.42

+60.61

1882

1,617,025

48.5

+35.33

—23.74

1883

1,551,067

42.4

— 4.08

—12.58

1884

1,795,528

35.7

+ 15.76

—15.80

1885

1,936,176

32.8

+ 7.83

— 8.12

1886

1,665,441

36.6

—13.98

+ 11.59

1887

1,456,161

44.4

—12.57

+21.31

1888

1,987,790

34.1

+36.51

—23.20

1889

2,112,892

28.3

+ 6.29

—17.01

1890

1,489,970

50.6

—29.48

+78.80

1891

2,060,154

40.6

+38.27

—19.76

1892

1,628,464

39.4

—20.95

— 2.96

1893

1,619,496

36.5

— .55

— 7.36

1894

1,212,770

45.7

—25.11

+25.21

1895

2,151,139

25.3

+77.37

—44.64

1896

2,283,875

21.5

+ 6.17

—15.02

1897

1,902,968

26.3

-16.68

+22.33

1898

1,924,185

28.7

+ 1.11

+ 9.13

1899

2,078,144

30.3

+ 8.00

+ 5.57

1900

2,105,103

35.7

+ 1.30

+ 17.82

1901

1,522,520

60.5

—27.67

+69.47

1902

2,523,648

40.3

+65.75

—33.39

1903

2,244,177

42.5

—11.07

+ 5.46

1904

2,467,481

44.1

+ 9.95

+ 3.76

1905

2,707,994

41.2

+ 9.75

— 6.58

1906

2,927,416

39.9

+ 8.10

— 3.16

1907

2,592,320

51.6

—11.45

+29.32

1908

2,668,651

60.6

+ 2.94

+ 17.44

1909

2,772,376

59.6

+ 3.89

— 1.65

1910

2,886,260

48.0

+ 4.11

—19.46

1911

2,531,488

61.8

—12.29

+28.75

89

90

Economic Cycles: Their Law and Cause

TABLE II. — The Production and the Price of Hay in the
United States

Year

Production of
Hay in Thou-
sands OF Tons
(Ton = 2000 Ibs.l

Average Farm,

Prick Per Ton

December 1,

IN Dollars

Percentage
C'hangf. in
Production

Percentage

Change in

Price

1866

21,779

10.14

1867

26,277

10.21

+20.65

+ .69

1868

26,142

10.08

— 2.42

— 1.27

1869

26,420

10.18

+ 1.06

+ .99

1870

24,525

12.47

— 7.17

+22 . 50

1871

22,239

14.30

— 9.32

+ 14.68

1872

23,813

12.94

+ 7.08

— 9.51

1873

25,085

12.53

+ 5.34

— 3.17

1874

25,134

11.94

+ .20

— 4.71

1875

27,874

10.78

+ 10.90

— 9.72

1876

30,867

8.97

+ 10.74

—16.79

1S77

31,629

8.37

+ 2.47

— 6.69

1878

39,608

7.20

+25.23

—13.98

1879

35,493

9.32

—10.39

+29.44

1880

31,925

11.65

—10.05

+25.00

1881

35,135

11.82

+ 10.05

+ 1.46

1882

38,138

9.73

+ 8.55

—17.68

1883

46,864

8.19

+22.88

—15.83

1884

48,470

8.17

+ 3.43

— .24

1885

44,732

8.71

— 7.71

+ 6.61

1886

41,796

8.46

— 6.56

— 2.87

1887

41,454

9.97

— .82

+ 17.86

1888

46,643

8.76

+ 12,52

—12.14

1889

66,831

7.04

+43,27

—19.63

1890

60,198

7.87

— 9 , 93

+ 11.79

1891

60,818

8.12

+ 1,03

+ 3.18

1892

59,824

8.20

— 1,63

+ .99

1893

65,766

8.68

+ 9,93

+ 5.85

1894

54,874

8.54

—16,56

— 1.61

1895

47,079

8.35

—14.21

— 2.22

1896

59,282

6.55

+25.92

—21.56

1897

60,665

6.62

+ 2,33

+ 1.07

1898

66,377

6.00

+ 9,42

— 9.37

1899

56,656

7.27

—14,65

+21.17

1900

50,111

8.89

—11,55

+22.28

1901

50,591

10.01

+ .96

+ 12.60

1902

59,858

9.06

+ 18.32

— 9.50

1 1903

61,306

9.07

+ 2.42

+ .11

i 1904

60,696

8.72

— 1.00

— 3.86

1905

60,532

8.52

— .27

— 2.29

I 1906

57,146

10.37

— 5.59

+21.71

[ 1907

63,677

11.68

+ 11.43

+ 12.63

i 1908

70,798

8.98

+ 11.18

—23.12

1909

64,938

10.62

— 8.28

+ 18.26

1910

60,978

12,26

— 6,10

+ 15.44

1911

47,444

14.64

—22.19

+ 19.41

The Law of Demand

91

TABLE III. — The Production and the Price of Oats in the
United States

Average

Production op

Farm Price

Percentage

Percentage

Year

Oats in Thod-

Per Bushel

Change in

Change in

SANDs OF Bushels

December 1,
IN Cent8

Production

Price

1866

268,141

35.1

1867

278,698

44.5

+ 3.94

+26.78

1868

254,961

41.7

— 8.52

— 6.29

1869

288,334

38.0

+ 13.09

— 8.87

1870

247,277

39.0

—14.24

+ 2.63

1871

255,743

36.2

+ 3.42

— 9.66

1872

271,747

29.9

+ 6.26

—17.40

1873

270,340

34.6

— .52

+ 15.72

1874

240,369

47.1

—11.09

+36.13

1875

354,318

32.0

+47.41

—32.06

1876

320,884

32.4

— 9.44

+ 1.25

1877

406,394

28.4

+26.65

—12.35

1878

413,579

24.6

+ 1.77

—13.38

1879

363,761

33.1

—12.05

+34.55

1880

417,885

36.0

+ 14.88

+ 8.76

1881

416,481

46.4

— .34

+28.89

1882

488,251

37.5

+ 12.43

—19.18

1883

571,302

32.7

+ 17.01

—12.80

1884

583,628

27.7

+ 2.16

—15.29

1885

629,409

28.5

+ 7.84

+ 2.89

1886

624,134

29.8

— .84

+ 4.56

1887

659,618

30.4

+ 5.68

+ 2.01

1888

701,735

27.8

+ 6.39

— 8.55

1889

751,515

22.9

+ 7.09

—17.63

1830

523,621

42.4

—30.32

+85.15

1891

738,394

31.5

+41.02

—25.71

1892

661,035

31.7

—10.48

+ .63

1893

638,855

29.4

— 3.36

— 7.26

1894

662,037

32.4

+ 3,63

+ 10.20

1895

824,444

19.9

+24.53

—38.58

1896

707,346

18.7

—14.20

— 6.03

1897 1

698,768

21.2

— 1.21

+ 13.37

1898 '

730,907

25.5

+ 4.60

+20.28

1899

796,178

24.9

+ 8.93

— 2.35

1900 I

809,126

25.8

+ 1.63

+ 3.61

1901

736,809

39.9

— 8 94

+54.65

1902

987,843

30.7

+34.07

—23.06

1903

784,094

34.1

—20.52

+ 11.07

1904 '

894,596

31.3

+ 14.09

— 8.21

1905

953,216

29.1

+ 6.55

— 7.03

1903

964,905

31.7

+ 1.23

+ 8.93

1907

754,443

44.3

—21.81

+39.75

1908 1

807,156

47.2

+ 6.99

+ 6.55

1909

1,(K)7,353

40.5

+24.80

—14.19

1910

1,186,341

34.4

+ 17.77

—15.06

1911

922,298

45.0

—22.26

+30.81

92

Economic Cycles: Their Law and Cause

TABLE IV. — The Production and the Price of Potatoes in
THE United States

Production of
pot.\toes in

AVER.\QB

Farm Price

Percentage

Percentage

Year

Per Bushel

Change in

Change in

Thous.\.nd.s OF

December 1,

Production

Price

Bushels

IN Cents I

1866

107,201

47.3

1867

97,783

65.9

— 8.79

+39.32

1868

106,090

59.3

+ 8.50

—10.02

1869

133,886

42.9

+26.20

—27.66

1870

114,775

65.0

—14.27

+51.52

1871

120,462

53.9

+ 4.95

—17.08

1872

113,516

53.5

— 5.77

— .74

1873

106,089

65.2

— 6.54

+21.87

1874

105,981

61.5

— .10

— 5.67

1875

166,877

34.4

+57.46

—44.07

1876

124,827

61.9

—25.20

+79.94

1877

170,092

43.7

+36.26

—29.40

1878

124,127

58.7

—27.02

+34.32

1879

181,626

43.6

+46.32

—25.72

1880

167,660

48.3

— 7.69

+ 10.78

1881

109,145

91.0

—34.90

+88.41

1882

170,973

55.7

+56.65

—38.79

1883

208,164

42.2

+21.75

—24.24

1884

190,642

39.6

— 8.42

— 6.16

1885

175,029

44.7

— 8.19

+ 12.88

1886

168,051

46.7

— 3.99

+ 4.47

1887

134,103

68.2

—20.20

+46.04

1888

202,365

40.2

+50.90

—41.06

1889

204,881

35.4

+ 1.24

—11.94

1890

148,290

75.8

—27.62

+ 114.12

1891

254,424

35.8

+71.57

—52 . 77

1892

156,655

66.1

—38.43

+84.64

1893

183,034

59.4

+ 16.84

—10,14

1894

170,787

53.6

— 6.69

— 9.76

1895

297,237

26.6

+74.04

—50.37

1896

252,235

28.6

—15.14

+ 7.52

1897

164,016

54.7

—34.97

+91.26

1898

192,306

41.4

+ 17.25

—24.31

1899

228,783

39.0

+ 18.97

— 5.80

1900

210,927

43.1

— 7.80

+ 10.51

1901

187,598

76.7

—11.06

+77.96

1902

284,633

47.1

+51.72

—38.59

1903

247,128

61.4

—13 . 18

+30.36

1904

332,830

45.3

+34.68

—26 . 22

1905

260,741

61.7

—21.66

+36.20

1906

308,038

51.1

+ 18.14

—17.18

1907

298,262

61.8

— 3.17

+20.94

1908

278,985

70.6

— 6.46

+ 14.24

1909

376,537

54.9

+34.97

— 22 24

1910

349,032

55.7

— 7.30

+ 1^46

1911

292,737

79.9

—16.13

+43.45

CHAPTER V

THE MECHANISM OF CYCLES

"Agriculture is the Foundation of Manufacture and Commerce."
— Motto of the United States Department of Agriculture.

Thus far in our investigation of the cause and law of
economic cycles, we have shown that the annual rainfall
in the principal grain-producing area of the United
States passes through definite, well-defined cycles; and
that the yield of typical, leading crops is so closely
related to the rainfall of their respective critical seasons
that the cyclical movement of the rainfall of the critical
seasons is approxmiately reproduced in the yield per
acre of the corresponding crops. These cycles of crops
constitute the natural, material current which drags
upon its surface the lagging, rhythmically changing
values and prices with which the economist is more
immediately concerned. In order to understand the
connection between the flow of the undercurrent of
agricultural yield and the surface changes of values and
prices, we have taken the necessary first step of con-
necting the prices of agricultural commodities with
their supply. But the supply varies with the acreage as
well as with the yield, and consequently to carry further
our investigation we must know how closely the prices
of crops are related to their yield.

93

94 Economic Cycles: Their Law and Cause

The Prices of Agricultural Commodities Correlated with
the Yield of the Several Crops

The method employed in the preceding chapter to
derive the law of demand of the several crops contained
two stages: As a first stage, the correlation between the
relative change in the total supply and the correspond-
ing relative change in price was assumed to be linear,
and upon the hypothesis of linearity of regression, the
demand curve was computed and the degree of accuracy
with which prices might be predicted from such linear
demand curves we showed how to measure. The second
stage in the theory of demand curves was to assume a
skew relation between relative changes in price and
supply, and we found that the degree of accuracy with
which prices might be predicted from the skew demand
curves was greater than when the law of demand was
assumed to be linear. We shall follow these two stages
in treating the relation between the yield per acre and
the price of the crops.

If the correlation between the relative change in
yield per acre and the relative change in price is as-
sumed to be linear, we obtain for the coefficients of
correlation in case of the four typical crops, the values
placed in the first row of the accompanying Table,
which, for purpose of comparison, also presents the
corresponding coefficients in case of the linear demand
curves.

The Mechanism of Cycles

95

A Comparison of the Coefficients of Correlation in
Case of Linear Yield-Price Curves and of Linear
Demand Curves

Corn

Hay

Oats

Potatoes

Relative change in
yield per acre and
relative change in
price

— .815

— .656

— .718

— .873

Relative change in
total supply and
relative change in
price

— .789

— .715

— .722

— .856

J

The data used in the above computation were, in
case of the yield-price curve, the average yield per acre
of the respective crops in the whole of the United
States and the corresponding average prices for the
United States, on the first of December of the years in
which the crops were produced. The data for the
demand curves, it will be recalled from the preceding
chapter, were the total supply of the respective crops
in the United States and the corresponding prices on
December 1. The period covered in both cases was
from 1866 to 1911, inclusively. The data were ob-
tained from recent Yearbooks of the United States
Department of Agriculture.

It appears, from the coefficients of correlation given
in the above Table, that it is possible to predict the
prices of the crops from the yield per acre with the same

96 Economic Cycles: Their Law and Cause

precision with which prices may be predicted from the
demand curves. Or, to put the idea in another form,
the productivity of the soil is as closely related to the
prices of crops as the supply of the commodity is related
to the same prices. In the chapter on the ''Law of
Demand," we found that, when the relative change in
the supply is given, the mean shift in the corresponding
change of price may be obtained from the regression
equation, and that, furthermore, the root-mean-square
deviation of the observations may be computed by
the formula S =^y^l—r''. This same formula may
be used for a similar purpose in case of the yield-price
curves.

We come now to the second stage in the derivation of
the relation between price and the yield per acre of
crops. We assume that the relation between the yield
per acre and the price of a crop is skew, and that the
relation between the two may be expressed by an
equation of the form y =a+bx-{-cx'^-{-dx^.

In Figure 21, the skew yield-price curves of our four
representative commodities are drawn to a percentage
scale. The equations to the curves, which were com-
puted by the Method of Least Squares, are given upon
the Figure. The root-mean-square deviation of the
observations from their respective yield-price curves
are given in the following Table which, for purposes
of comparison, reproduces the coefficients that were
found, in the preceding chapter, to measure the devia-
tion of the observations about the skew laws of de-
mand.

The Mechanism of Cycles

97

i^65

\^Si

^

Percenfgde chgnde in the yie/ii per acre of corn Percer^fsde chande /n the yie/d per acre of hay.

Percenfijde chdnie in the yield per sere ofosfs Percentdde chande in the yield per acre ofpotafdes

Figure 21. The relation between the price and the yield per acre of the

several crops.
When the origin is at (0, 0), the equations are

For corn, y = .17 — 1.2989.r + .01892.c2 — .000137.c3.
For hay, y = 1.17 — 1.0215x + .01549.c2 + .00009.r3.
For oats, y = — 1.49 — 1.1346x + .02324x2 — .000238x3.
For potatoes, i/ = .49 — 1.4863x + .01993x2 — .000141x^

98 Economic Cycles: Their Law and Cause

A Comparison of the Root-Mean-Square Deviation in
Case of Skew Yield-Price Curves and of Skew De-
mand Curves

Corn

Hay

Oats

Potatoes

Yield-Price
Curves

5.48

5.72

7.05

9.39

Demand

Curves

7.36

4.65

10.17

9.94

From the results given in the last two Tables, it is clear
that the prices of the representative crops are as closely
related to the yield per acre as to the total supply of the
crops. This conclusion is of importance in the task of
connecting the cycles in the productivity of the soil with
the cycles in values and prices.

In obtaining the preceding close relations between the
changes in prices and changes in yield, the figures for the
whole of the United States were employed. The object
of broadening the field of observation from the detailed
investigation of the Middle West to the whole of the
United States was two-fold: First, it seemed likely, a
priori, that a more intimate relation between prices and
yield would be obtained if the large market of the whole
country were substituted for the local market of Ilhnois;
secondly, because the object of this chapter is to bring
the physical cycles of crops into relation with the
industrial and commercial changes of the whole country,
and to this end it seemed desirable that the crops of the

The Mechanis7n of Cycles 99

whole country should be considered. We need, how-
ever, to assure ourselves that, in taking this more
comprehensive view of the yield of crops, we have not
lost the characteristic cyclical movement of the yield
which we discovered in the more limited study. We
desire to know how closely the yield per acre of the
whole country is correlated with the yield per acre of
our representative state of Illinois.

The correlations of the annual differences in the yield
per acre in Illinois and the annual differences in the
yield per acre in the United States were, in case of our
four typical crops, for corn, r = .855; for hay, r = .745;
for oats, r = .800; for potatoes, r = ,843. The period
covered in all cases was from 1866 to 1912 inclusively.
The data were obtained from Bulletins, 56, 58, 62, 63
of the Bureau of Statistics of the United States Depart-
ment of Agriculture and from the recent Yearbooks of
the same Department. A reference to the Table given
a moment ago will show that the yield per acre of crops
in Illinois is at least as closely related to the yield per
acre of the same crops in the United States, as the prices
of the several crops are related either to the supply
of the crops or to the yield per acre of the crops. More-
over, the very high values of the coefficients leave but
little room for doubt that the cyclical movement of the
yield per acre in the Middle West is representative of
the movement of the crop yield in the whole of the
United States.

100 Economic Cycles: Their Law and Cause

Rising and Falling Prices as Related to Yield-Price

Curves

Thus far it is clear that the prediction of agricul-
tural prices is dependent upon a knowledge (1) of the
law of the variations of price with the yield per acre,
and (2) of the law of the annual change in the yield per
acre of the several crops. If the relation between prices
and yield per acre were constant, the theory of agricul-
tural cycles would be completely elucidated; for, once
having discovered the law of the relation of price to
yield per acre, nothing more would be necessary then
to connect the yield with the meteorological conditions
of its critical season, and the resulting prices for a long
term of years could be predicted with great probabihty.
But the relation between the price of the crops and the
yield per acre varies with the level of general prices, and
it is of the first importance to know the manner of varia-
tion.

If the course of prices in the United States for the
period 1866 to 1911 is examined, it w411 be seen that,
in general terms, we may with justness characterize the
period 1866 to 1890 as a period of falling prices, and the
period 1890 to 1911 as a period of rising prices. If
therefore, in case of each of our representative com-
modities, we construct two yield-price curves, one
for the period of falling prices and one for the pe-
riod of rising prices, we shall, by comparing the two
curves for the two periods, discover how the demand
curves, or yield-price curves, vary in periods in which

The Mechanism of Cycles 101

the movement of general prices is in opposite direc-
tions.

In Figure 22, the eight curves are drawn. Compar-
ing the curves in the two periods for each of the four
representative crops we infer that

(1) the demand schedule or yield-price curve is high

when the general level of prices is high; and
the demand schedule is low when the general
level of prices is low;

(2) the general run of the curves remains nearly the

same. That is to say, the principal difference
between the period of falling prices and period
of rising prices is that the yield-price schedules
move down or up.

These are general statements in which quite obvious
deviations are ignored and which, consequently, do
not pretend to quantitative accuracy. The construc-
tion of the curves is dependent upon too few observa-
tions to admit of attaching significance to the apparent
exceptions to the rule.

Since the prices of the representative crops are, as we
know, dependent upon the yield per acre and the law
of the relation between prices and the yield per acre,
and since, as we have proved, the yield-price curves
move with the general level of prices, our desideratum
is to discover what determines the change in the level
of general prices.

102 Economic Cycles: Their Law and Cause

Percenf-d^e chande in iheyieJd per acre afoafs ^ercenfs^e chanSe in the yield per acre ofpofdfbes.

Figure 22. The relation between the price and the yield per acr;

several crops.
When the origin is at {0,0), the equations are

of the

For corn

For hay

For oats

For potatoes

yrs. 1866-1889, _ ._, i/=— 2.00— 1.0299x + .01926x2— .000312.r3.

yrs. 1890-1911, , xj = 3.06— 1.4894x + .01737j-2^.000049.r3.

yrs. 1866-1889, - _, ?/ = — 5.72— 1.6435x + . 07798x2— .000574j-'.

yrs. 1890-1911, ,y= 5.41— .7306x— .00591.r2+.000075x^

yrs. 1866-1889, ?/ = — 2.78— 1.6039x— .00546j-2 + .0OO778x».

yrs. 1890-191 1, — , y = .99— 1.0240x + . 02394x2— .000383x3.
yrs. 1866-1889, _, ?/ = - 3.92— 1.4424x + .01684x2— .000020x».
yrs. 1890-1911, ,2/ = — .91— 1.6068x + .03831x2— .000397x».

The Mechanism of Cycles 1 03

The Volume of Crops and the Activity of Industry

We shall approach the problem of the cause of the
changing level of prices by considering two preliminary
questions which will enter into the subsequent argu-
ment: (1) Is there any relation between the changing
volume of the crops and the changing volume of those
producers' goods whose fluctuations are generally re-
garded as indices of the activity of trade? (2) Is the
law of demand for crops the type of law that is repro-
duced in the demand for all commodities, or is it not
rather the case that the law of demand for pure pro-
ducers' goods is of a different type from the law of
demand for those commodities of which our four crops
are samples?

The first of these two questions we shall consider in a
form modified to bring its significance to bear upon the
results that have already been established. The volume
of crops varies with the extent of the acreage and with
the average yield per acre. The question of interest
to us at this point is whether the volume of producers'
goods fluctuates with the yield per acre of the crops.
We shall investigate this question, and, as a means of
carrying forward our inquiry, we first construct an
index number of the yield per acre of crops. The nine
crops of the United States whose yield per acre through-
out a long period is recorded in the Yearbooks of the
Department of Agriculture are: corn, wheat, oats, bar-
ley, rye, buckwheat, potatoes, hay, cotton.' If, in case
' The figures for the yield per acre of cotton, 1870-1910, were oh-

104 Economic Cycles: Their Law and Cause

of each of these crops, the mean yield per acre for the
years 1890-1899 is taken as a base, and the yield per
acre for each of the years 1870-1911 is expressed as a
ratio of the base, comparable indices for the crops dur-
ing the period of forty-two years will be obtained. In
order to combine the nine series of figures into a series
that shall be representative of the whole of agriculture,
the several series must be properly weighted. The
method of weighting that was adopted in this particular
case was to assign to each crop an importance propor-
tionate to its value as compared with the total value of
the nine crops in 1911. The several weights were: for
corn, 36; wheat, 12; oats, 9; barley, 3; rye, .7; buck-
wheat, .3; potatoes, 6; hay, 16; cotton, 17. The index
numbers are given in Table I of the Appendix to this
chapter.

Before comparing the index number for the yield
per acre of the crops with the volume of producers'
goods, we must make sure that we are keeping close
to the results obtained from a detailed investigation
of our four representative crops. If an index number of
the four representative crops is constructed upon the
same principle as the index for the nine crops, how
closely would the indices be correlated? In computing
the index of the yield per acre of the four representa-
tive crops, the weights assigned were: for corn, 50;
hay, 28; oats, 15; potatoes, 7. The index is given in

tainrd from Circular 32, Bureau of Statistics, U. S. Department of
Agriculture. The yield for 1911 was obtained from the Yearbook
of the Department of Agricultur(>, 1911.

The Mechanism of Cycles 105

Table I of the Appendix to this chapter. The coeffi-
cient of correlation between the index for the four
representative crops and the index for the nine crops,
is r = .960.

It is a common observation of writers on economic
crises that the production of pig-iron is an unusually
good barometer of trade. The amount of pig-iron
that is annually produced swells with the activity
and volume of industry and trade, and it is among the
first commodities to indicate the general shrinking in
the ultimate demand which checks the activity of
trade and causes its temporary decline. Is there any
relation between the movement of this barometer of
trade, the production of pig-iron, and the cycles of the
crops? Can it be that the increase and decrease of the
"ultimate demand" which lies back of the flow and
ebb of trade has its source in the cyclical movements
of the yield per acre of the crops?

The data for testing whether there is a relation be-
tween the yield per acre of the crops and the annual
production of pig-iron are the statistics of the annual
production of pig-iron and the index numbers of the
yield per acre of our nine crops.

The method of testing the relation presents difficul-
ties, and as it will be used again to measure the relation
between the cycles of crops and the cycles of general
prices, we shall have a firmer grasp upon our problem
if we stop now to gain a clear idea of the terms that
continually occur in the argument. In any one of the

106 Economic Cycles: Their Law and Cause

series of figures that we shall use there are three distinct
movements which need to be discriminated, and when
any two of the series are compared, another important
characteristic of the series requires to be taken into
account. The three movements that are combined in
each series are:

(a) The continuous fall or rise of the figures with the
flow of time. This movement will be referred
to as the secular trend of the figures ;
{h) The rhythmical fluctuation of the figures about
their secular trend. \\Tien this movement
superposed upon the secular trend is the ob-
ject of investigation, the combined movement
will be referred to as the general cyclical
movement of the figures. When the rhyth-
mical movement unaffected by the complicat-
ing trend is being considered, it will be referred
to simply as the cycles of the figures;
(c) The year to year temporary fluctuation about
the general cycUcal movement. These fluctua-
tions will be referred to as the deviations of
the figures.
When the cycles of any two series are compared, it will
frequently happen, particularly if the one series is the
cause of the other, that there is a considerable interval
between the corresponding parts of the cycles in the
two series. This interval will be referred to as the lag
of the second series.

We shall be interested throughout the rest of this
chapter primarily in the interrelations of cycles of

The Mechanism of Cycles 107

crops, cycles in the activity of industry, and cycles in
general prices. But we approach our general problem
by considering first the temporary fluctuations which
we have agreed to call deviations, and we inquire
whether there is a relation between the deviations of
the yield of the crops and the deviations in the produc-
tion of pig-iron. The method that was adopted was
first to obtain the general cyclical movements of the
two series by averaging, in case of each series, the
figures for each year with the figures that iimnediately
preceded and followed the given year. For example,
the index number of the yield per acre for the years
1870, 1871, 1872, 1873 were respectively 108, 105, 110,
99. The smoothed figure for the yield per acre in 1S71

would therefore be — - =^^^ = 107.7. Simi-

3 3

larly, the smoothed index for 1872 would be 104.7. In
Tables II and III of the Appendix to this chapter are
presented the original and the smoothed figures for the
production of pig-iron and for the index number of the
yield per acre of the nine crops. The statistics of the
production of pig-iron were obtained from the Statis-
tical Abstract of the United States for 1912, p. 774.

After the general cyclical movements of the two series
were determined, the deviations of the actual figures
from the smoothed figures for each of the years were
calculated for both series of figures. These deviations
are also given in Tables II and III of the Appendix to
this chapter. The question upon which these differ-
ences are to throw Ught may be put in this form: Is

108 Economic Cycles: Their Law and Cause

the deviation of the yield per acre of the crops from its
general cyclical movement associated with the devia-
tion, in the following year, of the production of pig-
iron from the general cyclical movement of pig-iron?
The answer is found by correlating the differences,
always remembering that the difference for the yield
per acre in any given year is to be taken with the dif-
ference of the production of pig-iron in the following
year. The coefficient of correlation is r = .254.

We come now to the association between the cycUcal
movement of the yield per acre of the crops and the
cyclical movement of the production of pig-iron. Each
of these movements is superposed upon a rising secular
trend, and before we can test the degree in which the
cycles are related the secular trends must be eliminated.
If, as a first approximation, the secular trend in each
case is assumed to be linear, then by fitting a straight
line ^ to the data, it is possible to calculate the fluctua-
tions of the cycles of crop yield and of production of
pig-iron about their respective trends, and these fluctua-
tions may be correlated. In Table IV of the Appendix
to this chapter, the data for the calculation of the con-
nection between the cycles are given. In columns 2
and 5 are tabulated the general cyclical movements of

' The equations to the hnear secular trends are, respectively,
v/ = .1844a;+98.57, for the yield per acre of crops; and ?/ = 582.71a;+
9525, for the production of pig-iron. The origin in the first case is
at 1871 and in the latter case, at 1890. The first equation was com-
l)uted from the data for the years 1871-1906, and the second equa-
tion, from the data for 1871 to 1910.

The Mechanism of Cycles 109

the yield per acre of the crops and of the production of
pig-iron; in columns 3 and 6, the values of the linear
secular trends are given; and in columns 4 and 7, the
deviations of the cyclical movement from the secular
trend are recorded. These last deviations are the ma-
terial for calculating the connection between the cycles
of the yield per acre of the crops and the cycles of the
production of pig-iron.

If the deviations of the cycles from their respective
secular trends are correlated, the coefficient of correla-
tion reaches the value, r = .625, but we must not be
content to assume that even this relatively high co-
efficient represents the full degree of the relation be-
tween the cyclical movement of the crops and the
cyclical movement of the activity of industry as that
activity is typified in the production of pig-iron. It is
quite likely that the good or bad crops may produce
their maximum effect at a considerable interval after
the period in which the crops are actually harvested.
Time is required for the changing productivity of
crops to work out its maximum effect, and this causes
a lag in the adjustment of the cycles of the activity of
industry to the cycles of the yield of the crops. We
must therefore measure the amount of the lag.

If instead of correlating the cycles of the yield of the
crops and of the production of pig-iron for correspond-
ing years, we correlate them for lags of various intervals,
we shall find it possible to determine the lag that will
give the maximum coefficient of correlation, and this
particular value of the lag we may then regard as the

110 Economic Cycles: Their Law and Cause

interval of time required for the cycles in the crops to
produce their maximum effect upon the cycles of the
activity of industry. W^ien the calculation of the co-
efficients of correlation is made according to this plan,
it is found that for a lag

Of zero years, r = .625;
Of one year, r = .7l9;
Of two j^ears, r = .718;
Of three years, r = .697;
Of four years, r=.572.

It is clear, therefore, that the cycles in the yield per
acre of the crops are intimately related to the cycles in
the activity of industry, and that it takes between one
and two years for good or bad crops to produce the
maximum effect upon the activity of the pig-iron in-
dustry. Figure 23 illustrates the general congruence
of the cycles of the crops and of the cycles in the produc-
tion of pig-iron when a lag of two years is eliminated.

As to the general question concerning the relation
between the harvests and the activity of industry, we
may conclude from our statistical inquiry that there is
a positive, intimate connection, and very probably a
direct causal relation, between the bounty or niggardU-
ness of nature and the flow or ebb of trade. ^

A NeiD Type of Demand Curve

A moment ago, we saw that two prehminary problems

had to be treated before we could pass to the direct

^ In a later section of the chapter the metliod that has been used
in treating this problem will be employed for another purpose and
will then be illustrated in detail by means of graphs.

The Mechanism of ( 'ycles

111

Devi a f /on ofthedenfrs/ cyc/icdl moi'Cment' of the product/ on ofp/J-zron /torn /ts sec/y/jr T/cnd.

\

\ \

3

1? ^

i

i

o-

~^^^

,y

7

/

"~~o--.

"\

p

>

V

""■cv.^

M
h

J

"S

4
/ -,

y

C

\

/

1

I

,.-«

f

\ o

'^tJ*^/ -/e/njjs <;// t^/o^ rdojojo jjjp J^d pfs// si/ijo^ujuj^/\ouj /pj'/^/j /PJ.fL/^^ jlu jo uoi^p/a^Q

112 Economic Cycles: Their Law and Cause

consideration of the cause and law of cycles of general
prices. The first of these preliminary problems, namely,
the influence of the bounty of nature upon the volume
and acti\dty of trade, we have just discussed, and we
come now to the second preliminary problem, which
we shall put in the form of a question: Are all demand
curves in a dynamic society of the same type as the
demand curves for the representative crops: corn, hay,
oats, and potatoes?

This question must be answered as a preliminary to
the more fundamental inquiry as to the cause of cycles
of general prices, because if we assume that all demand
curves are of the same negative type, we are confronted
with an impossibility at the very beginning of our in-
vestigation. Upon the assumption that all demand
curves are of the negative type, it would be impossible
for general prices to fall while the yield per acre of
crops is decreasing. In consequence of the decrease
in the yield per acre, the price of crops would ascend,
the volume of commodities represented by pig-iron
would decrease, and upon the hypothesis of the uni-
versality of the descending type of demand curves, the
prices of commodities like pig-iron would rise. In a
period of declining yield of crops, therefore, there would
be a rise of prices, and in a period of increasing yield of
crops there would be a fall of prices. But the facts are
exactly the contrary. During the long period of falling
prices from 1870 to 1890, there was a decrease in the
yield -per acre of the crops, and during the long period
of rising prices from 1890 to 1911, there was an increas-

The Mechanism of Cycles 113

ing yield of crops. It is obviously inadmissible to
assume that in a dynamic society there is one law of
demand for all commodities. The dogma of the uni-
formity of the law of demand is an idol of the static
state.

If there are differences in types of demand curves,
it is quite likely that as one type has been illustrated by
the crops, another type will be exemplified by pure
producers' goods. We shall accordingly investigate
the demand curve of pig-iron, our representative pro-
ducers' good.

In Table V of the Appendix to this chapter is con-
tained the material for the computation of the law of
demand for pig-iron. The annual percentage changes
in the production of pig-iron were computed from the
figures of annual production, which were taken from
the Statistical Abstract for 1912, p. 774. It was impos-
sible to obtain directly the mean prices for which the
annual production was sold, and consequently the per-
centage change in the mean price could not be com-
puted directly. The device that was utilized to ap-
proximate these percentage changes is illustrated in
Table V of the Appendix. As the data needed for the
solution of the problem were the annual percentage
changes in the mean price and not the actual mean
annual prices themselves, it was regarded as sufficient
for our purpose to substitute for the unobtainable an-
nual percentage changes in the mean price, the mean
annual percentage changes in the prices of representa-
tive kinds of pig-iron. The annual prices for the lead-

114 Economic Cycles: Their Law and Cause

ing four kinds of pig-iron were obtained from the Statis-
tical Abstract for 1912, p. 572, and the annual percentage
changes in the prices of the four kinds, together with
their mean annual percentage changes, are given in
Table V of the Appendix. The second and last columns
of Table V were used in computing the law of demand
for pig-iron in the United States.

The graph of the law of demand for pig-iron is given
in Figure 24. The correlation between the percentage
change in the product and the percentage change in the
price is r = .537. The equation to the law of demand
is ?/ = .521 Ix— 4.58, the origin being at {o,o). Our re-
presentative crops and representative producers' good
exempUfy types of demand curves of contrary charac-
ter. In the one case, as the product increases or de-
creases the price falls or rises, while, in the other case,
the price rises with an increase of the product and falls
with its decrease.

The two preliminary difficulties are now cleared
away. We know that as the yield per acre of the crops
increases the physical volume of trade for producers'
goods increases; and we know, furthermore, that the
law of demand for a representative producers' good is
such that as the product increases the price increases.
If now a third fact, which has already been established,
be added to these two, an hypothesis conformable to
the three facts may be made which will give a working
theory for examining whether the cycles in crops pro-
duce the cycles in general prices. The third fact to
which reference is made is that the law of demand for

The Mechanism of Cycles

115

uoji-^ic/jo 3yud ^Lfj. ui ^pupLfo spe^usoj^^j

116 Econo7nic Cycles: Their Law and Cause

the crops falls during a period of falling general prices,
and rises during a period of rising general prices. With
these facts in mind it is not difficult to conceive how
general prices may fall during a period of diminishing
yield per acre of the crops and rise during the period
that the yield is increasing. The falling yield in the
crops would lead to a diminution of the volume of trade,
a decline in the demand for producers' goods, a fall in
the prices of producers' goods, a decrease in employ-
ment, a fall of the demand curves for crops, with the
final result of a fall in general prices. Similarly, a
rising yield in the crops would lead to an increase in
the volume of trade, an increase in the demand for
producers' goods, an increase of employment, a rise
in the demand curves for crops, with the final result of
a rise in general prices. Provided the interrelation of
the economic factors are in accordance with this de-
scription, then it would follow that the cyclical move-
ments in the yield of the crops should be reproduced
in cyclical movements of general prices. If the actual
facts bear out this deduction, there can be no doubt
that the cause and law of economic cycles have been
discovered.

The Fundamental, Persistent Cause of Economic Cycles

To put the theory to the test of facts we require an
index number of general prices throughout the period
covered by most of the investigation in this Essay —
the period from 1870 to 1911. There is no one index
number covering this period for the United States, but

The Mechanism of Cycles 117

very fortunately there are two series that overlap in the
middle of the period, so that it is possible to construct a
series covering the whole term of years. The two series of
index numbers in question are the Falkner index for ' ' all
articles" extending from 1870 to 1890, and the index of
the Bureau of Labor for "all commodities" extending
from 1890 to 1911. Since these two have the year 1890
in common it is possible, by applying the simple rule of
proportion, to reduce the Falkner series to the base of
the series published by the Bureau of Labor. The two
original series and the continuous series are given in
Table VI of the Appendix to this chapter.

The test of the theory that the cause and law of
economic cycles are the cyclical movements of the
yield per acre of the crops will be given in answer to two
questions: First, are the deviations of the indices of
general prices from their general cyclical movement
correlated with the deviations of the indices of the yield
per acre of the crops from their general cyclical move-
ment? Secondly, are the cycles of prices and the cycles
of crops correlated? The answers to these two questions
are the substance of the following paragraphs.

In Tables III and VI of the Appendix to this chapter
are given the indices of the yield per acre of the crops
and the indices of general prices. The Tables like-
wise contain the smoothed indices and the deviations of
the actual indices from the smoothed indices. The
smoothed series were obtained in the manner that was
described when the relation between the yield of the
crops and the production of pig-iron was being treated.

118 Ecojiomic Cycles: Their Law and Cause

It will be recalled from that description that the
smoothed index for any given year is the mean of three
actual indices: the actual index for the given year, the
actual index for the year preceding the given year, and
the actual index for the year following the given year.
The quantities whose correlation is in question are the
deviations of the actual indices of general prices, and of
yield per acre, from their respective smoothed series.
The results of the computation are as follows :

From 1870-1911, r=.303,
From 1870-1890, r = .370,
From 1890-1911, r = .250.

In the first row the correlations were obtained from
the continuous series in which the Falkner index was
adjusted to the index of the Bureau of Labor. In the
second row the correlations were derived from the
Falkner index unaltered. In the third row the correla-
tions were computed from the index of the Bureau of
Labor. We infer that the deviations from their general
cyclical movement of thejndices of general prices vary
directly with the deviation from their general cyclical
movement of the indices of the yield per acre of the
crops.

The second of the two questions as to the cause and
law of the cycles of general prices was stated in this
form: Are the cycles of prices and the cycles of crops
correlated? The preceding paragraphs have presented
the results of the in(|uiry as to the relation between the
deviations of actual prices and of yield from their

The Mechanism of Cycles 119

respective general cyclical movements. The present
question concerns the relation of the cyclical move-
ments themselves, after their respective secular trends
have been eliminated.

It will be recalled that the general cyclical movements
were obtained by a process of smoothing the actual
series of the indices of prices and of yield per acre, the
process consisting in the formation of a progressive
mean of the indices for three consecutive years. These
smoothed series, which are given in Tables III and VI
of the Appendix to this chapter, form the data of the
present investigation.

The method of the investigation is presented in Fig-
ures 25, 26, 27. In the first of these three Figures, the
general cyclical movements of prices and of yield per
acre are described according to the data of Tables III
and VI. The graphs bring out clearly the rhythmical
motions of both prices and yield and a comparison
of the curves suggests that the price curve is a lagging
reproduction of the yield curve. But before the amount
of the lag and the degree of correlation between the
cycles can be computed, the secular trends in the two
series of values must be eliminated. From Figure 25 it
is apparent that the price cycles move upon a falling
secular trend while the yield cycles move upon a rising
secular trend. If it is assumed as a first approximation
that these secular trends are both linear, the equation to
the trend for prices is ?/ = — .3702x + 122.01, and to the
trend for the yield per acre, y = .1844x+98.57, the ori-
gin, in the former case, being at 1875 and, in the latter,

120 Economic Cycles: Their Law and Cause

1 1

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\

/

/

^^

\

\

•('■'la

«

\
\

X

/

\

\

\

1

/

4

1

/

/

1

/

1

f

1

>

v>^

1
j

\

>

-■'

1 1
1 1

•S33ud /PJJUjfjO Jfjpui p3l^-l.00LUS pUi? SaCUDJO 3^09 J3d p/')l/' OijfJO X9pu/ p^l^iOOLUQ

The Mechanism of Cycles

121

(

d

f-

/

k

V.

\:

^,

""-Q,

iN

/
<?

p'""

V

/

^J

/

.1

(

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Q O O oops

♦ + + V '

sdojjjo jjjp ^jc/ p/pi/ JO x^pui 31^4 JO sf.u3uijAouu /eP'/yXs /ejsua^ 3lj4Jo cuo/^p/a9q

122 Economic Cycles: Their Law and Cause

at 1871.^ These two equations make it possible to
eliminate the secular trends upon which move the
cycles of prices and the cycles of yield. The results of
the calculations are given in Table VII of the Appendix
to this chapter.

Figure 26 presents the cycles of yield per acre and the
cycles of general prices after the secular trends upon
which they were respectively superposed have been
eliminated. It is quite evident, now, from the appear-
ance of the graphs, that the cycles of yield per acre and
the C3''cles of general prices are closely related, and that
the cycles of prices lag several years behind the cycles of
crops. What is the amount of the lag and how closely
are the cycles; correlated? Both of these questions may
be answered at once by following the method that was
adopted to measure the lag in the cycles of pig-iron
production. If the cycles of the yield per acre are
correlated ^ with the cycles of general prices we find, for
a lag of three years in general prices, r = .786; for a lag
of four years, r = .800; for a lag of five years, r = .710.
The cycles in the yield per acre of the crops are, there-
fore, intimately connected with the cycles of general
prices, and the lag in the cycles of general prices is
approximately four years.

Figure 27 presents the two series of cycles with the
lag of four years in the cycles of prices eliminated. It is

1 The first equation was computed from the data for 1875-1910,
and the second equation, from the data for 1871-1906.

^ The data for the calculation are given in columns 4 and 7 of
Table VII in the Appendix to this chapter.

The Mechanism of Cycles

123

(

\ <

\

y

V

>

^^^s

•>

si

X'

y-"

9 y*

4

V
y

/

9

-J

\

1

^J

p

y

1

^■J:)e -/ad p/j/X 3Lf4jo Ar^pu/ stfj.jo s-^ujuj^/iocu /pj//j/d /p^ju^f ^i^^jo suo/^p/Ad/J

124 Economic Cycles: Their Law and Cause

surely not an exaggeration to say that the congruence of
the two rhythmical movements of crop yield and general
prices is so close as to justify the inference that the one
series is the cause of the other. Every important
rhythmical feature of the yield curve is reproduced in
the price curve : the long cycle which in both curves dips
below the horizontal between 1880 and 1900, and the
smaller superposed cycles that move upon the large
ground-swell. The one apparent exception occurs in
the price movement between 1887 and 1891 in which
the price curve does not keep close to the yield curve.
But this is not a real exception. For, in the first place,
the price curve is convex between these limits, that
is to say, it shows a tendency to conform to the yield
curve; and, in the second place, since in the price
curve a lag of four years has been eliminated, the date
at which the disturbance occurs is really four years
later than would appear from the dates on the chart.
That would place the disturbance at about 1893, which
was the year of the panic with extraordinary condi-
tions in the state of the currency and the money mar-
ket.

Considering the high correlation between the two
series of cycles and the harmony of their congruence
with the theory of economic cycles embodied in this
Essay, we conclude that the cycles of the yield per
acre of the crops cause the cycles of general prices and
that the law of the cycles of crops is the law of the cycles
of general prices.

The Mechanism of Cycles 125

The chief results of this chapter may be summarized
in a few propositions :

(1) The yield per acre, for the whole of the United

States, of the four representative crops, corn,
hay, oats, and potatoes is so closely correlated
with the yield per acre of these crops in Illinois
as to render it very probable that the cause of
the cycles of the yield in the United States
is the same as the cause of the cycles in Illinois.
The meteorological cause of the rhythmical
changes in the yield of Illinois has been dis-
cussed in an earlier chapter.

(2) The prices in the United States of the four

representative crops are as closely related to
the yield per acre of the crops as the prices are
related to the total supply of the respective
crops. For the purpose of prediction of prices,
therefore, the yield-price curve is as useful as
the demand curve.

(3) The curves representing the relation between the

yield per acre and price, in case of the four
representative crops, fall during a period of
falling yield and falUng general prices, and
rise under the contrary circumstances.

(4) The falling or rising yield per acre of the crops

leads to a falling or rising volume of trade in
producers' goods. If the production of pig-
iron be taken as a representative producers'
good, then

(a) The deviations of the annual production

126 Economic Cycles: Their Law and Cause

of pig-iron from the general cyclical
movement in the production of pig-iron
are directly correlated with the devia-
tions, in the preceding year, of the
yield per acre of the crops from their
general cyclical movement ;
(b) When the lag in the production of pig-
iron and the secular trend in both the
production of pig-iron and in the yield
per acre of the crops are eliminated, the
cycles of production of pig-iron are very
closely correlated with the cycles of the
yield per acre of the crops. The coeffi-
cient of correlation is r = .719.

(5) Unlike the law of demand for the crops, the law of

demand for a representative producers' good
is such that as the supply increases the price
rises, and as the supply decreases the price
falls.

(6) With the falling of the yield per acre of the crops

there is a falling volume of trade, a falling
price of producers' goods, an increase in un-
employment, and a fall in the yield-price
curves for the crops. The contrary conditions
prevail under a rising yield per acre of the
crops.

(7) The ultimate effect upon general prices of the

process described in (6) is that

(a) The deviations of general prices from
their general cyclical movement are

The Mechanism of Cycles 127

directly correlated with the deviations
of the yield per acre of the crops from
their general cycUcal movement ;
(b) When the lag in general prices and the
secular trend in both prices and yield
per acre are eliminated, the cycles of
general prices are very closely corre-
lated with the cycles of the yield per
acre of the crops. The coefficient of
correlation is r = .800.

(8) The law of the cycles of crops is the law of the

cycles in the activity of industry and the
law of the cycles of general prices.

(9) The fundamental, persistent cause of the cycles

in the activity of industry and of the cycles of
general prices is the cyclical movement in the
yield per acre of the crops.

128 Economic Cycles: Their Law and Cause

APPENDIX

TABLE I. — Index Number of the Yield Per Acre of Crops

Year

Index for

Nine Crops

Index for
Four Crops

Year

Index for
Nine Crops

Index for
Four Crops

1870

108

109

1891

108

107

1871

105

113

1892

98

93

1872

110

115

1893

92

95

1873

99

98

1894

90

85

1874

88

88

1895

102

104

1875

110

114

1896

102

111

1876

98

101

1897

102

102

1877

106

110

1898

111

108

1878

109

113

1899

105

108

1879

111

114

1900

104

105

1880

106

107

1901

89

83

1881

82

82

1902

114

117

1882

100

99

1903

107

111

1883

97

100

1904

114

117

1884

101

105

1905

116

121

1885

98

102

1906

119

120

1886

93

93

1907

106

107

1887

89

85

1908

109

110

1888

100

103

1909

108

111

1889

104

106

1910

109

113

1890

89

86

1911

99

95

The Mechanism of Cycles

129

TABLE II. — The General Cyclical Movement and the Dif-
ferences OF THE Production of Pig-Iron in the United
States

Year

Produc-
tion OP
Pig-iron
IN Thou-
sands OF
Long
Tons

The Gen-
eral Cy-
clical
Move-
ment
(Progres-
sive Av-
erages of
Three
Years)

Differ-
ence Be-
tween
THE Ac-
tual
Produc-
tion AND
THE Gen-
eral Cy-
clical
Move-
ment

Year

Produc-
tion of
Pig-iron
IN Thou-
sands of
Long
Tons

The Gen-
eral Cy-
clical
Move-
ment
(Progres-
sive Av-
erages OF
Three
Years)

Differ-
ence Be-
tween the
Actual
Produc-
tion AND
THE Gen-
eral Cy-
clical
Move-
ment

1870

1,665

1891

8,280

8,880

— 600

1871

1,707

1,974

1892

9,157

8,187

+ 970

1872

2,549

2,272

-f277

1893

7,125

7,647

— 522

1873

2,561

2,504

+ 57

1894

6,658

7,743

— 10S5

1874

2,401

2,329

-f 72

1895

9,446

8,242

+ 12j4

1875

2,024

2,(J9S

— 74

1896

8,623

9,241

— 018

1876

1,869

1,987

—118

1S97

9,653

10,017

— 364

1877

2,067

2,079

— 12

189S

11,774

11,683

+ 91

1878

2,301

2,370

— 69

1899

13,621

13,061

+ 5G0

1879

2,742

2,626

+ 116

1900

13,789

14,429

— 640

1880

3,835

3,574

-f261

1901

15,878

15,829

+ 49

1881

4,144

4,201

— 57

1902

17,821

17,230

+ 585

1882

4,623

4,454

+ 169

1903

18,009

17,442

+ 567

1883

4,596

4,439

+ 157

1904

16,497

19,166

—2669

1884

4,098

4,246

—148

1905

22,992

21,599

+ 1393

1885

4,045

4,609

—564

1906

25,307

2t,693

+ 614

1886

5,683

5,382

+301

1907

25,781

22,341

+3440

1887

6,417

6,197

+220

1908

15,936

22,501

—6568

1888

6,490

6,837

—347

1909

25,795

23,012

+2783

1889

7,604

7,766

—162

1910

27,301

23,583

+ 1721

1890

9,203

8,362

+841

1911

23,650

130 Economic Cycles: Their Law and Cause

TABLE III. — The General Cyxlical Movement and the Dif-
ferences OF THE Index Number of the Yield Per Acre of
Nl\e Crops

The Gen"

Differ-

The Gen-

Differ-

ERAL Cy-

ence Be-

eral Cy-

ence Be-

Index of

clical

tween the

Index of

CIICAL

tween THE

Yield

ISIOVE-

Actual

Yield

Move-

Actual

Year

Per

MENT

Index and

Year

Per

ment

Index and

Acre

(Progres-

the Gen-

Acre

fPROGRES-

THE Gen-

(Nine

sive Av-

eral Cy-

(Nine

sive Av-

eral Cy-

Crops)

erages OF

clical

Crops)

erages OF

clical

Three

Move-

Three

Move-

Years)

ment

Years)

ment

1870

108

1891

108

98.3

+ 9.7

1871

105

107.7

— 2.7

1892

98

99.3

— 1.3

1872

110

104.7

+ 5.3

1893

92

93.3

— 1.3

1873

99

99.0

0.0

1894

90

94.7

— 4.7

1874

88

99.0

—11.0

1895

102

98.0

+ 4.0

1875

110

98.7

+ 11.3

1896

102

102.0

0.0

1876

98

104.7

— 6.7

1897

102

105.0

— 3.0

1877

100

104.3

+ 1.7

1898

111

106.0

+ 5.0

1878

109

108.7

+ .3

1899

105

106.7

— 1.7

1879

111

108.7

+ 2.3

1900

104

99.3

+ 4.7

1880

106

99.7

+ 6.3

1901

89

102.3

—13.3

1881

82

96.0

—14 . 0

1902

114

103.3

+ 10.7

1882

100

93.0

+ 7.0

1903

107

111.7

— 4.7

1883

97

99.3

— 2.3

1904

114

112.3

+ 1.7

1884

101

98.7

+ 2.3

1905

116

116.3

— .3

1885

98

97.3

+ .7

1906

119

113.7

+ 5.3

1886

93

93.3

— .3

1907

106

111.3

— 5.3

1887

89

94.0

— 5.0

1908

109

107.7

+ 1.3

1888

100

97.7

+ 2.3

1909

108

108.7

— .7

1889

104

97.7

+ 6.3

1910

109

105.3

+ 3.7

1890

89

100.3

—11.3

1911

99

The Mechanis7n of Cycles

131

TABLE IV. — Cycles of Yield Per Acre of Crops and Cycles
OF Production of Pig-iron

Year

General
Cyclical
Move-
ment
OF Yield
Per Acre
OF Crops

Ordin.^te

OF THE

Secular
Trend

Cycles
OF Yield
Per Acre
OF Crops

General
Cyclical
move.ment
OF Produc-
tion OF Pig-
iron, in
Thousands
OF Tons

Ordinate
OF the

Secular
Trend

Cycles of
Production
OF Pig-iron

1871

107.7

98. 6

+

9.1

1,974

— 1,546

+3,520

1S72

104.7

9S . 8

+

5.9

2,272

— 964

+3,236

1873

99.0

9S.9

+

.1

2,504

— 381

+2,885

1874

99.0

99.1

—

.1

2,329

202

+2,127

1875

98.7

99.3

— ■

.4

2,098

784

+ 1,314

1876

104.7

99.5

+

5.2

1,987

1,367

+ 620

1877

104.3

99.7

+

4.6

2,079

1,950

+ 129

1878

108.7

99.9

+

8.8

2,370

2,532

— 162

1879

108.7

100.0

+ 8.7 1

2,626

3,115

— 489

1880

99.7

100.2

—

.5

3,574

3,698

— 124

1881

96.0

100.4

—

4.4

4,201

4,281

— 80

1882

93 0

100.6

—

7.6

4,454

4,863

— 409

1883

99.3

100.9

—

1.6

4,439

5,446

—1,007

1884

98.7

101.0

—

2.3

4,246

6,029

—1,783

1885

97.3

101.2

—

3.9

4,609

6,611

—2,002

1886

93.3

101.3

—

8.0

5,382

7,194

—1,812

1887

94.0

101.5

— ■

7.5

6,197

7,777

—1,580

1888

97.7

101.7

—

4.0

6,837

8,360

—1,523

1889

97.7

101.9

—

4.2

7,766

8,942

—1,176

1890

100.3

102 . 1

—

1.8

8,362

9,525

—1,163

1891

98.3

102.3

—

4.0

8,880

10,108

—1,228

1892

99.3

102.4

— ■

3.1

8,187

10,690

—2,503

1893

93.3

102.6

—

9.3

7,647

11,273

—3,626

1894

94.7

102.8

—

8.1

7,743

11,856

—4,112

1895

98.0

103.0

—

5.0

8,242

12,439

—4,197

1896

102.0

103.2

—

1.2

9,241

13,021

—3,780

1897

105 . 0

103.4

+

1.6

10,017

13,604

—3,587

1898

lOG.O

103.5

+

2.5

11,683

14,187

—2,504

1899

106.7

103.7

+

3.0

13,061

14,769

— 1,708

1900

99.3

103.9

—

4.6

14,429

15,352

— 923

1901

102.3

104.1

—

1.8 i

15,829

15,935

— 106

1902

103.3

104.3

—

1.0 !

17,236

16,518

+ 718

1903

111.7

104.5

+

7.2

17,442

17,100

+ 342

1904

112.3

104.7

+

7.6

19,166

17,6S3

+ 1,483

1905

116.3

104.8

+ 11.5

21,599

1S,2(;6

+3,333

1906

113.7

105.0

+

8.7

24,693

1S,84S

+5,845

1907

111.3

105.2

+

6.1

22,341

19,4:51

+2,910

1908

107.7

105.4

+

2.3

22,504

20,014

+ 2,490

1909

108.7

105 . 5

+

3.2

23,012

20,596

+2,416

1910

105.3

105.7

— ■

.4

25,583

21,179

+4.404

132 Economic Cycles: Their Law and Cause

TABLE y. — Percentage Change in the Production of Pig-
iron AND Mean Percentage Change in the Price of Pig-iron

1

YE.^.R

Percent-

TAGE

Change in
THE Pro-
duction OK
Pig-iron

Percentage Change in the Price op Piq-iron

Mean
Perce.nt-

age

Change in

Price of

Pig-iron

No. 1
Foundry
AT Phila-
delphia

Gray
Forge at
Philadel-
phia

Gray
Forge
Lake Ore
AT Pitts-
burg

Bessemer

AT

Pittsburg

1870

1871

+ 2.52

+ 5.57

+ 5.57

1872

-f49.33

+39.51

+39.51

1873

+ .47

—12.57

—12.57

1874

— 6.25

—29.45

—24.13

—26.79

1875

—15.70

—15.44

—12.85

—14.14

1876

— 7.66

—13.08

— 8.15

—10.61

1877

+ 10.59

—14.74

— 5.24

— 9.99

1878

+ 11.32

— 6.61

—12.18

— 9.39

1879

+ 19.17

+22.92

+22.44

+22.68

1880

+39.86

+31.12

+26.32

+28.72

1881

+ 8.06

—11.62

—18.01

—14.82

1882

+ 11.56

+ 2.38

+ 3.92

+ 3.15

1883

— .58

—13.00

—14.47

—20.13

—15.87

1884

—10.84

—11.64

— 8.38

— 9.82

— 9.95

1885

— 1.29

— 9.14

—12.03

—11.07

—10.75

1886

+41.61

+ 4.00

+ 5.26

+ 8.58

+ 5.95

1887

+ 12.92

+ 11.87

+ 8.48

+ 14.72

+ 12.71

+ 11.95

1888

+ 1.14

— 9.79

— 8.88

—15.93

—18.67

—13.32

1889

+ 17.16

— 5.93

— 4.50

— 4.00

+ 3.57

— 2.72

1890

+21.03

+ 3.66

+ 2.20

+ 2.80

+ 4.83

+ 3.37

1891

—10.03

— 4.83

— 8.22

—10.90

—15.47

— 9.85

1892

+ 10.59

—10.10

— 6.75

— 8.89

— 9.91

— 8.91

1893

—22.19

— 7.81

— 5.98

— 8.12

—10.44

— 8.09

1894

— 6.55

—12.81

—15.71

—17.16

—11.58

—14.32

1895

+41.87

+ 3.48

+ 7.08

+ 12.21

+ 11.78

+ 8.64

1896

— 8.71

— 1.15

— 3.48

— 5.03

— 4.56

— 3.55

1897

+ 11.91

— 6.56

— 5.50

—13.09

—16.56

—10.43

1898

+21.97

— 3.64

— 2.39

+ 1.66

+ 1.97

— .60

1899

+ 15.70

+66.04

+62.27

+82.14

+84.22

+73.67

1900

+ 1.23

+ 3.20

— .66

+ 1.08

+ 2.42

+ 1.51

1901

+ 15.15

—20.57

—14.61

—15.98

—18,27

—17.36

1903

+ 12.24

+39.82

+36.36

+37.25

+29.76

+35.80

1903

+ 1.05

—10.23

—10.78

—10.11

— 8.18

—10.07

1904

— 8.40

—21.84

—20.20

—26.43

—27.50

—23.99

1905

+39.37

+ 14.84

+ 13.97

+21.18

+ 18.90

+ 17.22

1906

+ 10.07

+ 17.34

+ 14.18

+ 16.45

+ 19.44

+ 16.85

1907

+ 1.87

+ 13.87

+ 18.38

+ 18.31

+ 16.89

+ 16.86

1908

—38.19

—25 91

—25.36

—29.23

—25.26

-26.44'

1909

+61.87

+ .62

+ 2.61

+ 2.10

+ 1.99

+ 1.83

1910

+ 5.85

— 2.53

— 2.54

— 1.99

— 1.26

— 2.08

1911

—13.38

— 9.50

— 8.21

— 8.33

— 8.61

— 8.66

1912

+25 . 70

+ 5.41

+ 6.65

+ 4.08

+ 1.46

+ 4.40

The Mechanism cf Cycles

133

TABLE VI. — The Index Number of General Prices.
General Cyclical Movement and its Differences

Its

Falkner's

j

' lENERA L

Difference

Year

Falkner's
Index of
Prices of
"All Ar-
ticles"

Bureau of
Labor's
Inde.x of
Prices of
" All Com-
modities"

Index

Adjusted

TO THE

Base of
THE Bur-
eau OF
Labor

The Co.v-

TINUOUS

I.vdex of
Prices

CrCLICAL
MOVEME.NI

OF THE
CONTI.NU-

ous Index
OF Prices

Between
THE .A.ctual|
Index and
THE Gen-
eral Cy-
clical
Movement

1870

117.3

143.5

143.5

1871

122.9

150.3

150.3

149. S

+ .')

1872

127.2

155.6

155 . 6

151.7

+3.9

1873

122.0

149.2

149.2

150.3

—1.1

1874

119.4

146.0

146.0

144.6

+ 1.4

1875

113.4

138.7

138.7

137.6

+ 1.1

1876

104.8

128.2

1-28.2

131.5

—3.3

1877

104.4

127.7

127.7

126.0

+ 1.7

1878

99.9

122.2

122.2

122.7

— .5

1879

96.6

118.2

118.2

123.7

—5 . 5

1880

106.9

130.8

130.8

126.1

+4.7

1881

105.7

129.3

129.3

130.9

—1.6

1882

108.5

132.7

132.7

130.6

+2.1

1883

106.0

129. 7i

129.7

12S.0

+ 1.7

1884

99.4

121.6

121.6

121.7

— .1

1885

93.0

113.8

113.8

115.9

—2.1

1886

91.9

112.4

112.4

113.2

— .8

1887

92.6

113.3

113.3

113.6

— .3

1888

94.2

115.2

115.2

114.6

+ .6

1889

94.2

115.2

115.2

114.4

+ .8

1890

92.3

112.9

112.9

113.3

— .4

1891

111.7

111.7

110.2

+ 1.5

1892

106.1

106.1

107.8

—1.7

1893

105.6

105.6

102.6

+3.0

1894

96.1

96.1

98.4

—2.3

1895

93.6

93.6

93.4

+ .2

1896

90.4

90.4

91.2

— .8

1897

89.7

89.7

91.2

—1.5

1898

93.4

93.4

94.9 !

—1.5

1899

101.7

101.7

101.9 1

— .2

1900

110.5

110.5

103.9

+3.6

1901

108.5

108.5

110.0

—2.1

1902

112.9

112.9

111.7

+ 1.2

1903

113.6

113.6

113.2

+ .4

1904

113.0

113.0

114.2 1

—1.2

1905

115.9

115.9

117.1 i

—1.2

1906

122.5

122.5

122.6

— .1

1907

129.5

129.5

124.9

+4 6

1908

122.8

122.8

126.3

—3.5

1909

126.5

126.5

127.0

— .5

1910

131.6

131.6

129.1

+2.5

1911

129.3

129.3

134 Economic Cycles: Their Law and Cause

TABLE VII. — Cycles of Yield Per Acre op Crops and Cycles
OF General Prices

Year

General
Cyclical

Move-
ment OF
Yield Per
Acre of

Crops

Ordinates

OF the

Secular

Trend

Cycles of
the Yield
Per Acre
of Crops

General
Cyclical

Move-
ment OF
General

Prices

Ordinates
OF the
Secular
Trend

Cycles of

General

Prices

1871

107.7

98.6

+ 9.1

149.8

123.5

+26.3

1872

104.7

98.8

+ 5.9

151.7

123.1

+28.6

1873

99.0

98.9

+ .1

150.3

122.8

+27.5

1874

99.0

99.1

— .1

144.6

122.4

+22.2

1875

98.7

99.3

— .4

137.6

122.0

+ 15.6

1876

104.7

99.5

-f 5.2

131.5

121.6

+ 9.9

1877

104.3

99.7

+ 4.6

126.0

121.3

+ 4.7

1878

108.7

99.9

+ 8.8

122.7

120.9

+ 1.8

1879

108.7

100.0

+ 8.7

123.7

120.5

+ 3.2

1880

99.7

100.2

— .5

126.1

120.2

+ 5.9

1881

96.0

100.4

— 4.4

130.9

119.8

+ 11.1

1882

93.0

100.6

— 7.6

130.6

119.4

+ 11.2

1883

99.3

100.9

— 1.6

128.0

119.0

+ 9.0

1884

98.7

101.0

— 2.3

121.7

118.7

+ 3.0

1885

97.3

101.2

— 3.9

115.9

118.3

— 2.4

1886

93.3

101.3

— 8.0

113.2

117.9

— 4.7

1887

94.0

101.5

— 7.5

113.6

117.6

— 4.0

1888

97.7

101.7

— 4.0

114.6

117.2

— 2.6

1889

97.7

101.9

— 4.2

114.4

116.8

— 2.4

1890

100.3

102.1

— 1.8

113.3

116.5

— 3.2

1891

98.3

102.3

— 4.0

110.2

116.1

— 5.9

1892

99.3

102.4

— 3.1

107. S

115.7

— 7.9

1893

93.3

102.6

— 9.3

102.6

115.3

—12.7

1894

94.7

102.8

— 8.1

98.4

115.0

—16.6

1895

98.0

103.0

— 5.0

93.4

114.6

—21.2

1896

102.0

103.2

— 1.2

91.2

114.2

—23.0

1897

105.0

103.4

-f 1.6

91.2

113.9

—22.7

1898

106.0

103.5

+ 2.5

94.9

113.5

—18.6

1899

106.7

103.7

+ 3.0

101.9

113.1

—11.2

1900

99.3

103.9

— 4.6

106.9

112.8

— 5.9

1901

102.3

104.1

— 1.8

110.6

112.4

— 1.8

1902

103.3

104.3

— 1.0

111.7

112.0

— .3

1903

111.7

104.5

-+- 7.2

113.2

111.6

+ 1.6

1904

112.3

104.7

+ 7.6

114.2

111.3

+ 2.9

1905

116.3

104.8

+ 11.5

117.1

110.9

+ 6.2

1906

113.7

105.0

+ 8.7

122.6

110.5

+ 12.1

1907

111.3

105.2

+ 6.1

124.9

110.2

+ 14.7

1908

107.7

105.4

+ 2.3

126.3

109.8

+ 16.5

1909

108.7

105.5

+ 3.2

127.0

109.4

+ 17.6

1910

105.3

105.7

— .4

129.1

109.0

+23.1

CHAPTER VI

SUMMARY AND CONCLUSIONS

These cycles of crops constitute the natural, material current
which drags upon its surface the lagging, rhythmically changing
values and prices with which the economist is more immediately
concerned.

The principal contribution of this Essay is the dis-
covery of the law and cause of Economic Cycles. The
rhythm in the activity of economic life, the alternation
of buoyant, purposeful expansion with aimless depres-
sion, is caused by the rhythm in the yield per acre of
the crops; while the rhythm in the production of the
crops is, in turn, caused by the rhythm of changing
weather which is represented by the cyclical changes in
the amount of rainfall. The law of the cycles of rainfall
is the law of the cycles of the crops and the law of
Economic Cycles.

We shall recapitulate the main stages by which this
conclusion was reached and shall take occasion, as the
stages are reviewed, to suggest the care that must
be observed in interpreting the statistical generaliza-
tions which form the structure of the argument.

When we begin to think seriously about the cause of
Economic Cycles we are greatly impressed by the wide
diffusion of these cyclical movements among the peoples
of the world, and the inference appears to be inevitable
that there must be some physical cause at work to

135

136 Economic Cycles: Their Law and Cause

account for so general a movement. As the most
fundamental need of mankind is the need for food, it
seems probable that the observed rhythmical economic
changes may be produced by the physical cause through
its effect upon the food supply. If this be so, then, as
the fluctuations of the food supply are known to be
subject to the supposed caprices of the weather, it
seems not unlikely that the physical cause may be one
or more of the elemental forces that are summarized
under the term weather. The variation in the quantity
of the rainfall is one of the weather changes known to
have a marked effect upon the yield of the crops, and
if this fact is taken into consideration with the preceding
reasoning, we have a working theory as to the cause of
Economic Cycles: The changes in the weather repre-
sented by the changes in the quantity of rainfall cause
the changes in the yield per acre of the crops, and the
variations in the yield of the crops cause the economic
changes known as Economic Cycles. With this work-
ing theory in mind, we examined appropriate data with
reference to three things: (1) The periodicity of rain-
fall; (2) the effect of rainfall on the crops; (3) the rela-
tion of the yield of the crops to Economic Cycles.

First, then, as to the periodicity of rainfall. The
problem as to whether the quantity of rainfall passes
through definite cycles involves two practical questions
that affect the utility and the validity of the results that
may be attained. These questions are, first, as to what
rainfall data shall be used in the investigation of possible
rainfall cycles; and, second, as to the method that shall

Sum77iary and Conclusions 137

be adopted to establish the existence of the cycles and
to ascertain their characteristic lengths, amplitudes and
phases. In our investigation, the choice of rainfall data
was suggested by the scope of our general problem.
Supposing that we could find definite periods in the
varying amount of the rainfall, we should then desire to
know the relation of rainfall to the yield of the crops,
and the relation of the yield of the crops to Economic
Cycles. It was necessary, therefore, that the data
of rainfall should refer to an area in which unportant
crops are produced, and it was desirable that the data of
both rainfall and crops should refer to a highly dynamic
society. For these reasons we collected the material
for our investigation from the central part of the United
States.

The method adopted in an investigation of the
periodicity of rainfall must satisfy three conditions:
(1) It must exhaust the data in the search for possible
cycles; that is to say, the data must be made to yield
all the truth they contain relating to the particular
problem in hand. Frequently in the past, spurious
periodicities have been presented as real periodicities,
chiefly because the investigator started with a bias in
favor of a particular period and did not pursue his
researches sufficiently far to determine whether his
result was not one among many spurious, chance
periodicities contained in his material. In the search for
real periodicities the data must be exhaustively ana-
lyzed. (2) The method must render possible the dis-
crimination between a true periodicity, having its

138 Economic Cycles: Their Law and Cause

origin in a natural cause and persisting with a change in
the samples of statistics, and a spurious periodicity
which is purely formal, having its origin in accidental
characteristics of the statistical sample and disappear-
ing, or radically altering its character, when different
samples of statistics are made the basis of the computa-
tion. (3) The method must not only make possible
the isolation of real periodicities, but it must likewise
enable one to determine their essential characteristics,
their length, phases and amplitudes. The method we
adopted in our researches, which is based upon the
harmonic analysis, satisfies these three conditions.

The result of our investigation as to the periodicity of
rainfall in the upper Mississippi Valley was the dis-
covery that the annual rainfall passes through two
cycles of approximately thirty-three years and eight
years in length. The amplitude and phases of these
two cycles were ascertained, and the equations to the
separate cycles were calculated. The two cycles were
then superposed, thus giving the general cyclical move-
ment of rainfall; the equation of this compound cycle
was computed and the graph was drawn. It was found
that the curve of the rhythmical movement of rainfall
computed from the equation to the superposed cycles
fitted excellently well the actual observations of rainfall.
These results constitute the solution of the first part of
our general problem : Rainfall in the principal crop area
of the United States passes through cycles of thirty-
three years and of eight years.

The caution that should be observed in the use of our

Summary and Conclusions 139

conclusions is suggested by the method that was em-
ployed and the subject that was investigated. The
inquiry is a statistical study of an aspect of meteorology,
and, therefore, the caution to be exercised in the use
of the conclusions is the caution that should be applied
to statistical work in general and to meteorology in
particular. As far as the statistical work is concerned,
it should be observed that the data were drawn from a
limited area of the United States and covered, at most,
seventy-two years. Consequently, while there seem to
be very good reasons in favor of the belief that, for the
purpose for which they were used, the data were repre-
sentative of the whole country, it is highly desirable
that similar studies should be made for other places and
other times. Furthermore, the present investigation
was limited to a study of the periodicity of rainfall, but
a more adequate research would embrace the periodicity
of temperature and of other weather elements, together
with an investigation of the interrelation of the elements.
Before passing on to consider the caution to be observed
in the use of statistical studies of meteorology, a word
should be said in justification of the hmitation of the
inquiry to the periodicity of annual rainfall. The ob-
ject of taking annual rainfall was to ascertain the mean
periodicity of the rainfall of the critical seasons of the
several crops. It would have been more satisfactory to
investigate the periodicity of the rainfall of the critical
season in case of each crop, but, because of the extreme
laboriousness of the calculations, a device had to be
adopted to limit the amount of computation.

140 Economic Cycles: Their Law arid Cause

In regard to the use of statistical generalizations in
meteorology, we have the cautious opinion of Lord
Kelvin: "I cannot say whether anything with reference
to Terrestrial Meteorology is done once for all. I
think probably the work will never be done." There
is always need of checking up statistical conclusions in
the light of new data, and this necessity applies to the
generalization that in the Mississippi Valley the annual
rainfall passes through a double cycle of thirty-three
years and eight years. This conclusion is undoubtedly
warranted by the data that lie at the basis of the in-
vestigation, but it would be a grave fault, indeed, to
hold that the cycles do not alter with the flow of time.
Whether they change or retain their characteristics can
be determined only by accumulating more data than
are at present available.

We come now to the second part of our general
problem, namely, to the consideration of the relation
between rainfall and the yield of the crops, and again
the questions of data and method must be settled.
In choosing the data, the prime consideration was to
make sure that the crops selected should be representa-
tive of the conditions of crop-producing in the Middle
West. The five principal crops in the Middle West are
corn, hay, wheat, oats, and potatoes, and of these five
all except wheat were taken to serve as representative
crops. Wheat was omitted because of technical dif-
ficulties: First, it is impossible, except for recent years,
to separate in the published statistics the yield per acre

Summary and Conclusions 141

of spring wheat from the yield of winter wheat; and,
secondly, since the growth seasons and critical periods
of these two varieties of wheat are different, it seemed
unwise to attempt to connect the rainfall of any season
with the yield per acre of wheat in which the figures for
the yield referred to spring and winter wheat taken
together. For these reasons the representative crops
were Umited to corn, hay, oats, and potatoes; and the
yield per acre of these several crops throughout a long
period of time, together with the rainfall of their
respective critical seasons, form the numerical data of
the investigation.

The method of determining the critical seasons was to
find, by the use of the statistical theory of correlation,
the month or months, in the lifetime of the several
crops, the rainfall of which gave the highest correlation
with the ultmiate yield. This preliminary inquiry
afforded a partial answer to our general question as to
the relation between rainfall and the crops. We found
that in case of each of the crops the yield per acre is
directly connected with the rainfall of some critical
period, and in all of the crops except oats the connection
is very close. It seemed probable, therefore, that since
the rainfall passes through definite cycles, and since
the yield per acre of the crops is intimately related with
the rainfall of their respective critical seasons, the yield
per acre of the crops should likewise pass through the
double cycle described by the rainfall of the critical
seasons.

The investigation of the relation of the cycles of the

142 Economic Cycles: Their Law and Cause

crops to the cycles of the rainfall of the critical seasons
was carried out in two ways, first for the crops taken
singly, and then for the crops taken all together. In the
inquiry relating to the separate crops, the equations to
the double cycle in the yield per acre and to the double
cycle in the rainfall of the corresponding critical seasons
were computed, and the graphs were drawn. When the
graphs of the cycles of the crops were superposed upon
the graphs of the cycles of rainfall of the respective
critical seasons, the two curves were found to present a
very remarkable congruence. In the inquiry relating
to the crops taken all together, an index number of the
yield per acre of the crops and an index number of the
mean effective rainfall of the critical seasons were con-
structed. The equations to the double cycle in both
indices were computed, their graphs were drawn and
then superposed. It was found that the characteristic
features of the rainfall curve were reproduced in the
curve of the index number of the yield per acre of the
crops.

These results, referring both to the crops taken singly
and to the crops taken all together, are the answers to
the second part of our general question: The yield per
acre of the representative crops is closely connected
statistically with the rainfall of the respective critical
seasons, and the relation is so close that the cycles of
the yield per acre of the crops reproduce in char-
acteristic ways the cycles of the rainfall of the critical
seasons. The fundamental, persistent cause of the
cycles of crops is, therefore, the rhythmical movement

Summary and Conclusions 143

in the conditions of the weather represented by the
cycles in the amount of rainfall.

In the cautious use of the preceding generalizations,
one will bear in mind that only four crops have been
investigated, and that, in ascertaining the critical
seasons, the monthly rainfall has been used. The
critical seaons could undoubtedly be determined more
accurately if the figures for the weekly rainfall were
employed. Furthermore, the inquiry has been limited
to the relation of the yield of the crops to rainfall,
whereas a more adequate study would include at least
the effects of temperature.

Thus far the investigation has established the law
and cause of the cycles of the crops: The cause of the
cycles in the physical productivity of the crops is the
cyclical variation of the weather represented by the
cycles of rainfall, and the law of the cycles of rainfall is
the law of the cycles of the crops. In order to bring
these physical results into relation with the rhythmical
movements of prices and values, we had first to show
how the prices of the several crops vary with their
respective supplies. In technical terms, we had to
discover the laws of demand for the individual crops.

The equations to the law of demand for corn, hay,
oats, and potatoes were computed, and the graphs were
drawn. The degree of precision with which these
demand curves might be used as formulae for predicting
prices was ascertained, and the coefficients of the
elasticity of demand for the representative commodities

144 Economic Cycles: Their Law and Cause

were calculated. The equations to the law of demand
for all four crops conformed to a single type, indicating
that as the supply of the commodity increases, the price
falls. For reasons that were explained in the discussion,
we named this type of demand curve the negative type.

It will be recalled that the three divisions of our
general problem were (1) the periodicity of rainfall;
(2) the effect of rainfall upon the crops; and (3) the
relation of the yield of the crops to Economic Cycles.
The elaboration of a method for calculating the demand
curves placed us in position to examine the third and
final part of the problem. The law of demand for the
crops connects the price of the several crops with their
respective supplies, but the supply is dependent upon
both the yield per acre and the extent of the acreage.
In order to bring our findings with regard to the period-
icity in the yield per acre into relation with prices and
values, it is clear that we must know the relation
between the variation in the price of the commodity
and the yield per acre of the commodity. This ques-
tion we examined at length, and found the tie between
price and yield per acre to be as close as the tie between
price and supply. To differentiate between demand
curves and curves showing the relation between yield
per acre and price, we called the latter curves, yield-
price curves. We deduced the equations to the yield-
price curves for the four representative commodities
and measured the degree of precision with which their
equations might be used as formulae for predicting

Summary and Conclusions 145

prices. In all of these relations, the yield-price curves
were found to be as accurate and as satisfactory as
the demand curves themselves.

With the possession of the yield-price curves, showing
the relation between the prices of the crops and their
varying yield per acre, it might seem that the problem
of agricultural cycles at least was completely elucidated.
As we know how the periodicity in the yield of the crops
follows upon the periodicity in the rainfall, and how the
prices vary with the yield, one might conclude that
the course of prices could be predicted for a long time.
The inference would be entirely true but for the fact
that the demand curves and the yield-price curves move
alternately up and down with the flow of time. This
complication made it necessary to investigate the
rhythmical movement of the yield-price curves, and
we found that the demand curves, or yield-price curves,
rise or fall with the level of general prices and with the
level of the index of the yield per acre of the crops.

The preceding facts seemed to involve a contradiction
with an a priori doctrine of theoretical economics.
According to the economic dogma of the uniformity of
the demand function, all demand curves are of the
negative type: As the amount of the commodity in-
creases, the price falls. But if this be true, how is it
possible for a fall of general prices to accompany a fall
in the index of the yield per acre of the crops? If the
yield per acre of the crops decreases, then, according to
the yield-price curves and the demand curves, the price
of the crops will rise. Moreover, as the profits of trade

146 Economic Cycles: Their Law and Cause

and commerce are largely dependent upon the volume
of the crops, it seems likely that the demand for general
commodities would decrease with a deficiency in the
harvests, and, according to the dogma of the uniformity
of the demand function, the prices of general commodi-
ties should rise. The ultimate result of bad harvests,
therefore, would be a rise in general prices. The facts,
however, bear out the contrary view. General prices
fall with a decrease in the yield per acre of the crops.
A consideration of this difficulty led to the discovery
that there is a positive type of demand curve as well as a
negative type. For a representative producer's good,
for example pig-iron, the law of demand is such that as
the amount of commodity increases the price of the
commodity rises, and as the amount of the commodity
decreases the price of the commodity falls. The exist-
ence of both positive and negative types of demand in a
highly dynamic society suggested a working theory
which seemed to account for the interrelation of all
the known relevant facts, and which may be stated in
compact form. The rhythmically varying yield per
acre of the crops is the cause of Economic Cycles:
When the yield increases, the volume of trade, the
activity of industry and the amount of employment
increase; the demand for producers' goods increases and
the prices of producers' goods rise; the demand curves
for agricultural commodities rise; with the ultimate
result of a rise of general prices. The contrary changes
would follow upon a fall in the yield per acre of the
crops.

Summary and Conclusions 147

Beyond what we had ah-eady established, this theory
of the interrelation of economic changes required for
its complete demonstration the proof of the existence of
two fundamental relations, to wit, that the cycles in the
yield per acre of the crops are reproduced

(1) in the activity of general industry;

(2) in the movement of general prices.

In order to test whether these relations actually exist,
an index number of the yield per acre of the crops was
constructed for the nine crops, corn, wheat, oats, barley,
rye, buckwheat, hay, cotton, and potatoes. To make
sure of keeping close to the results already established
for the representative commodities corn, hay, oats, and
potatoes, the correlation of the index of the nine crops
with the index of the four representative crops was
computed and found to be r = .960.

As the production of pig-iron is generally regarded as
a good "barometer" of the activity of industry, we
sought an answer to the above first question by in-
vestigating whether the cycles in the yield per acre of
the nine crops were reproduced in the cycles in the
production of pig-iron. The inquiry involved the
problems of the separation of the cyclical and the secular
movements in the production of pig-iron, and the
ascertainment of the amount of the lag in the cycles
of pig-iron behind the cycles in the yield per acre of the
crops. We found that it takes between one and two
years for the stimulation of increasing harvests to work
out its maximum effect in promoting the activity of
industry as that activity is represented in the ''barom-

148 Economic Cycles: Their Law and Cause

eter" of industry, the production of pig-iron; and
that, when an allowance is made for a lag of two years
in the adjustment of the pig-iron industry, the cycles
of the yield per acre of the crops are generally repro-
duced in the cycles of the production of pig-iron, the
relation being so close that the coefficient of correlation
is r = .718.

To find the relation of the cycles in the yield per acre
of the crops to the cycles in the movement of general
prices, we made use of an index number of general
prices extending from 1870 to 1910, and of our index
number of the yield per acre of nine crops covering the
same interval of time. The problem of separating the
cyclical movements in these two series from their
secular movements was solved, and the lag of the cycles
of general prices behind the cycles in the yield of crops
was found to be about four years. The coefficient of
correlation between the cycles in the yield of the crops
and the cycles in the general prices lagging four years
behind the crop cycles reached the very high value
r = .800. When the lagging cycles of general prices were
plotted and their graph superposed upon the graph of
the cycles in the yield per acre of the crops, the two
curves were found to present a degree of congruence so
close as to justify our working theory that the fun-
damental, persistent cause of the cycles of prices is the
rhythmical movement in the yield per acre of the crops.
The cycles in the yield per acre of the crops are followed
at an interval of about two years by the cycles in the

Summary and Conclusions 149

activity of industry and of the volume of trade, and at
an interval of about four years in the cycles of prices.
These conclusions brought to a close the last part of
our general problem of the cause and law of Economic
Cycles.

The links in the sequence of causation were com-
pletely estabhshed: The fundamental, persistent cause
of the cycles in the yield of the crops is the cyclical
movement in the weather conditions represented by the
rhythmically changing amount of rainfall; the cycUcal
movement in the yield of the crops is the fundamental,
persistent cause of Economic Cycles.

In the Introduction to this Essay it was observed that
economic dynamics stands in need of a law that shall
be to a changing society what the law of diminishing
returns is to a society in a relatively static state. We
may now formulate the law: The weather conditions
represented by the rainfall in the central part of the
United States, and probably in other continental areas,
pass through cycles of approximately thirty-three years
and eight years in duration, causing like cycles in the
yield per acre of the crops; these cycles of crops con-
stitute the natural, material current which drags upon
its surface the lagging, rhythmically changing values
and prices with which the economist is more immedi-
ately concerned.

T

HE following pages contain advertisements 'of jMac
millan books bv the same author.

LAWS OF WAGES

AN ESSAY IN STATISTICAL ECONOMICS
By Henry Ludwell Moore

Professor of Political Economy in
Columbia University

Cloth, SI. 60, net.

Extract from the Introduction: "In the following chapters
I have endeavored to use the newer statistical methods and
the more recent economic theory to extract, from data re-
lating to wages, either new truth or else truth in such new
form as will admit of its being brought into fruitful relations
with the generahzations of economic science."

CONTENTS

PAGE

Introduction 1

Chapter I

Statistical Laws

A Scatter Diagram 11

Definition of Terms 15

Characteristics of Statistical Laws 21

Chapter II

Wages, Means of Subsiste7ice, and the Standard of Life

Description of Data 26

Wages and the Means of Subsistence 29

Wages and the Standard of Life 33

Wages of Skilled and of Unskilled Laborers 39

Chapter III

Wages and the Productivity of Labor

Description of Data 45

Fluctuations in the Rate of Wages and in the Value of the Product 46

(over)

LAWS OF WAGES by Henry Ludwell Moore— Continued

CO^^TE^iTS— Continued page

Fluctuations in the Laborer's Relative Share of the Product and in

the Ratio of Capital to Labor 55

The General Trend of Wages 61

Ch-'vpter IV

Wages and Ability

An Hypothesis as to the Distribution of AbiUty 74

Grounds for the Hypothesis 76

The Expression of the Gaussian Law in a Form that will facihtate

the Testing of the Differential Theory of Wages 78

The Standard Population 82

The Apphcation of the Theory of the Standard Population 85

Remark upon the Preceding Demonstration 93

Chapter V

Wages and Strikes

Outcome of Strikes as affected by the Strength of Trades-Unions 105

Outcome of Strikes as limited by Economic Law 121

Summary 134

Chapter VI

Wages and the Concentration of Industry

Wages as affected by the Concentration of Industry 140

Amount of Employment 153

Continuity of Employment 156

Length of Working Day 161

Chapter VII

Conclusions

Statistical Economics and Industrial Legislation 169

Practical Aspects of the Results of Preceding Chapters 174

Statistical Economics and Synthetic Economics 196

COMMENTS OF SPECIALISTS

"Professor Moore brings to his task a wide acquaintance with the
most difficult parts of the literature of economics and statistics, a full
appreciation of its large problems, a judicial spirit and a dignified style."
F. W. Taussig, in the Quarterly Journal of Economics.

"Statistics of the ordinary official kind have often served to support
the arguments of poUtical economists. But this is the first time, we
believe, that the higher statistics, which arc founded on the Calculus of

LAWS OF WAGES by Henry Ludwell Moore— Continued

Probabilities, have been used on a large scale as a buttress of economic
theory." F. Y. Edgeworth, in the Economic Journal.

"Professor Moore has broken new ground in a most interesting field,
and while we may differ from him in the weight to be attached to this
or that result or the interpretation to be placed on some observed co-
efficient, we may offer cordial congi-atulations on the work as a whole.
G. U. Yule, in the Journal of the Royal Statistical Society.

"Die Fruchtbarkeit der verwendeten Methode scheint mir dm-ch
diese Untersuchungen zweifeUos erwiesen, ebenso wie die Erreichbarkeit
des Ziels, die Theorie ganz dicht an die Zahlenausdriicke der wu-tschaft-
Hchen Tatsachen heranzubringen. Und das ist eine Tat, zu der der Autor
nur zu begliickwijnschen ist. . . . Hat das Buch auch auf der Hand
liegende Fehler — in der Zukunft wird man sich seiner als der ersten
klaren, einfachen und zielbewussten Darlegung und Exemplifizierung der
Anwendung der ' hoheren Statistik ' auf okonomische Problerae dankbar
erinnern." Joseph Schumpeter, in the Archiv fur Sozialwissenschaft
und Sozialpolitik.

"Non seulement il nous enseigne I'emploi d'une methode qui dans de
certaines Umites pent etre tres feconde. Mais encore son habilet6
personnelle dans le maniement de cette methode est tres r^elle. II sait
scruter les statistiques d'une fa^on fort penetrante et exposer les re-
sultats de ses recherches avec beaucoup d'elegance. Le lecteur frangais
en particulier, appreciera I'ingeniosit^ avec laquelle il tire des statistiques
frangaises des inductions souvent nouvelles et justes." Albert Afta-
LiON, in the Revue d'hisloire des doctrines economiques.

"Alcuni dei risultati ottenuti dall'autore, sono nuovi e suggestivi
e da essi molte conclusioni si possono trarre (cui I'autore accenna nel
capitolo finale della sua opera) sia rispetto alle teorie del salario che
rispetto alia politica sociale. II libro e insomma, ripetiamo, un con-
tribute molto importante all'investigazione scientifica dei fenomeni
economici e vorremmo che esso stimolasse parecchi altri studiosi a fare
per altre Industrie o per altri paesi, recerche analoghe. Constantino
Bresciani Turroni, in the Giomale degli Economisti.

THE MACMILLAN COMPANY

Publishers 64-66 Fifth Avenue New York

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DATE DUE

RECDDECl 5 1984

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MAR 3

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