Are U.S. savings banks viable?

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Are U.S. Savings Banks Viable?

i |yv

of Urbana-Champafgn

C. Edward Chang Morgan J. Lynge,Jr.

Department of Finance Department of Finance

Southwest Missouri State University University of Illinois

Bureau of Economic and Business Research

College of Commerce and Business Administration

University of Illinois at Urbana-Champaign

BEBR

FACULTY WORKING PAPER NO. 92-01 14

College of Commerce and Business Administration

University of Illinois at Urbana-Champaign

March 1992

Are U.S. Savings Banks Viable?

C. Edward Chang

Department of Finance

Southwest Missouri State University

Morgan J. Lynge, Jr.

Department of Finance

University of Illinois

ARE U.S. SAVINGS BANKS VIABLE?

by

C. Edward Chang

Assistant Professor of Finance

Southwest Missouri State University

901 South National Avenue

Springfield, MO 65804

(417) 836-5563

and

Morgan J. Lynge, Jr.

Associate Professor of Finance

University of Illinois at Urbana-Champaign

1206 South Sixth Street

Champaign, IL 61820

(217) 333-7099

Paper for presentation at the Midwest Finance Association
Meetings, Chicago, Illinois, March 26, 1992.

ABSTRACT

Recent developments in the analysis of <nul t iproduc t cost
economies at other depository institutions have not been
incorporated in empirical work on savings banks ( SBs ) . The
purpose of this study is to examine the existence of multiproduct
cost economies, particularly economies of scale and scope in the
production of current services, provided by SBs. The generalized
translog cost function and data on all insured SBs in the period
1986—88 are used. Results indicate that SBs achieve scale
economies at small sizes and again beyond $500 million in total
assets. Measures of scope economies a^re always positive,
indicating that the joint product cost of the set of SB outputs
is less than the sum of the costs of producing the outputs
separately. Results suggest that the institutions that will
survive are those that are large and efficient or those that are
small but serving a particular niche market.

ARE U.S. SAVINGS BANKS VIABLE?

1 . Introduction

One of the many important repercussions of the savings and loan
crisis is that the savings and loan industry is shrinking rapidly in
both market share and the number of associations. Some savings and loan
associations (S&Ls) have been absorbed by commercial banks and other
healthy thrifts, while some S&Ls have converted their charters to become
savings banks (SBs). Thus, a by-product of the shrinkage of the S&L
industry is a growth in the number of SBs.

S&L conversion to a savings bank charter is motivated by several
important reasons. One reason is to escape the connection to an
industry with a negative public image. Another is to avoid the extra
regulatory pressure and costs imposed on a troubled, regulated
industry.

In addition, SBs have been given the flexibility to engage in a
wider spectrum of financial activities than S&Ls. Although the
liabilities of SBs are similar to those of S&Ls, SBs have a more
diversified portfolio of assets. SBs for many years have had broader
authority to invest in securities than S&Ls. As the number of SBs
increases, an issue is whether the cost structure of financial
intermediation by "typical" SBs can make them economically viable.

Recent developments in the analysis of multiproduct cost economies
have not been incorporated in the empirical work on SBs.2 Since the
early 1980s, the cost structure in multiproduct depository institutions,
including commercial banks, savings and loan associations, savings

banks, and credit unions, has been examined by a number of studies
[Murray and White (1983); Gilligan and Smirlock (1984); Gilligan,
Smirlock, and Marshall (1984); Kim (1986); Lawrence and Shay (1986);
Berger, Hanweck, and Humphrey (1987); Kolari and Zardkoohi (1987);
Mester (1987b); Cebenoyan (1988); Lawrence (1989); Cebenoyan (1990);
Hunter, Timme, and Yang (1990); Noulas, Ray, and Miller (1990); LeCompte
and Smith (1990); Buono and Eakin (1990); Berger and Humphrey (1991);
and Gropper (1991)]. Surveys of their results can be found in Mester
(1987a), Clark (1988), Hunter and Timme (1989), and Humphrey (1990).

The purpose of this study is to examine the existence of
multiproduct cost economies, particularly economies of scale and
economies of scope, in the production of current services provided by
SBs. This study is distinguished from other studies in banking by two
features. The first feature is the use of Call Report data to examine
multiproduct cost economies in SBs. One of the advantages of using this
data base is that the population rather than a sample of the
institutions can be analyzed.

The second feature of the study is the use of a state-of-the-art
functional form. The computation of the measures of economies of scope
and product-specific economies of scale require the assumption of a zero
level of output for at least one of the products being produced.
However, the translog cost function used in many other studies always
yields zero total costs whenever the output of even one product is
zero. The generalized translog cost function used here overcomes the
problem of zero output levels for some products. The output variables
are the Box-Cox metric transformations of the actual output levels.

3
The generalized translog functional form has been applied to
multiproduct cost studies in other industries. Some notable examples in
various industries are Fuss (1983) in telecommunications, Sing (1987) in
gas and electric utilities, Kim (1987) in U.S. railroads, and Kellner
and Mathewson (1983) and Fields and Murphy (1989) in life insurance.

The rest of this paper is divided into four sections. Section 2
specifies the model. Section 3 describes the data. Section 4 discusses
the estimation procedure and presents the results. Section 5 presents
the conclusions drawn from the analysis.

2. The Model

This study follows the development of the multiproduct cost
function in the commercial banking industry. In developing statistical
cost functions, researchers begin with the microeconomic principle that
production costs depend on input prices and the level and composition of
outputs. In a competitive environment, SBs are assumed to minimize the
costs associated with a given level of output; i.e.,

Min. C = JT WjX., f1)

3-1

subject to a production constraint F(Y,X) = 0

where C = total costs,

W = the vector of unit prices of m inputs (factors), W. = l,...,m,

X = the vector of m inputs, X., j = l,...,m, and

Y = the vector of n output quantities, Y , i = l,...,n.

4
This functional relationship follows from the property of duality
between the production and cost functions. A standard result of duality
theory is that the properties of the production transformation can be
derived from the reduced form cost function: Min. C(Y,W).

For purposes of this study, we are interested in the following
multiproduct cost concepts:

2.1 Output Cost Elasticities

CEi = ainC(Y,W)/ainYi (2)

2.2 Marginal Costs

MCi =aC(Y,W)/8Yi = (C(Y,W)/Yi)CEi (3)

2.3 Overall Scope Economies

sc _ SjC(Yx,W) - C(Y,W) (4)

C(Y,W)

SC measures the fraction cost savings (dissavings) that are due to joint
production, and will be positive (negative) if overall economies
(diseconomies) of scope exist. With nonjointness in production, SC will
be zero.

2.4 Product-Specific Scope Economies

_ C(YX,W) + C(YN,i;W) - C(Y,W) (5)

1 C(Y.W)

where C(Y-,W) and C(YU ;,W), respectively, represent the cost of
producing product i and all other products independently. This measure
indicates the difference between the cost of joint production of all of
the n outputs and the cost of producing n-1 outputs at their current
level while separately producing the other output at its current level.
Thus, if SC- > (<) 0, SC. measures the relative increase (decrease) in
cost if Y were produced in two groups i and N-i.

2.5 Overall Scale Economies

SL = C(Y,W)/(EiYiMCi) = l/(SiCEi) (6)

Overall scale economies are measured by the inverse of the sum of output
cost elasticities with respect to outputs. If SL > 1, then overall
scale economies exists; if SL = 1, then constant returns to scale exist;
and if SL < 1, then there are diseconomies of scale.

2.6 Product-Specific Scale Economies

IC^Y^) ICi/C(Y,W)
1 YjMC^Y^W) CE~

where IC-(Y,W) = C(Y,W) - C(YU ;,W), and

1 N ■ 1

C(YN.j,W) = C(Y1,...,Yj.1,0,Y. + 1,...,Yn,W)

6
The incremental cost of the i h product, IC(Y,W), is defined as
the difference in cost incurred by the firm to produce the given level
of product i as opposed to producing a zero level, while the quantities
of other products are held constant. If SL- > (<) 1, then scale
economies (diseconomies) exist in the production of output i; and if
SL- = 1, then constant returns to scale exist in the production of
output i.

The major models contain three equations - a cost function and two
share equations. The two share equations are included to increase the
efficiency of the estimations. We employ the generalized translog cost
function to represent the total cost function. The generalized translog
cost function which includes five bank outputs and these input prices
is:

3

ln(C) = A0 + £ M^i - 1)/*1 + E Bi In(Wj)

i-i j-i

+ X/2E E siJ(Y* - ii Ai ttt* - i)/*] (8)

i=l k-1

+ 1/2 E E Gjkln(W3)ln(Wh) ♦ £ V D„ [ (Y*1 - D/lIlnllfj]

j-1 h-l i = l j=l

The dependent variable is logarithmic total cost. The output variables
are transformed by the Box-Cox metric. Using Shephard's lemma, the
input demand share equations are derived by differentiating the above
generalized translog cost function with respect to the input prices:

Ca = 3ln(C)/ain(Wj)

3 5 (9)

= B: + E Gjhln(wh) + E Dij[(Yi" " 1]/X1 J - 1»2

h-l i-l

In addition, the system of equations must satisfy certain regularity
restrictions such as symmetry and homogeneity.

Sik = Ski for all i, k; and Gjh = Gh;j for all j, h. (symmetry)

(10)
and EDij =0' ■"■ =1, 2' 3' 4' 5* (homogeneity)

3 3

E B3 = L' E G3h = 0' J = 1« 2' 3;

j=l h-l

3

i

The multiproduct cost concepts discussed above can be obtained
from the generalized translog cost function as follows. The cost
elasticity of the i output obtained from the generalized translog cost
equation (8) can be expressed as:

CE, = [A, + EjSifcUYjJ - D/X) * BjDy InWjjYi1. f11)

When mean-scaled data are used in the estimation procedure, at the point
of approximation where Y- = W. = 1, the cost elasticity reduces to
CEj = A,-.

The degree of overall scope economies is measured by:

SC = [C(Y1,0,0,0,0,W) + C(0,Y2, 0,0,0, W) + C (0 , 0 , Y3 , 0 , 0 , W)

+ C ( 0 , 0 , 0 , Y4 , 0 , W) + C ( 0 , 0 , 0 , 0 , Y5 , W) ( 12 )

- C ( Y1 , Y2 , Y3 , Y4 , Y5 , W) ] /C ( Y: , Y2 , Y3 , Y4 , Y5 , W)

8
The degree of product-specific scope economies, for example for product
Y1 , is measured by

SC^ = [C(Y1,0,0,0,0,W) + C(0,Y2,Y3,Y4,Y5,W)

(13)

- C(Y1,Y2,Y3,Y4,Y5fW)]/C(Y1,Y2,Y3/Y4/Y5,W) .

Similarly, the degree of product-specific scale economies, for example
for product Y1 , is measured by

SLj. - {[C(Y1/Y2,Y3,Y4/Y5,W) - C (0, Y2, Y3 , Y4, Y5, W) ] /
C(Y1,Y2,Y3,Y4,Y5,W) }/CET.

(14)

Finally, the measure of overall scale economies at the
approximation point reduces to:

SL = 1/(2^) . (15)

3 . Data

All data were obtained from the Call Reports of Condition and
Income for the period 1986-1988. The numbers of available SBs insured
by Federal Deposit Insurance Corporation are 444 in 1986, 456 in 1987,
and 469 in 1988. The final list contains SBs which were in operation in
all three years. After SBs with missing values for variables were
dropped, a total of 417 "typical" SBs remained and were used for
empirical analysis. Table 1 categorizes all sample SBs according to
asset size for the three years. The variables used in the estimating
eguations are described below.

[Insert Table 1 about here]

9

3.1 Total Costs

Total costs, C, include all labor and physical capital expenses,
as well as interest expense; that is, total costs of inputs used to
provide the various outputs of the SBs. Humphrey (1990) found that
believable estimates for scale economies should be based on models using
total costs. We include interest expense in the measure of total costs
because it is significant in size and likely to differ among SBs.
Ignoring interest expense could lead to serious specification error and
inconsistent empirical estimation.

3.2 Output and Input Measures

As suggested by Sealey and Lindley (1977), our analysis employs
the intermediation approach to measuring SB output. Outputs are
measured as the dollar value of all of the SB's earning assets.
Earning assets include (1) interest-bearing balances due from depository
institutions, Y.., (2) securities and assets held in trading accounts,
Y2, (3) Federal funds sold and securities purchased under agreements to
resell, Y,, (4) total loans and leases net of unearned income, Y,, and
(5) direct and indirect investments in real estate ventures, Yc.

Three input categories, including labor, physical capital, and
funds (including deposits), are treated as inputs that are intermediated
to produce SB assets.

3.3 Input Prices

A separate input price is assigned to each input. Due to the
aggregated nature of Call Report data, the three input prices are
approximated in the following manner:

10

(1) price of labor, W. : calculated by dividing total salaries and
fringe benefits by the number of full-time eguivalent employees
(including SB officers);

(2) price of physical capital, W,: calculated by dividing total
expenses of premises and fixed assets by the dollar value of total
assets;

(3) price of funds, W3: calculated by dividing the total interest
expense paid on deposits, Federal funds purchased and securities
sold under agreements to repurchase, demand notes issued to the
U.S. Treasury, mortgage indebtedness, subordinated notes and
debentures, and other borrowed money by the sum of funds from these
sources. In line with traditional banking firm behavior, the cost
of deposits in the form of interest paid to attract them is
considered as the price paid for inputs.

The definitions of the variables are summarized in Table 2.
Summary statistics of the variables are presented in Table 3. Not all
SBs in our sample produce in all product lines. In fact, zero levels
are always present for some SBs in Y1 , Y,, and Ye. For the purpose of
examining economies of scope and product-specific economies of scale,
inclusion of such SBs is important. This allows extrapolation of the
multiproduct cost function to regions of zero outputs. Since Yp and Y^
do not have zero levels in our sample, we use the minimum to replace the
zeros in eguations (12) to (14) to avoid any overextrapolation.

[Insert Tables 2 and 3 about here]

11

4. Empirical Results

4 . 1 Estimation Procedure

Cost equations for SBs are estimated separately by year. All
variables entering the equations are standardized by dividing by their
respective sample means to eliminate the upward bias in t-statistics
associated with unsealed variables, as suggested by Spitzer (1984).6

While the estimates are unbiased and consistent, estimating only
the cost equation is relatively inefficient because of unused
information. We augment the total cost equation with two derived input
demand share equations using Shephard's lemma. Since these two
equations do not involve any new coefficients, greater efficiency in
estimation can be achieved by including such share equations along with
the cost equations. Only two share equations are estimated since any
attempt to estimate the complete system will lead to singularity in the
variance-covariance matrix because the shares sum to one for each
observation, as implied by the linear homogeneity in input prices. The
share equation corresponding to the third input is omitted. Barten
(1969) has shown that the parameter estimates are invariant to which
share equation is omitted.

The three equations (8) and (9) - one cost function and two share
equations - comprise the major models to be estimated. We estimate the
system of equations using Zellner's seemingly unrelated regressions
(SUR) procedure. This technique uses estimates of the covariance of the
residuals across equations to improve the efficiency of the estimates.

The system of equations to be estimated is linear conditioned
on X. The method used to determine the value of X is an iterative

12
least-square search. Specifically, we proceed by specifying a set of
values for X (in increments of 0.001), estimating the remainder of the
parameters conditional on X, and selecting those parameter estimates
that correspond to the X which maximizes the log of the likelihood
function for the system, therefore minimizing the residual sum of
squares.

The coefficients for the generalized translog cost function are
used to calculate the cost measures. Each of the cost measures is
computed by multiplying the estimated coefficients by the vector of
means of the variables. Since the function computes total costs in
logarithms, we take the exponential of each of the above components and
calculate the cost measure if they are involved with total costs.

All cost measures are estimated at mean output levels. Because we
deal with the population rather than a sample of the SBs in question,
standard deviations are not calculated. Since the effects on costs of
changes in the variables included in the cost function may differ
depending on the levels of the variables, the measures of overall scale
economies are evaluated at eight different points for both types of SBs:
(1) the point consisting of the means of the input prices and outputs,
which corresponds to the "typical" (or average) SB; and (2) the points
consisting of the means of the input prices, and the seven mean values
of the output variables which corresponds to the seven size categories
in Table 1.

4.2 Results

The parameter estimates and their t-statistics for the generalized
translog multiproduct cost functions are presented in Table 4. The

13
coefficients of output and input price variables carry their expected
positive signs and are, except for Yr in 1986, statistically significant
at the 0.01 level of significance.

[Insert Table 4 about here]

Goodness-of-f it measurements for the cost eguation and the two
estimated share eguations are given in Table 5. Measures show
F probabilities of 0.0001 for the cost and share eguations with adjusted
R-square of at least 0.9974, 0.5133, and 0.8905 for the cost, labor
share, and capital share eguations, respectively. This indicates that
the explanatory variables and the functional form specified do capture
the variations in the total costs and also have high explanatory
power .

[Insert Table 5 about here]

For convenience of discussion, as outlined in Table 2, we will
still use Y1 to represent interest-bearing balances due from depository
institutions, Y-, to represent securities and assets held in trading
accounts, Y, to represent Federal funds sold and securities purchased
under agreements to resell, Y4 to represent total loans and leases net
of unearned income, and Y5 to represent direct and indirect investments
in real estate ventures.

Table 6 gives the values at the means of output cost elasticity,
marginal cost, incremental cost, as well as degrees of product-specific
scale economies and product-specific scope economies for each output,
Y- ( i = 1, 2 , 3 , 4, 5 ) . We would expect positive marginal costs
associated with the production of banking services. As expected, the
marginal costs of producing outputs are all positive.

14
[Insert Table 6 about here]

Product-Specific Scale Economies

Since there may be scale economies associated with production of a
particular product, product-specific scale economies are investigated.
For SBs, the degrees of product-specific scale economies with respect to
Yp and Y, are less than one, while those for Y, and Y5 are greater than
one. The results of this measure for Y1 are mixed. From the standpoint
of cost alone, the typical SB would gain by increasing the levels of Y4
and Y5 while reducing the levels of Y2 and Y, on an individual basis.
The results also indicate that direct and indirect investments in real
estate ventures enjoy product-specific scale economies (though
declining) over the three-year period.

Product-Specific Scope Economies

Table 6 gives the estimates of product-specific scope economies,
SCj (i = 1, 2, 3, 4, 5) at the means. For SBs, the degrees of product-
specific scope economies with respect to Y2, Y,, and Y4 are positive,
while those for Yc are negative. The results of this measure for Y1 are
mixed. When they are positive (negative), the typical SB would gain by
producing that particular product and the other four products jointly
(separately). Interestingly, the joint production of direct and
indirect investments in real estate ventures and the other four products
always exhibit slight scope diseconomies.

15
Overall Scale Economies

Table 7 documents the estimates of overall scale economies at
means and additional seven mean points. The results at mean output
levels indicate that SBs exhibit constant returns to scale. Slow but
sure improvement in overall scale economies are found over the three-
year period.

[Insert Table 7 about here]

There is evidence that scale economies first decrease as SBs grow
larger and then increase as SBs grow even larger. In other words, the
pattern of estimates of scale economies is that in general the small and
large SBs exhibit overall scale economies while the SBs in between
exhibit slight overall scale economies or constant returns to scale.
More cost savings usually occur beyond $500 million in asset size.

Overall Scope Economies

Table 8 documents the estimates of overall scope economies at the
means. The measures of overall scope economies are always positive.
Thus, the results at mean output levels indicate that SBs exhibit
overall scope economies. That is, the joint product cost of the
existing five outputs is less than the sum of the costs of producing the
five outputs separately by five SBs.

[Insert Table 8 about here]

Table 8 also gives the estimates of overall scope economies at the
additional seven mean points. The results show that scope measures
first decrease as SBs grow larger and then increase as SBs grow even
larger. That is, the larger and smaller SBs enjoy more cost savings
from joint production than the SBs in between.

16

5 . Conclusions

The use of an expanded data base which contains all SBs in
question should provide the best possible information about multiproduct
cost economies of SBs. The generalized translog cost function used here
overcomes the problem of zero output levels for some products and,
therefore, enables us to examine the existence of overall economies of
scope as well as product-specific economies of scale and scope in SBs'
production of banking services.

Our results for product-specific scale economies indicate that the
typical SB would gain by increasing the levels of Y^ and Y5 while
reducing the levels of Y2 and Y-, on an individual basis. The results
for product-specific scope economies indicate that the typical SB would
gain by producing Y,, Y,, and Y^ (Yc) and the other four products jointly
( separately) .

Constant returns to scale were evidenced for typical SBs in recent
years. In general, larger and smaller SBs exhibit overall scale
economies while those of intermediate size exhibit slight overall scale
diseconomies or constant returns to scale. The results of overall scope
economies indicate that typical SBs exhibit overall scope economies -
that is, they incurred lower costs by engaging in multiproduct
production. SBs of all asset sizes exhibit overall scope economies
while larger and smaller SBs seem to enjoy even more cost savings from
joint production than the intermediate-sized SBs.

These results conform to the conventional view of depository
institution viability. That is, the institutions that will survive are
those that are large and cost-efficient or small but serving a

17
particular niche market. New laws allowing interstate mergers and
acquisitions may result in just such an industry structure for savings
banks.

H-ML.4-24

18

Footnotes

'New regulations under federal law have placed significant
restrictions on S&Ls. For example, S&Ls must have 70 percent of their
assets in home mortgages, this against a background of declining real
estate values. State-chartered SBs in many states have to meet only a
60 percent requirement for home mortgage lending.

2Of the very few studies on SBs, Benston (1972), Eisenbeis and
Kwast (1991), Rosen et al. (1989), and Stansell and Hollas (1990) use
approaches other than multiproduct cost function. Kolari and Zardkoohi
(1990) use a translog cost function approach to examine economies of
scale and scope in thrift institutions, but they study Finnish
cooperative and savings banks.

3To see why this is so, let the cost function be represented by:
In C = b In Y + X where X represents the remaining terms in cost
equation, then C = Y exp(x), which equals zero when Y is zero.

This function form was first used by Caves, Christensen, and
Tretheway (1980). As its name suggests, this function is a
generalization of the translog because the expression for output
approaches the natural logarithm of output as X approaches zero; i.e.,

(Yi-1)

lim -. = lnY,.

Jl-0 k

The authors are aware of the controversy regarding appropriate
measures of bank output, that is, the choice between the production
approach and the intermediation approach as discussed in Mester (1987a)
and Clark (1988). We believe that Sealey and Lindley make a compelling
case for using earning assets as outputs. Moreover, even if we wanted
to use the production approach, the limitations of Call Report data
preclude the best use of this approach for being lack of number of
accounts. Since there is no ideal way to disaggregate bank earning
assets into distinct categories, we simply go by the characterization of
the Call Reports.

6Spitzer (1984) suggested that the transformed variables be scaled
by their sample means before estimation. Failure to scale the
transformed variables can result in biased hypothesis testing. The
scale of this bias is likely to be substantial. The use of mean-scaled
variables in the estimation will reduce such bias.

The system estimates are preferred to the single-equation ordinary
least squares (OLS) estimates because of their greater efficiency, as
evidenced by the decreases in the magnitudes of standard errors. The
results of the OLS estimation are available upon request.

19

Q

Our estimated cost functions satisfy all the regularity conditions
when evaluated at the means of the relevant samples. Since the model
has imposed symmetry and homogeneity, the regularity conditions are
satisfied if the cost function is monotonically increasing and concave
in input prices.

20

References

Barten, A. , "Maximum Likelihood Estimation of a Complete System of

Demand Equations," European Economic Review 1 (Fall 1969), 7-73.

Benston, G. , "Savings Banking and the Public Interest," Journal of
Money, Credit and Banking 4 (1972), 133-226.

Berger, A., G. Hanweck, and D. Humphrey, "Competitive Viability in

Banking: Scale, Scope, and Product Mix Economies," Journal of
Monetary Economics 20 (December 1987), 501-520.

Berger, A., and D. Humphrey, "The Dominance of Inefficiencies over Scale
and Product Mix Economies in Banking," Journal of Monetary
Economics 28 (1991), 117-148.

Board of Governors of the Federal Reserve System, Reports of Condition

and Income, Washington, D.C., December 1986 through December 1988.

Buono, M. , and B. Eakin, "Branching Restrictions and Banking Costs,"
Journal of Banking and Finance 14 (December 1990), 1151-1162.

Caves, D., L. Christensen, and M. Tretheway, "Flexible Cost Functions
for Multiproduct Firms," Review of Economics and Statistics 62
(August 1980), 477-481.

Cebenoyan, A. , "Multiproduct Cost Functions and Scale Economies in
Banking," Financial Review 23 (November 1988), 499-512.

Cebenoyan, A. , "Scope Economies in Banking: The Hybrid Box-Cox
Function," Financial Review 25 (February 1990), 115-125.

Clark, J. , "Economies of Scale and Scope At Depository Financial

Institutions: A Review of the Literature," Federal Reserve Bank
of Kansas City Economic Review (September/October 1988), 16-33.

Eisenbeis, R. , and M. Kwast, "Are Real Estate Specializing Depositories
Viable? Evidence from Commercial Banks," Journal of Financial
Services Research 5 (1991), 5-24.

Fields, J., and N. Murphy, "An Analysis of Efficiency in the Delivery of
Financial Services: The Case of Life Insurance Agencies," Journal
of Financial Services Research 2 (October 1989), 343-356.

21

Fuss, M. , "A Survey of Recent Results in the Analysis of Production
Conditions in Telecommunications," in L. Courville,
A. de Fontenay, and R. Dobell (eds.)> Economic Analysis of
Telecommunications: Theory and Applications (New York: Elsevier
Science Publishers, 1983).

Gilligan, T. , and M. Smirlock, "An Empirical Study of Joint Production

and Scale Economies in Commercial Banking," Journal of Banking and
Finance 8 (1984), 67-77.

Gilligan, T. , M. Smirlock, and W. Marshall, "Scale and Scope Economies
in the Multi-Product Banking Firm, " Journal of Monetary Economics
13 (May 1984) , 393-405.

Gropper, D., "Empirical Investigation of Changes in Scale Economies for
the Commercial Banking Firm, 1979-1986," Journal of Money, Credit
and Banking (November 1991), 718-727.

Humphrey, D., "Cost Dispersion and the Measurement of Economies in
Banking, " Federal Reserve Bank of Richmond Economic Review
(May/June 1987), 24-38.

Humphrey, D., "Why Do Estimates of Bank Scale Economies Differ?,"
Federal Reserve Bank of Richmond Economic Review
(September /October 1990), 38-50.

Hunter, W. , and S. Timme, "Does Multiproduct Production in Large Banks
Reduce Costs?," Federal Reserve Bank of Atlanta Economic Review
(May/June 1989), 2-11.

Hunter, W. , S. Timme, and W. Yang, "An Examination of Cost Subadditivity
and Multiproduct Production in Large U.S. Banks," Journal of
Money, Credit and Banking 22 (November 1990), 504-525.

Kellner, S., and G. Mathewson, "Entry, Size Distribution, Scale, and
Scope Economies in the Life Insurance Industry," Journal of
Business 56 (January 1983), 25-44.

Kim, H. , "Economies of Scale and Economies of Scope in Multiproduct
Financial Institutions: Further Evidence from Credit Unions,"
Journal of Money, Credit and Banking 18 (May 1986), 220-226.

Kim, H. , "Economies of Scale and Scope in Multiproduct Firms: Evidence
from U.S. Railroads," Applied Economics 19 (1987), 733-741.

Kolari, J., and A. Zardkoohi, Bank Costs, Structure, and Performance
(Lexington, Mass.: D.C. Heath and Company, 1987).

Kolari, J., and A. Zardkoohi, "Economies of Scale and Scope in Thrift

Institutions: The Case of Finnish Cooperative and Savings Banks,"
Scandinavian Journal of Economics 92 (1990), 437-451.

22

Lawrence, C. , "Banking Costs, Generalized Functional Forms, and

Estimation of Economies of Scale and Scope," Journal of Money,
Credit and Banking 21 (1989), 368-379.

Lawrence, C. , and R. Shay, "Technology and Financial Intermediation in a
Multiproduct Banking Firm: An Econometric Study of U.S. Banks,
1979-1982," in C. Lawrence, and R. Shay (eds.), Technological
Innovation, Regulation and the Monetary Economy (Cambridge, Mass.:
Ballinger Publishing Company, 1986) .

LeCompte, R. , and S. Smith, "Changes in the Cost of Intermediation: The
Case of Savings and Loans," Journal of Finance 45 (September
1990), 1337-1346.

Mester, L. , "Efficient Production of Financial Services: Scale and

Scope Economies," Federal Reserve Bank of Philadelphia Business
Review (January /February 1987), 15-25 (a).

Mester, L. , "A Multiproduct Cost Study of Savings and Loans," Journal of
Finance 42 (June 1987), 423-445 (b).

Murray, J., and R. White, "Economies of Scale and Economies of Scope in
Multiproduct Financial Institutions: A Study of British Columbia
Credit Unions," Journal of Finance 38 (June 1983), 887-902.

Noulas, A., S. Ray, and S. Miller, "Returns to Scale and Input

Substitution for Large U.S. Banks," Journal of Money, Credit and
Banking 22 (February 1990), 94-108.

Rosen, R. , P. Lloyd-Davies , M. Kwast, and D. Humphrey, "New Banking

Powers: A Portfolio Analysis of Bank Investment in Real Estate,"
Journal of Banking and Finance 13 (July 1989), 355-366.

Sealey, C, and J. Lindley, "Inputs, Outputs, and a Theory of Production
and Cost at Depository Financial Institutions," Journal of Finance
32 (September 1977), 1251-1266.

Sing, M. , "Are Combinations Gas and Electric Utilities Multiproduct
Natural Monopolies?," Review of Economics and Statistics 69
(August 1987), 392-398.

Spitzer, J. , "Variance Estimates in Models with the Box-Cox

Transformation: Implications for Estimation and Hypothesis
Testing," Review of Economics and Statistics 66 (November 1984),
645-652.

Stansell, S., and D. Hollas, "An Examination of the Relative Economic
Efficiency of Mutual vs. Stock Savings Institutions," Journal of
Real Estate Finance and Economics 3 (1990), 73-89.

23

Table 1
Size Distribution of U.S. Savings Bank

1986

1987

1988

Asset size

Number

% of

Number

% of

Number

% of

(millions )

of

Total

of

Total

of

Total

Banks

Number

Banks

Number

Banks

Number

Less than $25

27

6.5

21

5.0

17

4.1

$25-49

41

9.8

40

9.6

40

9.6

$50-99

80

19.2

78

18.7

69

16.5

$100-299

152

36.5

151

36.2

156

37.4

$300-499

46

11.0

49

11.8

44

10.6

$500-999

37

8.9

41

9.8

48

11.5

$1,000 or more

34

8.2

37

8.9

43

10.3

Total

417

100.0

417

100.0

417

100.0

Table 2

Definitions of the Variables

Variable

C:
Y,:

W0:

Definition

Total costs

interest-bearing balances due from depository institutions

securities and assets held in trading accounts

Federal funds sold and securities purchased under
agreements to resell

total loans and leases net of unearned income

direct and indirect investments in real estate ventures

input price of labor

input price of physical capital

input price of funds

24

1986

c

Y1

Y2

Y3

Y4

Y5

W1

W2

w7

1987

c

Y1

Y2

Y3

Y4

Y5

W1

W2

w,

1988

c

Y1

Y2

Y3

Y4

Y5

W1

w2

w7

Table 3
Data Summary for U.S. Savings Banks

Variable Mean Standard Minimum Maximum

deviation

30186

85297

7873

30933

110265

432731

9828

22327

257748

574256

1709

9532

24.606

5.347

0.003

0.001

0.066

0.006

31161

90555

6963

33136

113641

484137

7434

18970

296365

621799

2379

11523

26.977

6.231

0.003

0.001

0.061

0.005

35122

92628

9039

57613

104033

409758

7089

17803

336077

674402

2698

13266

28.069

5.791

0.003

0.001

0.065

0.005

193 1396085

0 533189

6 7670028

0 220792

2614 7669261

0 129082

11.529 48.818

0.000 0.010

0.013 0.083

195 1505538

0 407974

25 8624492

0 205800

2787 7557750

0 148270

11.921 61.457

0.000 0.010

0.037 0.077

209 1450659

0 842642

25 7375876

0 179700

2974 6988041

0 159234

3.416 61.455

0.000 0.011

0.031 0.083

Table 4

Parameter Estimates (SUR) for U.S. Savings Banks

25

Variable

1986
Estimate

1987
Estimate

1988
Estimate

0.089

0.097

0.095

INTERCEP

W1

W2

W3
Y,*Y

*Y-

*YC

VY2

Y2*Y3

Y *Y

Y *Y
*2 X5

Y3*Y3

Y3*Y4

Y * Y
*3 X5

VY4

Y * Y
*4 Y5

Y5*Y5

0
(0

0
(5.

0,
(26,

0
(11,

0,

(51,

0,

(1.

0,

(42,

0,

(61,

0,

(261,

0.

(5.

-0.

("2.

-0.

(-2.

0.

(1.
-0,

(-1.

0.

(27.

-0,

(-5.

-0.

(-22.

-0.

(-1-
0.

(12.
0.

(1.

0.

(1.

0.

(6.

0.

(1.

0.

(0.

003
285)

018***

547)

256***

576)

044***

650)

684***

870)

005

169)

132***

820)

042***

159)

826***

906)

003***

688)

002***

991)

000**

013)

001

320)

000

515)

141 * * *

437)

006***

544)

148***

823)

002*

840)

008***

363)

002

334)

000*

653)

070***

762)

002*

784)

001

836)

0

(0

0

(5

0

(37

0

(9

0

(68

0

(3

0

(50

0

(81

0

(294

0

(4

-0

(-0

0

(2

-0

("1

0

(0

0

(28

-0

("2

-0

(-26

-0

("1

0

(10

-0

(-0

-0

(-2

0

(8

0

(1
0

(2

.006

.781)

.016***

.765)

.267***

.084)

. 029***

.158)

. 680***

.756)

.012***

.311)

. 142***

.783)

. 046***

.607)

. 812***

.438)

. 003***

.994)

.001

.853)

.000**

.127)

.002

.547)

.000

.036)

. 154***

.681)

.002**

.059)

. 168***

.341)

.001

.335)

. 006***

.347)

.001

.892)

.000**

.113)

. 084***

.641)

.002

.588)

.002***

.848)

0.

(0.

0.

(7.

0.

(31.

0.

(9.

0.

(73.

0.

(3.

0.

(54.

0.

(80.

0.

(326.

0.

(6.

-0.

(-0.

0.

(0.

-0.

(-2.

0.

(0.

0.

(26.

-0.

(-2.

-0.

(-24.

-0.

("2.

0.

(9.

-0.

(-1-

-0.

(-0.

0.

(8.

0.

(1-

0.

(3.

007

909)

019***

138)

222***

442)

026***

434)

719***

699)

013***

796)

138***

118)

045***

312)

817***

722)

003***

791)

000

272)

000

527)

002**

038)

000

364)

140***

049)

002**

126)

156***

175)

002***

593)

005***

779)

001

190)

000

074)

081***

387)

001

313)

002***

328)

Table 3 (continued)

26

Variable

1986
Estimate

1987
Estimate

1988
Estimate

w1*w1

w.,*w2

w1*w3

w2*w2

w2*w3

w3*w3

y1*w1

Y1*W2

Y1*W3

Y2*W1

Y2*W2

Y2*W3

Y3*W1

Y3*W2

Y3*W3

Y4*W1

Y4*W2

Y4*W3

Y5*W1

VW2

Y5*W3

0.061***

0. 067***

0 . 047***

(10.433)

(11.813)

(9.593)

0.008***

0. 003***

0 . 003***

(6.684)

(3.057)

(3.107)

-0. 069***

-0. 070***

-0.051***

(-11.495)

(-12.294)

(-10.240)

0. 034***

0.037***

0.037***

(59.342)

(68.379)

(65.001)

-0.042***

-0.040***

-0. 040***

(-32.977)

(-32.787)

(-33.369)

0. Ill***

0. 110***

0.091***

(17.485)

(18.418)

(17.422)

0.000

-0.000

-0.000

(1.539)

(-0.336)

(-0.853)

-0.000

-0.000

-0.000

(-0.535)

(-1.364)

(-0.675)

-0.000

0.000

0.000

(-1.393)

(0.620)

(1.020)

-0 . 014***

-0.011***

-0. 010***

(-8.575)

(-7.320)

(-6.617)

-0.000

0.000

0.000

(-0.605)

(0.476)

(0.234)

0. 014***

0.011***

0.010***

(8.528)

(7.313)

(6.678)

-0.001

-0.002***

-0.001*

(-1.415)

(-4.009)

(-1.821)

-0.000

-0.000

-0.000

(-0.346)

(-0.714)

(-0.833)

0.001

0 . 002***

0.001**

(1.462)

(4.207)

(2.041)

0.004*

0.002

-0.002

(1.817)

(0.770)

(-1.291)

-0.000

-0.001*

-0.000

(-0.829)

(-1.715)

(-0.824)

-0.003

-0.001

0.003

(-1.601)

(-0.425)

(1.500)

0.001***

0.001***

0.001***

(3.176)

(3.339)

(4.427)

-0.000

-0.000

-0.000

(-1.337)

(-0.351)

(-1.249)

-0.001***

-0.001***

-0.001***

(-2.816)

(-3.300)

(-4.216)

T statistics in parentheses.

***Signif icant at 0.01 level for a two-tailed test

**Signif icant at 0.05 level for a two-tailed test

*Signif icant at 0.10 level for a two-tailed test

27

Table 5

Goodness-of-Fit Measurements

SSE

DF

MSE

R2

1986

Cost Equation

1,

.63494816

381

0.00429120

0.

.9974

Labor Share

0.

,30073207

408

0.00073709

0,

.5154

Capital Share

0.

.01440929

408

0.00003532

0.

.8905

1987

Cost Equation
Labor Share
Capital Share

1.37969548

381

0.00362125

0.9977

0.28207297

408

0.00069136

0.5133

0.01150806

408

0.00002821

0.9090

1988

Cost Equation
Labor Share
Capital Share

1.25989230

381

0.00330680

0.9980

0.24000568

408

0.00058825

0.5379

0.01160510

408

0.00002844

0.9006

SSE: Sum of Squared Errors.

DF: Deqrees of Freedom.

MSE: Mean Square Error (MSE = SSE/DF)

R2: Adjusted R-squared.

28

1986
CE,.

ici
sci

1987

CE.

MCi

ici

1988

CEi
MC1-
ICj
SL,.
SC;

Table 6
Product-Specific Cost Measures at Mean Points

Y1 Y2 Y3 Y4 Y5

0.018

0.256

0.044

0.684

0.005

0.018

0.257

0.044

0.686

0.005

0.004

-2.871

-0.007

0.877

0.014

0.220

-11.166

-0.155

1.279

2.991

0.005

3.009

0.017

0.900

-0.006

0.016

0.267

0.029

0.680

0.012

0.016

0.268

0.029

0.684

0.012

0.029

-1.786

-0.017

0.864

0.018

1.834

-6.658

-0.587

1.264

1.499

0.021

1.906

0.026

1.291

-0.009

0.019

0.222

0.026

0.719

0.013

0.019

0.223

0.027

0.724

0.013

0.023

-1.865

0.004

0.890

0.018

1.195

-8.357

0.145

1.229

1.306

0.014

1.956

0.005

1.288

-0.009

29

Table 7

Estimates of Overall Scale Economies at Eight Mean Points

Asset Size 1986 1987 1988
(millions )

"Typical" bank 0.993 0.997 1.001

Less than $25 1.070 1.081 1.093

$25-49 1.047 1.047 1.057

$50-99 1.020 1.022 1.033

$100-299 1.001 1.004 1.012

$300-499 0.993 0.999 1.001

$500-999 0.994 1.003 1.002

$1,000 or more 1.010 1.032 1.023

Table 8

Estimates of Overall Scope Economies at Eight Mean Points

Asset Size 1986 1987 1988

(millions)

"Typical" bank 0.948 1.306 1.302

Less than $25 0.706 0.856 0.942

$25-49 0.311 0.443 0.445

$50-99 0.206 0.319 0.349

$100-299 0.396 0.568 0.528

$300-499 1.096 1.471 1.247

$500-999 1.817 2.475 2.146

$1,000 or more 6.967 9.493 8.065

HECKMAN

BINDERY INC.

JUN95

IBound-To-PleBi N. MANCHESTER
INDIANA 46962