Single-equation, multiple-regression methodology: Is it an appropriate methodology for the estimation of the structure-performance relationship in banking?

Journal of Monetary E.conomics 18 (1986) 295-312. North-Holland

SINGLE-EQUATION, MULTIPLEREGRESSION METHODOLOGY Is It an Appropriate Methodology for the Estimation of the Structure-Performance Relationship in Banking?

Jeffrey A. CLARK* Florida

State

University,

Tallahassee,

FL 32306-l

042, USA

Tests of the structure-performance paradigm of the industrial organization literature have been carried out almost exclusively using a single-equation, multiple-regression methodology. The purpose of this paper is to suggest that where the firms being considered are multiple product in nature and may pursue objectives in addition to m axinking the value of the firm, such a methodology may be inappropriate. The results presented in this paper suggest that the absence of a consistently strong, positive, and statistically significant relationship between market concentration and bank profitability may be traced in part to such an inappropriate methodology.

1. Introduction

Beginning in 1961 with a paper by Schweiger and McGee (1961), the applicability of the structure-performance model (hereafter SPM) to the commercial banking industry has received extensive testing. While the weight of the accumulated evidence would seem to support the existence of a ‘systematic interrelationship between market concentration and commercial bank profitability, where the relationship has been statistically significant, it has most often been quantitatively small [see Rhoades (1977), Gilbert (1984) and Heggestad (1979)]. The results of this paper suggest that the failure to identify a more consistently strong, positive, and statistically significant direct relationship between market concentration and commercial bank profitability may be due in part to problems with the methodology employed.

2. Problems encountered in using a single-equation methodology

Most tests of the existence of a direct relationship between market concentration and commercial bank profitability employ a single-equation, multiple*I would like to thank Robert G. King and an anonymous referee for their helpful comments on an earlier version of this paper. Any remaining errors are my own. 0304-3923/86/$3.5001986,

Elsevier Science Publishers B.V. (North-Holland)

296

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nrethodolos)*

regression methodology. The selection of this methodology for testing the SPM is problematic for several reasons. The problems can be illustrated with reference to the following linear multiple-regression model, the results of which were recently reported in the literature:’ AVGROA = a0 + a,SIZE + a,TTSDTD +a,AVGPI

+ a3G,

+ a&R + aJDROA

+ e,

(1)

where A VGROA SIZE TTSDTD G A b%PI CR SDROA

= rate of return on total bank assets, = average total deposits of the bank, = average ratio of time and savings deposits to total deposits, =ratio of t, retail sales in the market to t, retail sales, = average per capita income in the bank’s market, = three-bank concentration ratio for total bank deposits, and = standard deviation of A VGROA.

Using a single-equation model such as the one presented in eq. (1) a test of the existence of a statistically significant relationship between market concentration and commercial bank profitability is generally carried out by inspection of the estimated coefficient a5 = aAVGROA/aCR, and its standard error or r-statistic. The application of OLS to such a model must necessarily imply one of three possibilities. First, (regime 1) the economic structure underlying the determination of a bank’s profit rate can be adequately described through the use of a single structural equation. In this instance the direct effect of market structure on bank profitability can be assessed by applying OLS in the estimation of the structural parameters of the equation. The resulting estimates of these structural parameters will be unbiased and consistent. A second possibility (regime 2) is that the structural equation is part of a simultaneous-equations system. The application of OLS to a structural equation in a system of simultaneous equations will result in biased and inconsistent estimates of the parameters of the structural equation.2 Thus if eq. (1) is part of a simultaneous system of structural equations which describe the underlying economic structure, application of OLS to the equation may result in a biased and inconsistent estimate of the desired structural parameter, a5. A third possibility (regime 3) is that the model depicted in eq. (1) is a reduced-form model derived from an underlying simultaneous system of ‘This statistical model is drawn from a recent paper by Heggestad (1977, p. 1210) but is typical of the nature of most models which have been estimated. ‘See Judge et al. (1985, ch. 14) for a detailed discussion.

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structural equations. If so, the coefficients being estimated are reduced-form coefficients rather than the desired structural parameters. While the reducedform parameters can be consistently estimated using OLS, they are most useful for prediction and inappropriate for use in hypothesis tests of underlying structural parameters. 3. Underlying economic structure The conventional approach to testing the SPM in banking, as typified by the OLS estimation of eq. (1) must fall into one of the three regimes discussed above. As a basis for determining which of these three regimes would be most descriptive of the results obtained in employing the conventional methodology, it is necessary to describe the economic structure underlying the determination of the bank’s profit rate. While numerous models of the banking firm have been developed to deal with specific aspects of bank behavior [see Baltensperger (1980) and Santomero (1984)], no single model is acceptable as descriptive of all bank behavior. However, many of the important elements of the economic structure underlying bank behavior have been illustrated using a portfolio theory approach. Santomero (1984, pp. 588-590) has recently provided a concise description of the standard set-up employed and solution derived for this class of models. We adhere closely to his exposition. The bank manager (owner) is assumed to possess an exponential utility function which is concave in uncertain end of period profit. Then, maximizing expected utility is equivalent to maximizing the certainty equivalent of profit CT(n)

= E(a) - (b/2)&

(2)

subject to a balance sheet constraint, where E( ) is the expectations operator and b is a measure of the bank’s absolute risk aversion. Profit, variance, and the balance sheet constraint may be defined as follows: Tr= f

(ri-Ci)Ai-

i-l

c$=E[(n-E(r))*]

i

(r,+c,)D,,

k-l

and

fAi= i=l

i

D,,

(3)

k=l

where Ai and D, represent the feasible set of assets and liabilities with well defined sets of characteristics, and ri, rk, cir and ck represent the interest rates set by the bank and the per unit costs incurred in producing each of the i assets and k liabilities. The solution to this problem restricts the opportunity set of possible balance sheet compositions available to the bank to the efficient frontier where an

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increase in profit can only be obtained by accepting additional variance. The optimal balance sheet composition occurs at that point along the efficient frontier where the marginal rate of substitution between risk and return is equated with the market’s opportunity set. In particular, assuming uncertainty in asset demand and deposit supply given the selection of the r, and rk interest rates [Edwards and Heggestad (1973), Heggestad (1977)], the important determinants of this solution can be illustrated by considering the bank’s optimality condition derived from maximizi ng (2) subject to (3) with respect to the choice of ri and rkr Vi, k: ri[l

+

(l/e,i)]

[b/(aAi/ari)l

-ci-

x (ri-ci)uji+ j-l

I

X

k-l

i#j

trk+ck)Oik+

i

(r,+CI)uDkl+

i

(4 1

(ri-ci)u,diDk

9

i-l

El

where e represents the relevant demand and supply elasticities and u2 and u represent the variances and covariances identified by the attached subscripts.3 3Given the assumption of quantity uncertainty, u: can be written as d=m

2

(q-ci)2u:i+

i k-l

i-l

r~+cJ&+2f

(

i-l

f j-l

(ri-c,)(r,-cj)uA,j

i*j

+k~~,~~(rk+ck)(r,cc,)u~k,+2C

i-l -

C k-l

(ri-Ci)(rk+Ck)ahDk.

k’;l

After forming the LaGrangian function Q, and ditlerentiating with respect to the interest rates ‘; and rk, the following first-order conditions can be obtained under the simplifying assumption that all variances and covariances are insensitive to changes in interest rates (i.e., ao,2,/ari = a&.ark

= auAij/al;. = auDk,/ark =

hAiok/ari

= aoAiDk/ark

= o),

2(rj-ci)u:i+2~(r,-cj)uAij

a@//al;=(r,-ci)(aAi/ari)+Ai-(b/2)

itj

+2C(rk+ck)uAiom

-X(aA,/al;.)=O,

k

ao/ar,-

-

I

2(rk+ck)uik+2c

(rk+Ck)(aDk/ark)+Dk-(b/2)

(r,+cl)uDk/ k+l

+2C(ri-ci)uAiDk

I

1

+h(aDk/ark)=o.

J.A.

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Thus the determinants of the optimal structure the specifications of the returns and costs to all nature of the bank’s risk-return preferences. 4 It composition of the bank’s assets and liabilities, and profit are determined simultaneously.

nlethodologv

299

of the balance sheet include assets and liabilities, and the is therefore apparent that the together with its overall risk

3.1. Specification of a structural model

Since the preceding discussion of the underlying economic structure which determines the profit of the banking firm indicates that profit is determined simultaneously with overall bank risk and the composition of the bank’s balance sheet, the appropriate structural model must provide for this simultaneity. Further, the structural model must include variables which capture the influence of the efficient frontier along which the bank operates, the risk-return preferences of the bank management (ownership), as well as any elements of the market, regulatory and organizational structures which may have an impact upon the return and cost attributes of the assets and liabilities selected by the bank. Though not strictly derived from the preceding theory, the following structural econometric model may be specified. Given the highly aggregated nature of most available banking data, this model allows for simultaneity between the bank’s profit, risk, and the structure of the balance sheet while controlling for the effects that important elements of the market, regulatory and organizational structures may have on these variables.5 Consequently, the results obtained from estimating this model should be indicative of those that would be obtained if the theoretical model could be estimated, AVGROE=a0+a,SDROE+a,ALAR+a,ATSTL+a4AVGPI +a,AVGHI+a,AVGMS+a,DUMHC+a,MFRS +a,BRNCH +a,,SIZE,

+ a,,SIZE, + a,,SIZE6

+ a,,SIZE,

+ a,,SIZE,

+ e,,

4Adar, Agmon and Orler (1975) have demonstrated theoretically that in the presence of jointness in production, the optima) structure of assets and liabilities will not be separable. Empirical evidence of jointness in bank production has recently been reported by Smirlock, Gilligan and Marshall (1984) for banks, and by Murray and White (1983) for Canadian credit unions. 5The highly aggregated nature of the asset and liability composition variables is made necessary by the data restriction of the Report of Income and Condition data employed in estimating the model. However, more specific data is available only through implementation of a survey.

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SDROE = b, + b,ALAR + b,ATSTL + b,DUMHC

methodology

+ b,CVSDPI + b,AVGHI

+ b,MFRS + b,BRNCH

+ b,SIZE, + b,,SIZE,

+ b,SIZE2

+ b,,SIZE5 + b,,SIZE,

+ e,, (W

ALAR = c,, + c,SDROE + c2ATSTL + cj A VGPI + c4A VGHI +c,DUMHC+

c,MFRS + c,BRNCH

+c,AVGIRL + q$IZE,

+ c,,AVGIRTS + c,,SIZE,

+d,DUMHC+

d,MFRS

+ d,,SIZE,

+ c&?IZE,

+ claSIZE6 + e3,

+ d,AVGPI + d,BRNCH

+ d,A VGCOBF + d,,SIZE, +d,,SIZE,

+ c,,AVGIROS

+ qJIZE,

ATSTL = d, + d,SDROE + d,ALAR

+ c,AVGRLL

(54

+ d,AVGHI + d,AVGRTSD

+ d,,SIZE,

+ d,,SIZE,

+ e4.

(5d)

The endogenous variables AVGROE, SDROE, ALAR, and ATSTL represent measures of bank profit, overall bank risk, and the relative compositions of bank assets and liabilities, respectively. The variables CVSDPI, AVGPI, AVGHI, MFRS, DUMHC, BRNCH, and SIZE, (i = 1,. . . ,6) are included as measures of important elements of the market, regulatory, and organizational structures, with AVGHl measuring the degree of market concentration. Finally, the variables A VGRTSD, A VGCOBF, A VGRLL, A VGIRL, A VGIRTS, and AVGIROS are included as measures of return and risk attributes of alternative assets and liabilities which may influence the bank’s choice of the composition of its balance sheet. To maintain the continuity of the methodological focus of this paper, the definition and discussion of these variables is deferred to the appendix. 3.2. The reduced-from model Making use of the structural equations presented above, the reduced-from expression for profitability can also be derived. The reduced-form model takes

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the following form: A VGROE = &, + r#@4DPI

+ &A VGPZ + Cp,DUMHC

+ &A VGHI + cpaBRNCH + @IZE, +&SIZE,

+ +,,SIZE,

+&,AVGCOBF+ ++,,AVGIRTS

+ &, MFRS

+ +JIZE3

+ +11SIZE6 + &AVGRTSD

+,,AVGRLL

+ $J~~AVGIRL

+ +17AVGIROS + E,

(6)

where I#J~(i = 0,. . . , 17) are the reduced-form coefficients. Thus an hypothesis test of the null hypothesis that the reduced-form coefficient, ( dA VGROE/aA

VGHI) = &,

is equal to zero, is not equivalent to a test of the null hypothesis that the structural parameter a5 is zero. This must be true since ~s=~,+~,(E/A)+a,[(~/Q>

+d(WQ)

+(RWA)I

+ (R’E/A)l~

where U = cd + c2d,, U’=d,+d,c,, R = [@I + wW(l R’ = [(d, + &d/(1-

- cd,)] cd,)]

9 9

E=b,(l-c,d,)+b,(c,+c2d4)+b2(d4+d2c4), A = (1 - c2d,) - b,(c, + czd,) - b,(d, + d,c,), Q = (1 - c,d,). 3.3. Classification of single-equation tests of the SPM Given the preceeding discussion of the underlying economic structure and the subsequent specification of simultaneous-equations and reduced-form models, it is now appropriate to consider the regime into which single-equation tests of the SPM might be classified. The use of OLS to estimate single-equation models which employ the implicit assumption that such vatiables as overall bank risk and the composition of bank assets and liabilities are determined exogenously from bank profit, must necessarily fall into either the

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first or second regimes. To determine the appropriate classification of these models, it is necessary to test the assumption of the exogeneity of these variables. If such a test is able to reject the assumption of exogeneity for these variables, previous estimates of a, obtained using such a methodology may have been biased and inconsistent. Alternatively, previous applications of OLS to single-equation expressions for bank profit which do not include these (or similar) variables and thus resemble eq. (6) must necessarily fall in the third regime. Thus, while previous OLS estimates of +, are consistent, they are useful only for prediction purposes. They are not useful for hypothesis tests of the structural parameter, a,, as implied in most papers employing this methodology. 4. The data The primary source of data employed in the estimation of these models is derived from the Report of Income and Report of Condition publications of Federal Deposit Insurance Corporation for the ten-year period 1973 to 1982. The sample consists of 1,857 banks, located in 152 SMSAs, in states permitting either unit or limited branch banking. The banks vary in size from an average low of 1.11 million to an average high of 1.41 billion dollars of total assets for the ten-year period. The Herfindahl Index employed as a measure of market concentration varies from a high of 0.861 to a low of 0.034.6 5. Misspecification

test for simultaneous linear equations

A limited information misspecification test for single equations, proposed by Spencer and Berk (1981) can be used to provide evidence of whether previous estimates of the SPM using OLS fall in regimes one or two.’ The proposed test is a test of the orthogonality of an assumed exogenouslydetermined variable to the error term of the structural equation. A failure to reject the null hypothesis would suggest that the variable could be treated as predetermined. A rejection of the null hypothesis would provide evidence that the variable in question should be specified as endogenous.’ 6The mean value of the Herfindahl Index for the sample is 0.109. The mean value for the average asset size of banks in the sample is 81.32 million dollars. ‘The Spencer-Berk limited-information test is selected for use over the Hausman (1978) full-information test for two reasons. First, it is generally not feasible to use the Hausman test to isolate particular equations in which misspecification occurs. Second, the Spencer-Berk test does not require the assumption that any other equations are correctly specified. ‘Tests of orthogonality are non-constructive in the sense that rejection of the orthogonality assumption can occur for reasons other than the endogeneity of the variable [see Spencer and Berk (1981, pp. 1079-1080)]. However, the nature of tbe underlying economic structure discussed above would tend to support an alternative hypothesisof endogeneity.

J.A. Clark. Single-equaiion, multiple-regression methodology

303

Table 1 F-statistics for tests of orthogonality. Equation numbers Variable SDROE ALAR A TSTL

64 1.79Sb 1.825b 55.875’

W)

(54 8.944a

13.4178 3.678’

(54 65.080P 7.360’

13.184’

‘F-statistic significant at the 1 percent level. bF-statistic significant at the 5 percent level.

5.1. Results of the misspecijication test The F-statistics resulting from the application of the Spencer-Berk test of orthogonality to all equations of the structural model are presented in table 1. Inspection of this table suggests that the hypotheses of the orthogonality of overall risk, asset composition, and liability composition variables to the respective error terms of eqs. (5b) through (5d) can be rejected at the one percent level in all cases.9 More importantly, the hypotheses of the orthogonality of the overall risk, asset composition, and liability composition variables to the error term of the structural equation for profit [eq. @a)] can be rejected at the five percent, five percent, and one percent levels of significance, respectively. Thus the overall risk, asset, and liability composition variables would appear to be properly treated as endogenous variables in the equations of the structural model. Based upon the results of this test, it may be inferred that OLS should not be applied to a structural equation for bank profit which includes these variables. The application of OLS to such an equation may produce biased and inconsistent estimates of the structural parameter as. Therefore, previous tests of the SPM which employ this methodology should be classified as falling in the first regime. 6. A comparison of estimates of the SPM under alternative methodologies

To demonstrates the implications for previous tests of the SPM arising from the application of an incorrect methodology, the results obtained from using OLS to estimate three alternative single-equation models for profitability can ‘The critical F-statistic, F,t,,U, can be found for each selected level of a by determining the numerator degrees of freedom u equal to the number of exogenous variables appearing in the equation and the denominator degrees of freedom v equal to the number of observations less the number of exogenous variables appearing in the structural model [see Spencer and Berk (1981, pp. 1082-1083)].

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be compared with 2SLS estimates of the structural model.‘O Using the variables as defined in the appendix, OLS was employed to estimate eqs. (1) (5a), and (6). In addition, 2SLS was employed to estimate eqs. (5a) through (5d) which comprise the structural model. l1 The resulting parameter estimates are reported in tables 2 and 3. 6.1. 2SLS estimates of the structural equations

Table 2 contains the estimated parameters and t-statistics obtained from the application of 2SLS to the structural model of section 3.1. The signs obtained on the estimated structural parameters of the model are generally consistent with expectations and are highly supportive of the SPM. The estimated structural parameter on the market concentration variable of structural equation for the bank’s average rate of return on equity, a5, is positive and statistically significant (a = 0.05) as suggested by the SPM. A ten percent increase in A VGHI will, ceteris paribus, directly increase the average rate of return on equity by approximately 0.53 percent. In addition, the estimated structural parameters on the market concentration variable in the remaining three structural equations are also statistically significant at either the one or five percent level of significance. 6.2. OLS estimates of structural and reduced-form equations

Table 3 contains the estimated parameters and t-statistics obtained from the application of OLS to structural [eqs. (1) and (5a)] and reduced-form [eq. (6)] equations for bank profitability. 6.2.1. OLS estimates of structural equations

The results presented in section 5 of this paper suggest that the estimation of a structural equation for bank profitability will result in biased and inconsistent estimates of the structural parameters. This result is important in assessing the validity of most of the previous tests of the SPM in banking. The “‘Alternatively. 3SLS could have been used to obtain parameter estimates. If all of the equations of the structural model are correctly specified, 3SLS would provide greater efficiency than ZSLS. However, if any of the structural equations are misspecihed, 3SLS will result in inconsistent estimates of all model parameters while 2SLS will result in consistent estimates of all parameters except those appearing in the misspecitied equation(s). Since some misspecification is likely given the highly aggregated nature of the data employed, 2SLS was selected to minimize its effects. ‘lEacb of the structural equations of the model were evaluated against both rank and order conditions. In each case the rank condition was satisfied. However, the order condition indicated that each equation is over-identified. A visual check of error terms for all models failed to reveal the presence of heteroscedasticity.

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potential severity of the problem can be demonstrated through the inspection of results reported for eqs. (1) and (5a) of table 3. Eq. (1) includes both the risk and liability composition variables as exogenously determined, but does not include a measure for the composition of bank assets. Further, this structural equation does not include variables to account for interbank variation in profit rates attributable to differences in organizational form and regulatory environment. Based upon the resulting OLS estimates of the structural parameters of eq. (1) one would be led, incorrectly, to accept a null hypothesis of no relationship between market concentration and bank profitability in contrast to what is suggested by the SPM. The estimated structural parameter, (Yeof eq. (l), is negative but not statistically significant ((Y= 0.05). Eq. (5a) of table 3 reports the OLS estimates of the structural parameters of the profit equation from the structural model. Though the OLS estimate of the structural parameter CQ is positive, it is much smaller in comparison with the 2SLS estimate of table 2. Further, the applicability of the SPM to banking would once again be rejected. The null hypothesis of no relationship between market concentration and the rate of return on equity cannot be rejected (a = 0.05). 62.2.

OLS estimates of the reduced-form model

OLS estimates of the reduced-form parameters of eq. (6) are also presented in table 3. While these parameter estimates are useful for prediction purposes rather than for directly testing the validity of the SPM in banking, several observations can be made. First, the OLS estimate of the reduced-form parameter I& is positive and statistically significant (CJ= 0.05). This result provides indirect support for the SPM by suggesting that together the direct and indirect effects of an increase in market concentration will increase bank profitability. Second, the magnitude of the overall effect of market concentration on the rate of return on equity, as captured by the reduced-form parameter +,, is quantitatively much smaller than the direct effect captured by the structural parameter a5 obtained using 2SLS. The order of magnitude of the difference is approximately fifty percent. Thus the estimate of the reduced-form parameter appears to understate the direct effect of market concentration on bank profitability as suggested by the SPM. 6.2.3. Additional

evidence

Some additional evidence of the potential for obtaining biased and inconsistent estimates of structural parameters can be found in the OLS estimates of a, in eqs. (l), (la), and (5a) of table 3. In all three instances the estimate of the

Table Two-stage

least-squares

2 estimation

Dependent

variables

of the SPM.n and equation

numbers

Explanatory variables

A VGROE W

SDROE (5’3

ALAR (SC)

INTERCEPT

0.232ab (6.8495)

0.0491b (3.9539)

- 0.2471 ( - 1.6464)

SDROE

0.3642 (0.6645)

a.4424b (2.6176)

- 9.664ab (- 6.6067)

ALAR

- 0.0130 (-0.2355)

0.0842b (6.5312)

ATSTL

- 0.2107b (- 5.0237)

A VGPI

1.9 x 10-6 (1.1925)

- 0.0682b ( - 4.8832) 1.5 x lo-SC (2.1452)

ATSTL (5d) 0.6116b (7.7109)

0.7302b (3.4527) 0.5069b (3.2989) - 3.5 x 10-6 (-0.5191)

BRNCH

- 0.C085b ( - 3.4202)

- 0.0021c (- 2.0978)

0.0263b (2.9584)

- 0.0136 (- 1.1943)

MFRS

- 0.0074b (- 2.9492)

-0.0029b (- 3.3760)

0.0186 (1.6047)

- 0.0331b (- 3.6007)

DUMHC

- 0.0017 ( - 0.7730)

- 0.0006 ( - 0.6239)

0.0121 (1.1619)

- 0.0187c (- 1.9872)

A VGHI

0.0525’ (2.4587)

- 0.0211b ( - 3.2719)

0.332gb (4.0319)

- 0.2076’ (- 2.2416)

- 0.0271 (- 1.1282)

- 0.0132 (- 1.4021)

A VGMS A VGRLL

- 0.2792 ( - 0.1789)

A VGIRL

- 0.4012b ( - 2.5781)

A VGIRTS

- 0.0476b (- 3.4953)

A VGIROS

- 0.3874 ( - 0.8819)

A VGR TSD

1.9529 (1.9179)

A VGCOBF

- 0.0142 ( - 0.1724)

SIZE,

0.0174b (2.7999)

- 0.0062b (- 5.5704)

0.0587b (3.0295)

- 0.0619b ( - 4.2342)

SIZE,

0.015ab (2.5343)

- 0.0103b (- 8.1289)

0.1009b (3.4974)

- 0.107Sb (- 5.5374)

SIZE,

0.0121C (2.0580)

- 0.0094b ( - 6.2093)

0.1092b (3.4022)

-O.lllgb (- 5.4410)

SIZE,

- 0.0020 ( - 0.1870)

- 0.0166b ( - 5.7092)

0.19Oab (3.7696)

-0.2135b (- 6.5926)

SIZE,

- 0.0075 ( - 0.7375)

- 0.012ab (- 3.3938)

0.1917b (4.0465)

- 0.206Sb ( - 6.0024)

CVSDPI

- 0.0116 ( - 0.5940)

‘Values appearing in parentheses are the relevant r-statistics. bCwfficient significant at the 1 percent level (two-tail test). CCoefficient significant at the 5 percent level (two-tail test).

Table OLS estimation

Explanatory variables INTERCEPT SDROE

3

of single-equation

tests of the SPM.”

Deoendent

and eauation

variables

A VGROE

A VGROE

(1)

(la)

W

0.1346b (13.245)

0.1377b (13.289)

0.1435b (13.720)

- 0.1654b ( - 3.6720)

-0.1674b (- 3.7342)

-0.2070b (-4.6138) 0.0076 (0.9202)

- 0.0273b (- 2.7237)

-0.021P (- 2.7665)

- 0.0198’ ( - 2.5203)

ALAR A TSTL A VGPI

numbers

A VGROE

0.82 x 10-b (0.7532)

0.38 x 10-e (0.3373)

0.45 x 1o-6 ( - 0.4076)

CVSDPI

A VGROE

(6) 0.0075 (0.4788)

0.52 x IO+ (0.4803) 0.2406 b (8.1332)

BRNCH

-0.0113b ( - 6.4351)

- 0.0089b (- 5.2870)

MFRS

- 0.0054b ( - 3.6025)

0.0003 (0.0274)

-0.0060b (- 3.8993) 0.X161h (3.8466) 0.0135 (1.1886)

- 0.0273 (- 1.5200)

- 0.0325 (- 1.8380)

- 0.0268 ( - 1.5668) 0.2590 (1.5537)

DUMHC A VGHI

- 0.0596 ( - 0.5730)

A VGMS A VGRLL

0.0026 (1.6655) 0.0229’ (2.1190)

A VGIRL

0.7494b (7.1235)

A VGIR TS

0.0051 (1.9184)

A VGIROS

-0.1199 ( - 1.7992)

A VGRTSD

- 0.4547b (- 3.0402)

A VGCOBF

- 0.0331’ ( - 2.5725)

SIZEz

0.0046c (2.3791)

0.0049’ (2.5149)

0.0076b (3.7722)

0.0104b (5.2721)

SIZE,

0.006Sb (3.0958)

O.O1llb (4.8867)

0.0151h (6.5942)

SIZE,

0.0029 (1.2655)

0.0071h (3.3161) 0.0047 (1.8011)

0.0101b (3.6534)

0.0146b (4.7796)

SIZE,

- 0.0037 ( - 0.8289)

0.0060 (1.1750)

SIZE,

0.0085 (1.6889) 0.0099 (1.3596)

R=

0.0012 (0.2189) 0.0158

- 0.0002 ( - 0.0415) 0.0064 (1.0182)

F

4.3020

0.0165

0.0119 (1.8663) 0.0512

4.1056

7.9940

OValues appearing in parentheses are the relevant r-statistics. bCoefficient significant at the 1 percent level (two-fail test). ‘Coefficient significant at the 5 percent level (two-tail test).

0.1219 15.3123

308

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structural parameter on the variable include as a measure of overall bank risk, SDROE, is negative and statistically significant ((Y= 0.01). This result is contrary to both expectations and the 2SLS estimates of table 2 and might be interpreted as suggesting that bank managers are risk lovers. 7. Summary and conclusions Testing the SPM requires a direct test of the relationship between market concentration and bank profitability. Conducting this test necessitates the estimation of a structural equation for bank profitability. In nearly every instance, previous tests of the SPM in banking have been conducted by applying OLS to a single-equation model of bank profitability. However, the underlying economic structure indicates that a bank’s profit will be determined simultaneously with the composition of its balance sheet and level of risk, and that market structure can be expected to have an effect on these variables as well. Thus the application of OLS to a structural equation for bank profit which includes measures of balance sheet composition and risk may result in biased and inconsistent estimates of the structural parameters of the equation. To demonstrate the potential bias for tests of the SPM, a four-equation structural model is specified to capture the effects of important elements of the underlying economic structure. The application of OLS to the model’s structural equation for bank profit results in quantitatively small and statistically insignificant estimated coefficients on the market concentration variable. This result is consistent with the results reported in most of the existing literature. However, when the structural parameters are estimated using 2SLS, the estimated structural coefficient on the market concentration variable becomes statistically significant and quantitatively larger. Appendii A. 1. Variable dejinitions The definitions of both the exogenous and endogenous variables of the model are presented below. In most instances the expected relationships between the dependent and explanatory variables of each equation are well documented in the literature or can be inferred from the discussion of the underlying economic structure in section 3. Thus the expected signs are presented without further explanation, but with reference to the literature where appropriate. The expected signs on most of the variables can be found from discussions which appear in the following papers: Edwards and Heggestad (1973, pp. 464-69), Heggestad (1977, pp. 1210-1212), Rhoades and Rutz (1982, pp. 78-80), Carson and Scott (1964, pp. 421-424), and Gilbert (1985).

J.A.

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Endogenous variables

AVGROE = average of the year-end ratios of net income after taxes to equity, 1973-1982. AVGROE is employed in the model as the measure of bank profitability. In general the strongest evidence of a concentration-profitability relationship has been found using the rate of return on assets. However, the rate of return on equity is a more appropriate measure of profitability since it is more consistent with the aggregate which ownership would seek to optimize [see Smirlock (1985, p. 75)]. SD IROE

ALAR

ATSTL

= standard deviation of the year-end rates of return on equity, 1973-1982. SDROE is employed in the model as a measure of overall bank risk. It .is analogous to the measure employed by Heggestad (1977) and is directly related to measures employed by Edwards and Heggestad (1973) and Rhoades and Rutz (1982); (a, > 0, c1 > 0, d, -c 0). = average of the year-end ratios of total loans to total assets, 1973-1982. ALAR is employed in the model as a proxy for the composition of bank’s assets. The Report of Income does not provide information on the interest and fees on each of the loan classes thus making it impossible to more completely disaggregate each bank’s loan portfolio; (a* > 0, b, > 0, d, > 0). = average of the year-end ratios of total time and savings deposits to total liabilities, 1973-1982. ATSTL is employed in the model as a proxy for the composition of bank liabilities; ( a3 < 0, b, < 0, c2 > 0).

A. 1.2. Exogenous variables A VGHI

MFRS

BRNCH’

=average Herfindal Index calculated for the market in which the bank is located, 1973-1982. AVGHI is employed as a measure of local market concentration; (as > 0, b4 < 0, c4 ><0, d, ><0). =dummy variable given a value of one for banks which are members of the Federal Reserve System, zero otherwise. MFRS is included to capture differences in the structure of bank regulation; ( a8 < 0, b, < 0, c9 ><0, d, ><0). = dummy variable given the value of one for banks operating one or more branches during the period 1973-1982, zero otherwise. This variable is included to capture the bank’s ability to expand and diversify geographically; (a, 3 0, b, < 0, c7 > 0, d, -c 0).

310

A VGPI

CVSDPI

A VGMS

DUMHC

SIZE, SIZE, SIZE, SIZE, SIZE, SIZE, SIZE,

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=average of the yearly per capita income in the relevant market (SMSA), 1973-1982. This variable is included in the model as a proxy for the market demand for bank services; ( a4 > 0, cj > 0, d, ><0). =coefficient of variation of the market per capita income, 1973-1982. This variable is included in the model to capture variation in the demand for bank services; (b3 > 0). = bank’s average market share of total market bank deposits, 1973-1982. In a recent paper, Smirlock (1985) reports evidence which suggests that market concentration and high profitability are the result of the superior efficiency of leading firms in a market rather than joint profit-maximizing behavior. This variable is included to capture the relationship suggested by this Efficient Structure Hypothesis [see Ravenscraft (1983) Smirlock et al. (1984), and Smirlock (1985)]; (aa ><0). =dummy variable given a value of one for banks which are afhliated with a holding company, zero otherwise. DUMHC is included in the model to capture differences in bank behavior attributable to holding company affiliation; (a, ><0, 6, ><0, c8 ><0, d, 2 0). =set of dummy variables defining bank size in terms of the average of total year-end assets, 1973-1982, as follows: = 1 if A VGSIZE c 25 m., 0 otherwise, = 1 if 25 m. I A VGSIZE -c 50 m., 0 otherwise, = 1 if 50 m. I AVGSIZE < 100 m., 0 otherwise, = 1 if 100 m. I A VGSIZE < 300 m., 0 otherwise, = 1 if 300 m. 5, A VGSIZE < 500 m., 0 otherwise, = 1 if A VGSIZE 2 500 m., 0 otherwise.

These binary variables are included in the model to capture differences in size. a, (i = 10,. . . ,14) ><0, ci (i = 12,. . . ,16) > 0, bi (i = 8,. . . ,12) -C0, di (i = 10,. . . ,15) -C0. A VGRL

A VGIRL,

= average of the year-end ratio of reserves for possible loan loss to total loans, 1973-1982. This variable is included as a proxy for the perceived default risk or quality of the loan portfolio; (c,
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311

is some evidence that interest rates charged by banks may be higher in more highly concentrated banking markets, there is also evidence that price competition may be minimal and that market concentration may be important in determining other elements of the multiple loan pricing options employed by banks [see Heggestad and Ming0 (1976), Heggestad and Rhoades (1978), and White (1976)]. Measures for such other elements as origination fees, points, rate adjustments, rate caps and compensating balance requirements cannot be inferred from available data. Consequently both the AVGIRL and a measure of market concentration appear in the structural equation for the bank’s asset composition. Further, the pairwise correlation coefficient between the two variables is low (- 0.0174) making the potential bias from including both variables appear to be small; ( cg ><0). A VGIRTS

=average of the year-end ratios of interest received on U.S. Treasury securities to total dollar volume of U.S. Treasury securities, 1973-1982. AVGIRTS is included to capture the effect of returns on alternative assets on the composition of bank assets; (cl0 < 0).

A VGIROS

= average of the year-end ratios of interest received on the sum of the following reported aggregates: (1) other U.S. Government securities, (2) securities of other states and local political subdivisions, (3) and all other securities, to the total dollar volume of these aggregates, 1973-1982. AVGIROS is included in the model to capture the effects of returns on alternative assets on the composition of bank assets; (cl1 < 0).

A VGRTSD = averaged of year-end ratios of interest paid on time and savings deposits to total time and savings deposits, 1973-1982. A VGRTSD is included in the model to capture the effects of differences in the per dollar cost of acquiring these funds on the composition of bank liabilities. An argument similar to the argument made in defining AVGIRL can be made for including both A VGHI and A VGRTSD as exogenously determined variables in the structural equation explaining the composition of bank liabilities. Again any bias from such a specification is likely to be small given a pairwise correlation between the variables of -0.0218; (d, > 0). A VGCOBF = average of the year-end ratios of the sum of interest paid on: (1) federal funds purchased, (2) notes and debentures, (3) other borrowed money, to the sum of the dollar volumes of these

312

aggregates. AVGCOBF is included in the model to capture the effects of differences in the cost of acquiring alternative liabilities on the composition of bank liabilities; (d, > 0). References Adar, Zvi, Tamir Agmon and Yair Orgler, 1974, Output mix and jointness in production in the banking firm, Journal of Money, Credit, and Banking 7, 235-243. Baltensperger, Ernst, 1980, Alternative approaches to the theory of the banking firm, Journal of Monetary Economics 6,1-37. Carson, Dean and Ira Scott, 1971, Commercial bank attributes and aversion to risk, in: Dean Carson, ed., Banking and monetary studies (Richard D. Irwin, Homewood, IL). Edwards, Franklin R., 1977, Managerial objectives in regulated industries: Expense-preference behavior in banking, Journal of Political Economy 85, 147-162. Edwards, Franklin R., and Arnold Heggestad, 1973, Uncertainty, market structure, and performance: The Galbraith-Caves hypothesis and managerial motives in banking, Quarterly Journal of Economics 87,455-473. Gilbert, R. Alton, 1984, Bank market structure and competition: A survey, Journal of Money, Credit, and Banking 16, part 2,617-644. Hannan, Timothy H., Expense-preference behavior in banking: A reexamination, Journal of Political Economy 87.891-895. Hausman, J.A., 1978, Specification tests in econometrics, Econometrica 46, 1251-1271. Heggestad, Arnold A., 1977, Market structure, risk, and profitability in commercial banking. Journal of Finance 32,1207-1216. Heggestad, Arnold A., 1979, A survey of studies on banking competition and performance, in: Franklin R. Edwards, ed., Issues in financial regulation (McGraw-Hill New York) 449-490. Heggestad, Arnold A. and John J. Mingo, 1976, Prices, nonprices, and concentration in commercial banking, Journal of Money, Credit, and Banking 8,107-117. Heggestad, Arnold A. and Stephen A. Rhoades, 1978, Multi-market interdependence and local market competition in banking, Review of Economics and Statistics 60, 523-532. Judge, George G., W.E. Griffiths, R.C. Hill, H. Lutkepohl and T.C. Hill, 1985, The theory and practice of econometrics, 2nd ed. (Wiley, New York). Murray, John H. and Robert W. White, 1983, Economies of scale and economies of scope in multi-product financial firms: A study of British Columbia credit unions, Journal of Finance 38, 887-902. Ravenscraft, David, 1983, Structure-profit relationships at the line of business and industry level, Review of Economic and Statistics 55, 22-32. Rhoades, Stephen A., 1977, Structure-performance studies in banking: A summary and evaiuation, StatI economic studies no. 92 (Board of Governors of the Federal Reserve System, Washington, DC). Rhoades, Stephen A. and Roger D. Rutz, 1982, Market power and firm risk: A test of the ‘quiet life’ hypothesis, Journal of Monetary Economics 9, 73-85. Santomero, Anthony M., 1984, Modeling the banking firm: A survey, Journal of Money, Credit, and Banking 16, 576-602. Schweiger. Irving and J.S. McGee, 1961, Chicago banking: The structure and performance of banks and related financial institutions in the Chicago and other areas, Journal of Business 34, 203-366.

Smirlock, Michael, 1985, Evidence on the (non) relation&in between concentration and nrotitability in banking, Journal of Money, Credit,‘and Banking 17,69-73. Smirlock. Michael. Thomas Gilliean and William Marshall. 1984. Tobin’s CI and the structure-performance relationship, American Economic Review 74, lb51-1060. ’ Spencer, David E. and Kenneth N. Berk, 1981, A limited information specification test, Econometrica 49,1077-1085. White, Lawrence J., 1976, Price regulation and quality rivalry in a profit maximizing model: The case of bank branching, Journal of Money, Credit, and Banking 8. 97-106.