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 1196 COPY 2 
 
 BEBR 
 
 FACULTY WORKING 
 PAPER NO. 1196 
 
 Economies of Scale and Organization 
 Efficiency in Banking 
 
 Warapatr Todhanakasem 
 Walter J. Primeaux, Jr. 
 Morgan J. Lynge, Jr. 
 Paul Newbold 
 
 College of Commerce and Business Administration 
 Bureau of Economic and Business Research 
 University of Illinois, Urbana-Champaign 
 
BEBR 
 
 FACULTY WORKING PAPER NO. 1196 
 College of Commerce and Business Administration 
 University of Illinois at Urbana-Champaign 
 October, 1985 
 
 Economies of Scale and Organization Efficiency in Banking 
 
 Warapatr Todhanakasem 
 Thai Farmers Bank 
 
 Walter J. Primeaux, Jr., Professor 
 Department of Business Administration 
 
 Morgan J. Lynge, Associate Professor 
 Department of Finance 
 
 Paul Newbold, Professor 
 Department of Economics 
 
Digitized by the Internet Archive 
 
 in 2011 with funding from 
 
 University of Illinois Urbana-Champaign 
 
 http://www.archive.org/details/economiesofscale1196todh 
 
ABSTRACT 
 
 Economies of Scale and Organisation Efficiency 
 
 in Banking 
 
 Warapatr Todhanakasem, Walter J. Primeaux , Jr . , 
 Morgan J. Lynge.Jr., Paul Newbold* 
 
 A number of previous studies have attempted to assess the 
 extent to which economies of scale exist within banking firms. 
 Most of these studies have relied upon cost functions of one form 
 or another and their findings have been inconclusive. A major 
 difficulty involved in the cost function approach is the 
 selection of an appropriate measure of bank output. 
 
 The profit function and its duality relationship with the 
 production function offer an alternative approach to examining 
 economies of scale and organizational efficiency in commercial 
 banking. This alternative enjoys several advantages over the 
 cost function method, consequently, that is the approach used in 
 this study. 
 
 A risk adjusted profit function is used in the estimation of 
 economies of scale of unit and branch banks ; and the effects of 
 bank holding company affiliation on the level of bank profits is 
 also examined. The results indicate larger economies of scale 
 for branch banks than for unit banks and bank holding company 
 affiliates were found to be more efficient than independent 
 banks . 
 
 * The authors are Vice President Thai Farmers Bank; and 
 Professor of Business Administration, Associate Professor of 
 Finance, and Professor of Economics at the University of Illinois 
 at Urbana-Champaign . 
 
ECONOMIES OF SCALE AND ORGANIZATION EFFICIENCY IN BANKING 
 
 By 
 
 Warapatr Todhanakasem, Walter J. Primeaux, Jr., 
 Morgan J. Lynge, Jr., Paul Newbold 
 
 INTRODUCTION 
 
 After Alhadeff's [1954] pioneering work on bank costs, several 
 empirical studies were conducted to examine economies of scale in com- 
 mercial banks. Most of these studies relied upon cost functions of 
 one form or another and their findings have been inconclusive about the 
 existence of economies of scale in banking. A major difficulty involved 
 in the cost function approach is the selection of an appropriate measure 
 of bank "output." Benston (1965, 1972), Bell and Murphy (1968), and 
 Murphy (1972) utilzed pnysical measures of Bank outputs in estimating 
 cost functions. Powers (1969), Longbrake and Haslem (1975), Langer 
 (1980), and Kalish and Gilbert (1973) used either multiple output 
 measures or an index with multiple weighted components as a measure of 
 output. Research results have been highly sensitive to the choice of 
 output variables. 
 
 Development of the profit function and its duality relationship 
 with the production function offer an alternative approach to the 
 study of economies of scale and organizational efficiency in commercial 
 banking. Advocates of this approach explain that it is more desirable 
 than the cost function because the level of output is not a variable in 
 the profit function. Furthermore, the procedure also captures a more 
 complete concept of efficiency than the cost function approach. 
 
-2- 
 
 Mullineaux (1978) tested a hybrid profit function which is 
 transcendental Logarithmic (translog) in labor input prices and 
 
 Cobb-Douglas in the prices of output and other inputs and the quan- 
 
 2 
 tities of fixed factors of production. His samples contained banks 
 
 participating in the Functional Cost Analysis Program in 1971 and 
 
 1972. However, the Functional Cost Analysis data which he used have 
 
 often been criticized as not being representative of the banking 
 
 industry, since participation is voluntary and most of the data tend 
 
 to be from small banks. 
 
 The main purpose of this study is to conduct separate empirical 
 
 tests of banking economies of scale and organizational efficiency, 
 
 utilizing a risk-adjusted profit function on randomly-selected samples 
 
 of unit and branch banks. The contributions of the work compared with 
 
 previous research consist of the use of more recent data (1978, 1979, 
 
 1980), the introduction of elements of risk into the profit function, 
 
 and the development of separate estimations for banks operating under 
 
 different branching arrangements (unit and branch banks). 
 
 PROFIT FUNCTION 
 The profit function approach offers a convenient analytical tool 
 which captures both the technical efficiency and price efficiency 
 dimensions of economic efficiency. Technical efficiency deals with 
 the quantity of output produced from a given level of inputs. Price 
 
 efficiency deals with the quantity of profit produced from a given 
 
 3 
 level of technical efficiency. 
 
 Following McFadden (196b) and Lau and Yotopoulos (1971), profit 
 
 4 
 is defined as current revenue less current total variable cost. The 
 
-3- 
 
 profit function expresses a firm's maximized profit as a function of 
 the prices of output and variable inputs and the quantities of fixed 
 factors. The derivation of the profit function assumes that the firm 
 is a price-taker in both the output and variable input markets. It 
 also assumes that the quantities of fixed factors are given. The last 
 assumption implies profit maximization in the short run, and the pro- 
 fit function thus derived is called the "restricted profit function." 
 
 Duality was developed by Hotelling [1932] , Shephard [1953] , and 
 Uzawa [1964]. McFadden [1966] later demonstrated that it is possible 
 to consider only the profit functions in analyses of profit- 
 maximizing, price-taking firms without explicitly specifying their 
 corresponding production functions. 
 
 In the context of the profit function theory, the goal of an indi- 
 vidual commercial bank is to maximize profits by taking deposits or 
 borrowing funds and converting them into various types of earning 
 assets. Banks also provide other financial-related services, for 
 example, safe deposit boxes, for fees. In the regular conduct of 
 their business, banks expose themselves to many kinds of risk. 
 
 On the asset side of the balance sheet, assets held by a bank can 
 be divided into two broad classes: earning assets and non-earning 
 assets. Given the characteristics and distribution of its liabili- 
 ties, the bank attempts to structure its portfolio of assets in such a 
 manner as to yield the greatest return. The higher the percentage of 
 the bank's total assets held in earning assets, the greater is its 
 expected profit, ceteris paribus. 
 
-4- 
 
 It is desirable to distinguish between the ex ante and the ex post 
 measures of risk. When granting a loan a bank, can only make a subjec- 
 tive judgment of the risk of it culminating in default. The higher 
 the probability of default, the riskcier is the loan and the higher the 
 rate of interest charged by the bank. The ex ante measures, essen- 
 tially, are the characteristics of a portfolio that would indicate the 
 actual performance. If the risky loans turn out to have lower default 
 
 rates than expected, the bank will realize higher than expected pro- 
 
 7 
 fits and vice versa. 
 
 Most studies of risk have traditionally used the variance or 
 
 8 
 covariances of earnings as measures of riskiness. These measures are 
 
 ex post in nature. Rhoades [1981] argued that a good ex ante measure 
 
 of the bank portfolio risk is the ratio of total loans to total assets 
 
 because it is generally accepted that loans tend to be riskier than 
 
 9 
 other types of assets typically held by a bank. 
 
 In the framework of the profit function, the loans to assets ratio 
 can be viewed as a variable input factor. The higher ratio means 
 higher portfolio risk exposure. If the cost due to defaulted loans is 
 high, realized profit for this period will be low, and vice versa. 
 
 Banks are exposed to risk on the liability side of their balance 
 sheets as well. We consider the two broad categories, namely, liabili- 
 ties and equity capital. For equity capital, the ratio of equity to 
 total assets has been a popular ratio used by bank regulators as a 
 measure of bank: soundness. As the ratio rises, the bank's financial 
 
-5- 
 
 risk is reduced. For liabilities, as the bank relies less on tradi- 
 tional (stable) deposits and more on borrowed sources of funds from 
 the money market, the ratio of borrowed funds to total liabilities 
 rises and the bank is subject to greater liquidity risk. Management 
 policy on liabilities and equity capital, therefore, can have signifi- 
 cant impacts on the risk and profitability on the bank. During 
 periods of tight money, for example, bank equity capital, as an indef- 
 inite term-to-maturity source of funds, can reduce the bank's exposure 
 to high borrowing costs and disintermediation. If banks are faced 
 with rising short-term money market costs of funds that cannot be 
 passed on to the borrowing customers through floating rates on loans, 
 
 then banks that depend largely on borrowed funds from the money 
 
 12 
 markets may suffer seriously from leverage risk. At other times 
 
 general interest rates in the money market may decline and banks may 
 
 benefit from access to cheaper costs of borrowed funds. 
 
 Over a period of time the bank's ratio of equity capital to total 
 assets and its ratio of borrowed funds to liabilities can be con- 
 sidered variable cost factors which, depending on market conditions 
 and the bank's liability and equity positions, may cause high or low 
 realized bank profits. 
 
 Hence, we use three measures of risk from both sides of the 
 
 balance sheet: the ratios of total loans to total assets, equity 
 
 13 
 capital to total assets, and borrowed funds to total liabilities. 
 
-6- 
 
 THE MODEL AND DATA 
 
 The full Cobb-Douglas specification has properties which make it 
 convenient for economies of scale estimation. Lau and Yotopoulos 
 [1971] have proved that, given the Cobb-Douglas production function 
 conditions, differences in technical efficiency and/or differences in 
 price efficiency translate into constant differences in the level of 
 profits, given market prices. They have also proved that a test of 
 
 the hypothesis of constant returns in all inputs is a test of the 
 
 b * 
 
 hypothesis Z 8. = 1, where the B.'s are the elasticities of the pro- 
 11 
 
 1 = 1 14 
 
 fit function with respect to the fixed factors of production. This 
 
 property allows us to test for scale economies or diseconomies by 
 
 adding the coefficients of all the fixed factors of production to see 
 
 whether the sum is equal to, or larger or small than unity. 
 
 The Cobb-Douglas risk-adjusted profit function model that will be 
 
 used for our estimations is: 
 
 In PROFIT = a n + E a.lnP. + E b.lnq. + £ c, InZ, 
 1=1 j=l J k=l 
 
 where P^ are the bank output prices, q are the variable input prices, 
 including risk factors, and Z, are the quantities of fixed factors. 
 All data were obtained from the FDIC computer tapes containing 
 balance sheet and income statement data for all insured banks for 
 1978-1980. All balance sheet data are measured as annual average 
 values. The years 1978-1980 were chosen for this empirical work 
 because during the first two of these years the banking industry had 
 
-7- 
 
 returned to a relatively normal operating condition following the tur- 
 bulent periods during and immediately after the recession of 
 1974-1975. Interest rates were rising steadily and became much more 
 volatile in 1980. Competition intensified in several areas of the 
 banking industry; commercial banks were faced with aggressive com- 
 petition from the finance companies in the business loan market and 
 from the thrift institutions and finance companies in the consumer 
 loan market. 
 
 To examine how banks of different sizes and forms of organization 
 fared during the period of relatively stable economic condition and 
 increasing competition in the industry, we test two specifications: 
 
 Equation for Unit Banks 
 
 In PROFIT = lna + b In LRATE + b In ATW 
 
 1 2 
 
 + b In INTTS + b In INTCD + b In TLTA 
 3 4 5 
 
 + b In EQTA + b In BFLB + b In PREM 
 6 7 8 
 
 + b In TD + b LB + B SWB + b BHC 
 9 10 11 12 
 
 Equation for Branch Banks 
 
 In PROFIT = lna + b In LRATE + b In ATW 
 
 1 2 
 
 + b In INTTS + b In INTCD + b In TLTA 
 3 4 5 
 
 + b In EOTA + b In BFLB + b In PREM 
 6 7 8 
 
 + b In TDBR -I- b In BR + b . Lb + b „ BbtC 
 9 10 ll 12 
 
-8- 
 
 where 
 
 PROFIT = total operating revenue minus total operating expenses 
 LRATE = average rate of interest and fees on total loans 
 
 ATW = average total wages per full-time equivalent employee 
 INTTS = average interest rate on time and savings deposits 
 INTCD = average interest rate on large certificate of deposits 
 TLTA = ratio of total loans to total assets 
 EQTA = ratio of equity capital to total assets 
 BFLB = ratio of borrowed funds to total liabilities 
 PREM = bank premises and furnitures and fixtures 
 PREMBR = average bank premises per branch 
 BR = number of branches 
 TD = total deposits 
 TDBR = total deposits per branch 
 
 LB = limited-branching state dummy variable (1 = limited 
 branching state; = otherwise) 
 SWB = statewide-branching state dummy variable (1 = statewide 
 
 branching state; = otherwise) 
 BHC = bank holding company affiliation dummy variable (1 = 
 affliated bank; = independent bank) 
 These profit function specifications assume that banks are 
 price takers in output and variable input markets but allow for an 
 empirical test of this assumption. If banks are not price takers in 
 the output market, output prices will not be significant explanatory 
 variables in the profit function. The output price variable, there- 
 fore, is expected to have a positive and significant coefficient. 
 
-9- 
 
 As the theory of the profit function suggests, the expected signs 
 for the coefficients of the quantities of the fixed factor variables 
 are positive. That is, as a bank increases its premises, deposits, or 
 number of branches, profits should increase. The signs for the coef- 
 ficients of variable input prices other than the risk factors are 
 expected to be negative. That is, as the variable costs increase 
 profits are expected to decline. 
 
 The expected signs for the coefficients of the risk factors, 
 however, need some further elaboration. As discussed earlier, the 
 total loans to total assets ratios (TLTA), as an ex ante measure of 
 risk, may produce either a positive or negative effect on actual bank 
 profits, depending on the actual performance of the loans. The coef- 
 ficient of EQTA is expected to have a positive sign because as the 
 ratio increases the bank avoids paying "outright" interest as would be 
 necessary on deposits or borrowed funds. Since our measure of profits 
 is total revenue less total operating expenses, which essentially is 
 income before dividend payments , the higher the ratio of equity capi- 
 tal to total assets (EQTA), the higher profit will be. Also, as the 
 ratio of borrowed funds to total liabilities (BFLB) increases, the 
 interest payments on borrowed funds grow and this is expected to have 
 a negative effect on profits. Therefore, a priori the sign for the 
 coefficient of BFLB is negative. 
 
 Most previous studies have suggested that the holding company form 
 of organization in commercial banking is more profitable than the non- 
 holding form. These findings are reasonable because bank holding 
 
-10- 
 
 companies have access to more diverse business opportunities than 
 banks which are restricted to only "pure" banking business. 
 Consequently, the coefficient for BHC is expected to have a positive 
 sign. 
 
 The unit bank sample contains mainly banks from unit banking 
 states but also include some unit banks drawn from states permitting 
 limited or statewide branching. A bank which operates a single 
 office in an environment where some forms of branching are allowed 
 would be expected to earn lower profits because it fails to exploit 
 the larger geographical market opportunities and also must face strong 
 competition from other branch banks. The expected signs for the 
 coefficients of LB and SWB, therefore, are expected to be negative 
 for the unit bank equation. For the branch bank equation, only branch 
 banks located in the LB or SWB states were included in the sample. 
 It could probably be argued that branch banks in LB states may face 
 less competition than those operating in SWB states. If this is 
 correct, branch banks located in the LB states would be expected to 
 have higher profits. 
 
 EMPIRICAL RESULTS 
 Unit Banks 
 
 The results reported in Table 1 show that the coefficients of the 
 output price variable (LRATE) consistently take positive values and 
 are statistically significant. These results are as expected and sup- 
 port our assumption that banks are price takers in the output market. 
 
-11- 
 
 The average coefficient over the three-year period is 1.224, indi- 
 cating that a 1 percent increase in the average loan rate would yield 
 a 1.224 percent increase in bank profits. Average total wages per 
 full-time equivalent employee (ATW), however, has unexpected positive 
 coefficients for all three years; however, none of the values are sta- 
 tistically significant. 
 
 Variable input prices both of the average interest rates on time 
 and savings deposits (INTTS) and large CD's (INTCD) have expected 
 negative coefficients for all years. However, only the coefficient of 
 INTTS in the 1979 equation is statistically significant. 
 
 For the risk factors, the ratio of total loans to total assets 
 (TLTA) has negative coefficients for all years but is significant only 
 in the 1979 equation. This seems to indicate that unit banks that 
 held a large portion of their earning assets in the form of loans during 
 1979 actually realized lower profits than unit banks whose portfolio 
 risk was smaller. The ratio of equity capital to total assets (EQTA) 
 produces the expected coefficients which are positive and statisti- 
 cally significant. The ratio of borrowed funds to total liabilities 
 (BFLB), on the other hand, does not have a significant coefficient, 
 although the coefficient signs are negative, as expected, for two of 
 the three years. 
 
 As for the fixed factors, it is interesting to note that the coef- 
 ficients of bank premises (PREM) are negative and statistically signi- 
 ficant. These seem to suggest that, given the level of business, unit 
 banks either overinvested in fixed physical facilities and equipment, 
 
-12- 
 
 TABLE 1 
 
 OLS REGRESSION RESULTS FOR UNIT BANKS 
 
 (a) 
 
 Variable 
 
 1978 
 
 1979 
 
 1980 
 
 Average 
 
 LRATE 
 
 ATW 
 
 INTTS 
 
 INTCD 
 
 TLTA 
 
 EQTA 
 
 BFLB 
 
 PREM 
 
 TD 
 
 LB 
 
 SWB 
 
 BHC 
 
 .915*** 
 
 1.046*** 
 
 1.712*** 
 
 (.195) 
 
 (.159) 
 
 (.208) 
 
 .042 
 
 .101 
 
 .123 
 
 (.099) 
 
 (.079) 
 
 (.101) 
 
 -.199 
 
 -.409*** 
 
 -.093) 
 
 (.141) 
 
 (.134) 
 
 (.112) 
 
 -.039 
 
 -.056 
 
 -.003 
 
 (.042) 
 
 (.034) 
 
 (.045) 
 
 -.077 
 
 -.138* 
 
 -.124 
 
 (.081) 
 
 (.073) 
 
 (.085) 
 
 .589*** 
 
 .780*** 
 
 1.109*** 
 
 (.088) 
 
 (.079) 
 
 (.108) 
 
 -.010 
 
 .013 
 
 -.010 
 
 (.019) 
 
 (.017) 
 
 (.020) 
 
 -.163*** 
 
 -.150*** 
 
 -.082*** 
 
 (.028) 
 
 (.024) 
 
 (.031) 
 
 1.285*** 
 
 1.154*** 
 
 1.107*** 
 
 (.042) 
 
 (.035) 
 
 (.044) 
 
 .042 
 
 -.058 
 
 .008 
 
 (.046) 
 
 (.041) 
 
 (.048) 
 
 -.060 
 
 -.184*** 
 
 -.162** 
 
 (.090) 
 
 (.058) 
 
 (.074) 
 
 .099** 
 
 .115*** 
 
 .202*** 
 
 (.048) 
 
 (.038) 
 
 (.047) 
 
 1.224 
 
 .089 
 
 -.234 
 
 -.033 
 
 -.113 
 
 .826 
 
 -.002 
 
 -.132 
 
 1.182 
 
 -.003 
 
 -.135 
 
 .139 
 
-13- 
 
 Variable 1978 1979 1980 Average 
 
 Intercept -3.337*** -1.936*** .963 -4.31 
 (.669) (.577) (.684) 
 
 N 547 542 531 
 
 J 2 
 
 .7751 
 
 .8139 
 
 .7492 
 
 S.E. 
 
 .4577 
 
 .3730 
 
 .4668 
 
 F 
 
 157.824 
 
 198.107 
 
 132.951 
 
 (a) 
 
 standard errors in parentheses 
 
 *** significant at the 1 percent level 
 
 ** significant at the 5 percent level 
 
 * significant at the 10 percent level 
 
-14- 
 or failed to utilize the premises for the profit maximization objec- 
 tive. On the other hand, the deposit base variable (TD) has 
 coefficients that are positive and statistically significant with 
 magnitudes larger than unity for all three equations. Total deposits, 
 therefore, provide the sources of loanable funds which help generate 
 enough profits to offset any tendency toward diseconomies of scale 
 which may exist in the use of premises. 
 
 Overall, the banks turn out to have slight scale economies. If a 
 unit bank increases its premises and total deposits in the same pro- 
 portions, the overall economies of scale are 1.122, 1.004 and 1.025 
 for 1978, 1979 and 1980 respectively, with the average value of 1.05. 
 These figures indicate that unit banks do enjoy some modest economies 
 of scale. 
 
 The coefficients of SWB and BHC indicate that (1) unit banks in 
 statewide branching states are less profitable than unit banks in unit 
 banking states, and (2) banks affiliated with holding companies are 
 more profitable than independent banks. 
 
 Branch Banks 
 
 Regression results for branch banks are reported in Table 2. Like 
 the unit bank equations, the output price variable (LRATE) generates 
 coefficients which are positive and statistically significant. The 
 average value is 1.45, slightly above the 1.22 average of the unit 
 bank equations. Also resembling the pattern results of the unit banks 
 are the coefficients of (ATW), and the other variable input prices, 
 the average interest rates on time and savings deposits (INTTS) and on 
 CD's (INTCD). 
 
-15- 
 
 TABLE 2 
 
 OLS REGRESSION RESULTS FOR BRANCH BANKS^ a ) 
 
 Variable 
 
 1978 
 
 1979 
 
 1980 
 
 Average 
 
 LRATE 
 
 ATW 
 
 INTTS 
 
 INTCD 
 
 TLTA 
 
 EQTA 
 
 BFLB 
 
 PREMBR 
 
 TDBR 
 
 BR 
 
 LB 
 
 BHC 
 
 1.236*** 
 
 1.293*** 
 
 1.837*** 
 
 (.222) 
 
 (.290) 
 
 (.286) 
 
 .048 
 
 .076 
 
 -.103 
 
 (.110) 
 
 (.152) 
 
 (.119) 
 
 .366** 
 
 -.480** 
 
 -.269 
 
 (.157) 
 
 (.212) 
 
 (.237) 
 
 -.004 
 
 -.111* 
 
 -.087 
 
 (.044) 
 
 (.060) 
 
 (.069) 
 
 .132 
 
 .162 
 
 .108 
 
 (.103) 
 
 (.155) 
 
 (.158) 
 
 .863*** 
 
 .882*** 
 
 1.051*** 
 
 (.085) 
 
 (.117) 
 
 (.130) 
 
 -.015 
 
 -.041 
 
 -.030 
 
 (.021) 
 
 (.030) 
 
 (.036) 
 
 -.273*** 
 
 -.256*** 
 
 -.267*** 
 
 (.036) 
 
 (.050) 
 
 (.051) 
 
 1.359*** 
 
 1.316*** 
 
 1.289*** 
 
 (.046) 
 
 (.061) 
 
 (.063) 
 
 1.049*** 
 
 1.023*** 
 
 1.004*** 
 
 (.023) 
 
 (.033) 
 
 (.035) 
 
 -.025 
 
 .031 
 
 -.006 
 
 (.036) 
 
 (.050) 
 
 (.052) 
 
 .083** 
 
 .134** 
 
 .032 
 
 (.041) 
 
 (.054) 
 
 (.055) 
 
 1.445 
 
 .007 
 
 -.128 
 
 -.067 
 
 .133 
 
 .932 
 
 -.029 
 
 -.265 
 
 1.321 
 
 1.025 
 
 .083 
 
-16- 
 
 TABLE 2 
 
 (continued) 
 
 Variable 
 
 1978 
 
 1979 
 
 1980 
 
 Average 
 
 Intercept 
 
 -.188 
 (.794) 
 
 509 
 
 -2.568** 
 (1.000) 
 
 489 
 
 .417 
 (.997) 
 
 478 
 
 -2 
 R 
 
 .8602 
 
 .7685 
 
 .7447 
 
 S.E. 
 
 .3965 
 
 .5212 
 
 .5377 
 
 F 
 
 261.447 
 
 135.984 
 
 116.939 
 
 -.780 
 
 (a) standard errors in parentheses 
 *** significant at the 1 percent level 
 ** significant at the 5 percent level 
 * significant at the 10 percent level 
 
-17- 
 
 Among the three risk, factors, only (EQTA) consistently yields coef- 
 ficients with the hypothesized positive signs that are also statisti- 
 cally significant. Again, these results resemble those of the unit 
 banks' and suggest that both unit and branch banks realize higher pro- 
 fits as they use less leverage. (TLTA) and (bFLB), however, do not 
 generate coefficients which are statistically different from zero. 
 
 The coefficients of the three fixed factors (namely, PREMBR, TD8R, 
 and BR) add up to 2.135, 2.083, and 2.02b for 1978, 1979 and 1980 
 respectively, with an average of 2.08. These values are approxi- 
 mately twice those of the corresponding unit bank equations. They 
 suggest that branch banks realize greater economies of scale than unit 
 banks and that the major sources of scale economies are the total 
 deposits per branch and the number of branches. Like unit banks, 
 branch banks' premises per branch are also the sources of disecono- 
 mies. Its coefficients are negative and significant for all years 
 with an average value of -.27. 
 
 The coefficients on (LB) and (BHC) indicate that (1) the profit of 
 branch banks in limited branching states is not significantly dif- 
 ferent from branch banks in statewide branching states, and (2) branch 
 banks affiliated with holding companies have greater profit than inde- 
 pendent branch banks. 
 
 Test of Equality of Coefficients 
 
 Like other industries, commercial banks experienced changes during 
 the period 1978-1980. To examine whether the behavior of commercial 
 banks has changed significantly, tests of equality of coefficients 
 
-18- 
 
 were conducted on some variables for both the unit and branch banks. 
 
 Applying the normal distribution test of the difference between two 
 means, with the null hypothesis that the two population means are 
 equal, the Z-statistic is computed in our case as: 
 
 P i(80) P i(78) 
 z = 
 
 / 
 
 2 2 
 
 S 8 + S 8 
 
 i(80) P i(78) 
 
 where 8. /0 n\ = coefficient of variable i obtained from the 1980 
 i(80) . 
 
 equation, and 
 
 8./-,o\ = coefficient of variable i obtained from the 1978 
 i(78) 
 
 equation. 
 
 Tables 3 and 4 show Z-statistics and significance levels only for 
 the coefficients of variables which are statistically significant in 
 both 1978 and 1980 in the unit bank equations and the branch bank 
 equations respectively. 
 
 Table 3 shows that although the (BHC) variable is not found to 
 contribute differently to unit bank profits in 1978 and 1980, sta- 
 tistically the Z-statistics for three other variables, (LRATE), 
 (EQTA), (TD), are statistically significant at 5% or above and one 
 variable, (PREM), at the 10% level. Table 1 shows that the coefficient 
 of (LRATE) almost doubles its original value, increasing from .915 in 
 1978 to 1.712 in 1980. This is probably the result of banks adjusting 
 their loan rates upward by amounts greater than the increased cost of 
 funds. The coefficient of (EQTA) in 1980 is almost double its value in 
 1978. The coefficients of (LRATE) and (EQTA) in 1978 and 1980, therefore, 
 
-19- 
 
 TABLE 3 
 
 TEST OF EQUALITY OF COEFFICIENTS OF UNIT BANKS 
 Z-STATISTICS AND SIGNIFICANCE LEVELS 
 
 Variable 
 
 Z-Statistics 
 
 Significance Level 
 
 LRATE 
 
 EQTA 
 
 PREM 
 
 TD 
 
 BHC 
 
 2.80 
 3.69 
 1.80 
 -2.83 
 1.54 
 
 .05 
 .01 
 .10 
 .05 
 
 TABLE 4 
 
 TEST OF EQUALITY OF COEFFICIENTS OF BRANCH BANKS 
 Z-STATISTICS AND SIGNIFICANCE LEVELS 
 
 Variable 
 
 Z-Statistics 
 
 Significance Level 
 
 LRATE 
 
 EQTA 
 
 PREMBR 
 
 TDBR 
 
 BHC 
 
 1.66 
 
 1.21 
 
 .10 
 
 -.90 
 
 -1.08 
 
 .10 
 
-20- 
 
 provide some evidence that banks adjust their loan rates quite 
 promptly and efficiently, while reducing their financial leverage 
 during a period of rising market rates. Although the coefficients of 
 PREM and TD are statistically different between 1978 and 1980, the 
 magnitudes are relatively small. Together, they suggest that the 
 reduction in economies of scale for unit banks from 1.122 in 1978 to 
 1.025 in 1980. 
 
 As for branch banks, Table 4 shows that only the coefficients of 
 LRATE are significantly different between the two years. As in the 
 case of unit banks, this indicates that branch banks also adjust 
 loan rates upward to a greater extent than the increase in their costs 
 of funds. Unlike unit banks, however, the coefficients of all other 
 variables remain statistically unchanged. Therefore, branch banks 
 appear not to have changed their behavior to the same extent as unit 
 banks between the years 1978 and 1980. 
 
 CONCLUSIONS AND IMPLICATIONS 
 
 This work has dealt with the issues related to economies of scale, 
 economic efficiency, and organizational efficiency in commercial 
 banks. Through the application of the risk-adjusted profit function, 
 we have estimated economies of scale of unit and branch banks and 
 examined the effects of bank holding company affiliation on the level 
 of bank profits. Separate estimations of unit and branch banks are 
 
 more appropriate than the combined estimation because unit and branch 
 
 19 
 banks are basically different in structure and operations. 
 
-21- 
 
 Overall, the results of this study indicate larger economies of 
 scale for branch banks than unit banks. The levels of economies of 
 scale for unit banks are also found to have declined between 1978 to 
 1980, although the magnitudes are small. Regardless of the branching 
 status, bank holding company affiliates are found to be more efficient 
 than independent banks. 
 
 These results have several implications for bank regulators and 
 managers. Regulators should encourage (or at least not discourage) 
 the branching form of organization. The greater economies of scale of 
 
 branch banks occurs along with the greater number of offices in 
 
 18 
 branching states, both beneficial to the bank customer. Achieving 
 
 branching via a limited branching arrangement is satisfactory because 
 of the evidence that no greater efficiency occurs in statewide 
 branching states. The increased efficiency of banks affiliated with 
 holding companies should encourage the recent moves toward interstate 
 banking. 
 
 At the bank level, both unit and branch banks should scrutinize 
 their investment in premises and equipment. The evidence strongly 
 suggests that banks have over invested in facilities or failed to uti- 
 lize these physical facilities efficiently. 
 
-22- 
 
 Notes 
 
 *The authors are vice-president Thai Farmers Bank.; and Professor 
 of Business Administration, Associate Professor of Finance and Professor 
 of Economics at the University of Illinois at Urbana-Champaign. An 
 earlier version provides extensive detail of various aspects of the 
 material shortened in this presentation, including the nature of the 
 variables in the estimating equation, the data used and characteristics 
 of the earlier studies. It is available from the authors on request. 
 
 See McFadden [1966] and Lau [1969]. 
 
 2 
 Majumdar [1980] applied the profit function concept to the study 
 
 of economies of scale of the 200 largest commercial banks in the U.S. 
 
 in 1977. The profit function equations used, however, consisted of 
 
 only one independent variable. Moreover, profit was defined as rate of 
 
 return on assets rather than operating revenue minus operating expenses. 
 
 A more sophisticated profit function study after Mullineaux can be 
 
 found in the work of Richards and Villanueva [1980] which utilized the 
 
 Philippines banking data. 
 
 3 
 Lau [Reprint No. 269]: 206. 
 
 4 
 Fixed costs are not considered because they do not affect the 
 
 optimal combination of the variable inputs. See Lau and Yotopoulos 
 
 [1971J: 97. 
 
 See Varian [1978] for more detail. In the short run, some of the 
 firm's inputs are fixed and only production plans compatible with 
 these fixed factors are possible. Over the long run, however, these 
 factors may be variable and the firm's technological possibilities may 
 change. 
 
 There have been a number of theoretical and empirical works on 
 the relationship between risk and rate of return. For non-bank 
 studies, see Cootner and Holland [1970] and Fisher and Hall [1969]. 
 For a list of earlier works on risk and rate of return, see Fisher and 
 Hall, ibid., footnote 1. See also Heggestad [1977] for a similar 
 study in banking. 
 
 From the regulatory viewpoint, bank examiners regularly evaluate 
 the quality of loans held by banks and formally classify or "criticize" 
 some of the loans as "doubtful." Wu [1969] attempted to study the 
 relationship of the "ex ante" data on the quality of bank loans, as 
 measured by bank examiners criticism, and the "ex post" measure, which 
 is the subsequent loan defaults. He found that the criticisms were 
 "relatively accurate as an indicator of bank loan quality." 
 
 u 
 
 See, for example, Fisher and Hall [1969], Cootner and Holland 
 [1970], and Heggestad [1977]. 
 
-23- 
 
 9 Rhoades [1981]: 165. 
 
 See Mingo and Wolkowitz [1977]: 120. 
 
 See Pringle [1974] . 
 
 12 
 
 See Wojnilower [1966] and Heimann [1981]. 
 
 13 
 
 Rose and Scott [1978] use loans/assets, captial/loans , and vola- 
 tile deposits/liabilities as measures of bank's business and financial 
 risk. 
 
 14 
 
 Lau and Yotopoulos [1972]: 13-14. 
 
 The number of branches is a measure of plant size. See Richard 
 and Villaneuva [1980]. 
 
 1 6 
 
 A finding that bank output price makes no significant contribu- 
 tion to the empirical explanation of banking profits or yields a nega- 
 tive coefficient would suggest that banks are not price takers or that 
 the equation is misspecif ied. See Mullineaux (1978): 263. 
 
 See, for example, Mayne [1977] and Graddy and Reuben Kyle, III 
 [1980]. 
 
 1 8 
 
 See Seaver and Fraser [1979]. For earlier related studies, see 
 
 Horvitz and Shull 11964], Jacobs [1965], Lanzilotti and Saving [1969], 
 
 and Savage and Humphrey [1979]. 
 
 19 
 
 This proposition is also supported by a previous cost function 
 
 study by Mullineaux [1975]. tie rejected the hypothesis of identical 
 
 coefficients of the variables for branch and unit banks. 
 
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