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79-2 C <0 E E uo "O C ro £ CO *> <L» O' c (0 R E F E R E N C E L IB R A R Y E FEDERAL RESERVE BANK OF CHICAGO Q) O u. ro CL ro <V d) O' <0 A Series of Occasional Papers in Draft Form Prepared by Members'o THE EFFECT OF HOLDING COMPANY AFFILIATION UPON THE SCALE ECONOMIES OF BANKS Dale S. Drum 73 > 1 70 m LD m 70 < m 00 > Z 7. n z n > o o Research Paper No. 79-2 (Revised version of No. 78-3) THE EFFECT OF HOLDING COMPANY AFFILIATION UPON THE SCALE ECONOMIES OF BANKS by Dale S . Drum Department of Research Federal Reserve Bank of Chicago The views expressed herein are the author’s and as such do not necessarily reflect the views of the Federal Reserve Bank of Chicago or the Federal Reserve System. The material contained is of a preliminary nature, is circulated to stimulate discussion, and is not to be quoted without permission of the author. THE EFFECT OF HOLDING COMPANY AFFILIATION UPON THE SCALE ECONOMIES OF BANKS* While bank holding companies have existed for nearly a century, only in the past two and one-half decades has the extent and nature of their regulation become one of the most controversial issues within the banking sector. With the passage of the Bank Holding Company Act of 1956, and the subsequent amendments in 1966 and 1970, increasing cognizance has been taken of this form of business organization by regulators and legislators, both state and federal. Increasing concern is being expressed in both the public and private sectors regarding the impact bank holding companies (BHCs) have upon bank structure, conduct, and performance. The Bank Holding Company Act and its amendments establish the parameters within which the Board of Governors of the Federal Reserve System evaluates requests either to establish a holding company or to permit existing holding companies to acquire one or more banks. The principal competitive concern relates to the probable effect that an acquisition or formation will have upon competition in any relevant banking market. Applications involving adverse competitive effects are denied by the Board unless there is evidence of sufficient public benefits to outweigh the adverse competitive effects. *The author wishes to acknowledge the helpful comments of Donald D. Hester of the University of Wisconsin— Madison, and David Allardice, Chayim Herzig-Marx, Larry Mote, and Randall Merris of the Federal Reserve Bank of Chicago. -2- This proviso has stimulated a number of research efforts examining the performance of BHCs and their affiliated banks. One of the more frequently studied questions is the effect BHCs have upon the costs of their affiliates. In support of an acquisition, holding companies frequently argue that through affiliation some type of economies in the operation of the acquired bank can be achieved. This may reflect the adoption of new technologies or new organizational methods for the acquired firm. If operating economies do result and can be passed on to the public, then it may be argued that the resulting public benefits are substantial enough to offset, in part or perhaps in whole, any anti competitive effects inherent in the application. While this argument is frequently presented by holding company applicants, it is less frequently supported by relevant data. Thus, it is the purpose of this paper to explore further the impact of the holding company form of organization upon the costs of production of affiliate banks. Methodology The theoretical basis for this study rests upon the proposition that the cost function of a cost minimizing competitive firm is the mirror image of its production function [18, 22, 24]. Thus, if in creasing returns to scale characterize the production function, econo mies of scale should be reflected in the cost function. In order to avoid spurious results, however, it is necessary to specify correctly the cost-output relationship and to measure both cost and output properly. - 3- Three basic approaches have been taken to the study of cost functions in banking. Early studies tended to use an unweighted stock as the measure of bank output— for example, Gramley’s use of total assets [8 ]. Using this sort of measure assumes that the bank produces only one type of output and ignores the multiproduct nature of the banking enterprise. To remedy this difficulty, more recent analyses have emphasized two other approaches. The first is to assume an independent production function (and thus cost function) for each of the different activities performed by banks. This approach has been taken by Bell and Murphy [1], Benston [2], Longbrake and Haslem [14], and Mullineaux [16, 17]. The main criticism of this approach is that it assumes the production functions for the various bank activities are technologically indepen dent and, as a consequence, (seemingly) defines banking activities too narrowly. The other approach, taken by Greenbaum [9], Powers [20], Schweit zer [21], and Kalish and Gilbert [13], is to build a weighted index of bank output utilizing items from both the income statement and the balance sheet to produce an estimate of bank output. The regression coefficients obtained by regressing loan revenue against a number of loan categories are viewed as interest rate approximations. These are then used to weight the corresponding loan categories to construct an index of total bank output. ployed in the present study. It is this methodology which is em -4- The Present Study Cross-sectional analysis is used to test the equality of the cost functions of independent and affiliated banks. The sample is comprised of 208 Seventh Federal Reserve District commercial banks participating in the Federal Reserve System’s Functional Cost Analysis Program in 1976. Data are taken from the individual bank’s Report of Income and Report of Condition for the year 1976. Characteristics of the sample and the subgroups are described in Table I. Estimating loan revenue. Bank output is defined as estimated loan revenue for a competitive bank plus revenue from securities plus revenue from other sources.^ Similar to the definition employed by others [9, 13, 20, 21], the first step in estimating loan revenue is to establish index weights for the different loan categories in a bank’s portfolio. This is accomplished by deriving a regression equation predicated upon the accounting identity, n LNREV = E r.L. (1) i=i1 1 where LNREV is loan revenue, the r^'s are the interest rates for each loan category, and n is the total number of loan categories. The objective, however, is to approximate a competitive return as closely as possible. To do so requires the inclusion of those factors hypothesized to cause rates to vary among banks. The following struc tural factors are selected for inclusion in the estimating equation: Revenue from other sources includes such things as interest on balances with other banks, income from direct lease financing, and trust department income. TABLE I CHARACTERISTICS OF BANK SAMPLE A Number Range-Total Assetsa Mean-Total Assetsa SMSA MBHC OBHC Range-Lending Output3 28 5.6/24.9 16.680 10 2 2 .26/1.65 B 47 25/49.9 36.234 24 6 4 1.7/3.7 aMeasured in millions of dollars. c 78 50/99.9 71.016 36 10 15 3.1/6.7 D 34 100/199.9 145.308 28 6 6 6.2/13.0 E 21 200/635.1 345.847 21 9 6 13.0/44.9 TOTAL 208 5.6/635.1 95.73 119 33 33 .26/44.9 -6- Numbers Equivalent (NE) - The inverse of the Herfindahl Index, such that larger numbers imply lower concentration in a market. The relevant market for the purpose of this study is the SMSA if applicable, the county otherwise. While not ideal as a definition, there is ample precedent for its usage. If market concentration is a factor, loan revenue should be negatively related to NE (-). Growth (GRO) - Defined as the percentage change in total assets from 1975 to 1976. No sign is hypothesized for this variable Appending these variables to the loan revenue accounting identity, equation (1), the competititve loan revenue equation to be estimated is: n * LNREV = a + I r.L. + b-,NE + b 9GR0 + y (2 ) i=l 1 1 1 2 where n = 16 and the r^’s are estimates of the gross yields on the elements in the bank’s loan portfolio. 2 Recognizing the wide range in the sizes of the banks in the sample, this equation was tested for heteroskedasticity. The most likely cause of heteroskedasticity is the size dispersion of the banks in the sample, which was preliminarily substantiated by an analysis of the residual plot. The Goldfeld-Quandt test was performed by sorting the sample into ascending order according to asset size and then dividing it into three groups: tively). small, medium, and large (76, 56, and 83 observations, respec Comparing the adjusted error sum of squares for the large group with the adjusted error sum of squares for the small group, heteroskedasticity was found to be present (F = 11.996). The finding of heteroskedasticity in the residuals indicates that this equation is not an efficient estimator of the regression coefficients and must be respecified. Since bank size appears to be the cause of the misspecification, the remedy chosen is to deflate all variables in equation (2) by total assets. Thus the general form of the normalized Some loan categories, as noted in Table II, were combined because they comprised a very small proportion of the balance sheet. -7- equation to be estimated becomes: 16 A LNREV/TA - a(1.0/TA) + Z r,(L,/TA) + b,(NE/TA) + b,(GRO/TA) + e i=l 1 * requiring the reciprocal of total assets (1.0/TA) be included in the new equation with the dependent variable being interpreted as loan revenue per dollar of total assets. Reciprocal of Total Assets (1.0/TA) - There seems to be agreement that larger banks tend to make larger loans at lower interest rates. If so, this variable should be positively related to loan revenue per dollar of assets (+). Since total assets is not specified as an independent variable in equation (2), Ta ’ becames the coefficient of the reciprocal of total assets and there is no intercept term in equation (3). Total assets was considered as an explanatory variables in equation (2) but rejected as it could be collinear with a number of the loan portfolio components resulting in unreliable estimates of their coefficients. When tested for heteroskedasticity, equation (3) showed no evidence of this problem (F = .320). Estimates for the competitive yields on sixteen loan categories are found in Table II. Most have high t-statistics and seem to be reasonable estimates, with the exception of the rate on mobile home loans which appears lower than one might expect. The years 1974, 1975, and 1976 were, however, marked by rather high delinquency and default rates on this type of loan, a fact that could explain at least in part the small size of this coefficient. The structure variables GRO and the reciprocal of total assets both enter the equation with the expected sign, the former being significant at the .01 level (two-tail test) and the latter being significant at the .05 level (one-tail test). (3) - 8- The concentration variable, numbers equivalent (NE), included to represent a summary measure of concentration taking account of both the number and size distribution of the firms, has the expected sign but is not statistically significant. Alternative specifications were tried using the Herfindahl Index and also the market share held by each bank. In both cases these variables had the predicted sign, but were not statistically significant. Estimating loan revenue. The procedure for the calculation of the loan revenue for each bank is predicated on the rearrangement of the 16 terms in equation (3) to solve for the expression E r.L.. Since the 16 . i=l 1 adjustment is not entirely straightforward, E r.*L. is substituted for 16 . i-1 1 1 E r.L as the amount of loan revenue per bank to be included as part of i=l 1 1 bank output. 16 * l ri*L± = (LNREV^/TA _.)TA_. - a(l. 0/TA JTA.. - where j = 1,...,208. (GRO/TAj)TA^ (4) Numbers Equivalent (NE) is omitted from the adjust ment since its coefficient is not significantly different from zero. Calculating bank output. As indicated earlier, bank output, 16 ~ (OUTPUT), is defined as the summation of the three items: E r.*L., the 1=1 1 1 calculated loan revenue for each bank, plus the revenue from securities 3 (SECREV), plus the revenue from other sources (OTHREV). Revenue from securities is assumed to be determined in a nearly competitive market, while the components of OTHREV individually comprise a very small per centage of total bank output. Although there could be some monopoly influences operating in these components, the complexities and problems involved in accounting for this influence are prohibitive. Thus, bank output is viewed as the value of credit extended plus the value of other services performed by the bank. ^For the definition of OTHREV, see footnote 1. -9- The Model The form of the model selected here as the mode of investigation is a cost function of the Cobb-Douglas type. In its logarithmic form this function has a long history of successful application in the empirical analysis of the cost and production relationships of firms in a wide variety of industries. This equation takes the general form: tc - k q1/nra/nw e/n where k = n(aaag^) (5) q = output, r and w are the prices of two different inputs, and n = a + g. When converted to logarithms equation (5) becomes: TC = K + (l/n)Q + (a/n)R + (£/n)W (6) where the capital letters denote the logarithms of the lower case 4 letters in equation (5). It has been shown by Shephard and Uzawa that there is a unique relationship between the cost function as estimated here and its underlying production function; namely, these are two different, but equivalent ways of looking at the same thing. Two conditions must be met, however. Cost minimization on the part of the firm must be assumed and the prices of the inputs must be included in the cost function. There are several advantages to the Cobb-Douglas specification of4 4 Nerlove [18, p. 107]. The derivation of the cost function from the production function has had wide exposure in a large variety of literature; consequently this derivation will not be presented here. See, among others, Bell and Murphy II], Nerlove [18], or Wallis [25]. -10- the cost function. First, it is log-linear with respect to output and the input prices, so that the coefficients can be interpreted as elasticities, although a disadvantage is that these coefficients are constant over the range of observations of the sample. Second, this functional form can accommodate increasing, decreasing, or constant costs and often, erroneously, an estimate of the degree of homogeneity of the production function (returns to scale) is derived by taking the reciprocal of the coefficient of the output variable.^ Last, this form also tends to reduce heteroskedasticity in the data. Cost of loan output. The definition of the dependent variable, the cost of loan output (CLO), for the banks as employed in this study is the same as that used by Schweitzer [21], namely, the "bank’s total operating expenses, less service and exchange charges on deposit accounts" (p. 259). These charges are a reimbursement of the costs incurred in acquiring one of the inputs (demand deposits), and repre sent an approximation, although admittedly a deficient approximation, of the costs incurred by the bank in clearing checks. To the extent clearing costs actually exceed these charges, they should be included in the cost of loan output. While this definition can be criticized, It is frequently stated that the reciprocal of the coefficient of the output term represents the degree of homogeneity of the pro duction function. For example, an output coefficient of .944 supposedly implies a production function homogeneous of degree 1.059. If the error term, e, has a log-normal distribution, and the usual assump tions about the error term are made, the regression coefficients are unbiased, efficient, and consistent. Taking the reciprocal of the regression coefficient, however, involves a non-linear operation which does not result in an unbiased estimate of n since E(l/b) does not equal 1/E(b). See Wallis [25]. -li the alternatives appear less desirable. Independent variables. The output variable (OUTPUT) is defined and calculated in the previous section. Several other variables are hypothesized to play a role in determining bank costs. As indicated, the prices of inputs must be included to maintain the unique relation ship between the cost function and the production function, despite the fact that their inclusion in other studies has not shown them to have a significant impact. Unfortunately, the prices of only two inputs, time and savings deposits and labor, could be approximated with any degree of accuracy. Price of Time Deposits (PRIDEP) - Calculated by dividing total interest paid on time and savings deposits by total time and savings deposits. The average rate of interest should be positively related to the cost of loan output (+). Price of Labor (WAGE) - Calculated by dividing total salaries by the number of employees. This variable should also be positively related to the cost of loan output (+). Because no estimate of nor proxy for the price of capital could be found, it is assumed constant over the sample of banks. Another factor considered potentially important in influencing bank costs is whether the bank is located in an SMSA: SHSA - An intercept dummy with a value of 1 if the bank is in an SMSA, 0 otherwise. If competition is greater in SMSAs than in non-SMSAs, banks located in SMSAs may be required to make larger expenditures for advertising or they may be required to offer more services, or both. This variable should be positively related to total cost (_+). Of the 208 banks included in this study, 66 are affiliated with a bank holding company; thirty-three are owned by one-bank holding companies (OBHC) and a like number are subsidiaries of multibank holding -12- companies (MBHC). As there is no a priori reason to anticipate that similar traits will characterize both types of affiliates, the sample is grouped by the form of organizational structure: independent, OBHC affiliates, and MBHC affiliates. To test whether the organizational form has any impact upon the scale economies of the individual bank, a multiplicative dummy variable is introduced for each type of holding company affiliate. OBHCD = (OUTPUT • D) where D takes on a value of 1.0 for affiliates of onebank holding companies and zero otherwise and MBHCD = (OUTPUT • D) where D takes on a value of 1.0 for multibank affiliates and zero otherwise. Consequently, the coefficient of the output term (OUTPUT) represents the elasticity of cost with respect to output for independent banks. The coefficients of these multiplicative dummy variables measure the magnitudes of the differential scale effects attributable to the different organizational forms. In addition, the coefficient of either slope dummy can be combined linearly with the coefficient of the output variable. A t-test can then be performed on the resultant coefficient to determine if it is' significantly different from unity, thereby implying economies or diseconomies of scale. The significance test for a linear combination of the regression coefficients takes the form: s w* (X'X)"^ with w Tb representing the sum or difference of the two coefficients under consideration. In this instance the null hypothesis is that W q = unity, subject to a two-tail test. See Theil [23, p. 138]. -13- The final factor taken into account is the impact of branching upon the costs of the individual bank. BR^ - Five intercept dummy variables with a value 1 for each branch up to five with BR^ representing five or more branches. Branch offices should increase the cost of operations for the individual bank through increased overhead and problems that arise coordinating the operations of multiple offices. This variable should be positively related to total cost (+).^ The cost function thus takes the form, log CLO = a + b-^log OUTPUT + b2log PRIDEP + b3log WAGE + b ^ M S A + b5MBHCD + b6OBHCD + byBRl + bgBR2 + bgBR3 + b1()BR4 + bj^BR^ + e with a = log 1a f and incorporating the prices of all omitted factors of production. The regression coefficients represent elasticities and the error term, e, is assumed to be independent and normally distributed with 2 a mean of zero and a constant variance, a . The Results The regression results for the total sample and for the five subsamples are presented in Table III and Table IV. The adjusted coefficients of determination suggests that for the entire sample and the subgroups both specifications do a good job in explaining the variation in total cost. The following discussion will center around Table III and will first focus upon the total group and then upon the subgroups. An alternative specification is to include only one intercept dummy variable with a value of 1 if the bank has branches, 0 otherwise. These regression results are shown in Table IV. As can be seen, alternative specification does result in some change in the other variables, but does not alter the basic conclusions. -14- The Total Sample* The overall equation gives evidence that there are statistically significant, but not substantial, economies of scale accruing to independent banks over the range of observations• The scale coefficient of .944 implies that there are increasing returns to scale for the production function. The equation also suggests that banks located in SMSAs tend to incur higher costs than non-SMSA banks. As indicated, this could be due to greater competition necessitating greater advertising, more (free) services or both. Examination of the branching dummies indicate that banks with three or more branches tend to have higher costs than banks with fewer than three branches. The branching dummy in Table IV suggests, however, that banks with branches, in general, have higher costs than do banks without branches. Since the coefficient of the multiplicative output dummy variable, MBHCD, is positive and significantly different from zero (although mar ginal at the 10 per cent level), it appears that banks belonging to multibank organizations have a smaller degree of scale economies than do independent banks. When the coefficients of OUTPUT and MBHCD are com bined linearly (.944 + .015 = .959), the resulting coefficient is signi ficantly different from unity (t = 4.074). This means that multibank affiliates, for the total sample, are characterized by decreasing costs but the scale coefficient is closer to unity than that of independent banks. In contrast, the multiplicative dummy representing one-bank affiliates is not significantly different from zero, but the test on the linear combination of the coefficients of OUTPUT + OBHCD (.944 + .003 = .947) indicates the resultant coefficient is significantly different from unity -15- (t = 4.291). One-bank affiliates, therefore, share the same production function as independent banks. Small and Medium Small Banks. to scale seem to prevail. For Groups A and B, constant returns Representing output up to approximately $3.7 million and assets up to $50.0 million, the scale coefficient of neither group of banks is significantly different from unity. Also, neither of the dummy output variables is significantly different from zero for either group. When the coefficient of the dummy output variables are combined with the output coefficient and tested, none are found to be statistically different from unity. Thus the two smallest size classes appear characterized by a cost function exhibiting constant costs, regardless of organizational structure. Medium Banks. esting properties. The medium size group, Group C, shows some inter The scale coefficient indicates that independent banks are recipients of rather substantial scale economies with an elasticity coefficient of .868 implying a production function char acterized by increasing returns. Furthermore, the model indicates that banks in this group located in SMSAs incur significantly higher costs than do non-SMSA banks. The coefficient of the output dummy for multibank affiliates, while not significantly different from zero, is statistically different from unity when combined linearly with the coefficient of OUTPUT (t = 2.460). This indicates that multibank affiliates and independent banks in this size class share the same production function. The coefficient of OBHCD, on the other hand, is statistically different from zero and when combined with the output coefficient shows that one-bank affiliates display greater scale economies than do independent banks (t = 3.394) -16- and thus do not share the same production function. Medium Large Banks. The regression results from the medium large group, Group D, give evidence of some economies of scale accruing to independent banks (.902) although less than that for medium size banks. The production function is therefore subject to increasing returns. With regard to the other explanatory variables the price of time and savings deposits (PRIDEP) takes on statistical significance for the first time and has the correct sign. The dummy variable denoting banks with five or more branches (BR^) is also statistically significant and indicates that these banks tend to have higher costs. In addition, Table IV suggests that medium large banks with branches tend to have higher costs overall. Neither of the two output dummy coefficients is statistically different from zero, but, when added to the output coefficient, both are different from unity. This indicates that multibank and one-bank affil iates have the same elasticity of cost with respect to output as do independent banks (t = 1.915 and t = 1.778, respectively). Large Banks. The last group, Group E, represents banks larger than $200 million in assets and $13 million in output. These banks are characterized by constant costs since the output scale coefficient is not significantly different from unity. As might be expected with banks of this size* all are located in SMSAs and consequently this variable is not included in the equation. The branching dummies suggest that large banks with branches do not incur higher costs until the number of branches is at least five, although this is still not a statistically significant difference. Once again, however, the branching dummy in Table IV indicates that large banks with -17- branching systems have significantly higher costs than do large banks without branching systems. The reconciliation of these results is not completely apparent. The multiplicative dummy output variables, when combined with the output variable for independent banks, are not significantly different from unity. Thus it appears that the production function is essentially the same for all banks in this size class, regardless of whether they are independent or affiliated with a one-bank or a multibank holding company, and that this cost is characterized by constant costs. Summary and Conclusions Least squares estimates of the scale coefficients in this study indicate that some moderate economies of scale are exhibited by inde pendent banks, but that these economies manifest themselves primarily in the medium and medium large banks. The more important question hinges on the impact of affiliation upon the cost functions of banks and whether the introduction of scale economies can be considered as a possible offset to any anticompetitive consequences inherent in the acquisition of a bank or the formation of a bank holding company. This question rarely arises in the case of one-bank holding com panies, by their very nature. Nevertheless, by way of recapitulation, it appears that one-bank holding company affiliates do not, with a single exception, have cost functions significantly different from those of independent banks. The exception is the case of medium size banks, where affiliates exhibit greater scale economies. Since total operating costs, as defined here, do not include taxes, this result cannot be -18- attributed to any tax advantage accruing from the holding company form of organization. It could be attributable to greater diversification or specialization on the part of the holding company, but this assumes that holding companies participate in a larger number of nonbank activities than do independent banks. 8 For banks belonging to multibank holding companies the situation is completely different. The question of whether inherent anticompetitive effects can be offset by scale economies takes on a premiere role. The evidence found here suggests that, overall, multibank affiliates actually have a scale coefficient closer to unity than do the other two organizational forms. Medium and medium large affiliates in particular exhibit scale economies but only to the degree as independent banks. It would thus appear that the often voiced argument that some economies of scale can be achieved through affiliation which are not available to independent banks is without foundation. At best, the affiliate can only expect to achieve the same degree of scale economies. The concept of minimum optimal scale is a crucial one for microeconomic theory and for industrial organization in particular. Analysis of the subgroups presented in Table III indicates that long-run total cost is increasing less than proportionately to output only in the medium and medium large groups. Since the output coefficients for these two groups are approaching unity from below, and since the output coefficient for the large group is not significantly different from unity, it appears This assumption is not as obvious as it might first appear, since national banks, and probably many state banks, can participate in nearly all the nonbank activities that holding companies can, and some that holding companies cannot. See [Drum]. -19- that long-run average cost reaches, a minimum, and thus minimum optimal scale is achieved, somewhere in the upper range of the medium large group (i.e., around $200 million in assets). This conclusion holds regardless of the organizational form under consideration. The estimate for the overall scale economies for unit banks is quite similar to that found by both Bell and Murphy [1] and Schweitzer [2l] and is close to that found by Mullineaux [17], although another study by Mullineaux [15] found substantially greater scale economies. Comparison of the subgroup results with other studies is not possible as there are no other studies with comparable subgroups. While the evidence here indicates that the cost curve for multibank affiliates lies above that of unit banks, which is consistent with the findings of Kalish and Gilbert [13], it contradicts, in part, the findings of Schweitzer [21], who found that banks belonging to large bank holding company groups incur lower costs than do independent banks. Mullineaux [17] found that affiliation with a group increases the costs of branch banks but leaves the costs of unit banks unchanged. Last, whether a bank has a branching system or not appears to play an important role in explaining the costs incurred by banks in general and medium large and large banks in particular. Since this coefficient is positive in all cases, it indicates that there are some organiza tional diseconomies associated with branching, a finding consistent with a number of other studies. Since this sample is drawn from states allowing only limited branching or limited service branching, this conclusion cannot be extended for cases involving statewide branching. -20- TABLE II ESTIMATE OF LOAN REVENUE EQUATION 1 Variable Loans for Construction Loans Secured by Farmland Residential Real Estate Loans - Single and Multi-Family, Insured Residential Real Estate Loans - Single and Multi-Family, Conventional Nonfarm, Nonresidential Real Estate Loans Loans to other Financial Institutions (Including REIT and Mortgage Companies) Loans to Farmers Commercial and Industrial Loans Automobile Loans Loans for Credit Card and Revolving Credit Plans Mobile Home Loans Loans for Other Retail Consumer Goods Loans for Repair and Modernization Other Instalment Loans Single-Payment Loans All Other Loans^ Reciprocal of Total Assets Growth Number of Equivalent -2 R Standard Error F d.f. Coefficient t-Value .0868 .0955 4.566 8.085 .0795 3.317 .0815 .0861 26.504 12.436 .0500 .0640 .0807 .0964 .1626 .0544 .1117 .0681 .0988 .0649 .0499 2.173 20.264 24.877 13.657 9.691 4.085 5.660 3.606 7.258 8.223 3.839 .0388 -.0005 -.0012 1.875 3.078 .480 .9957 .0029 2546.0 189 ^All loan categories are taken as a percent of total assets. 2 Comprised of the categories: All Other Loans, Loans to Domestic Commercial Banks, Loans to Banks in Foreign Countries, Loans to Brokers and Dealers in Securities, and Loans for Purchasing and Carrying Securities. -21TABLE III ESTIMATED COST FUNCTION FOR ALL BANKS AND SUBGROUPS Variables Intercept OUTPUT* ALL BANKS GROUP A GROUP B GROUP C GROUP D GROUP E .009 (.105) .175 (.547) .084 (.272) -.040 (.264) -.188 (.799) -.186 (.366) .944 .861 (5.914)° (1.645) 1.021 (.236) .868 (2.809) b .902 (1.867)b .938 (1.068) PRIDEP -.070 (.783) -.153 (.576) -.373 (1.011) .176 (.942) .212 (.770) .179 (.324) WAGE -.008 (.199) 0.113 (.715) .103 (.907) -.080 (1.111) .035 (.422) .039 (.224) SMSA .019 (3.167)a -.011 (.336) .023 (1.459) .028 (3.087)a -.002 (.121) MBHCD .°15 (1.667; .625 (1.574) .039 (.590 .012 (.672) .001 (.031) .012 (.764) OBHCD .003 (.355) -.859 (.929) .089 (1.130) -.°30 (1.962)b -.002 (.137) .005 (.289) BR, X .011 (1.447) br2 .003 (.266) BR„ .°19 (1.907)b BR, .029 (2.166)b — BR .035 (3.480)b ____ j 5 .021 (.540 .008 (.480) .012 (1.007) .010 (.733) .053 (1.598) .064 (1.448) .007 (.285) -.012 (.919) .025 (1.038) .019 (.426) .064 (.835) .010 (.356) .020 (1.481) .016 (1.112) .002 (.047) .049 (1.366) .014 (.765) .026 (1.327) .023 (.608) ____ .024 (1.775)b .039 (2.265)b .035 (1.725) R" .990 .909 .784 .860 .930 .973 SEE .038 .052 .045 .034 .024 .028 1887.2 31.0 17.7 44.0 40.6 73.8 18 36 66 22 10 F d.f. 196 Significant at the .05 level (one-tail test). ^Significant at the .10 level (two-tail test). cTested gainst the null hypothesis that b-^ = 1.0. Figures in parentheses are t-ratios. -22- TABLE IV ESTIMATED COST FUNCTION FOR ALL BANKS AND SUBGROUPS GROUP A GROUP B GROUP C GROUP D GROUP E .020 (.239) .185 (.757) .021 (.075) -.044 (.289) -.301 (1.410) -.391 (1.324) .951 (5.291) .869 (1.663) 1.033 (.412) .878 (2.601)b .904 (2.069) .964 (.806) PRIDEP -.075 (.829) -.154 (.695) -.275 (.806) .188 (1.019) .404 (1.731) .369 (1.080) WAGE -.020 (.477) -.125 (.980) .090 (.866) -.093 (1.302) .018 (.232) .074 (.568) SMSA .019 (2.997)a -.004 (.172) .025 (1.604) .030 (3.244)a -.012 (.905) MBHCD .°16 (1.801)° .642 (1.681) .026 (.419) .013 (.739) -.001 (.108) .003 (.205) OBHCD -.001 (.068) -.834 (.958) .086 (1.134) -.032 (2.152)b .002 (.152) .005 (.362) .015 (2.589)b .041 (1.383) .011 (.788) .019 (2.141) (2.265) Variables Intercept OUTPUT* BRANCH ALL BANKS .011 (1.250) -2 R .990 .914 .793 .855 .943 .978 SEE .038 .051 .044 .034 .023 .025 2892.8 42.2 26.2 65.8 68.1 149.6 20 39 70 26 F d.f. 200 Significant at the .05 level (one-tail test). 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