Productive Efficiency in Commercial Banking: The Effects of Size and Legal Form of Organization On the Cost of Producing Demand Deposit Services Author(s): William A. Longbrake and John A. Haslem Reviewed work(s): Source: Journal of Money, Credit and Banking, Vol. 7, No. 3 (Aug., 1975), pp. 317-330 Published by: Ohio State University Press Stable URL: http://www.jstor.org/stable/1991625 . Accessed: 07/10/2012 13:28 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp
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http://www.jstor.org Electronic copy available at: http://ssrn.com/abstract=2165010
WILLIAN1A. LONGBRAKE and JOHN A. HASLEN1*
ProductiveEfElciency in Commercial Banking TheEffectsof SizeandLegalFormof Organization OntheCostof ProducingDemandDepositServices Important changes are occurring in the structure of the commercialbanking industry as witnessed by the rapid expansion of branchbanking and the growth of one- and multi-bankholding companies. In regulatedindustries, such as banking, public interest considerationsdictate that these structural changesshould be guidedto protect the viability of the bankingsystem while at the same time preservingcompetition and promotingproductiveefficiency. However,if economies of scale are importantin the production of bankingservices,maximization of productive efficiency, by encouragingthe growth of a few relativelylarge institutions, may not be consistentwith a competitivemarketstructure.Therefore, from the regulatorypoint of view it is importantto have informationabout the effects of bank size and legal form of organizationon competition and productive efficiency. Suchinformationcan be used to determinethe type of bankingstructure which will promote productiveefficiency without adverselyaffecting competition. This study examines the effects of bank size and legal form of organization(unit, branch, and holding company) on the cost of producingdemand deposit services. *The authorswish to acknowledgethe help Neil B. Murphyprovidedin initiatingthis study. Discussionswith RobertA. Eisenbeisand Manferd0. Petersonwere most helpful. This researchwas supported,in part, by a grant to ProfessorHaslem from the Bureauof Businessand EconomicResearch,Universityof Maryland.The analysesand conclusions,however, are those of the authorsand should not necessarilybe attributedto the individualsmentioned above,the FDIC,or the bureau.
WilliamA. Longbrakeis senior planningspecialist, Office of CorporatePlanning, Federal Deposit Insurance Corporation.John A. Haslem is associate professor of finance, Collegeof Businessand Management,Universityof Maryland.
Electronic copy available at: http://ssrn.com/abstract=2165010
318 : MONEY,CREDIT, AND BANKING
Servicingdemand deposits is one of the more important productive activities of commercialbanking. In section 1, a methodology is developed for handling the complexities of the cost-output relationshipin the commercialbankingindustrywithin the framework of a statisticalcost function derivedfrom a Cobb-Douglasproductionfunction. The parametersof the statistical cost function for demand deposits are estimated and the results are discussedin section 2. In section 3, the effects of bank size and legal form of organizationon the costs banksincurin producingdemanddeposit services are evaluatedby simulatingaveragecosts for given sets of conditions. I. METHODOLOGY
Numerous studies of productive efficiency have been conducted for the commercialbankingindustry.l The methodologiesused in these studies are diverse,and the conclusions reached have frequently been inconsistent with each other.2 The inability of these studies to handle completely the complexities of production in bankingis responsiblefor their inconsistenciesand contradictoryconclusions.The traditional theory of production has been developed principally for single-plant firms producingone homogeneousproduct. However,in bankingthere are multiple plant firms (not to mention multiple-firmorganizations)producingmultiple, nonhomogeneous products. Although some theoretical developmenthas occurredfor the multiple-productfirm,3 very little has taken place for the multiple-plantfirm. Thus, theory offers little help for handlingthe cost-outputrelationshipin banking. The chief difficulty lies in how to define a measureof output that is sensitiveto the production of several nonhonlogeneous products produced by a firm operating severalplants. This difficulty is compoundedfurtherbecausebanksproduceservices which, because of their intangibility,are not directly measurable. Bell and Murphy[1, pp. 12-20] have demonstratedthat under certainconditions, which seem reasonablefor banking [1, pp. 21-34], a cost function can be derived from a Cobb-Douglasproductionfunction havingthe following generalform: C= GQl/l' rall' wPll'
(1)
where C= total direct operatingcosts allocatedto demanddeposits G = r/Fll ll} p/^> Q = quantity of demanddeposit services r = price of physicalcapital lSee Benston [3, pp. 312-41] for a reviewof existingcost studiesof the commercialbanking industry.See Borts [4, pp. 4I9-21] for a critiqueof this review. 2For example, determinationof whetherthe productionof bankingoutput is accomplished more efficiently by branchbanks or unit banks appearsto dependcruciallyupon the methodolo3gyusedAlthoughseveralstudieshave appearedwhich deal with the theory of the multiple-product firm, the ones with the greatestrelevancyfor the cost-outputrelationshipas it is consideredin this study are those by Mundlak[11] andWeldon[ 13] .
LONGBRAKEAND HASLEM : 3 19
w= averageannualwagerate = the returnsto scaleparameter og= elasticityof outputwithrespectto capital ,B= elasticityof outputwithrespectto labor productionfunctionconstant. F = Cobb-Douglas v
Manydifferentmeasuresof the outputof bankingserviceshavebeenproposedin previousbankingcost studies.For example,Benston[2] andBellandMurphy[1] [6] useda weightedindex measuredoutputas the numberof accounts;Greenbaum of total revenue;Horvitz[7] usedtotal earningassets;and othershaveused total deposits.In all of thesestudies,it hasbeenassumedthatthe outputof servicescan givento whether by a singlemeasurewithoutmuchconsideration be approximated this single measureis appropriatefor definingthe cost-outputrelationshipin services.Before firmsproducingseveraltypes of nonhomogeneous multiple-plant the. output of services,the natureof the proposinga measurethat approximates firmsis discussed. multiple-plant in multiple-product, cost-outputrelationship firmis independentof If the productionof eachproductin a multiple-product the productionof every other product,a separateproductionfunctioncan be specifiedfor eachproduct.4However,the productionof severalproductsordinarily Althoughthe quantitiesand costs of someof the factorsof occurssimultaneously. productionarelinownforeachproduct,otherfactorsarecommonto simultaneous production,and the cost of utilizingthesefactorscannotbe assignedaccuratelyto a methodfor the outputof individualproducts.5Johnston[8, p. 92] summarizes testing the hypothesisof independentproductionfunctionsin multiple-product firms.The hypothesisis supportedwhen productioncosts for one productare withan indexof the outputof all otherproducts(interactionvariable) uncorrelated giventhatthe outputof the productin questionis heldconstant.6 it maybe ppssibleto constructa weightedindexof outputin firms Alternatively, severalproducts.Whenan outputindexis constructed,it is not necessary producing to be concernedabout the allocationof productioncosts to specificproducts. However,the indexmustbe insensitiveto changesin productmix fora givenlevel output.It mustalsobe adjustedfor differencesin factorpricesandfor of aggregate index marketvariationsin productprices.Mostempiricalstudiesusinganaggregate an indexthatis free of outputhavenot been completelysuccessfulin constructing andthe difficulof bias.7Becauseof the complexityof the cost-outputrelationship [1] relyonthisassumption. 4senston[2] andsell andMurphy costs. production of common [13] fora discussion 5SeeWeldon andits loancostfunctioIl in hisbusiness variable an interaction 6senston[2] included loanservices of business betweentheproduction interaction significant indicated parameter andloanservices. of otherinvestment andtheproduction in problem of theaggregation description [11, pp.433-36]fora complete 7SeeMundlak [6] usedfixedprices firm.Greenbaum anoutputindexforthemultiple-product constructing thattheindividual he didnotdemonstrate however, output; anindexof banking to construct asthey werehomogeneous to whichthefixedpriceswereapplied of eachproduct measures thattheoutputindex [1] argued sell andMurphy mustbe if theoutputindexistobereliable. unique requires service typeof banking of eachgeneral theproduction because is inappropriate production alsothattheseparate It canbeargued andcapitaL labor, of resources, combinations the because functionapproach production is betterthanthe aggregate functionapproach of coststhanthelatter. aboutthebehavior information inmoredetailed results former
3 20 : MONEY,CREDIT, AND BANKING
ties of constructingan appropriateaggregateoutput index, demanddeposit services will be treated as a separateproduct. However,an interaction variablewill be included in the cost function to test the hypothesis of independence. Multiple-plantfirms can increaseoutput either by expandingexisting plants or by building new plants. The choice should depend on which method of expansion is least costly in the long run. (The choice may depend also on marketstructureand the demand for banking services.)Increasesin plant size may facilitate the implementation of greater division and specialization of labor or the utilization of improved or advancedequipment and technology, all of which may contributeto the realization of lower averagecost per unit of output. Increasesin the number of plants may facilitate the centralizationof some productionactivitiesin some plants and other production activities in other plants and in so doing achieve similaradvantages from the division and specialization of labor and the utilization of advanced technology. However, the economies realizedfrom increasesin plant size or from increasesin the number of offices may be offset by increasesin coordination, communication, and transportationcosts. If the organizationof production in a multiple-plantfirm does affect production costs, the measureof output must take this possibility into account.8 The complexities of production in a multiple-plantfirm producingseveralnonhomogeneous products suggest that output may be representedbetter by several variablesthan by the customary single variable.For example, total deposits is an approximatemeasureof output, but as the measureof output, it may not servewell in explaining the cost-output relationship.9 However, three dimensions of total deposits can be distinguishedwhich may enable the total deposits measureof output to servebetter in explainingthe cost-output relationship: Q = D = NSf,
(2)
where D equals total deposits, N equals the numberof deposit accounts per office, S equals the averagesize of a deposit account, and ¢ equals the numberof offices. The averagesize of account is a representativemeasureof the type of depositorand allows for the possibility that different types of depositors will consume varying amounts of services per dollar of deposits. The two variablesN and ¢ reflect dif8Both Benston [2] and Bell and Murphy [1] attempted to handle organizational arrangements in banking by using dummy variables for differing numbers of branch offices to permit the cost function constaIlt to shift. A problem with their approach was that one dummy variable was defined for all banks with five or more branch offices. Greenbaum [6, p. 427] defined a branch-code variable which took on values from 0 to 9 depending on the number of branches operated by a bank. Several of the codes apply to a range in the number of offices. For example, the cost of going from one to two branches is presumed to equal the cost of going from 20 to 50 or more branches. The methods employed in these studies do not deal effectively with the organization of production in multi-plant firms and its effect on operating costs. Other studies dealing with costs in unit and branch banks have been no more effective than those cited above in handling the cost-production relationship and multi-plant firms. For an elaboration of these criticisms, see Longbrake and Haslem [ 10] . 9Total loans or total assets could be substituted for total deposits as an approximate measure of output without materially affecting the explanation of the relationship between the organization and production of output and the costs of production.
LONGBRAKE AND HASLEM : 3 2 1
ferences in the organizationof productionin a multiple-plantfirm, and the variable S reflects nonhomogeneityin the output of deposit services. Equations(1) and (2) imply that Ql/l)
= N1/I}
sl/l}
¢81/IJ
(3)
Equation (3) states that an increasein the volume of deposits througha changein the averagenumber of accounts per office, the averagesize of an account, or the number of offices causes the same change in costs regardlessof how the changein deposits is accomplished.However, if changesin office size (N), changesin type of depositor (S), and changes in firm structure(¢) affect costs differently, then the scale parametersof N, S, and ¢ will not necessarilybe equal and equation (3) will not be the proper method for specifying output in the cost function. The more generalcase of equation (3) would allow the scale parametersto be unrestricted: Ql/l}=ff6l
S62
¢63.
(4)
The unrestrictedscale parametersin equation (4) are defined as follows: 1. Account-quantity (plant-size)effect (6 1)-the percentagechange in operating costs caused by a given percentagechange in the averagenumberof accounts per office when the averagesize of an account and the number of offices remain unchanged. 2. Account-size (type of customer) effect (62)-the percentage change in operating costs causedby a givenpercentagechangein averageaccount size when the averagenumber of accounts per office and the number of offices remain unchanged. 3. Firm-structureeffect (63 )-the percentagechangein operatingcosts caused by a given percentagechange in the number of offices when the averagenumber of accounts per office and the averagesize of an account remainunchanged. The parametersin equation (4) can be interpretedin the same way as 1/r, the economies of scale parameter(r is the returnsto scale parameter),for Q in equation (1). Values of the parametersassociatedwith the three components of deposits which are greaterthan one indicate diseconomies of scale with respect to account quantity, account size, or number of offices (firm-structure),while valuesless than one indicate economies of scale with respect to account quantity, account size, or numberof offices. Therefore,three concepts of scale, not one as has been presumed, may be relevant for explaining the relationship between output and the cost of producingit. It is possible that differencesbetween types of customersmay not be captured completely by the averagesize of account variable.As a consequence, it may be useful to consider a secondaryset of output homogeneity variableswhich contain more detailed information about differences in customers than can be providedby
322:
MONEY,CREDIT, AND BANKING
averageaccount size.l° lShesecondaryvariablesare defined as those variableswhich reflect deviations from the averagequantity of services,as representedby the three componentsof deposits, when specific changesoccur in the types of customers. The statistical cost function, presented in equation (5), substitutes equation (4) for Qlll' in equation (1), adds the secondaryset of output homogeneity variables, and includes an interaction variable,I, to test for cost interrelationshipsbetween the production of demand deposit services and the production of other banking services: C = HN61
S62
¢63
ACTQ1 MQ2Wp/> IP eu
(S)
where
H
= Ge/V 11
N
= the average number of demand deposit accounts per office and is the variableselected to representplant size S = the averagedollar balance in a demanddeposit account and is the variable selected to representthe type of customer ¢ = the numberof bankingoffices andis the variableselected to representElrm structure ACT= a weighted index of home debits, deposits, transit checks, and checks cashed and was selected to reflect deviationsfrom the averagequantity of services consumed by a customer (due to variationsin account activity) which are not explainedby S,12 M = the ratio of the number of regularchecking accounts to total checking accounts and was selected to reflect deviations from the averagequantity of services consumed by a customer (due to differences in accountmix) which are not explainedby s,l3 I = the ratio of the dollar volume of demanddeposits to the dollarvolume of total deposits,l4 u = a disturbanceterm. l°Bell and Murphy's [1] output homogeneity variables served a purpose similar to that proposed for the secondary variables in this study. l Although data may exist which permit the calculation of the price of physical capital for a bank, such data were unavailable. It seems plausible to assume that there is little variation in the price of physical capital among banks because the marketing of equipment is conducted by nationally based firms. If such an assumption is valid, the price of capital may be impounded in the cost function constant. l2The procedure for calculating activity weights is described by Murphy [12] and Longbrake [9] . The weights were based on the marginal costs of each type of activity item. Home debits were assigned a weight of 1.0000. Weights of the other activity variables were set relative to the weight of home debits. The weights are 4.5680 for deposits, .6965 for transit checks, and 2.0283 for checks cashed. Each activity item was then multiplied by its weight and the results were summed to form the activity variable. l3The parameter of the mix variable indicates the change in costs when a special checking account is replaced by a regular checking account with exactly identical characteristics. A regular account has a minimum balance requirement; a special account usually does not. 14If banks have been able to allocate costs accurately to the proper general categories of services, there should be no effect on direct operating costs for demand deposits when the volume of time deposits changes. This means that the coefficient of the interaction variable
LONGBRAKEAND HASLEM : 3 23
Data for estimating the parametersof equation (5) were obtained from a sample of 967 banks which participatedin the Federal ReserveBanks' 1968 Functional Cost Program.Sample banks represent7.1 percent of all banks in existence at the end of 1968. With respect to the four legal forms of bank organizationwhich are consideredin this study, 367 or 3.8 percent of existing unit nonaffiliatesof holding companies,452 or 13.2 percent of existing branchnonaffiliates,76 or l9.i percent of existing unit affiliates of holding companies,and 72 or 29.2 percent of existing branch affslliatesare representedin the sample. Unit nonafElliatesare underrepresented while branchnonaffiliatesand holding companyafElliatesareoverrepresented in the sample relativeto the proportionsof all existirlgbankswhich have these legal forms of organization.EIowever,this does not present any difficulty because separate cost functions are estimated for bankswith each form of legal organization. Banks in the Northeastern United States are more heavily representedin the sample and banks in the Tenth Federal ReserveDistrict are not represented.As a rule, the largera bank was the more likely it was that it participatedin the Functional Cost Program.fIowever, enough small banks participated so that the $5 million to $5 billion size rangein total deposits is adequately representedfor purposes of statistical estimation. Although the Functional Cost banks do not constitute a truly random sample, the coverage of the sample with respect to legal form of organization,geographicallocation, and size is adequate and the detail of the data is sufficient to permit conclusions to be reachedwhich fairly reflect the generalbehaviorof the bankingindustry.
II. STATISTICALRESULTS
Equation (5) was transformedby taking logarithms and the parametersof the transformed equation were estimated by means of ordinary least squares. The regressionresults for the demand deposit statistical cost functions for banks belonging to each of the four legal forms of organizationand for all banks are shown in Table 1.l5 The regressioncoefficients of log N, log S, and log ¢ measurethe magnitudes of the account-quantity, account size, and firm-structureeffects, respectively.The magnitudesof these coeff1cientsrelativeto unity indicatewhether economies or diseconomies of account quantity, account size, or firm structure occur. Therefore,statisticaltests of significanceare based on the differenceof these coefficients from unity ratherthan their difference from zero. should not differ significantlyfrom zero. If the coefficientis significantlynegative, an increase in time depositsincreases demanddeposit costs. Such a result would indicatethat the production of demand deposit servicesis not entirely distinct from the productionof time deposit services.However,if the coefficient is significantlypositive, an increasein time depositsdecreases demanddeposit costs. Such a result could occur if a largerbank size (in termsof total deposits) enabledmore efficient productionof demanddeposit servicesregardlessof the actual dollarvolumeof demanddeposits. l5Two sampleunit nonaffiliatesand two samplebranchnonaffiliateswere omitted from the unit andbranchnonaffiliateregressionsbecauseof inadequatedata.
3 24 : MONEY,CREDIT,AND BANKING TABLE 1 Regression Results for the Demand Deposit Statistical Cost Functiona Variable log H log N log S
Unit Banks Affiliates Nonaffiliates (UA) (UN) -2.8118** -2.4059** (.61 33) (.2787) .9266t 1.0320 (.0343) (.0197) .3116tt .3l32tt (.0687) (.0388)
log ¢ log ACT logM log w log I R2 S.E.b F n
.2951** (.0531) -.1952** (.0415) .5166** (.0797) .0022 t.0500) .9497 .0993 1142.7000 365
.3505** (.0936) -.0067 (.0790) .6955** (.1657) -.0632 (.0992) .9712 .0716 416.2400 76
Branch Banks Affiliates Nonaffiliates (BA) (BN) -1.5875* -1.9785** (.6418) (.2413) .8219tt .9283tt (.0643) (.0193) .1874tt .3598tt (.0900) (.0338) .9766 1.0110 (.0281) (.01 10) .7240** .3116** (.1137) (.0443) .0295 -.0631* (.0863) (.0256) .3059 .4467** (.1784) (.0684) .0639 -.1068** (.1648) (.0407) .9749 .0829 2490.9000 450
.9696 .0919 319.7500 72
All Banks (All) -2.1575** (. 1674) *9755t (.0118) .325ltt (.0235) l.Ol90t (.0080) .3534** (.0307) -.1095** (.0212) .4505** (.0475) -.0595* (.0296) .9707 .0912 4555.4000 963
*Significantly different from zero at the 5 percent level. * *Significantly different from zero at the 1 percent level. tSignificantly different from unity at the 5 percent level. ttSignificantly different from unity at the 1 percent level. aStandard errors of the regression coefficients are enclosed by parentheses. bStandard error of the estimate.
of accountquantityoccuras the average No statisticallysignificantdiseconomies numberof accountsperoffice (N) increasesin unit nonaffiliates.Therearestatistically significanteconomiesof accountquantityat the 5 percentlevel in unit A 10 peraffiliatesandat the 1 percentlevelin branchaffiliatesandnonaffiliates. cent increasein N causescosts to increaseby 9.3 percentin unitaffiliates,9.3 percent in branchnonaffiliates,and8.2 percentin branchaffiliates.It is evidentfrom these resultsthat economiesof accountquantityassociatedwith increasesin the averagenumberof accountsper office are greaterin unit affiliatesthan in unit nonaffiliates,greaterin branchaffiliatesthanin branchnonaffiliates,andgreater in branchbanksthan in unit banks.This does not imply,however,that branch banksaremoreefficientthanunit banks.The magnitudeof the account-quantity effectindicatesonly the shapeof the cost functionandnot the actuallevelof costs. Therefore,even thoughunit nonaffiliatesexhibitno significanteconomiesof accountquantity,it is entirelypossiblethat actualoperatingcosts arelowerin unit applies nonaffiliatesthanin otherbanksfor somevaluesof N. Thisconsideration effectsamongthe four of the account-sizeand firm-structure also to comparisons forms.Finally,it shouldbe noted that the account-quantity legalorganizational effectsfor the effect for all banksappearsto be an averageof the account-quantity effects forms.The differencesamongthe account-quantity four organizational indicatethatit is importantto considerthelegalformof bankorganization.
LONGBRAKEAND HASLEM : 325
Statistically significant and substantial economies of account size occur in all organizationalforms as the averagesize of an account (S) increases.This means that a 10 percent increasein S causes costs to increaseby only 3.1 percent in unit nonaffiliates, 3.1 percent in unit affiliates, 3.6 percent in branchnonaffiliates,and 1.9 percent in branch affiliates. These results indicate that demand-depositoperating costs are affected less by changesin account size in affiliated branchbanks than in other banks. These substantialeconomies of account size should encourage banksto pursuepolicies which promote largeraccounts. For example, lower service charge rates could be established for largeracc()unts,or other nonpriced services could be offered. The considerable difference in the magnitudes of the account-quantity and account-size effects overwhelminglypoints out the importance of disaggregating the averagedollarvolume of demanddeposits per office into the averagenumberof accounts per office and the averagesize of account. It is obvious that direct operating costs areinfluencedmore by changesin the output of demanddeposit services associated with changes in the average number of accounts per office than to changes in output associated with changesin averageaccount size. If the average volume of demand deposits per office were used to reflect the output of demand deposit services, it would be found that substantialeconomies of size exist for demand deposits for banksbelongingto all four bank organizationalforms.l6 However, this might lead to the erroneousconclusion that attractingnew accounts with balancessimilarto the prevailingaverageenables a bank to enjoy these substantial economies of size. This is clearly not the case. Therefore,the unrestrictedform of the output measure in equation (4) appears to be more appropriatethan the restrictedform in equation (1). No statistically significanteconomies or diseconomies of firm structureoccur in branchnonaffiliates or branch affiliates. Therefore,it appearsthat the number of offices operatedby a branchbankhas little effect on the cost of producingdemand deposit services. For example, doubling the number of accounts handled by a banking organizationby doubling the number of offices causes costs to increase 101.1 percent in branchnonaffiliatesand 97.7 percent in branchaffiliates. Regressioncoefficients of the weighted index of activity variableindicate that account activity has a greaterimpact on costs in holding companyaffiliates than in nonaffiliates. The effect of account activity is smallest in unaffiliatedunit banks and greatest in affiliated branch banks. Some possible explanationsfor the large positive coefficient for branchaffiliates include: (1) branchaffiliatesprovidemore servicesto active accountsthan other banks,(2) branchaffiliatesareless efficient in organizingoperations for more active accounts, (3) branch affiliates have adopted advancedtechnological equipmentwhich is less efficient from a cost standpoint.l7 The regressioncoefficient of the wage rate for branch affiliates implies that these banks are more capital intensive than other banks. This suggests that the third explanation of the high activity variablecoefficient may be the most relevantone. l6The term "economiesof size" refers to the combined effects of economies of account quantityand economiesof accountsize. l7For a discussionof the impact of technology on the costs of producingdemanddeposit services,see Daniel,Longbrake,and Murphy[5] .
3 26 : MONEY,CREDIT, AND BANKING
Because differences in the costs of providingservices to regularand special demand deposit accounts may be explainedby averageaccount size, account activity, and the service chargerate, the coefficient of the mix variablemeasureschangesin costs caused by the substitution of a regularaccount for a special account which are not already explained by these other variables.The negativecoefficients of the mix variable for unaffiliated unit and branch banks indicate that costs decrease when a regularaccount is substituted for a special account. However,the coefficients of the mix variableare not statistically significantin the cost functions for the two affiliated forms of bankingorganization. Coefficients of the wage rate variableindicate that demand deposit operations are more labor intensive in unit banks than in branchbanks.The coefficient of the interaction variableis statistically significantonly in the unaffiliatedbranch bank regression.Therefore,except for branchnonaffiliates, the hypothesis that the cost of demand deposit services is independent of the output of time deposit services (as measuredby the level of time deposits) can be accepted. However,costs rise in unaffiliatedbranchbanks as the volume of time deposits increaseswhen the level of demanddeposits remainsconstant.
III. THE EFFECTSOF BANK SIZE AND LEGAL FORM OF ORGANIZATIONON PRODUCTIVEEFFICIENCY
Basisfor ComparingUnit and BranchBanks Existing banking studies dealing with productive efficiency and organizational form do not agree on the proper basis for comparingthe productiveefficiency of unit and branchbanks. In some, the bankingoffice serves as the basis of comparison while in others the banking organization serves as the basis of comparison. This lack of agreement is responsible for conflicting conclusions about the efficiency of branch banks relative to unit banks. A basis for comparisonshould be selected which is responsivenot only to the realities of bank marketstructurebut which will also provide answersto frequently asked questions about the effect of organizationalform on productive efficiency. There are at least three such questions. One is concerned with the effect that the expansion of a single-banking facility has on its costs of operation, i.e., the effect of plant size. A second is concerned with the effect on productive efficiency of adding banking facilities, i.e., the effect of firm structure. A third is concerned with the effect on productive efficiency of merging severalbankingfacilities into a branch or holding-company bankingorganization. In most instances the deposit activities of a unit bank or a branch office are limited to a local marketareaand it is only with some difficulty that these activities can be extended beyond the local market area. Therefore,it seems reasonableto postulate that the bankingoffice and not the bankingorganizationshould serveas the relevantbasis for comparingproductiveefficiency in alternativetypes of banking organization.
LONGBRAKEAND HASLEM: 327
Analysis of ProductiveEffeiency by SimulatingAverageCosts The product of N, S, and ¢, the three primarymeasuresof the averagequantity of demand deposit servicesproduced by a bank, equalsD, the total dollaramount of demand deposits. This relation makes it possible to evaluatethe effects of bank size and bank organizationalform on productive efficiency by using the average cost per dollar of demanddeposits. An averagecost equation expressedin terms of the cost per dollarof demanddepositscan be derivedfrom equation (5) by dividing both sides by D and assumingthat the variablesother thanN, S, and ¢ are equal to their geometricmeans. This resultsin equation (6): 18 AC=-= H' N6l-l S62-1¢,63-1 D
(6)
When logs of equation (6) are taken and the appropriateregressionresults from Table 1 are inserted, four averagecost functions, one for each legal form of banking organization,result: log ACUN= .3380 + .0320 log N - .6868 log S
(7)
log ACUA = .7404 - .0734 log N - .6884 log S
(8)
logACBN = .5708 - .0717 logN- .6402 logS+ .0110 log ¢
(9)
logACBs
=
1.4984- .1781 logN- .81261OgS- .02341Og¢.
(10)
Simulated average costs derived from equations (7) to (10) are shown in Table 2 for the four types of bankingorganizationfor selected valuesof N, S, and f. Values for N and S were fixed at the 10, 50, and 90 percentiles of their respectivedistributions for all samplebanks. Equations (7) to (10) and the figures in Table 2 show that avqragecosts in all four legal forms of organizationare much more sensitive to averageaccount size than they are to the averagenumber of accounts per office or the number of offices. It can be seen also in Table 2 that the productiveefficiency of one organizational form relative to another depends on the values for the averagenumberof accounts per office, the averagesize of an account, and the numberof offices. For example, when N = 1,400 and S= $1,000, averagecosts are 16 percent higher in unit affiliates than in unit nonaffiliates.However,when N= 9,400 and S = $2,950, averagecosts are 5 percentlower in unit affiliates than in unit nonaffiliates. In general, the results presented in Table 2 show that unaffiliated unit banks l8Thenew constant,H', is equalto theproductof theconstantin equation(5) andvaluesof powers. at theirgeometricmeanswhichhavebeenraisedto theappropriate the othervariables thepowers However, comparability. meansforallsamplebanksareusedto maintain Geometric fromthe estimated parameters to whichthesegeometricmeansareraisedare the regression costequation Thus,theaverage organization. statisticalcost functionsforeachtypeof banking form may have a differentvaluefor H'. The geometricmeansin for each organizational computedfor all samplebanksare:5.3757 forC, 3.5174forN, 3.2302forS, .3765 logarithms for¢, 2.7368forACT,-.1422 for M, 3.6957 for w, and -.3428 for I.
_
_
_
TABLE 2 Average Costs Per $100 of Demand Deposits for Various Combinations of the Averag OfElce (N), Average Size of Account (S), Number of Offices (¢), and Types of O 1,400 = Accounts Per Office $1,000 = Average Account Size $1,4G0,000 = Average Deposits Per Office
1,400 = Accounts Per Office $1,600 = Average Account Size $2,240,000 = Average Deposits Per Office
Nuomffber of Deposits UnitBanks BranchBanks Nuomffberof Deposits ,p (°°°) UN* UA8 BN* BA*
