A Non Parametric Approach for Assessing the Productivity Dynamics of Large US Banks

8/6/2019 A Non Parametric Approach for Assessing the Productivity Dynamics of Large US Banks

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A Nonparametric Approach for Assessing Productivity Dynamics of Large U.S. Banks

Author(s): Ila M. Semenick AlamSource: Journal of Money, Credit and Banking, Vol. 33, No. 1 (Feb., 2001), pp. 121-139Published by: Ohio State University PressStable URL: http://www.jstor.org/stable/2673875 .

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ILA M. SEMENICKALAM

A Nonparametricpproach orAssessingProductivity ynamicsof LargeU.S. Banks

The 1980s markedan era of substantialchange for the U.S. com-mercialbanking ndustry.An issue of considerable nterest o bank-ing analysts and economists alike is whether the intensifiedcompetitivepressure,generatedby deregulationand notable finan-cial innovations,enhancedproductivity.To investigate he responseto these changes, the nonparametricMalmquist index is used toevaluate productivitydynamics. A statistically significantproduc-tivity surge found between 1983 and 1984 is followed by produc-tivity regress the next period; post-1985, sustained productivityprogress s observed for the remainderof the decade. Productivitymovements are primarily attributableto technological changesrather han scale changes or convergence o the production rontier.THE BANKINGSECTORs constantly and rapidly evolving;

the last two decades, n particular, epresenta substantialmetamorphosis or bankingsectors in countries around he world. For example, the Norwegian banking sectorwas deregulated n the 1980s, while U.K. banks faced increased competitiondue tothe entry of other nonbank ending institutions.Meanwhile, n the United States, thederegulationmovement,which began in the 1970s, expandedto many industries n-cluding banks in the 1980s. Under the loosening of regulatoryconstraints,whichcontinues into the l990s, U.S. banks have found greaterversatility in their opera-tions. In addition, he industrynow has availablemany new financial nstruments ndtechnological advances.l Finally, the restructuringand consolidation wave of the1980s, which engulfed the industry,2has continued nto the present with the recenttrend owardmegamergers eneratingempiricalevidence that fuels the debateon na-

The author hanks the following for helpful comments: Robin Sickles, Allen Berger, RobertAdams,Joe Hughes, two anonymousreferees, and participants t the GeorgiaProductivityConferenceIII,Athens,and the 1998 SouthernEconomic Association Conference,Washington,D.C.1. For an in-depthdiscussion concerningbanking nnovations including ncreasedautomation uch asATMs, and improved nformationprocessing and credit scoring) and commercial bank deregulation in-cluding the removalof interestceilings on certaindeposits, creationof new types of accounts, and the re-laxationof branching estrictions) n the United States, see Berger,Kashyap,and Scalise (1995).2. Approximately ive thousandcommercialand savings banks were the object of takeoversduring he1980s; in 1995, record volume levels were reached due to a large numberof mega-mergers Peristiani1997).ILA M. SEMENICK LAM is an associateprofessorof economicsat TulaneUniversity.E-mail:[email protected]

Journal f Money,Credit, ndBanking, ol. 33, No. 1 (February 001)Copyright2001 by The Ohio State University


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122 : MONEY,CREDIT,AND BANKING

tionwidebranching.As aresultof thesefactors,a substantialiteraturehasdevelopedaroundthe issues of banking efficiency and productivity.3This literaturehas beenfacilitatedby the presenceof comprehensiveand reliabledata sets that area conse-quence of the regulatoryenvironment.In addition, the analysis of relative perfor-manceamong banks is aided by a large degree of producthomogeneity.In ordertomake validcomparisonsbetween efficientand inefficientoperations, irmsmust havethe samefundamental haracteristicsn termsof environment ndoperations.Because it encompasses the initial deregulatorypush as well as other dramaticfundamental hanges, the decade of the 1980s is anespecially interestingepisode inU.S. banking sector history. It was expected that increased competitive forces,broughtabout by the changing bankingenvironment,would act as a stimulant tothose firmsoperating nside the productionfrontier.Banks not allocatingtheir re-sourcesefficiently would perish unless they could become more like theirefficientcompetitorsby producingmore outputwithexisting inputs.Alam andSickles (2000)find support or this hypothesis in the case of the U.S. airline industry; hey presentevidencethat the AirlineDeregulationAct of 1978 led to more efficientresourceuti-lization by firms n thatindustryover the next decade. Thisresult of mountingcom-petition is separate from the notion of technological innovation although theconsequencesmay be similar.In additionto improvingefficiencyperformance ela-tive to theproduction rontier n response to greatercompetition,firmsmayinnovatemore as well and, hence,push out the frontier.

ThepresentstudyevaluatesU.S. bankingproductivityusing the Malmquist ndexapproach.This index is a valuable tool since it allows for the decompositionof pro-ductivityinto the two componentsdiscussed above: innovation and imitation. Thefirstcomponent,also calledtechnologicalchange, capturesany expansionof the pro-ductionpossibilities frontier.The second componentcaptures the convergence offirms toward the existing technology; this phenomenonis also called efficiencychange or"catchingup." The Malmquist s calculatedwithin the frameworkof dataenvelopmentanalysis(DEA), which is a linearprogrammingmethodologythat con-structs a nonparametric, iecewise-linear,"best-practice"rontier from observableinput andoutputdata. Otherauthorshaveused the DEA techniqueto studythe effi-ciency of the bankingsectorbeginning with ShermanandGold (1985); more recentstudiesinclude Aly et al. (1990), Elyasianiand Mehdian(1990, 1992, 1995), Ferrierand Lovell (1990), andAthanassopoulos 1998), interalia.5 Most of these studies,however,have only one or two time periods of data available and hence considermainlyefficiency levels since they can not examineproductivity hanges in detail.3. As evidenced by the survey articles of Colwell and Davis (1992), Berger, Hunter,and Timme(1993), Bergerand Mester (1997) and Berger andHumphrey 1997). The degree of attention his research

area has attracted s apparentby the dramatic ncreasein the numberof articles publishedbetween 1992and 1997, the dates of these reviews. Most recently,Adams, Alam, and Sickles (1998) andBauer et al.(1998) discuss the robustnessof various measuresof bankingtechnicalefficiency and cost efficiency, re-spectively.4. An enhanceddecomposition s furtherpossible. Efficiency change (or imitation) can be separatedinto two terms:change in scale andchange in pureefficiency. See footnote10 as well as Fare et al. (1994,p.75).5. Refer to Berger and Humphrey 1997), Table 1 for a recent comprehensive ist of DEA bankingstudies;69 of the 122 papers isted are linearprogramming tudies, with 62 of the 69 being DEA.


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ILA M. SEMENICKALAM : 123

The focus here is on identifying the degree of productivityprogress(or regress) nthe 1980s and the degree to which this productivitycan be attributed o innovationversus imitation.These measuresof productivity, onvergence,and innovationhavewide-spread appeal since they have numerous international applications and aheightened relevance in today's volatile operating and regulatory environments.Many industries n many countriesare undergoingsweeping changes and this indexcan help identify how the firms in those industries are reacting. For example, asnoted by Berger and Humphrey 1997), a primarygoal of deregulation s to improveresourceallocation. Such a deregulatory esponse would reduce the degree of ineffi-cient production ausing firmsto convergeto the production rontier.The Malmquistindex enables one to test this premise since it can distinguishbetween convergenceand innovation.Furthermore, onfidence ntervals,generatedusing the CentralLimitTheorem as well as a nonparametric ootstrapping echnique,can be used to deter-mine the statisticalsignificance of the findings.The paperproceeds as follows. Section 1 reviews the related iteraturewhile sec-tion 2 discusses the DEA and Malmquistmethodologies, and the issue of statisticalsignificance.Section 3 presents he bankingdata and section 4 reports he empiricalfindings.Section 5 concludes.1. RELATEDANKING RODUCTIVITYITERATURE

Berg, F0rsund, and Jansen (1992) used the Malmquist to analyze Norwegianbanks between 1980 and 1989. They identifiedproductivityregress prior to deregu-lation of the Norwegian banking system, and rapidproductivityprogresspostdereg-ulation with large banks exhibiting the most rapid growth. The productivitygainswere mostly attributable o gains in relative efficiency rather han frontiershifts; inother words, under the increased competitive forces of deregulation, inefficientbanks converged to the frontier n order to survive. The U.S. deregulatoryexperi-ence, which also occurred n the 1980s and focused on the asset side of the balancesheet, was quite different rom the Norwegianone. Thus, Norway's experience s notnecessarilygeneralizable o the Americanone. Berg et al. (1993) expanded he Nor-wegian study to an internationalcomparison by including Finnish and Swedishbanking ndustries.The authorsemployed the Malmquistapproach n orderto makecross-country omparisonsusing data from a single year.Elyasianiand Mehdian(1995), workingwith U.S. data, selected 1979 and 1986 asroughproxies for the pre- and postderegulation eriods. Using DEA, they calculatedefficiency scores for samples of U.S. banks from these two years. The authors oundthat, for large banks, technical efficiency declined by 3 percentand, using a time-de-pendentratio analysis,6 echnology regressedby 2 percentover this eight-year span.

6. Efficienciesor eachbank rom he 1986 samplewerecalculatedwo ways:once relative o the1979 rontier ndoncerelativeo the 1986 rontier. heratioof the ormer fficiency coreover he atterefficiency corewas defined s the rateof technologicalhange or thatbank Elyasiani ndMehdian1995).Thisapproachs dependentn the yearchosen or the benchmark.y following he Malmquist


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methodologyas outlined in Fare et al. (1994), this paper avoids choosing an arbitrary eferencepoint inorderto measure echnological shifts.


Unfortunately, n analysis limited to only two, widely spaced yearsof datamutes theindustry'sresponsepattern.As will be shown, a large advance n one year can be off-set by a large pullback n anotheryear, yielding the impressionof little activity overthe entiretime period under study.Thus, there is a distinctadvantage o a more de-tailed,annual nvestigation.Wheelock and Wilson (1999) usedthe Malmquistdecomposition o examine U.S.banksfrom 1984 to 1993. The authorsdocumenteda drop n averageproductivityaswell as technical efficiency; however,there was considerable echnological advance-ment during this ten-year period.The degree and timing of the productivity,effi-ciency,and technological changesvariedwith bank size.OtherU.S. productivity tudiesinclude Humphrey 1991) who analyzed the rela-tionshipbetween deregulationand productivity or U.S. banks between 1977 and1987. He focused on the growthaccountingapproach ather hanon econometricorlinearprogrammingmethodologies.The very low, to negative,productivitygrowth(estimatesrange between-0.07 percent and 0.6 percentper annumfor the produc-tion andcost approaches espectively) s attributed o the deregulationof the 1980s.Almostall of the remainingU.S. studies estimate technicalchange using profitorcost function models. Humphrey(1993), working with banks from states that al-lowed statewideor limited branching,pooled data between 1977 and 1988 and esti-mated a translog cost function. He found that the very largest banks experiencedaverageannualproductivity hangebetween-0.5 percentand-0.9 percent.This isin contrastto Hunter and Timme (1991) who, using a similar model and data set,found a positive annual growth rate of 1 percent between 1980 and 1986. Mean-while, Berger and Humphrey 1992), using a thick-frontier ost function approach,evaluatedtechnical change andproductivityand found little change in these mea-suresduringthe 1980s. Bauer,Berger,and Humphrey 1993), employing data from1977 to 1988, used the stochasticeconometricand thick frontierapproaches o esti-mate totalfactorproductivitywith a cost function model. Theyfound productivity obe between-3.55 percent and 0.16 percent growthper annum.Humphreyand Pul-ley (1997) looked at the technological and efficiency response to deregulation nterms of profitfunctions.Theyaveraged he databetween 1977 and 1988 by consec-utive four-year ntervals (1977-80, 1981-84, and 1985-88) andfound productivityregress in the 1980s (-7 percentbetween the 1981-84 period andthe 1985-88 pe-riod forthe largerbanks n theirsample). Finally, BergerandMester (1999) includeddatathrough 1997 and found that, in the 1990s, cost productivitydeterioratedwhileprofitproductivity ose considerably, specially for banks involvedin mergers.The present paper complementsand extends the literaturediscussed above. Byutilizing the flexible, nonparametricMalmquist ndex methodology, the robustnessof the findings across countries as well as across methodologiescan be assessed.This study is an especially good counter-point o the econometric studies since it


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provides a means of checking the sensitivity of results which rely upon an a priorispecificationof a functionalform for the production echnology.

2. METHODOLOGYAn output-efficient irm is one which cannot increase its output unless it also in-creases one or more of its inputs;7such a firm has an efficiency score of 1. Con-versely, an output-inefficient irm has an efficiency score less than 1. Figure 1 isillustrativeof a single-input, single-outputproductionscenario. The bold rays fromthe origin, labeled Tt and Tt+ , represent he boundariesof technology at time t andt+ 1, respectively,under the assumptionof constant returns o scale.8 Since Tt+l is

Y A oT,+,

Ynt a / t (X"l,nl)O Xn Xn,+w X

FIGE1. ingle-Input, Single-Output ProductionTechnology IllustratingDeterminationof EfficiencyScores and Malmquist ndex of Total FactorProductivityunderConstantReturns o Scale

7. Similarly,an input efficient firm is one which cannot contract ts inputs without decreasing one ormore of its outputs.8. Alternativeassumptions nclude nonincreasing,nondecreasing,or variablereturns o scale; Seifordand Thrall 1990) have a detaileddiscussion. Underthe Malmquistparadigm,nonconstant eturns o scaleraises uniqueness, nternalconsistency,and measurementaccuracy ssues; Grifell-Tatje nd Lovell (1995,1998), Bjurek (1996), Ray and Desli (1997), and Fare, Grosskopf, and Norris (1997) are among thosewho have contributed o this emerging literature.McAllister and McManus (1993) provide evidence thatCRS holds for large banks (>500 million in assets), which is the set of banks dealt with in this paper.Alam (2000, 2001) examines the Malmquistproductivitydynamics, ncluding scale issues, for a databaseincludingbanks below 500 million in assets.


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126 : MONEY, REDIT, NDBANKING

above Tt,technologicalprogresshas occurredbetween t and t+ 1. Considerthe caseof firm n in period t representedas (xtlt,Ytlt). ince it is interior o Tt,this firm is notefficient and its outputinefficiency is measured as the ratio Oa/Ob.Similarly, thesame firm n t+ 1, denoted(xtl +1,Ytl +l), is inefficient with respect to the Tt+l fron-tier and its inefficiencyscore is given by Oe/O%.DEA is used to define the boundaryof the technology and obtain the efficiencyscore for each bank in each time period. It does so by creating an envelope of ob-servedproductionpoints (Charnes,Cooper, and Rhodes 1978). DEA provides forflexible piecewise-linearapproximations o model the best-practicereference tech-nology. One advantageof programmingmethods over econometricmodels is thatthey do not require an assumptionof cost minimizationor profitmaximization.Inaddition, inearprogrammingmethods arenonparametric nd thus do not requireapriorispecification of a production unction. Finally, these methods do not smootheffects and,therefore, heyallow for greater lexibility n that substantialannualvari-ations in efficiency can occur if they exist in the data.9To identify productivitydynamics, the Malmquist ndex procedure s used. It isable to accountfor changesin bothtechnicalefficiency(catchingup) andchanges infrontiertechnology (innovation). In a study of industrializedcountries,Fare et al.(1994) note that this decomposition allows for a more comprehensivemeasure ofproductivitygrowthconvergence since earlier endeavorsfailed to distinguish be-tween thesetwo components.Thedecompositioncan be illustratedby referringbackto Figure 1. For firmn the decomposition s

Malmquist ndex = (OQ/ (ORY ) FO/d?) j

( Of )( Oa ) |( Oc )( Ob) | = Et+, * At+, * (1)This indexcaptures hedynamics of productivitychange by incorporatingdata fromtwo adjacentperiods:Et+1reflects changesin relativeefficiency while At+1reflectschanges in technologybetween t and t+ 1. For the index and its components,valuesbelow 1 indicateproductivitydecline(regress)while valuesabove 1 indicate growth(progress).For the firmn in the example,both componentsexceed 1. In terms of rel-ative technical efficiency, the firm moved closer to the relevantcontemporaneousfrontier indicating that production for this firm is converging to the frontier(Et+1>l). In terms of technology shifts, the frontier,as measuredat inputlevels xt

9. Econometricalternatives stochastic frontier, hick frontier,anddistribution ree analyses existfor measuring emporalproductivity;upon implementationof these methodologies, however,the authorhas found thatthey, unlike the linear programming pproach,do not tendto reveal the richdynamicsem-bedded in thedata.


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and xt+l, moved out between periods t and t+1 (At+lzl). The efficiency changecomponent can be further decomposed into pure efficiency change and scalechange.To determinewhetheror not the index and its componentsare significantlydiffer-ent from 1, confidence ntervalsare derived n two ways. Asymptotic confidence in-tervals based on the central limit theorem (CLT) are determined irst. In a samplewith a large number of firms (large N), the distributionof time means (averagingover firms at a point in time) becomes asymptoticallynormal under the CLT.TheStudent's distribution an then be used to calculate the appropriate onfidence in-tervals.One drawbackof this approach,however, s that n studies with a small num-ber of firms, he ability to use the CLT s obviated since the asymptoticresults do nothold when discussing patterns n means based on a small sample. Small sample sizeis a problemoften faced by not only linearprogramming ut also econometricanaly-ses in this literature.Anothercomplication arises if the researcher s specifically in-terested n the statisticalsignificance of the efficiency scores themselves as opposedto time or firm means. In the case of DEA scores, Charnesand Cooper (1980) showthat an assumptionof normality s probably ncorrect; his problem s also present neconometric models, which have a composed error term with inefElciencybeingmodeled as a truncatednormal,exponential,or gamma distribution.In order to addressthese issues, Atkinson and Wilson (1995) present a nonpara-metric bootstrapping lgorithmas a means of calculatingconfidence intervals.As adistribution-free lternative,bootstrapping s a methodology that can be used to ob-tain a sampling distributionof a sample statistic which, in this application, s thegeometric mean of the Malmquist ndex and its components.l3. BANKING ANELDATASETI2

The data set consists of all large (>$500 million in total assets) U.S. insuredcom-mercial banks with complete data over the ten-year ntervalfrom 1980 to 1989. Thedata are from the Reportof Conditionand Income (Call Report)and the FDIC Sum-mary of Deposits. In orderto allow for the distinct regulatoryand, hence, competi-tive circumstances of each state, the banks are separated by type of regulatoryenvironment s advocatedby Bergerand Humphrey 1991,1992), Berger (1993) andAdams, Berger, and Sickles (1999). The resulting balanced panel consists of 112banks n states allowing statewidebranching,43 banks n states with limited branch-ing, and 11 banks in unit-banking tates; as expected, more banks meet the size con-

10. hEfficiency APureEfficiency AScale.ThehEfficiency omponents calculated nderCRSwhile he PureEfficiency omponents efficiency hangeunder ariable eturnso scale,VRS.A scalechange alue xceeding indicates movementowardCRSwhilea valuebelow1 indicates movementaway romCRS.11. Or,equivalently,hearithmetic eanof the og of thesevariables.12. Thedatadescriptionollows hatof Berger 1993).


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dition understatewide (STATE)branching han undereither limited (LIMIT)or unit(UNIT) branching.Table 1 presents the variables used in the DEA productionfunction linear pro-grams and reports he means by regulatory nvironment.Outputs the yks,k= 1,. . .,4)consist of securities and three disaggregated oan categories real estate, commer-cial, and industrial,and installment; nputs (the xjs,j= 1,...,6) consist of two disag-gregated deposit categoriesl3 demand, and other deposits that contain time andsavings deposits-in addition o purchased unds, capital, labor, and equity.l4Meansfor several aggregatedvariablesare also reported: otal loans 05), core deposits (X7)and loanable funds (x8). These aggregatedvariablesallow for various specificationsin the input-outputcombinations for the productiontechnology. lSourmodels arespecified and listed at the bottom of Table 1.4. RESULTSEJjQciencyynamics

Levels: Table 2 reports he averagetechnical efficiencyl5 underthe DEA method-ology for this sample of largerbanks by regulatoryenvironment.The last category(ALL) combines all the banks and assumes that banks underall three regulatoryen-vironmentshad similartechnologies which is unlikely and violates the homogeneityrequirement; his category s presentedmainly for comparativepurposes.First, within each regulatory nvironment,notice how overall decennial efficiency(that is, average efficiency over the decade) consistently declines as the numberofinputs and/or outputs is reduced: Model 1 has four outputs and six inputs whilemodel 4, using aggregateddata, has two outputs and four inputs. STATEbanks, forexample, exhibit a drop in averageoverall efficiency of almost 10 percentfrom 0.94to 0.85. This observation s a well-known DEA phenomenon:as the numberof vari-ables increases, averageefficiency rises because each firm has a greateropportunity13. The speciElcationof deposits as inputs is a common practice. Studies include Elyasiani andMehdian (1990, 1992, and 1995), Humphrey 1991), English et al. (1993), Lang and Welzel (1996) andAdams, Berger, and Sickles (1999). Adams, Berger, and Sickles (1999) presentpreliminary esults indi-cating that this specification s favored based on statistical grounds. For completeness, models with de-posits and purchased unds as outputsrather han inputs were also run. The trendswere generally robustwith a few exceptions as noted in the results section.14. Securitiesand equity are controlledfor in the model specification o mitigate bias. Holding assetsconstant, if some banks hold fewer securities investments and relatively greater amounts of loans overtime, the Malmquistproductivity ndex will show that those banks have experiencedgreaterproductivitygrowthwhen all that has occurred s a shift in assets from securities nto loans. Similarly,on the liabilityside of the balance sheet, banks that use small amountsof deposits relative to equity capital will tend tolook more efficient than banks that use large amountsof deposits relative to equity. If banks tend to rely

more on equity over time then this will show up as increased productivity(Hughes and Mester 1998Hughes et al., 1996). The author hanksan anonymousreferee for these observations.For completenessthe model was also run without the securities or equity variables;as expected, levels changed but trendpatternswere robustacross these two specifications.15. Averagetechnical efficiency is often quoted as being approximately80 percentfor the U.S. bank-ing industry. n fact, this average performance evel is what is usually found by stochastic frontier andthick frontierapproaches o efficiency measurement; he linearprogramming pproachof DEA yields es-timates that are more variableacross studies, ranging from below 50 percent to over 90 percent averageefficiency for banks (Berger 1993).


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TABLE 1VARIABLEEscRIPrIoNs NDDECENNIALEANS OR ARGE .S. BANKS;MODELPECIFICATIONS

Sample eanVariable Definition unit Limit StateYl Dollaramountof securities: 746991.30 493249.03 912908.35Y2 Dollaramountof real estate loans: 615220.75 338379.40 1105255.23y3 Dollaramountof commercialand industrial oans: 2677530.10 603571.63 1964542.00y4 Dollaramountof installment oans: 397734.36 259609.72 632140.24y5 Dollaramountof total loans (Y2+Y3+Y4): 3690485.21 1201559.75 3701937.47xl Dollaramountof bank equity capital: 475809.72 172135.20 465461.57x2 Dollar valueof physical capital: 79156.67 34294.80 101490.11X3 Labor: 3840.09 1722.40 4433.32X4 Dollaramountof purchased unds: 5545728.47 1063539.70 4164013.63x5 Dollaramountof demanddeposits: 1156512.63 479294.70 1224962.40x6 Dollaramountof other (retail and time) deposits: 1003056.42 898456.27 1863388.33X7 Dollaramountof core deposits (x5+x6): 2159569.05 1377750.96 3088350.73x8 Dollaramountof total loanable funds (X4+X7): 7705297.52 2441290.66 7252364.36Model o. Outputs Variables Inputs Variables1: Securities, Yl Equity, xlReal estateloans, Y2 Capital, x2Commercialandindustrialloans, y3 Labor, X3Installmentloans. y4 Purchased unds, X4

Demand deposits, x5Otherdeposits. x62: Securities, Yl Equity, xlTotalloans. y5 Capital, x2Labor, X3Purchased unds, X4Demand deposits, X5Otherdeposits. x63: Securities, Yl Equity, xlTotal oans. y5 Capital, x2Labor, X3

Purchased unds, X4Core deposits. x14: Securities, Yl Equity, xlTotal oans. y5 Capital, x2Labor, X3Loanable funds. x8NarEs:llvariables,xceptabor,ren housandsf 1982dollars.aborsmeasurednnumberf full time-equivalentmployees.


to be efficient in some dimensionof production.Thus, when comparingaverageeffi-ciency acrossstudies, attentionmust be paidto the numberof variables.Second,within each model, notice thatSTATEbanks are consistently the least ef-ficient of thethreebankingenvironments.UNIT bankshave the highestdecennialef-ficiency undermodels 1-3 but falls to second place behind LIMITbanksfor model4. Berger(1993) similarly found that UNIT banks tend to be the most efficient andSTATE the least. This performancerankingmay at first appearcounter-intuitivesince it is contrary to the expectation that the greater competition in statewide


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TABLE 2AVERAGE EFFICIENCY BY REGULATORYENVIRONMENT,YEAR, AND MODEL SPECIFICATION

UNIT BANKS LIMITBANKSModel Model

Year 1 2 3 4 1 2 3 41980 0.9933 0.9766 0.9566 0.9301 0.9746 0.9327 0.8822 0.85971981 0.9952 0.9738 0.9614 0.9092 0.9722 0.9412 0.9030 0.86401982 0.9797 0.9407 0.9261 0.8728 0.9680 0.9386 0.9223 0.87501983 0.9985 0.9656 0.9363 0.8578 0.9608 0.9256 0.9135 0.87441984 0.9791 0.9732 0.9243 0.8966 0.9599 0.9271 0.8998 0.84341985 0.9847 0.9717 0.9513 0.9140 0.9671 0.9396 0.9187 0.89011986 0.9831 0.9551 0.9254 0.8833 0.9698 0.9427 0.9170 0.89931987 0.9888 0.9480 0.9182 0.8530 0.9803 0.9603 0.9375 0.92231988 0.9892 0.9705 0.9358 0.7975 0.9745 0.9550 0.9420 0.92611989 0.9964 0.9387 0.8864 0.7882 0.9720 0.9437 0.9302 0.9151Overall 0.9888 0.9614 0.9322 0.8703 0.9699 0.9406 0.9166 0.8869

STATEBANKS ALLBANKSModel Model

Year 1 2 3 4 1 2 3 41980 0.9240 0.8941 0.8574 0.8354 0.8970 0.8706 0.8384 0.82201981 0.9300 0.8913 0.8546 0.8394 0.8994 0.8691 0.8399 0.82301982 0.9268 0.8865 0.8494 0.8312 0.8938 0.8550 0.8259 0.80641983 0.9306 0.8850 0.8499 0.8291 0.8999 0.8552 0.8260 0.80281984 0.9361 0.8931 0.8621 0.8372 0.9026 0.8593 0.8321 0.80271985 0.9441 0.9102 0.8815 0.8520 0.9202 0.8829 0.8555 0.82431986 0.9606 0.9302 0.9068 0.8739 0.9413 0.9066 0.8854 0.84961987 0.9614 0.9363 0.9055 0.8583 0.9464 0.9149 0.8856 0.83791988 0.9551 0.9378 0.9096 0.8588 0.9380 0.9153 0.8937 0.84021989 0.9534 0.9330 0.9086 0.8695 0.9292 0.8989 0.8698 0.8122Overall 0.9422 0.9097 0.8785 0.8485 0.9168 0.8828 0.8552 0.8221NarEs: N = 11 for UNIT Banks; 43 for LIMIT Banks; 112 for STATEBanks; 166 for ALL Banks. Model specifications are defined inTable 1.

branching tates shouldresult n greaterefficiency.A possible explanation s that t ispurely a statisticalphenomenonreliantupon thenumberof firmsusedto estimatethetechnical efficiencyscores (Caves and Barton1990). As the numberof observationsdrawnfrom a distributionncreases, so too will the numberof extreme values (bothhigh and low). Caves andBarton (1990) maintain hat therelationshipbetween esti-mated technicalefficiency and the numberof observationsmay be similarly linked.The more draws takenfrom a distribution, he more likely the researcher s to en-counter a highly efficient firm, which makes all other firms in the sample less effi-cient in comparison.Using an orderstatisticargument hey contendthat the range ofvalues increases at a rateapproximately quivalent o the squarerootof the numberof observations.To test this, UNIT (N=11), LIMIT (N=43), and STATE N=112)technical efficiency scores were combined and regressed on the square root of thenumberof observations SQRTN).As expected, SQRTN has a negative and signifi-



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ILAM. SEMENICKALAM : 131

cant coefficient.l6The fact that STATEbanks arethe least efficienton averagemay,therefore,simply be a reflectionof the statisticalfactor identifiedby Cavesand Bar-ton. Thisexplanations furtherupheldby the observation hat,when all thebanks aregrouped ogether (N= 166), averageefficiency is less than thatfor the threeindivid-ual categories;if SQRTN and technicalefficiency were not correlated,one wouldexpect the ALL groupingto be a weighted averageof the threeregulatoryenviron-ments and fall somewherebetween, rather hanbelow, STATE,LIMIT,and UNITaverageefficiency.Thus,when interpreting fficiencylevels, one must be verycircumspect,as the re-sults aresensitive to the numberof observationsas well as the numberof variables.Trends:Efficiencytrends, on the other hand,tend to be more robust acrossthesedimensions.STATE s the most robustwith correlationsbetweenthe models averag-ing 95 percent;correlationsbetweenthe models average90 percentfor ALL and 71percentfor LIMIT.Correlationsarethe weakestfor UNIT, which exhibitsno signif-icant correlationbetweenmodel 1 and the othermodels but averages69 percent onthe remainingpairs.In general,when averageefficienciesfrom Table2 are plottedover time, the over-all technicalefficiencytrend is slightly increasingfor all models across the regula-tory categories.AgainUNIT is thenotable exceptionas wouldbe expectedbased onthe abovecorrelations: fficiency risesbetween 1980 and 1989 for model 1 but mod-els 2 and3 have a pronounceddip for 1989 while model 4 has an even morenotice-able decline over time. Furthermore,whereas UNIT is entirely above the othercategoriesfor model 1, it falls furtherand furtherbelow LIMIT,STATE,andALL asone moves from models 2 to 4. The relative sensitivityof UNIT to model specifica-tion is probably he resultof its small sample size; therefore, ts results mustbe sub-ject to greaterscrutiny.In summary, he maindistinctionsamong themodels are (i) the level of efficiency,which falls as one moves from model 1 to 4; and(ii) the degreeof variability,whichrises as one moves from model 1 to 4 (variability s heighteneddue to the smallernumberof inputs and/oroutputs).Productivityand Its Components:

Levels:Turningnow to the Malmquist ndex and its components,referto Table 3which presentstheseresultsby regulatory nvironmentor model 1. Significancere-sults, based on both asymptotic andbootstrapped onfidenceintervals, are also re-ported in Table 3.17Recall that values significantlygreaterthan 1 are indicativeof16. Model 1, for example,has a coefficienton SQRTNof-0.00664 (t-ratio= 8.71) indicating hat n-creasingN by 100 would decreaseaverageefficiency by 6.64 percent.17. In addition, othernonparametric ests (Wilcoxon, median, van der Waerden,Savage, and Kol-mogorov-Smirnov)were performed o determine f differencesbetween STATEand LIMIT,STATEandUNIT, andUNIT and LIMITare statisticallysignificant.Theresults supported hose patternsestablishedwith the bootstrapping ndCLTapproachesn several aspects.First, considerTable 3. AScale,for exam-ple, for STATE1985-1986, is significantat the 1 percent evel (AScale = 1.0126) but it is insignificantlydifferent rom 1 for UNIT (AScale = 0.9981) and LIMIT (AScale = 1.0026). The above nonparametrictests pickedthis result up:UNIT versus STATE,and LIMITversus STATEaresignificantlydifferent rom


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progress in relative performance,values significantly less than 1 are indicative ofregress or deterioration,and values not different rom 1 are indicative of no changein relative performance.Differences between the bootstrappedand asymptotic ap-proachesare most apparent or UNIT which has a sample size of only 11. In one case(Malmquist,1985-1986), a value significantat the 5 percent evel becomes insignif-icant under the asymptotic approach; n three other cases (Malmquist, 1983-1984and 1988-1989; I\Technology, 1988-1989), significance drops from 1 percent to 5percent. The remaining categories have a total of four disagreementsbetween thetwo sets of confidence intervals; he lower numberof discrepancies s the result ofthe larger sample sizes (N=43, 112, and 166 for LIMIT,STATE,and ALL, respec-tively). Thus, even for moderately arge samples, differencesmight still arise.Atkin-son and Wilson (1995), working with a sample of forty-two firms, found enoughdifferencesbetween confidence intervalsgeneratedby the bootstrapmethod and theasymptoticprocedure o suggest that the researchermay not wish to rely solely onthe latter.Total cumulatedgrowthfor the entire decade is largestfor LIMITbanks (4.3 per-cent) due to technological nnovation 4.6 percent)which offset a slight decline in ef-ficiency (-0.2 percent; firms, on average, were moving farther away from theefficient frontieras the leaderspulled furtherahead).This would indicate thatLIMITbanks were especially successful at incorporatingnew technological advances intotheir operation.The level of productivitygrowth for STATEbanks was comparable(3.2 percent) but was due to convergence to the frontier (3.5 percent) ratherthantechnologicalchange (-0.3 percent).Finally,UNIT banks actuallyexhibited a smalldecline in productivity -0.3 percent) due to technological regress (-0.7 percent)which offset convergence (0.3 percent). This patternof cumulative growth is intu-itively appealing: those banks operating under less restrictive regulatory environ-ments (namely, LIMIT and STATE)exhibited enhancedproductivitywhile bankingproductivity n a more restrictivemilieu (namely,UNIT) suffered.Finally, considering the ALL category,total productivityactually falls more thanUNIT (-0.9 percent) and is attributed o a large degree of technological regress(-4.6 percent) which outweighs convergence (3.9 percent). Note how pooling thedata conceals the distinctly different cumulativeresults for banks in the individualregulatory nvironments.Trends: f the results from Table 3 are plotted over time, one would notice that theMalmquisthas a pronouncedpeak for 1983-1984 followed by a significant trougheach other (at the 8.7 percent evel or better)for 1985-1986. Since AScale for UNIT and LIMIT are notdifferent rom 1, while AScale for STATE s different rom 1, it makes sense that both UNIT and LIMITbanks are significantlydifferentfrom STATEAScale. Second, these nonparametric ests again illustratethe importanceof separatingbanksby regulatory nvironment: he Malmquistand componentsare signif-icantly differentacross regulatory nvironments or several time periods.Also, the time periods of signif-icance can vary depending on which pair of regulatoryenvironmentsare being compared(for example,1982-1983 and 1988-1989 are significantly different for UNIT versus LIMIT, and for UNIT versusSTATE,but not for LIMITversus STATE).Finally, the patternof results s consistent. Namely, wheneverthe Malmquistproductivity ndex is significantlydifferentbetween bank environments, he ATechnologycomponent s also significantlydifferent.This patternwas originally observed in Table 3: it is primarilyATechnologydrivingthe productivity esults rather han AScale or APureEfficiency.


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TABLE 3AVERAGE ANNUAL CHANGE FOR MALMQUIST PRODUCTIVITY INDEX AND COMPONENTS (MODEL 1 )

UNIT BANKSYear Malmquist ATechnology APureEfficiency AScale1980-1981 0.9696 0.9676 1.0050 0.99711981-1982 0.9475 0.9631 0.9916 0.99221982-1983 0.8751 ** 0.8581 ** 1.0094 1.01031983-1984 1.1223** 1.1467** 1.0000 0.97871984-1985 0.8660** 0.8606** 1.0000 1.00631985-1986 1.0559*-- 1.0579 1.0000 0.99811986-1987 1.0329 1.0256 1.0000 1.00711987-1988 1.0398* 1.0398 1.0000 1.00001988-1989 1.0918** 1.0832** 1.0000 1.0079

LIMIT BANKSYear Malmquist ATechnology APureEfficiency AScale1980-1981 0.9334** 0.9358** 0.9993 0.99811981-1982 0.9534** 0.9588** 0.9947 0.99971982-1983 0.9854 0.9920 0.9952 0.99811983-1984 1.1287** 1.1303** 0.9948 1.00391984-1985 0.8846** 0.8774** 1.0113 0.99711985-1986 1.0311* 1.0277**, 1.0008 1.00261986-1987 1.0392** 1.0270* 1.0052 1.0066*-1987-1988 1.0326** 1.0391** 0.9992 0.9945*1988-1989 1.0153 1.0185 0.9944 1.0024

STATE BANKSYear Malmquist ATechnology APureEfficiency AScale1980-1981 0.9474** 0.9409** 0.9973 1.00961981-1982 0.9784*,- 0.9824 0.9974 0.99861982-1983 0.9831 0.9784* 1.0017 1.00311983 1984 1.1025** 1.0953** 1.0076 0.99901984-1985 0.9451** 0.9368** 1.0007 1.0082*1985-1986 0.9835* 0.9654** 1.0060 1.012641986-1987 1.0396** 1.0383** 1.0015 0.99971987-1988 1.0282** 1.0357** 0.9994 0.9934*1988-1989 1.0021 1.0038 0.9983 1.0000

ALL BANKSYear Malmquist ATechnology APureEfficiency AScale1980-1981 0.9479** 0.9448** 0.9983 1.00491981-1982 0.9676** 0.9749** 0.9929 0.99971982-1983 0.9749** 0.9672** 1.0002 1.0078*$1983-1984 1.1066** 1.1035** 0.9995 1.00331984-1985 0.9270** 0.9080** 1.0101** 1.0107**1985-1986 0.9914 0.9677** 1.0122** 1.0122**1986-1987 1.0392** 1.0327** 1.0061 1.00021987-1988 1.0287** 1.0385** 0.9973 0.993341988-1989 1.0094 1.0195** 0.9955 0.9946*NarEs:The symbols (*) and (**) indicatesignificanceat 5 percentand 1 percent evels, respectively,underboth asymptoticand bootstlappedapproaches. f the asymptoticconfidence ntervalresults n a differentconclusion regarding ignificance this is indicatedby either a (-), in-dicating insignificance under he asymptotic approach,or a (0, indicating significance at the 5 percent significance level. Regulatoryenvi-ronment s presented rom most restrictive UNIT) to least restrictive STATE).


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for 1984-1985; it then grows againabove 1. Note thatAPureEfficiencyandAScalearerelativelyflatindicatingthatalmostall the changes in productivityweredue,notto diffusion of technology or scale changes, but ratherto technologicaladvances.Upon examinationof the /\Technologycolumnof Table3, it is apparenthatthosevaluesclosely mirror hatof theMalmquistcolumn.Note alsothatthevaluesthataresigniIScantlyifferent rom 1 aremostly in theMalmquistandATechnology olumnswith APureEfficiency and AScale registeringsignificanceonly occasionally.Thisfindingcontrastswith thatof Berg,F0rsund,andJansen(1992) who foundthatNor-wegianbanksconvergedrather haninnovatedduring he 1980s. However, t is con-sistentwithWheelock andWilson's (1999) U.S. study,which foundlargeadvancesin technologybetween 1984 and 1993.Considering each regulatoryenvironmentindividually the following patternsemerge. For LIMITbanks productivitywas less than 1 between 1980 and 1983;then between 1983 and 1984, productivityrose dramatically 12.9 percent)relativeto otheryearsbefore falling backdown below 1 (indicatingproductivitydecline of11.5percentfor 1984-1985). After 198Sftherewas sustainedprogressas productiv-ity rose above 1 for the durationof the decade. The patternfor LIMITbanks liessomewherebetweerlUNIT andSTATE.STATEbanks arevery similarto, althoughsomewhatless volatile than, LIMIT,its 1983-1984 peak is 10.3 percent and its1984-1985 troughis 5.5 percent.Finally UN1Tbanks are the most volatile of thethreeregulatory onditions; ts peaksandtroughsareusuallymorepronounced hanthoseforLIMITandSTATEbanks.Forexample,UNIThas a significantproductiv-ity decline of 12.5 percentfor 1982-1983 not apparent or LIMITor STATE; tspeakin 1983-1984 of 12.2 percentandtrough n 1984-1985 of 13.4 percentareatleast as largeas those for LIMITbanks.Thus, UNIT banksarereactingin a morevolatilemanner o changesin theirenvironments.lSFigure 2 showsthecumulativeeffect of productivitygrowthforeach subperiodofthe 1980s. The Malmquist s trendingupwardbutdoes not get above 1 for STATEand LIMITbanksuntil late in the decade.l9Contrastthis with the DEA study of

18. Analysts in the industrybelieve the transformationpproachs (perhapsweakly)dual to themar-gin approach.Toexplorethis issue, two additionalmodel specificationswere run:(i) deposits aretreatedas an outputrather hanan input,and(ii) purchased unds, in additionto deposits,aretreatedas outputs.Compared o each other,models (i) and (ii) yield similargraphs.Comparisonof models (i) and(ii), withthe transformation pproach ocused on in the paper,yields both distinctsimilaritiesas well as differ-ences. Forexample, a mainfinding of this paper s thatproductivity rendsoverthe decadeareprimarilydue to innovationrather hanimitationor scale change.This observations mirroredwith themarginap-proach: hegraphsof l\TechnologyandMalmquistarevery similarAlso, beforethe 1982-83 periodandafter the 1984 85 period,the trendsfor the marginandtransformation pproachesarevery similar;thedifferences thatdo arise appearbetween 1982 and 1985. The dramaticpeak and troughapparent or1983-84 and 1984-85 under he transformationiew is mutedandshifted.Forexample,while UNITstillhas a peak for 1983-84, it is only between2.3-4 percent(dependingon whetheryou considerModel (i)or (ii); this is smallerthanthe 12 percentunderthe transformationiew); also, it is followed by a troughthatis between3.4-4.7 percent(as compared o 13.4 percentfor the transformationiew). Althoughthelevel of theresponsemaydiffer,theoverallpattern or UNIT is remarkablyimilarto thatexhibitedunderthe transformation pproach.STATEand LIMITexhibit mutedlevels as well as shifted patterns.Bothhavepeaks in 1982-83 and 1984-85 while thetroughnow occurs in the 1983-84 period.l9. The cumulativeplots for ATechnology,APureEfficiency,andAScaleexhibit the same patternes-tablishedearlierwith the discussionfor Table 3; ATechnologyclosely mirrors he Malmquistplot whileAPureEfficiencyandAScalearerelativelyflat.


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1980-1981 1980-1982 1980-1983 1980-1984 19861985 1980-1986 1980-1987 1980-1988 1980-1989FIG. 2. CumulatedGrowth or Malmquist ndex by RegulatoryEnvironment Model 1)

Elyasiani and Mehdian (1995) that found technological and efficiency regress forlarge banks. That analysis was limited to two years of data (1979 and 1986) whichmay have maskedthe overall productivity ffects. In addition,rather han separatingthe data by regulatoryenvironment, he data was pooled. To make a more directcomparison of their results with the current study, a vertical line is drawn at the1980-1986 cutoff and the ALL cumulative results are also plotted. Note that theMalmquist s below 1 for all three regulatory nvironmentsas well as the ALL cate-gory at that point in time. It is only when the analysis is carried further nto thedecade do values above 1 start appearing or two of the three regulatoryenviron-ments; the ALL grouping never makes it above 1. In addition, the currentstudy isdone annuallyover a decade which reveals a more detailed picture than comparingthe end points of an eight-year span as in Elyasiani and Mehdian.Thus, as noted byBergerand Humphrey 1997), measurementover longer time periods s necessarytodiscern f the deregulatory nd othershocks of the 1980s had a net positive impactonproductivity, fficiency and technology.

5. CONCLUSIONS

This paper quantifiesthe productivity,efficiency, and technological changes forlarge U.S. commercial banks during the 1980s using the Malmquist productivityindex. One advantageof this index is the ability to separateout diffusion of technol-ogy (movement toward the productionfrontier) from shifts in technology (move-ment out of the frontier) and scale changes (movements toward or away fromconstant-returns-to-scaleperation).Another advantage s that, unlike econometricapproaches, t does not smooth effects; the flexibility inherent n this nonparametricmethodology allows for substantialannual variations o be detected if they exist in


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thedata.Thispaperalso utilizesrecentbootstrappingiteratureo identifysignificantchanges in productivity,mitationandinnovation.Resultssuggestthatbanksunderthreedifferentregulatory nvironments UNIT,LIMIT,andSTATE actedsimilarlyin termsof trend,althoughby varyingdegrees(levels were different),to the deregulatory,inancial,andtechnologicalinnovationswhich were rapidlyoccurringduringthis decade.All banktypes made tremendousgainsin productivityandtechnologicaladvancesbetween 1983 and 1984.Thisexer-tion led to a recovery period of one or two years during which productivity re-gressed.Finally,afterthe wave of shocks,whichroiledthe industry n the earlypartof the decade,the banksadjustedandsettleddowninto a patternof slower,steadiergrowthandinnovation.Considering he entirebody of evidence presented n this paper,thereappears obe a several-year lag time between when the deregulatorybills were passed andwhen the industry finished reacting and returnedto relatively stable levels ofgrowth.20 hepresenceof anadjustment eriodhasbeenobservedby HumphreyandPulley(1997). These authorsaveraged heir dataoverthreeconsecutivefour-year n-tervals andfound thatlargebanksexperiencedsizableadjustment osts between the1977-80 and1981-84 intervals n responseto deregulation.Theyconcludedthattheadjustment o deregulationwas essentially complete after four years. The presentstudyfine-tunes he analysisand is able to pinpointtheend of the adjustmentperiodto 1985, a yearlater,because it is ayear-by-yearbreakdown hatdoes not smooth theannualchanges.The averagebankdid not move closer to the frontier; he measuredchanges inproductivityareduealmostentirelyto shifts in technologyrather hanchangesin ef-ficiency.The lack of dramatic ncreases in terms of efficiencymay be explained bythefactthat,by the 1980s,banksalready acedsignificantcompetition romother fi-nancialinstitutions.For example, starting n the late 1970s, money marketmutualfundsexpanded,erodingsome of the competitiveadvantageof thebanking ndustryby thebeginningof the 1980s (Berger,Kashyap,andScalise 1995). It is important orealize thatAPureEfficiencyheld nearone throughout he decade indicatingthat,even though the productionfrontierwas being pushed out by technological ad-vances, firms on averagewere not falling furtherbehind.Thus, even thoughtherewere no greatgains in efficiency, neitherwere there any great losses: banks werekeeping up despite the fact they were being measuredrelative to more advancedtechnology.The resultspresentedhere arein agreementwith those studiesfindingslightpro-ductivityprogressduringthe 1980s. It is apparent,however,thatby groupingtheregulatoryenvironments ogether the productivityeffects become muted:the ALLgroupingindicatesproductivityregress of approximately1 percentfor the decade

20. The DepositoryInstitutionsDeregulationand MonetaryControlAct (DIDMCA) was passed byCongress n late 1980. This was followedtwo yearslater by theGarn-St.GermainDepositoryInstitutionsAct (DIA).


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A Non Parametric Approach for Assessing the Productivity Dynamics of Large US Banks