Directorate Supervision

Large Bank Efficiency in Europe and the United States: Are There Economic

Motivations for Geographic Expansion in Financial Services?

J.W.B. Bos, J.W. Kolari

Research Series Supervision no. 61

July 2003

De Nederlandsche Bank

Samenvatting

In dit paper maken we gebruik van stochastische grensmodellen om schaalvoordelen,scope voordelen en X-effficiëntie te schatten voor zeer grote Europese en Amerikaansebanken over de periode 1995-1999. Met betrekking tot schaalvoordelen tonen onzeempirische resultaten dat grote Europese en Amerikaanse banken deels zeer veelovereenkomsten vertonen. Schaalvoordelen zijn positief, zowel voor onze winst- alsvoor onze kostenmodellen. Scope voordelen zijn negatief voor onze kostenmodellenen positief voor onze winstmodellen. Wanneer we vervolgens onderzoek in hoeverrestochastische winst- en kostengrenzen vergelijkbaar zijn, ontdekken we dat van eengezamenlijke winstgrens mogelijk sprake is. Voor een gezamenlijke kostengrens vin-den we echter overtuigend bewijs. Bovendien zijn Amerikaanse banken gemiddeldgenomen meer winst-efficiënt dan banken in de meeste Europese landen. Uit onzeverdere analyse blijkt dat potentiële efficiëntievoordelen mogelijk te behalen zijnmiddels geografische expansie van grote Europese en Amerikaanse banken.

Key words: X-efficiency, scale economies, scope economies, distance, stochasticfrontiers, bankingJEL classification: G21, L11, L22, L23

Large Bank Efficiency in Europe and theUnited States: Are There Economic

Motivations for Geographic Expansion inFinancial Services?

J.W.B. Bos a,1,2, J.W. Kolari b,1

aj.w.b.bos@dnb.nl, Banking and Supervisory Strategies, De Nederlandsche Bank,P.O. Box 98, 1000 AB, Amsterdam, the Netherlands

bProf. Dr. James Kolari, j-kolari@tamu.edu, Texas A&M University, Lowry MaysCollege and Graduate School of Business, College Station, TX 77843-4218, USA.

Abstract

This paper employs stochastic frontier cost and profit models to estimate economiesof scale as well as X-efficiency for multi-billion dollar European and U.S. banks inthe period 1995-1999. Empirical results with respect to separate analyses of largeEuropean and U.S. banks are strikingly similar with decreasing (increasing) cost(profit) returns to scale. We find that large banks in Europe and the U.S. have costand profit functions that are similar with increasing returns to scale and decreasing(increasing) scope economies for the cost (profit) model. Further analyses evaluatethe reasonableness of estimating a combined cost or profit frontier for Europeanand U.S. banks. We find that, while a single profit frontier may exist, separatecost frontiers are implied. Although profitability in absolute terms is equal, largeU.S. banks tend to exhibit higher average profit efficiency than European bankson average. Moreover, banks in the U.S. are more profit efficient than banks inmost individual European countries. We conclude that the empirical results tendto support the notion that potential efficiency gains are possible via geographicexpansion of large European and U.S. banks.

Key words: X-efficiency, scale economies, scope economies, distance, stochasticfrontiers, bankingJEL classification: G21, L11, L22, L23

1 Introduction

Deregulation of the banking industry in Europe and the United States in the1980s and 1990s stimulated an unprecedented merger and consolidation wave(see Berger and Strahan (1998)). However, most geographic expansion hasbeen limited to continental borders, rather than crossing over the AtlanticOcean (Berger and Humphrey (1997)). In view of recent changes in Europeanand U.S. banking laws, the next expansion wave may involve an internationalconsolidation. 3 Over the past half-century, financial systems in Europe andthe U.S. have become increasingly integrated by virtue of the international flowof money and capital in securities markets. In the near future the process ofintegration may be completed by increasing structural overlap among financialinstitutions via cross-Atlantic consolidation. 4

The prospect of joint European-U.S. consolidation of financial services raisesnumerous questions. Will such inter-continental expansion result in publicgains in terms of the quality and prices of financial services? What are thedriving forces motivating large banks in Europe and the U.S. to expand?In this regard, is it possible that mega-institutions combining geographically-dispersed operations are more efficient in terms of costs and profits than other-wise? If increasing returns to scale are available to large banking institutions,an economic rationale for further geographic expansion would exist. More-over, efficiency differences between large banks in Europe and the U.S. would

1 The authors thank seminar participants at Maastricht University and De Ned-erlandsche Bank for their helpful remarks. We are especially thankful for valuablecomments from Jaap Bikker, Lawrence Goldberg, Clemens Kool, Iman van Lelyveldand Erik de Regt on earlier drafts of this paper, as well as from participants at the2002 annual meetings of the Financial Management Association in Copenhagen,Denmark. We also thank Alan Montgomery for excellent research assistence. Theauthors gratefully acknowledge financial support from the Netherlands Organiza-tion for Scientific Research (NWO) and Center for International Business Studies,Mays Business School, Texas A&M University. The usual disclaimer applies.2 The views expressed in this article are personal and do not necessarily reflectthose of De Nederlandsche Bank.3 In the European Union, recent banking legal reforms are the Second Banking Co-ordination Directive of 1988 and the establishment of the single market for financialservices in 1993. In the U.S., the Riegle-Neal Interstate Banking and BranchingAct of 1994 and the Financial Services Modernization Act of 1999 have expandedgeographic and financial services powers of banking institutions.4 We refer to geographic expansion as any means by which a bank can expandgeographically, both within and across borders. As such, geographic expansion ismore encompassing than bank mergers. A second and related reason for our focuson geographic expansion is the fact that there have been very few cross-Atlanticmergers to date, which would worsen the Lucas-critique in any test of these mergers’success.

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imply that there is an opportunity to enhance efficiency via cross-Atlantic ex-pansion. 5 Of course, aside from cost and profit considerations, cross-Atlanticconsolidation of large banks could be motivated by a variety of other factors,including market power, diversification, and management incentives (e.g., seeMilbourn, Boot, and Thakor (1999)).

This paper seeks to examine the question of economic motivations for cross-Atlantic geographic expansion by conducting stochastic frontier cost and profitanalyses to estimate economies of scale as well as X-efficiency for multi-billiondollar European and U.S. banks in the period 1995-1999. Based on separateanalyses of large European and U.S. banks, we find that cost and profit func-tions for banks in both regions are strikingly similar with increasing returns toscale and decreasing (increasing) scope economies for the cost (profit) model.Importantly, X-efficiency scores derived from these cost and profit models re-veal that on average European banks have lower cost and profit efficienciescompared to U.S. banks, and the dispersion of both profit and cost efficiencyscores is considerably smaller for U.S. banks than for European banks.

Further analyses evaluate the reasonableness of estimating a combined costor profit frontier for European and U.S. banks. A necessary condition forcomparable-shaped frontiers is for economies of scale to be similar amongefficient banks in Europe and the U.S. We therefore test for differences ineconomies of scale by moving progressively closer to the frontier in an effortto evaluate the appropriateness of estimating a single frontier for both regions.In brief, we find that, while no single cost frontier exists, a single profit frontieris implied. U.S. banks tend to exhibit higher average profit and cost efficiencythan European banks in general and compared to most individual Europeancountries. In a separate analysis, we find that small banks are less cost andprofit efficient than large banks in Europe and the U.S.. We conclude that,based on profit model evidence of both increasing returns to scale and differ-ences in cost and profit X-efficiency, our empirical results tend to support thenotion that potential profit efficiency gains are possible in cross-Atlantic bank

5 The literature on the performance benefits of bank mergers is mixed (see Bergerand Humphrey (1992), Rhoades (1994), and Peristiani (1997)). However, a recentstudy by Rhoades (1998) performed case studies of nine large U.S. bank mergersand found that cost efficiency improved in each case. Seven of the bank mergercases exhibited increased profitability relative to their peers. In general, acquiring(acquired) banks were more (less) efficient than their peer group. Thus, while notall mergers yielded increased performance, most large bank combinations providedeconomic benefits relative to peer banks. Moreover, Siems (1996) has reported evi-dence that shareholder wealth significantly increased in response to megamergers ofU.S. banks in 1995. The author inferred that the results tended to support in partthe synergy hypothesis, whereby acquiring banks reap economies of scale and scopevia cutting costs of redundancies and duplication of operations.

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mergers between European and U.S. banks.

Section II overviews related literature on the efficiency of European and U.S.banks. Section III describes our methodology, Section IV gives details of thedata, and Section V reports the empirical results. The last section gives con-clusions.

2 Related Literature

A large body of literature that spans a half-century exists on banking effi-ciency in the U.S. (e.g., see surveys in Berger and Humphrey (1997), Bergerand Strahan (1998), and Berger, Demsetz, and Strahan (1999)). Likewise,a more recent but growing literature on European banking efficiency is de-veloping (e.g., see Molyneux, Altunbas, Gardener (1997), Sheldon (1999), andAltunbas, Gardener, Molyneux, and Moore (2001)). Studies prior to the 1980stended to report U-shaped cost curves with economies of scale exhausted attotal assets worth $100-$500 million for the most part. Results for economiesof scope (i.e., joint production of outputs) were mixed, with most authorsconcluding that banks do not gain efficiencies from providing multiple finan-cial services to the public. Altering the path of efficiency research, Berger andHumphrey (1991) showed that U.S. banks could improve their cost efficiencymore by reducing frontier inefficiencies than by reaching some optimal level ofscale and scope economies to minimize average costs. Subsequent research fur-ther investigated this issue using both parametric and non-parametric frontierestimation methods (e.g., see Lovell (1993)). Moreover, recent research hasexpanded the analyses to consider both cost and profit efficiency (e.g., seeBerger and Mester (1997), Berger and Humphrey (1997), and others), as wellas risk variables (e.g., see Berg, Førsund, and Jansen (1992), McAllister andMcManus (1993), Mester (1996), Berger and DeYoung (1997), and others).In general, studies have confirmed Berger and Humphrey’s result that costand profit frontier inefficiencies outweigh output inefficiencies associated withscale and scope economies by a considerable margin.

A major gap in early bank efficiency literature was the scant evidence on largebanks. This shortfall was substantial due to the pivotal role of large institu-tions in shaping the structure of the banking industry. If large bank size isclosely related to the efficient production of financial services, the implicationis that the post-deregulatory consolidation movement will result in a highlyconcentrated banking industry dominated by a relatively small number of in-stitutions. Conversely, if inefficiencies occur as banks expand output beyondsome size threshold, it is likely that the organizational structure of the indus-try would be less concentrated with a larger number of banks offering servicesto the public. Without research on large bank cost and profit efficiencies, noinferences about deregulation and related policy implications to banking in-dustry structure could be made.

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In the 1980s and 1990s numerous studies on large U.S. banks were publishedto overcome this shortfall in the literature. 6 Summarizing this literature, scaleeconomies were found for banks between $1 billion and $15 billion in assetswith diseconomies thereafter. The existence of scope economies was more elu-sive with most studies reporting insignificant results. One exception is that,upon resolving some econometric problems plaguing previous work in thisarea, Pulley and Humphrey (1993) reported significant scope economies inthe joint production of two types of deposit services and three credit areas.Finally, consistent with Berger and Humphrey, studies have confirmed thatfrontier inefficiencies are far greater than scale and scope inefficiencies.

To our knowledge no European studies have focused on large bank efficiencyper se; instead, banks of different sizes are comparatively examined. 7 Only afew studies have been published on the subject of large bank efficiency outsidethe U.S. Allen and Rai (1996) estimated a global cost function for 194 banksin 15 countries (including the U.S.). Banks were divided by asset size intotwo groups (i.e., small versus large banks below and above the median assetsize of a country’s banks, respectively) and by regulatory environment (i.e.,countries with functionally integrated or universal banking versus those withfunctionally separated banking). Since the median bank asset size in mostcountries exceeded 40 billion U.S. dollars, most banks in the study can beconsidered large banks. They found that universal banking countries weremore efficient than non-universal banking countries, which implies that banksoffering a variety of financial services (e.g., loans, deposits, insurance, securitiesinvestment, real estate, etc.) are more competitive than banks offering selectedfinancial services. Also, France, Italy, the U.K., and the U.S. had the mostinefficient banking institutions.

Another study by Saunders and Walters (1998) measured scale and scope

6 See studies by Hunter and Timme (1986), Shaffer and David (1986), Kolari andZardkoohi (1987), Noulas, Ray, and Miller (1990), Hunter, Timme, and Yang (1990),Elyasiani and Mehdian (1990), Evanoff and Israilevich (1990), Berger, Hunter, andTimme (1993), Saunders and Walters (1994), Hunter (1995), Jagtiani, Nathan, andSick (1995), Jagtiani and Khanthavit (1996), Miller and Noulas (1996), Mitchelland Onvural (1996), Rhoades (1998), and Rogers (1998).7 For example, see studies by Berg, Førsund, and Jansen (1992), Fecher and Pestier(1993), Berg, Førsund, Hjalmarsson, and Suominen (1993), Pastor, Pérez, and Que-sada (1994), Vander Vennet (1994), Altunbas and Molyneux (1996), Griffell-Tatjeand Lovell (1996), Ruthenberg and Elias (1996), Soares de Pinho (1996), Molyneuxet al. (1997), Economic Research Group (1997), Mendes and Rebelo (1997), Pas-tor, Pérez, and Quesada (1997), Resti (1997), Altunbas and Chakravarty (1998),Dietsch, Ferrier, and Weill (1998), Battese, Heshmati, and Hjalmarsson (1998), Al-tunbas, Goddard, and Molyneux (1999), Bikker (1999), Sheldon (1999), VanderVannet (1999), Berger, DeYoung, Genay, and Udell (2000), Hassan, Lozano-Vivas,and Pastor (2000), and Altunbas, Gardener, Molyneux, and Moore (2001).

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economies for 133 of the largest 200 banks in the world at year-end 1988.Based on a translog cost model, they found that, while banks with loans lessthan $10 billion and more than $25 billion exhibited scale diseconomies, banksin the middle range had scale efficiencies. Also, scope diseconomies betweenfee-earning and interest-earning financial services existed. Given that theirsample banks typically operated in multiple countries, they concluded thatinternational expansion may well offer economies of scale opportunities formany financial institutions. They also concluded that it was too early in the1980s to make clear inferences about potential scope economies, which theybelieved might materialize after some initial fixed costs of expanding beyondtraditional commercial banking activities had been incurred.

The aforementioned large bank studies are unique from other European workin that consolidated data are employed in the analyses. By consolidating thedata from the entire organization, they provide insight into bank efficiencyat the firm level, rather than at divisional or branch levels. There have beenother efficiency studies of European banking that provide some large bankresults, but they typically have employed unconsolidated data. For example,Berger, DeYoung, Genay, and Udell (2000) reported efficiency results for Eu-ropean banks with assets exceeding $100 million; however, they are careful toobserve that their results are only relevant for subsidiaries of banking orga-nizations due to the use of unconsolidated data. In this regard, they notedthat transfer pricing can shift profits from one affiliate to another and affectefficiency estimates for subsidiaries. While they did not believe that this po-tential bias was significant in their study, it is not possible to determine theextent to which transfer pricing, shared inputs, and other intra-organizationalarrangements might impact efficiency assessments. The authors estimated sep-arate cost and profit functions for 2,123 commercial banks (i.e., other types ofbanks are excluded) with data available for the period 1993-1998 in France,Germany, Spain, U.K., and the U.S. Comparative analyses revealed that do-mestic banks on average had higher cost and profit efficiency than foreignbanks in these countries. However, when the results were disaggregated on acountry-by-country basis, they found that foreign banks from some countrieswere equal to or more efficient than domestic banks. Interestingly, U.S. banksoverseas tended to be more efficient than domestic banks in their respectivecountries. They inferred that, since there is not necessarily a home field ad-vantage, additional global consolidation is likely in the future. Relevant to ouranalyses, they recommended that future empirical work in this area shouldexpand the analyses to a substantial number of countries.

Another study by Sheldon (1999) used unconsolidated data for 1,783 com-mercial and savings banks in the EU, Norway, and Switzerland for the period1993-1997. Data envelopment analysis (DEA) was employed to examine costand profit efficiency. They found that large banks, specialized banks, and retail

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banks are more cost and profit efficient than small banks, diversified banks,and wholesale banks, respectively. Average frontier efficiency was fairly low,at about 45 percent for costs and 65 percent for profit. Banks in Denmark,France, Luxembourg, and Sweden had the highest average efficiency, and banksin Greece, Italy, Portugal, Spain, and U.K. had the lowest average efficiency.Furthermore, estimates of economies of scale in costs and profits indicatedthat most banks in their sample were sub-optimal in size, with optimal scalesin the range of 0.5 to 1.5 billion U.S. dollars. Decreasing cost and profit returnsto scale were reported for most multi-billion dollar banks. These and other re-sults led them to conclude that inefficient operations, rather than unexploitedeconomies of scale, explain cost and profit differences across European banks.The authors inferred that diseconomies of large scale with respect to both costsand profits prohibit a high degree of industry concentration in the Europeanbanking market.

In view of previous literature, the present study contributes new empiricalevidence on large bank efficiency. Comparative analyses of European and U.S.large banks provide perspective in understanding similarities and differencesbetween institutions located in these two regions of the world. Unlike pre-vious European bank studies, we employ consolidated data for independentbanks, as opposed to all entities contained within the organization. Whilesome studies do use consolidated data, they do not exclude banking entitiesfor which the organization does not have a controlling interest (e.g., at least25 percent ownership of common stock). 8 Instead, they include banks thatare under controlling interest by others as separate entities. Consequently,these studies suffer from double counting and tend to include banks that arenot independent organizations. To a significant extent, this also runs counterto the profit-maximization and/or cost-minimization assumptions behind theefficiency measures employed, where banks are assumed to choose the in-put/output mix that is most efficient. Finally, we extend prior work by Allen

8 We select independent bank accounting statements for European banks by onlyincluding entities that are not controlled by other firms. Most research has usedconsolidated data from IBCA/BankScope. However, BankScope has ownership datathat are kept on record for only the last year of a sample period; moreover, as notedby the publisher of BankScope, or Bureau van Dijk, ownership data are incompleteand dependent upon availability. National accounting standards require majorityownership to be published in some countries, whereas for others this informationis provided on a voluntary basis. With the kind assistance of Mark Wessels andPatrick Oosterling of Bureau van Dijk, we were able to manually retrieve updatedownership and control data from the 1995-2000 issues of BankScope. Gaps in thesereports were filled by gathering further data from Dunn and Bradsheet Linkages,Reuter’s News, and banks’ annual reports. In this way we constructed a completeset of large, independent commercial banks for each of the years included in oursample.

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and Rai (1996) and Saunders and Walters (1998) by collecting larger sam-ples of multi-billion dollar banks and updating analyses to the last half ofthe 1990s. Like Allen and Rai, we give some comparative results for small,independent banks also. We next turn to further details of our methodology.

3 Methodology

3.1 Bank Efficiency 9

The general concept of efficiency refers to the difference between observed andoptimal values of inputs, outputs, and input/output mixes. Efforts to measurehow efficiently a firm produces outputs from its inputs have led to the devel-opment of a number of efficiency concepts, including scale efficiency, scopeefficiency, and X-efficiency. Berger, Hunter and Timme (1993) have defined X-efficiency as the economic efficiency of any single firm minus scale and scopeefficiency effects, thereby allowing for sub-optimal (beneath-frontier) opera-tions. 10 In this paper we employ stochastic frontier models that allow us tomeasure scale and scope efficiency as well as X-efficiency. According to Bergerand Humphrey (1991) and Berger, Hunter, and Timme (1993), the signifi-cance of scale and scope inefficiencies (amounting to about 5 percent) is lessimportant in the banking industry than X-inefficiencies (in the range of 20-25percent). 11

We use stochastic frontier (SFA) models for two important reasons: (1) theyallow for measurement error, which is an important feature in light of thefact that measuring bank production can be difficult due to data availabilityand the choice of a set of inputs and outputs; and (2) they generate firm-specific efficiency estimates, which allow us to test for differences in efficiencyamong banks from different countries as well as measure the scale and scopeeconomies of banks that operate close to the frontier. 12

9 We refer to Lovell (1993) and Coelli, Prasado Rao, and Battese (1998) for anin-depth discussion of different efficiency measures. See also Berger, Hunter andTimme (1993) for an excellent overview of the use of different efficiency concepts inbanking.10 Economic efficiency is the sum of technical and allocative efficiency. Technicalefficiency is a measure of a bank’s distance from the frontier, minimizing inputsgiven outputs or vice versa. Allocative efficiency measures the extent to which abank is able to use inputs and outputs in optimal proportions given prices and theproduction technology.11 See also Berger and Humphrey (1997) and Molyneux, Altunbas and Gardener(1997).12 Concerning the measurement of X-efficiency, Bauer, Berger, Ferrier, andHumphrey (1997) imposed six consistency conditions and examined the extent towhich stochastic frontier (SFA) models, thick frontier models (TFA), distributionfree models (DFA), and data envelopment analysis (DEA) meet these consistency

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3.2 Model Specification

We employ SFA cost and profit models similar to those in Humphrey andPulley (1997), Berger and Mester (1997), and DeYoung and Hassan (1998).Banks are assumed to face perfectly competitive input markets but operate inoutput markets where price differentiation is potentially possible. This frame-work easily accommodates our cost model with only trivial modifications. Italso allows for market power in our profit model. Hence, banks can competevia their output pricing strategies by adjusting prices and fees according tomarket conditions. The extent to which they can influence prices depends onoutput quantities, input prices, and other factors, all of which are given atthe time of price setting. Additional features of the profit model are that itcan account for differences in the quality of outputs (to the extent that itis reflected in prices) as well as correct for scale bias. Also, output prices,which are subject to severe measurement problems according to Berger andMester (1997) and Vander Vennet (1999), are not required for the empiricalanalysis. 13

For the estimation of the cost and profit frontier functions, we use the translogfunctional form. This form has been widely employed and allows for the nec-essary flexibility when estimating frontier models. Berger and Mester (1997)have compared the translog to the Fourier Flexible Form (FFF). Despite thelatter’s added flexibility, the difference in results between these methods ap-pears to be negligible (see also Swank (1996)). Moreover, previously cited bankefficiency studies have shown that the translog cost and profit functions arelocally stable in large bank applications.

We define profit before tax as PBT, outputs as Y, and input prices as W. 14

Also, let control variable Z reflect differences in risk-taking behavior of banks.We also include linear and quadratic trend terms. For the specific choice ofvariables, we refer to the next section. In the specification below, the optimalprofit level for bank k in period t is now a function of the number of outputs,input prices, and the control variable Z. In a three-input, three-output translogsetting, u and v are the inefficiency and random error terms, respectively, andai, aij , bi, bij, ci,di, dij , ei, fi, gi, and hi are parameters:

conditions. They found that the choice between these different models did not ap-pear to significantly alter efficiency measures. In a study comparing DEA and SFA,Eisenbeis, Ferrier, and Kwan (1999) reported that SFA efficiency scores were moreclosely related to risk-taking behavior, managerial competence, and bank stock re-turns than those for DEA.13 For a theoretical framework for the SFA models used here, see Coelli, PrasadoRao, and Battese (1998) and Bos (2002).14With respect to notation, we use lower case symbols in italics to denote loga-rithms. Upper case symbols represent actual values of the variables.

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pbtkt(y, w, z)= a0 +3P

i=1aiwikt +

1

2

3Pi=1

3Pj=1

aijwiktwjkt +3Pi=1

biyikt (1)

+1

2

3Pi=1

3Pj=1

bijyiktyjkt + c0zkt +1

2c1z

2kt +

3Pi=1

3Pj=1

dijwiktyjkt

+3P

i=1eiwiktzkt +

3Pi=1

fiyiktzkt + g0T +1

2g1T

2 +3P

i=1diwiktT

+3P

i=1hiyiktT + c2zktT + vkt − ukt

The error term vkt is normally distributed, i.i.d. with vkt ∼ N(0, σ2v). Theinefficiency term ukt is drawn from a non-negative half-normal distributiontruncated at µ and i.i.d. with ukt ∼ |N (µ, σ2u)|. The trunctation mean µresults from the MLE. It carries a negative sign because all inefficient firmswill operate below the efficient profit frontier. For the estimations involvingU.S. and European banks, we also use n-1 dummies for each of the Europeancountries. For the cost model the left-hand side is replaced with the log of totalcosts (after an identical transformation) and the inefficiency term ukt carriesa positive sign, as all inefficient firms operate above the efficient cost frontier.

Duality requires the imposition of symmetry and linear homogeneity in inputprices to estimate our cost and profit models (see Beattie and Taylor (1985)and Lang and Welzel (1999)):

aij = aji ∀i,j, bij = bji ∀i,j,3Xi=1

ai = 1,3Pi=1

aij = 0 ∀i,3P

i=1aij = 0 ∀j,

3Pi=1

dij = 0 ∀j,3P

i=1ei = 0,

3Pi=1

di = 0

We impose linear homogeneity in input prices by normalizing the dependentvariable and all input price variables (W) before taking logarithms (see Coelli,Prasado Rao, and Battese (1998)). 15

Profit efficiency for bank k at time t is defined as: 16

15 Each of these variables is included as a ratio to one of the input price variables, andthe coefficient for each input price is inferred ex post from the imposed restriction.This procedure only ensures homogeneity of degree one in factor prices. Imposingconstant returns to scale would require normalization of the output variables aswell.16 The complete derivation of the maximum likelihood estimator is available uponrequest.

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PEkt = E [exp (−υκτ)] |εκτ ] (2)

This measure takes on a value between 0 and 1 (fully efficient) and indicateshow close a bank’s profits (conditional on its outputs, input prices, and thecontrol variable) are to the profits a fully efficient bank under the same con-ditions. Cost efficiency also takes on a value between 0 and 1 (fully efficient)and is defined as 17 :

CEkt = {E [exp (υκτ)] |εκτ}−1 (3)

In estimating our profit and cost models, we apply the usual reparameteriza-tion by replacing σ2u and σ2v with σ2 = σ2u + σ2v and γ = σ2u/(σ

2u + σ2v).

18 Weevaluate CE and PE for the whole sample as well as for four asset quartilesize classes.

3.3 Scale economies for Profit and Cost Frontiers in Europe andthe U.S.

As mentioned earlier, in order to evaluate whether a single profit frontierand a single cost frontier for Europe and the U.S. can be estimated, it isnecessary to determine the shape of the individual frontiers. We should onlyestimate a joint frontier if estimated European and U.S. frontiers are similar inshape. Characteristics of cost and (to a lesser extent) profit functions are oftenexpressed in terms of economies of scale measures. Output-specific economiesof scale are calculated by taking the derivative of the profit (or cost) modelwith respect to an output. For example, based on equation (1), scale economiesfor output Y1 can be estimated as:

17 A bank that lies above the cost frontier has cost efficiency in the range from 1(efficient) to∞. We invert this measure in order to get efficiency scores comparableto those of our profit model.18 The parameter γ represents the share of inefficiency in the overall residual vari-ance and ranges between 0 and 1. A value of 1 for γsuggests the existence of adeterministic frontier, whereas a value of 0 represents evidence in favor of a stan-dard OLS estimation. Note that a deterministic frontier is by no means necessarilyidentical to a DEA model, given the latter’s restrictions on the shape of the frontierand the distribution of the inefficiency. See Coelli, Prasado Rao, and Battese (1998)for further discussion. As part of our robustness tests, we vary maximum likelihoodconvergence criteria (one-by-one) from 0.1 to 10−4 to see whether our results arerobust. In these estimations the likelihood value, model coefficients, and efficiencymeasurements do not change significantly but the number of iterations does vary.

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∂ pbtkt∂ y1

= a1+a11y1kt+1

2a12y2+

1

2a13y3+d11w1kt+d21w2kt +d31w3kt+f11zkt

(4)

For the profit function a value larger (smaller) than one indicates increasing(decreasing) returns to scale, and unity indicates constant returns to scale. Forthe cost function scale estimates are oppositely interpreted. Overall economiesof scale are simply the sum of output-specific economies of scale. When mea-sured at the frontier, economies of scale are a good indicator of the shape ofthe frontier.

Berger, Hunter, and Timme (1993) identified four aspects of the measurementof economies of scale that are relevant to our analyses. First and foremost,research has confirmed that banks have U-shaped cost curves. Economies ofscale increase up to a relatively modest size, often estimated in the range of$100-$500 million in total assets, after which they tend to decrease (albeitslowly). Since the large banks in our samples normally operate well beyondthe minimum average cost point, we need only match one segment of the costcurve, rather than the entire curve.

Second, risk variables are often excluded when measuring economies of scale.Following Mester (1996) and Berger and Mester (1997), we attempt to over-come this problem by including an equity/total assets ratio that enters scalemeasures via interaction terms.

Third, many studies base their scale measures on observations that do notlie on or close to the efficient frontier. As such, economies of scale (i.e. themarginal effects of outputs on profits or costs) cannot be separated from X-efficiency (i.e., the distance from the efficient frontier). In this case economiesof scale will be biased to the extent that banks do not lie on or close to theefficient frontier. Unlike DEA, in which actual observations make up the edgesof the frontier, the frontier is estimated in SFA. For this reason even the mostefficient bank is rarely 100 percent efficient and, in turn, identifying the banksthat are most important in shaping the frontier is not possible. This problemis worsened by the fact that the distribution of efficiency measures, whentruncated towards the frontier, is generally highly skewed, with the majorityof banks lying close to the frontier. 19 For these reasons choosing a set ofefficient banks is an arbitrary decision. Interestingly, we do not need a singlecut-off point beyond which we have a number of efficient banks; instead, oursolution to this problem derives from the fact that, if for example the costfrontiers in Europe and the U.S. have the same shape, we should expect to seea decrease in the difference in economies of scale as we get closer to the frontier.

19 This is reflected by a positive, significant value for µ/σu.

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By measuring cost and profit efficiencies as we gradually move closer to thefrontier, we decrease the bias from X-efficiency but simultaneously decreasethe number of observations in our independent sample tests. We therefore startwith the 50th percentile as a cut-off point and end with the 90th percentile,which still provides sufficient observations to obtain reliable estimates. Ateach increment we test the significance of the difference in average economiesof scale for European and U.S. banks, both with and without correction for thedifference in variance. If the frontiers do have the same shape, this significanceshould decrease as attention is narrowed to the most X-efficient banks.

Fourth, the most reliable measure of economies of scale is an overall estimate,defined as the sum of output-specific economies of scale. The sum of the partialderivatives of each output is less dependent on changes and differences inthe output mix. Therefore, we report overall economies of scale, rather thanoutput-specific economies of scale, to compare the results for Europe and theU.S. and to evaluate the shape of the frontiers. We report both results for thewhole sample as well as for four asset quartile size classes.

3.4 Scope economies

Unfortunately, calculating scope economies is not as straightforward as calcu-lating scale economies. However, scope economies are not crucial to evaluatingwhether European and U.S. banks operate under a single frontier. In addition,Berger and Humphrey (1991) and Berger, Hunter, and Timme (1993) haveshown that scope economies are far less significant than X-efficiencies. Berger,Hanweck, and Humphrey (1987) observed that for translog functions comple-mentarities cannot exist at all levels of output. Berger and Humphrey (1994)noted that an additional problem with scope estimation is the possible exis-tence of zero outputs. Also, another potential pitfall is that there is often anextrapolation problem. Given a sample containing both universal banks andother banks, only the former banks typically offer the full range of financialservices. Consequently, the economies of scope derived from the cost (or profit)function tend to overestimate the true economies of scope among most samplebanks. A further problem is that the measurement of average economies ofscope yields values that are biased due to the inclusion of X-(in)efficiencies. Inthe search for a better functional form, some researchers have used a Box-Coxtransformation for outputs, while others have used a composite function witha separate fixed-costs component of scope economies.

For cost models Molyneux, Altunbas, and Gardener (1997) proposed a com-parison of the separate cost functions for individual outputs with the jointcost of production. However, the plant and firm level data required for thistype of analysis are not available for our sample banks. We cannot claim tosolve all these problems. Instead, we propose a rather simple way of measur-ing economies of scope that overcomes some problems and mitigates other

13

problems.

In our models we have three outputs, or Y1, Y2, and Y3, which sum to Y. Westart by taking the ratios Y1/Y (= a), Y2/Y (= b) and Y3/Y (= c). If such aratio is high, a bank is relatively specialized. For overall scope economies, wecalculate d = a2+b2+c2. This measure is bounded between 1/3 (not special-ized) and 1 (specialized). We define ‘high’ [H] as referring to the upper 25th

percentile, and ‘low’ [L] for the remainder of the observations. 20 Next, for thecost model we calculate the ratio (TCH − TCL)/TCL for Y1, Y2, Y3, and Y.Likewise, for the profit model we calculate the ratio(PBTL − PBTH)/PBTL.Total costs and total profit are divided by total revenues to adjust for thepossibility that banks in high and low bank groups may have different size.In both cases, if scope economies exist, the ratio is greater than 0. Note thatthese ratios can only be constructed using averages; as such, the scope mea-sure itself does not have a standard deviation. This is a common problem, asrecognized in Berger and Humphrey (1994). Instead, we report a t-value foran independent samples test for TCH -TCL (similar to our x-efficiency tests).Note that by varying the cut-off point to more or less than the 25th percentile,we can check for extrapolation problems. Also, by measuring scope economiesfor four size classes as well as for the whole sample, we control for some of theX-(in)efficiencies which can differ between size classes.

4 Geographic Expansion

As noted by an anonymous referee, a major factor potentially affecting dif-ferences in efficiency among large banks is the geographic distance betweenbanking offices. Recent papers by Berger and DeYoung (2001, 2002) have ar-gued that efficient lead banks in a multi-bank organization can export manage-ment skills, technology, and operating practices that enhance the efficiency ofsmaller affiliated banks. On the other hand, geographic distance could dimin-ish lead bank control, cause organizational diseconomies, strain relationshipsand related information monitoring, and lead to agency costs in overseeingjunior managers. In general, their empirical findings reveal that, even thoughorganizational control over affiliates does decrease as distance from the leadbank increases, the effect is small. Also, affiliates tend to benefit from efficientorganizations, which suggests that technology overcomes barriers to efficientoperation of widely dispersed banking facilities. More benefits were found interms of profit than cost efficiency.

Following Berger and DeYoung, we conduct multivariate regression tests withcost and profit efficiency scores (CE and PE) as dependent variables andgeographic distance (in miles) between banks in banking organizations as the

20We tested for the robustness of our results by taking other cutoff points. Ourresults stay qualitatively the same for a range of approximately +/- 10%.

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focal independent variable. We also include the following as control variables:asset size (rescaled to a 0,1 range) and cost and profit levels (i.e., total costor total profit divided by size defined as total assets plus off-balance sheetactivities). Since distance and size are highly correlated with one another,we orthogonalized these variables by regressing distance on size and usingthe residual as the distance measure. Data was available for 516 Europeanbanks and 410 U.S. banks. For both Europe and the U.S. distance data havebeen gathered for 1997, the middle year in the sample period. In this regard,data were not available on European bank affiliate locations in all five sampleyears. If locational data were missing in 1997, data for the closest availableyear were available. For U.S. banks this approach simplified the collection ofgeographic distances for thousands of banking offices. As in the Berger andDeYoung study, geographic distance for Europe is measured by the sum ofdistances from the lead bank to affiliated banks (including affiliated banksoutside of Europe) divided by the total assets of the banking organization.For the U.S. we compute the sum of distances from the lead bank to affiliatedbanks (including foreign bank affiliates) as well as branch offices divided bytotal assets. The reason for the latter definition is that many U.S. banksconverted their organizations to one-bank holding companies in the 1990s bymerging bank affiliates into the lead bank as branch offices.

5 Data

5.1 Sample Data

Data on European banks are collected from IBCA reports found in BankScope.For U.S. banks data are gathered from the Call Reports for Income and Con-dition provided by the Federal Reserve System. Data for both samples arepooled for the period 1995 to 1999. The beginning year 1995 was chosen dueto the advent of interstate banking in the U.S. in 1995 as well as a singlemarket for financial services in the European Union in 1993. Because the Fi-nancial Modernization Act was effective in 2000 and fundamentally alteredthe organizational structure of U.S. banks to include greater securities and in-surance powers, we ended our analyses in 1999. During our sample period, fewregulatory changes occurred in European and U.S. banking markets, with theexception of the introduction of the Euro in 1999. It should also be mentionedthat economic conditions were stable in both regions during this period. 21

Since we comparatively examine both cost and profit efficiency, sample banksmust be profit maximizing. Also, in order to test for one cost frontier andone profit frontier for all banks, it is necessary to include banks with similar

21 An exception is the Asian crisis in 1997. Since we do not estimate a panel datamodel, and given the fact that this crisis affected all of the countries involved in ourstudy, we do not expect it to significantly affect the comparative results.

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output mixes. In this respect we exclude brokerage firms with a banking li-cense due to their large securities activities and relatively small commerciallending services. Likewise, while general banks and bank holding companiesare included in the analyses, cooperative banks, credit unions, mutual banksand credit card banks 22 are excluded.

To ensure that variables are computed similarly across countries and overtime, all values are expressed in constant 1995 U.S. dollars. 23 We then seta bank asset size cut-off point of $1 billion 1995 U.S. dollars. Although thisrestriction substantially reduces our sample size, multi-billion dollar banksrepresent the dominant share of the banking assets in Europe and the U.S.due to concentration of resources among larger banks and are most likely toengage in cross-Atlantic expansion.

As recommended by an anonymous reviewer, we conducted tests of the possibleeffect of the Euro’s introduction on January 1, 1999. A dummy variable equalto 1 in 1999 and 0 in other sample years was included in the U.S., Europe, andcombined cost and profit models. The dummy variable was mixed in sign andrarely significant across models. Importantly, the correlation of X-efficiencyscores generated from models with and without the Euro dummy exceeded0.90 in all cases and was more than 0.96 in five out of the six models. Furtheranalyses on the correlation of predicted values of the dependent variables (i.e.,the total derivative) for the sample periods 1995-1998 and 1995-1999 yieldedresults exceeding 0.97 in all models. Rank tests for both X-efficiency andpredicted values with and without the year 1999 did not significantly affectrank orders. Thus, we infer our results were not significantly affected by theadvent of the Euro.

Only independent banks and bank holding companies (BHCs) that are notowned or controlled by other firms are included in our sample. In this regard,our models presume banks have some degree of freedom to choose their in-puts and set output prices, which would not be entirely true of component

22 In the U.S. the Comptroller of the Currency defines credit card banks as thosebanks with credit card loans totaling 6.5 percent or more of total assets. We excludedbanks that exceeded this threshold from the analyses.23 As a robustness check, we also used German marks as a reference currency withno change in results. The dollar exchange rate in the sample period was relativelystable for the 17 European countries with banks in our analyses. CPI and exchangerate series were taken from EIU Country Data. All European data and U.S. dataare expressed in 1995 dollars using the U.S. CPI. Note that, since both dependentand independent variables are expressed in the same currency, our transformationto constant 1995 U.S. dollars only has an impact on the cutoff value of 1 billion 1995U.S. dollars. As shown in Table 1, only a fraction of our sample banks are close tothis cutoff point. In this regard, changing the cutoff point to slightly higher valuesdid not change our results.

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Table 1: Descriptives

A. European Banks (N = 519)a

Variable Mean Std. Dev. Skew Kurtosis Minimum Maximum

TC (total cost) 4,791,070 8,124,660 2.27 8.11 16358.6 49,246,900

PBT (profit before taxes) 831,208 1,443,620 2.66 11.03 655.76 9,177,220

Y1 (loans) 32,366,000 56,840,900 2.53 9.77 13382.7

Y2 (investments) 12,396,900 26,578,300 3.31 15.58 116.78

Y3 (off-balance sheet) 19,342,800 42,105,800 3.78 22.51 2058.87

W1 (labor price) 0.013 0.013 3.69 21.03 0.0003 0.11

W2 (financial capital price) 0.041 0.039 4.89 32.44 0.0013 0.38

W3 (physical capital price) 0.012 0.014 4.22 26.62 0.0003 0.13

Z (equity/assets) 0.083 0.093 3.84 18.51 0.01 0.66

ASSETS (total assets) 64,400,000 2.7 10.62 1,012,440

B. U.S. Banks (N = 476)a

Variable Mean Std. Dev. Skew Kurtosis Minimum Maximum

TC (total cost) 2,684,750 9,692,600 6.28 50.14 18426 98,457,300

PBT (profit before taxes) 854,247 3,124,390 6.76 59.64 3654 34,826,600

Y1 (loans) 24,701,600 89,628,300 6.69 57.58 42092

Y2 (investments) 92,70,800 32,095,400 5.91 42.34 1715

Y3 (off-balance sheet) 2.50E+09 9.53 100.49 24638 3.13E+10

W1 (labor price) 0.011 0.004 -0.92 5.34 8.29E-06 0.03

W2 (financial capital price) 0.024 0.007 -1.47 5.63 4.65E-04 0.05

W3 (physical capital price) 0.003 0.001 -0.07 5.8 5.39E-08 0.01

Z (equity/assets) 0.094 0.027 3.99 22.04 0.05 0.26

ASSETS (total assets) 42,986,500 6.37 52.55 1,020,880 1.60E+09a = Total costs, profit before taxes, outputs, and total assets are measured in thousands of 1995 U.S.

dollars.

subsidiaries within the organization. Also, and as cited earlier, Berger, DeY-oung, Genay, and Udell (2000) have noted that transfer pricing and otherintra-organizational funds flows could affect efficiency estimates. We thereforeuse consolidated statements and set limits on the maximum ownership andcontrol by outside parties. With respect to ownership, U.S. law requires banksthat are 25 percent or more owned by a single shareholder to be included in aBHC. For U.S. bank data we applied this legal criterion to the construction ofour sample banking organizations. In Europe, under the First Banking Coor-dination Directive of 1977, similar rules allow us to apply the same criterionto European banks. 24 Due to numerous mergers and takeovers in Europe andthe U.S. during the sample period, ownership thresholds are checked for alllarge banks in each year of the sample period.

24 The First Banking Directive of 1977 and further requirements set forth in 1983state that: 25 percent ownership of a bank’s shares constitutes official participation;50 percent ownership requires that proportional consolidation take place; and own-ership below 50 percent is left to the discretion of member states concerning theconsolidation procedure, with most member states requiring proportional consoli-dation for ownership between 25 percent and 50 percent.

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We also exclude all observations with variable values missing and values lessthan or equal to zero. A negative or zero value for a variable implies thatthe respective bank’s production function is quite different from other samplebanks. Moreover, if such observations were included in the analyses, an arbi-trary transformation would be required due to the fact that zero and negativevalues are disallowed in the translog model. For the combined data set only10 observations were dropped for this reason.

Lastly, outliers are considered by estimating the models with all observationsand checking for outliers in the efficiency scores. As found in other studies,outliers tend to have higher scores than other sample banks. If outliers in theindependent variables are consistent with outliers in the dependent variable,we omit the observations as long as skewness is not substantially altered. Wethen re-estimate the models and report the results with all observations (withoutliers omitted) if the coefficients have not changed (have changed) signif-icantly. To avoid heteroskedasticity problems we use weighted least squares,with weights based on the log of total assets. 25

5.2 Variables

Consistent with the intermediation approach used by most SFA studies, bankoutputs are defined as follows: loans (Y1), investments (Y2), and off-balancesheet activities (Y3). Loans aggregate commercial and industrial, real estate,consumer, agriculture, and other outstanding credit. Investments include se-curities, equity investments, and all other investments reported on the balancesheet. Off-balance sheet activities are credit items and other guarantees, loancommitments, derivative securities, and other loan and securities exposuresnot reflected on the balance sheet. Of course, these activities are particularlyimportant among large banks.

Turning to input prices, it is not possible to calculate a traditional measureof the price of labor due to incomplete data on the number of employeesin BankScope. Even if the number of employees were available, part-time em-ployees are not counted despite their increasing usage in the banking industry.Also, given the dispersion in the types of jobs at large banks (from cashier toinvestment banker), the price of labor as measured by average labor cost isnot likely an accurate proxy for the marginal cost of labor. In an effort to over-come these difficulties, we express prices as the input-specific cost per unit oftotal output. Therefore, we define the price of labor (W1) as total employeeexpenses divided by the sum of assets and off-balance sheet activities. As such,difficulties related to missing employee data, part-time workers, and averagelabor costs are mitigated.

25 In the presence of heteroskedasticity, the least squares estimator is not efficientbut still unbiased, consistent, and asymptotically normally distributed.

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Likewise, the price of financial capital (W2) equals total interest expensesdivided by the sum of assets and off-balance sheet activities, and the price ofphysical capital (W3) equals non-interest operating expenses divided by thesum of assets and off-balance sheet activities. As justification for this approach,we argue that, to the extent that inputs are substitutes for one another, theyindividually contribute to the cost per dollar output in the same way. Becauseall input prices have the same denominator, we checked for multicollinearitybut found it was not important among input prices. We also performed arobustness check by re-running the models using observations that had dataavailable for the number of employees but the results were unchanged forthe most part. Finally, as mentioned earlier, the control variable equity/totalassets (Z) is included in the model to adjust for differences in equity capitalrisk across banks.

Table 1 contains descriptive statistics for input prices, outputs, and dependentvariables. Total costs, profit before tax, outputs, and input prices as well astotal assets are in thousands of 1995 PPP dollars. Our samples consist of 519European banks and 476 U.S. banks, or 995 banks in total. As shown in Table1, the size distributions of European and U.S. banks in our samples differ tosome extent. Compared to U.S. banks, the European bank distribution has alarger mean size (i.e., on average $20 billion larger), is less skewed, and has alower maximum size.

6 Bank Efficiency Results

Forthcoming results and discussion focuses on how the X-efficiency of largeEuropean and U.S. banks compares in the period 1995-1999. To begin we esti-mate separate frontiers for Europe and the U.S., respectively. Next, economiesof scale and scope are calculated, and economies of scale are compared as mea-sured at the frontier for Europe and the U.S., respectively. In this respect thescale estimates are evaluated for whether they are similar enough to estimate asingle profit frontier and cost frontier. Additionally, profit and cost efficiencyresults are compared for each of the European countries separately and forEurope as a whole and the U.S. too.

OLS models were initially run to examine goodness of fit. In all cases ad-justed R2values exceeded 95 percent, with most models exceeding 99 percent.These results provide strong support for our model design. Since our focus ison frontier analyses, to conserve space we only report the SFA models andresults (i.e., OLS results are available from the authors upon request). Also,we should mention that the price of financial capital (W2) is used to ensurelinear homogeneity in input prices.

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6.1 European Banks

Panel A of Table 2 reports results for the estimated SFA cost and profitmodels for large European banks. 26 For both economies of scale/scope andX-efficiency, we report results for four asset quartiles as well as for the totalsample. Importantly, X-efficiency estimates based on the cost model for Eu-ropean banks average 0.947, which implies that frontier efficient banks couldfurther reduce operating costs by 5.3 percent on average. As in other SFAstudies, the distribution of efficiency scores is highly skewed (e.g., the mini-mum is 0.064). Relative to the cost results, X-efficiency estimates based on theprofit model for European banks are on average considerably lower at 0.721,which implies potentially large profit improvements of 27.9 percent on averageare possible for frontier banks. With a standard deviation of 0.219 (i.e., ap-proximately twice that of the cost model), the distribution of profit efficiencyscores is quite large. Apparently, large banks in Europe had wide disparitiesin profit X-efficiency but much smaller disparities in cost X-efficiency duringour sample period. These results are generally consistent with previous Eu-ropean studies of bank cost and profit X-efficiency (e.g., see Ruthenberg andElias (1996), Dietsch, Ferrier, and Weill (1998), and Vander Vennet (1999)).However, some studies have reported profit X-efficiencies ranging between 0.20and 0.25 for large European banks (e.g., see Griffell-Tatje and Lovell (1996),Resti (1997), and Altunbas, Gardener, Molyneux, and Moore (2001)). Assum-ing that profit efficiency is a function of not only internal production (as in thecase of cost efficiency) but external market forces, higher cost efficiency andlower profit efficiency could be attributable in part to differences in marketpower among large banks. Alternatively, Sheldon (1999) has argued that theseresults could be due to high-cost outputs with service and quality features thatare not in demand by bank customers.

Panel A of Table 2 also contains average scale estimates derived from thecost and profit SFA models for large banks in Europe. As discussed earlier,scale estimates are derived from the estimated coefficients for the entire cost

26 Since estimated coefficients for λ (i.e., the ratio of the variance of the truncatednormal inefficiency term to the variance of random noise) are significantly greaterthan zero (at the 0.01 level) in both models, we infer support for our frontier ap-proach relative to OLS. The total variance of the error term (or σ) is low. Similarresults hold for all our estimations. Results with respect to individual variables aredifficult to interpret due to second order and interaction variable effects. For ex-ample, in the cost model the estimated coefficient for loans (Y1) was negative andsignificant, which implies lower operating costs as loans are increased, all else thesame. However, this interpretation does not take into account the nonlinear costimplications of loans captured in squared loans (Y1Y1) and multiple interactions ofloans with other variables in the model. For these reasons we do not report estimatedcoefficients for the cost and profit models.

20

or profit equation, rather than a single estimated coefficient. Consistent withprior studies of large banks (e.g., Allen and Rai (1996), and Altunbas, Gar-dener, Molyneux, and Moore (2001)), cost model estimates suggest decreasingeconomies of scale for outputs. An increase of 1 USD in total output resultsin an increased cost of almost 1.13 USD for European banks. Since overalleconomies of scale are negative and significant, the results imply cost disec-onomies of scale. Contrary to the cost model findings, overall scale economiesfor the profit model are increasing and significant at 1.15 USD for large Eu-ropean banks. This result suggests that large banks can increase profits byexpanding their size. 27 The scale economies results were similar across quar-tile size ranges.

Finally, scope economies are negative but insignificant for the cost model. Eu-ropean banks that produce a disproportionate amount of a particular outputhave total costs that are approximately 34 percent lower (but statistically in-significant) than banks that have a more balanced output mix. These resultsare in line with the large international bank results of Allen and Rai (1996), aswell as work by Vander Vennet (1999). For the profit model scope economiesare positive (with total profits approximately 37 percent higher among bankswith a more balanced output mix) but again insignificant. This result is con-sistent with the finding of higher revenues and profitability among universalbanks compared to specialized banks by Vander Vennett (1999). The insignif-icance of the cost and profit scope estimates suggests that scope economiesare small in general, which agrees with the consensus in the empirical bankingliterature (e.g., see Berger (2003)).

6.2 U.S. Banks

Panel A of Table 2 further reports the economies of scale/scope and X-efficiency results from estimating the cost and profit SFA models for largeU.S. banks. For the cost model the average X-efficiency score is 0.976 (orhigher than European banks) with a standard deviation of 0.047 (or lowerthan European banks). 28 When evaluated at their respective cost frontiers,

27 The negative relationship between cost and profit scale economies as bank outputexpands is consistent with work by Berger and Mester (1997), who found that costand revenue inefficiencies can be negatively correlated (i.e., cost inefficiencies do notnecessarily imply profit inefficiencies). On the other hand, our results differ fromSheldon, who reported decreasing returns to scale for both costs and profits.28 For the U.S. data we observe very high kurtosis for the dependent variables andoutputs. The variable assets used in weighted least squares (WLS) also has high kur-tosis, potentially aggravating estimation problems arising from heteroskedasticity.This latter condition appears to be the case for our U.S. cost model. We checked forrobustness of our results by using different WLS estimations; in general, this prob-lem does not significantly affect our efficiency estimates and our coefficients, which

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Table 2: Comparison of Independent, Large Banks in Europe and the U.S.

A. Efficiencya Cost Models Profit Models

Europe U.S. Europe U.S.

Quart. Mean t Mean t Mean t Mean t

Scale Q1 1.143 4.767 1.055 17.108 1.208 3.646 1.134 11.186

Q2 1.126 4.699 1.071 17.376 1.159 3.497 1.148 11.322

Q3 1.153 5.661 1.049 13.572 1.169 4.387 1.098 8.856

Q4 1.095 7.494 0.938 8.376 1.100 5.986 0.907 5.237

Total 1.127 5.991 1.042 9.294 1.151 4.564 1.099 5.808

Scope Q1 -0.231 0.327 -0.947 3.357 0.455 1.658 0.895 0.404

Q2 -0.009 0.680 -0.975 1.038 0.245 1.516 0.934 1.135

Q3 -0.166 0.986 -0.989 11.006 0.248 0.264 0.982 4.808

Q4 -0.631 0.561 -0.867 15.932 0.534 0.714 0.865 15.955

Total -0.340 0.083 -1.024 10.484 0.367 0.590 0.950 1.362

X-eff. Q1 0.924 5.755 0.973 12.281 0.636 2.169 0.676 3.711

Q2 0.924 5.573 0.976 21.321 0.600 1.977 0.754 5.381

Q3 0.962 15.571 0.978 35.126 0.714 3.074 0.778 6.542

Q4 0.957 12.235 0.978 190.13 0.831 7.353 0.866 15.232

Total 0.947 8.454 0.976 18.098 0.721 2.964 0.749 4.790

B. Frontier Testa

Independent samples test Europe U.S.

Perc. F t Neurope Nus Mean SD Mean SD

Cost 50th 26.3 8.934 259 238 1.156 0.186 1.032 0.113

60th 12.9 8.957 207 191 1.163 0.186 1.023 0.122

70th 7.2 7.986 155 143 1.167 0.193 1.016 0.129

80th 3.6 6.595 104 95 1.176 0.213 1.007 0.145

90th 8.2 5.282 51 47 1.227 0.249 1.009 0.153

Profit 50th 40.7 2.246 260 238 1.167 0.260 1.124 0.151

60th 27.8 1.766 208 190 1.164 0.262 1.126 0.153

70th 28 1.899 155 143 1.186 0.285 1.137 0.145

80th 22.3 0.876 104 95 1.173 0.311 1.144 0.142

90th 13.6 1.027 52 47 1.201 0.383 1.14 0.185

C. X-Eff. Testa

Independent samples test Europe U.S.

F t Neurope Nus Mean SD Mean SD

Cost 59.8 -5.005 519 476 0.947 0.112 0.976 0.054

Profit 96.3 -2.181 519 476 0.721 0.243 0.749 0.156a = Asset quartiles (in millions of U.S. dollars) are distributed as follows: Q1 = [1012435,1982082],Neurope=93, Nus=155; Q2 = [1982083,4420897], Neurope=84, Nus=166; Q3 = [4420898,30193469],

Neurope=165, Nus=84; Q4 = [30193470,160096490], Neurope=177, Nus=71. All independent samples testsuse Levene’s test (at the 5% level) for the equality of variances. We only report the absolute t-values formean differences that are not rejected by this F test. Scope t-values correspond to an independent samples

test that expected cost (or profit) is equal for specialized and non-specialized banks.

we infer that large U.S. banks have higher cost efficiency on average com-pared to European banks. For the profit model the average X-efficiency score

are still unbiased and consistent. Also, the mean efficiency and efficiency rankingswere not significantly affected.

22

is also relatively higher compared to European banks at 0.749 with a stan-dard deviation of 0.092. 29 This result contrasts with that of Miller and Noulas(1996), who conducted a DEA analysis of large U.S. banks and found profit X-efficiency of 0.97 with almost half the banks 100 percent technically efficient.Not surprisingly, the U.S. market is more homogeneous than the Europeanmarket, as confirmed by the lower standard deviation for both cost and profitX-efficiency. Also, as implied by the descriptive data in Table 1, whereas aver-age return on assets is higher in the U.S., the standard deviation of the returnon assets is lower than in Europe. The average cost ratio of U.S. banks is lowerthan for European banks also.

Cost model results in panel A of Table 2 show that overall economies of scalefor U.S. banks significantly decrease but are smaller in magnitude than thosefor the European cost model (i.e., 1.127 and 1.042 for European and U.S.banks, respectively). 30 Average scale economies for U.S. banks generated fromthe profit model are positive, but somewhat smaller than those for Europeanbanks — for example, a 1 USD increase in total outputs results in an almost1.10 USD increase in profits (compared to 1.15 USD for European banks). Asin Europe, it appears that large U.S. banks’ expansion tends to boost profits.One exception is the profit economies of scale result of 0.907 for U.S. banksin the largest size quartile. For these banks profit scale diseconomies appearto exist.

Scope economies for large U.S. banks are negative and significant (at the 0.01level) for the cost model, whereas they are positive but insignificant for theprofit model. Cost scope diseconomies for U.S. banks are about three timeslarger than for European banks. This difference in results could be due togreater number of specialized banks in the U.S. and universal banks in Europe.Previous U.S. studies on large U.S. banks and scope economies are generallymixed, with relatively small economies or diseconomies as mentioned earlier(e.g., see Pulley and Humphrey (1993) and Mitchell and Onvural (1996) andcitations therein). Our results are likewise mixed with scope economies inprofits but scope diseconomies in costs for both Europe and the U.S. Also,like most previous work, most scope economies are not significant.

In general, our efficiency results for large European and U.S. banks reflect moresimilarities than differences. Estimates of scale economies for costs and profitsreveal functional relationships between output level and efficiency that arestrikingly comparable to one another. However, on average European banks

29 Comparing the values for µ/σu, truncation is very similar for the U.S. and Europebank samples, with a large proportion of efficient banks.30Our finding of decreasing returns to scale is consistent with numerous prior studiesof large U.S. banks (e.g., see Noulas, Ray, and Miller (1990), Hunter, Timme, andYang (1990), Jagtiani and Khanthavit (1996), and Miller and Noulas (1996)).

23

have lower cost and profit X-efficiencies compared to U.S. banks, and thedispersion of both profit and cost efficiency scores is considerably smaller forU.S. banks than for European banks. Consistent with previous literature, wedo not normally find scope economies, with the exception of significant costdiseconomies of scope for U.S. banks. We should mention that our results donot necessarily imply that U.S. banks are more efficient than European banks,as each sample of banks is evaluated against its own efficient frontier. It ispossible that the most efficient U.S. banks are only average when comparedto the European banks. In order to compare efficiency results for Europeanand U.S. banks, we next turn to a combined analysis of both samples.

7 European and U.S. Banks Combined

Panel B of Table 2 reports the results for a series of independent sample t-testsfor mean differences in economies of scale estimates among European and U.S.banks. As discussed earlier, these tests are based on bank samples that pro-gressively move closer to the frontier (i.e., from the 50th to the 90th percentile).The t-statistics test for the mean differences in average scale estimates for Eu-ropean and U.S. banks that are not rejected by Levene’s F-test for equality ofvariances. The cost models’ t-tests for all percentile cut-off points are signifi-cant, which is evidence against a single cost frontier. For the profit models theevidence is mixed, with significant t-tests for the 50th, 60th, and 70th percentilesamples but insignificant t-tests for higher percentile samples. Placing greaterweight on the 90th percentile banks that are closest to the profit frontier, dueto insignificant differences in mean scale economies, we infer that the evidencefavors estimating a single profit frontier for European and U.S. banks.

We next estimate the cost model for the combined sample with the additionof dummy variables for 17 countries and a dummy variable for Europe (versusthe U.S.), respectively. These tests seek to capture geographic differences incost scale estimates. The left-hand side of Table 3 reports the results. Whilesome of the country-specific dummy variables are significant, it is noteworthythat the Europe dummy variable is not significant. Since average X-efficiencyis 0.961 for the country dummy cost model and 0.958 for the Europe dummycost model, overall cost efficiency results are not affected by the inclusion ofcountry-specific dummy variables. 31 In both estimations µ/σu is significantand negative, as a relatively large number of bank observations can be foundin the tail of the efficiency distribution.

31 As a further test, we also estimated the European model with country dummieswhere Germany is the reference country. Efficiency scores and rankings were notsignificantly different using the model without dummies as presented in Table 2.Thus, whereas Europe’s banking market as a whole may be quite heterogeneous,the estimation of a single European frontier poses no problems.

24

Table 3: Combined Cost and Profit Frontiers

Cost Modelsa Profit Modelsa

Country dummy Europe dummy Country dummy Europe dummy

Variable b t b t b t b t

Intercept 4.767 12.948 2.334 5.934 11.074 16.822 0.048 0.068

Europe 0.031 1.598 0.225 4.497

Austria 0.197 2.336 -0.160 -0.910

Belgium -0.017 -0.472 -0.149 -1.428

Switzerland 0.099 4.878 0.016 0.320

Germany -0.110 -4.694 -0.295 -5.582

Denmark 0.167 5.263 -0.237 -3.662

Spain 0.173 9.552 0.102 2.097

Finland 0.084 1.466 0.078 1.265

France 0.270 9.942 -0.488 -9.374

Great Britain -0.042 -2.179 0.187 4.298

Greece 0.116 4.48 0.676 9.010

Ireland 0.094 3.161 0.452 4.130

Italy -0.063 -2.827 -0.164 -3.715

Luxembourg 0.156 2.847 -0.144 -0.903

Netherlands -0.067 -2.189 -0.204 -2.908

Norway -0.092 -1.718 -0.440 -2.027

Portugal -0.176 -2.739 -0.33 -2.656

Sweden -0.023 -0.709 0.218 3.287

W1 0.663 8.060 0.582 7.551 0.885 4.319 1.555 8.639

W3 0.303 3.895 0.270 3.712 0.090 0.517 -0.847 -5.085

Y1 -0.106 -1.912 0.110 1.701 -0.875 -7.762 0.384 3.202

Y2 0.374 10.694 0.561 17.510 0.179 2.304 0.425 6.002

Y3 0.384 11.739 0.243 6.554 0.628 8.512 0.106 1.354

Z -0.703 -7.83 -0.765 -7.380 -0.166 -0.913 -1.563 -9.038

T 0.020 1.470 0.014 0.893 0.094 2.924 0.129 3.537

0.5T2 -0.005 -1.251 -0.004 -0.750 -0.012 -1.127 -0.027 -2.117

µ/συ -2.423 -4.476 -1.754 -3.824 2.139 3.437 0.500 0.841

λ 2.936 22.914 2.362 21.074 4.208 13.345 1.203 12.694

σ 0.249 23.422 0.239 22.660 0.625 13.881 0.364 24.387

LLF 743.850 611.660 90.430 -129.170

ss(v) 0.009 0.009 0.021 0.054

ss(u) 0.076 0.048 0.369 0.078

Mean 0.961 0.958 0.735 0.853

Std. Dev. 0.090 0.081 0.207 0.118

Obs. 995 995 995 995a = Variables are defined as follows: Y1 — loans, Y2 — investments, Y3 — off-balance sheet activities, W1 —price of labor, W2 — price of financial capital, W3 — price of physical capital, Z — equity/total assets ratio,and T — time. Other terms are: LLF — the log likelihood ratio test, ss(v) — the variance of random noise, orσ2ν , ss(u) — the variance of the truncated efficiency term, or σ

2υ , µ/συ — the truncation point for υ divided

by the standard deviation of the truncated efficiency term, — the ratio of standard deviations of thetruncated normal efficiency term and random noise, or συ/σν , and σ — the total variance of the error termequal to the sum of the variance of random noise plus the variance of the truncated efficiency term, or σ2

= σ2υ + σ2ν . The full estimation results are available from the authors upon request.

In panel C of Table 2, we employ the results from the country dummy costmodel to test whether the European banks jointly are on average as costefficient as U.S. banks. Mean efficiency for European banks is 0.947, which

25

is significantly less than U.S. banks at 0.976, albeit by only 2.9 percent. Weinfer that European banks are slightly less cost efficient than U.S. banks onaverage but the difference is not economically meaningful.

The left-hand side of Table 4 compares each European country’s bank costefficiency to U.S. bank cost efficiency. Given the relatively low number of ob-servations for some countries, and in order to take into account the differentmarket structures, we weighted the efficiency scores for each bank in a partic-ular country by its share of the country’s total banking assets. For the U.S.the weighted cost efficiency is 0.974. The F-statistic tests for the equality ofvariances fail to accept the null hypothesis (except for Italy); as such, TypeII t-tests under the assumption of unequal variances are most appropriate. Anegative and significant t-statistic means a country’s banks are less cost effi-cient than U.S. banks. Excluding some countries due to relatively low samplesizes (i.e., Austria, Finland, Luxembourg, and Portugal), the Type II t-test re-sults are mixed, with five (eight) countries’ banks having cost efficiency similarto (different from) U.S. banks. Only banks in Italy and the Netherlands hadsignificantly higher average cost efficiency scores than U.S. banks. 32 Banks inBelgium stand out as the least efficient among the European countries. Finally,while banks in Germany, Denmark, France, Great Britain, and Norway wereless efficient than U.S. banks from a statistical standpoint, the magnitude ofthe difference appears to be fairly modest in economic terms.

Turning to the estimated profit models for the combined sample, recall thatearlier tests moving progressively closer to the profit frontier implied differ-ences between European and U.S. banks that became insignificant. The right-hand side of Table 3 shows the estimated models with the addition of dummyvariables for 17 countries and a Europe dummy (versus U.S.), respectively.Profit X-efficiency scores averaged 0.735 for the country dummy model and0.853 for the Europe dummy model. Hence, relative to the cost model results,country-specific dummy variables (which are generally statistically significant)provide incremental information that is averaged out upon lumping togetherthe European countries. Focusing on the Europe dummy variable t-test, X-efficient frontier U.S. banks’ scale economies are not significantly higher thanthose for European banks. Also, µ/συ is positive and significant, implying thatmost banks are efficient. This evidence tends to confirm our earlier finding of asingle profit frontier for European and U.S. banks. As mentioned earlier, panelC of Table 2 shows that for U.S. banks the average profit efficiency score is0.749 compared to 0.721 for European banks, which are significantly differentat the 5 percent level.

32 As shown in Table 8, these findings are not related to the individual coefficientsfor the country dummies, as these dummies capture country-specific effects but notX-efficiency.

26

Figure 1: Mean Weighted Cost an Profit Efficiency for Large Banks

Ireland

Netherlands

Italy

Portugal

Finland

GreeceNorway

FranceDenmark

Great Britain

Germany

Luxembourg

Belgium

Austria

U.S.

Spain

Sweden & Switzerland

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.87 0.89 0.91 0.93 0.95 0.97 0.99

Cost Efficiency

Pro

fit E

ffic

ienc

y

We next consider the independent sample tests for mean differences in weightedprofit efficiency scores between individual European countries’ banks and U.S.banks, where the latter have a profit efficiency weighted by assets of 0.865.Again excluding selected countries due to small sample sizes (i.e., Austria, Fin-land, Luxembourg, and Portugal), the Type II t-test results in Table 4 clearlyindicate that U.S. banks are significantly more profit efficient than banks ineleven countries and that only banks in Ireland and Sweden had similar profitefficiency to U.S. banks.

In sum, the profit efficiency results for banks in Europe and the U.S. are consis-tent with the cost efficiency results. As a robustness check, we also estimatedthe cost and profit models using traditional labor prices for U.S. banks aswell as using flow outputs (e.g., substituting interest earnings on loans for thestock of loans, securities earnings for the stock of investments, and noninterestincome for the stock of off-balance sheet activities), but the cost and profitefficiency results remained qualitatively the same. Figure 1 graphically sum-marizes the mean cost and profit efficiency scores for large banks by country.Casual inspection of this graph suggests that cost efficiency and profit effi-ciency are correlated with one another to some extent. Viewing countries inthe upper right quadrant of the graph as operating within a relevant range ofcost and profit efficiency, there is considerable dispersion among sample coun-tries’ cost and profit efficiency. Banks in the U.S., Ireland, and the Netherlandstend to dominate other countries’ banks in cost/profit efficiency space. Therelative strength of U.S. banks is consistent with Berger, DeYoung, Genay,

27

Table 4: Independent Sample Tests of X-efficiencies Compared to the U.S.

Cost Model Profit Model

Countrya N Mean F t Mean F t

Austria 5 0.902 777.18 -1.23 0.518 2313.37 -1.69

Belgium 16 0.877 813.72 -2.79 0.791 316.61 -1.73

Switzerland 46 0.974 1874.98 0.23 0.824 26.14 -4.94

Germany 64 0.940 1363.42 -4.20 0.805 386.44 -6.09

Denmark 47 0.956 5848.73 -5.42 0.796 47.91 -9.86

Spain 52 0.973 626.19 -1.60 0.849 10.66 -3.54

Finland 10 0.971 674.15 -0.76 0.772 176.69 -1.89

France 44 0.969 240.28 -6.09 0.783 325.63 -5.37

Great Britain 63 0.947 714.38 -4.28 0.831 60.53 -6.83

Greece 22 0.973 215.42 -1.32 0.739 41.74 -12.96

Ireland 16 0.976 1222.10 0.66 0.865 8.68 0.03

Italy 54 0.976 0.06 13.20 0.803 194.26 -7.47

Luxembourg 13 0.937 1905.46 -4.11 0.683 843.00 -2.96

Netherlands 24 0.981 205.55 2.67 0.845 17.94 -2.38

Norway 16 0.971 205.55 -2.67 0.751 327.08 -4.45

Portugal 11 0.971 606.82 -0.93 0.855 0.18 -1.22

Sweden 18 0.974 244.06 -0.31 0.823 218.79 -1.35a = The F-statistic is Levene’s test (at the 5% level) for the equality of variances. We only report thet-values for mean differences in average scale economies that are not rejected by the F test. Efficiencyscores are weighted by assets per country in each year to avoid small banks in small countries biasing

results. The reference country is the U.S. with an average weighted cost efficiency of 0.974 and an averageweighted profit efficiency of 0.865.

and Udell (2000), who found that U.S. banks tended to be relatively efficientcompared to banks in France, Germany, Spain, and U.K. Belgian banks haverelatively low cost efficiency but their profit efficiency is well within the rangeof profit efficiency of other countries’ banks. Only banks in Luxembourg andAustria, for which the number of observations is small, appear to be outsiderelevant ranges for cost and profit efficiency. While differential regulatory andeconomic environments in the past no doubt influenced the relative efficiencyof banks in these and other countries, harmonization of banking services asEuropean countries move toward a single market will likely lead to increas-ing convergence of cost and profit efficiency among large banks in the future.In the meantime differential competitive advantages exist for large banks lo-cated in different European countries; moreover, large banks in the U.S. arecompetitive relative to the most efficient countries in Europe.

8 Geographic Dispersion and Bank Efficiency

Here we report the results for empirical tests on the relationship between ge-ographic dispersion as measured by distance between banks within a bankingorganization and efficiency measures. Table 5 gives the descriptive statisticsfor the six independent variables discussed previously. U.S. banks have highermean distances than European banks; nonetheless, U.S. banks’ average costand profit efficiency scores are higher, average cost ratios are lower, and aver-

28

age profit ratios are higher compared to European banks. Table 6 shows thecorrelation coefficients between these variables. As may be expected, a highercost efficiency is negatively and significantly correlated with the cost ratio.

Table 5: Descriptive Statistices: Geographic Distance Analyses

A. European Banksa

(516 obs.) Mean Std. Dev. Minimum Maximum

Distance 14,356.000 30,041.000 0.0000 165,215.0000

Size 84,235,200.000 151,781,000.000 1,071,080.0000 956,470,000.0000

CE 0.949 0.105 0.1059 0.9953

PE 0.721 0.244 0.0153 0.9895

Cost ratio 0.0652 0.056 0.0051 0.5028

Profit ratio 0.0136 0.016 0.0001 0.1322

B. U.S. Banksa

(410 obs.) Mean Std. Dev. Minimum Maximum

Distance 53,662 226,378 0 1,454,040

Size 454,657,000 2,799,080,000 1,045,520 31,869,400,000

CE 0.9744 0.058 0.2009 0.9902

PE 0.766 0.1459 0.0583 0.9874

Cost ratio 0.0448 0.0134 0.0009 0.1188

Profit ratio 0.014 0.0066 0.0003 0.084a = Distance is the sum of geographic distances in miles between banks within the banking organization.Size is total assets and off-balance sheet items in thousands of dollars. CE and PE are cost and profitefficiency scores, respectively. Total costs and total profits divided by total assets and off-balance sheet

items are the cost and profit ratios.

Likewise, a higher profit efficiency is positively and significantly correlatedwith the profit ratio. Interestingly, the cost and profit ratios are positively andsignificantly correlated, with a value of 0.645. Distance was not significantlycorrelated with any of the other variables. As defined previously, distance isorthogonalized with respect to size.

Table 6: Correlations Between Independent Variables

Distancea Size CE PE Cost ratio Profit ratio

Distance 1.000 0.000 -0.018 -0.026 -0.001 0.055

Size 0.000 1.000 0.013 0.076 * -0.121 ** -0.108 **

CE -0.018 0.013 1.000 -0.059 -0.262 ** -0.245 **

PE -0.026 0.071 * -0.059 1.000 -0.114 ** 0.236 **

Cost ratio -0.001 -0.121 ** -0.262 ** -0.114 ** 1.000 0.645 **

Profit ratio 0.055 -0.108 ** -0.245 ** 0.236 ** 0.645 ** 1.000a = Distance is the sum of geographic distances in miles between banks within the banking organization.Size is total assets and off-balance sheet items in thousands of dollars. CE and PE are cost and profitefficiency scores, respectively. Total costs and total profits divided by total assets and off-balance sheetitems are the cost and profit ratios. The symbols * and ** denote 5% and 1% significance (two-tailed),

respectively. Distance is orthogonalized with respect to size (see also Table 7).

Table 7 reports the results for the multivariate regression models using costefficiency and profit efficiency as dependent variables. We ran three modelsfor each efficiency measure due to the inclusion of the following three dummyvariables: (1) outside country (i.e., 1 for banks with affiliates outside their

29

home country in Europe or the U.S, 0 otherwise), (2) outside EU (i.e., 1 forEuropean banks with affiliates outside the European Union or U.S. bankswith offices outside the U.S., 0 otherwise), and (3) outside Europe (i.e., 1 forEuropean banks with affiliates outside of Western and Eastern Europe or U.S.banks with offices outside the U.S., 0 otherwise).

Table 7: Geographic Expansion and Bank Efficiency

Cost Efficiency Dependent Variablea

Model (1) Model (2) Model (3)

b t b t b t

Intercept 0.102 22.80 2.920 30.13 7.919 25.11

Distance -8.26E-09 -0.66 -2.17E-07 -0.57 -4.48E-07 -0.41

Size 5.68E-04 2.47 1.47E-02 -2.19 3.11E-02 0.47

Total Cost Ratio -3.62E-02 -1.97 -1.172 -2.15 -3.239 -2.06

Total Profit Ratio -0.338 -4.75 -9.725 -4.75 -26.450 -4.43

Outside Country -0.178 -6.33

Outside EU -0.452 -6.49

Outside Europe -1.231 -5.61

F Value 19.33 18.61 18.17

Adjusted R2 0.090 0.087 0.085

Profit Efficiency Dependent Variablea

Model (1) Model (2) Model (3)

b t b t b t

Intercept 0.388 31.94 0.389 33.17 0.389 33.18

Distance -1.57E-07 -2.29 -1.50E-07 -2.19 -1.54E-07 -2.23

Size 1.85E-02 2.43 1.61E-02 2.27 1.65E-02 2.27

Total Cost Ratio -1.883 -11.72 -1.96 -12.25 -1.945 -11.85

Total Profit Ratio 9.360 13.21 9.603 13.59 9.446 12.38

Outside Country 0.030 2.54

Outside EU 0.048 4

Outside Europe 0.048 3.87

F Value 43.27 45.35 45.57

Adjusted R2 0.186 0.193 0.194a = We estimate a truncated regression model, with truncation at 1 from above. Mean cost efficiency is0.960, and mean profit efficiency is 0.741. Distance is the sum of geographic distances in miles betweenbanks within the banking organization. It is computed orthogonal to size (i.e., the residual of a regressionof distance on size and a constant) to avoid multi-collinearity problems. Size is total assets plus off-balancesheet items. CE and PE are cost and profit efficiency scores, respectively. Total costs and total profits

divided by total assets plus off-balance sheet items are the cost and profit ratios. Three dummy variablesare defined as follows: (1) outside country (i.e., 1 for banks with affiliates outside their home country inEurope or the U.S, 0 otherwise), (2) outside EU (i.e., 1 for European banks with affiliates outside theEuropean Union or U.S. banks with offices outside the U.S., 0 otherwise), and (3) outside Europe (i.e., 1for European banks with affiliates outside of Western and Eastern Europe or U.S. banks with officesoutside the U.S., 0 otherwise). We use a White estimator to correct for possible heteroskedasticity

problems.

The estimated distance coefficients have negative signs for all cost and profitefficiency models, with significant coefficients (at the 0.01 level) for all profitmodels. Hence, as banks become more geographically diversified, profit effi-ciency tends to significantly diminish. For example, an increase of total dis-tance within the banking organization of 1,000 miles would decrease profit

30

efficiency by about 0.016 percent, and vice versa for a decrease in distance.The results for the dummy variables reflecting foreign versus domestic bank-ing operations are negative (positive) and significant in the cost (profit) ef-ficiency models. These results suggest that cost (profit) efficiency diminishes(increases) as banks move beyond their domestic geographic area. The positiveeffect on profit efficiency may reflect the net positive diversification benefitsbanks reap from their geographical expansion. Regarding the control vari-ables, all three control variables (i.e, profit ratios, cost ratios, and asset size)are significant in both the cost and profit models, except for cost model 3 inwhich asset size is insignificant. The latter finding as well as the relativelylow spread in cost efficiency explain the higher OLS adjusted R2 values in theprofit models compared to the cost models.

In sum, based on the distance variable results, we infer that geographic dis-persion tends to negatively affect banks’ profits. The dummy variable resultsfurther reveal that expansion outside of a bank’s domestic area can have neg-ative effects on cost efficiency but positive effects on profit efficiency. Thesefindings are generally consistent with Berger and DeYoung, who found moreprofit than cost efficiency benefits of geographic expansion.

8.1 Small Bank Results

In this section we broaden our analyses to include small banks. Internationalmergers and acquisitions are most likely to occur between large institutionsand smaller banks as the former seek a foothold position in new markets.Historically, small, independent banks are much more common in the U.S.than in Europe. Our European sample includes all small banks not affiliatedwith a bank holding company or other banking organization in the 1995-1999 period for which data was available. A total of 383 observations metthese criteria. 33 For the U.S. we randomly sampled 500 small, independentbanks. Compared to our large bank samples, the size distribution is much lessdispersed.

Repeating the empirical methodology applied to large banks, Table 8 containsthe results for small, independent commercial banks with less than $1 billion inconstant 1995 dollars. 34 The estimated cost and profit frontier X-efficiency re-sults for small banks in Europe, the U.S., and combined reveal relatively highercost efficiency but lower profit efficiency compared to large banks, especiallyamong European banks. Cost X-efficiency is on average 0.743 and 0.871 for

33Most small, independent European banks are located are in Germany, Switzer-land and Denmark. No observations were obtained for Finland, Greece, Ireland andSweden.34 Complete details of the empirical results are available upon request from theauthors.

31

Table 8: Comparison of Independent, Small Banks in Europe and the U.S.

A. Efficiencya Cost Models Profit Models

Europe U.S. Europe U.S.

Quart. Mean t Mean t Mean t Mean t

Scale Q1 0.895 3.814 1.149 6.387 0.359 0.836 1.324 6.337

Q2 0.996 4.243 1.142 6.343 0.252 0.589 1.295 6.198

Q3 1.026 5.096 1.144 9.927 0.413 0.976 1.308 11.077

Q4 1.111 6.85 1.142 6.938 0.601 1.324 1.339 8.586

Total 1.059 5.068 1.145 8.007 0.490 1.079 1.311 7.701

Scope Q1 -0.113 1.286 -0.437 3.312 0.091 0.519 0.485 0.115

Q2 0.739 2.383 -0.573 0.585 -1.608 0.102 0.55 1.097

Q3 0.699 3.297 -0.596 0.297 -0.429 1.714 0.554 1.016

Q4 1.501 0.872 -0.578 0.370 -1.201 0.299 0.663 0.884

Total 0.816 3.037 -0.599 2.369 -0.507 1.777 0.608 0.805

X-eff. Q1 0.814 6.292 0.877 9.699 0.527 2.448 0.615 3.933

Q2 0.817 4.165 0.854 7.361 0.564 2.561 0.65 4.278

Q3 0.710 3.273 0.882 9.514 0.586 2.753 0.692 6.362

Q4 0.740 3.416 0.892 8.351 0.638 3.554 0.625 3.156

Total 0.743 3.495 0.871 8.519 0.607 3.042 0.644 4.249

B. Frontier Testa

Independent samples test Europe U.S.

Perc. F t Neurope Nus Mean SD Mean SD

Cost 50th 25.6 4.561 191 260 1.061 0.211 1.136 0.141

60th 12.3 3.274 153 208 1.073 0.199 1.136 0.152

70th 6.4 2.772 115 156 1.071 0.206 1.136 0.17

80th 10.6 3.763 76 104 1.043 0.213 1.145 0.119

90th 6.2 2.526 38 52 1.034 0.25 1.147 0.132

Profit 50th 163.8 26.459 191 259 0.496 0.44 1.304 0.189

60th 180.6 22.026 153 207 0.497 0.441 1.312 0.144

70th 162.4 18.441 115 156 0.487 0.465 1.319 0.154

80th 122.4 14.94 76 104 0.436 0.49 1.308 0.161

90th 57.7 12.25 38 51 0.344 0.469 1.326 0.180

C. X-efficiency Testa

Independent samples test Europe U.S.

F t Neurope Nus Mean SD Mean SD

Cost 261.3 11.95 383 519 0.743 0.213 0.871 0.102

Profit 47.2 2.999 383 519 0.607 0.200 0.644 0.151a = Asset quartiles (in millions of U.S. dollars) are distributed as follows: Q1 = [4069,45720], Neurope =24, Nus =201; Q2 = [45721,102338], Neurope = 39, Nus = 187; Q3 = [102339,264629], Neurope = 122,Nus = 103; Q4 = [264630,990942], Neurope = 198, Nus = 28. All independent samples tests use Levene’s

test (at the 5% level) for the equality of variances. We only report the absolute t-values for meandifferences that are not rejected by this F test. Scope t-values correspond to an independent samples test

that expected cost (or profit) is equal for specialized and non-specialized banks.

small European and U.S. banks, respectively. Cost economies of scale are neg-ative, especially for small U.S. banks. While our sample tests show significantdifferences between the European and U.S. cost frontiers, these differences be-come less significant as we approach the frontier. Cost scope economies arealso more negative in the U.S. with mixed significance in Europe and the U.S.

32

Figure 2: Mean Weighted Cost and Profit Efficiency for Small Banks

Netherlands

ItalyPortugal

N orw ay

France

Denm ark

Great Britain

Germ any

Luxem bourg

Belg ium

A ustria

U.S.

Spain

Sw itzerland

0.50

0 .52

0 .54

0 .56

0 .58

0 .60

0 .62

0 .64

0 .66

0 .68

0 .70

0 .60 0.65 0.70 0.75 0.80 0.85 0 .90

C ost Efficiency

Pro

fit

Eff

icie

ncy

Consistent with our large bank results, cost-efficient small banks in Europeand the U.S. are comparable. However, based on joint frontier results, thereare more inefficient banks in Europe than in the U.S., as reflected by the dif-ference between the average cost X-efficiency of U.S. (0.871) and European(0.743) banks.

Regarding the small bank profit efficiency results, average profit X-efficiency is0.607 in Europe and 0.644 in the U.S. As in the large bank analyses, Europeansmall banks have lower profit X-efficiencies compared to U.S. small banks.However, for all percentile sample cutoff points we find significant differencesbetween the two frontiers. For the separate profit frontier results, small U.S.banks gain more than small European banks on a dollar of additional output(i.e., the estimated coefficients are 1.31 and 0.49, respectively). This higherprofit efficiency among small U.S. banks may well be due to the fact thatindependent, small U.S. banks tend to operate in rural areas in which there isless competition than experienced by their European counterparts. When thesetwo groups of banks are compared using a joint frontier, we find that small U.S.banks are also significantly more profit efficient than small European banks,albeit by a small absolute margin (i.e., 0.644 for U.S. banks versus 0.607 forEuropean banks). Scope economies are also higher for U.S. banks but are notsignificant.

Figure 2 shows the mean cost and profit efficiencies of each country’s smallbanks, which are weighted by assets as before. Similar to the large bank results,

33

there appears to be a positive correlation between cost and profit efficiencyscores. Also, like the results for large banks, small banks in the U.S. and theNetherlands dominate other banks in the cost/profit efficiency space. Luxem-burg was relatively inefficient among large banks but is highly efficient in smallbank comparisons. Small banks in Spain and France are relatively cost/profitinefficient. Unlike the large bank results, there is much higher dispersion ofcountries’ cost/profit efficiency scores for small banks.

In general, the small bank efficiency results are similar in some ways to thosefor large banks in Europe and the U.S. but different in other respects. SmallU.S. banks tend to have greater cost and profit X-efficiencies than small Eu-ropean banks, which is similar to our findings for large banks. One differencein results is the normally lower average cost and profit X-efficiency scores forsmall banks relative to large banks. We infer that small banks tend to be lessefficient than large banks. One possible implication of these findings is thatsmall banks face less competitive pressure to be cost and profit efficient thanlarge banks. If this is indeed true, an efficiency motive for large banks to mergeor acquire small banks exists.

9 Conclusion

The last two decades of the 20th century witnessed rapid bank consolidationaround the world, which has taken place for the most part within countriesand on an intra-continental basis. At some point, when regional concentrationof bank resources becomes satiated, it is reasonable to believe that inter-continental mergers will be the next phase in the merger movement. In thispaper we examine the question of economic motivations for further geographicexpansion by conducting stochastic frontier cost and profit analyses to esti-mate economies of scale as well as X-efficiency for multi-billion dollar Europeanand U.S. banks. Comparable data for input prices and outputs are gatheredfor large banks for the period 1995-1999.

Our empirical results with respect to separate analyses for large European andU.S. banks’ cost and profit curves are strikingly similar. For the cost modelin both regions, we found small, increasing and significant returns to scale.Returns to scale for the profit models are positive and significant for the mostpart. Generally speaking, these results suggest that large banks in Europe andthe U.S. can increase profits via output expansion. Based on these cost andprofit models, X-efficiency scores revealed that on average European bankshave lower cost and profit efficiencies compared to U.S. banks. In absoluteterms U.S. banks have lower (higher) cost (profit) ratios. Also, the dispersionof both profit and cost efficiency scores is considerably smaller for U.S. banksthan for European banks. This result is not surprising in view of the greaterhomogeneity of banking markets in the U.S. compared to Europe. Scope esti-mates were generally not significant, with the exception of cost diseconomies

34

of scope among U.S. banks.

Further analyses evaluated the reasonableness of estimating a combined costor profit frontier for European and U.S. banks. For this purpose we measuredeconomies of scale moving progressively closer to the cost or profit frontier, asbanks closest to the frontier are most important in terms of assessing the fea-sibility of a single cost or profit frontier. We found that mean scale economiesfor European and U.S. banks measured very close to the profit frontier arenot significantly different and, therefore, imply a single profit frontier. ProfitX-efficiency scores revealed lower average efficiency among different Europeancountries’ banks compared to U.S. banks. By contrast, the results for costscale economies comparisons failed to accept the null hypothesis of a singlecost frontier. Results of X-efficiency comparisons revealed that U.S. banks’cost efficiency tended to be higher than that of European banks.

We conclude that our empirical results tend to support the notion that poten-tial profit efficiency gains are possible in cross-Atlantic bank mergers betweenEuropean and U.S. banks. Thus, an economic motivation appears to exist infavor of geographic expansion in the years ahead. Likewise, in view of consid-erable heterogeneity in cost and profit efficiency, our evidence suggests thatintra-European mergers among large banks are possible.

Direct tests for how geographic distance affects cost and profit efficiencies oflarge banks in the U.S. and Europe indicated that efficiency tends to declineas banking organizations spread out their offices. However, profit efficiencytended to increase with respect to expansion beyond their home country. Sincefurther analyses showed that small banks tend to have lower average cost andprofit X-efficiency scores than large banks, large banks may well be expectedto expand via small bank mergers.

Today’s global banks developed gradually over time by expanding abroad tomeet their domestic business clients’ international financial needs. As such,branch office acquisitions and mergers and de novo entry have traditionallybeen utilized to achieve a foothold in foreign locations. While other motiva-tions may well exist for cross-Atlantic mergers among large banks, potentialprofit efficiency gains appear to be a plausible factor in decisions to mergebeyond continental shores and form global organizations comprised of largeEurope/U.S. bank combinations.

35

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41

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