Banking Markets: Productivity, Risk, and Customer Satisfaction

Transcription

1 Fnancal Insttutons Center Banng Marets: Productvty, Rs, and Customer Satsfacton by Gerald R. Faulhaber 95-14

2 THE WHARTON FINANCIAL INSTITUTIONS CENTER The Wharton Fnancal Insttutons Center provdes a mult-dscplnary research approach to the problems and opportuntes facng the fnancal servces ndustry n ts search for compettve excellence. The Center's research focuses on the ssues related to managng rs at the frm level as well as ways to mprove productvty and performance. The Center fosters the development of a communty of faculty, vstng scholars and Ph.D. canddates whose research nterests complement and support the msson of the Center. The Center wors closely wth ndustry executves and practtoners to ensure that ts research s nformed by the operatng realtes and compettve demands facng ndustry partcpants as they pursue compettve excellence. Copes of the worng papers summarzed here are avalable from the Center. If you would le to learn more about the Center or become a member of our research communty, please let us now of your nterest. Anthony M. Santomero Drector The Worng Paper Seres s made possble by a generous grant from the Alfred P. Sloan Foundaton

3 Banng Marets: Productvty, Rs and Customer Satsfacton 1 Abstract: A structural model s developed whch ncorporates ban decsons on productvty, rs tang and customer satsfacton nto an equlbrum model of banng marets. Ths structural model s estmated drectly for 219 large US bans, The results are: () bans dffer wdely n ther ablty to manage rs; () there are substantal neffcences due to demand/capacty msmatches; () greater customer satsfacton correlates wth greater proftablty, prncpally due to hgher levels of demand; (v) very large ban-specfc effects that prevous research dscovered appear to have been largely captured n the structural model. Key Words: banng, structural estmaton, qualty, productvty, effcency, rs Gerald R. Faulhaber s Professor of Management and of Publc Polcy and Management at the Wharton School. Ths research was supported by a grant from the Wharton Fnancal Insttutons Center funded by the Sloan Foundaton and Delotte & Touche. The author wshes to than Larry Brown, Kermt Danel and Dan Raff, as well as partcpants n the Fnancal Insttutons Center semnars for ther comments and suggestons. Jalal Ahaven and Tony Ca provded nvaluable research assstance.

4 BANKING MARKETS: PRODUCTIVITY, RISK, AND CUSTOMER SATISFACTION 1. Introducton The past ffteen years have seen substantal changes n banng marets. Advances n computng and telecommuncatons have drven these global changes, but they have been most pronounced n US marets. A volumnous lterature has developed, n part as a result of these changes, whch has generally addressed two ssues: () ban productvty, ncludng economes of scale 1, economes of scope, and X- effcency; () ban rs-tang and ts costs. Are bans the rght sze? Do they have the approprate product scope? Are they usng best practce technques? How does sze affect the effcency of rstang? For a defntve revew of ths wor, the reader s referred to Berger, Hunter, and Tmme (1993). Studes of economes of scale and scope have domnated the lterature. The consensus of the lterature s that for large bans, scale economes are largely nonexstent and scope economes are small, a result confrmed n ths paper. Ban rs was examned n McAllster and McManus (1993), where an nventory model to assess scale economes assocated wth rs poolng. Hughes and Mester (1994) model ban managers rs preferences, usng the leverage rato as ther rs measure. Addtonally, Hughes and Mester (1993) assess the mpact of the too-bg-to-fal doctrne on ban rs-tang, a matter we consder n ths paper. More recent nnovatons n the lterature have focused on () the use of the proft functon rather than the cost functon, to help dentfy both demand sde and supply sde effects (see Berger, Hancoc, and Humphrey (1993)); and () the use of fronter methods to dentfy possble X-neffcency. A seres of papers has explored varous methods for fronter estmaton: data envelopment analyss, effcent fronter analyss, thc fronter analyss, and dstrbuton-free analyss. Berger (1993) provdes a dscusson and analyss of these varous methods and ther dfferences n the context of banng. Kaparas, Mller, and Noulas (1994) use a stochastc fronter approach and fnd that ban sze, n partcular the number of branches, has a negatve mpact on short-run effcency. Mester (1994) uses cost fronter methods to assess the effcency of bans n the Federal Reserve s thrd dstrct, fndng sgnfcant X-neffcences. Grabows, Rangan, and Rezvanan (1994) use a nonparametrc fronter approach to assess the effect of deregulaton on ban effcency, fndng a declne over the years , prncpally focused on techncal rather than allocatve neffcency. Overall, these papers have dentfed potental X- neffcences as substantally greater than ether scale or scope effects, and have thus turned scholarly

5 - 2 - attenton toward dentfyng possble sources for these large effcency dfferences among bans. For example, Mester (1993) has examned effcency dfferences between stoc and mutual savngs and loan nsttutons, fndng that the mutual form of ownershp s assocated wth greater effcency. In ths paper, three questons are addressed: () the cost of ban rs s assessed, usng bans stoc maret betas as a broad measure of total rs. 2 In partcular, the effect of sze on rs-tang s analyzed, as well as the decomposton of rs on a product bass; () productvty losses due to msmatches between demand and capacty s modeled and estmated; () the effect of customer satsfacton, or qualty, on ban proftablty s measured. Each of these ssues s new (n varyng degrees) to the lterature. Addtonally, the paper provdes strong confrmaton of prevous research results on economes of scale and scope, and t provdes sgnfcant new evdence on the X-effcency/fronter analyss ssue. There are several features of ths paper, other than the questons addressed, that mae ths paper unque: Most of the prevous emprcal wor employed reduced form estmaton: a cost functon or a proft functon s specfed and ts parameters are estmated. In ths paper, a full structural model s developed: bans face long- and short-run cost functon choces, they optmally choose capacty levels and rs levels wth lmted nformaton, and they nteract n marets, leadng to an asymmetrc Cournot-Nash equlbrum. Each ban s proft functon s derved from the maret equlbrum condtons, and t s parameters are drectly estmated (n structural, not reduced, form). The emprcal analyss ncorporates sx ban products, and develops a unfed approach to thnng about what a ban s products are. Specfcally, ths analyss ncludes off-balance-sheet tems as an ndvdual product lne; to date, only Hasan, Karels, and Peterson (1994) and Jagtan, Nathan, and Sc (1994) have examned ths product lne. The dataset on customer satsfacton s new to the lterature, developed explctly for ths paper. Most of the prevous emprcal wor examned one or a few very specfc factors, attemptng to measure ther mpact n solaton from other decsons and actvtes undertaen by the frm. In ths paper, all of the relevant factors are ntegrated nto a sngle model, so that all parameters are estmated smultaneously. Developng an explct ntegrated structural model of banng marets ncreases the complexty of the analyss and ncreases the dffculty of estmaton. Further, ths s not the standard approach n the exstng emprcal banng lterature. The motvaton to undertae ths effort s two-fold. Frst, dervng the estmatng equatons from a model of maxmzng agents, ther opportunty and nformaton sets, and ther maret nteractons tghtly tes the emprcal estmaton to the underlyng economcs. Second, wth

6 - 3 - ths approach, specfc hypotheses of ban behavor that can be reflected n the economc model can be explctly estmated. For example, msmatches n ban demand and ban capacty, due (possbly) to management forecastng errors, are bult nto the economc model, so that allocatve neffcences due to ths potental msmatch can be explctly estmated for each ban. Ths second pont s partcularly mportant, gven the current state of the emprcal banng lterature. Usng the methods of fronter analyss, Berger and Humphrey (1991) have shown that there are large unexplaned dfferences among the cost functons of bans. Berger, Hancoc, and Humphrey (1993), derve smlar but more powerful results usng a ban proft functon. Unfortunately, fronter methods (or fxed effects methods, as used n ths paper) smply allow us to characterze ban-specfc effects that are not captured n our models, but do not explan why t s that a ban s neffcent compared to other bans. We have thus reached a lmt on what econometrc analyss can tell us usng generc functonal forms and generc operatng data (such as the Call Report data tradtonally used for ths purpose), f we wsh to understand the underlyng economcs of banng marets. One ngenous approach to get beyond ths lmt s n Berger, Leusner, and Mngo (1994), n whch a generc cost functon approach s combned wth a unque dataset on ban branches s used to estmate a specfc type of potental neffcency. Ths paper represents another approach: use generc banng data but wth a rcher structural model of banng marets, combned wth a unque dataset (customer satsfacton data) whch prses open yet another dmenson for analyss. As researchers are better able to model and then observe potental causes of neffcency, the fxed effects, whch capture the unobserved varaton among bans, become less mportant. The results of ths paper tae us a very long way toward that goal. There are fve dstnct parts of our model of bans and banng marets. ()operatng actvtes; each ban s assumed to produce (at most) sx products: demand deposts, tme deposts, commercal and ndustral (C&I) loans, consumer loans, real estate loans, and off-balance-sheet tems. The short-run cost of producng these sx products s represented by a famly of functons whch capture potental complementartes among the products. The long-run cost functon s the lower envelope of ths famly of cost functons. In each perod, each ban chooses a short-run cost functon based upon ts estmates of demand for ts products. These estmates may prove naccurate, but ts choce of technology s sun (for one perod) so that the ban ncurs a cost penalty, operatng off the long-run cost functon. () rs; a defnng property of bans s that rs and rs management s at the core of ther busness. Each product, ndeed each transacton, nvolves tang rs. We measure the overall rs of the ban usng the beta of the ban s stoc, whch captures not only credt and nterest rate rs (such as would be assocated wth loans and securtes) but all busness rs (for example, expandng nto new geographcal marets). () the demand for banng products; the maret demand functons capture potental cross-elastctes among these sx products. (v) customer satsfacton, or qualty; bans may dffer n ther ablty to provde

7 - 4 - hgh-qualty servce, as defned by how satsfed ther customers are. 3 For reasons explaned below, we treat the ablty to delver hgh qualty (or not) as a characterstc of a ban rather than as a choce the ban maes. (v) compettve nteractons; each ban havng chosen a short-run cost functon, all bans wthn each metropoltan statstcal area (MSA) then play a Cournot-Nash quantty game (nvolvng sx marets); the output vector for each ban and prce s determned as the equlbrum of ths game. It s an asymmetrc game, as bans n general wll have chosen dfferent short-run cost functons and dfferent product rs levels, and therefore have dfferent margnal costs. Ths wll result n dfferent output vectors for dfferent bans n the same MSA. The paper s organzed as follows. Secton 2 lays out the fve dstnct components of the model. Also ncluded n ths secton s our treatment of what a ban s products are. Ths ssue has generated some controversy n the lterature, and our approach dffers from any n the lterature thus far; t s closest n sprt to the user cost method, outlned n Berger and Humphrey (1992). Secton 3 uses these results to derve the estmatng equatons. In Secton 4, the data s descrbed, ncludng how varous anomales n the several datasets were treated. Secton 5 contans the results of the estmaton, and Secton 6 lsts our conclusons as well as possble future research along the lnes developed n ths paper. 2. The Model The model conssts of four dstnct components, whch are descrbed n turn. Cost of Operatng actvtes A ban can offer up to sx products: 1. Demand deposts; 2. Tme deposts; 3. Commercal and Industral (C&I) loans; 4. Consumer loans; ths category ncludes credt card accounts as well as the usual consumer credt loans such as automoble loans, etc. 5. Real estate loans; ths ncludes home mortgages (though not mortgaged-baced securtes) and commercal real estate loans; 6. Off-balance-sheet tems; we nclude n ths category all counterparty guarantees, such as letters of 4 credt; we do not nclude futures contracts, such as swaps.

8 - 5 - Each ban s producton of these sx outputs n a tme perod s measured by the outstandng stoc of each output on the ban s balance sheet at the end of the perod (for products 1-5, and analogously for product 6). In the short run, producton nvolves both fxed and varable costs; for each perod, a ban must plan for and nvest n capacty before demand s realzed, based upon, among other thngs, ts demand forecasts. Each ban faces a famly of short-run cost functons of the form α α j j = 1 = 1 j= + 1 j C( q; F, c ) = F + c q + ν ( q q ), (1) where ν and α are symmetrc matrces common to the entre famly of short-run cost functons. The ban chooses a specfc member of ths famly by selectng an F and c = (c 1,...,c 6 ), whch choce varables completely characterze the menu of short-run cost functons. In turn, the lower envelope of ths famly of short-run cost functons defnes the long-run cost functon; for every output vector n the postve orthant, q R 6, there exsts a short-run cost functon that () s equal to the long-run cost functon at q; () s tangent to the long-run cost functon at q; and () les everywhere above the long-run cost functon. The long-run cost functon s of the form 6 C( q ) = λ ( q q ) 6 = 1 j= γ j j j (2) where λ and γ are symmetrc 6 6 matrces. For each vector q ~ n the postve orthant, there exsts a unque short-run cost functon (F, c) defned by the total condton (): C( ~ q; F, c) = C ( ~ q), or γ j α α j j j j j = 1 j= = 1 = 1 j= + 1 F( ~,, ) ( ~ q ~ q ) c ~ 2 q; c, α, γ λ ν = λ q ν ( ~ q ~ q ) (3) and the tangency condtons (): C( q ~ ; F, c) = C ( ~ q), or c ~ 2α q j j j = ( ~ 2γ q + [ j j ( ~ q ~ γ qj ) j j ( ~ q ~ α 2β λ β λ α ν qj ) ]), = 1,...,n. (4) 2α j We assume the second-order condtons are satsfed.

9 - 6 - The ntuton here s straghtforward. Bans choose a short-run cost functon from the avalable menu; f they expect relatvely low demand, they choose a low fxed cost, hgh varable cost technology. If they expect relatvely hgh demand, they choose a hgh fxed cost, low varable cost technology. The avalable menu of short-run cost functons s defned by ts lower envelope, whch s therefore the long-run cost functon. To help vsualze these short-run and long-run cost functons, an example for two products s wored out n detal and shown graphcally n Fgure 1. The parameters of ths example are: α =, γ =, λ =, ν 1, 2 = The long-run cost functon s completely determned by the parameters λ and γ. All members of the famly of short-run cost functons share parameters α and ν. We select a partcular member of the famly ~ of short-run cost functons by specfyng an output vector q = (3,3) at whch the short-run functon s tangent and equal to the long-run cost functon. We then solve for F, c by solvng equatons (3) and (4), whch results n: c 1 = c 2 = 0.071, F = Wth these parameter values, the long-run cost functon exhbts economes of scale and dseconomes of scope. The short-run cost functon exhbts dseconomes of scale for reasonably large values of q, and economes of scope. Ths s llustrated n the graph of the two functons, below. Note that the cost functons are equal and tangent at (3,3).

10 - 7 - Input Prces It wll be noted that both our long-run and short-run cost functons nclude the output vector but do not nclude nput prces, as theory demands that they should. Only f nput prces are assumed constant across bans and tme perods s ther omsson justfable. Snce all varables are n constant (1982) dollars, nflaton s not a source of varaton n nput prces. However, other tme-related factors could cause varaton n nput prces, and more obvously, dfferent sectons of the country are lely to have dfferent wage rates, leadng to dfferent nput prces. In the estmaton descrbed below, however, both tme dummes and (hgh-wage) geographc area dummes are not sgnfcantly dfferent than zero, suggestng that such sources of varaton are not present (or a perfectly canceled out by some other unobserved effect). Therefore, we mantan the assumpton that varatons n nput prces are small enough so that we may safely assume nput prces are relatvely constant and can therefore be gnored. Cost of Rs Bans are unque n that the management of rs s the core of ther busness. Yet our ablty to measure rs s much less than our ablty to measure, say, the cost of processng checs. In ths paper, we use maret measures of rs, based on the theory of fnancal marets, n order to measure the aggregate rs of the ban. Our rs measure s the ban s (or ts holdng company s) stoc maret beta, the measure of rs that stocholders bear (and must be compensated for) derved from the Captal Asset Prcng Model. Beta measures the covarance of a stoc s prce performance wth that of the aggregate 6 maret, fully reflectng the effects of stocholders portfolo dversfcaton. Costs are normally denomnated n dollars per unt tme, whle the stoc maret beta s a dmensonless quantty. Snce we wsh to treat rs cost le any other cost of the ban, we develop a transform of the stoc maret beta whch s a cost of rs commensurate wth all other costs. We quantfy the ban s total rs cost as the dfference between current earnngs and what the earnngs of the ban must be to acheve the same value of the frm f the ban carred no rs. Let the value of the ban be V, the earnngs of the ban n future perod t be the random varable Π t. Then the maret dscount rate of the ban s s, where s satsfes t V = E Π t t + s, = 1 ( 1 ) and E s the expectaton operator. The dscount rate s ncorporates the stoc maret s assessment of rs β. 7 Defne the unform expected earnngs as π, the unform certan level of earnngs whch would yeld the same value of the frm f dscounted at s: V = t= 1 π ( 1 + s) t.

11 - 8 - Now defne the rs-free earnngs as ~ π, the unform certan level of earnngs whch would yeld the same value of the frm f t were completely free of rs, and the earnngs dscounted at r f : π V = ~ t ( 1 + r ), or t= 1 rf π~ = π rf + β( rm r f ) f Now the rs cost s defned to be the addtonal earnngs, π rs that the ban carres. Ths s smply π ~, that nvestors demand because of the β( rm rf ) R = π rf + rm r ; normalzng by expected earnngs, β( f ). (5) R β( rm rf ) = p rf + β( rm r f ) = rs / earnngs rato. Aggregate rs for a ban s comprsed of rss from many ndvdual transactons, each of whch s assocated wth a specfc product. We assume the most straghtforward reduced form model that decomposes total ban rs nto rs by product: R = 6 = 1 r q. (6) A more general functonal form nvolvng hgher order terms would no doubt conform more closely to our vew of rs. However, we are estmatng ban-specfc coeffcents n ths study, so the per-ban sample sze s qute lmted, thereby restrctng the parameters that can usefully be estmated. 8 As a result, we must be content wth capturng frst-order effects only. Demand Total maret demand for these products s nterdependent and s gven by the nverse demand system 9 : 6 j η j j= 1 p = A Q, = 1,...,6. (7)

12 - 9 - where the matrx η s symmetrc. Ths demand system has the property that the self- and crossflexbltes Q p j p Q j = η are constant. The more famlar self- and cross-elastctes can be obtaned j from the flexbltes by nvertng the flexblty matrx, and they are (of course) constant as well: η 1 = ε, the elastcty matrx. m = 1 Each frm = 1,...,m supples a porton q = ( q,..., q 1 6 ) of ths total demand, wth Q = q. Customer Satsfacton/Qualty Bans may dffer n ther ablty and wllngness to provde servce qualty that leads to hgher satsfacton of ther customers. Recent reports n the trade press suggest that customer satsfacton may be a hghly proftable strategy for bans. Fnancal mareters appear to have overlooed the fundamental truth that the longer an nsttuton eeps a customer, the more proftable the customer becomes. [Bans need ]...to maxmze ther satsfacton wth [the] nsttuton, accordng to Vavra (1995). The ncluson of customer satsfacton n ths analyss s unque among econometrc studes, and s merted not by ts ntrnsc nterest but also by the current nterest among practtoners n qualty. The qualty measure we use s an ndex derved from an extensve and long-standng survey of commercal ban customers conducted by Greenwch Assocates, Inc., a maret research frm specalzng n the commercal banng sector. The ndex merges survey responses nto a sngle number, normalzed between 1 and 100, wth a hgher ndex number correspondng to greater customer satsfacton. The detals of the survey and the constructon of the ndex from the survey nstrument are dscussed below n Secton 4. We note here the ey features of the ndex that valdate ts use n ths study as a measure of customer satsfacton: () actual ban customers are surveyed to assess ther opnons regardng ther degree of satsfacton wth ther banng relatonshps. () The survey has been conducted annually for over twenty years; the ndex s therefore based on a set of questons and responses that have been consstent over the perod of our study. () The survey results are consdered nformatve by the bans themselves, as attested to by the fact that Greenwch Assocates prncpal source of ncome over ths perod has been the sale of the survey results to ndvdual bans. The valdty of the results has thus passed a maret test. The qualty measure may be modeled as ether a choce varable of the ban, or a characterstc of the ban over whch t has lttle or no control n the short term. In ths paper, we treat qualty as a characterstc of the frm rather than a choce varable. If the technology for provdng qualty n banng were well-understood and completely dffused throughout the ndustry, then modelng t as a choce

13 - 10- varable would be approprate. In our vew, ths s not the case. Whle bans were subject to the pervasve regulaton that characterzed the ndustry pre-1980, t appears that qualty was defned more by the brand of toasters the ban gave depostors for openng accounts than by how well bans determned and then provded what customers actually wanted. However, as competton ntensfed over the last ffteen years, many bans have sought to dfferentate themselves as hgh-qualty provders as a means of compettve advantage. Pursung ths strategy requres a ban to actually learn how to provde hgh-qualty servce; ths strategy may requre major changes wthn the ban, whch may not easly be mtated. Thus, the dffuson of the technology of provdng hgh-qualty servce could be rather slow, so that over the tme perod of our study, bans had ether acqured the technology or they hadn t. If ths s an accurate descrpton of the dffuson of the technology of hgh-qualty servce, then treatng qualty as a characterstc rather than a choce varable s more approprate, and that s our ratonale for so treatng t. There are several emprcal mplcatons of ths assumpton. Frst, f qualty s a choce varable, then n equlbrum we would expect to see returns equalzed across qualty choce; hgh-qualty bans would be no more nor no less proftable than low-qualty bans. However, f qualty s a characterstc of bans, determned by the speed of dffuson of the technology, there may ndeed be rents to provdng hghqualty servce. Second, f qualty s a choce varable, then n equlbrum we would expect that hgher qualty necessarly results n hgher cost. If qualty depends upon the relatvely slow dffuson of a new technology, then adopters of the new technology need not have hgher costs; n fact, they could have lower 10 costs, f the technology both ncreases qualty and reduces costs. Unfortunately, the qualty ndex constructed from the Greenwch Assocates survey apples only to commercal customers. Ths suggests that the qualty we measure affects only products assocated wth ths maret segment. The product most clearly assocated wth ths segment s C&I loans. 11 Hgher qualty can affect both demand and costs; f we denote the qualty ndex by X, then we modfy the shortrun cost functon (1) and the long-run cost functon (2) as follows (assumng C&I loans are product 3): 2 2 C( q; F, c ) = F + c q + ν j ( qq j ) + X c3q3 + ν 3 j ( q3q j ) 3 3 j j 3 α α j δ α α 33 3 j 6 γ δ j j 3 j 3 j γ 3 j 3 j j= 1 j 3 j C( q ) = λ ( q q ) + X λ ( q q ) The sgn of the exponent δ determnes whether ncreasng qualty ncreases or decreases cost. Smlarly, the demand system (7) can be modfed to reflect qualty as well. Snce only C&I loans (product 3) are affected, ths reduces to:

14 - 11- ς p3 = X P3 Q j 6 j= 1 η3 j Assumng ς > 0, ncreasng qualty ncreases customers wllngness to pay. To reduce notaton n the followng exposton, we wll suppress the explct appearance of X n the cost functons demand functons. In equlbrum, the maret may respond to qualty n two ways: bans may charge hgher prces for hgher qualty servce, more busness may come to hgher qualty bans, or both. Thus, the effect of hgher qualty servce on ban proftablty s potentally threefold: the ablty to charge a prce premum, a hgher level of demand, and a change n costs. If qualty s correctly vewed as a ban characterstc, then we have no predcton of ts effect on proftablty. If qualty s a very slowly dffusng nnovaton whch bans are unable to adopt easly, then we would not expect that hgh qualty would lead to lower profts, but t could certanly lead to hgher profts, especally durng the perod of slow dffuson where qualty rents may be possble. Products and Prces There s some controversy wthn the lterature as to what a ban s outputs are. The asset approach taes ban deposts as nputs and ban loans as outputs. The user cost approach dentfes as outputs those tems for whch revenues exceed costs, and nputs as those assets for whch costs exceed revenues. In ths analyss, we adopt the user cost method, but wth the specal focus that t s the net economc revenue, rather than the accountng revenue, that s the approprate measure. We tae the measured quanttes of each of the sx products to be ts stoc n dollars. Ths then focuses attenton on what the prce of the sx products specfed above really s. The prce of a loan that the ban maes to a customer s obvous: t s the nterest rate, denomnated n dollars per dollar-year. The approprate unt of loan quantty s agan obvous: the total amount of loans outstandng n a gven year. More dffcult s the prcng of demand deposts, and t s to ths that we now turn. There are several types of pecunary transactons assocated wth demand deposts: () nterest payments to depostors, usually pad f a substantal mnmum balance s held; () varous fees charged depostors, such as ATM usage, returned checs, per-chec fees, etc. On balance, the total net revenue to a ban from these fees s very small and can be negatve. What s mssng from the pecunary transactons s the opportunty cost of demand deposts to depostors. By eepng funds n a demand account, depostors are gvng up earnng returns (n an equvalently low-rs nstrument of equvalent lqudty) n exchange for the transacton and depostory servces provded by the ban. In turn, the ban gets the use of ths money for loan purposes whle payng mnmal nterest costs. Assume that the next best alternatve for the ban s customer s 90- day Treasury blls (hghly lqud, very safe), then the opportunty cost to the depostor s the nterest rate on the 90-day T-blls. The total prce that the customer pays, ncludng opportunty cost, s the rate for

15 day T-blls plus ban account fees mnus ban nterest payments. A smlar calculaton apples to tme deposts, n whch the customer s gvng up potentally hgher nterest payments on T-blls for the convenence of readly avalable nsured deposts. The mplct prce s thus the 90-day T-bll rate mnus the ban nterest rate on tme deposts; ths calculaton generally yelds a postve prce pad by tme depostors for ths servce, though generally not as hgh a prce as for demand deposts, for whch the ban typcally provdes more servce. If these opportunty costs are counted as a prce the customer pays the ban, then revenues are attrbuted to the ban that do not actually show up on ts boos. Agan, we use the opportunty cost approach to handle ths. The ban uses these free (n the pecunary sense) funds n order to mae loans, funds t would have to pay for f t dd not have a depost base to draw upon. Therefore, the opportunty cost revenues mputed from depostors should be mputed to borrowers. Thus, the prce of a loan to a borrower s not the quoted nterest rate, but that nterest rate less the opportunty cost of funds collected from depostors. Baners are famlar wth ths concept n the form of net nterest ncome; nterest from borrowers less the cost of funds. Ths approach dffers n detal but not n sprt, and t permts the total revenues of the ban to equal the booed revenues. Ths prcng approach can be vewed as allocatng booed revenues to products based on an opportunty cost vew of banng. 3. Maret Equlbrum and the Estmatng Equatons In ths secton, the varous parts of the model are brought together. The model of the banng maret s developed and the equlbrum of the multproduct game s derved. Usng these equlbrum condtons, equatons whch depend only upon observables and parameters are derved; these are the equatons to be used to estmate the model parameters. Informaton and Tmng of Play Pror to the begnnng of each perod, the managers of each ban must decde on the short-run cost functon to deploy for the comng perod, whch requres that they commt to a fxed cost F pror to observng actual demand condtons. Ths amount s fxed n the short run and cannot be changed untl the begnnng of the next perod. 12 Ban managers are assumed to now α, γ, λ, ν, and equatons (3) and (4), but they do not now next perod s demand. In order to optmally choose the short-run cost functon, bans must forecast demand, choosng the cost functon whch mnmzes ther expected cost over the forecast dstrbuton. A model of how bans can optmally do ths s presented n Appendx A. Two ey features of ths model are: () snce bans use prvate nformaton n ther forecasts, ther optmal choce of short-run cost functons wll dffer; () ban s choce of cost functon can be expressed as a choce of planned-for

16 - 13- demand = ( q 1,..., q ), whch s not necessarly equal to expected demand. If bans are mang q n unbased forecasts, then f costs are nonlnear t wll be effcent to choose a planned-for demand not equal to ts expected demand. Thus, any msmatches between capacty and demand may be an effcent response to forecast uncertanty. On the other hand, ban managers may exhbt a bas n ther capacty plannng. Bans whch are consstently over-optmstc wll tend to have excess capacty n most perods, whle under-optmstc bans wll tend to be short on capacty. If such msmatches of demand and capacty are due to bas, then these msmatches represent allocatve neffcency. An objectve of ths analyss s to determne the extent of allocatve neffcency due to ths source. We denote the total bas of the ban by m ; our assumpton s thus: m = ~ q q, for =1,...,6, and all tme perods. (8) The bas m s a ban-specfc parameter to be estmated. Maret Equlbrum We assume that the number of bans n the maret s fxed. In the case at hand, we dentfy metropoltan statstcal areas (MSA) as the relevant banng marets. At the begnnng of the perod, demand s revealed. All bans n the maret then play a Cournot-Nash quantty game, now wth full nowledge of demand Q, n whch they offer q (not necessarly equal to q ) n the maret. The tmng of the game s llustrated n Fgure 1. Fgure 1

17 - 14- The form of the game suggests two questons: () s the Cournot-Nash assumpton reasonable for these marets? and () are bans the only players n these sx product marets? In fact, the Cournot quantty game wth a fxed number of players s unquely suted to banng marets. Entry nto these marets s restrcted (though not prohbted) by government regulaton, so that the no entry assumpton s a reasonable though not perfect approxmaton to realty, especally for larger bans. Prces tend to be maret-determned, and are often strongly affected by captal maret actvty over whch bans have lttle effect. By choosng capacty, such as sze of branch networ, extent of tradng actvtes, number of credt offcers hred and traned, bans are choosng quanttes to offer the maret, concdent wth the Cournot quantty game. More troublng s our assumpton that the bans n our sample are the only players n the game. In fact, there are many more players n these marets, ncludng smaller bans, non-ban fnancal nsttutons, and commercal paper marets. In vrtually all of the products n ths model, bans n our sample compete wth nsttutons not n our sample. Lac of avalable data on these non-ban nsttutons constrans all researchers from addressng ths ssue. The results of ths paper, as well as the results of vrtually the entre emprcal banng lterature, must be understood n lght of ths defcency. Another concern s our assumpton that the relevant maret s the MSA. For retal products and many mddle maret products ths s a good assumpton. However, for some servces such as corporate loans the maret may well be natonal. Ths suggests that the maret share of bans s less than that used here, so that prce-cost margns would also be less. Ban chooses the quantty vector q to maxmze economc proft. Usng equatons (1) and (6), ths can be wrtten as: 2α j max π = p ( Q) q F c ( q ) ν ( q q ) r q q n n n 1 j = 1 = 1 = 1 j= + 1 n j α n = 1 (9) The frst order condtons are: π q = MR MC = p ( 1 + s φ θ ) MC = 0, n j j j j= 1 where s j p jqj Q p q j j =, φ j = = η j, θ j =, p Q p Q Q j j

18 - 15- whch are, respectvely, the share of product j total revenues relatve to product total revenues, the flexblty of prce j wth respect to quantty (constant for the assumed functonal form of the demand system), and the maret share of frm for the j th product. Ths frst-order condton can be put nto ths more famlar form: p MC p n = s η θ j= 1 j j j (10) Now the margnal cost of product for frm conssts of two parts: the operatons cost and the rs cost: j j MC = 2α c ( q ) + α ν ( q ) ( q ) + r. 2α 1 n α 1 j j α j solvng out the full FOC for the coeffcent c we obtan: c = n p ( j j 1 s η θ ) α ν ( q ) ( q ) r j j j j= 1 2α n j ( q ) j j 2α 1 α 1 j α (11) Ths equaton specfes what c must have been for frm, based on the observatons p and q, as well as the parameters α, ν, and η. We denote ths relatonshp c ( p, q ; α, ν, η ). Equaton (3) shows that F also depends upon ~ q, so equaton (8) can be used to express F as a functon of the ban-specfc parameters m and observables q. Ban s proft can be expressed as a functon of parameters and observables: π n n n α j j = 1 = 1 j= = 1 2α j = p q c ( q ) ν ( q q ) F( m q ;c, α, γ, λ, ν ) r q.(12) Estmatng Equatons Economc proft cannot be observed from the boos of the ban, as t ncludes rs costs, among other possble costs not accounted for. We assume n ths wor that rs costs are the only costs that do not appear on bans boos, so that economc proft s equal to accountng earnngs (whch s observable) less rs cost: π = π - R. R n turn depends upon maret observables r f, r m, and β, as well as the growth rate g. In addton, we also nclude a dummy varable B for each ban. These are the fxed effect coeffcents, desgned to assess any ban-specfc effects not pced up by the parameters of the model.

19 - 16- There are thus two estmatng equatons, one for rs and the other for operatonal actvtes. We use actual ban earnngsπ as a proxy for unform expected earnngs: R = π β ( rm rf ) 6 rf + ( rm r f ) = = β 1 r q (13) π n α j = p q c ( q ) 2 ν ( q q ) F( m q ;c, α, γ, λ, ν ) + B (14) = 1 = 1 j= 6 6 j j α Everythng n these two equaton s ether observable (π, r f, r m, β, p, q ), s a parameter (α, γ, ν, λ, m, B), or s derved from observables and parameters (c, F ). Therefore, we can estmate t usng nonlnear methods. Note that these two equatons are not smultaneous. Fxed Effects and Fronter Methods Much of the recent wor n the emprcal banng lterature has used fronter methods to examne ban effcency dfferences that are not explaned by the parameters of the model. The prncpal feature of all fronter methods n ban panel data s the dervaton of the effcent fronter, ether cost or proft, from consstent dfferences n ban-specfc resduals. The dea s that bans wth consstently hgh (for proft) resduals dentfy the best practce fronter, and that bans wth lower resduals are off ths fronter and are thus X-neffcent, n the sense of Lebensten (1966). These methods are best vewed as consstng of two parts: () the dentfcaton of consstent dfferences among bans based on ther average resdual or smlar measure; () the nference from these dfferences that bans wth the most favorable average resduals represent a best practce fronter. There s no queston that the recent wor has been extremely valuable n that t has uncovered very large systematc dfferences among the costs and proftablty of bans; these dfferences are so large as to dwarf potental scale and scope economes (see Berger and Humphrey (1991)). However, ths value nheres n the frst part of the analyss. The second part, n whch nferences are made about the best practce fronter on the bass of these dfferences, appears to be more speculatve. The assumpton of fronter analyss s that the observed dfferences among frms are due to superor management of resources (Berger (1993)). However, dfferences n bans abltes to manage resources should n prncple be observable, f the relevant varables are ncluded n the model. Sgnfcant observed fxed effects are best vewed as a measure of our gnorance, as an ndcaton that researchers need to loo harder for possble omtted varables. Therefore, our approach n ths paper s to focus exclusvely on the systematc dfferences among bans, and not on nferences regardng best practce fronters.

20 - 17- To do so, we use a fxed effects model, n whch a dummy varable s ncluded for each ban. Ths s the functon of the varable B n equaton (14). In ths analyss, the role of B s to measure the extent to whch ban-specfc factors whch we have not ncluded n the model are mportant n determnng ban proftablty. 4. The Data Three dfferent datasets were employed n ths study: operatng data, captal maret data, and customer satsfacton data. Operatng Data Ths data s taen from the Report of Condton and Income ( Call Report ), whch all nsured bans operatng n the US are requred to fle wth Federal regulators. We use quarterly data, from 1984 to 1992 nclusve, for all bans wth over $1 bllon n assets n The varables n ths dataset nclude: quanttes; end-of-perod balance sheet entry for each ban for each of the sx products lsted; revenues; total perod net revenue for each ban for each of the sx products lsted; earnngs; ncome before extraordnary tems and after taxes for each ban. All quanttes are expressed n thousands of 1982 dollars. Ths data s collected from the bans themselves by the FDIC, whch s mantans the dataset. It s accountng data. Captal Maret Data Ths data s taen from the CRSP (Center for Research n Stoc Prces) dataset, whch contans end-of-day prces of stocs traded on major exchanges and other securtes, such as bonds. The varables n ths dataset nclude: maret rate of return; ths s the total return (dvdends plus captal gan) for the NYSE. rs-free rate of return; ths s the nterest rate on 90-day Treasury blls. beta; the β of each ban for each quarter was computed usng the actual prce data together wth the maret rate and the rs-free rate.

21 - 18- Ths data s collected from US stoc marets by the Center for Research n Stoc Prces at the Unversty of Chcago. It s maret data. The mappng from banng nsttutons lsted on stoc exchanges to bans lsted n the Call Report s not trval. The reportng unt for the Call Report s a state ban; often, ths ban s part of a holdng company that operates bans n several states. In turn, ths company may be owned by another holdng company, whose assets n prncple could nclude non-banng frms. It s generally the hghest holdng company that s lsted on a stoc exchange. Even the mappng from hgh holdng companes reported to the FDIC and stoc exchange lstng s not trval; after extensve detectve wor, 219 of the bans wth greater than $1 bllon n 1984 assets were dentfed for whch ther hgh holdng company was lsted on a stoc exchange. The holdng companes often held more than one ban n the sample, and may well have held other frms, all of whch contrbuted to ther rs. In ths analyss, the hgh holdng company s beta was mputed to all ts subsdares. Not all bans had data whch covered the entre perod. Indeed, many bans were merged nto new bans durng ths perod. Snce there s nothng n the model that s nherently dynamc, these mergers dd not consttute a problem; as of the date of the merger, the old bans dropped from the dataset and the new one was nserted. The total number of data ponts (bans quarters) s Customer Satsfacton Data Ths data s taen from an ongong survey conducted by Greenwch Assocates, Inc., a maretng research frm that has been conductng surveys of commercal customers of US bans snce The survey s desgned to elct from customers () ther degree of satsfacton wth the bans they do busness wth; and () the specfc factors and attrbutes mportant to them, and how ther bans fared on these tems. From ths extensve survey data, Greenwch Assocates constructed a sngle ndex, expressly for ths study, to measure overall customer satsfacton for each ban. The detals of the survey methods and the constructon of the ndex s contaned n Appendx B. The ey ponts about ths ndex: () t s scaled to range from 0 to 100, wth a mean of 50; hgher scores correspond to greater customer satsfacton; () only commercal customers are surveyed; thus, the qualty ndex only apples to commercal products, n partcular C&I loans; () due to data lmtatons, only 112 bans (from our larger sample) are ncluded, durng the perod 1985 to The surveys are conducted annually (at most), so quarterly data s not avalable. The total number of data ponts (bans years) s Emprcal Results The emprcal results are presented n three parts. Frst, the results of thers estmaton are presented, as equaton (13) can be estmated by tself. Next, the results of the operatng results estmatonare

22 - 19- presented, and last the results of the qualty estmaton. Whle these last two are nomnally smultaneous, certan regulartes n the data permt ther separaton. Rs Estmaton The rs cost/earnngs rato (on the left-hand sde of (13)) was computed 13 for each ban n each quarter for whch data was avalable. The emprcal cumulatve dstrbuton of the mean (across all quarters) of ths rato s plotted below: Dstrbuton of Avg Rs/Earnngs Mean Fracton of Bans Avg Rs/Earnngs Fgure 2 On average, the cost of rs accounts for 38% of earnngs. If we use actual earnngs as a proxy for unform expected earnngs, then the cost of rs s about 3% of booed cost. More nterestng s the rather substantal spread of rs/earnngs; for some bans rs accounts for 2/3 of ther booed earnngs, ndcatng that accountng earnngs overstates ther economc proft by a factor of three. Other bans apparently are able to manage rs more successfully, achevng negatve β s and leadng to an economc proft greater than accountng earnngs. Ths suggests that the ablty to manage rs well s a scarce resource n banng. The perod of study was a turbulent one for banng marets, wth very good tmes alternatng wth very bad tmes. These tme patterns are evdent n the plot of the mean and standard devaton of the rs costearnngs rato by year:

23 - 20- Average and Standard Devaton of Rs Cost/Earnngs by Year Avg Rs/Earnngs Year Fgure 3 The effect of the S&L crss s clearly evdent n the ncrease n mean rs-earnngs rato for 1986, and partcularly the large one-tme ncrease n the standard devaton of the dstrbuton across bans. The progressvely greater rsness of all bans nto the early 1990s s evdent n the mean rs; the fact that ths ncreasng rsness appled to all bans s suggested by the relatvely stable standard devaton over ths perod. Perhaps even more nterestng s the relatonshp between sze and rs. For bans under $1 bllon n assets, McAllster and McManus (1993) found that ncreasng sze permtted lower rs costs for bans resultng from nventory economes. Our fndngs, based on bans over $1 bllon n assets and a stoc maret-based rs measure, are overall that the rs-earnngs rato s ncreasng n ban sze. A lnear regresson of annual rs-earnngs rato on ban revenues yelds a postve coeffcent that s sgnfcant at the 99% level.. However, the relatonshp between sze and rs s a complex one; n order to understand the fne structure of the data, the nonparametrc curve-fttng Trewess method (Velleman, 1980) was used. The data and results of these analyses:

24 - 21- Fgure 4 The Trewess ft yelds nterestng results: rs decreases wth sze for very small bans (< $1.5 M n revenues) and then ncreases sharply wth sze up to about $15 M n revenues, and s then relatvely constant for larger bans. The decrease of rs for very small bans s consstent wth the results of McAllster and McManus (1993). The ncrease n rs wth sze s more puzzlng. There are at least three possble explanatons of the postve and sgnfcant rs-sze relatonshp: () t s possble that as bans ncrease n sze and layers of management, effectve control of rs n the feld s more dffcult. () It could also be that large bans become large by management s overly aggressve growth, whch drves them to utlze excess capacty wth rser busness. () It may also be an optmal response to the so-called too bg to fal doctrne; f ban managers and depostors of large bans are protected from losses, they are encouraged to undertae rser actons. Equty holders are not so protected, so these rsy actons are reflected n what equty nvestors are wllng to pay for the shares of such bans. The frst two hypotheses would suggest that rs would ncrease wth sze wthout lmt, whch s not what we observe. 14 The too bg to fal hypothess, however, s consstent wth our observatons; for bans between $2.5 M and $18 M there s some probablty that n the event of a falure they wll be baled out, and ths probablty s ncreasng n sze. The hgher ths probablty, the more wllng the ban managers are to engage n rsy behavor, as they may avod exposure to ths rs va a balout. Bans above $18 M are vrtually assured of a balout, so that ncreasng sze does not yeld ncreases n rs-tang; these

25 - 22- bans are already at the maxmum rs they wsh to tae, gven the costs of balouts. Note that ths result s consstent wth that of Hughes and Mester (1993). Operatng Results The estmaton of equaton (14) presents several problems. The frst problem s the number of parameters and the estmatng equaton s nonlnearty. The full model has 99 structural parameters (α, γ, λ, ν ), 219 ntercept dummes (B ) and 219 slope dummes (m ). The full model s estmated usng an teratve procedure; frst, the dummy varables are assumed nown and the 99 parameters are estmated usng nonlnear least squares. Second, the estmated structural parameters are assumed nown, the ntercept dummes set equal to the ban average resduals, and the slope dummes are estmated usng nonlnear least squares. These dummy values are then used to repeat the frst step; the procedure s contnued untl convergence of all parameters s acheved. The second problem s that whle the operatng results are avalable for 6190 data ponts, the qualty results are only avalable for a subset of sze 473, a reducton of over an order of magntude. The loss of degrees of freedom nvolved n ths reducton of sample sze, especally wth a nonlnear equaton, s substantal. The full model was therefore estmated n four confguratons: () the full 6190 sample, wthout qualty; () an annual sample of 1533 data ponts, 15 wthout qualty; () the reduced sample of 473, wthout qualty; and (v) the reduced sample of 473, wth qualty. The structural parameter estmates were nearly dentcal for all four confguratons; however, the standard errors of the estmates dffered substantally, wth the largest sample sze yeldng rather good estmates of many parameters. The stablty of the parameter estmates suggested a sequental estmaton strategy: estmate the operatng parameters usng the 6190 dataset, then reduce the ftted values to the 473 dataset to estmate only the qualty parameters. In ths secton, therefore, the results of the operatng estmaton s reported. Intal estmates of the full model yelded nsgnfcant results for both the long-run and the short-run cost coeffcents for the followng cross-terms (refer to Secton 2 for product numbers): (1,2), (1,3), (1,4), (2,4), (2,5), (2,6), (3,4), (3,5), (3,6), (4,5), (4,6). Consequently, these terms were dropped n subsequent estmaton. The overall regresson results are Table 1 R Adjusted R F-statstc log lelhood

26 - 23- Scale Effects Ray scale economes are defned n the usual way. For a scalar h and any output vector q, the long-run scale elastcty s defned as σ LR = 6 6 = 1 j= 6 6 = 1 j= 2 γ j j j( h qq j ) 2γ λ λ 2 γ j j( h qq j ), wth {constant returns, ncreasng returns, decreasng returns} to scale as σ LR s {=,<,>} 1. It s clear from ths formula that f all γ j 0. 5, then there cannot be ncreasng returns to scale. If the nequalty s strct for at least one coeffcent, then there are decreasng returns to scale. Inspecton of the left-hand sde of Table 2 shows that ths s ndeed the case. All coeffcents are ether not sgnfcantly dfferent from 0.5, or they are sgnfcantly greater than 0.5 (γ 11 and possbly γ 23 ). The scale analyss of the short-run cost functons s complcated by the fact that the fxed costs lead to a wea form of scale economes: spreadng the fxed cost. However, f we examne only varable costs, the left-hand sde of Table 2 shows hghly sgnfcant ncreasng margnal cost, wth no coeffcent sgnfcantly less than 0.5 and all the drect coeffcents sgnfcantly above ths number. Table 2 Estmate Std. Error p-value* Estmate Std. Error p-value* γ α γ α E-06 γ α E-20 γ α γ α γ α E-07 γ α γ α E-05 γ α E-65 α * probablty that the true value of the coeffcent les on the opposte sde of 0.5 than the pont estmate.