WP/09/143 Bank Competton, Rsk and Asset Allocatons John H. Boyd, Gann e Ncolò and Abu M. Jalal
2009 Internatonal Monetary Fund WP/09/143 IMF Workng Paper Research epartment Bank Competton, Rsk, and Asset Allocatons Prepared by John H. Boyd, Gann e Ncolò and Abu M. Jalal 1 Authorzed for dstrbuton by Krshna Srnvasan July 2009 Abstract Ths Workng Paper should not be reported as representng the vews of the IMF. The vews expressed n ths Workng Paper are those of the author(s) and do not necessarly represent those of the IMF or IMF polcy. Workng Papers descrbe research n progress by the author(s) and are publshed to elct comments and to further debate. We study a bankng model n whch banks nvest n a rskless asset and compete n both depost and rsky loan markets. The model predcts that as competton ncreases, both loans and assets ncrease; however, the effect on the loans-to-assets rato s ambguous. Smlarly, as competton ncreases, the probablty of bank falure can ether ncrease or decrease. We explore these predctons emprcally usng a cross-sectonal sample of 2,500 U.S. banks n 2003, and a panel data set of about 2600 banks n 134 non-ndustralzed countres for the perod 1993-2004. Wth both samples, we fnd that banks probablty of falure s negatvely and sgnfcantly related to measures of competton, and that the loan-to-asset rato s postvely and sgnfcantly related to measures of competton. Furthermore, several loan loss measures commonly employed n the lterature are negatvely and sgnfcantly related to measures of bank competton. Thus, there s no evdence of a trade-off between bank competton and stablty, and bank competton seems to foster banks wllngness to lend. JE Classfcaton Numbers: G21, G32, 1 Keywords: Bank Competton, Concentraton, Rsk, Asset Author s E-Mal Address: gdencolo@mf.org 1 Boyd, Carlson School, Unversty of Mnnesota. e Ncolò, Research epartment, Internatonal Monetary Fund. Jalal, Suffolk Unversty. Ths paper s a substantally revsed verson of the paper ttled Bank Rsk-Takng and Competton Revsted: New Theory and New Evdence, IMF WP 06/297.
2 Table of Contents I. Introducton...3 II. The Model...4 Entrepreneurs...5 epostors...6 Banks...6 Equlbrum...8 III. Evdence...12 A. Measurement of competton...13 B. Measurement of rsk...14 C. Samples...15. Results for the U.S. Sample...17 E. Results for the Internatonal Sample...19 IV. Alternatve Rsk Measures...21 A. oan oss Measures of Rsk...22 B. Actual Falures (or near falures) as the ependent Varable...23 V. Concluson...23 References...25 Tables 1. U.S. Sample...30 2. U.S. Sample Regressons...31 3. Internatonal Sample...32 4. Internatonal Sample Regressons...33 5. U.S. Sample oan oss Measures...34 6. Internatonal Sample oan oss Measures...35 7. Internatonal Sample: Proxy Measures of (near) Falure...36
3 I. INTROUCTION Snce the Great epresson at least, t has been wdely held by polcy makers that more competton n bankng results n ceters parbus greater nstablty (more falures). Snce bank falures are frequently assocated wth negatve externaltes, ths has been seen as a socal cost of too much competton n bankng. A number of mportant and nfluental studes have provded support for the conventonal wsdom, ncludng Keeley (1990), Allen and Gale (2000, 2004), Hellmann, Murdock and Stgltz (2000), Repullo(2004), and others. All ths work modeled banks strategc nteractons n depost markets but gnored competton n loan markets. Now, f takng deposts s the Yn of bankng, makng loans s the Yang; thus, ths lterature studed the Yn, gnored the Yang, and n so dong overlooked the earler, semnal work of Stgltz and Wess (1981). When banks compete for loan customers, they cannot generally take market condtons as gven. In the presence of adverse selecton or moral hazard, bank strateges wll affect the pool of potental loan applcants, the actons of loan customers, or both. Recently, we studed a standard model of depost market competton (Allen and Gale, 2004) modfed n one respect: we allowed for loan market competton a la Stgltz- Wess (Boyd and e Ncolò, 2005). The result was to reverse the conventonal wsdom. In a modfed model where rsk choces are jontly determned by frms and banks, more bank competton was assocated wth less, not more, rsk of falure. In the present study, we generalze Boyd and e Ncolò (2005) n a fundamental way. The new model stll allows for mperfect depost market competton and loan market competton a la Stgltz-Wess. What s new s that we add banks holdng of a rsk-free asset. Realstcally, we know that banks asset choces are not lmted to just lendng n nformatonally opaque loan markets. Therefore, t s mportant to consder an envronment n whch both knds of actvty can occur smultaneously. That s not done n Allen and Gale op. ct. or n Boyd e Ncolò, op. ct. or n any other exstng lterature we have seen. The new model yelds a rch set of results and predctons. Frst, the asset allocaton between bonds and loans becomes a strategc varable, snce changes n the quantty of loans wll change the return on loans relatve to the return on bonds. Second, bank s optmal asset portfolo choce wll depend on the degree of competton. Such a relatonshp s of more than theoretcal nterest. One of the key economc contrbutons of banks s beleved to be ther role n effcently ntermedatng between borrowers and lenders n the sense of amond (1984) or Boyd and Prescott (1986). But banks play no such role when they rase depost funds and use them to acqure rsk free assets, such as government bonds. Thus, f competton affects banks choces between loans and bonds, as we wll fnd t does, there wll be welfare consequences. To our knowledge, ths margn has not been recognzed or explored elsewhere n the theoretcal lterature on bank competton. 3
4 In the new envronment, t s shown that ncreased competton can ether ncrease or decrease the rsk of bank falure. Ths s dfferent from our prevous fndngs (Boyd and e Ncolò, 2005, and Boyd, e Ncolò and Jalal, 2006) and reflects the greater generalty of the new model. In addton, we fnd that ncreased competton wll generally affect the rato of loans to deposts, but the drecton of the effect can be ether postve or negatve. In ths work we allow for the exstence of a moral hazard problem on the part of frms. As banks rase loan rates, frms endogenously respond by ncreasng ther own rsk of falure. We call ths the BN effect, a term that wll be made precse n what follows. We then prove that, f no BN effect s present, an ncrease n bank competton wll always result n an ncrease n the rsk of bank falure. However, ths result can be reversed f and only f the BN effect s present and suffcently strong,.. Thus, the exstence of the BN effect s a necessary but not suffcent condton to observe decreasng rsk of bank falure as competton rses. We provde numercal examples of both cases;.e. rsk rses (falls) as competton ncreases. We explore the predctons of the model emprcally usng two data sets: a cross-sectonal sample of 2,500 U.S. banks n 2003, and an nternatonal panel data set wth bank-year observatons rangng from 13,000 to 18,000 n 134 non-ndustralzed countres for the perod 1993-2004. Then, we present a set of regressons relatng measures of rsk of falure and the loan-to-asset rato to measures of concentraton controllng for all factors that affect concentraton ndependently of the exstence of market power rents. Thus, these measures of concentraton are proxy measures of bank s market power rents. The emprcal fndngs are three. Frst, banks probablty of falure (measured n two dfferent ways) s postvely and sgnfcantly related to concentraton, ceters parbus. Second, the loan-to-asset rato s negatvely and sgnfcantly assocated wth concentraton. Both results are obtaned wth both samples. Thrd, snce the data ndcate that rsk of bank falure falls as competton ncreases, the model mples that a BN effect must be present n the data. To nvestgate ths predcton, we employ several standard loan loss varables as proxy measures for the probablty of loan customers default rsk. In all tests and wth both samples, as competton ncreases, banks loan loss ratos deterorate. These results, as well as other emprcal results n the lterature, suggest that a BN effect s present n the data. The remander of the paper s composed of three sectons. Secton II analyzes the model. Sectons III and IV present the evdence, and Secton V concludes. II. THE MOE The economy lasts two dates: date 0, the nvestment perod, and date 1, the consumpton perod. There are three classes of agents: entrepreneurs, depostors and banks. All agents are rsk-neutral. 4
5 Entrepreneurs There s a contnuum of entrepreneurs who have no resources but are endowed wth effort. They are unquely endowed wth access to productve actvtes that requre effort as an nput. Specfcally, they can operate one dentcal project of fxed sze, normalzed to 1. The project yelds an output y+ z at date 1 per unt nvested at date 0. The component of total output y s random, dstrbuted wth densty functon f ( y ) and cumulatve densty F( y) on the closed nterval [0, A ]. The component of total output z s determnstc, obtaned one-to-one wth entrepreneurs effort. The cost of effort s cz, ( ) where cz ( ) s a strctly ncreasng, convex and twce dfferentable cost functon. As an alternatve to operatng a project, an entrepreneur can employ effort to obtan a utlty level b [0, B]. Entrepreneurs utlty levels are dstrbuted on [0, B ] wth cumulatve densty Gb ( ). The outcome of the project y+ z can be observed by banks only at a (verfcaton) cost, whch for smplcty s normalzed to zero. Entrepreneurs who decde to undertake a project wll borrow only from banks, as depostors are assumed to ncur verfcaton costs so large as to make drect lendng to entrepreneurs too costly. Banks offer smple debt contracts. The bank receves R f the entrepreneur does not default, whch occurs when y + z R. The entrepreneur defaults when y + z < R. In ths case, the bank verfes the outcome of the project and receves the entre output y+ z. The entrepreneur chooses z to maxmze expected profts: A A ( y + z R ) f( y) dy c( z) = yf( y) dy ( z R )(1 F( R z)) c( z) R z +. R z A Integratng the term yf( y) dy by parts, expected profts can be wrtten as: R z. A A + z R F ( y ) dy c ( z ) (1). R z We assume that (1) s strctly concave n z, whch mples that F ( R z) c ( z) < 0. The optmal z satsfes: 1 FR ( z) c ( z) = 0 (2). enote wth z( R ) the functon assocatng each optmal z to a gven loan nterest rate defned mplctly by (2). fferentatng (2), we get: F ( R z) z ( R ) = < 0 (3). F ( R z) c ( z) Thus, the hgher s the loan rate, the lower s the entrepreneur s effort. As noted, we have called ths the BN effect, whch s nduced by optmal contractng wth entrepreneural 5
6 moral hazard. Hence, entrepreneurs choose rsker projects n the form of a smaller determnstc porton of output when the loan nterest rate s hgher e We now derve entrepreneurs aggregate demand for funds. et π ( R ) denote the entrepreneurs expected profts f they choose to undertake the project. It s e straghtforward to show that π ( R ) s strctly decreasng n R. Thus, an entrepreneurs e wll undertake the project f the expected profts π ( R ) are not lower than her reservaton utlty: e π ( R ) b (4). et b denote the value of b that satsfes (4) at equalty. The total demand for loans s e thus gven by = Gb ( ) = G( π ( R )). Ths expresson defnes mplctly a downwardslopng nverse supply of loans, whch we denote wth R = R ( ), wth R ( 0) > 0, R < 0 by assumpton. epostors There s a contnuum of depostors who place all ther funds n banks. 2 The deposts of N bank are denoted by d, and total deposts by d = 1. By assumpton, depost contracts are smple debt contracts. eposts are nsured, so that ther supply does not depend on rsk, and for ths nsurance banks pay a flat rate depost nsurance premum standardzed to zero. The nverse supply of deposts s denoted by R = R ( ) wth, by assumpton, R > 0, R 0. Banks There are N banks that have no ntal resources. They collect deposts and nvest the proceeds n a rskless technology and n rsky loans to entrepreneurs. By nvestng an amount x of date 0 resources, the rskless technology yelds rx output at date 1. enote the loans of bank by l, wth total loans gven by sheet of bank s l + x = d. N l = 1. Thus, the balance 2 If bank deposts provde a set of auxlary servces (e.g. payment servces, opton to wthdraw on demand, etc.) and depostors can nvest ther wealth at no cost n a rsk-free asset, then deposts and the nvestment n the rsk-free asset can be mperfect substtutes, and deposts may be held even though the nvestment n the rsk-less asset domnates deposts n rate of return. For smplcty, nvestments n a rsk-less asset by depostors are ruled out. 6
7 Bank profts for each realzaton of the random component of output are as follows. If y R z, no entrepreneur defaults and bank profts are ( R ( ) r) l + ( r R ( )) d, where we have used x = d l. If y < R z, then all entrepreneurs fnanced by a bank default, and a bank s lmted lablty mples ts profts are: enote wth max{0,( y+ z r) l + ( r R ( )) d }. Y the realzaton of y for whch bank profts equal to zero that s, ( Y z r) l ( r R ( )) d 0. If + + = Then, y Y R z ( r R ( )) d Y ( l, d) r z (5) l [, ), then all entrepreneurs fnanced default and fal, but the bank does not. If y < Y then a bank fals. Thus, Y s the bank falure threshold, hence, F( Y ) s a bank s probablty of falure. By choosng deposts, loans, and the nvestment n the rskfree asset, a bank also chooses ts level of rsk-takng Y and ts probablty of falure F( Y ). Each bank maxmzes expected profts, takng nto account the best response of entrepreneurs choce of effort to ther choce of the loan rate, as gven by (3). We denote ths best response wth the functon z( ) = z( R ( )). Therefore, bank expected profts are gven by: A R ( ) z( ) R ( ) z( ) Y ( l, d) [( R ( ) r) l + ( r R ( )) d ] f( y) dy+ [( y + z r) l + ( r R ( )) d ] f( y) dy (6). 7
8 Equaton (6) can be re-wrtten as: 3 R ( ) z( ) ( R ( ) r) l + ( r R ( )) d l F( y) dy (7) Y ( l, d) We focus on unque solutons by assumng that (7) s strctly concave n l and d. Equlbrum As n Allen and Gale (2004), banks compete à la Cournot. In our two-perod context, ths assumpton s farly general. As shown by Kreps and Schenkman (1983), the outcome of ths strategc nteracton s equvalent to a two-stage game where n the frst stage banks commt to nvest n observable capacty (depost and loan servce facltes, such as branches, ATM, etc.), and n the second stage they compete n prces. l d R ++ In an nteror Nash equlbrum, each bank chooses (, ) that s the best response to the strateges of other banks. By the assumed strct concavty of the bank s proft functon (7), an nteror equlbrum s characterzed by: R z ( ) [ ( )( ) ( ) ] 0 Y l = (8), R r F y dy l F R z R z R F Y Y r R Rd lf ( Y ) Yd 0 + =. (9), ( r R Rd) where Yd = (10), l and Y l ( r R ) d = zl (11). l 2 Observe that an nteror threshold bank falure pont satsfes Y (0, A), whch mples FY ( ) (0,1). Assumng and nteror soluton, and substtutng (10) n (9), Equaton (9) smplfes to: r R R d = 0. (12), Thus, total deposts are determned ndependently of total loans. 4 3 Equaton (7) s obtaned by addng and subtractng R ( ) z [( R ( ) r) l ( ( )) ] ( ) Y + r R d f y dy to equaton (6), ntegratng by parts the term R ( ) z Y yf ( y) dy, and substtutng (5) n the resultng expresson. 8
9 An nteror symmetrc Nash equlbrum has = Nl and = Nd. Substtutng these condtons n (8), (10), (11) and (12), yelds: R z GN (,, ) R r Fydy ( ) [ FR ( z)( R ) ( ) ] 0 z R FY Yl = (13), Y N r R R = 0. (14), N ( r R ) Y (, ) r z (15) where, n (13). and usng (14). Y 2 R = z 2, obtaned by substtutng = Nl and = Nd n (11) N Equaton (13) says that the lendng rate s the sum of the rsk free rate r, plus two R z terms. The frst of these two terms RP F( y) dy s a rsk premum, snce t Y s the probablty that the level of realzed output s such that all entrepreneurs fnanced default and fal, and the larger s such probablty, the hgher s the charged loan rate. The thrd term R [ F( R z)( R z) R F( Y ) Yl ] represents market power N rents on the loan sde, snce t captures how loan prcng s chosen takng nto account the elastcty of loan demand as well as the loan choces of compettors. Smlarly, Equaton (14) says that the depost rate s the sum of the rsk-free rate plus market power rents on the depost sde, gven by the term R R. N Indeed, n ths model wth uncertanty the classcal erner ndex of market power, defned as the excess of prce over margnal costs, ncludes a rsk premum, and s gven by R R = RP+ R+ R. As N ncreases, market power rents R and R declne, and vansh as N. Equaton (15) s the equlbrum bank falure threshold. In equlbrum, such threshold r R R ncreases wth total deposts, snce Y =. By (14), 1 r R R= R( 1) < 0 for N > 1. Thus, Y > 0. N 4 Ths result s obtaned by ermne (1986) n a model of a monopolst bank as well as under perfect competton. 9
10 However, ceters parbus, the bank falure threshold can ether ncrease or decrease n the 2 R amount of loans. Note that, substtutng (14) n (11), Y = z 2. The frst term N 2 R s postve, but the second term z ( ) 2 = z R R s also postve, snce R < 0 N 2 R and z ( R ) < 0 by (3). Thus, Y > 0 f the BN effect s weak, snce z <, whle 2 N 2 R Y < 0 f the BN effect s suffcently strong, snce z >. 2 N Next, we llustrate the comparatve statcs wth respect to an ncrease n the number of banks whch can be ether the result of a lft of entry restrctons or lower sunk costs of the ntermedaton technology. fferentatng (14), we get: d R = > 0 dn N( R( N + 1) + R) Thus, total deposts ncrease wth N. (16). Substtutng the total depost functon defned mplctly by (14) n (13), and dfferentatng, we get: d dn G N = (17). G By the assumed concavty of bank s profts n loans, G < 0. Thus, d sgn( ) sgn( GN ) dn = (18) Recall that we defned R [ F( R z)( R z) R F( Y ) Yl ]. Then, N dfferentatng GN (, ( ), N ) wth respect to N (keepng fxed at the equlbrum level), we obtan: R d N ( ) dr G + F Y Y R d + = + F( Y ) Y dr +. (19) N dn d N dn dn The term R s postve, as the rents on the loan sde cannot be negatve, otherwse N profts due to loans would be negatve and a soluton wth > 0 could not be an equlbrum. The term F( Y ) Y s postve, snce we have shown that Y > 0 for N > 1. The last term s: dr = R, whch cancels out wth the frst term. dn N 10
11 Thus, total loans also ncrease wth N. Next, we dscuss the jont emprcal mplcatons for rsk takng and asset allocaton of an ncrease n competton. In ths model, the asset allocaton s summarzed by the rato of loans to deposts /, as deposts are the only source of banks fundng.. The change n Y hence, the change n the rsk of falure F( Y ) resultng from a change n the number of banks s gven by: d d Y = N Y Y dn + dn (20) d The term Y s postve, so that, ceters parbus, an ncrease n total deposts wll dn result n a larger set of output realzatons for whch a bank falure occurs. As we have d seen, total loans ncrease wth N ( 0 dn > ). It s clear that f Y > 0, that s, f the BN effect s weak, then rsk unambguously ncreases, snce Y N > 0. Note that ths, n prncple, may occur under any asset allocaton, that s, whether / ncreases or declnes wth N. Thus, f the BN effect s weak, then rsk wll ncrease ndependently of the asset allocaton. Conversely, f Y < 0, that s, f the BN effect s strong, then the change n rsk wll generally depend on both the strength of the BN effect as well as on the asset allocaton. However, note that for any economy, Y z as N. Thus, there exsts a threshold value of N such that for all numbers of banks greater than such threshold, the BN effect becomes strong. In other words, the BN effect becomes more mportant as competton ncreases. In all cases, though, the magntude of the change n total loans relatve to total deposts wll depend on all the parameters of the model, such as the elastcty of the demand for loans and supply of deposts, moral hazard costs and the assumptons regardng the dstrbuton of the random component of the return on the rsky nvestment. Ths can be seen by the numercal examples reported n the Table below for a smple economy wth lnear demand and supply schedules and a unform dstrbuton of the return of the rsky technology. Panel A reports the case where there s no BN effect: rsk ncreases as N goes up, whle / frst declnes and then ncreases wth N. Panel B reports the same economy, but wth a strong BN effect: here rsk monotoncally declnes wth N, whle, smlarly to the prevous case, / exhbts a U-shaped relatonshp wth the number of banks. 5 5 The senstvty of the behavor of rsk to the underlyng parameters of the model s also underscored by other specal versons of our model wth no asset allocaton choce. Boyd and e Ncolò (2003) n an Allen and Gale (2000) model wth bankruptcy costs show that there can be a non-lnear U-shaped relatonshp between the number of banks and bank rsk. On the other hand, Martnez-Mera and Repullo (2008) (contnued ) 11
12 Table Number of profts total total loans/deposts Probablty of banks per bank loans deposts bank falure [F(Y)] Panel A: No BN effect 2 3.953 5.36 7.00 0.766 0.059 3 2.255 5.97 7.88 0.758 0.070 5 1.023 6.59 8.75 0.753 0.082 10 0.315 7.16 9.55 0.750 0.092 20 0.090 7.49 10.00 0.749 0.098 30 0.043 7.61 10.16 0.749 0.100 50 0.016 7.72 10.29 0.750 0.102 100 0.003 7.84 10.40 0.754 0.104 Panel B: Strong BN effect 2 4.181 5.66 7.00 0.808 0.077 3 2.503 5.95 7.88 0.755 0.067 5 1.515 5.50 8.75 0.629 0.062 10 0.672 5.66 9.55 0.593 0.050 20 0.293 5.94 10.00 0.594 0.041 30 0.142 6.66 10.16 0.655 0.034 50 0.011 7.81 10.29 0.759 0.027 100 0.003 7.86 10.40 0.756 0.025 In sum, as N ncreases, rsk ncreases f the BN effect s weak, but can decrease f such effect s strong. Moreover, any economy wll exhbt a strong BN effect for a suffcently large number of banks. As our numercal examples llustrate, when the BN effect s strong (weak), there exsts economes where beyond a certan level of N, rsk decreases (ncreases) as the loan to asset rato ncreases. Next, these predctons are confronted wth the data. III. EVIENCE In a recent survey of the emprcal lterature, Beck (2008) ponts out that studes of banks n ndvdual countres have reached mxed conclusons on the relatonshp between competton and rsk n bankng, whle cross-country studes tend to ndcate a postve relatonshp between competton and the stablty of bankng systems. We should note two mportant drawbacks of many exstng emprcal studes: 1. the measures of competton used have been ether ad-hoc ; or 2. they have lacked a clear theoretcal underpnnng. Examples of the former are studes that have used the so-called H-statstcs ntroduced by Panzar and Rosse (1987) as a contnuous measure of compettve condtons. It s well known n the lterature that usng ths statstc as a contnuous measure of compettve condtons s napproprate, and that t produces compettve rankngs consder a specal modfcaton of our prevous model (Boyd and e Ncolò, 2005) wth no competton n the depost market, and where our assumpton of perfectly correlated loans returns à la Allen and Gale (2000) s replaced wth mperfect correlaton. A non-lnear nverted-u shaped relatonshp between the number of banks and bank rsk can be obtaned under some assumptons, n contrast to Boyd and e Ncolò (2003). 12
13 opposte to those obtaned by other measures proposed n the so-called New Industral Organzaton (NIO) lterature (see the dscusson n Shaffer, 2004). Importantly, ths and other NIO competton measures are constructed gnorng key features of bankng, such as rsk and uncertanty. 6 Examples of the second group are studes that have consdered some proxy measure of a erner ndex as a measure of competton. The endogenety of such measures s typcally tackled emprcally by usng nstrumental varables. Yet, n many studes the choce of nstruments seems often to be dctated more by data avalablty than by an explct theoretcal dervaton. Most mportantly, as demonstrated by Vves (2008) n the context of workhorse models of frm competton under certanty, even measures such as the erner ndex are not model-ndependent, so that.. t cannot be taken for granted that a good proxy for the degree of product substtutablty, as an ndcator of compettve pressure, s the erner ndex (Vves, 2008, p.445). Thus, the results obtaned usng measures of competton not supported by some explct theoretcal construct are dffcult to evaluate and compare, and, as known snce Cort (1999), estmates of measures of competton can be sgnfcantly based. 7 Our emprcal analyss dffers from prevous studes n three key respects. To our knowledge, ths s the frst emprcal study n bankng that assesses the jont mplcatons of changes n compettve condtons on both bank rsk and asset allocatons wth the gudance of an explct theoretcal model. Second, we employ measures of bank competton and rsk that are dctated by our theory. Thrd, we consder two very dfferent samples, a U.S. sample and an nternatonal sample, to assess whether country-specfc and cross-country evdence dffer n key respects. Next, we explan these features of the emprcal work n detal. A. Measurement of competton A standard measure of market structure s the Hrschmann-Hrfendahl Index (HHI). In symmetrc Cournot-Nash competton models such as ours, the HHI ndex s gven 6 Recent publshed studes usng the H-statstcs as a contnuous measure of competton and gnorng rsk nclude Bkker and Haaf (2002) Claessens and aeven (2004, 2005), and evy-yeyat and Mcco (2007). 7 Recent examples of ths knd of studes are Jmenez, opez and Saurna (2007) and Berger, Klapper and Turk-Arss (2009). Jmenez, opez and Saurna (2007) correct ther erner ndex wth a rsk premum, whch s assumed to be determned under the assumpton that the bank cost of fundng s determned compettvely, thus gnorng market power rents on the fundng sde. In addton, ths premum s proxed by the probablty of default of ther loan categores, gven by the rato of defaulted loans to total loans, whle ther dependent varable s the rato of non-performng loans to total loans: thus, the dependent varable s regressed on a hghly correlated ndependent varable (to gve a perspectve, the correlaton between delnquences and charge off rates on all loans for the US commercal banks durng 1991Q1-2008Q3 s 0.86). Berger, Klapper and Turk-Arss (2009) employ a erner ndex n whch margnal costs are estmated assumng that the cost of bank fundng s provded compettvely, thereby mssng by constructon any market power on the depost sde. Further they gnore any measure of a rsk premum. 13
14 2 by N. Ceters parbus, ths HHI s postvely assocated wth prce-cost margns (erner ndex), a standard measure of the degree of compettveness, as we have shown. However, n realty both banks and markets are heterogeneous. Thus, the relatonshp between concentraton measures and the degree of competton needs to be condtonal on certan factors that are not drectly connected wth the ablty of frms to extract market power rents, but may affect the level of concentraton. 8 Banks dffer both wth respect to scale (ds)economes and wth respect to ther cost structures. In theory, t has been well known snce esmetz (1973) that, ceters parbus, a hgh HHI may reflect dfferences n banks technologes, snce more effcent banks wll be able to gan larger market shares due to ther ablty to set prces lower than ther compettors. kewse, markets dffer wth respect to sze and the demand for bankng servces. Comparng HHIs across markets requres that we take nto account dfferences n market sze (see Bresnahan, 1989), snce an HHI may be lower n a larger market, n whch a greater number of frms can proftably operate. fferences n the demand for bankng servces across markets can also result n dfferences n HHIs not necessarly drectly related to the ablty of banks to extract market power rents. Thus, our proxy measure of the degree of competton s the HHI ndex condtonal on measures of banks sze and costs, sze of market and proxy measures of the demand for bankng servces. As remarked by Sutton (2007) wth reference to studes of nonfnancal frms n whch frm and market heterogenety s accounted for,..that a fall n concentraton wll lead to a fall n prces and prce-cost margns s well-supported both theoretcally and emprcally. 9 Smlarly, egryse and Ongena (2008), n ther recent comprehensve survey of the emprcal bankng lterature, show that the results of studes conducted n many countres and dfferent tme perods ndcate that more concentrated markets are assocated wth sgnfcant nterest rate margns n both depost and loan markets. B. Measurement of rsk Our frst emprcal measure of bank rsk s the Z-score, whch s defned as Z = ( ROA + EA)/ σ ( ROA), where ROA s the rate of return on assets, EA s the rato of equty to assets, and σ ( ROA) s an estmate of the standard devaton of the rate of return on assets, all measured wth accountng data. Ths rsk measure s monotoncally assocated wth a bank s probablty of falure and has been wdely used n the emprcal bankng and fnance lterature. Specfcally, t represents the number of standard devatons below the mean by whch a bank s profts would have to fall so as to deplete 8 It s well known that n the context of Cournot-Nash competton, the drect relatonshp between concentraton and the degree of market power holds only for specfc forms of frm heterogenety (see for example Trole, 1988). 9 Recent evdence of a sgnfcant postve relatonshp between concentraton and prce-cost margns s n Al, Klasa and Yeung (2008). 14
15 equty captal. It does not requre that profts be normally dstrbuted to be a vald probablty measure; ndeed, all t requres s exstence of the frst four moments of the return dstrbuton (Roy, 1952). 10 Our second rsk measure s specfcally related to the rskness of banks loan portfolos. Recall that n the theoretcal model, there are two dstnct falure probabltes: the probablty that loan customers default (represented by F( R z) ), and the probablty that the bank fals (represented by F( Y )). As dscussed earler, loan customers default rsk s partly determned by a moral hazard problem n whch, as loan rates rse they supply less effort whch causes ther rsk of falure to rse. We have referred to ths as the BN effect. We nvestgate the sze of the BN effect by lookng at the rsk assocated wth bank loan portfolos. Although explct loan default probablty measures are not avalable, we can employ standard measures of loan portfolo losses as proxy measures. These procedures and the attendant caveats are dscussed n the next secton. Our thrd rsk measure s an ndcator of actual bank falures, or near-falures, and we can only use ths measure wth the nternatonal sample. Unfortunately, we cannot employ such a measure wth the US cross-secton of banks, snce 1993 was a bengn year and none of the 2500 sample banks was even close to falure or under regulatory supervson. In the nternatonal panel, observng actual bank falures s dffcult because the authortes frequently ntervene wth problem banks, re-organze, and recaptalze, makng t dffcult to dentfy the tmng of actual falures. What we do as an alternatve s to look at the accountng sum of captal plus current profts standardzed by assets and defne extremely low (outler) observatons as faled or near faled banks. Ths procedure s dscussed n detal below. C. Samples We employ two samples wth very dfferent characterstcs, each wth ts own advantages and dsadvantages. The frst sample, a sngle cross-secton of US banks, s specfcally chosen so as to reduce measurement problems n market defnton to the absolute mnmum. In makng ths choce we admttedly gve up sample sze and representatveness of the sample. The second sample, an nternatonal panel of banks n many countres, has enormous sze and s representatve of many dfferent markets and economc envronments. However, measurement ssues arse n defnng bankng markets and measurng competton theren. 10 In our model banks are for smplcty assumed to operate wthout equty captal. However, n the model the defnton of a bank falure s when gross profts are nsuffcent to pay depostors. If there were equty captal n the theory model, bankruptcy would occur precsely when equty captal was depleted. Thus, the emprcal rsk measure s dentcal to the theoretcal rsk measure, augmented to reflect the realty that banks hold equty. 15
16 The frst sample s composed of 2500 U.S. banks that operated only n rural non- Metropoltan Statstcal Areas, and s a cross-secton for one perod, June, 2003. The banks n ths sample tend to be small and the mean (medan) sample asset sze s $80.8 mllon ($50.2 mllon). They exhbt extreme varaton n compettve condtons. 11 By lmtng ourselves to these banks we are able to use the Federal Reserve s Facltes dataset. For ant-trust purposes, n these rural market areas the Federal Reserve Board (FRB) defnes a compettve market as a county and mantans depost HHIs for each market. These computatons are done at a very hgh level of dsaggregaton. Wthn each market the FRB defnes a compettor as a bankng faclty, whch could be a bank or a bank branch. There s a substantal lterature on the topc of competton n rural US bankng markets, one that s too large to be adequately revewed here. 12 However, two measurement problems are commonly recognzed n ths research. One s that the FRB only reports HHI ndces for deposts, not for loans. It s entrely possble that the loan market s dfferent from the depost market n many cases so that the depost market HHI s not the approprate measure for loan market condtons. Another wdely-recognzed problem s that many banks operate n more than one depost and/or loan market. When that occurs, the researcher must somehow aggregate HHI measures across markets and there s no unanmty on how that should be done. A related problem, mportant for our purposes, s that banks do not publcly report balance sheets at the branch level. Ths means that we cannot compute the loan/depost rato at the county level, and that s a key varable for our nvestgaton. In an attempt to mtgate all these problems smultaneously, we asked the FRB staff to delete from our sample all banks that operated n more than one depost market. 13 By lmtng our sample to such unt banks, we neatly avod the problem of havng to aggregate HHI ndces. In addton, wth these unt banks we are able to match up compettve market condtons as represented by depost HHIs and loan/depost ratos as represented by bank balance sheet data. 14 Obvously, computaton of the HHI statstcs was done before these deletons, and was based on all compettors (banks and branches) n each market. Fnally, ths dataset allows us to nclude (or not) savngs and loans as compettors wth banks, whch could provde a useful robustness test. S& deposts are 11 For example, when sorted by HHI, the top sample decle has a medan HHI of 5733 whle the bottom decle has a medan HHI of 1244. The sample ncludes 32 monopoly bankng markets. 12 Some recent studes nclude Adams et al.(2007), Rosen (2007), Berger, Rosen and Udell (2007), and Hannan and Prager (2004, 2006). 13 The bankng facltes data set s qute dfferent from the Call Reports whch take a bank as the unt of observaton. These data are not user-frendly and we thank Allen Berger and Ron Jawarczsk for ther great assstance n assemblng these data. 14 These unt banks have offces n only one county; however, they may stll lend or rase deposts outsde that county. To the extent that they do, our method for lnkng depost market competton and asset portfolo allocatons wll stll be nosy. 16
17 near perfect substtutes for bank deposts, whereas S&s compete wth banks for some classes of loans and not for others. The second sample s a panel data set of about 3,000+ banks n 134 countres excludng major developed countres over the perod 1993 to 2004, whch s from the Bankscope (Ftch-IBCA) database. We consdered all commercal banks (unconsoldated accounts) for whch data are avalable. The sample s thus unaffected by selecton bas, as t ncludes all banks operatng n each perod, ncludng those whch exted ether because they were absorbed by other banks or because they were closed. 15 The number of bankyear observatons ranges from about 13,000 to 18,000, dependng on varables avalablty. The advantage of ths nternatonal data set s ts sze, ts panel dmenson, and the fact that t ncludes a great varety of bankng systems and economc condtons. The dsadvantage s that bank market defntons are necessarly mprecse, snce t s assumed that the market for each bank s defned by ts home naton. Thus, the market structure for a bank n a country s represented by an HHI for that country. To reduce possble measurement error from ths source, we excluded banks from the U.S., the European Unon, Swtzerland, the Nordc countres, and Japan. In these cases, defnng the naton as a market s especally problematc, both because of the country s economc sze and because of the presence of many nternatonal banks. 16. Results for the U.S. Sample Table 1 defnes all varables and sample statstcs, whle correlatons are reported n Table 2. Here, Z-score ( Z = ( ROA + EA)/ σ ( ROA) ) s constructed settng EA equal to the rato of the quarterly average over three years of the book value of equty over total assets; ROA equal to the rato of net accountng profts after taxes to total assets; and σ ( ROA) equal to the quarterly standard devaton of the rate of return on assets computed over the 12 most recent quarters. As shown n Table 1, the mean Z-score s qute hgh at about 36, reflectng the fact that the sample perod was one of proftable and stable operatons for U.S. banks. The average depost HHI s 2856 f savngs and loans are not ncluded, and 2655 f they are. 17 Forty sx of the ffty states are represented. 15 Coverage of the Bankscope database s ncomplete for the earler years (1993 and 1994), but from 1995 coverage ranges from 60 percent to 95 percent of all bankng systems assets for the remanng years. ata for 2004 are lmted to those avalable at the extracton tme. 16 Ths problem mars the sgnfcance and nterpretaton of the results obtaned by Berger, Klapper and Turk-Arss (2009), who consder HHI ndexes as measures of competton precsely for the countres we exclude. 17 To put these HHI s n perspectve, suppose that a market had four equal szed banks. Then ts HHI would be 4 x 25 2 = 2500. 17
18 We estmate versons of the followng cross-sectonal regresson: X = α + βhhi + γy + δz + ε j j j j j where X j s Z-score, or the loan-to-asset rato of bank n county j, HHI j s a depost HHI n county j, Y j s a vector of county-specfc controls, and Z j a vector of bankspecfc controls. Our control varable for bank sze s the natural logarthm of total bank assets, ASSET. fferences n techncal effcency across banks are accounted for by the rato of nonnterest operatng costs to total ncome, CTI. In addton, as noted, comparng HHIs across markets requres that we control for market sze. An HHI may be mechancally lower n large markets, snce a greater number of frms can proftably operate there. Our control varable for economc sze of market s the product of medan per capta county ncome and populaton, TOTAY, whch s a measure of total household ncome n county. fferences n economc condtons across markets especally dfferences n the demand for bank servces are controlled by three varables computed at the county level: the percentage growth rate n the labor force, ABGRO; the unemployment rate, UNEM; and an ndcator of agrcultural ntensty, FARM, whch s the rato of rural farm populaton to total populaton. Ths varable s ncluded because many of the countes n our sample are prmarly agrcultural, but others are not. To further control for regonal varatons n economc condtons all regressons nclude state fxed effects. For each dependent varable, we present two basc sets of regressons. The frst set s robust OS regressons wth state fxed effects, and the second set adds a clusterng procedure at the county level to correct sgnfcance tests for possble locaton-specfc correlaton of errors. Fnally, snce the range of the rato of loans to deposts s the unt nterval, we use a Cox transformaton to turn ths nto an unbounded varable. 18 In Table 3 we present regressons n whch the dependent varables are the Z-score and the transformed rato of loans to assets, A_cox. 3.1 s a regresson of Z-score aganst HHI0, the sx control varables dscussed above, and wth state fxed effects (whch, for brevty, are not shown n the tables). The coeffcent of HHI0 s negatve and statstcally sgnfcant at usual confdence levels. The same s true when HHI100 s employed nstead of HHI0. (results wth HHI100 are shown n the last row.) Among the control varables, the coeffcent of CTI s negatve and hghly sgnfcant, suggestng that cost neffcency may adversely affect rsk of falure. The coeffcent of ASSET enters wth a negatve and hghly sgnfcant coeffcent suggestng that n ths sample larger banks are rsker than small ones. Regresson 2.2 s dentcal to 2.1 except that t employs 18 The Cox transformaton for x s ln( x /(1 x)). Throughout, varables transformed n ths way are labeled x_cox. 18
19 clusterng at the county level, there beng 1280 countes ncluded. Ths procedure seems to have lttle effect on estmated standard errors. 2.3 shows that the (transformed) rato of loans to deposts s negatvely and sgnfcantly related to both HHI measures at about the one percent confdence level. The loan to depost rato s postvely and sgnfcant related to growth rate n county labor force ABGRO, the sze of the market TOTAY, and to bank sze ASSET; t s negatvely and sgnfcantly related to bank operatng costs CTI. Regresson 2.4 adds the county clusterng procedure, but ths seems to have lttle effect on confdence ntervals. To summarze, results wth the U.S. sample suggest that more compettve bank markets are assocated wth greater rsk of falure and a hgher rato of loans to assets. Both fndngs seem robust, and are consstent wth the predctons of the theoretcal model when the BN effect s present and s suffcently strong. 19 We return to ths ssue n the next secton. E. Results for the Internatonal Sample Table 3 reports defntons of varables and some sample statstcs for banks and macroeconomc varables. There s a wde varaton across countres n terms of ncome per capta at PPP (rangng from US$ 440 to US$ 21,460), and n terms of bank sze. Here, the Z-score at each date s defned as Zt = ( ROAt + EAt) / σ ( ROAt), where ROA t s the return on average assets, EA t s the equty-to-assets rato, and 1 σ ( ROAt) = ROAt T ROAt. When ths measure s averaged across tme, t t generates a cross-sectonal seres whose correlaton wth the Z-score as computed prevously s about 0.89. The medan Z-score s about 19. It exhbts a wde range, ndcatng the presence of banks that ether faled (negatve Z) or were close to falure (values of Z close to 0), and banks wth mnmal varatons n ther earnngs, wth very large Z values. We computed HHI measures based on total assets. The medan HHI s about 1900, and ranges from 391 to the monopoly value of 10,000. Some of the correlatons between bankng and macroeconomc varables (not shown) are noteworthy. 20. The hghest correlaton s found between the HHI and GP per capta. 19 There s a branch of the lterature on bank competton n the Unted States that deserves menton because t supports, or at least seems to support, our fndng that more competton s assocated wth greater bankng stablty. Carlson and Mtchener (2006) fnd that ncreased competton brought about by branch bankng ncreased fnancal stablty durng the Great epresson. A smlar concluson was reached by Jayaratne and Strahan (1996, 1998) who studed the effect of bank deregulaton n the 1980 s and 1990 s. In all ths work, cross-sectonal and nter-temporal varatons n measures of bank competton are prmarly due to varatons n regulatory restrctons on the locaton of banks and branches. As banks were permtted to expand geographcally, ths drectly affected ther ablty to dversfy. Therefore, t s dffcult to separate the effects of mproved dversfcaton and ncreased completon. In our analyss, of course, regulatory restrctons of ths nature play no drect role. 20 Correlatons tables for both sample are reported n our prevous workng paper (Boyd, e Ncolò and Jalal, 2006) 19
20 Ths correlaton s negatve (-0.30) and sgnfcant at usual confdence levels, ndcatng that relatvely rcher countres have less concentrated bankng systems. Ths s unsurprsng, snce GP per capta can be vewed as a proxy for the sze of the bankng market. 21 The second hghest correlaton s between the HHI ndex and asset sze whch s negatve (-0.26) and sgnfcant. Because of ths hgh value, as detaled below, we wll use regressons specfcatons wth and wthout frm specfc varables so as to check the possble mpact of multcollnearty between the HHI and asset sze. We estmate panel regressons of the followng form: where X = α + βhhi + γy + δz + ρx + ε jt jt 1 jt 1 jt 1 jt 1 jt X j s the Z-score or the (transformed) loan-to-depost rato of bank n country j, α s a tme-nvarant frm fxed effect, Index n country j, Y j s a vector of country-specfc controls, and HHI j s a Hrschmann-Hrfendahl Z j a vector of bankspecfc controls. The HHI, the macro varables and bank specfc varables are all lagged one year so as to capture varatons n the dependent varable as a functon of predetermned past values of the ndependent varable. 22 The vector of country-specfc varables Y jt ncludes: real GP growth and nflaton, whch control for cross-country dfferences n the economc envronment; GP per capta and the logarthm of populaton, whch control for dfferences n relatve and absolute sze of markets (countres); and the exchange rate of domestc currency to the US dollar, snce bank balance sheet values are all expressed n dollar terms. For the reasons mentoned earler, the vector of frm varables Z j may nclude the natural logarthm of total bank assets, ASSET and the rato of non-nterest operatng costs to total ncome CTI to control for dfferences n banks technologes and cost structures. We present two basc types of regressons wth the Z-score and the transformed loan-toasset rato as dependent varables. The frst type of regresson s a standard fxed effect statc panel regresson ( ρ = 0 ), wth standard errors clustered by country. We report two specfcatons: one wthout frm specfc varables, and one wth all varables ncluded. The second type s a dynamc panel regresson (all varables are ncluded) wth one lag of the dependent varable. We apply the GMM estmaton procedure developed by Arellano and Bond (1991). The lagged dependent varables and all ndependent varables are treated as pre-determned, and we nstrument these varables usng ther lags at tme t- 21 Interestngly, the U.S. sample exhbts an dentcal negatve and sgnfcant correlaton (-0.30) between medan county per-capta ncome and HHI0. 22 Ths s a farly standard specfcaton consstent wth our two-perod models. See, for example, emsetz and Strahan (1997). 20
21 2, t-3, and so on. Estmates of coeffcents are reported for the one-step Arellano-Bond estmator, whle Sargan specfcaton tests are based on the relevant two-step estmator. Table 4 reports the results. For both the Z-score and the (Cox-transformed) rato of loans to assets, the sgn assocated wth the HHI s negatve and sgnfcant n the fxed effects panel regressons as well as n the dynamc panel regressons. 23 Remarkably, n the dynamc panel regressons wth the Z-score as dependent varable (4.3), the sgn of the HHI coeffcent s not only negatve and sgnfcant, but doubles ts sze (n absolute value). By contrast, the sze of the HHI coeffcent n the regressons wth the loans-to-assets rato as the dependent varable (4.6) declnes. Ths ndcates the mportance of takng nto account the dynamcs of rsk and asset allocaton measures n these regressons, as wtnessed by the sgnfcance of the coeffcents assocated wth the lagged values of the dependent varables. It s also noteworthy that n these tests, as well as n those of the U.S. sample, larger banks exhbt hgher nsolvency rsk, as the coeffcent assocated wth bank sze s negatve and hghly sgnfcant. Comparable results have been obtaned for samples of U.S. and other ndustralzed country large banks by e Ncolò (2000) for the 1988-1998 perod; and wth nternatonal banks by e Ncolò et al. (2004). Thus, a postve relatonshp between bank sze and rsk of falure seems to have been common n both developed and developng economes durng the past two decades. In sum, smlar to the U.S. sample, we fnd that more concentrated bank markets are ceters parbus assocated wth hgher rsk of bank falure and lower loan-to-asset ratos. Agan, these results are consstent wth the predctons of our model but only f the BN effect s suffcently strong. IV. ATERNATIVE RISK MEASURES In the emprcal lterature on bank rsk, t has been qute common to use measures of loan losses as proxy measures for rsk n loan portfolos. Two caveats must be emphaszed. Frst, such rsk does not necessarly mply a hgher rsk of bank falure f the asset allocaton tlts towards a larger holdng of rsk free assets. Our theoretcal analyss shows that borrower falure and bank falure are dfferent events and that the probablty of bank falure can ncrease (decrease) at the same tme that the probablty of borrower falure decreases (ncreases). Second, such measures at best capture the default rsk assocated wth the loan portfolo; the default rsk assocated wth other bank assets (rsky nvestments) s not captured by these measures. For our purposes, however, ndcators of loan qualty have ndependent nterest, at least to the extent that they are correlated wth the probablty of borrower falure. We have obtaned evdence that, as competton, 23 In both dynamc panel regressons, the autocorrelaton tests ndcate that coeffcent estmates are unbased, and the Sargan tests do not reject the null hypothess that the over-dentfyng restrctons are vald. 21
22 measured by the HHI ncreases, rsk of bank falure decreases. The model requres that a necessary condton for observng both at same tme s that there exst a strong BN effect. A. oan oss Measures of Rsk For the U.S. sample, we use two measures of loan losses, both of whch have been commonly used n the lterature. One s loan loss provsons, whch s an expense tem on the ncome statement and reflects manageral judgment concernng future loan loss wrte-offs. The other s the loan loss allowance, whch s supposed to summarze hstorcal loan loss experence. Both these varables are scaled by net loans and leases. Results wth both varables are presented n Table 5, where the frst two columns show robust OS regressons, and the second two columns have robust OS regressons wth county clusterng. We nclude all the controls dscussed prevously. In all four regressons, the coeffcent of the HHI ndex s postve and sgnfcant at usual confdence levels. Ths suggests that more concentraton n US unt bankng markets s ceters parbus assocated wth greater loan losses as a percentage of total loans. To the extent that loan losses are a proxy for the default rsk of loan customers, these results suggest that there s a BN effect n our sample of unt banks n the Unted States. Specfcally, as concentraton ncreases and banks rase loan rates, the rsk of loan default systematcally ncreases. 24 Wth the nternatonal data, the comparablty of accountng defntons or standards across countres s uncertan, although the complers of the database spend substantal effort to classfy accountng tems nto homogenous categores. Keepng n mnd ths caveat, we estmated fxed effects regressons usng the rato of mpared loans to gross loans as defned n the Bankscope database. As shown n Table 6, the sgn assocated wth the HHI s postve and sgnfcant n both regressons wthout and wth frm controls. Thus, for the nternatonal sample more concentraton s ceters parbus assocated wth greater loan losses, consstent wth the fndngs of the prevous regressons wth the U.S. sample. 24 On ths ssue, a recent study by Cerquero (2008) s extremely useful. Workng wth hghly dsaggregated data, he nvestgates both the attrbutes of bank loans extended, and of the pool of applcants from whch loan customers are drawn. He fnds robust evdence that more concentraton s assocated wth sgnfcantly hgher loan rates. In turn hgher loan rates are assocated wth a lower qualty loan applcant pool and lower qualty loans extended. Hs results clearly ndcate endogenous customer reacton n response to terms of bank lendng. Ths could reflect a moral hazard problem such as the one we modeled, or an adverse selecton problem n whch the pool of loan applcants changes. But ether of these mechansms wll produce a BN effect. 22