Market power and banking failures

International Journal of Industrial Organization 20 (2002) 1341 1361 www.elsevier.om/ loate/ eonbase a Market power and banking failures Ramon Caminal *, Carmen Matutes a, a,b Institut d Analisi ` Eonomia ` (CSIC) and CEPR, Ballaterra, E-08193 Barelona, Spain b University of Edinburgh, Edinburgh, UK Reeived 5 May 2000; reeived in revised form 7 August 2000; aepted 17 January 2001 Abstrat We investigate whether more ompetition in the banking industry neessarily results in a higher probability of banking failures, as it is often suggested. In our model borrowers fae a moral hazard problem, whih indues banks to hoose between ostly monitoring and redit rationing. We show that investment dereases with the lending rate and inreases with monitoring effort. Sine inentives to monitor are enhaned by market power, the relationship between market struture and investment is ambiguous. In the presene of non-diversifiable risk and dereasing returns to sale, more investment implies higher failure rates. As a result, the relationship between market power and banking failures is ambiguous. 2002 Elsevier Siene B.V. All rights reserved. JEL lassifiation: D4; D82; G21 Keywords: Moral hazard; Credit rationing; Monitoring; Market power; Banking failures 1. Introdution Can exessive ompetition jeopardize the solveny of the banking system? Does prudential regulation beome more neessary after restritions on deposit interest rates, branhing, and other anti-ompetitive measures are lifted? Suh questions * Corresponding author. Present address: Institut d Analisi ` Eonomia, ` Campus UAD, Ballaterra, E-08193 Barelona, Spain. Tel.: 134-9-3580-6612; fax: 134-9-3580-1452. E-mail address: ramon.aminal@uab.es (R. Caminal). 0167-7187/ 02/ $ see front matter 2002 Elsevier Siene B.V. All rights reserved. PII: S0167-7187(01)00092-3

1342 R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 are at the heart of the poliy debate over banking deregulation. Our aim is to provide some new insights into these issues, in partiular regarding the exposure of banks to aggregate risk under alternative market strutures. Market power is often assoiated with a lower probability of a banking failure. Suh a negative relationship is usually attributed to various reasons. Firstly, higher lending rates result in lower investment levels and thus a higher expeted return of the marginal projet, whih implies a lower probability of bankrupty. Seondly, the higher are the future expeted profits of a bank, the larger is the opportunity ost of going bankrupt, whih redues the inentive to over invest in risky assets. Finally, on the deposit side, ompetition will tend to inrease deposit rates pushing the margin further down and failure probabilities up. Some of the existing 1 theoretial models onfirm these intuitions. However, this literature disregards the fat that a major harateristi of banks is their ability to redue the sope of moral hazard and adverse seletion problems, exploiting their omparative advantage in the provision of monitoring servies. In this paper we argue that market power may affet bank solveny not only through the traditional hannels, but also by altering banks inentives to invest in reduing information asymmetries about projet seletion. We show that if suh an effet is strong enough tighter ompetition in the loan market may atually be assoiated with higher bank solveny. The main ingredients of the model are the following. Firstly, beause of limited liability and non-verifiable ations, ontrats annot be omplete and entrepreneurs inentives to alloate funds to alternative projets are distorted. Similarly as in our ompanion paper (Caminal and Matutes, 1997), banks have two ways to indue appropriate projet hoies. On the one hand, by rationing redit, the bank inreases the marginal return of the apital invested and thus makes it less attrative for entrepreneurs to deviate and undertake exessively risky projets. On the other hand, the bank an deal with the ageny problem by monitoring borrowers in the interim of the relationship. Thus, redit rationing and monitoring are imperfet substitutes: by spending resoures the bank an lend more apital sine the firm s inentive problem vanishes when the firm s ativities are 2 monitored by the bank. Seondly, we assume that all projets are ex-ante idential and are subjet to a multipliative aggregate shok. In this ase, the riskiness of a loan inreases with its size. The reason is that, under dereasing returns to sale and multipliative unertainty, the distribution of the rate of return of a projet shifts to the left when the level of investment inreases. In the real world, firms fae both idiosynrati 1 See, for instane, Chan et al. (1992), and Matutes and Vives (1996, 2000). 2 Our approah to monitoring is analogous to that in Besanko and Kanatas (1993), in the sense that in both ases bank monitoring implies that borrowers take more effiient deisions.

R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 1343 and aggregate risk. However, as long as banks hold a well diversified loan portfolio, bank solveny is only affeted by aggregate risk. Thus, for simpliity, we abstrat from idiosynrati risk and fous exlusively on aggregate unertainty. We explore the trade-off between rationing and monitoring for two extreme market strutures, monopoly and Bertrand ompetition, so as to investigate the impliations of banks hoies on the likelihood of bankrupty. Our main onlusion is that the relationship between market struture and banking failure is ambiguous. The argument goes as follows. The relationship between market power and loan sizes is ambiguous sine it depends on the net effet of two ountervailing fores. On the one hand, a monopoly bank by setting a higher interest rate worsens the unmonitored firm s inentive problem, whih in turn tightens the redit onstraint. On the other hand, a monopoly bank has a bigger inentive to exert monitoring effort and thus dereases the likelihood of redit rationing. Sine larger loans are more exposed to multipliative unertainty, it follows that lak of market power and solveny risk do not always move together. Speifially, when monitoring osts are so high that banks do not monitor regardless of market struture, ompetitive banks are more likely to fail. Indeed, they set lower lending rates implying that firms inentive onstraint is not so tight and thus they an extend redit further than a monopoly bank. For intermediate monitoring osts, only a monopoly bank will exert monitoring effort and hene faes no need to redit-ration loan appliants. In suh irumstanes, the monopoly bank is more exposed to aggregate risk than ompetitive banks and it is thus more likely to fail. For very low monitoring osts every bank will monitor and lend the effiient apital amount. In this latter ase the banking failure probability is independent of market struture. Our paper is onsistent with the empirial evidene in Petersen and Rajan (1995), whih unovers a positive orrelation between market onentration and investment in ustomer relationships, whih in turn inreases the likelihood of finaning redit-onstrained firms. Indeed, this paper provides further support for the idea that market power provides positive inentives to redue ageny problems through monitoring, whih results in firms enjoying easier aess to external 3 finaning. Our main ontribution here is to show that as a onsequene of this there may be higher failure rates as banking beomes more onentrated. Undoubtedly, it may still be the ase that in the real world the traditional hannels dominate and tighter ompetition redues the solveny of the banking 3 In Caminal and Matutes (1997) we haraterize the optimal banking market struture without aggregate shoks and when monitoring effort is not ontratible, and show that in general some market power improves welfare beause inentives to exert monitoring effort inrease with market power. In the present paper, we allow banks to ommit to monitoring (i.e. monitoring is ontratible) and do not arry out a welfare analysis of market struture. In an adverse seletion framework, Villas-Boas and Shmidt-Mohr (1999) also show that less ompetition in banking may atually inrease welfare.

1344 R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 4 system. The ontribution of this paper is preisely to demonstrate that the relationship between market power and bank solveny is omplex, and it is not suffiient to fous on how liberalization affets the harter value of banks and the assoiated inentives to risk taking. In Setion 2 we present the model. Setion 3 haraterizes the features of optimal debt ontrats with and without monitoring. Setions 4 and 5 investigate the inentives to monitor, and the equilibrium lending levels of a ompetitive and a monopoly bank, respetively. Setion 6 derives the impliations of our model on failure probabilities and welfare. Conluding remarks lose the paper. 2. The model In this setion we present a stati model of a redit market subjet to aggregate unertainty and where lending is restrited by a moral hazard problem. There are three types of agents: depositors, banks and entrepreneurs. Banks intermediate between depositors and borrowers. They are risk neutral and have limited liability. Depositors supply their funds inelastially at the gross interest rate I. Moreover, deposits are fully insured and hene the fae value of deposit ontrats is also I. For simpliity, we assume that insurane premia are flat. 2.1. Investment tehnology Entrepreneurs are risk neutral, endowed with zero wealth and have aess to investment opportunities whose return is determined by the ombination of three elements: (i) dereasing returns to sale in investment, (ii) a multipliative aggregate shok, and (iii) the projet hoie. More speifially, entrepreneurs (we will use the term entrepreneur and firm interhangeably) have aess to a ontinuum of investment projets, indexed by a, and are subjet to limited liability. Given ai in the interval [a, 1 and the investment level k i, entrepreneur i obtains a stohasti return given by: mw(a i) f(k i) with density ai h(m) F(k i, a i) 5H0 with probability (1 2 a ) where m is a maroeonomi shok with a density funtion h( m), whih takes i 4 Keeley (1990) provides some evidene for the US eonomy that bank default risk inreases with the liberalization of the finanial system. Demirguç-Kunt and Detragiahe (1998), looking at rossountry evidene, onlude that when the institutional environment is strong the relationship between liberalization and finanial fragility is weak.

R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 1345 stritly positive values, and is ontinuous and twie differentiable in the interval 5 [m, m. The realization of m is the same for all projets and entrepreneurs. For simpliity, we solve the model for speifi funtional forms that, as we will see below, allow simple parametrizations. Speifially, and l f(k) 5 k 0, l, 1 1 1 (1 2 z)lna w(a) 5 0, z, 1. a 6 Thus, an inrease in 1% in investment inreases expeted return by l%. Also, notie that aw(a) is an inreasing funtion of a. Thus, the expeted return of the projet inreases with a. Sine the probability of failure is 1 2 a, learly the effiient projet is haraterized by a 5 1. Also, w(a) monotonially inreases if a, exp h2 z/(12 z) j, and dereases otherwise. Thus, by assuming that a < exp h2 z/(12 z) j, sine no entrepreneur will ever hoose a projet in the inreasing setion of w(a), we do not need to worry about the possibility of having orner solutions at a. The parameter z measures the intensity of the moral hazard problem. For a given value of a and onditional on the projet suess (whih ex-ante ours with probability a), the higher the value of z, the higher the return. Given that under limited liability entrepreneurs only are about the non-negative interval of the return distribution, the parameter z provides an indiation of the inentives to hoose ineffiient projets. The variable a an literally be interpreted as a tehnology hoie, but also more generally as refleting any deision taken by the entrepreneur that is ostly to verify and that influenes the distribution of returns (R&D poliy, quality of supplies, and so on). A similar framewrok was presented in Bahetta and Caminal (2000). 2.2. Information struture A ruial feature of the model is that the projet type a is the entrepreneur s private information. However, the bank, by inurring a ost, an observe and also ollet hard evidene on a. Thus, by monitoring the bank makes a 5 In fat, all we need is that banks annot perfetly diversify their portfolio of loans. This ours, for instane, when banks are speialized in a partiular type of borrower with orrelated risks. Clearly, this is also the ase with aggregate shoks. For simpliity we make the latter assumption. 6 Constant elastiity of the prodution funtion failitates the presentation but it is not essential. However, if we allow the elastiity to inrease with the investment level, then the first order ondition of some of the optimization problems we analyze may have multiple solutions.

1346 R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 ontratible. The idea is that the bank an get somewhat involved in the deision making of the firm. For instane, a bank representative may sit in the firm s board of diretors, or a bank agent may meet regularly with the borrower to hek that the funds are appropriately used. On the other hand, we assume that the realization of the maroeonomi shok is publily observable but not verifiable, and hene payments annot be onditional on m. Furthermore, one the return of the projet, F, is realized, a signal s is observed by everyone. The entrepreneur an hoose between two ations: (i) to be honest, in whih ase s 5 F (output is publily observable), and (ii) to hide the projet s return, in whih ase s 5 0. In either ase, the bank an verify ex-post the return of 7 the firm by paying a ost d, whih is assumed to be suffiiently large. For simpliity, we assume that the osts involved in the monitoring ativity at the interim stage,, as well as in the ex-post verifiation of returns, d, are non-peuniary, so that they do not affet the bank s failure probability. Thus, we are desribing a situation in whih there is no onflit of interest between the owners and the managers of the bank, and the latter must exert effort to monitor firms at the interim stage and to verify returns ex-post. Therefore, the organization as a whole maximizes the differene between peuniary profits and the osts of effort. Suh an assumption is learly extreme but allows us to onentrate on loan sizes as the only determinant of the probability of failure, whih makes the 8 analysis muh more transparent. 2.3. Contrats Given that it is ostly to verify output ex-post, debt ontrats (fixed repayment r per unit borrowed) are optimal. However, if the bank monitors the firm then the ontrat an speify a. Debt ontrats require the bank s ommitment to verify output ex-post when the borrower does not meet her payment obligations. Suh a ommitment is intended to avoid strategi default. In our ase, the firm may be unable to repay the loan due to a low realization of the maroeonomi shok, whih is publi information. Thus, in order to minimize verifiation osts the bank an ommit to verify and seize all output ex-post if one of the two things happens: either s 5 0, or the firm does not pay min hrk, sj. Suh a ommitment disourages strategi default, and it implies that expeted verifiation osts are (1 2 a)d. 2.4. Timing The timing of the game is the following. Stage 1: ompetition in ontrats. 7 See footnote 10. 8 In the last setion we disuss the impliations of relaxing suh an assumption.

R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 1347 Banks simultaneously offer ontrats (r, k), and may also ommit to monitor the firm at stage 2 in whih ase the ontrat inludes a projet hoie, a. After observing all the ontrats offered by the banks, eah entrepreneur hooses one of them. Stage 2: investment and interim monitoring. Capital is assigned to firms and banks fulfil the monitoring ommitment. Stage 3: projet seletion. Firms hoose projet a, possibly restrited by the ontrat they signed. Stage 4: outomes. Projet returns, F, are realized, the signals s are observed and payments are made. Verifiation osts are inurred if required. We disuss in Setion 6 the extent to whih relaxing the banks ability to ommit to monitoring would affet our onlusions. 2.5. Further assumptions In order to avoid trivial outomes, we require that if the firm is offered the optimal level of apital and a loan rate r, r > I, then it has inentives to hoose an ineffiient projet. Given our parametrization this is equivalent to the following assumption: Assumption 1. l. 1 2 z. We also assume that: Assumption 2. m, Esmds1 2 z d. As we will see this assumption implies that, in the absene of bank monitoring, there is suffiient variability of the maroeonomi shok that the firm fails with positive probability. 9 Finally, for tehnial reasons we require that h( m) be suh that Assumption 3. h(m) 2 h9(m),. m 9 Assumption 3 rules out the existene of multiple equilibria of the ontinuation game for a given ontrat.

1348 R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 3. Preliminaries 3.1. Optimal ontrats under bank monitoring Given that the bank has ommitted to monitoring the firm, the ontrat onsists of a triple (r, k, a). The payoff of the firm an be written as follows: p 5 aefmwsadfk s d2 rkg dhsmd m F where rk m F ; maxhm, J, wa s dfk s d is the threshold level of m suh that the entrepreneur annot meet her payment obligations. For (a, r, k) suh that ar. I, then even when all the firms go bankrupt the bank need not, and the payoff to the bank is: where m m F B 5Efsar 2 Ik d g dhsmd 1Efawsadfkm sd 2 Ikg dhsmd2 2s1 2 add mf B mb is the threshold level of m below whih the bank goes bankrupt, i.e. H J Ik m B; max m, < m F. awsadfk s d Notie that the probability that the bank goes bankrupt inreases with k and dereases with a. With ex-ante monitoring, the optimal ontrat (r, k, a) is the solution to Maximize p subjet to B >B Unsurprisingly, in the optimal ontrat parties are willing to ommit to the effiient projet hoie (a 5 1). The reason is that a 5 1 maximizes the joint payoffs, for any value of investment. The next step is to haraterize the effiient investment level. Let us denote by S(k) the aggregate surplus obtained by the bank and the firm for a given level of investment when a 5 1, i.e. Sk sd5efmf(k) 2 IkgdH(m). m B Let k* 5 argmax S(k). In Appendix A it is shown that k* is the unique solution to:

R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 1349 Efmum > mbg f 9sk* d5 I. The next lemma summarizes the main features of the optimal ontrat. Lemma 1. The optimal ontrat under bank monitoring speifies a 5 1 and a level of apital k 5 k*. The interest rate inreases with B. The formal proof an be found in Appendix A. The main idea is that bank monitoring eliminates asymmetri information and, as a result, there exists an investment level, k 5 k*, and a projet hoie, a 5 1, suh that joint payoffs are maximized independently of how they are distributed. The distribution of surplus an be done through the interest rate. That is, r and hene the share of the surplus of the bank, depends on B (market struture) but it does not interfere with the maximization of the total surplus. Therefore, in equilibrium total surplus, gross of monitoring osts, is S* 5 S(k*). 3.2. Optimal ontrating in the absene of bank monitoring In the absene of ex-ante monitoring a annot be ontrated upon. At the ontrat design stage parties antiipate that given (r, k) the firm will selet a in order to maximize expeted profits: m Maximize ae fmwsadfk s d2 rkg dhsmd a m F subjet to a [ fa, 1. g The first order ondition for an interior solution implies that: s1 2 zemm. d f u mfg fk s d a* sr, kd5. rk In Appendix A we show that the first order ondition uniquely haraterizes the solution. Notie that the diret effet of k and r on a is negative. However, r and k also influene a through m F, and this indiret effet is positive. In any ase, we show that the diret effet always dominates and thus inentives improve by reduing k or by reduing r. That is, due to limited liability the larger the required payment rk the bigger the inentives of the firm to deviate and hoose inreasingly ineffiient projets. Conversely, restriting k results in a higher average return of the safe and effiient projet and thus it redues the inentives to deviate. The question remains as to how the optimal ontrat (in the absene of monitoring) trades-off ineffiient projets and ineffiient investment levels. To address this issue we must investigate the pairs (r, k) that:

1350 R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 Maximize p subjet to B >B, and a 5 min (a*, 1) The next lemma haraterizes these ontrats. Lemma 2 (redit rationing). In the absene of ex-ante monitoring, the optimal ontrat inludes a level of apital, k, k, k*, whih is the unique solution to: s1 2 zemm. d f u m g f(k ) 5 rk F and indues the firm to hoose a 5 1. The level of investment, k, and the interest rate, r, dereases and inreases with B, respetively. Thus, in the absene of monitoring it is effiient to restrit lending in order to indue the entrepreneur to hoose the effiient projet. Sine the interest rate inreases with the bank s monopoly power (B), the level of investment must be redued to maintain the projet hoie unhanged. Hene ageny osts translate exlusively into ineffiiently low levels of investment, but not into projet hoies whih are dominated in terms of risk and return. This will be true in general if 10 ex-post verifiation osts are suffiiently high. Otherwise, the equilibrium outome of a wider lass of moral hazard problems ould involve a ombination of both ineffiient investment levels and exessively risky projet hoies. This seond element would unneessarily ompliate the analysis and make less transparent the analysis of how alternative market strutures deal with nondiversifiable risk. Sine k dereases with r, then we an write aggregate surplus as a dereasing funtion of r. More speifially, S sd r ; Sk f sd r g. Also sine k (r), k*, S (r), S(k*) for all r > I. In words, under redit rationing, total surplus (gross of monitoring osts) is lower than under the effiient 10 If the probability that the entrepreneur annot meet her payment obligations, H(m F), were exogenous, then the optimal ontrat would indue a 5 1 even in the extreme ase of zero verifiation osts. The reason is that any arbitrary ontrat (k, r) that indues a, 1 is dominated by a ontrat with the same level of investment and a lower interest rate. A redution of 1% in the interest rate improves the firm s inentives, and auses exatly a 1% inrease in the probability of suess. As a result, the bank s payoff are unhanged but the firm s payoff stritly inreases. However, in general, a lower interest rate implies a lower probability of default (a lower m F) and as a result a derease in r also improves the firm s inentives, but the indued inrease in a is smaller (see expression (A.1) in Appendix A). Therefore, in general we need stritly positive verifiation osts to make sure that the optimal ontrat always indues the effiient projet hoie. See Eq. (A.4) in Appendix A for an indiation of the minimum size required.

R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 1351 investment level. Moreover, total surplus dereases with the bank s monopoly power (with the interest rate). 4. Bertrand ompetition Until now we have not speified the number of banks, n. Given the struture of the game, it only makes a differene whether n is greater than or equal to one. In the first ase, we have Bertrand ompetition and in the seond we have a monopoly. With Bertrand ompetition (n. 1), the first step is to speialize the disussion of the previous setion to the ase B 5 0. Following Lemma 1, if the bank monitors the firm then the ontrat inludes a 5 1, k 5 k*, and r suh that B 5 0. Indeed, notie that the firm s and the bank s profits derease and inrease with r, respetively; hene the onstraint B > 0 is binding. As a result, r. I in order to over monitoring osts. Following Lemma 2, if the bank does not monitor the firm then the ontrat speifies k 5 k (r) (whih indues a 5 1). Sine in this ase the bank must not reover any monitoring ost, then r 5 I. The next step is to haraterize the onditions under whih Bertrand ompetitors offer redit with and without monitoring. Let p* and p be the firm s payoff with and without ex-ante monitoring. Under Bertrand ompetition, monitoring will take plae if and only if: p* > p. Given that in both ases the bank s expeted payoff is zero, this is equivalent to: < S* 2 S (I). Hene, we have the following result: Proposition 1. There exists a threshold level of monitoring ost below whih Bertrand ompetitors monitor the firms. More speifially, let 5 S* 2 S sd I. Then under Bertrand ompetition, equilibrium an be haraterized as follows: (1.1) if <, banks ommit to monitor and sign ontrats with a 5 1, k 5 k*, and an interest rate that allows them to break even; (1.2) if., banks offer ontrats with k 5 k (I), r 5 I and do not monitor firms. Nevertheless, firms find it optimal to hoose the effiient projet. 5. Monopoly In the ase of a single bank, the equilibrium ontrat is better understood as the solution whih maximizes B subjet to p > 0. If there is ex-ante monitoring then,

1352 R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 following Lemma 1, the ontrat inludes k 5 k*, a 5 1, and r arbitrarily large. In this ase the bank an appropriate all the surplus (gross of monitoring osts), S*. When the bank does not monitor the firm, following Lemma 2, the bank offers k (r), whih indues the firm to selet the effiient projet hoie (a 5 1). In this ase, the monopolist faes a downward sloping redit shedule, whih is determined by the firm s inentive onstraint, and as a result the bank annot appropriate all the surplus. In other words, firms are able to apture some informational rents. More formally, the problem of the monopolist onsists of hoosing r in order to maximize: Br sd5f1 2 Hsm dg(r 2 I) k (r) 1Efmffksd rg2 Ik sd r gdhsm d. F m F m B It is suffiient to notie that the monopoly interest rate, r M, is above I (positive M margin). It follows that k sr d, k sd I. Indeed, with r 5 I, mf 5 mb and profits equal zero, while higher lending rates yield positive profit. Let B* and B denote the payoff (gross of monitoring osts) earned by a monopoly bank with and without monitoring, respetively. The monopolist monitors the firm if and only if: < B* 2 B. Notie that: M B* 2 B. S* 2 S sr d. S* 2 S sd I. The first inequality omes from the fat that in the absene of bank monitoring M firms earn positive profits (informational rents), and thus S sr d. B. The seond inequality is due to the fat that S (r) is a stritly dereasing funtion. Therefore, Proposition 2 follows: Proposition 2. The threshold level of monitoring ost below whih a monopoly bank monitors firms is higher than the threshold level for ompetitive banks. More speifially, under monopoly, there exists a., suh that the following hold: (1.1) if <, the bank ommits to monitoring, imposes a 5 1 and lends k 5 k*, at an arbitrarily large interest rate; M M (1.2) if., the bank offers ontrats with k 5 k (r ), r. I, and does not monitor firms. Nevertheless, firms hoose the effiient projet. 6. Banking failures and market struture In our model banks fail only if the realization of the maroeonomi shok is very low, i.e. if and only if:

R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 1353 Ik m, m B ;. fk sd Therefore, the probability that a bank fails depends exlusively on its exposure to aggregate risk, whih in turn depends on the average loan size. Speifially, a higher level of investment implies a higher probability of failure. In this setion we examine the relationship between market struture, the loan size and the probability of banking failures. The analysis in the previous setions shows that whenever banks monitor entrepreneurs, under both market strutures, the level of apital is k* and hene the probability of banking failure is H. 0, where 1 S D Ik* H 1 ; H. fk* s d If banks do not monitor firms then the level of apital does depend on banks market power. In the ase of Bertrand ompetition, r 5 I and k 5 k (I), k* and the probability of banking failure is H, where 2 S Ik sd I H 2 ; H. fk f sd Ig D M M In the ase of a monopoly bank, r 5 r. I and k 5 k (r ), k (I), and the probability of banking failure is H 3, where M Ik sr d H 3 ; H S MD. ffk sr dg Hene, 0 < H, H, H. 3 2 1 Also, Propositions 1 and 2 indiate that a monopoly bank has larger inentives to monitor. As a result, the relationship between monopoly power and loan sizes (and hene probability of banking failure) is in general ambiguous, sine it will be the net effet of two ountervailing fores. On the one hand, more monopoly power implies higher inentives to monitor and larger investment levels. On the other hand, for a given monitoring effort, more monopoly power implies larger interest rates and lower investment levels. In our model the sign of the net effet of these two fores depends on the size of monitoring osts. Let us onsider three regions. (i) If,, then under both market strutures banks have inentive to monitor and hene the probability of banking failure is H 1, independent of the degree of market power. (ii) If [ f, g, Bertrand ompetitors do not monitor firms but a monopoly bank

1354 R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 does. As a result, the probability of banking failure under monopoly is higher than under ompetition: H 1. H 2. (iii)if., banks do not monitor independently of the degree of market power. As a result, a monopoly bank sets a higher interest rate, grants lower levels of investment and hene fails with lower probability: H 3, H 1. The following proposition summarizes our findings: Proposition 3. The relationship between market struture and the probability of banking failure is ambiguous. With multipliative shoks the probability of banking failure inreases with the average loan size. However, a monopoly bank may lend more or less than ompetitive banks, depending on the relative osts of monitoring and redit rationing. More speifially, there exist threshold values (, ), 0,,, suh that: (i) if,, the probability of failure is independent of the market struture; (ii) if [ f, g, a monopoly bank fails with higher probability than ompetitive banks; (iii) if., a monopoly bank fails with a lower probability than ompetitive banks. As far as welfare is onerned, the impliations of the model should be taken with are sine we are not modelling banks private and soial bankrupty osts, and our analysis is very partial in this sense. Bearing this limitation in mind, however, the model has lear ut impliations that are worth exploring. To do so, it is onvenient to distinguish two stages; firstly, the welfare impliations onditional on the information struture, and, seondly, the welfare impliations regarding information aquisition. Given the information struture, it is lear that ompetitive banks lend the effiient levels of apital and hene their exposure to the aggregate shok is effiient given the information they have. A monopoly, on the other hand, restrits redit beyond the effiient level in the presene of a moral hazard problem and hene it is underexposed to aggregate shoks relative to the seond best. The next question is whether banks take the effiient deision regarding the aquisition of information. In our model, ompetitive banks monitor if and only if it is effiient while a monopoly bank has exessive monitoring inentives sine M M r. I and thus S sr d, S sd I. As a result, while a ompetitive bank is always effiiently exposed, a monopoly s exposure to aggregate shoks an be exessive or insuffiient from a welfare point of view. The welfare impliations onditional on the information struture depend only on two ruial features: (i) in the absene of monitoring, banks hoose to ration redit (rationing and monitoring are substitutes), (ii) the firm s inentives worsen

R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 1355 with the interest rate. These two features are likely to appear in a wider lass of models. However, it is worth disussing the extent to whih the inentives to aquire information are model-dependent. In partiular, if monitoring effort were non-ontratible then we would be faing a double moral hazard problem and hene the ontrat must provide inentives to the bank as well. As a result the inentives to aquire information would be redued. In a related paper (see Caminal and Matutes, 1997) we show that, in a similar framework but without aggregate shoks, when monitoring effort is not ontratible then the ompetitive bank under supplies monitoring effort relative to the first best, while a monopoly monitors if and only if total welfare inreases. Therefore, we annot laim that the welfare impliations drawn above are robust. 7. Conluding remarks Our main onlusion is that there is no lear-ut relationship between market struture in banking and exposure to non-diversifiable risk. How relevant is aggregate portfolio risk? To the extent that banks are restrited to speifi regions whih are speialized in a small set of industries, it is obviously very important. Even when the regulatory environment allows banks to diversify aross regions, maroeonomi shoks are still relevant for any geographi area. Furthermore, banks may hoose not to diversify their loan investments to redue total monitoring ost by speializing in ertain types of firms faing orrelated risks. It is ommonly believed that deregulation in the banking industry, by inreasing the degree of ompetition, may inrease the likelihood of banking rises. Our analysis shows that this is not neessarily the ase. The reason why a monopolist might go bankrupt more often than a ompetitive bank is that bigger inentives to solve ageny problems translate into more inentives to take aggregate risk. Our result has been derived within the setting of a speifi moral hazard problem with the feature that in equilibrium firms and banks only fail due to maroeonomi shoks. Clearly, in the real world both firms and even banks may fail beause of projet hoies. Also projet hoies themselves may depend on the market struture. Thus, the atual relationship between market power and finanial fragility is learly very omplex. Yet the question is whether the driving fores behind our results are likely to be present or are artefats of the model. Thus, the issue arises as to what are the essential assumptions leading to the ambiguity result. An essential ingredient is that risk exposure inreases with the level of investment. If aggregate shoks are multipliative then it simply requires dereasing returns to sale to investment. The other two key ingredients are that monitoring and redit rationing are substitutes to alleviate a moral hazard problem, and that a monopoly is more likely to monitor firms than ompetitive banks. Regarding the former, there is some empirial support for the idea that lose ties

1356 R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 11 with banks alleviate redit onstraints, whih indiates that the trade-off between monitoring and redit rationing is rather plausible. Regarding the latter, a monopoly bank is more likely to monitor than ompetitive banks beause market power allows the bank to appropriate a higher proportion of the rents reated by monitoring. It holds in the present framework where monitoring is ontratible, but it also holds in frameworks where it is not ontratible (see Caminal and Matutes, 1997). Our model has also abstrated from peuniary osts of monitoring and verifiation, as well as from adverse seletion problems. If monitoring osts were peuniary then, eteris paribus: (i) a bank with a higher exposure to aggregate risk would have more inentives to monitor (sine the osts of monitoring would be paid only in ase of non-failure) and (ii) by monitoring a bank would bear a higher risk of failure (beause of higher osts). These two new hannels would 12 ompliate the analysis without bringing substantial additional insights. In an adverse seletion framework, with ex-ante sreening instead of interim monitoring, new effets are possible. Nevertheless, the type of effets analyzed in this paper are likely to be present, provided individual investment exhibits dereasing returns to sale and there exist aggregate portfolio shoks. For instane, more sreening (indued by higher monopoly power) is likely to be assoiated with lower individual risk, and as a result the bank would be willing to aept larger exposure to aggregate shoks. If borrowers are small with respet to the bank s portfolio, then the relationship between bank solveny and market power would be analogous to our model. However, if the size of individual loans is signifiant with respet to the bank s portfolio, then the probability of banking failure would depend on the interplay between individual and aggregate risk, and either ould dominate. Aknowledgements This is a ompletely revised version of Bank Solveny, Market Struture and Monitoring Inentives (CEPR d.p. [1665). We thank Sugato Bhattaharya, Jim Fairburn and Mihael Riordan for helpful disussions, and two anonymous 11 See for instane Petersen and Rajan (1994), Hoshi et al. (1990a,b), Lummer and MConnell (1989) and Berger and Udell (1995). 12 For values of a stritly less than one, the probability of banking failure is also higher if verifiation osts are peuniary. This fat ombined with banks limited liability imply that the inentives to take exessive risk (to offer ontrats that indue values of a below one) are higher than in the ase of non-peuniary verifiation osts. However, provided that d is higher than a ertain threshold, the optimal ontrat would still indue a equal to one, although the level of the threshold is likely to be higher than in the ase of non-peuniary osts. In expression (A.4) in Appendix A, peuniary verifiation osts translate into a higher value of m B. Clearly, suh a derivative would still be negative if d is suffiiently high.

R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 1357 referees and the editor of this journal, Dan Kovenok, for very useful omments on a previous draft. This researh has been supported by TMR networks FMRX- CT98-0203 and FMRX-CT98-0222, and by the Spanish Ministry of Eduation through DGCYT grants PB95-0130 and PB98-0695. Appendix A Proof of Lemma 1. The payoffs of the entrepreneur and the bank an be written as follows: p 5 awsad f(k)e m dh(m) 2 arkf1 2 HsmFdg m F B 5s1 2 zf(k)e d m dh(m) 1 awsadf(k) E m dh(m) mf 2f1 2 HsmBdgfIk 1 ds1 2 a dg. Notie that one again p and B inrease and derease, respetively, with r. Therefore, the onstraint B >B is always binding. Thus, the optimization problem to haraterize the optimal ontrat an be written as follows: hoose (k, a) in order to maximize m F mb p 5 awsadf(k)e m dh(m) 2f1 2 Hsm dgfik 1s1 2 addg2b. m B Notie that p stritly inreases with a, and hene the optimal value of a is equal to 1. Hene, the problem is now to maximize S(k) 2B. Given that, the optimal value of k is, by definition, k 5 k*. Finally, we show that k* is the unique solution of the first order onditions to the problem of maximizing S(k), and that m B.m. The first order ondition is given by: f 9(k)E m dh(m) 2 If1 2 H(m ) g5 0. m B B B Given the definition of mb above expression and have: and the funtional form of f(k), we an rewrite the le m dh(m) 2 mbf1 2 H(m B) g5 0. m B Sine there is a one to one relationship between k and m, if we show that there B

1358 R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 exists a unique mb that solves the above expression, then there exists a unique k that solves the original first order ondition. Let us define Fm s 0d; lem dh(m) 2 m0f1 2 Hsm 0dg. Notie that, m 0 Fm s d5 lesmd2m. 0, by Assumption 2. Also, F 9sm d521 f 2 Hsm dg1s1 2 lmh(m d ) 0 0 0 0 F 0sm d5s2 2 ldhsm d1s1 2 lmh9(m d ). 0, 0 0 0 0 by Assumption 3. Finally, Fm s d5 0 F 9(m). 0. As a result, there exists a unique mb that solves Fm s Bd5 0 with F 9sm Bd, 0 (and thus the seond order ondition holds). Proof of Lemma 2. We searh for ontrats on the effiient frontier, given the entrepreneur s moral hazard problem. Thus, we need to find the pair (r, k) that solves the following optimization problem: Maximize p subjet to B >B and a 5 min (a*, 1) where s1 2 zemm. d f u mfg fk s d a* sr, kd5. (A.1) rk Notie that, beause of Assumption 1, it is impossible to have a 5 1, if k 5 k*, and r 5 I. In fat, if k 5 k*, and r 5 I, then mf5 m B, and thus: lf(k*)e m dh( m) m B a*, 51. Ik* f12 H(m ) g B Suppose that in the optimal ontrat (r, k) are suh that a* < 1 and m.m. In F this ase

R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 1359 rk mf 5. (A.2) wa s dfk s d Solving (A.2) for r and plugging it into (A.1) and rearranging: s1 2 zemm. d s u mfd awsad5. (A.3) m F First of all, we show that if a 5 1, then the probability of default is indeed positive as assumed, i.e. Hsm d. 0. Define F m C(m a) ; s1 2 zdem dh(m) 2 maf1 2 H(m a). g m a Notie that when C 5 0, (A.3) is satisfied at a 5 1, we searh for a number m F, m [ m, F s md suh that Cm s Fd5 0. Notie that and Hene, C(m) 5s1 2 ze(m) d 2m. 0 C(m) 5 0 C 9(m ) 521 f 2 H(m ) g1 zm h(m ). a a a a C 9(m) 5 zmh(m). 0. Also, notie that C(m a) is onvex. Its seond derivative an be written as: C 0(m a) 5 (1 1 z) h(m a) 1 zmah9(m a) and from (A.3) it is positive. Therefore, there exists a unique value of m [ m, F s m d suh that Cm s Fd50 and C 9sm Fd, 0. Seondly, we show that we annot have a 5 1 and zero failure probability. Suppose we do, i.e. k satisfies: s1 2 zem d s df(k) 5 rk. Also, it must be the ase that: rk m F <. f(k) Combining these two equations: 1 2 zem < m. s d s d F

1360 R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 By Assumption 2 we reah a ontradition. Thirdly, from Eq. (A.3) if a, 1, then the probability of default is always positive. To see this, we use the impliit funtion theorem to obtain: dmf 1 2 HsmFd2 zmfhsmfd 52. da 1 2 z m f1 2 Hsm dg F F a Sine C 9sm Fd, 0, the numerator is positive and thus mf inreases if a falls. It follows, then, that for any a* < 1 the failure probability is positive as assumed. In suh a ase, the bank s payoff an be written as a funtion of k and m F (for a given k, a higher value of r implies a higher value of m F): B 5s1 2 zf(k)e d m dh(m) 1 awsadf(k) E m dh(m) mf 2f1 2 HsmBdgfIk 1 ds1 2 adg where a is a dereasing funtion of m, and m is a funtion of both k and m. F B F Computing the partial derivative: m F mb B 5 [aw(a) 2 (1 2 z) f(k) mf h(m F) m F m F (A.4) 5 6 F 1 2 z da 1 f(k) E m dh(m) 1f1 2 H(m B) gd a dm m B The first term is positive and the seond is negative. However, sine we have assumed that the verifiation osts (d) are suffiiently large, then the bank s payoff dereases with m F. In other words, it is never optimal to set an interest rate so high so as to indue the firm to hoose a, 1. Finally, sine at the optimal ontrat a 5 1, from Eq. (A.3) we have that mf is determined independently of r and k. Indeed, from (A.3) mf 5 m where m is the unique solution to: s1 2 zemum d s. m d 5 m. (A.5) Therefore, the optimal ontrat onsists of a pair (k, r) suh that: (i) s1 2 zemum d s. m d f(k ) 5 rk (A.6) where m is given by (A.5) (ii) B(r, k ) 5B. Hene, from (A.6) it is immediate that k the bank s payoff for a 5 1 as: dereases with r. Also, we an write

R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341 1361 1361 m B B 5s1 2 zf(k d )Em dh(m) 1 f(k )E m dh(m) 2f1 2 Hsm dgik. m mb It is immediate to show that, starting at k (I), B inreases as k dereases until we reah the maximum level of B (at the monopoly interest rate). Hene, in the relevant region, a higher value of B an only be reahed through a higher interest rate and lower investment. Referenes Bahetta, P., Caminal, R., 2000. Do apital market imperfetions exaerbate output flutuations? European Eonomi Review 44, 449 468. Besanko, D., Kanatas, G., 1993. Credit market equilibrium with bank monitoring and moral hazard. Review of Finanial Studies 6, 213 232. Berger, A., Udell, G., 1995. Relationship lending and lines of redit in small firm finane. Journal of Business 68, 351 381. Caminal, R., Matutes, C., 1997. Can ompetition in the redit market be exessive. Center for Eonomi Poliy Researh, Disussion paper [1725. Chan, Y., Greenbaum, S., Thakor, A., 1992. Is fairly pried deposit insurane possible? Journal of Finane 47, 227 245. Demirguç-Kunt, A., Detragiahe, E., 1998. Finanial liberalization and finanial fragility. The World Bank, Mimeo. Hoshi, T., Kashyap, A., Sharfstein, D., 1990a. Bank monitoring and investment: evidene from the hanging struture of Japanese orporate banking relationship. In: Hubbard, G. (Ed.), Asymmetri Information, Corporate Finane and Investment. NBER and University of Chiago Press. Hoshi, T., Kashyap, A., Sharfstein, D., 1990b. The role of banks in reduing the osts of finanial distress in Japan. Journal of Finanial Eonomis 27, 67 88. Keeley, M., 1990. Deposit insurane, risk, and market power in banking. Amerian Eonomi Review 80, 1183 1200. Lummer, S., MConnell, J., 1989. Further evidene on the bank lending proess and the apitalmarket response to bank loan agreements. Journal of Finanial Eonomis 25, 99 122. Matutes, C., Vives, X., 2000. Imperfet ompetition, risk taking, and regulation in banking. European Eonomi Review 44, 1 34. Matutes, C., Vives, X., 1996. Competition for deposits, fragility, and insurane. Journal of Finanial Intermediation 5, 184 216. Petersen, M., Rajan, R., 1995. The effet of redit market ompetition on lending relationships. Quarterly Journal of Eonomis 110, 407 443. Petersen, M., Rajan, R., 1994. The benefits of lending relationships: evidene from small business data. Journal of Finane 49, 3 37. Villas-Boas, J.M., Shmidt-Mohr, U., 1999. Oligopoly with asymmetri information: differentiation in redit markets. Rand Journal of Eonomis 30, 375 396.