market power and banking failures ramon caminal , carmen matutes

International Journal of Industrial Organization20 (2002) 1341–1361

www.elsevier.com/ locate/econbase

Market power and banking failuresa , a,b*Ramon Caminal , Carmen Matutes

a ` `Institut d’ Analisi Economica (CSIC) and CEPR, Ballaterra, E-08193 Barcelona, SpainbUniversity of Edinburgh, Edinburgh, UK

Received 5 May 2000; received in revised form 7 August 2000; accepted 17 January 2001

Abstract

We investigate whether more competition in the banking industry necessarily results in ahigher probability of banking failures, as it is often suggested. In our model borrowers facea moral hazard problem, which induces banks to choose between costly monitoring andcredit rationing. We show that investment decreases with the lending rate and increases withmonitoring effort. Since incentives to monitor are enhanced by market power, therelationship between market structure and investment is ambiguous. In the presence ofnon-diversifiable risk and decreasing returns to scale, more investment implies higherfailure rates. As a result, the relationship between market power and banking failures isambiguous. 2002 Elsevier Science B.V. All rights reserved.

JEL classification: D4; D82; G21

Keywords: Moral hazard; Credit rationing; Monitoring; Market power; Banking failures

1. Introduction

Can excessive competition jeopardize the solvency of the banking system? Doesprudential regulation become more necessary after restrictions on deposit interestrates, branching, and other anti-competitive measures are lifted? Such questions

* ` `Corresponding author. Present address: Institut d’Analisi Economica, Campus UAD, Ballaterra,E-08193 Barcelona, Spain. Tel.:134-9-3580-6612; fax:134-9-3580-1452.

E-mail address: [email protected] (R. Caminal).

0167-7187/02/$ – see front matter 2002 Elsevier Science B.V. All rights reserved.PI I : S0167-7187( 01 )00092-3

1342 R. Caminal, C. Matutes / Int. J. Ind. Organ. 20 (2002) 1341–1361

are at the heart of the policy debate over banking deregulation. Our aim is toprovide some new insights into these issues, in particular regarding the exposureof banks to aggregate risk under alternative market structures.

Market power is often associated with a lower probability of a banking failure.Such a negative relationship is usually attributed to various reasons. Firstly, higherlending rates result in lower investment levels and thus a higher expected return ofthe marginal project, which implies a lower probability of bankruptcy. Secondly,the higher are the future expected profits of a bank, the larger is the opportunitycost of going bankrupt, which reduces the incentive to over invest in risky assets.Finally, on the deposit side, competition will tend to increase deposit rates pushingthe margin further down and failure probabilities up. Some of the existing

1theoretical models confirm these intuitions.However, this literature disregards the fact that a major characteristic of banks is

their ability to reduce the scope of moral hazard and adverse selection problems,exploiting their comparative advantage in the provision of monitoring services. Inthis paper we argue that market power may affect bank solvency not only throughthe traditional channels, but also by altering banks’ incentives to invest in reducinginformation asymmetries about project selection. We show that if such an effect isstrong enough tighter competition in the loan market may actually be associatedwith higher bank solvency.

The main ingredients of the model are the following. Firstly, because of limitedliability and non-verifiable actions, contracts cannot be complete and entrep-reneurs’ incentives to allocate funds to alternative projects are distorted. Similarlyas in our companion paper (Caminal and Matutes, 1997), banks have two ways toinduce appropriate project choices. On the one hand, by rationing credit, the bankincreases the marginal return of the capital invested and thus makes it lessattractive for entrepreneurs to deviate and undertake excessively risky projects. Onthe other hand, the bank can deal with the agency problem by monitoringborrowers in the interim of the relationship. Thus, credit rationing and monitoringare imperfect substitutes: by spending resources the bank can lend more capitalsince the firm’s incentive problem vanishes when the firm’s activities are

2monitored by the bank.Secondly, we assume that all projects are ex-ante identical and are subject to a

multiplicative aggregate shock. In this case, the riskiness of a loan increases withits size. The reason is that, under decreasing returns to scale and multiplicativeuncertainty, the distribution of the rate of return of a project shifts to the left whenthe level of investment increases. In the real world, firms face both idiosyncratic

1See, for instance, Chan et al. (1992), and Matutes and Vives (1996, 2000).2Our approach to monitoring is analogous to that in Besanko and Kanatas (1993), in the sense that in

both cases bank monitoring implies that borrowers take more efficient decisions.

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 loanportfolio, bank solvency is only affected by aggregate risk. Thus, for simplicity,we abstract from idiosyncratic risk and focus exclusively on aggregate uncertainty.

We explore the trade-off between rationing and monitoring for two extrememarket structures, monopoly and Bertrand competition, so as to investigate theimplications of banks’ choices on the likelihood of bankruptcy. Our mainconclusion is that the relationship between market structure and banking failure isambiguous. The argument goes as follows.

The relationship between market power and loan sizes is ambiguous since itdepends on the net effect of two countervailing forces. On the one hand, amonopoly bank by setting a higher interest rate worsens the unmonitored firm’sincentive problem, which in turn tightens the credit constraint. On the other hand,a monopoly bank has a bigger incentive to exert monitoring effort and thusdecreases the likelihood of credit rationing. Since larger loans are more exposed tomultiplicative uncertainty, it follows that lack of market power and solvency riskdo not always move together. Specifically, when monitoring costs are so high thatbanks do not monitor regardless of market structure, competitive banks are morelikely to fail. Indeed, they set lower lending rates implying that firms’ incentiveconstraint is not so tight and thus they can extend credit further than a monopolybank. For intermediate monitoring costs, only a monopoly bank will exertmonitoring effort and hence faces no need to credit-ration loan applicants. In suchcircumstances, the monopoly bank is more exposed to aggregate risk thancompetitive banks and it is thus more likely to fail. For very low monitoring costsevery bank will monitor and lend the efficient capital amount. In this latter case thebanking failure probability is independent of market structure.

Our paper is consistent with the empirical evidence in Petersen and Rajan(1995), which uncovers a positive correlation between market concentration andinvestment in customer relationships, which in turn increases the likelihood offinancing credit-constrained firms. Indeed, this paper provides further support forthe idea that market power provides positive incentives to reduce agency problemsthrough monitoring, which results in firms enjoying easier access to external

3financing. Our main contribution here is to show that as a consequence of thisthere may be higher failure rates as banking becomes more concentrated.

Undoubtedly, it may still be the case that in the real world the traditionalchannels dominate and tighter competition reduces the solvency of the banking

3In Caminal and Matutes (1997) we characterize the optimal banking market structure withoutaggregate shocks and when monitoring effort is not contractible, and show that in general some marketpower improves welfare because incentives to exert monitoring effort increase with market power. Inthe present paper, we allow banks to commit to monitoring (i.e. monitoring is contractible) and do notcarry out a welfare analysis of market structure. In an adverse selection framework, Villas-Boas andSchmidt-Mohr (1999) also show that less competition in banking may actually increase welfare.


4system. The contribution of this paper is precisely to demonstrate that therelationship between market power and bank solvency is complex, and it is notsufficient to focus on how liberalization affects the charter value of banks and theassociated incentives to risk taking.

In Section 2 we present the model. Section 3 characterizes the features ofoptimal debt contracts with and without monitoring. Sections 4 and 5 investigatethe incentives to monitor, and the equilibrium lending levels of a competitive and amonopoly bank, respectively. Section 6 derives the implications of our model onfailure probabilities and welfare. Concluding remarks close the paper.

2. The model

In this section we present a static model of a credit market subject to aggregateuncertainty and where lending is restricted by a moral hazard problem. There arethree types of agents: depositors, banks and entrepreneurs. Banks intermediatebetween depositors and borrowers. They are risk neutral and have limited liability.Depositors supply their funds inelastically at the gross interest rateI. Moreover,deposits are fully insured and hence the face value of deposit contracts is alsoI.For simplicity, we assume that insurance premia are flat.

2.1. Investment technology

Entrepreneurs are risk neutral, endowed with zero wealth and have access toinvestment opportunities whose return is determined by the combination of threeelements: (i) decreasing returns to scale in investment, (ii) a multiplicativeaggregate shock, and (iii) the project choice.

More specifically, entrepreneurs (we will use the term ‘entrepreneur’ and ‘firm’interchangeably) have access to a continuum of investment projects, indexed bya,and are subject to limited liability. Givena in the interval [a, 1] and thei ]investment levelk , entrepreneuri obtains a stochastic return given by:i

mw(a ) f(k ) with densitya h(m)i i iF(k , a )5Hi i 0 with probability (12a )i

wherem is a macroeconomic shock with a density functionh(m), which takes

4Keeley (1990) provides some evidence for the US economy that bank default risk increases with¨the liberalization of the financial system. Demirguc¸-Kunt and Detragiache (1998), looking at cross-

country evidence, conclude that when the institutional environment is strong the relationship betweenliberalization and financial fragility is weak.


strictly positive values, and is continuous and twice differentiable in the interval5][m, m ]. The realization ofm is the same for all projects and entrepreneurs.

]For simplicity, we solve the model for specific functional forms that, as we willsee below, allow simple parametrizations. Specifically,

lf(k)5 k 0,l, 1

and

11 (12 z) ln a]]]]]w(a)5 0, z ,1.

a

6Thus, an increase in 1% in investment increases expected return byl%. Also,notice thataw(a) is an increasing function ofa. Thus, the expected return of theproject increases witha. Since the probability of failure is 12a, clearly theefficient project is characterized bya 51. Also, w(a) monotonically increases ifa ,exp 2 z /(12 z) , and decreases otherwise. Thus, by assuming thata < exph j ]2 z /(12 z) , since no entrepreneur will ever choose a project in the increasingh j

section ofw(a), we do not need to worry about the possibility of having cornersolutions ata.

]The parameterz measures the intensity of the moral hazard problem. For a

given value ofa and conditional on the project success (which ex-ante occurs withprobability a), the higher the value ofz, the higher the return. Given that underlimited liability entrepreneurs only care about the non-negative interval of thereturn distribution, the parameterz provides an indication of the incentives tochoose inefficient projects.

The variablea can literally be interpreted as a technology choice, but also moregenerally as reflecting any decision taken by the entrepreneur that is costly toverify and that influences the distribution of returns (R&D policy, quality ofsupplies, and so on). A similar framewrok was presented in Bacchetta and Caminal(2000).

2.2. Information structure

A crucial feature of the model is that the project typea is the entrepreneur’sprivate information. However, the bank, by incurring a costc, can observe andalso collect hard evidence ona. Thus, by monitoring the bank makesa

5 In fact, all we need is that banks cannot perfectly diversify their portfolio of loans. This occurs, forinstance, when banks are specialized in a particular type of borrower with correlated risks. Clearly, thisis also the case with aggregate shocks. For simplicity we make the latter assumption.

6Constant elasticity of the production function facilitates the presentation but it is not essential.However, if we allow the elasticity to increase with the investment level, then the first order conditionof some of the optimization problems we analyze may have multiple solutions.


contractible. The idea is that the bank can get somewhat involved in the decisionmaking of the firm. For instance, a bank representative may sit in the firm’s boardof directors, or a bank agent may meet regularly with the borrower to check thatthe funds are appropriately used. On the other hand, we assume that the realizationof the macroeconomic shock is publicly observable but not verifiable, and hencepayments cannot be conditional onm.

Furthermore, once the return of the project,F, is realized, a signals is observedby everyone. The entrepreneur can choose between two actions: (i) to be honest, inwhich cases 5F (output is publicly observable), and (ii) to hide the project’sreturn, in which cases 5 0. In either case, the bank can verify ex-post the return of

7the firm by paying a costd, which is assumed to be sufficiently large.For simplicity, we assume that the costs involved in the monitoring activity at

the interim stage,c, as well as in the ex-post verification of returns,d, arenon-pecuniary, so that they do not affect the bank’s failure probability. Thus, weare describing a situation in which there is no conflict of interest between theowners and the managers of the bank, and the latter must exert effort to monitorfirms at the interim stage and to verify returns ex-post. Therefore, the organizationas a whole maximizes the difference between pecuniary profits and the costs ofeffort. Such an assumption is clearly extreme but allows us to concentrate on loansizes as the only determinant of the probability of failure, which makes the

8analysis much more transparent.

2.3. Contracts

Given that it is costly to verify output ex-post, debt contracts (fixed repaymentrper unit borrowed) are optimal. However, if the bank monitors the firm then thecontract can specifya. Debt contracts require the bank’s commitment to verifyoutput ex-post when the borrower does not meet her payment obligations. Such acommitment is intended to avoid strategic default. In our case, the firm may beunable to repay the loan due to a low realization of the macroeconomic shock,which is public information. Thus, in order to minimize verification costs the bankcan commit to verify and seize all output ex-post if one of the two things happens:eithers 50, or the firm does not pay minhrk, sj. Such a commitment discouragesstrategic default, and it implies that expected verification costs are (12a)d.

2.4. Timing

The timing of the game is the following.

Stage 1: competition in contracts.

7See footnote 10.8 In the last section we discuss the implications of relaxing such an assumption.


Banks simultaneously offer contracts (r, k), and may also commit to monitor thefirm at stage 2 in which case the contract includes a project choice,a. Afterobserving all the contracts offered by the banks, each entrepreneur chooses one ofthem.

Stage 2: investment and interim monitoring.Capital is assigned to firms and banks fulfil the monitoring commitment.

Stage 3: project selection.Firms choose projecta, possibly restricted by the contract they signed.

Stage 4: outcomes.Project returns,F, are realized, the signalss are observed and payments are

made. Verification costs are incurred if required.

We discuss in Section 6 the extent to which relaxing the banks’ ability tocommit to monitoring would affect our conclusions.

2.5. Further assumptions

In order to avoid trivial outcomes, we require that if the firm is offered theoptimal level of capital and a loan rater, r > I, then it has incentives to choose aninefficient project. Given our parametrization this is equivalent to the followingassumption:

Assumption 1.

l.12 z.

We also assume that:

Assumption 2.

m ,E m 12 z .s ds d]

As we will see this assumption implies that, in the absence of bank monitoring,there is sufficient variability of the macroeconomic shock that the firm fails withpositive probability.

9Finally, for technical reasons we require thath(m) be such that

Assumption 3.

h(m)]]2 h9(m), .m

9Assumption 3 rules out the existence of multiple equilibria of the continuation game for a givencontract.


3. Preliminaries

3.1. Optimal contracts under bank monitoring

Given that the bank has committed to monitoring the firm, the contract consistsof a triple (r, k, a). The payoff of the firm can be written as follows:

p 5aE mw a f k 2 rk dH mf s d s d g s dmF

where

r k]]]m ;max m, ,H JF w a f ks d s d]

is the threshold level ofm such that the entrepreneur cannot meet her paymentobligations.

For (a, r, k) such thatar . I, then even when all the firms go bankrupt the bankneed not, and the payoff to the bank is:

mF

B 5E ar 2 I k dH m 1E aw a f k m 2 Ik dH m 2 c 2 12a dfs d g s d f s d s d g s d s dm mF B

wherem is the threshold level ofm below which the bank goes bankrupt, i.e.B

Ik]]]m ;max m, <m .H JB Faw a f ks d s d]

Notice that the probability that the bank goes bankrupt increases withk anddecreases witha.

With ex-ante monitoring, the optimal contract (r, k, a) is the solution to

Maximizep]

subject toB >B

Unsurprisingly, in the optimal contract parties are willing to commit to theefficient project choice (a 5 1). The reason is thata 51 maximizes the jointpayoffs, for any value of investment. The next step is to characterize the efficientinvestment level. Let us denote byS(k) the aggregate surplus obtained by the bankand the firm for a given level of investment whena 51, i.e.

S k 5E mf(k)2 Ik dH(m).s d f gmB

Let k* 5argmaxS(k). In Appendix A it is shown thatk* is the unique solutionto:


E m um >m f 9 k* 5 I.f g s dB

The next lemma summarizes the main features of the optimal contract.

Lemma 1. The optimal contract under bank monitoring specifies a 51 and a]

level of capital k 5 k*. The interest rate increases with B.

The formal proof can be found in Appendix A. The main idea is that bankmonitoring eliminates asymmetric information and, as a result, there exists aninvestment level,k 5 k*, and a project choice,a 5 1, such that joint payoffs aremaximized independently of how they are distributed. The distribution of surpluscan be done through the interest rate. That is,r and hence the share of the surplus

]of the bank, depends onB (market structure) but it does not interfere with themaximization of the total surplus. Therefore, in equilibrium total surplus, gross ofmonitoring costs, isS* 5 S(k*).

3.2. Optimal contracting in the absence of bank monitoring

In the absence of ex-ante monitoringa cannot be contracted upon. At thecontract design stage parties anticipate that given (r, k) the firm will selecta inorder to maximize expected profits:

]m

MaximizeaE mw a f k 2 rk dH mf s d s d g s da

mF

subject toa [ a, 1 .f g]The first order condition for an interior solution implies that:

12 z E m m .m f ks d s du gf F]]]]]]]a* r, k 5 .s d rk

In Appendix A we show that the first order condition uniquely characterizes thesolution. Notice that the direct effect ofk andr ona is negative. However,r andkalso influencea throughm , and this indirect effect is positive. In any case, weF

show that the direct effect always dominates and thus incentives improve byreducingk or by reducingr. That is, due to limited liability the larger the requiredpaymentrk the bigger the incentives of the firm to deviate and choose increasinglyinefficient projects. Conversely, restrictingk results in a higher average return ofthe safe and efficient project and thus it reduces the incentives to deviate. Thequestion remains as to how the optimal contract (in the absence of monitoring)trades-off inefficient projects and inefficient investment levels. To address thisissue we must investigate the pairs (r, k) that:


Maximizep]

subject toB >B, anda 5min (a*, 1)

The next lemma characterizes these contracts.

Lemma 2 (credit rationing). In the absence of ex-ante monitoring, the optimalccontract includes a level of capital, k , k , k*, which is the unique solution to:c

c c12 z E m m .m f(k )5 rks d f u gF

cand induces the firm to choose a 51. The level of investment, k , and the interest]

rate, r, decreases and increases with B, respectively.

Thus, in the absence of monitoring it is efficient to restrict lending in order toinduce the entrepreneur to choose the efficient project. Since the interest rate

]increases with the bank’s monopoly power (B), the level of investment must bereduced to maintain the project choice unchanged. Hence agency costs translateexclusively into inefficiently low levels of investment, but not into project choiceswhich are dominated in terms of risk and return. This will be true in general if

10ex-post verification costs are sufficiently high. Otherwise, the equilibriumoutcome of a wider class of moral hazard problems could involve a combination ofboth inefficient investment levels and excessively risky project choices. Thissecond element would unnecessarily complicate the analysis and make lesstransparent the analysis of how alternative market structures deal with non-diversifiable risk.

Sincek decreases withr, then we can write aggregate surplus as a decreasingc

function of r. More specifically,

c cS r ; S k r .f gs d s d

c cAlso since k (r), k*, S (r), S(k*) for all r > I. In words, under creditrationing, total surplus (gross of monitoring costs) is lower than under the efficient

10If the probability that the entrepreneur cannot meet her payment obligations,H(m ), wereF

exogenous, then the optimal contract would inducea 51 even in the extreme case of zero verificationcosts. The reason is that any arbitrary contract (k, r) that inducesa , 1 is dominated by a contract withthe same level of investment and a lower interest rate. A reduction of 1% in the interest rate improvesthe firm’s incentives, and causes exactly a 1% increase in the probability of success. As a result, thebank’s payoff are unchanged but the firm’s payoff strictly increases. However, in general, a lowerinterest rate implies a lower probability of default (a lowerm ) and as a result a decrease inr alsoF

improves the firm’s incentives, but the induced increase ina is smaller (see expression (A.1) inAppendix A). Therefore, in general we need strictly positive verification costs to make sure that theoptimal contract always induces the efficient project choice. See Eq. (A.4) in Appendix A for anindication of the minimum size required.


investment level. Moreover, total surplus decreases with the bank’s monopolypower (with the interest rate).

4. Bertrand competition

Until now we have not specified the number of banks,n. Given the structure ofthe game, it only makes a difference whethern is greater than or equal to one. Inthe first case, we have Bertrand competition and in the second we have amonopoly.

With Bertrand competition (n . 1), the first step is to specialize the discussion]

of the previous section to the caseB 5 0. Following Lemma 1, if the bankmonitors the firm then the contract includesa 5 1, k 5 k*, and r such thatB 5 0.Indeed, notice that the firm’s and the bank’s profits decrease and increase withr,respectively; hence the constraintB > 0 is binding. As a result,r . I in order tocover monitoring costs.

Following Lemma 2, if the bank does not monitor the firm then the contractcspecifiesk 5 k (r) (which inducesa 5 1). Since in this case the bank must not

recover any monitoring cost, thenr 5 I.The next step is to characterize the conditions under which Bertrand competitors

coffer credit with and without monitoring. Letp* andp be the firm’s payoff withand without ex-ante monitoring. Under Bertrand competition, monitoring will takeplace if and only if:

cp* >p .

Given that in both cases the bank’s expected payoff is zero, this is equivalent to:cc < S* 2 S (I).

Hence, we have the following result:

Proposition 1. There exists a threshold level of monitoring cost below whichcBertrand competitors monitor the firms. More specifically, let c 5 S* 2 S I . Thens d]

under Bertrand competition, equilibrium can be characterized as follows:

(1.1) if c <c, banks commit to monitor and sign contracts with a 5 1, k 5 k*, and]

an interest rate that allows them to break even;c(1.2) if c .c, banks offer contracts with k 5 k (I), r 5 I and do not monitor firms.

]Nevertheless, firms find it optimal to choose the efficient project.

5. Monopoly

In the case of a single bank, the equilibrium contract is better understood as thesolution which maximizesB subject top > 0. If there is ex-ante monitoring then,


following Lemma 1, the contract includesk 5 k*, a 5 1, andr arbitrarily large. Inthis case the bank can appropriate all the surplus (gross of monitoring costs),S*.

When the bank does not monitor the firm, following Lemma 2, the bank offersck (r), which induces the firm to select the efficient project choice (a 5 1). In this

case, the monopolist faces a downward sloping credit schedule, which isdetermined by the firm’s incentive constraint, and as a result the bank cannotappropriate all the surplus. In other words, firms are able to capture someinformational rents. More formally, the problem of the monopolist consists ofchoosingr in order to maximize:

mF

c c cB r 5 12H m (r 2 I) k (r)1E mf k r 2 Ik r dH m .f f g gs d s d s d s df s dgF

mB

It is sufficient to notice that the monopoly interest rate,r , is aboveI (positiveMc M cmargin). It follows thatk sr d, k I . Indeed, with r 5 I, m 5m and profitss d F B

equal zero, while higher lending rates yield positive profit.cLet B* and B denote the payoff (gross of monitoring costs) earned by a

monopoly bank with and without monitoring, respectively. The monopolistmonitors the firm if and only if:

cc <B* 2B .

Notice that:c c M cB* 2B . S* 2 S sr d. S* 2 S I .s d

The first inequality comes from the fact that in the absence of bank monitoringc M cfirms earn positive profits (informational rents), and thusS sr d.B . The second

cinequality is due to the fact thatS (r) is a strictly decreasing function. Therefore,Proposition 2 follows:

Proposition 2. The threshold level of monitoring cost below which a monopolybank monitors firms is higher than the threshold level for competitive banks. More

]specifically, under monopoly, there exists a c .c, such that the following hold:]

](1.1) if c <c, the bank commits to monitoring, imposes a 5 1 and lends k 5 k*, atan arbitrarily large interest rate;

c M M](1.2) if c .c, the bank offers contracts with k 5 k (r ), r . I, and does notmonitor firms. Nevertheless, firms choose the efficient project.

6. Banking failures and market structure

In our model banks fail only if the realization of the macroeconomic shock isvery low, i.e. if and only if:


Ik]m ,m ; .B f ks d

Therefore, the probability that a bank fails depends exclusively on its exposureto aggregate risk, which in turn depends on the average loan size. Specifically, ahigher level of investment implies a higher probability of failure. In this section weexamine the relationship between market structure, the loan size and theprobability of banking failures.

The analysis in the previous sections shows that whenever banks monitorentrepreneurs, under both market structures, the level of capital isk* and hence theprobability of banking failure isH .0, where1

Ik*]]H ;H .S D1 f k*s d

If banks do not monitor firms then the level of capital does depend on banks’cmarket power. In the case of Bertrand competition,r 5 I and k 5 k (I), k* and

the probability of banking failure isH , where2

cIk Is d]]H ;H .S c D2 f k If gs d

M c M cIn the case of a monopoly bank,r 5 r . I and k 5 k (r ), k (I), and theprobability of banking failure isH , where3

c MIk sr d]]]H ;H .S D3 c Mffk sr dg

Hence, 0<H ,H ,H .3 2 1

Also, Propositions 1 and 2 indicate that a monopoly bank has larger incentivesto monitor.

As a result, the relationship between monopoly power and loan sizes (and henceprobability of banking failure) is in general ambiguous, since it will be the neteffect of two countervailing forces. On the one hand, more monopoly powerimplies higher incentives to monitor and larger investment levels. On the otherhand, for a given monitoring effort, more monopoly power implies larger interestrates and lower investment levels.

In our model the sign of the net effect of these two forces depends on the size ofmonitoring costs. Let us consider three regions.

(i) If c ,c, then under both market structures banks have incentive to monitor and]

hence the probability of banking failure isH , independent of the degree of market1

power.](ii) If c [ c, c , Bertrand competitors do not monitor firms but a monopoly bankf g]


does. As a result, the probability of banking failure under monopoly is higher thanunder competition:H .H .1 2

](iii) If c .c, 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 ofinvestment and hence fails with lower probability:H ,H .3 1

The following proposition summarizes our findings:

Proposition 3. The relationship between market structure and the probability ofbanking failure is ambiguous. With multiplicative shocks the probability ofbanking failure increases with the average loan size. However, a monopoly bankmay lend more or less than competitive banks, depending on the relative costs ofmonitoring and credit rationing. More specifically, there exist threshold values (c,

]] ]c), 0,c ,c, such that:]

(i) if c ,c, the probability of failure is independent of the market structure;] ](ii) if c [ c, c , a monopoly bank fails with higher probability than competitivef g]

banks;](iii) if c .c, a monopoly bank fails with a lower probability than competitive

banks.

As far as welfare is concerned, the implications of the model should be takenwith care since we are not modelling banks’ private and social bankruptcy costs,and our analysis is very partial in this sense. Bearing this limitation in mind,however, the model has clear cut implications that are worth exploring. To do so,it is convenient to distinguish two stages; firstly, the welfare implicationsconditional on the information structure, and, secondly, the welfare implicationsregarding information acquisition. Given the information structure, it is clear thatcompetitive banks lend the efficient levels of capital and hence their exposure tothe aggregate shock is efficient given the information they have. A monopoly, onthe other hand, restricts credit beyond the efficient level in the presence of a moralhazard problem and hence it is underexposed to aggregate shocks relative to thesecond best.

The next question is whether banks take the efficient decision regarding theacquisition of information. In our model, competitive banks monitor if and only ifit is efficient while a monopoly bank has excessive monitoring incentives since

M c M cr . I and thusS sr d, S I . As a result, while a competitive bank is alwayss defficiently exposed, a monopoly’s exposure to aggregate shocks can be excessiveor insufficient from a welfare point of view.

The welfare implications conditional on the information structure depend onlyon two crucial features: (i) in the absence of monitoring, banks choose to rationcredit (rationing and monitoring are substitutes), (ii) the firm’s incentives worsen


with the interest rate. These two features are likely to appear in a wider class ofmodels. However, it is worth discussing the extent to which the incentives toacquire information are model-dependent. In particular, if monitoring effort werenon-contractible then we would be facing a double moral hazard problem andhence the contract must provide incentives to the bank as well. As a result theincentives to acquire information would be reduced. In a related paper (seeCaminal and Matutes, 1997) we show that, in a similar framework but withoutaggregate shocks, when monitoring effort is not contractible then the competitivebank under supplies monitoring effort relative to the first best, while a monopolymonitors if and only if total welfare increases. Therefore, we cannot claim that thewelfare implications drawn above are robust.

7. Concluding remarks

Our main conclusion is that there is no clear-cut relationship between marketstructure in banking and exposure to non-diversifiable risk. How relevant isaggregate portfolio risk? To the extent that banks are restricted to specific regionswhich are specialized in a small set of industries, it is obviously very important.Even when the regulatory environment allows banks to diversify across regions,macroeconomic shocks are still relevant for any geographic area. Furthermore,banks may choose not to diversify their loan investments to reduce totalmonitoring cost by specializing in certain types of firms facing correlated risks.

It is commonly believed that deregulation in the banking industry, by increasingthe degree of competition, may increase the likelihood of banking crises. Ouranalysis shows that this is not necessarily the case. The reason why a monopolistmight go bankrupt more often than a competitive bank is that bigger incentives tosolve agency problems translate into more incentives to take aggregate risk. Ourresult has been derived within the setting of a specific moral hazard problem withthe feature that in equilibrium firms and banks only fail due to macroeconomicshocks. Clearly, in the real world both firms and even banks may fail because ofproject choices. Also project choices themselves may depend on the marketstructure. Thus, the actual relationship between market power and financialfragility is clearly very complex. Yet the question is whether the driving forcesbehind our results are likely to be present or are artefacts of the model.

Thus, the issue arises as to what are the essential assumptions leading to theambiguity result. An essential ingredient is that risk exposure increases with thelevel of investment. If aggregate shocks are multiplicative then it simply requiresdecreasing returns to scale to investment. The other two key ingredients are thatmonitoring and credit rationing are substitutes to alleviate a moral hazard problem,and that a monopoly is more likely to monitor firms than competitive banks.Regarding the former, there is some empirical support for the idea that close ties


11with banks alleviate credit constraints, which indicates that the trade-off betweenmonitoring and credit rationing is rather plausible. Regarding the latter, amonopoly bank is more likely to monitor than competitive banks because marketpower allows the bank to appropriate a higher proportion of the rents created bymonitoring. It holds in the present framework where monitoring is contractible, butit also holds in frameworks where it is not contractible (see Caminal and Matutes,1997).

Our model has also abstracted from pecuniary costs of monitoring andverification, as well as from adverse selection problems. If monitoring costs werepecuniary then, ceteris paribus: (i) a bank with a higher exposure to aggregate riskwould have more incentives to monitor (since the costs of monitoring would bepaid only in case of non-failure) and (ii) by monitoring a bank would bear a higherrisk of failure (because of higher costs). These two new channels would

12complicate the analysis without bringing substantial additional insights.In an adverse selection framework, with ex-ante screening instead of interim

monitoring, new effects are possible. Nevertheless, the type of effects analyzed inthis paper are likely to be present, provided individual investment exhibitsdecreasing returns to scale and there exist aggregate portfolio shocks. For instance,more screening (induced by higher monopoly power) is likely to be associatedwith lower individual risk, and as a result the bank would be willing to acceptlarger exposure to aggregate shocks. If borrowers are small with respect to thebank’s portfolio, then the relationship between bank solvency and market powerwould be analogous to our model. However, if the size of individual loans issignificant with respect to the bank’s portfolio, then the probability of bankingfailure would depend on the interplay between individual and aggregate risk, andeither could dominate.

Acknowledgements

This is a completely revised version of ‘Bank Solvency, Market Structure andMonitoring Incentives’ (CEPR d.p.[1665). We thank Sugato Bhattacharya, JimFairburn and Michael Riordan for helpful discussions, and two anonymous

11See for instance Petersen and Rajan (1994), Hoshi et al. (1990a,b), Lummer and McConnell(1989) and Berger and Udell (1995).

12For values ofa strictly less than one, the probability of banking failure is also higher if verificationcosts are pecuniary. This fact combined with banks’ limited liability imply that the incentives to takeexcessive risk (to offer contracts that induce values ofa below one) are higher than in the case ofnon-pecuniary verification costs. However, provided thatd is higher than a certain threshold, theoptimal contract would still inducea equal to one, although the level of the threshold is likely to behigher than in the case of non-pecuniary costs. In expression (A.4) in Appendix A, pecuniaryverification costs translate into a higher value ofm . Clearly, such a derivative would still be negative ifB

d is sufficiently high.


referees and the editor of this journal, Dan Kovenock, for very useful commentson a previous draft. This research has been supported by TMR networks FMRX-CT98-0203 and FMRX-CT98-0222, and by the Spanish Ministry of Educationthrough DGCYT grants PB95-0130 and PB98-0695.

Appendix A

Proof of Lemma 1. The payoffs of the entrepreneur and the bank can be writtenas follows:

p 5aw a f(k)Em dH(m)2ark 12H ms d f s dgF

mF

mF

B 5 12 z f(k) Em dH(m)1aw a f(k) Em dH(m)s d s dm mF B

2 12H m Ik 1 d 12a .f s dgf s dgB

Notice that once againp and B increase and decrease, respectively, withr.]

Therefore, the constraintB >B is always binding. Thus, the optimization problemto characterize the optimal contract can be written as follows: choose (k, a) inorder to maximize

]p 5aw a f(k)Em dH(m)2 12H m Ik 1 12a d 2B.s d f s d gf s dgB

mB

Notice thatp strictly increases witha, and hence the optimal value ofa is equal]

to 1. Hence, the problem is now to maximizeS(k)2B. Given that, the optimalvalue of k is, by definition,k 5 k*.

Finally, we show thatk* is the unique solution of the first order conditions tothe problem of maximizingS(k), and thatm .m. The first order condition is givenB ]by:

f 9(k)Em dH(m)2 I 12H(m ) 50.f gB

mB

Given the definition ofm and the functional form off(k), we can rewrite theB

above expression and have:

lEm dH(m)2m 12H(m ) 5 0.f gB B

mB

Since there is a one to one relationship betweenk andm , if we show that thereB


exists a uniquem that solves the above expression, then there exists a uniquekB

that solves the original first order condition.Let us define

F m ; lEm dH(m)2m 12H m .s d f s dg0 0 0

m0

Notice that,

F m 5lE m 2m .0,s ds d] ]

by Assumption 2. Also,

F9 m 5 2 12H m 1 12l m h(m )s ds d f s dg0 0 0 0

F0 m 5 22l h m 1 12l m h9(m ). 0,s d s ds d s d0 0 0 0

by Assumption 3. Finally,

]F m 5 0s d

]F9(m).0.

As a result, there exists a uniquem that solvesF m 50 with F9 m , 0 (ands d s dB B B

thus the second order condition holds).

Proof of Lemma 2. We search for contracts on the efficient frontier, given theentrepreneur’s moral hazard problem. Thus, we need to find the pair (r, k) thatsolves the following optimization problem:

Maximizep]

subject toB >Banda 5min (a*, 1)

where

12 z E m m .m f ks d s du gf F]]]]]]]a* r, k 5 . (A.1)s d rk

Notice that, because of Assumption 1, it is impossible to havea 51, if k 5 k*,and r 5 I. In fact, if k 5 k*, and r 5 I, thenm 5m , and thus:F B

l f(k*)Em dH(m)mB

]]]]]a* , 51.Ik* 1 2H(m )f gB

Suppose that in the optimal contract (r, k) are such thata* < 1 andm .m. InF ]this case


rk]]]m 5 . (A.2)F w a f ks d s d

Solving (A.2) for r and plugging it into (A.1) and rearranging:

12 z E m m .ms d u ds F]]]]]]aw a 5 . (A.3)s d

mF

First of all, we show that ifa 51, then the probability of default is indeed positiveas assumed, i.e.H m .0. Defines dF

]m

C(m ); 12 z Em dH(m)2m 12H(m ) .s d f ga a a

ma

Notice that whenC 5 0, (A.3) is satisfied ata 5 1, we search for a numberm ,F]m [ m, m such thatC m 50.s ds dF F]Notice that

C(m)5 12 z E(m)2m . 0s d] ]

]C(m)50

and

C9(m )5 2 12H(m ) 1 zm h(m ).f ga a a a

Hence,

] ] ]C9(m)5 zmh(m).0.

Also, notice thatC(m ) is convex. Its second derivative can be written as:a

C0(m )5 (11 z) h(m )1 zm h9(m )a a a a

]and from (A.3) it is positive. Therefore, there exists a unique value ofm [ m, ms dF ]such thatC m 50 andC9 m , 0.s d s dF F

Secondly, we show that we cannot havea 5 1 and zero failure probability.Suppose we do, i.e.k satisfies:c

12 z E m f(k)5 rk.s d s d

Also, it must be the case that:

rk]m < .F f(k)

Combining these two equations:

12 z E m <m .s d s d F


By Assumption 2 we reach a contradiction.Thirdly, from Eq. (A.3) if a , 1, then the probability of default is always

positive. To see this, we use the implicit function theorem to obtain:

dm 12H m 2 zm h ms d s dF F F F]] ]]]]]]]5 2 .da 12 z

]]m 12H mf s dgF F a

SinceC9 m , 0, the numerator is positive and thusm increases ifa falls.s dF F

It follows, then, that for anya* < 1 the failure probability is positive asassumed. In such a case, the bank’s payoff can be written as a function ofk andmF

(for a givenk, a higher value ofr implies a higher value ofm ):F

mF

B 5 12 z f(k)Em dH(m)1aw a f(k) Em dH(m)s d s dm mF B

2 12H m Ik 1 d 12af s dgf s dgB

wherea is a decreasing function ofm , andm is a function of bothk andm .F B F

Computing the partial derivative:

≠B]] 5 [aw(a)2 (12 z)] f(k) m h(m )F F≠mF

mF (A.4)12 z da]] ]]1 f(k) Em dH(m)1 12H(m ) df gBa dm5 6 F

mB

The first term is positive and the second is negative. However, since we haveassumed that the verification costs (d) are sufficiently large, then the bank’s payoffdecreases withm . In other words, it is never optimal to set an interest rate so highF

so as to induce the firm to choosea ,1.Finally, since at the optimal contracta 5 1, from Eq. (A.3) we have thatm isF

c cdetermined independently ofr andk. Indeed, from (A.3)m 5m wherem is theF

unique solution to:c c12 z E mum .m 5m . (A.5)s ds d

Therefore, the optimal contract consists of a pair (k, r) such that:c c c(i) 12 z E mum .m f(k )5 rk (A.6)s ds d

cwherem is given by (A.5)]c(ii) B(r, k )5B.

cHence, from (A.6) it is immediate thatk decreases withr. Also, we can writethe bank’s payoff fora 51 as:


cm

c c cB 5 12 z f(k )Em dH(m)1 f(k ) Em dH(m)2 12H m Ik .s d f s dgB

c mm B

cIt is immediate to show that, starting atk (I), B increases ask decreases until wec

reach the maximum level ofB (at the monopoly interest rate). Hence, in therelevant region, a higher value ofB can only be reached through a higher interestrate and lower investment.

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market power and banking failures ramon caminal , carmen matutes

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