Deposit competition and loan markets

Journal of Banking and Finance 80 (2017) 108–118

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Deposit competition and loan marketsR Stefan Arping University of Amsterdam, Amsterdam Business School, Finance Group, Plantage Muidergracht 11, 1018 TV Amsterdam, The Netherlands

a r t i c l e

i n f o

Article history: Received 12 April 2016 Accepted 7 April 2017 Available online 11 April 2017 JEL classification: G2 G3 L1 L3

a b s t r a c t Less-intense competition for deposits, by mitigating banks’ incentive to take excessive risks, is traditionally believed to lead to lower non-performing loan (NPL) ratios and more-stable banks. This paper revisits this proposition in a model with borrower moral hazard in which banks’ NPL ratios depend endogenously on their loan pricing. In relatively uncompetitive loan markets, less-fierce competition for deposits (i.e., lower deposit rates) leads to lower loan rates and, thus, safer loans. In more-competitive markets, the opposite can occur: As banks’ deposit-repayment burdens decline, they become less eager to risk-shift; this softens competition for risky loans, leading to higher loan rates and, ultimately, riskier loans. Overall, the model predicts a hump-shaped relationship between banks’ pricing power in deposit markets and their NPL ratios. © 2017 Elsevier B.V. All rights reserved.

Keywords: Bank competition Loan pricing Financial stability

1. Introduction Despite a vast literature on the welfare and stability aspects of competition in banking, many challenging questions are left unanswered: How does the intensity with which banks compete for deposits affect economic outcomes in loan markets? And how does the answer to this question, in turn, depend on the intensity of competition for loans? Would higher deposit rates due to fiercer competition for deposits lead to more-expensive loans? If the answer to this question were affirmative, more-intense competition for deposits might be undesirable simply because of its potentially harmful effect on loan markets. More generally, then, how do deposit and loan markets interact? The objective of this paper is to address these questions within a simple model of “two-sided” competition in banking, and to draw implications for real sector outcomes, credit risk in the economy and banking stability. That the degree of competition for deposits would matter for loan pricing is not obvious. As Klein (1971) points out, a bank’s economic cost of extending a loan is not given by the rate that it pays on its deposits, but by its opportunity cost of capital—that is, the expected return of similarly risky investments in the financial marketplace. As a result, a rise in deposit rates due to fiercer comR I thank two anonymous referees, Carol Alexander (the Editor), Arnoud Boot, Gabriella Chiesa, Torsten Jochem, Yoshiaki Ogura, Steven Ongena, Klaus Schaeck, Xavier Vives, and Tanju Yorulmazer, as well as seminar audiences at University of Amsterdam, VU University Amsterdam, Gerzensee, and FIRS and EFA conferences for very helpful comments and suggestions. E-mail address: [email protected]

http://dx.doi.org/10.1016/j.jbankfin.2017.04.006 0378-4266/© 2017 Elsevier B.V. All rights reserved.

petition for deposits has no bearing on loan pricing in frictionless settings: It reduces banks’ profit from deposit taking, but it does not alter the pricing of their loans—banks’ deposit taking and lending activities are separable.1 This article studies an economy in which banks’ deposit taking and lending activities are non-separable due to agency frictions. In my model, banks have two economic roles: They facilitate the extension of credit to productive enterprise (entrepreneurs), and they provide households—agents with limited financial market access—with accessible stores of value by accepting deposits. There is a double-moral-hazard problem: Entrepreneurs fail to internalize the effects of their decision-making on their lenders (banks), and banks fail to internalize the effects of their loan pricing on bank liability holders. Higher loan rates worsen borrower moral hazard and, thus, raise the likelihood of loan default. Higher loan default rates, in turn, lead to higher bank credit risk in my model, so they impose a negative externality on bank liability holders. The question I am primarily interested in is how, in this setting, a change in the intensity of competition for deposits affects economic outcomes through its effect on banks’ loan pricing. Interestingly, it turns out that the direction of this effect depends critically on the intensity with which banks compete for loans. In relatively monopolistic loan markets, banks can charge fairly high loan rates without risking the loss of prospective borrowers to the competition. In this environment, optimal loan rates are determined by a risk-return trade-off between higher loan default risk 1

Cf., also, Chiaporri et al. (1995) and Freixas and Rochet (2008, chapter 3).

S. Arping / Journal of Banking and Finance 80 (2017) 108–118

and higher income in non-default states. As is well known from the banking literature, heightened deposit competition, by raising banks’ deposit-repayment burdens, can make banks eager to take on more risk (e.g., Hellmann et al., 20 0 0; Matutes and Vives, 20 0 0; Allen and Gale, 20 0 0; 20 04; Repullo, 20 04). Thus, fiercer deposit competition tilts the risk-return trade-off in favor of riskier loans and, hence, more-aggressive rent extraction and higher loan rates. Conversely, in more-competitive loan markets, banks’ loan pricing is constrained by the threat of losing borrowers to the competition. As deposit rates rise, banks become more eager to invest in risky assets as opposed to safe ones. This spurs competition for risky loans, causing banks to cut their loan rates. Loan rates decline and borrower incentives improve; so, intriguingly, the very presence of a risk-shifting bias that causes banks to compete more aggressively for loans ultimately makes loans safer. The model’s implications for financial (banking) stability are subtle. More-intense competition for deposits can affect financial stability through its effect on loan performance. Yet, as discussed, the direction of this effect is contingent on the degree of loan competition. In addition, there is a direct effect: Fiercer deposit competition entails lower margins, which raises bank credit risk. Matters are further complicated by the fact that heightened deposit competition, by making banks more eager to invest in risky assets, can improve credit availability. The flip side of this observation is that, as deposit markets become less competitive, banks may extend fewer risky loans at the margin and, thus, become safer. The model’s key empirical prediction pertains to the relationship between banks’ deposit market power and their nonperforming loan (NPL) ratios. The model suggests that, in relatively competitive environments, there should be an upward-sloping relationship between banks’ deposit market power and loan default rates, while in less-competitive environments, the relationship should be reversed. Jiménez et al. (2013) report evidence that is suggestive of such relationship (see Section 6 for a more detailed discussion). A second implication is that the stability aspects of competition in banking can be complex and—in terms of both sign and magnitude—contingent on market structure. Consistent with this observation, Beck et al. (2012) report substantial cross-country variation in the link between bank market power and banking stability (bank Z-score). In my model, banks operate in “local” deposit and loan markets, and they derive market power from the fact that prospective customers find it costly to shop for financial services elsewhere— “more-distant” lenders or, in the case of depositors, non-bank savings devices. A bank’s deposit market power, then, depends on the ease with which depositors can access their outside options, and its loan market power depends on prospective borrowers’ cost of “switching” to more-distant lenders.2 Besides being tractable and straightforwardly capturing the essence of market power, this approach has the key advantage that it allows me to disentangle the economic effects of a change in deposit market power from those of a change in loan market power. This can be accomplished by varying the market power parameter in one of the markets, holding the market power parameter in the other market constant. At the same time, one can allow for positive correlations between changes in deposit and loan market power by simultaneously varying both market power parameters.

2 In practice, the magnitude of such costs can depend on differentiation in geographical or product space; technological progress making it easier to borrow from distant lenders or to access non-bank savings vehicles; the level of customers’ sophistication and financial literacy; prior business relationships and the degree of customer lock-in; etc. See Degryse and Ongena (2008) for an excellent empirical overview.

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2. Related literature Much of the extant literature on the stability and welfare aspects of bank competition focuses on the deposit market (e.g., Hellmann et al., 20 0 0; Matutes and Vives, 20 0 0; Allen and Gale, 20 0 0; 20 04; Repullo, 20 04). A common theme of this literature is that fiercer competition for deposits can make banks more fragile by encouraging risk taking: As banks pay higher deposits rates, they face higher deposit-repayment burdens; this exacerbates riskshifting moral hazard and causes banks to take excessive risks.3 In this literature, banks invest in investment technologies with risk profiles under their direct control—the loan market is a black box. This differs from my model in which banks’ asset risk depends endogenously on their loan pricing through its effect on borrower incentives. Boyd and De Nicolo (2005) develop a model of bank competition in which, similar to mine, asset risk is under the direct control of borrowers. This has the interesting consequence that the “traditional” negative link between competition and stability is reversed: As competition for loans intensifies, loan rates decline; this mitigates borrowers’ incentive to take excessive risks, making loans— and, in their model, banks—safer.4 Similarly, in my model, heightened loan competition can reduce loan default risk. However, the main point I wish to make is a different one. The question I am interested in is how banks’ pricing power in deposit markets affects economic outcomes through its effect on their loan pricing. A rise in deposit rates caused by more-intense competition affects the liability side of banks’ balance sheets; this, in turn, alters their risk-taking incentive on the asset side—the central point of the aforementioned literature focusing on the deposit market. The main contribution of my article is to derive implications of the risk-shifting channel for loan pricing, and to show how the direction of the ensuing effect can depend on the intensity of loan competition. Martinez-Miera and Repullo (2010) present a model of imperfect loan competition—but, in contrast to my model, perfect deposit competition—in which higher loan rates provide a buffer against losses from defaulting borrowers. However, they also lead to higher default rates, so the overall effect of loan competition on bank failure rates is ambiguous.5 My simple framework abstracts from the loan market margin effect identified by MartinezMiera and Repullo (2010); thus, as in Boyd and De Nicolo (2005), loan competition is (weakly) stabilizing in my model. Still, the overall impact of competition on stability is ambiguous in my setting, simply because deposit and loan competition can have opposing effects. This article adds to a small literature that disentangles the effects of deposit competition from those of loan competition. Chiaporri et al. (1995) have a Salop model of competition in loan and deposit markets that allows for varying loan and deposit price elasticities; however, default risk—central to my analysis—plays no

3 This static effect is, then, reinforced by the charter value effect that arises in dynamic models—that is, as banks compete more fiercely, the present value of future profits declines, making failure less costly. 4 Wagner (2010) shows that this effect may be reversed when banks have control over their risk taking. In his model, more-intense competition for loans causes banks to switch to riskier borrowers, which can more than offset the stabilizing effect of competition on borrower incentives. Relatedly, it has been argued that fiercer loan competition can erode bank monitoring incentives (e.g., Caminal and Matutes, 2002). 5 Caminal and Matutes (2002), too, show that the stability aspects of loan competition can be subtle. In their model, banks can mitigate moral hazard through credit rationing or loan monitoring. As loan competition intensifies, borrowers face lower loan rates, making it more profitable to expand risky investment; this, in turn, raises bank failure rates. However, competition also reduces banks’ monitoring incentive, so banks rely more on credit rationing; this, in turn, reduces risky investment and makes banks safer.

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role in their model. Boyd and De Nicolo (2005) allow for imperfect competition in loan and deposit markets; however, in their model, banks’ deposit volumes are assumed to be tied to their loan volumes. This differs from my model in which banks would accept deposits even if they did not extend loans. Indeed, a critical feature of my model is that banks, in accepting deposits, perform a useful service, and that they, thanks to their market power, can appropriate at least part of the corresponding surplus gains. In other words, deposit taking is an operating activity for banks. Yanelle (1997) presents a model in which banks compete à la Bertrand in deposit and loan markets, and in which competition may lead banks to corner the deposit market in an attempt to obtain a monopoly position in the loan market. The focus of my analysis is different from hers; furthermore, in the baseline model, I will abstract from cornering incentives by positing that no single bank can corner the market for deposits. As discussed, the way in which competition is modeled in this article differs from much of the related literature in which the exogenous variable that is to be varied to gauge the effects of competition is often the number of banks in the economy. A drawback of the traditional approach is that it does not easily lend itself to investigating the economic effects of a ceteris paribus shock to deposit or loan market power. In my model, banks’ market power depends on the ease with which prospective bank customers can access their respective outside options (for recent theoretical work using a similar approach, see Wagner, 2010; Inderst, 2013). This approach is not only tractable but also flexible since it allows for the possibility that institutional and technological changes affecting competition in banking may have a stronger effect in one market and little or no effect in the other market (for instance, consider the introduction of money market funds in the U.S. during the 1970s). 3. The model 3.1. Agents and technology Consider a two-period economy (t = 0, 1) in which two ownermanager-run banks, 1 and 2, compete for extending a loan to a single entrepreneur. The entrepreneur is penniless and requires a $1 loan for a project. Banks are identical, except that one of the banks (say, bank 1) may have a strategic advantage in the loan market, as specified below. The bankers who own and run the banks have unique loan-extension skills, and they also have costless access to a storage technology—call it the money market—that carries dollars from period 0 to period 1. Bankers have no funds on their own, and they finance their banks through mobilizing deposits from households. Per bank, there is a continuum of size one of households, each with an endowment of $1. Households value consumption only in period 1. All agents, except households, are risk-neutral, and there is no discounting. In period 0, banks first quote deposit rates and mobilize deposits. Households are price takers. Subsequently, banks quote loan rates, and the entrepreneur picks the best offer. Deposits are insured by the government (say, because households are highly averse to risk, making them unwilling to invest in banks unless their claims are guaranteed).6 In period 1, the entrepreneur’s project either succeeds and generates a gross return of  > 1, or it fails and yields zero. The probability of project success depends on the entrepreneur’s unobservable effort: If the entrepreneur exerts effort e ∈ [0, 1], then the probability of project success is e. There is a private effort cost ψ (e ) = β e2 /2, with β ≥  to ensure 6 As in much of the related literature, deposit insurance premia are, for simplicity’s sake, normalized to zero. Bank capital requirements are normalized to zero, too. However, neither assumption is crucial.

interior solutions. For a given gross loan rate R, the entrepreneur exerts effort as to maximize her payoff e( − R ) − ψ (e ). Thus, the entrepreneur is subject to moral hazard, and the higher the loan rate, the lower is loan performance. To make the analysis interesting, I assume that

max {e − ψ (e )} > 1. e

(A1)

3.2. Financial geography As mentioned, bank 1 may have a strategic advantage in the loan market. This is modeled in the simplest possible way as follows: If the entrepreneur undertakes her project with bank 2, she incurs a disutility s ≥ 0. The entrepreneur incurs no such cost if she borrows from bank 1. Thus, assuming that the entrepreneur is a price taker, the term s measures bank1’s pricing power in the loan market. In a setting with differentiation in geographical space, it could refer to the “transportation” cost that the entrepreneur would incur if she “travelled” to bank 2. More importantly, perhaps, the cost could be related to technological progress in lending processes or differences in regulation across regionally separated markets (cf., Inderst, 2013). As lending technologies become more advanced or differences in regulation become less pronounced, it becomes less cumbersome to borrow from “distant” lenders, leading to a decline in bank1’s loan pricing power. Yet another possibility is that the entrepreneur already has a business relationship with bank 1, making it costly to switch to bank 2. Next, l model the market for deposits. Let each bank be endowed with a “local” deposit market that is populated by a unit mass of households, each with an endowment of $1. Households can save by depositing their endowments in banks, and they also have the option to invest in the money market, where they would receive the riskless (gross) rate of one.7 Banks derive deposit pricing power from the fact that households find it most convenient to do business with their respective local banks. Formally, if a household that is located in deposit market i ∈ {1, 2} deposits its endowment in bank j = i or accesses the money market, then it incurs a disutility sD ∈ (0, 1). The household incurs no such cost if it deposits its endowment in bank i. Banks cannot price differentiate, so they must offer the same deposit rate to all households, irrespective of where they are located. Consider, then, a candidate equilibrium in which each bank offers an effective deposit (gross) rate of RD = 1 − sD (for instance, each bank may charge a deposit account fee of sD and offer an interest rate of zero). At this effective rate, households that are located in market i strictly prefer bank i to bank j, and they are just indifferent between bank i and their money market outside option. Thus, if bank i deviated and offered a lower rate, its local depositors would be better off accessing the money market, so bank i would receive no deposits. Clearly, given that bank j quotes a rate of RD = 1 − sD , quoting a rate of RD ∈ (1 − sD , 1 ) cannot be optimal either. However, quoting a rate of RD = 1 (or slightly higher) could be optimal for bank i. At this rate, households that are located in market j (weakly) prefer bank i to bank j, so they would “switch” to bank i, depriving bank j of deposits; this, in turn, may give bank i a competitive advantage in the loan market (cf., Yanelle, 1997). In the baseline analysis, I am going to abstract from such cornering incentives simply by positing that each bank can accept at most $1 of deposits. For instance, one can imagine that mobilizing lots of deposits would require substantial marketing efforts, making it prohibitively costly for a bank to corner the deposit market. Furthermore, in practice, most banks do have access to wholesale

7 Yet another option would be informal “home storage.” I assume that home storage is very costly.

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Notice that, as sD declines, the profit from investing deposits in the money market is decreasing faster than the profit from extending risky loans. In other words, as competition for deposits becomes fiercer and deposit rates rise, the bank becomes more eager invest in risky assets (loans), as opposed to safe ones. This is nothing else than the standard risk-shifting effect of leverage that is at the heart of the literature on the stability aspects of deposit competition: As deposit rates and deposit-repayment burdens rise, banks become more eager to take on risk in an attempt to reduce the expected payout to depositors. However, while the incremental profit from lending, UB (e, R ) − sD , is decreasing in sD , the “marginal” profit from lending, ∂ UB (e, R)/∂ e, is increasing in sD ,

∂ 2UB (e, R ) = 1 > 0. ∂ e∂ s D Fig. 1. Model structure. The entrepreneur requires a $1 bank loan for a project. She has an intrinsic preference to undertake her project with bank 1. Households wish to save. They can invest in the money market (at cost sD ) or deposit their endowments in banks. In the baseline model, each bank can accept at most $1 of deposits. Banks invest deposits in loans and/or the money market.

funding. Thus, to obtain a monopoly position in the loan market, a bank would have to corner not only the market for retail deposits, but also the wholesale market, which, presumably, is infeasible or prohibitively costly. Thus, conveniently, the deposit market has a straightforward equilibrium: Each bank mobilizes $1 of deposits against a rate of RD = 1 − sD . At this rate, households are just indifferent between depositing their endowments in their respective local banks and accessing the money market. Thus, as households find it easier to access their outside option—say, because of advances in information technology or improved financial literacy—banks face additional competitive pressure, forcing them to offer more attractive deposit rates. Fig. 1 summarizes the industrial organization of the banking economy. 4. Equilibrium I start with the case of a monopolistic loan market in which the entrepreneur relies on bank1’s lending services (i.e., s is sufficiently large). Subsequently, I consider the case of a perfectly competitive loan market in which neither bank has a strategic advantage in the loan market (s = 0), and banks compete à la Bertrand. Finally, I combine these two polar cases and consider the more general case of imperfect loan market competition (s > 0). 4.1. Monopolistic loan market To start with, suppose that bank 1 has a monopoly position in the loan market (say, s = ∞). Having mobilized $1 of deposits against a rate of RD = 1 − sD , bank1’s loan pricing problem is to maximize its expected profit,





max UB (e, R ) = e R − 1 − sD (e,R )



,

s.t. UE (e, R ) = e( − R ) − ψ (e ) ≥ 0,

(IR)

∂ UE (e, R )/∂ e =  − R − ψ  (e ) = 0,

(IC)

where (IR) and (IC) are the entrepreneur’s participation and incentive constraints, respectively. The bank is willing to extend the loan if and only if its profit from loan extension is not lower than its profit from investing deposits in the money market:





UB (e, R ) = e R − 1 − sD







≥ 1 − 1 − sD = sD .

(1)

In other words, as deposit rates (RD = 1 − sD ) decline, the bank benefits more strongly from an increase in its borrower’s effort. This is because, as 1 − sD declines, the bank benefits less strongly from a reduction in the expected payout to depositors through an increase in its own default risk. These observations will be central to the following analysis. I now derive the loan market equilibrium with monopolistic pricing. Obviously, the entrepreneur’s participation constraint (IR) cannot be binding; otherwise, she would exert zero effort. Substituting for R(e ) =  − ψ  (e ) from (IC), the bank’s problem reduces to

max UB (e, R(e )) = e − ψ (e ) − (eψ  (e ) − ψ (e )) e







project value







entrepreneur’s rent

− e ( 1 − sD ) .

  

(2)

MV liabilities

If, at the optimum, the bank’s participation constraint (1) holds, then it will extend the loan and the project will be undertaken. In what follows, I am going to assume that the underlying parameter values are such that, in equilibrium, no credit rationing occurs and the project is undertaken (for details, see the Appendix, as well as Section 5.1). The first two terms in (2) represent the expected value of bank assets; this, in turn, equals project value less the share that accrues to the entrepreneur. The last term is the market value of bank liabilities (i.e., the expected payout to depositors). Equilibrium effort, denoted by eM , is uniquely characterized by the first-order condition

 − ψ  (e ) = eψ  (e ) + (1 − sD ).

(3)

The equilibrium loan rate is, then, RM =  − ψ  (eM ). The left-hand side of (3) is marginal project value, and the right-hand side represents the bank’s costs of eliciting higher effort (or, equivalently, cutting its loan rate). The first term on the RHS is the marginal rent to the entrepreneur, and the second term involves the effect of improved loan performance on the market value of bank liabilities. Thus, relative to the efficient allocation (LHS of (3)), loan pricing is distorted through two channels: (i) the risk-return trade-off between rent extraction and loan performance (loan market), and (ii) the risk-shifting bias from leverage (deposit market). Crucially, however, as deposit rates decline, the latter distortion becomes less pronounced. Formally, by implicit differentiation of (3) and ψ ( e ) = β e2 /2,

1 deM =− = 1/ ( 2β ) > 0. dsD −2ψ  (eM ) − eM ψ  (eM ) Moreover, dRM /dsD = −ψ  (eM ) deM /dsD = −1/2 < 0, so equilibrium loan rates are decreasing and intermediation margins (i.e., RM − (1 − sD )) are increasing in sD .

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Proposition 1. In monopolistic loan markets, a rise in deposit market power leads to lower loan rates, higher loan performance and higher intermediation margins. Proof. All proofs can be found in the Appendix.



As the bank’s deposit-repayment burden declines, it has more “skin in the game,” making it more costly for the bank to stifle loan performance by charging overly high loan rates. Consequently, heightened deposit market power leads to lower loan rates and, thus, safer loans. Thus, interestingly, changes in deposit market power do have implications for loan pricing, so the bank’s deposittaking and lending businesses are non-separable. 4.2. Competitive loan market Next, consider the case of a perfectly competitive loan market in which banks compete à la Bertrand (i.e., s = 0). Having collected deposits against a rate of RD = 1 − sD , banks simultaneously quote loan rates. The entrepreneur observes these quotes and picks the best one. In the case of indifference, she is assumed to undertake her project with bank 1. The Bertrand equilibrium maximizes the entrepreneur’s payoff,

max UE (e, R ) = e( − R ) − ψ (e ) (e,R )

s.t. e(R − (1 − sD )) − sD = 0,

(ZP)

but by the opportunity cost of capital—here, the riskless rate of zero. A bank’s benefit from extending risky loans is, in turn, twofold: (i) interest revenue, and (ii) the reduction in the market value of its liabilities from investing in risky assets as opposed to safe ones. As banks’ deposit-repayment burdens rise, the second benefit becomes more pronounced; thus, banks become more eager to invest in risky assets (as opposed to safe ones); this, in turn, intensifies competition for risky loans, causing banks to cut their loan rates. 4.3. Imperfect loan market competition The next step is to combine the two polar cases of monopolistic and competitive loan markets. Banks simultaneously make loan rate offers, and the entrepreneur picks the best quote. In the case of indifference, she is assumed to undertake her project with bank 1. To derive the loan market equilibrium, observe that if, in equilibrium, the entrepreneur is indifferent between bank 1 and bank 2, then bank 2 must have quoted the competitive rate; otherwise, bank 2 could have profitably undercut bank 1, which cannot occur in equilibrium (otherwise, bank 1 would have charged a lower loan rate in the first place). The lowest loan rate at which bank 2 does not make losses is the competitive loan rate R∗ from above. Thus, the loan market equilibrium maximizes bank1’s payoff subject to (i) the entrepreneur weakly preferring to stay with bank 1 if bank 2 quotes the competitive rate, and (ii) her incentive constraint (IC). Formally, substituting for R(e ) =  − ψ  (e ) from (IC), the loan market equilibrium solves:



 − R − ψ  ( e ) = 0,

(IC)

max UB (e, R(e )) = e − ψ (e ) − eψ  (e ) − ψ (e ) e



project NPV

s.t.

−

















E’s payoff

− e ( 1 − sD ) ,

  

MV liabilities

UE (e, R(e )) = eψ  (e ) − ψ (e ) ≥ UE (e∗ , R∗ ) − s

MV bank liabilities

1 − (1 − e )(1 − sD ) = ψ  ( e ). e



s.t.

max e − 1 − ψ (e ) + (1 − e )(1 − sD ),





project value

where (ZP) is the bank’s zero-incremental-profit constraint—the incremental profit from lending must be zero. Substituting for (ZP), the problem can be rewritten as e



= e∗ ψ  (e∗ ) − ψ (e∗ ) − s,

(IC )

The first term in the objective function is project NPV, and the second term is the amount by which risky lending allows the bank to reduce the expected payout to depositors relative to staying inactive in the loan market. In a competitive loan market, this amount is passed on to the entrepreneur in the form of a cheaper loan, improving incentives. However, as banks pay lower deposit rates, the risk-shifting gains from investing in risky loans decline; thus, in a competitive loan market, heightened deposit market power (lower deposit rates) must entail higher loan rates; otherwise, banks would not break even on their loans. Proposition 2. In competitive loan markets, a rise in deposit market power leads to higher loan rates, lower loan performance and higher intermediation margins. In competitive loan markets, the risk-shifting gains from risky lending are passed on to entrepreneurs in the form of cheaper loans. As banks pay lower deposit rates, risk-shifting gains decline, and, thus, loan rates must rise. Thus, in competitive markets, lower deposit rates entail higher loan rates and, consequently, lower loan performance. This is in sharp contrast to the case of monopolistic pricing, in which precisely the opposite occurs. A corollary of the proposition is that, in competitive loan markets, more-intense competition for deposits leads to lower loan rates. To see the intuition, recall that a bank’s economic cost of extending a loan is not given by the rate that its pays on its deposits,

(IR )

where (IR’) is the entrepreneur’s reduced-form participation constraint. Intuition suggests that (IR’) should be binding for low levels of loan market power s. As loan market power rises, (IR’) should eventually become slack. This is confirmed by the following result: Proposition 3. There is a loan market power threshold sˆ(sD ) ∈ (0, UE (e∗ , R∗ )), strictly decreasing in deposit market power sD , such that: (i) In relatively uncompetitive loan markets, s ≥ sˆ(sD ), (IR’) is slack. Equilibrium effort and loan rates coincide with those in a monopolistic loan market. Thus, a rise in deposit market power leads to lower loan rates and higher loan performance. A further rise in loan market power has no effect on loan pricing. (ii) In relatively competitive loan markets, s < sˆ(sD ), (IR’) is binding. Heightened deposit and loan market power both lead to higher loan rates and lower loan performance. Fig. 2 illustrates the proposition. The key observation is that loan performance is first decreasing in deposit market power and then increasing.8 Reiterating the intuition, in relatively uncompetitive environments, banks can charge fairly high loan rates without “risking” the loss of prospective borrowers to the competition. 8 However, the threshold sˆD (s ) (the inverse of sˆ(sD )) is not always interior. Thus, there could also be parameter constellations under which default rates are unambiguously decreasing or increasing in sD . To see this, note that for s close to zero, (IR’) must be binding; thus, e∗∗ is unambiguously decreasing in sD . Conversely, for s large enough, (IR’) cannot be binding; thus, e∗∗ = eM , which is increasing in sD .

S. Arping / Journal of Banking and Finance 80 (2017) 108–118

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Fig. 2. Deposit market power and loan performance. The dashed lines depict loan performance in perfectly competitive (e∗ ) and monopolistic (eM ) loan markets, and the solid line depicts loan performance in an imperfectly competitive loan market (e∗∗ ). For sD < sˆD (s ) (the inverse of sˆ(sD )), (IR’) is binding and, thus, e∗∗ > eM . For sD ≥ sˆD (s ), (IR’) is slack and, thus, e∗∗ = eM . As the loan market becomes more competitive (s declines), sˆD (s ) shifts to the right and e∗∗ (sD < sˆD (s )) shifts upwards. In the limit, as s approaches zero, e∗∗ converges to e∗ . Conversely, as s becomes larger, e∗∗ approaches eM .

Banks’ loan pricing is, then, shaped by a trade-off between higher loan default risk and higher income in non-default states. An increase in deposit market power tilts this trade-off towards taking less risk and, thus, less-aggressive rent extraction. By contrast, in more-competitive environments, banks’ loan pricing is constrained by the threat of losing borrowers to the competition. What matters in this case is the effect of deposit market power on entrepreneurs’ outside option payoff; this, in turn, depends on banks’ incremental profit from lending. As deposit rates decline, banks become less eager to extend risky loans—i.e., the incremental profit from lending declines. This worsens entrepreneurs’ outside option, so loan rates rise. The effect of loan market power is standard: Heightened loan market power entails higher loan rates, unless the loan market is highly uncompetitive, in which case a further rise in the loan rate would have too adverse an effect on incentives and, thus, would be too costly. 5. Discussion 5.1. Under- and overinvestment Thus far, I have assumed that the parameter values are such that, in equilibrium, the entrepreneur will receive a loan—i.e., I have abstracted from credit rationing. This section analyses the effects of competition on credit availability and investment efficiency. In an equilibrium in which the project is undertaken, the joint surplus of the entrepreneur, the loan-extending bank, its depositors and the regulator is





e( − R ) − ψ (e ) + e R − 1 − sD





UE (e, R )

 



UB (e, R )

 











= e 1 − sD









project NPV



or, substituting for ψ (e ) = β e2 /2,

where the third term is depositors’ payoff, and the fourth term is the regulator’s expected compensation payout to depositors. These two terms add up to e(1 − sD ), which is the bank’s expected payout to depositors. Conversely, if the project is not undertaken, then the parties’ joint surplus is 1 − (1 − sD ) + (1 − sD ) = 1. Thus, if one momentarily abstract from the potentially detrimental effect of risky lending on banking stability (see Section 5.3), and if one also abstracts from other, hard-to-assess externalities that investment









 MV liabilities

The second term is the amount by which risky lending allows the bank to reduce the expected payout to depositors. Since this expression can hold even if project NPV is negative, the private sector could have an incentive to over-invest and undertake a negativeNPV project. The underlying source of inefficiency stems from the agency conflict between bank shareholders and its liability holders. As competition for deposits intensifies and deposit rates rise (RD = 1 − sD ↑), this loan market distortion becomes more severe. Another potential source of inefficiency stems from the agency conflict between the entrepreneur and her lender. If effort were contractible, then, by (A1), the project would always be undertaken (sometimes inefficiently so, see above). However, since the entrepreneur is subject to moral hazard, it may very well be that, in equilibrium, no loan is extended. In the Appendix, I show that the project is undertaken if and only if a bank’s incremental profit from lending under monopolistic pricing is non-negative,

UB (eM , RM ) − sD = (eM )2 ψ  (eM ) − sD ≥ 0,

= e − ψ ( e ),



UB (e, R ) − UE (e, R ) − sD = e − ψ (e ) − 1 + (1 − e ) 1 − sD ≥ 0.



+ 1 − sD − ( 1 − e ) 1 − sD



may impose on society (consumer surplus, growth externalities, etc.), investment is efficient for society if and only if, in equilibrium, project NPV is non-negative, e − ψ (e ) − 1 ≥ 0. Investment is jointly efficient for the bank and the entrepreneur (disregarding the effect on other agents’ payoffs) if and only if their joint surplus from undertaking the project is not smaller than their joint surplus from investing deposits in the money market—i.e.,   UB (e, R ) + UE (e, R ) ≥ 1 − 1 − sD = sD , which reduces to

sD ≤



β−



2 β − ( − 1 ) ≡ sˇD .

(4)

In other words, investment occurs if and only if, with monopolistic pricing, the bank at least breaks even on the loan. This is intuitive: If the bank cannot break even with monopolistic pricing, it cannot possibly break even with less-than-monopolistic pricing. Conversely, if the loan is extended in a monopolistic loan market, then it will also be extended in less-monopolistic markets. The conclusion is that while, in this model, loan competition has no

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S. Arping / Journal of Banking and Finance 80 (2017) 108–118 Table 1 Effects of increase in bank market power.

Deposit rates (RD ) Loan rates (R) Loan performance (e) NPL ratios (1 − e)

bank credit risk equals the product of the probability of default (PD) and the loss given default (LGD),

Competition high

Competition low

Down Up Down Up

Down Down Up Down

effect on credit availability,9 fiercer competition for deposits does improve credit availability. The intuition stems from the earlier observation that risky lending is particularly lucrative when deposit rates are high since, then, the risk-shifting benefits from risky lending are high, too. Consequently, greater competition makes banks more eager to lend. However, this does not necessarily imply that heightened deposit competition makes society better off. The additional projects brought to life might be negative-NPV projects; if so, the additional lending would be wasteful and detrimental to welfare. As discussed above, this scenario is more likely to occur when competition for deposits is fierce. Furthermore, conditional on a loan being extended, greater deposit competition could lead to lower loan performance; however, as we saw earlier, this effect will depend on the degree of loan competition. 5.2. Correlating deposit and loan market power Next, I allow for the possibility that changes in deposit and loan market power could be positively correlated. The underlying premise is that changes to the competitive landscape in banking— caused by, e.g., technological progress—will often alter banks’ pricing power in both markets. For instance, advances in information technology may make it less cumbersome for depositors to access their outside options. At the same time, lending processes become more efficient, making it easier for entrepreneurs to borrow from “distant” lenders.10 However, the effect could be stronger in one market than in the other—i.e., the effect may not be uniform. To capture this, I posit that s = φ sD , where φ > 0, and vary sD to analyze the effect of a simultaneous rise in deposit and loan market power. The parameter φ simply measures how strongly changes in deposit and loan market power are correlated. Table 1 reports the comparative statics results. In relatively competitive markets, heightened market power leads to lower deposit rates, higher loan rates, and lower loan performance (and, thus, higher non-performing loan ratios). In less-competitive environments, it leads to lower deposit rates, lower loan rates, and higher loan performance. In this case, however, the effects of heightened market power on loan rates and performance are caused by changes in deposit market power (since, as explained, a further rise in loan market power has no effect on loan pricing when the loan market is already fairly uncompetitive). 5.3. Banking stability Thus far, I have analyzed the effects of competition on loan pricing and loan performance. This section draws implications for banking stability. To motivate, suppose that bank failure is costly to society (think of contagion costs), and that the cost is proportional to the loss given default. Following the standard definition,

9 This might be different in a more complex setting in which some degree of loan market power would be required for lenders to recoup ex ante relationship-building costs—see Petersen and Rajan (1995). 10 However, there are also examples of changes to the competitive landscape in banking that affect only one market. For instance, the introduction of money market funds in the 1970s presumably affected banks’ pricing power in deposit markets but not in loan markets, at least not directly so.

σ = PD × LGD = (1 − e )(1 − sD ). The empirical counterpart of the inverse of this measure would be the “Z-score,” a widely used measure of financial stability in the empirical literature (e.g., Beck et al., 2012). Thus, heightened deposit market power can affect bank credit risk in two ways: First, it reduces banks’ deposit-repayment burdens, which mechanically reduces credit risk. Second, it affects the probability of default through its effect on loan performance. As above, I posit that changes in deposit and loan market power are positively correlated, s = φ sD , where φ > 0. Differentiating bank stability 1 − σ with respect to sD , one obtains

>0    d (1 − σ ) de de = ( 1 − e ) + D ( 1 − sD ) + d sD ds    ds < 0 (> 0)

φ ( 1 − sD ) .   ≤0

The first term captures the direct, stabilizing effect of lower deposit rates. The second term captures the effect of deposit market power on loan performance, which is destabilizing in morecompetitive environments and stabilizing in less-competitive ones. The third term captures the effect of heightened loan market power—a weakly destabilizing effect in my simple model. Overall, the effect of competition on stability is ambiguous. To gain further insight into the stability aspects of competition in this setting, let me consider the closed-form solution of the model. Straightforward algebra shows that loan performance in monopolistic (eM ) and perfectly competitive (e∗ ) loan markets is

eM = ∗

e =

 − ( 1 − sD ) , 2β  − ( 1 − sD ) +



( − (1 − sD ))2 − 4β sD . 2β

Loan performance in imperfectly (Section 4.3), then, amounts to

e∗∗ = max



competitive

loan

markets

(e∗ )2 − 2s/β , eM .

where s = φ sD . Thus, bank credit risk is

 

σ = (1 − e∗∗ )(1 − sD ) = 1 − max (e∗ )2 − 2φ sD /β , eM × ( 1 − sD ). The first term inside the maximum operator is loan performance in relatively competitive environments (low-marketpower regime), and the second term is loan performance in lesscompetitive ones (high-market-power regime). Thus, in the highmarket-power regime, bank credit risk, σ = (1 − eM )(1 − sD ), is unambiguously decreasing in market power: As sD rises, banks’ deposit-repayment burdens decline (direct effect) and loan performance rises (indirect effect). In the low-market-power regime, market power has a detrimental effect on loan performance, so the overall effect of market power on stability is ambiguous. Fig. 3 illustrates the relationship between bank market power and credit risk for  = β = 4 and three scenarios for the parameter φ : 1.5, 1, and 0.5.11 Under the first and second scenario, there is a hump-shaped relationship between market power and credit risk. Under the third scenario, bank credit risk is highest 11 Under these parameter constellations, sˇD = 1, so there is no credit rationing; furthermore, investment is always efficient. For  = β < 4, credit rationing can occur, and investment is not necessarily efficient.

S. Arping / Journal of Banking and Finance 80 (2017) 108–118

115

Fig. 3. The effect of market power on bank credit risk. The figure illustrates the relationship between bank market power and credit risk for three scenarios for the parameter φ : 1.5, 1, and 0.5. Under the first and second scenario (φ = 1.5 and φ = 1.0), there is a hump-shaped relationship between bank market power and credit risk. Under the third scenario (φ = 0.5), credit risk is highest when competition is most fierce.

when competition is most fierce. In this case, the destabilizing effect of market power on loan performance in the low-marketpower regime happens to be outweighed by the stabilizing effect on banks’ deposit-repayment burdens. Thus, while there are scenarios under which credit risk is highest when competition is neither too high nor too low, there are other scenarios under which competition, through its effect on banks’ deposit-repayment burdens, is unambiguously destabilizing. 5.4. Cornering incentives In the baseline model, I have assumed that no single bank can corner the market for deposits. In this section, I show that as long as competition in deposit and loan markets is not overly fierce, this assumption is redundant. To sharpen the analysis, let me suppose that banks do not have access to wholesale funding. Recall that banks cannot price differentiate—i.e., they must offer the same rate to households, irrespective of where they are located. Suppose, then, that bank 1 (i.e., the bank that already has a competitive advantage in the loan market) deviates from the equilibrium in Proposition 3 and corners the deposit market. This means that bank 1 quotes a deposit rate RD such that bank2’s de1 positors at least weakly prefer to “switch” to bank 1, taking into account the cost sD that depositors in market 2 would incur if they switched to bank 1. Since bank 2 quotes a rate of RD = 1 − sD , the 2 lowest such rate is RD = 1 . Thus, cornering the deposit market has 1 costs and benefits for bank 1. The cost is that bank 1 loses its deposit market rents: To deprive bank 2 of deposits, it must price its deposit-taking services very aggressively. The potential benefit is that it may allow bank 1 to extract higher rents in the loan market; after all, once bank 1 has cornered the market for deposits, bank 2 can no longer compete in the loan market (given that banks do not have access to wholesale funding). Having cornered the deposit market, bank1’s loan pricing problem is to maximize its profit,

max UB (e, R(e )) e

= e( − ψ  (e ) − 1 ),

where R(e ) =  − ψ  (e ), subject to entrepreneurs’ participation constraint,

UE (e, R(e )) = eψ  (e ) − ψ (e ) ≥ 0, which, obviously, is slack. This problem is solved for e = ( − 1 )/(2β ), yielding profits ( − 1 )2 /(4β ). Thus, bank 1 has no in-

centive to corner if and only if

⎧ ( − (1 − sD ))2 ⎪ for s ≥ sˆ(sD ), ⎪ ⎪ 4β ⎪ ⎨   ( − 1 )2 ≤ UB∗∗ = e∗∗ R(e∗∗ ) − (1 − sD ) 4β ⎪ ⎪ D 2 ⎪ ⎪ ⎩ < ( − (1 − s )) for s < sˆ(sD ), 4β

(5)



where e∗∗ = (e∗ )2 − 2s/β . The right hand side of this expression is bank1’s profit when it does not deviate from the proposed strategy, given that bank 2 does not deviate. Thus, a sufficient condition for bank 1 to not deviate is that s is above or sufficiently close to the threshold sˆ(sD ). The intuition is straightforward: If bank 1 already has substantial pricing power in the loan market, the cost of a cornering strategy (lost deposit market rents) must outweigh the benefit. As s approaches zero, UB∗∗ converges to sD , so (5) reduces to ( − 1 )2 /(4β ) ≤ sD . Thus, even in perfectly competitive loan markets, it can occur that bank 1 has no incentive to corner the deposit market. Conversely, as sD approaches zero, bank 1 has no incentive to deviate if and only if s ≥ sˆ(0 )—i.e., the loan market is not too competitive. Bank 2 faces a similar trade-off in that, if it deviated, it would obtain a monopoly position in the loan market, but it would lose its deposit market rents. Thus, bank 2 has no incentive to corner the deposit market if either the entrepreneur’s cost s of “switching” to bank 2 or deposit market rents sD are high enough. The conclusion is that, as long as competition in deposit and loan markets is not overly fierce, the proposed equilibrium is robust to cornering possibilities, even if mobilizing deposits requires no marketing expense, and even if banks do not have access to wholesale funding. Of course, a bank’s incentive to corner the market for retail deposits would be even weaker if its rival banks had access to wholesale funding—as, in practice, most banks do. 5.5. Bank control In the baseline model, project risk is non-contractible. This section provides a brief discussion of how the analysis would be altered if entrepreneurs were not subject to moral hazard. For instance, one can imagine that banks, through their monitoring function, exert control over entrepreneurs and, in doing so, align borrower incentives with their own interests. The setting is as above, except that entrepreneurs’ incentive constraint can be dispensed with. To start with, consider the case

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S. Arping / Journal of Banking and Finance 80 (2017) 108–118

of a perfectly competitive loan market. The loan market equilibrium solves

max UE (e, R ) = e( − R ) − ψ (e ), (e,R )

s.t. UB (e, R ) = e(R − (1 − sD )) ≥ sD . This problem reduces to maximizing the parties’ joint surplus,

max e − ψ (e ) − e(1 − sD ), e

and the solution, denoted by eFB (sD ), is characterized by the firstorder condition

 − ψ  ( e ) − ( 1 − sD ) = 0. Thus, in contrast to the baseline analysis, loan performance is strictly increasing in sD , even in competitive loan markets. The intuition is that, as deposit rates decline, it becomes less attractive to the bank-borrower coalition to shift risk to depositors; thus, since, now, the entrepreneur’s incentives are aligned with the bank’s interests, the bank-borrower coalition will commit to exert more effort. The equilibrium loan rate is R∗ = (1 − (1 − e∗ )(1 − sD ))/e∗ , where e∗ = eF B (sD ). Differentiating the loan rate with respect to sD yields

de∗ sD dR∗ 1 − e∗ = − D ∗ 2. e∗ dsD ds (e ) For sD close to zero, this term is positive. However, for sD large, ∗ D D it could be negative (formally, dR /ds < 0 if and only if s > β ( − 1 ) − ( − 1 )). Thus, in contrast to the earlier analysis, it can occur that loan rates in competitive markets are decreasing in sD . Next, consider the case of imperfect (including monopolistic) loan market competition. The loan market equilibrium solves

max UB (e, R ) = e(R − (1 − sD )), (e,R )

s.t. UE (e, R ) = e( − R ) − ψ (e ) ≥ max [0, UE (e∗ , R∗ ) − s], (IR) where (e∗ , R∗ ) is the competitive outcome, and (IR) is the entrepreneur’s participation constraint (note that, in the earlier analysis with moral hazard, the constraint UE (e, R) ≥ 0 cannot be binding). This problem has a straightforward solution: e = eF B (sD ) = e∗ , and

R=

  − ψ (e∗ )/e∗ =  − β e∗ /2 for s ≥ UE (e∗ , R∗ ), R∗ + s/e∗ for s < UE (e∗ , R∗ ).

In the first case, the bank pushes the entrepreneur’s payoff to zero. Thus, in relatively uncompetitive loan markets, loan rates are decreasing in deposit market power and do not depend on loan market power. In more-competitive markets, loan rates are increasing in loan market power, and the effect of deposit market power is ambiguous. Summing up, if banks can and do align borrower incentives with their interests, then loan performance is increasing in deposit market power, but it does not depend on loan market power. The intuition is straightforward: Conditional on borrower incentives being aligned with banks’ interests, all that matters for incentives is how the total surplus is divided between the bank-borrower coalition and the remaining agents. The division of the surplus of the bank-borrower coalition among itself does not matter. Clearly, this might be different if the division of the surplus of the bankborrower coalition mattered for the way in which banks exert their control (e.g., Caminal and Matutes, 2002; Wagner, 2010).

6. Implications One broad implication of the analysis is that the financial stability aspects of bank competition can be complex and—in terms of both sign and magnitude—contingent on market structure. The stability effects of competition may, thus, differ from country to country, from banking market to banking market, and from time period to time period. This prediction is consistent with Beck et al. (2012), who document substantial cross-country heterogeneity in the link between bank market power and banking stability (bank Z-score). However, they also document that the correlation between market power and banking stability is, on average, positive and that market power is stabilizing in the majority of the countries in their sample. This is also consistent with the broader empirical evidence on the competition-stability nexus: Although some empirical studies, such as Schaeck (2009), document a positive relationship between competition and stability, most of the literature seems to point to a negative relationship (for an excellent survey, see Schaeck, 2009). This should not be surprising. Banks operating in morecompetitive environments tend to face tighter margins. Thus, even if one abstracts from the risk-shifting effects that fiercer deposit competition may entail, one would expect heightened competition to often make banks more fragile. Any stabilizing effects of competition must, then, stem from “behavioral” channels, such as the impact on borrower risk-shifting incentives (Boyd and De Nicolo, 2005);12 however, such effects will not necessarily dominate the effect of competition on margins, which should be destabilizing (Martinez-Miera and Repullo, 2010). Some studies use non-performing loan (NPL) ratios as the dependent variable. While empirical designs that use NPL ratios as the outcome variable may not necessarily allow us to draw conclusions regarding the competition-stability nexus (see MartinezMiera and Repullo, 2010), they may provide cleaner tests of the behavioral (risk taking) channels. Again, the empirical evidence is not conclusive. Jiménez et al. (2013), using credit registry data from Spain and constructing Lerner indices separately for deposit and loan markets, provide evidence that is suggestive of a hump-shaped relationship between banks’ deposit market power (deposit Lerner indices) and their NPL ratios, which would be consistent with my model. However, the corresponding coefficients, while having the predicted sign, are not significant at conventional levels, so the evidence is weak.13 In a related study, Berger et al. (2009) test for non-linearities in the relationship between bank market power and NPL ratios in a sample of 23 developed countries (but excluding Spain, the country under investigation in Jiménez et al., 2013). By and large, their evidence points to an upward-sloping relationship between market power and NPL ratios. The model also has implications for loan pricing. In particular, it suggests that heightened competition for deposits leads to higher loan rates in relatively uncompetitive banking markets but lower loan rates in more-competitive environments. At the same time, more-intense deposit or loan competition leads to (weakly) lower intermediation margins. To my knowledge, the empirical literature has not yet tackled the question of how changes in deposit market (or loan market) power causally affect loan pricing. Indeed, we

12 Another channel has to do with the disciplining effect of competition on managerial incentives (e.g., Schmidt, 1997): Competition may induce bankers do “work harder,” possibly making banks less fragile. 13 However, in other regression specifications, in which deposit market power is proxied by concentration (Herfindahl index) or the market share of the five largest banks in a region, Jiménez et al. (2013) do detect a significant hump-shaped relationship between banks’ deposit market power and their NPL ratios.

S. Arping / Journal of Banking and Finance 80 (2017) 108–118

know surprisingly little about how bank market power in funding markets shapes loan pricing. With the exception of Jiménez et al. (2013), I am also not aware of empirical studies that seek to disentangle the economic effects of deposit market power from those of loan market power by constructing Lerner indices separately for each market—or by exploiting natural experiments. Presumably, this is because shocks to the competitive landscape in banking that have isolated effects on one of the markets are not easy to come by. Having said that, there are examples of such shocks; consider, for example, the introduction of money market funds in the U.S. during the 1970s.14 At any rate, identifying the causal effects of competition in either funding (deposit) or loan markets appears to be important but challenging.

117

Let me also derive a necessary and sufficient condition for investment to occur under monopolistic pricing. In equilibrium, the project will be undertaken if and only if the bank’s incremental profit from lending is non-negative—i.e.,









UB eM , RM = eM  − ψ  (eM ) − (1 − sD ) ≥ sD . By (7), this reduces to (eM )2 ψ   (eM ) ≥ sD , which, by ψ (e ) = β e2 /2, can be solved for

sD ≤



β−



2 β − ( − 1 ) ≡ sˇD .

(8)

Thus, in monopolistic loan markets, investment will occur if and only if (8) holds. 

7. Conclusion

Proof of Proposition 2. Suppose that the underlying parameter values are such that, in equilibrium, the project is undertaken. Let

The primary objective of this article is to explore how banks’ pricing power in deposit markets affect real economic outcomes through its effect on banks’ loan pricing. I find that the economic effects of deposit competition can be qualitatively dependent on the degree of loan competition. In relatively uncompetitive loan markets, fiercer deposit competition leads to higher loan rates, whereas in more-competitive markets, the opposite occurs. Intuitively, as banks pay higher deposit rates and deposit-repayment burdens rise, they become more eager to invest in risky assets; this can intensify competition for risky loans, causing banks to cut their loan rates. However, banks also become more inclined to aggressively extract rents from those loan customers who would find it difficult to obtain loans elsewhere. Whether the former effect dominates the latter depends on the ease with which customers can “switch” to rival lenders, which, in turn, hinges on the degree of loan competition. Overall, the analysis illustrates that the welfare aspects of “bank competition” can be subtle—and even more subtle than the extant literature may suggest. Indeed, the very concept of “bank competition” is elusive: Are we talking about competition for loans, competition for deposits, or both? This suggests that a fruitful strategy for empirical work might be to exploit shocks to the banking landscape that have clearly identified and isolated effects on competition in one market and, then, to explore how this change in competition affects economic outcomes and how it spills over to other markets in which banks operate.

S(e ) = UE (e, R ) + UB (e, R ) = e − ψ (e ) − e(1 − sD ) denote the joint surplus of the entrepreneur and the bank. The bank’s binding zero-incremental-profit constraint yields UB (e, R ) = sD . Thus, the Bertrand equilibrium solves

max UE (e, R(e )) = S(e ) − sD = e − ψ (e ) − 1 + (1 −e )(1 −sD ), e

s.t.

ϕ (e ) = e − eψ  (e ) − 1 + (1 − e )(1 − sD ) = 0,

(9)

where (9) follows from multiplying both sides of (IC’) by e. Equilibrium effort, denoted by e∗ , is a solution of (9). By assumption, (9) must have a real solution; otherwise, the project would not have been undertaken. Furthermore, ϕ (0 ) = −sD < 0 and ϕ (1) < 0, so the solution must be interior. The unconstrained optimum is characterized by S (e ) = 0 or, multiplying both sides by e,

eS (e ) = e − eψ  (e ) − e(1 − sD ) = 0. Evaluating this expression at e = e∗ , we have, by (9), e∗ S (e∗ ) = sD > 0. Thus, by concavity of S(e), equilibrium effort e∗ is strictly inferior to the unconstrained optimum. Thus, equilibrium effort is given by the largest solution of (9). At this solution, it generically must be the case that ϕ  (e) < 0. Thus, by implicit differentiation of (9),



− (1 − e )  de∗ =− < 0.  ϕ  ( e ) e= e∗ dsD

(10)

Now, the entrepreneur’s payoff is strictly positive, e∗ ψ  (e∗ ) − ψ (e∗ ) > 0, and the bank’s payoff equals its outside option pay-

Appendix

off; thus, a necessary and sufficient condition for the project to be undertaken is that (9) has a real solution. By inspection, ϕ (e) is strictly concave in e, and we have ϕ (0) < 0 and ϕ (1) < 0. Thus, (9) has a real solution if and only if max e {ϕ (e)} ≥ 0. Now,

Proof of Proposition 1. The monopolist bank’s problem is to

max UB (e, R(e )) = e( − ψ  (e ) − (1 − sD )), e

s.t. UE (e, R(e )) = eψ  (e ) − ψ (e ) ≥ 0,

(6)

where R(e ) =  − ψ  (e ) by (IC), UE ( · ) is the entrepreneur’s payoff, and UB ( · ) is the bank’s profit. Clearly, (6) cannot be binding. The first-order condition for an interior optimum eM is

UB (e, R(e )) =  − ψ  (e ) − eψ  (e ) − (1 − sD ) = 0.

(7)

Clearly, UB (0, R(0 )) > 0 and UB (1, R(1 )) < 0, so the solution must be interior. Furthermore, by concavity of UB (e, R(e)), the optimum is unique. By implicit differentiation,



1 deM  = −  > 0.  UB (e, R(e )) e=eM dsD 14 One might also exploit instances of foreign bank entry in which new entrants operate in one of the markets but not in both. However, in this case, the empirical inference might still be contaminated by the endogeneity of the decision of which market to operate in (unless it is driven by exogenous regulation).

ϕ  (e ) =  − ψ  (e ) − eψ  (e ) − (1 − sD ) = 0 precisely at e = eM . However, ϕ (eM ) ≥ 0 if and only if UB (eM , RM ) ≥ sD , or condition (8) in the proof of Proposition 1 holds. Thus, the project will be undertaken if and only if (8) holds.  Proof of Proposition 3. As discussed in the proofs of Propositions 1 and 2, for sD > sˇD , the project is not undertaken in monopolistic or perfectly competitive markets. Clearly, in this case, it is not undertaken in imperfectly competitive markets either. For sD = sˇD , investment is just feasible in monopolistic or perfectly competitive loan markets; however, this parameter constellation has zero mass, so let sD < sˇD to ensure that investment is generically feasible in monopolistic or perfectly competitive markets and, thus, also in imperfectly competitive loan markets. Bank1’s loan pricing problem is to

max UB (e, R(e )) = e( − ψ  (e ) − (1 − sD )), e

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s.t.

by

UE (e, R(e ))

= eψ  (e ) − ψ (e ) ≥ UE (e∗ , R(e∗ )) − s = e∗ ψ  (e∗ ) − ψ (e∗ ) − s,

UE (e∗ , R∗ ) = e∗  − ψ (e∗ ) − 1 + (1 − e∗ )(1 − sD ). (11)

where R(e ) =  − ψ  (e ), (11) is the entrepreneur’s reduced-form participation constraint, and (e∗ , R∗ ) is the loan market outcome under perfect loan competition (Proposition 2). For a more detailed discussion, see the text. Let e∗∗ denote the optimum. Clearly, if (11) is slack, then e∗∗ = eM (Proposition 1). Evaluating UB (e, R(e )) at e∗ , one obtains, by (9) and sD < sˇD ,

UB (e∗ , R∗ ) = sD − (e∗ )2 ψ  (e∗ ) < 0. Thus, by concavity of UB (e, R(e)), we have eM < e∗ , and, thus, (11) would be violated at eM for s close to zero. Thus, for s small, (11) is binding. If (11) is binding, then e∗∗ is the unique (positive) root of (11). Thus, for s close to UE (e∗ , R∗ ), (11) cannot be binding. Otherwise, e∗∗ would be close to zero and the bank would make losses. Thus, since (11) is linear in s, there is some threshold sˆ ∈ (0, UE (e∗ , R∗ )) such that (11) is binding if and only if s < sˆ. By inspection, this threshold is given by

sˆ = UE (e∗ , R∗ ) − UE (eM , RM ) = e∗ ψ  (e∗ ) − ψ (e∗ )





− eM ψ  ( eM ) − ψ ( eM ) .

As UE (e∗ , R∗ ) is strictly decreasing in sD and UE (eM , RM ) is strictly increasing in sD , the threshold sˆ is strictly decreasing in sD . Furthermore, for s < sˆ, we have

de∗∗ de∗ e∗ ψ  (e∗ ) = D ∗∗  ∗∗ < 0, dsD ds e ψ (e ) by total differentiation of e∗∗ ψ  (e∗∗ ) − ψ (e∗∗ ) − (UE (e∗ , R∗ ) − s ) = 0 and de∗ /dsD < 0. Summing up, there is a threshold sˆ(sD ) ∈ (0, UE (e∗ , R∗ )), strictly decreasing in sD , such that

de∗∗ dsD



< 0 for s < sˆ(sD ), >0

for s ≥ sˆ(sD ).

Let me also confirm that bank1’s participation constraint, UB (e, R(e)) ≥ sD , is slack. Clearly, the bank’s equilibrium profit is at least weakly increasing in s. Yet, at s = 0, we have e∗∗ = e∗ , and, hence, the bank’s payoff at s = 0 is

UB (e∗∗ , R∗∗ )|s=0 = sD + e∗  − ψ (e∗ ) − 1 − UE (e∗ , R∗ ) + (1 − e∗ )(1 − sD ) = sD ,

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