productivity and lending fluctuations?

Transcription

1 Does the heterogeneity in bank efficiency matter for aggregate productivity and lending fluctuations? Thibaut Duprey Job market paper [link to the latest version] October 29, 2014 Abstract This paper shows that heterogeneity in the distribution of banks abilities become relevant when the banking sector is imperfectly competitive. I develop a model of two-sided group matching whereby banks offer a menu of loan contracts to entrepreneurs that self-select their banks and decide to make more or less effort accordingly. The endogeneous market segmentation is such that effort making entrepreneurs undertake high yield projects financed by the most efficient bank. The most efficient bank has a comparative advantage and thus extracts a rent that distorts incentives, but it also offers loans in a more procyclical way to keep incentives aligned. Thus the cross-sectional distribution of bank efficiency in screening abilities matters (i) for aggregate productivity, with more banking heterogeneity being detrimental to productivity and (ii) for lending fluctuations, with less efficient banks featuring a lower cyclicality. The implications of the model are consistent with observations from 20 OECD countries over the period Keywords : banking heterogeneity, moral hazard, adverse selection, imperfect competition, market segmentation, allocation efficiency, lending fluctuations, aggregate productivity. JEL Classification : G21, E30, O47. I am grateful to Xavier Ragot for guidance, and wish to thank Régis Breton, Brunos Biais, Zhili Cao, Nicolas Coeurdacier, Jean Imbs, Enisse Kharroubi, Guillaume Plantin, Annukka Ristiniemi for helpful comments on previous drafts. This paper also benefited from comments by seminar participants at the Paris School of Economics, the Banque de France, the 2013 French Economic Association Congress, the 2013 European Economic Association Congress as well as the 2014 Royal Economic Society Congress. Previously circulated under the title Heterogeneous Banking Efficiency: Allocative Distortions and Lending Fluctuations. I gratefully acknowledge financial support from the Banque de France. The opinion expressed herein may not reflect the position of the Banque de France. Any remaining errors are mine. Paris School of Economics and Banque de France. thibaut.duprey@gmail.com. 1

2 1 Introduction One of banks key roles is to channel funds efficiently by tailoring loan contracts that help preserve borrowers incentives to behave. Thus lending standards and borrowers productivity depend on the ability of banks to acquire information about borrowers effort willingness. However, this fundamental role of intermediated finance needs to be re-considered after the recent financial crisis. Financial intermediaries cannot be thought of as being a representative agent anymore, which means banking heterogeneity is no longer irrelevant. The least efficient intermediaries may survive and distort banks information acquisition. And as a consequence they can influence the allocation of credit 1 as well as productivity choices. 2 The focus of this paper is on how the cross-sectional distribution of banks efficiency in their screening abilities interacts with the choice of a loan contract and the provision of effort by borrowers, so that the allocation of credit and aggregate productivity are distorted. I develop a model with heterogeneous banking and endogeneous market segmentation. I call it two-sided group matching as both banks and entrepreneurs choose each other and adjust their behaviour accordingly. I obtain a separating equilibrium between groups of more or less efficient banks and more or less efficient entrepreneurs. The equilibrium is such that efficiently screening banks contract with the most efficient entrepreneurs, precisely those who value most being screened out. I show that, in an imperfectly competitive banking sector (i.e. without free entry and contestability), when banks are heterogeneous in their screening efficiencies, a larger distribution of bank efficiency is detrimental to aggregate productivity. But I also note that, in the meantime, such a setting features a lower cyclicality of lending by the less efficient banks. Thus the analysis is consistent with the existence of a trade-off between the efficiency in the allocation of credit and the sensitivity of loans to variations in aggregate productivity. The mechanism works as follows. Competition among banks with different abilities to screen borrowers generates a rent for the most efficient financial intermediary, which distorts the allocation of credit in the economy. As a result, this bank offers a lower reward for effort and the design of loan contracts impacts borrowers effort incentives. A lower share of high yield projects are undertaken, which decreases aggregate productivity. Meanwhile, imperfectly competitive banks generate an endogeneous market segmentation between more or less efficient 1 For instance investment banks are more volatile (Adrian and Shin, 2010) while government-owned banks are less cyclical (Duprey, 2014; Bertay et al., 2014). 2 Giannone et al. (2011) suggest that the presence of a less efficient banking system limited the reduction in output growth in the initial phase of the 2008 recession. 2

3 banks and more or less effort-making entrepreneurs, which may make aggregate lending less volatile depending on the market share of each bank. In particular, banks that specialise in screening out borrowers feature a more procyclical lending policy. First, a good productivity shock makes borrowers more trustworthy. So screening banks that finance only high yield projects offer procyclical loans to match procyclical moral hazard. Second, a good productivity shock makes effort more attractive and more entrepreneurs are likely to decide to make efforts. As a result, screening banks have more customers and offer more loans due to procyclical adverse selection. The market segmentation is crucial to the analysis. By choosing the loan contract of a bank that gathers entrepreneur-specific information, the entrepreneur is likely to have access to a larger loan size if he is of the high ability/low effort cost group. But at the same time, the bank makes this entrepreneur bear a larger interest rate on loans to cover the costs of information acquisition. As a result, the net benefit from contracting with a screening bank is larger for an entrepreneur with lower effort costs. In a parallel manner, the bank with the lowest cost of acquiring information has a comparative advantage in specialising in screening loans. Thus there exists a fully separating equilibrium where the best bank pays the cost to acquire information and attracts effort making entrepreneurs that are most efficient when providing effort, while the other banks do not screen and attract entrepreneurs that are less efficient in terms of effort. The different ingredients of the model are the following. First I consider three types of projects, among which two have a positive net present value (NPV): if I had only two projects (one positive NPV, one negative NPV) then there would be only one equilibrium contract, and screening would allow only the most efficient bank to exist in equilibrium, leaving no room for banking heterogeneity. Second, moral hazard is necessary to obtain a cap on the maximal loan amount that prevents shirking associated with the negative NPV project. This is the standard source of procyclicality as in Holmstrom and Tirole (1997). Third, if there exists at least two heterogeneous banks, then banks offer a pool of contract from which each entrepreneur picks the one that best suits his need, giving rise to adverse selection. Switching to random matching between banks and firms would remove any rationale for bank contract competition, making the heterogeneity in banks cost efficiency irrelevant. Last, in an environment with contestability and free entry in banking, no such market seg- 3

4 mentation would occur. As banks would just break even, a pooling equilibrium could arise with banks indifferent to investing in screening technologies. Also the absence of banks profits would make the distribution of screening costs completely irrelevant among them: banks behaviour would be driven by their absolute level of efficiency, not their relative efficiency. Thus, bank competition determines the importance of heterogeneity in banking efficiency for lending dynamics and credit allocation. The main outcome of the paper seems to be in line with the data. The empirical investigation on a panel of 20 OECD countries over the period is consistent with the existence of a trade-off between bank allocation efficiency and bank cyclical pattern in the presence of bank heterogeneity, especially when bank competition is low. On the one hand more banking heterogeneity in screening abilities is detrimental to aggregate productivity. But on the other hand banks less efficient in their screening abilities tend to feature a lower cyclicality of their lending so that they could contribute to reducing the volatility of lending fluctuations. Capturing banks efficiency in screening abilities is an empirical challenge while most of the literature focuses on bank cost efficiency. However cost efficiency and screening abilities are two closely related concept. Berger and De Young (1996) suggest that cost-inefficient managers are also poor portfolio managers associated with a future increase in non-performing loans. In order to capture the screening efficiency of banks, I use several standard cost to income ratios from which I net out effects that are not related to screening abilities, such as bank business model, bank risk taking profile or macroeconomic conditions. Overall, the results of the paper shed light on the importance of bank heterogeneity, an issue that has received too little attention so far. First the main policy implication would be that overall banking efficiency is not enough to ensure allocation efficiency: a more granular approach is required to make a sound assessment of a banking sector efficiency, as more banking heterogeneity is detrimental to aggregate productivity. Second, it may not be desirable to favour the development of banking structures that feature a lower cyclicality of aggregate lending unless the sources of cyclicality are well understood. Indeed less cyclicality at the bank level can signal a lower efficiency in screening abilities. Third, lower bank competition for loans to low yield entrepreneurs can indirectly increase the incentives to provide effort and favour more productive projects. Fourth, banking structure reforms that would modify the competitive setting or impact 4

5 banks incentives to engage in screening should not implicitly favour banking heterogeneity. Else possibilities of rent extraction, for instance across different level playing fields, would lead to larger allocation inefficiencies. This is one way to understand the Basel II credit risk framework that generates some degree of market segmentation. Banks that paid the cost to the more flexible regulatory status (internal-ratings-based approach) benefit from a comparative advantage that gives them an incentive to engage in lending that requires more bank equity as they can adjust the risk weights more easily. Fifth, my framework calls for a more cautious analysis of banks optimal business model. On the one hand externalities and competition across business lines can generate sub-optimal specialisation by modifying borrowers incentives. But on the other hand lending to the most efficient entrepreneurs is not necessarily the optimal specialisation for all banks. The structure of the loans market is an endogeneous feature that depends on banks comparative advantage. This paper takes a new stance on two unsettled debates. The granular hypothesis whereby the distribution of banks abilities in acquiring entrepreneurs specific information matters provides a new explanation for the trade-off between financial deepening 3 that favours growth but may harm financial stability 4 : the extent of the heterogeneity in banks screening costs can harm allocation efficiency while reducing the sensitivity of aggregate lending to productivity changes. In addition, the paper may to some extent explain the mixed result on the impact of banking competition. 5 The lack of sufficient competition is more detrimental on market segments for high yield projects while on market segments for lower yield projects it may favour incentives to make effort. The next section presents the two-sided group matching model with heterogeneous banking that builds on Holmstrom and Tirole (1997). Section 3 derives the equilibria with or without free entry and contestability in the banking industry and concludes that the competitive set-up is crucial for banking heterogeneity to have real consequences. Section 4 presents the distortions associated with banking heterogeneity, whether in terms of aggregate productivity or lending 3 The finance and growth literature backs the idea that deeper financial markets (Levine, 2005; Rajan and Zingales, 1998; Wurgler, 2000) and a larger financial sector (King and Levine, 1993; Demirgüç-Kunt et al., 2008; Hartmann et al., 2007) would have a positive impact on capital allocation efficiency and growth. 4 A more developed financial sector increases volatility (Kose et al., 2003; Levchenko et al., 2009), with crises being usually preceded by rapid out-of-trend growth in financial aggregates (Kaminsky and Reinhart, 1999; Alessi and Detken, 2009) 5 Banking competition can favour (see among others Shaffer, 1998; Cetorelli and Gambera, 2001 Berger et al., 2004) or harm (see for instance Petersen and Rajan, 1995 or Bonaccorsi and Dell Ariccia, 2004) firms creation and access to lending. 5

6 cyclicality. Eventually section 5 provides evidences suggesting the implications of the model are consistent with the data. Last section 6 concludes. 2 Model 2.1 Heterogeneous entrepreneurship sector A firm, set up by an entrepreneur, can only have recourse to a single financial intermediary to get a financing; the type of firms I focus on here is small and medium sized firms that cannot issue debt directly on the stock markets. Entrepreneurs can undertake three types of project, High, Medium or Low, which are associated with a high, medium or low probability of success, respectively p H, p M and p L, with p H > p M > p L > 0. Denote H = p H p M and M = p M p L. For a given productivity level α, interest rate r, cost of effort e and bank information acquisition costs c, both H and M projects have a positive NPV, while project L has a negative NPV: Assumption 1. αp H r e c > αp M r > 0 > αp L r Because of the presence of the negative NPV project, I have the classical source of moral hazard which forces banks to provide an adequate loan contract in order to prevent entrepreneurs from diverting part of the resources supposed to be invested in the firm in order to reap a private benefit b. Then the simultaneous existence of two positive NPV projects creates an other source of moral hazard, which is the natural counterpart of having an heterogeneous entrepreneurship sector. I consider a continuum of entrepreneurs indexed by their effort cost e per unit of capital invested in the firm; for simplicity the density function f(e) is assumed to follow a uniform distribution e U [ e min ; e max]. Thereafter in the paper, I use e as the cost of effort of some entrepreneur picked in the previous distribution. Thus entrepreneurs face the following moral hazard problem: if they choose to undertake a high yield project H, they will have to bear a pecuniary cost of effort e. However, if they choose to undertake a medium yield project M, the cost of effort will be γe, i.e. proportionally less than the entrepreneurs type if the maximum effort was provided; for simplicity, I set γ = 0 as it allows to derive closed-form solutions. Effort cost depending on the project undertaken is thus given by: 6

7 e, for j=h, then proba of success p H E j = 0, for j=m, then proba of success p M b, for j=l, then proba of success p L Then entrepreneurs will default with a positive probability 1 p j, j {H, M, L}, and I assume that everything is lost in case of default. Henceforth the capital needed by an entrepreneur to run his firm has to be borrowed at a higher cost than the market risk-free interest rate. Entrepreneurs will first invest their own wealth A, which is homogeneous across all of them, and borrow B, which will depend on entrepreneurs type, to run a project of size k = A + B. Note that, by definition, for the same positive NPV project and a linear production function, an entrepreneur will seek to contract with the bank offering the largest loan. The profit of an entrepreneur is expressed as follows: π j = p j (y i R i B i ) E j k i (1) with k i = B i + A, i {h, l} the type of bank and j {H, M, L} the type of project undertaken, with high or low effort. y = αk i is a constant return to scale production function with productivity parameter α; the price of the output is normalized to 1. Assumptions 2 and 3 below are necessary conditions for the borrowed amounts to be positive in the presence of moral hazard. It can be understood as follows: due to the presence of fixed costs E j A and constant returns p j αa, the marginal gain of making effort (behaving) is lower than shirking (diverting funds), even if, on average, the entrepreneur is better off making effort and behaving. Assumption 2. H α > e > H (α R i ) Assumption 3. M α > b > M (α R i ) 2.2 The heterogeneous banking sector I introduce some heterogeneity in the banking sector in the form of a different cost structure. I consider N competing banks 6 ranked by their different cost of acquiring information about { } entrepreneurs type 7 c c l,1, c h,2,..., c h,n. c l stands for the bank featuring the lowest cost of 6 As N, I am back in the perfectly competitive case as the cost difference between banks becomes infinitesimal. Conversely, with the Bertrand duopoly approach N = 2, I get a closed form solution for the equilibrium degree of monopoly power. 7 Throughout the paper, I use information acquisition and screening costs interchangeably. 7

8 acquiring information, while c h,n {2,...,N} for the banks featuring higher costs of doing so, that is to say for some n {2,..., N}, I have c h,n = (1 + φ n )c l with φ n > 0. In the duopoly case where N = 2, φ is the degree of bank heterogeneity in information acquisition abilities. This screening cost c includes both the cost of information acquisition about the type e of the entrepreneur the bank faces, but also the cost of premium banking services s that are offered to high yield and effort making entrepreneurs. To some extent, being financed by a bank that rightly identified effort making entrepreneurs helps to implement the high yield project as financial services can be adjusted to specific needs (for instance overdraft allowances, credit lines, personal adviser...). When an entrepreneur undertakes effort but without being recognised as such by a bank, he saves on the part of the information acquisition cost that would have been included in the interest rate of the loan, but he still has to bear the cost associated with the premium banking account that would have been offered by the bank; equivalently, the entrepreneur faces a pecuniary cost s of not benefiting from those banking services. 8 Each competing financial institution may design several loan contracts C(R, B) given by the interest rate R and the loan size B for a given level of personal contribution A. The type of the entrepreneur is not observed at the contract design stage, but the bank knows that some entrepreneurs will have to be compensated for their effort and takes it into account when designing a contract from which the entrepreneur will not deviate. Henceforth, each bank will design at most two types of contracts for entrepreneurs making effort (H project) and those making less effort or shirking but who do not misbehave (M project). In addition, when designing its set of contracts, each bank will take into account the fact that entrepreneurs will compare the different loan contracts, so that banks engage in ex-ante contract competition with each other before finalising their contracts. This seems realistic as banks usually fix their credit standard every month by taking into account both their financing ability as well as the situation of competitors, and on a day-to-day basis they only adjust generic contracts to each borrower, depending on their assessment of the type of the borrower they face. To finance their loans, banks have to levy funds on the capital markets at the risk-free interest rate r; their role is thus to pool idiosyncratic risks associated with individual loans in order to offer a constant return on savings that does not depend on the probability of success of the firms. Thus a bank will offer a loan contract that covers both the cost of financing 8 The presence of this cost allows obtaining closed form solutions by introducing a trade-off so that screening is indeed chosen by all good entrepreneurs despite the additional costs. However this does not impact the results of the paper, neither on the productivity nor cyclicality statement about the impact of banking heterogeneity. 8

9 r (or opportunity cost of providing a loan), and the screening cost c if it decides to acquire information on borrowers. Π i = p j R i B i c i k i rb i (2) with i {h, l}. For consistency with the NPV assumptions, financing the High yield entrepreneurs by screening them needs to be within the feasible set of the bank so that, at the margin, if the bank does not adjust its loan size nor its interest rate on loan to entrepreneurs effort, the bank is better off financing H-yield projects compared to the M-yield ones: Assumption 4. H R i c i Note that I abstract from differences on the liability side between banks in order to isolate the effect of bank screening cost heterogeneity both on credit allocation and credit fluctuations, and show that despite the fact that one type of bank is clearly dominated higher information acquisition costs are not compensated for instance by easier access to capital markets, it may have non trivial implications in equilibrium in a model with entrepreneurs heterogeneity. 2.3 Information and payoffs Information. Ex-ante, the banks do not know the specific features of the entrepreneurs neither e nor b but know each distribution among the pool of entrepreneurs. Ex-post, after the contracts have been designed by the banks, for each entrepreneur who enters a bank, it immediately reveals its private benefit from shirking and diverting funds b, and, upon information acquisition by the bank, its effort cost e is revealed. entrepreneur decision effort or not observable unobservable distribution of effort cost individual effort cost bank decision get information about effort type observable information acquisition cost Note that contract commitment is not strictly speaking necessary in equilibrium as the incentives are such that neither the entrepreneurs nor the banks would find it profitable to 9

10 Table 1: Matrix of costs for entrepreneurs/banks info acquisition/ no info acquisition/ (entrepreneurs ; bank) tailored contract standard contract low cost bank l high cost bank h High yield/effort (e; c l ) (e; c h ) (e + s; 0) Medium yield/no effort (0; c l ) (0; c h ) (0; 0) Low yield/run away ( b; c l ) ( b; c h ) ( b; 0) Table 2: Matrix of payoffs for entrepreneurs info acquisition/ tailored contract no info acquisition/ standard contract High yield/effort p H αk i H p HR i H Bi H eki H p H αk i H p HR i H Bi H (e+s)ki H Medium yield/no effort p M αk i M p MR i M Bi M p M αk i M p MR i M Bi M deviate as their decision to match with each other is driven by their respective maximisation program. Payoffs. Table 1 summarises the costs faced by entrepreneurs and banks, depending on the amount of effort provided as well as the action taken by the banks to screen borrowers or not. I assume that banks specific ability compared to market finance is to screen out bad projects for sure. So the last line of the table with low yield negative NPV projects cannot be an equilibrium and thus I do not display it in further tables. Then tables 2 and 3 diplay the payoffs of the different players depending on their action. The part highlighted in blue corresponds to the cost of the loan for the entrepreneur that is also the revenue of the bank. Model representation. The representation of the model is displayed in figure 1. At the contract design stage, each bank offers two contracts with or without information acquisition. The set of contract active in equilibrium as well as its precise definition (B, R) will depend on the bank competition setting. The contract labelled tailored is adjusted to each entrepreneurs Table 3: Matrix of payoffs for banks info acquisition/ tailored contract no info acquisition/ standard contract High yield/effort p H R i H Bi H cki H rbi H p H R i H Bi H rbi H Medium yield/no effort p M R i M Bi M cki M rbi M p M R i M Bi M rbi M 10

11 specificities as the bank acquired the information about the actual cost of effort. Then the entrepreneurs will self-select the contract that best suits their needs and provide effort accordingly. I call the model two sided group matching as banks and entrepreneurs choose each other: the banks take into account which type of projects it is likely to finance (H, M or L) depending on banking competition, and the entrepreneurs decide which project to undertake and select the bank contract that maximises their profit depending on their individual effort type. Here the social benefit in having financial intermediaries lies in their ability to perfectly screen out bad projects with negative NPV (L project). If one was to allow financing by outside experts, they would not be able to monitor and discriminate depending on the cost of effort, hence leading to a pooled equilibrium where outside financiers would treat everyone like the worst agent. 11

12 Figure 1: Sketch of the model of two-sided group matching 1 Bank l,1 information acquisition cost c l,1 tailored contract 1 effort H project e min p H 1 p H αk l 0 12 competition? Bank h,2 no information no information information acquisition cost c h,2 standard contract standard contract tailored contract 2? run away L project? no effort M project entrepreneurs e max p M 1 p M αk h 0 contract design two-sided group matching production

13 3 Equilibria I want to investigate the impact of banking heterogeneity and thus I will compare the market equilibrium with different degrees of banking heterogeneity for different market setup. Comparisons with the optimum are left for the appendix A. The model of two sided group matching has four main ingredients, all of them being necessary to analyse banking heterogeneity and its consequence on lending allocation and lending variation. Three types of projects, among which two have a positive NVP. If I had only two projects (one positive NPV, one negative NPV) then there would be only one equilibrium contract, and only the most efficient bank would exist in equilibrium. Thus having two positive NPV projects is the pre-condition to investigating the impact of competition among heterogeneous banks. Moral hazard. It is necessary to get a cap on the maximal loan amount to prevent shirking associated with the negative NPV project. This is the standard source of procyclicality as in Holmstrom and Tirole (1997). Adverse selection. If there exists several heterogeneous banks, firms can always compare deals across banks. This is the source of cross-sectional heterogeneity in the cyclicality of bank lending. When banks all offer the same contract, i.e. there is a pooling equilibrium for banks, then adverse selection is not relevant. Instead, switching to a random matching between banks and firms would remove any rationale for competition between banks, so that the relative cost structure of banks becomes irrelevant and heterogeneity no longer matters. Competition. This is a key ingredient as it will determine the market structure and thus the importance or not of the presence of less efficient banks. This is what makes banking heterogeneity relevant for lending dynamics and credit allocation. If banks do not compete, their relative efficiency is irrelevant. Conversely if there is free entry and perfect competition, the infinitesimal difference across banks makes the impact of bank relative efficiency vanish. 13

14 3.1 Equilibria with free entry in the banking industry Pooled equilibrium If banks do not obtain information on entrepreneurs type, then the only source of difference between banks disappear. All banks offer the same type of contract, which is found recursively depending on the expected provision of effort by entrepreneurs. Indeed, even if entrepreneurs are not screened so that the bank ignores their willingness to undertake effort and thus does not adjust the loan offers, some of them may still find it profitable to provide effort: their cost of effort is still partly compensated by the larger probability of success, but not by more attractive borrowing conditions. Entrepreneurs find themselves better off making efforts if the following effort compatibility (EC) condition is satisfied: p H (αk RB) ek p M (αk RB) (3) which holds for entrepreneurs with a cost of effort e ē 1. For a sufficiently small private benefit b, the incentive compatibility (IC) condition that prevents entrepreneurs from undertaking the negative NPV project is always met: p M (αk RB) p L (αk RB) + bk (4) If banks technology did not allow banks to screen out negative NPV projects, it is easy to show that the loans market would collapse with a markets for lemons argument. As the production function is linear, entrepreneurs will always ask for the largest possible loan, so that the pooling equilibrium loan contract C 1 (B 1 ; R 1 ) is given by the maximal loan size B 1 that can prevent funds diversion, i.e. that satisfy b b 1 in equation 4. The interest rate banks will offer is then given by the free entry condition depending on the relative share of entrepreneurs making efforts or not, i.e. below or above the effort threshold ē 1. Proposition 1. When there is free entry in the banking sector, under assumptions 1, 3, there exists a pooling equilibrium such that all banks provide a single loan contract C 1 (R 1, B 1 ) without information acquisition. High yield projects are undertaken by low cost of effort entrepreneurs e ē 1 and Medium yield projects are undertaken by high cost of effort entrepreneurs e > ē 1. As the comparative advantage of efficient banks in acquiring informations about the effort 14

15 Table 4: Matrix of costs for entrepreneurs/banks: equilibrium selection (entrepreneurs ; bank) info acquisition/ no info acquisition/ tailored contract standard contract High yield/effort (e; c l ) (e + s; 0) Medium yield/no effort (0; c l ) (0; 0) type of entrepreneurs vanishes in the presence of free entry, no bank would make positive profits by screening firms so that banks have no incentive to deviate from the pooled loan contract Partly separating equilibrium If banks decide to invest in information acquisition, then the most efficient bank will have a comparative advantage in screening the type of entrepreneurs it faces (c l < c h ). Thus the matrix of possible choices is reduced to 4. The most efficient bank l will be able to offer more attractive loan contract after paying the information acquisition cost. The banks participation constraint (PC) with free entry of the contract with high yield entrepreneurs is given by: p H RB c i k = rb (5) Where the expected return of the High yield project net of the screening cost equals the opportunity cost of financing the project. So the equilibrium interest rate R 2,H is more attractive for the most efficient bank with a low screening cost c l. When the bank knows entrepreneurs type, the loan size it offers is a function of the cost of effort of each entrepreneur and is given by the maximal amount that satisfies the (EC) constraint of equation 3. The interest rate R 2,H is positive if the expected marginal return of an entrepreneur making effort is larger than the marginal cost of acquiring information on entrepreneurs type: Assumption 5. c < p H (α e H ) Note that, due to the linear setup, it is meaningful here to focus on a restricted parameter space. If the previous assumptions 2 to 5 ensure quantities and prices to be positive, the following assumption ensures that, when an entrepreneur is incentivised to make more efforts for a given loan size, he does not simultaneously have incentives to divert funds, and vice-versa, which would be economically meaningless. Assumption 6. b < e M H 15

16 But at the same time, all banks, whether more or less efficient, can also offer a loan contract without information acquisition, as mentioned in the previous subsection. However, as the best entrepreneurs prefer to be screened to get access to more attractive lending standards adjusted to their individual cost of effort, only a smaller subset of entrepreneurs could possibly decide to make effort without being screened. Thus the mass of entrepreneurs that have a cost of effort below the threshold ē 1 and choosing a bank loan contract without screening is smaller. This makes the pooling interest rate higher (the proportion of non-effort making entrepreneurs is higher), which, in turn, decreases the incentive of entrepreneurs to make effort if they do not benefit from the more attractive lending standards associated with bank screening. Eventually, no entrepreneur chooses to make effort if his type is not revealed to the bank. Only non-effort making entrepreneurs accept to sign up for a loan contract that does not include information acquisition by the bank. Then entrepreneurs self-select the contract, with or without information acquisition on behalf of the bank, that maximises their profits. Thus entrepreneurs choose their bank and their contract type depending on their position relative to the cut-off effort cost ē 2 that makes entrepreneurs indifferent between the loan contracts with or without information acquisition. Proposition 2. When there is free entry in the banking sector, under assumptions 1 to 6, there exists an equilibrium that is partly separating such that only the most efficient bank with low screening cost attracts low cost of effort entrepreneurs e ē 2 that undertake High yields projects, while Medium yield projects are undertaken by high cost of effort entrepreneurs e > ē 2 that obtained a loan contract offered by any bank that does not require the bank to invest in information acquisition. Two sufficient conditions are s > s and the cost c of information acquisition by banks not too large, else it is down to the pooling equilibrium of proposition Equilibria without free entry in the banking industry I now turn to the more interesting cases where the banking industry is not fully competitive, that is to say the assumption of contestability of the incumbent banks does not hold. As a result, banks can extract rents and design their menu of loan contracts in order to maximise their profits, while in the previous section the equilibrium was given by entrepreneurs maximising their profits as banks would just break even. 16

17 3.2.1 Partly separating equilibrium : limit pricing competition On the High yield segment of the market, the most efficient bank in terms of information acquisition will be able to offer the most attractive loan contract that includes screening. As all banks allow for the maximum leverage demanded by the entrepreneurs, entrepreneurs will choose the contract offering the lowest interest rate. So ex-ante, the high-ability bank will design a contract that offers an interest rate which will be low enough to drive the low-ability banks out of the market. As a result, the most efficient bank will be able to extract a surplus by offering a limit interest rate R 3,H = r Q higher than the fair pricing of default risk r p H. Henceforth 1 Q can be thought of as the risk premium adjusted for competition so that the bank most efficient in screening generates a positive net interest margin which features a countercyclical markup. R 3,H is positive under assumption 5. On the segment of the market serving entrepreneurs that undertake Medium yield projects, all banks make zero profits as they are perfectly competitive since banks have the same opportunity cost of lending, with a PC given by: p M RB = rb (6) Entrepreneurs self-select the loan contract they find most profitable among the menu of contracts offered by the different banks, which generates an endogeneous market segmentation between High and Medium yield projects whether entrepreneurs have an effort cost above or below the cut-off ē 3. Proposition 3. With limit pricing competition, under assumptions 1 to 6, there exists an equilibrium that is partly separating such that only the most efficient bank attracts low cost of effort entrepreneurs e ē 3 that undertake High yields projects, while Medium yield projects are undertaken by high cost of effort entrepreneurs e > ē 3 that obtained a loan contract offered by any bank that does not require information acquisition. Last, there is no incentive to deviate from the equilibrium. This can be readily observed from the payoff matrices. For the banks, there is no incentive to start acquiring information if the entrepreneur is not making efforts as the bank would make losses and its participation constraint in 6 would be violated (table 6). Likewise for entrepreneurs, they would have no incentive to select a bank that does not screen them if they undertake efforts (table 5). On the one hand, screening allows obtaining a larger loan size without paying the access to premium 17

18 Table 5: Matrix of payoffs for entrepreneurs : equilibrium selection info acquisition/ no info acquisition/ tailored contract standard contract High yield/effort p H αkh l p HRH l Bl H ekl H p H αkh i p HRH i Bi H (e + s)ki H Medium yield/no effort p M αkm l p MRM l Bl M p M αkm i p MRM i Bi M Table 6: Matrix of payoffs for banks : equilibrium selection info acquisition/ tailored contract no info acquisition/ standard contract High yield/effort p H R l H Bl H ckl H rbl H p H R i H Bi H rbi H Medium yield/no effort Π l H > 0 Πi H = 0 p M R M l Bl M ckl M rbl p M M RM i Bi M rbi M Π l H < 0 Πi H = 0 banking s. On the other hand, the entrepreneur who is not screened saves on the cost of the loan that does not include the premium due to screening costs nor monopoly power. So there necessarily exists a s > s for which the absence of screening is excessively detrimental to the entrepreneurs. However, for s < s, some effort making entrepreneurs could still prefer not being screened out. They would then enjoy the pooling equilibrium described in the previous section, but it is not stable anymore. Indeed this deviation of entrepreneurs from the bank point of view means that it makes less profits as it only breaks even in the case of pooling equilibrium (table 6). Thus the screening bank l should still acquire information about the entrepreneur, but it should reduce the extent of its monopoly power to prevent any deviation from the (screening;effort) equilibrium. The case with s < s would only create a discontinuity in the ability of the most efficient bank to use its monopoly power, but it does not change any result without adding further intuition. Hence I do not elaborate further on this case. Corollary 1. With limit pricing competition, (i) the markup on the interest rate offered to effort-making entrepreneurs is countercyclical and (ii) the most efficient bank makes positive profits. Figure 2 displays the state space (B,R) for the case of the High yield-compatible type of contract. The demand of funds corresponds to the possible contract that would maximise entrepreneurs profits while still avoiding shirking; it is a function decreasing in the cost of the loan size. Then the supply of funds by the banks is such that the least efficient bank (bank h for 18

19 Figure 2: H-type contract indifference curves B Π l < 0 Π l > 0 supply iso-profit for Π h = 0 demand entrepreneurs A 1 E A 2 supply iso-profits for Π l = 0 Π h < 0 Π h > 0 R = r Q R high costs) would require a larger interest rate for an equivalent loan size offered by the most efficient bank (bank l) as it has to cover higher screening costs. The competitive equilibrium with heterogeneous banking in is depicted by point E, i.e. when the least efficient bank with higher information acquisition costs c h is driven out of the market and makes no profit (Π h = 0 while Π l > 0) as a result of the competition in contracts. To the left of point E, only the most efficient bank operates and as long as its monopoly position cannot be contested on this segment (contrary to the case with free entry), it has no incentives to move to point A 1 where it would break even. Figure 3 displays the equilibrium of the model with limit pricing competition given in proposition

20 Figure 3: Equilibrium with limit pricing competition 1 Bank l,1 information acquisition cost c l,1 tailored contract 1 (B3,H, R 3,H ) effort H project e min p H 1 p H αk l 0 20 competition Bank h,2 no information no information information acquisition cost c h,2 standard contract (B3,M, R 3,M ) standard contract tailored contract 2 since c l,1 < c h,2 run away L project no effort M project entrepreneurs e max cutoff ē 3 p M 1 p M αk h 0 contract design two-sided group matching production

21 3.2.2 Fully separating equilibrium : strategic competition Now, due to heterogeneous screening abilities or information acquisition costs, a rent is extracted by the most efficient bank on the High yield segment of the market. In principle the Medium yield segment of the market is such that all banks make zero profits as they all have the same opportunity cost of lending. But instead of competing on the M-segment of the market, the most efficient bank will seek to enter the Medium yield segment of the market only if it does not reduce its profitability on the High yield segment of the market. That is to say, the most efficient bank will take into account the adverse selection process of the entrepreneurs that result from the menu of contracts offered both on H and M yield segments, and solve for the equilibrium contract backward. So the design of the Medium yield contract by the most efficient bank will now be subject to a Profits-Preserving (PP) constraint. Indeed, with a fairly priced M-contract, some entrepreneurs will find it relatively more attractive than the contract supporting High yield. However, the efficient bank, by reducing its competition to attract Medium yield projects would implicitly leave some degree of market power to the less efficient banks on the M-segment of the market. Thus this setting would ensure that the Medium yield compatible contract is now relatively less attractive for some entrepreneurs than the High yield compatible contract. Henceforth, as the most efficient bank relaxes the competition on the M-segment of the market, more entrepreneurs would choose H-yield projects, which means more profits for the efficient bank that is the only one operating on the High yield segment of the market. Then, in the duopoly case, the less efficient bank with higher screening costs h will benefit from the market power it gets on the M-segment of the market and thus will maximise its now positive profits which are given by the following equation: e max e max Π h total = Π h de = ē 4 ē 4 (p M R 4,M B 4,M rb 4,M ) de = (e max ē 4 ) (p M R 4,M r) B 4,M (7) Where ē 4 corresponds to the threshold cost of effort resulting from the adverse selection process of the menu of loan contract, above which entrepreneurs prefer to make the minimum effort and undertake M-yield project without the bank investing in information acquisition. To pin down the equilibrium interest rate associated with the rent extraction, the less efficient bank faces the following trade-off given in equation (7): by increasing its market power, it 21

22 extracts more rent per unit of loan (second term), but the size of each individual loan decreases (third term) and the number of customers choosing M-projects decreases (first term) as H- supporting contracts become relatively more attractive. Proposition 4. With strategic and imperfect competition, under assumptions 1 to 5, there exists an equilibrium that is fully separating such that only the most efficient bank attracts low cost of effort entrepreneurs e ē 4 that undertake High yields projects, while less efficient banks, offering loan contract without information acquisition, attract entrepreneurs with high costs of effort e > ē 4 that undertake Medium yield projects. In the duopoly case, the equilibrium interest rate is such that it maximises the profits of the most efficient bank argmax R 4,M >r/p M Π h total. In the N banks case, the equilibrium interest rate depends on the extent of the imperfect competition in the banking industry. Corollary 2. With strategic and imperfect competition, all banks, whether more or less competitive in their screening abilities, make positive profits and the markup on High yield projects is countercyclical. The competitive equilibrium on the M-yield segment of the market with heterogeneous banking is depicted in figure 4 by point E. A 1 corresponds to the crossing between the demand schedule of an entrepreneur that maximises his profits and the break-even curves of the two banks i {h, l} in the competitive case. If the most efficient bank (bank l for low cost) decides not to compete, the less efficient bank (bank h for high costs) can move to a point at the right of A 1. By moving from point A 1 towards E, the less efficient bank decreases the attractiveness of its M-contract and de facto increases the profits of the efficient bank on the H segment of the market. The H-segment of the market becomes relatively more attractive via the process of adverse selection of bank contract. Beyond point E, the less efficient bank increases so much its market power that it starts making less profits as more and more entrepreneurs decide not to undertake M-projects any more and the size of M-projects still undertaken is reduced. Figure 5 displays the equilibrium of the model with strategic competition given in proposition 4. 22

23 Figure 4: M-type contract indifference curves B demand entrepreneurs A 2 supply iso-profit for Π h > 0 A 1 E A 3 supply iso-profits for Π i = 0 Π h Π h R = r p M R R 23

24 Figure 5: Equilibrium with strategic competition 1 Bank l,1 information acquisition cost c l,1 tailored contract 1 (B4,H, R 4,H ) effort H project e min p H 1 p H αk l 0 24 competition Bank h,2 no information no information information acquisition cost c h,2 standard contract standard contract (B4,M, R 4,M ) tailored contract 2 since c l,1 < c h,2 run away L project no effort M project entrepreneurs e max cutoff ē 4 p M 1 p M αk h 0 contract design two-sided group matching production

25 4 Distortions associated with banking heterogeneity Banking heterogeneity in screening abilities matters only when it interacts with imperfect banking competition. If the cost of information acquisition itself impacts the offered interest rate of the contract supporting bank screening, the cost differential φ between the most efficient bank and the less efficient ones has no impact on the menu of loan contracts in case of free entry and contestability in the banking sector. Proposition 5. When the banking sector is perfectly competitive, the extent of banking heterogeneity in information acquisition costs has no impact on lending volumes and lending fluctuations. In this static model, the impact of banking heterogeneity in the presence of imperfect competition can be analysed along two dimensions, comparative statics of both the levels of aggregate variables and the deviations after a productivity shock. This would correspond respectively to long run distortions (efficiency) and short run fluctuations (procyclicality). 4.1 Allocative distortions associated with banking heterogeneity Effort decision and adverse selection: the extensive margin With limit pricing competition, when the intensity of banking heterogeneity increases, i.e. the difference of bank efficiency in screening abilities widens, the rent the most efficient bank can extract on high ability entrepreneurs increases. As a result, it is relatively less attractive for entrepreneurs to remain on the High yield, effort-compatible segment of the market, which de facto increases the pool of shirking entrepreneurs who would have otherwise provided effort. However, with strategic competition, a second effect on incentives and effort-making goes in the opposite direction. The introduction of less efficient banks generate a profits-preserving behaviour for the most efficient bank: the residual market power of the less efficient bank on the M-segment of the market increases which reduces the incentive of entrepreneurs to shirk. If the intensity ψ of the market power on the M-segment by the less efficient bank is too small, that is to say if the financing condition of the M-contract become too attractive, then there is an excessive number of entrepreneurs choosing not to undertake efforts. In the meantime, if the heterogeneity in bank efficiency φ is too high, then having less efficient banks allows for an excessively high rent to be extracted on the H-segment of the market which will discourage effort. So, in this strategic set-up, the worst case in terms of the distortions induced by banking 25

26 heterogeneity on effort making, that channel via the adverse selection process, would be a very high level of heterogeneity in screening efficiency and high market competition in the non-effort making segment of the market. Proposition 6. If the banking sector is imperfectly competitive, the introduction of heterogeneity in bank information acquisition efficiency distorts effort making incentives towards less productive projects compared to the equilibrium without bank heterogeneity. In a strategic competition setting, the distortions on effort making is worst when (i) bank heterogeneity is high and (ii) the market power of the less efficient banks is low. The natural consequence of proposition 6 is that if less effort is provided, less high-yield projects are undertaken, which reduces realised aggregate productivity further for a given aggregate productivity parameter. Corollary 3. A shock on the distribution of bank information acquisition efficiency reduces average entrepreneurial productivity which is further away from the social optimum. With respect to the social optimum, the logical implication for competition in banking is the following: what is more problematic is the existence of monopolistic competition on market segments for good effort-making and high yield projects entrepreneurs, while the presence of monopolistically competitive financial institutions able to extract rents on low effort, low yield entrepreneurs can improve aggregate productivity and allow for a better allocation of resources Entrepreneurs leverage and moral hazard: the intensive margin The endogenous market segmentation that result from the introduction of banking heterogeneity generates some degree of market power that allows banks to extract a rent over the fair pricing of the loan contract. Consequently, banking heterogeneity in information acquisition costs generates a missallocation of resources that limits the extent of entrepreneurs leverage (as their own funds A is constant and identical for all). Funds are not channelled efficiently to the most productive entrepreneurs, as larger financing costs reduce their willingness to make effort, so that the size of their loan has to be reduced by the bank in order to preserve effort incentives, i.e. banks profits. Proposition 7. If the banking sector is imperfectly competitive, the introduction of heterogeneity in bank information acquisition efficiency reallocates resources away from entrepreneurs, especially effort making ones, towards banks. 26