Credit, Bankruptcy Law and Bank Market Structure

Transcription

1 Credit, Bankruptcy Law and Bank Market Structure Manos Kitsios January 4, 212 Abstract Bankruptcy law and the degree of competition among financial intermediaries vary across countries. This paper examines their interaction in the creation of financial frictions and their effect on aggregate economic activity. It is shown that, under a perfectly competitive credit market, any deviation from providing absolute priority to creditors over shareholders in bankruptcy claims leads to a greater credit rationing of investment projects, a higher spread between loan and deposit interest rates and a larger number of business failures. Nevertheless, violations of the Absolute Priority Rule APR) are often observed in practice, as under Chapter 11 of the US Bankruptcy Code. The violation of APR is shown in this paper to be justified on efficiency grounds when there is a monopolistic intermediation structure or implicit collusion among banks in setting the loan interest rates. 1 Introduction The recent financial crisis has led economists to re-examine the behaviour of financial institutions over the business cycle. The standard macroeconomic models have established that credit frictions may amplify macroeconomic fluctuations. Nevertheless, the focus has been largely on the frictions resulting from information imperfections pertaining to borrower behavior before or after a loan agreement. This paper follows the recent surge in the macroeconomic literature that attempts to include frictions emanating from an imperfectly competitive banking sector. By accounting for various types of banking competition, we analyze the resulting spread in the interest rate faced by borrowers and depositors. The interaction of the degree of banking competition with the bankruptcy law regime is shown to affect credit conditions and, therefore, the nature of business cycle phenomena. Government credit programs may generate efficiency improvements when there is imperfect banking competition and/or a debtor friendly bankruptcy system is in place. The purpose of this paper is to examine the macroeconomic implications of credit rationing and the interest rate spread under various combinations of supply and demand conditions in the loan market. On the supply side of the loan market, we examine perfect competition, monopolistic intermediation and implicit collusion between oligopolistic banks. Under perfect competition in I am grateful to Professor David Newbery for his valuable comments and encouragement. I would also like to thank Oliver de Groot, Dr. Flavio Toxvaerd and seminar participants at the Doctoral Conference of the Judge Business School and the PhD Theory Workshop of the University of Cambridge for helpful comments. All errors are mine. Address for correspondence: Faculty of Economics, University of Cambridge, Austin Robinson Building, Sidgwick Avenue, Cambridge CB3 9DD, United Kingdom. ek337@cam.ac.uk 1

2 intermediation, the difference between borrowing and lending rates is driven by the agency cost arising from information asymmetries regarding the investment outcomes of the borrowers. While entrepreneurs freely observe the return on their projects ex-post, banks are able to do so only by incurring a monitoring cost. This ex-post information asymmetry concerning the project return is the source of agency costs in our framework that lead to credit rationing 1. Banking market power that arises in the context of monopolistic intermediation and implicit collusion between banks introduces an additional wedge in the credit spread. Each bank pools funds from many depositors and is able to fully diversify its loan portfolio by financing a continuum of entrepreneurial projects with idiosyncratic returns distributed independently and identically across firms 2. The savings market is perfectly competitive under the assumption that deposits are perfect substitutes to Treasury bills and the supply of loanable funds is assumed to be sufficiently high as to finance all entrepreneurial projects. The existence of banks in our paper can be justified on the basis that they provide a solution to the lenders coordination problem of monitoring their borrowers. Banks issue deposits and monitor loan contracts just as in the costly state verification models of Diamond 1984) and Williamson 1986, 1987). Under the information asymmetry regarding project outcomes described earlier, the optimal financing contract between an entrepreneur and a bank takes the form of debt. Default on debt contracts is governed by bankruptcy law. It is shown in this paper that the standard debt remains the optimal contract even when the bankruptcy law features violations of the absolute priority rule 3. The absolute priority rule suggests that creditors should be paid when the borrowing firm goes bankrupt before the firm s owners receive any value 4. Adherence to the absolute priority rule varies across countries. The United States and France, for example, allow for violations of the APR, whereas the UK and Sweden do not. In this paper, we discuss our model in relation to the bankruptcy procedures followed in the United States, but the model applies to any bankruptcy regime that allows the violation of the APR with some probability. Incorporated firms file for liquidation under Chapter 7 or for reorganization under Chapter 11 of the US Bankruptcy Code. Under Chapter 7, the proceeds from the sale of the firm s assets are distributed to claimholders according to the APR. Chapter 11 allows equity-holders of firms that default on their debt to obtain some value, even when their creditors are not paid in full. During the reorganization process, no payment of interest and principal are made to creditors and no foreclosures on collateral are allowed. Overall, creditors cannot derive any value until a reorganization plan is adopted. The firm emerges from Chapter 11, only when a reorganization plan has been accepted that restructures and redistributes the financial claims on the firm. The Bankruptcy Code encourages bargaining among claimholders during the reorganization process. The debtor can extract deviations from the APR by exploiting the bargaining power provided to him from the exclusive right to propose a reorganization plan to the creditors and by delaying its adoption. Creditors may agree to a deviation from the APR in order to avoid the deterioration of asset values resulting from the delay 1 By assuming that the distribution of project returns is not affected by the action or effort of the entrepreneur, we abstract away from other determinants of credit rationing such as moral hazard or adverse selection. 2 This assumption holds under all intermediation market structures considered in this paper. 3 In our paper, we assume away strategic default on the basis that it is incompatible with the notion of costly state verification. The entrepreneur that has generated enough revenue to repay the debt does not have the incentive to default on the debt, because then the state of the realized return on the investment project is revealed to the creditor and the bankruptcy court via a costly monitoring mechanism. Contrary to Longhofer 1997), we demonstrate that the optimal loan contract takes the form of a standard debt contract by making the realistic assumption that APR violations occur with a probability less than one. 4 The APR also specifies that senior creditors should be paid prior to junior creditors. In this paper, we consider only APR violations between the borrower and a lender. 2

3 in the adoption of a reorganization plan. The early empirical literature on APR violations suggests that these were frequent and significant in size during the 198s. Estimates of the magnitude of the deviations from APR in favor of equity vary between 4 and 1 percent of the firm s value 5, and violations can be observed up to 75% of the sampled bankrupt firms under chapter 11. Bharath et al. 27) provide more recent evidence according to which the frequency and average magnitude of APR violations have declined significantly over the 199s and the 2s. Deviations from the APR were observed 22% of the time, throughout the period from , while the average magnitude of the violations declined to less than 2% of firm value. Deviations from the APR are shown to increase credit rationing under all alternative banking market structures in our paper. Nevertheless, a significant side effect of APR violations is that the interest rate spread declines in the cases of monopolistic intermediation and implicit collusion between banks. In these cases, banks enjoy market power that allows them to profitably introduce an interest rate wedge on the loans received by entrepreneurs. This interest rate wedge is optimally reduced as the magnitude or the frequency of the APR violations increase, because there is a reduction in the liquidation value of the firm that the bank expects to receive in the event of default. The intuition behind this result is that by reducing the interest rate on the loans, the bank indirectly reduces the expected probability of default and, therefore, the probability of experiencing the APR violation. This reduction in the loan interest rate is not possible under the assumption of a competitive banking system, where each bank expects a zero net profit on each loan. Under perfect competition among banks, a more debtor friendly bankruptcy law leads to a higher interest rate spread that reflects the increased agency costs. In section 2, we lay out the partial equilibrium analysis of the contracting agreement between the bank and the entrepreneur. First, we examine the loan contract under perfect banking competition and then we consider the contract terms that a monopolistic bank would set. Section 3 considers the possibility of implicit collusion between oligopolistic banks over the business cycle. It is shown that violations of the Absolute Priority Rule under bankruptcy law might be socially desirable when they mitigate the excessive market power of banks. Section 4 concludes and describes the extensions to the model that will be included in future versions of the paper. 2 Credit Market Entrepreneurs have no assets when they contact the bank for a loan. They own an investment technology that allows them to convert units of output at the beginning of period t into output at the end of the same period. We allow for two sources of heterogeneity among the entrepreneurs with regards to their transformation technology. Entrepreneurs are ex-ante heterogeneous in the fixed cost required to finance their investment at the beginning of period t, because they differ in their ability to set up their individual project. Each entrepreneur has access to one investment project that requires a fixed amount of B z) units of the consumption good, where z is a measure of how costly the entrepreneurial project is. The cost-type of the project is publicly known. Let z be uniformly distributed on [, 1] and B z z) >, so that higher values of z imply a higher cost of investment needed to finance the project 6. 5 See evidence from Franks and Torous 1989, 1994), Eberhart, Moore and Roenfeldt 199), Weiss 199), and Betker 1995). 6 In the example to be introduced later on, we will adopt a simple linear functional form for the investment cost, i.e., B z) = 2 + z. The analysis and conclusions, nevertheless, hold for any functional form that respects the 3

4 The distribution of returns is ex-ante identical across cost-types and is not affected by any action of the entrepreneur. Entrepreneurs are heterogeneous in terms of the ex-post success of their project. The amount of consumption good produced by each entrepreneurial project i is given by: ω i, t t 2.1) where t denotes an economy-wide productivity shock that is known at the beginning of period t and ω i, t denotes an idiosyncratic productivity shock that occurs at the end of period t. Both the entrepreneur and the bank agree on the loan terms at the beginning of period t sharing a common knowledge of the economy-wide productivity shock. Neither the entrepreneur, nor the bank observe the idiosyncratic productivity shock ω i, t at the time of the loan contract. The random variable ω i, t lies in the support [, ω H] and is independently and identically distributed across time and firms with distribution Φ ) and density φ ) which are common knowledge to all agents 7. Let the mean value of the idiosyncratic shock be equal to E ω) = ω H ωφω)dω. The realized return on investment is costlessly observed by the entrepreneurs at the end of period t, whereas an individual banker can learn the return on the entrepreneurial project by paying a monitoring cost µ per unit of the realized output. The asymmetry of information between the borrower and the lender regarding the realized return of the project introduces the first source of financing frictions in our model. Costly verification of the project outcome implies that there is an expected deadweight loss associated with financial contracting. In this setting, the standard debt contract is the optimal contract which minimizes the expected deadweight loss arising from monitoring costs Bankruptcy Law The court decides whether to violate the Absolute Priority Rule, once the entrepreneur defaults on his debt and monitoring takes place. We assume away any possibility of strategic default, so that the entrepreneur does not file for bankruptcy when the realized return of the project allows him to repay the debt. To preclude strategic default, it is sufficient to assume that the court punishes the entrepreneur with a zero payoff when the latter strategically defaults on the debt. Thus, violations of the APR may occur only when the entrepreneur is truly unable to repay the debt in full. In addition, the violation of the APR cannot be contracted away in a loan agreement between the entrepreneur and the bank. Once the entrepreneur files for bankruptcy, it is the court that decides whether the APR violation will take place. Violations of the APR in the credit market are incorporated in the model by assuming that the bankrupt entrepreneur receives a payoff equal to v ω t t ) with an exogenous probability p v. The parameter v, 1) denotes the fraction of the realized value that is kept by the entrepreneur and the probability p v denotes the frequency with which the APR violations occur in bankruptcy proceedings. In what follows, we examine the effect of bankruptcy law on credit market conditions under alternative banking market structures 9. assumptions stated in the main body of the text. 7 Note that the distribution and density functions are independent of the cost-type of the entrepreneurs. 8 Monitoring is assumed to be deterministic, rather than stochastic. Deterministic monitoring yields a standard debt contract as the optimal contract, just as in Townsend 1979), Gale and Hellwig 1985) and Williamson 1986; 1987). Boyd and Smith 1994) calibrate the welfare losses from deterministic relative to stochastic monitoring using U.S. data and conclude that these are very small. 9 The time subscript is suppressed for tractability in the sections that follow. The timing assumptions, nevertheless, are preserved. 4

5 Period t Beginning of period t End of period t - Loan Agreement - ω i is realized - B z), and Φ ω) are known - Entrepreneur repays or defaults - µ, v and p v are known - Bank monitors in the event of default - Court decides on APR violation - Payments are realized Figure 2.1: Timing of the credit market 2.2 Optimality of the debt contract In the appendix, we demonstrate that the optimal contract takes the form of the standard debt contract when the APR violation is taken into account under both a perfectly competitive and a monopolistic intermediary market structure. For each cost-type, the debt contract specifies a fixed payment F z) to the bank under the repayment region and a zero return for the borrower in the case of default. Given that the entrepreneur borrows Bz) units of the consumption good, we can express the fixed payment F z) as R B z)bz), where R B z) is the implicit rate of return on the loan 1 when it is fully repaid. The debt contract can, then, be characterized by the given amount of borrowing B z), the contractual borrowing rate R B z) and the threshold value ω of the idiosyncratic shock ω below which the loan is not fully repaid and monitoring takes place. Bankruptcy is defined as: ω i z) < R B z) B z).the cutoff value of the idiosyncratic productivity shock below which verification takes place and the entrepreneur goes bankrupt is: ωz) = RB z) B z) The cutoff level ω is determined in 2.2) by R B and the borrowing amount B z) for a given value of the productivity parameter. The optimal contract can, therefore, be sufficiently characterized by R B z) for a given loan size B z), since ω can be derived from a combination of these two according to 2.2). 2.3 Competitive credit market structure Let Π F irm and G Bank denote the total expected revenue derived from the loan contract for the entrepreneur and the bank respectively. In the current version of the paper we do not model the savings decision. Each bank holds a diversified portfolio by lending to a large number of borrowers and by borrowing from a large number of depositors. Therefore, contracts with depositors can specify a non-contingent payment of R D per unit deposited, where R D is the market expected return faced by depositors. Deposits are considered to be perfect substitutes to Treasury bills 1 In this paper we use interchangeably the terms implicit rate of return and interest rate. In addition, we will show that the rate of return depends on other parameters as well, not just the cost-type of the project. Given that the rest of the parameters do not differ across entrepreneurs, we will make the dependency on this terms explicit whenever this is necessary to avoid excessive notation. 2.2) 5

6 and they both receive the same rate of return which is the risk-free interest rate i.e., R D = R f ). Under a competitive financial market structure, the banks engage in Bertrand price competition in the loan market. Therefore, the optimal loan contract maximizes the expected profit of the entrepreneur, Π F irm, subject to the participation constraint of the bank provided by 2.4), and the incentive compatibility constraint of the entrepreneur provided by 2.5): s.t. max Π F irm R B ; z ) ˆ R B Bz) ˆ ωh = p v v ω) φω)dω + ω R B B z) ) φω)dω, 2.3) {R B } R B Bz) G Bank R B ; z ) R D B z), 2.4) where Π F irm R B ; z ), 2.5) G Bank R B ; z ) = = ˆ R B Bz) ˆ R B Bz) {1 p v ) ω + p v 1 v) ω µ ω)} φω)dω + 1 p v v µ) ωφω)dω + ˆ ωh R B Bz) ˆ ωh R B Bz) R B B z) ) φω)dω R B B z) ) φω)dω In words, the entrepreneur expects to receive a fraction of the realized value of the project equal to v ω i ) with an exogenous probability p v under bankruptcy i.e., when ω i < RB Bz) ). When solvent, the entrepreneur expects to receive the difference between the realized return of the project ω i and the loan amount R B B z). Under the assumption of limited liability, there cannot exist any loan agreement that would yield a negative payoff to the entrepreneur. Therefore, the participation constraint of the entrepreneur is always satisfied under all loan agreements and under all banking market structures examined in this paper, given that he has no assets and no outside options other than investing in his project. The expected revenue of the bank from the loan contract, G Bank, equals the sum of the expected full repayment of the loan when ω i RB Bz) and the expected realized value of the project net of i) the expected exempted value decided by the court under the APR violation and ii) the proportional monitoring costs incurred when the entrepreneur defaults on the loan i.e., when ω i < RB Bz) ). The participation constraint of the bank given by 2.4) suggests that the expected return on the loan should be above the opportunity cost of lending which is the risk-free interest rate, R D, that deposits receive, multiplied by the loan amount lent to the entrepreneur. One notable difference with similar contracting settings found in the literature is the bankruptcy law feature of APR violations that we have added to the model. The objective function Π F irm ) of the entrepreneur would be decreasing in R B in the absence of APR violations. In that case, the entrepreneur s incentive would be to minimize the value of R B as much as possible, without violating the bank s participation constraint. In section A.1) of the appendix, we demonstrate that the incentive to minimize the value of R B is preserved under the assumption of APR violations The derivations in the appendix assume that the density function φ ) of the idiosyncratic shock ω is nondecreasing. 6

7 and the participation constraint of the bank becomes binding. Let RF B irm be the optimal value of the interest rate chosen by the entrepreneur. Then, RF B irm is the smallest R B for which the following binding participation constraint holds for the bank: G Bank R B F irm;, µ, p v, v, z ) = R D B z) 2.6) The intuition behind this result is that the entrepreneur will extract as much surplus as possible from the loan agreement. The maximum amount of surplus, that can be generated without credit rationing, is obtained when the monitoring costs are the lowest possible. The participation constraint for the bank becomes binding, because the expected profit for the entrepreneur becomes maximal when the bank extracts the smallest possible portion of the generated surplus. We assume that G Bank ) is strictly concave. The strict concavity assumption holds when the density function φ ) satisfies the regularity condition 12 [ωφω)] = φ ω) + ωφ ω ω ω) >. A sufficient condition for this inequality to hold is that the density function is non-decreasing in ω. An example of a distribution that satisfies this condition is the uniform distribution. If G Bank ) is strictly concave, then there exists a unique RBank B arg max G Bank R B ;, µ, p v, v, z ), where RBank ) B, ωh Bz). Let G Bank, µ, p v, v, z) = G Bank RBank; B, µ, p v, v, z ) denote the maximum expected return a bank can earn on a loan to an entrepreneur. Banks take the interest rate on deposits as given. The maximum expected return for the bank net of the lending cost is equal to Π Bank = G Bank, µ, p v, v, z) R D B z), where R D B z) is the cost of providing a loan to a z-type of an entrepreneur. The maximum net profit of the bank Π Bank is decreasing in z, which is the cost type of the entrepreneur. Entrepreneurs with relatively higher borrowing cost B z) may be credit rationed. By credit rationing, we refer to the case where the entrepreneur does not receive a loan because it is not possible for the bank to make a non-negative expected net profit. Let ẑ denote the type of the marginal entrepreneur that is implicitly determined by the equality G Bank, µ, p v, v, z)= R D B ẑ). The corresponding interest rate that fully characterizes the loan contract for the ẑ type is provided by ˆR B arg max G Bank R B ;, µ, p v, v, z ). Hence, the two equations specifying the pair ẑ, ˆR B), that characterizes the marginal entrepreneur who receives credit, are: Zero profit condition of the bank ˆ ˆR B Bẑ) ˆ ωh 1 p v v µ) ω) φω)dω + ˆRB B ẑ) ) φω)dω = R D B ẑ). 2.7) ˆR B Bẑ) Profit maximization condition of the bank ) [ )] p v v µ) ˆR ˆRB B B ẑ) ˆRB B ẑ) B ẑ) φ + B ẑ) 1 Φ =. 2.8) Any entrepreneur with a cost type that is higher than ẑ is credit rationed and does not receive a loan. Entrepreneurs with a cost type of z ẑ receive a loan with a loan rate that is determined by the binding participation constraint of the bank given in 2.7). Under a competitive financial 12 The strict concavity of G Bank ) is satisfied when p v v µ) [φ ω) + ωφ ω ω)] φ ω) <. This condition holds when [ωφω)] ω = φ ω) + ωφ ω ω) > or when φ ω) is non-decreasing. 7

8 market structure, banks will compete each other in offering a loan interest rate to a z-type entrepreneur as long as they do not expect losses from investing in the z-type project. The binding participation constraint implies that the optimal loan contract yields a zero expected net profit to each bank. The objective function of the entrepreneur is strictly convex in R B, by convexity of the expected profit function Π F irm R B ;, p v, v, z ) which is demonstrated in 2.1): Π F irm R B = p vv RB B 2 z) R B ) [ B z) R B )] B z) φ B z) 1 φ 2.9) 2 Π F irm R B ) 2 = p vv B2 z) R B ) [ B z) φ + p v v RB B 2 ] z) + B z) B z) φ ) R B Bz) ) >. 2.1) R B Bz) The last inequality in 2.1) follows from the assumption of the non-decreasing density function φ ) that we maintain throughout the paper. Denote as R B the level of R B ΠF irm R that satisfies =. Then, R B B = R RB yields the minimum expected profit that the entrepreneur expects given the parameter values, p v, v, z). The B entrepreneur wishes to maximize the expected profit, rather than to minimize it. An expression that will be useful later on, is derived from adding up Π F irm and G Bank : Π F irm R B ;, p v, v, z ) + G Bank R B ;, µ, p v, v, z ) = E ω) µ R B Bz) ω) φω)dω. We can now express Π F irm in terms of G Bank : Π F irm R B ;, p v, v, z ) ˆ R B Bz) = E ω) µ ω) φω)dω G Bank R B ;, µ, p v, v ) 2.11) Based on the definition of R B, we know that: Π F irm R B ;, p v, v, z ) R B =. 2.12) R B = R B Substituting into equation 2.12) for Π F irm in terms of G Bank as expressed in equation 2.11), we get: 8

9 Π F irm R B ;, p v, v, z ) R B = R B = { R B E ω) µ R B Bz) ω) φω)dω G Bank R B ;, µ, p v, v, z ) } R B = R B = R B µ RB B z) R B ) B z) φ GBank R B ;, µ, p v, v, z ) R B = R B = R B GBank R B ;, µ, p v, v, z ) R B = µ RB B z) R B ) B z) φ <. 2.13) R B = R B From the inequality above, we conclude that the expected return on the loan is decreasing in R B for all R B R B. Assuming strict concavity of the bank s expected return function, there exists a unique interior value R Bank B such that its expected profit is maximized and the first order condition is satisfied, i.e., GBank R =. We have shown in 2.13) that GBank R < holds. R B B =RBank B R B B = R B Hence, it must be the case that RBank B < R B. It logically follows that if credit rationing holds for all R B [, R B) for a given a cost-type z, then it will continue to hold for all R B RB, ω H] as well. This result implies that there does not exist any R B RB, ω H] such that the entrepreneur would escape credit rationing in the case that he faced credit rationing at all values of R B in the interval [, R B). We have already argued that an entrepreneur who is not credit-rationed will choose RF B irm, which is the lowest possible R B, such that the participation constraint of the bank becomes binding. In the case that he is not the marginal entrepreneur, it must be the case that RF B irm < RBank B due to the the assumption of strict concavity of the bank s expected return function 13. In other words, the bank expects a zero net profit from the loan and does not maximize its revenue from the loan at RF B irm. Therefore, the interest rate RF B irm that is chosen 14 by each cost type z is such that the bank s expected return on the loan is increasing in R B : G Bank R B R B =RF B irm >. 2.14) This conclusion will prove useful for proving the comparative static result in proposition 2.1). The binding participation constraint of the bank in 2.6) combined with the inequality in 2.14) suggest that the conditions for the optimal contract are met at an interest rate RF B irm, where the bank expects a zero net profit and its expected return on the loan is increasing in the interest rate R B chosen by the entrepreneur. 13 A strictly concave expected return function for the bank guarantees that a maximum of two values for the R B will yield a binding participation constraint for the bank. In the case of an entrepreneur that is not marginal, the lowest value RF B irm for which the participation constraint binds is such that the expected net profit function for the bank is increasing in R B. 14 Note that different cost types will choose a different RF B irm, given that the participation constraint for the bank differs depending on the cost type of the entrepreneur. 9

10 Solving the binding participation constraint implicitly for the lowest interest rate R B F irm we can express it in terms of the exogenous variables z,, p v, v and µ: R B F irm ) +) z, ), +) µ, +) p v, +) v Having defined the contract terms for all types of entrepreneurs, we are now ready to state our first comparative statics results 15 : Proposition 2.1. An increase in either the frequency or the extent of the APR violation under a competitive banking market structure will lead to i) an increase in credit rationing ii) an increase in the loan interest rate iii) a deterioration in the credit quality of each project that is not credit rationed iv) an increase in the expected number of failed projects v) an increase in the expected overall deadweight losses from foregone consumption. Proof. The proof illustrates the effects of changes in the extent of the APR violation v, holding constant all other exogenous parameters. The proof can be easily adjusted to obtain the comparative statics effects of changes in the frequency parameter p v. i) An increase in v will reduce the maximum expected profit that a bank can make on the loan contract provided to the marginal entrepreneur of type ẑ, since from 2.11) we get: Π Bank v = GBank By applying the envelope theorem, we get: Π Bank, µ, p v, v, z) v R B ;, µ, p v, v, z ) v ˆ R B Bz) = p v ωφω)dω < 2.15) = ΠBank R B ;, µ, p v, v, z ) v R B =R B Bank The reduction in the maximum expected profit of the loan provided to the marginal entrepreneur of type ẑ implies that the bank would expect losses from this loan contract. Denote ẑ as the new marginal type of entrepreneur who is not credit-rationed. Since, Π Bank is decreasing in z, then it must be the case that ẑ < ẑ. Any type less than ẑ is not credit rationed. Thus, the set of credit rationed entrepreneurs has increased as a consequence of the increase in v. ii) An increase in v will increase the optimal value of the interest rate R B that corresponds to each cost-type that is not credit-rationed. This can be seen by totally differentiating the binding participation constraint 2.6) of the bank with respect to v and the interest rate RF B irm : 15 By credit quality we refer to the probability of loan repayment. Failed projects is the terminology used in this paper for projects that either become bankrupt or do not materialize because of credit rationing. < 1

11 dπ Bank RF B irm;, µ, p v, v, z ) = R B F irm;, µ, p v, v, z ) dv + ΠBank v ΠBank drb F irm z) dv Π Bank R B = Π Bank R B F irm Using 2.15), we can show that: From 2.14), we get: F irm ;, µ, pv, v, z) v ;, µ, pv, v, z) R B F irm Π Bank R B F irm;, µ, p v, v, z ) v Π Bank RF B irm;, µ, p v, v, z ) ω R B F irm;, µ, p v, v, z ) R B F irm ˆ RB F irm Bz) = p v ωφω)dω < R B =R B F irm = GBank R B R B =RF B irm Using 2.16) and combining the last two inequalities, we conclude that: dr B F irm = > 2.16) drf B irm z) > dv iii) An increase in the interest rate, given an unchanged distribution of project returns, results in an increase in the probability of default Φ R B F irm z)bz) ) for each entrepreneur that is not credit rationed. iv) The increase in credit rationing together with the increase in the probability of default for each financed project imply a larger number of failed projects. v) Increased credit rationing leads to a reduction in expected production. In addition, each project that is not credit rationed faces a higher probability of default, implying a higher expected monitoring cost per financed project. Combining the reduction in potential consumption resulting from unrealized projects and the deadweight loss from monitoring costs, we can deduce that the overall welfare losses will increase after an increase in v. The next proposition describes changes in the credit market conditions resulting from changes in the monitoring cost parameter. Proposition 2.2) is of relevant interest in evaluating the bankruptcy law regime, to the extent that monitoring costs reflect the efficiency of the judicial system and the transaction costs incurred in bankruptcy proceedings. Proposition 2.2. An increase in the monitoring costs under a competitive banking market structure will lead to i) an increase in credit rationing ii) an increase in the loan interest rate iii) a deterioration in the credit quality of each project that is not credit rationed iv) an increase in the expected number of failed projects v) an increase in the overall expected deadweight losses due to bankruptcy. Proof. The proof follows similar steps to those provided in the proof of proposition 2.1). 11

12 2.4 Monopolistic credit market structure In this section, we obtain the optimal loan contract when the entrepreneur is facing a monopolistic banking sector. The bargaining power of setting the contract terms is now on the hands of the monopolistic bank. The decision problem for the bank is the following: s.t. max Π Bank R B ; z ) = G Bank R B ; z ) R D B z) 2.17) {R B } G Bank R B ; z ) R D B z) 2.18) Π F irm R B ; z ) 2.19) We have already claimed that G Bank ) is strictly concave in R B due to the assumption of a non-decreasing φ ). This implies that there exists a unique optimal RBank B that maximizes the objective function of the monopolistic bank for a given cost type. The entrepreneur is assumed to have no outside option in the event of no loan agreement. Consequently, the entrepreneur would accept any loan agreement that does not result in net losses for him. Under the assumption of limited liability, there cannot exist any loan agreement that would yield a negative payoff to the entrepreneur. Therefore, his participation constraint is always satisfied under all loan agreements. The pair ẑ, ) ˆRB that characterizes the marginal entrepreneur who receives credit, is obtained in the same manner as in the case of competitive banks. Similarly to the competitive loan market case, any entrepreneur with a cost type that is higher than ẑ is credit rationed and does not receive a loan. The important difference compared to the competitive market structure lies on the contract terms of those entrepreneurs with a cost type of z ẑ who receive a loan. The loan agreement in these cases specifies an interest rate RBank B that is determined by the following profit maximization condition of the monopoly bank for each cost type z: p v v µ) R B BankB z) φ R B BankB z) ) [ )] R B + B z) 1 Φ BankB z) = 2.2) Solving the above F OC Bank implicitly for R B Bank we can express it in terms of the exogenous variables z,, p v, v and µ: R B Bank ) ) z, +), ) µ, ) p v, ) v Proposition 2.3. An increase in either the frequency or the extent of the APR violation under a monopolistic banking market structure will lead to i) an increase in credit rationing ii) a reduction in the loan interest rate iii) an improvement in the credit quality of each project that is not credit rationed iv) an ambiguous change in the expected number of failed projects v) an ambiguous change in the expected overall deadweight losses from foregone consumption. Proof. i) The proof is identical to the one provided in Proposition 2.1). An increase in either v or p v will reduce the maximum expected profit of the loan contract provided to the marginal entrepreneur of type ẑ, since the conditions that determine the pair ẑ, ˆRB ) remain the same. ii) We perform comparative statics with respect to the parameter that represents the fraction of the project s realized value that is allocated to the entrepreneur by partially differentiating the bank s optimality condition 2.2) with respect to v: 12

13 {F OC Bank } v = p v R B BankB z) φ R B BankB z) By application of the implicit function theorem, we conclude that the optimal value RBank B is decreasing in the parameter v. A similar result is obtained if we perform comparative statics with respect to the parameter p v. An increase in either v or p v, therefore, leads to a reduction of RBank B and a reduction of the interest rate R B associated with each loan that is not credit rationed. iii) A lower interest rate for each z-type entrepreneur that obtains a loan implies a lower probability of default Φ R B Bank Bz) ) < ) on each contract, given an unchanged distribution of project returns. iv) The expected number of failed projects might increase or decrease, following an increase in either v or p v. The outcome depends on the relative importance of credit rationing vis-a-vis the reduction in the probability of default for each project that is not credit rationed. v) Similarly to iv), the change in overall deadweight losses depends on whether the reduction in potential consumption due to increased credit rationing dominates the increase in welfare resulting from a reduction in the welfare losses incurred under bankruptcy. More discussion on this point is offered in section 2.5) which provides an example that illustrates the possibility of deriving a welfare gain from violating the APR. Proposition 2.4. An increase in the monitoring costs under a monopolistic banking market structure will lead to i) an increase in credit rationing ii) a reduction in the loan interest rate iii) an improvement in the credit quality of each project that is not credit rationed iv) an ambiguous change in the expected number of failed projects v) an ambiguous change in the expected overall deadweight losses from foregone consumption. Proof. i) The proof is identical to the one provided in Proposition 2.2). An increase in either v or p v will decrease the maximum expected profit of the loan contract provided to the marginal entrepreneur of type ẑ, since the conditions that determine the pair ẑ, ˆRB ) remain the same. ii) We perform comparative statics with respect to the monitoring cost parameter by partially differentiating the bank s optimality condition 2.8) with respect to the µ: {F OC Bank } µ = R B BankB z) φ R B BankB z) By application of the implicit function theorem, we conclude that the optimal interest rate that the bank sets RBank B is decreasing in the parameter µ for all projects that receive credit. The results in iii), iv) and v) are derived using similar arguments to the ones discussed in the corresponding iii), iv) and v) parts of proposition 2.3). 2.5 An illustration of the effects of APR violation This section provides a diagrammatic exposition of the most important results obtained in the previous sections. In addition, we show via numerical examples that overall deadweight losses might increase or decrease following an increase in the extent of the APR violation in the monopolistic case. First, we provide a parametrization of the general functional forms presented in the previous sections. We assume that ω is uniformly distributed in the support [, ω H]. The uniform distribution 13 ) <

14 is non-decreasing. Therefore, the objective function of the bank is strictly concave. Furthermore, we assume that the investment cost function Bz) takes the linear form Bz) = α + βz. Under the competitive banking sector, we obtain the following results: Π Bank R B ; z ) = 1 1 p v v µ) R B) 2 α + βz) 2 ) +R B α + βz) ω H RB α + βz) R D α + βz) 2 The rate of return on the loan under a competitive banking market can then be obtained via the following formula: R B F irm = [ωh ω H ) 2 ] p v v + µ) α + βz) R D α + βz) 1 + p v v + µ) In the monopolistic banking case, the rate of return is given by: R B Bank = ω H α + βz) 1 + p v v + µ) The social welfare SW ) criterion that we adopt to compare the two market structures is given by the combined profit generated by the firm and the bank: SW R B ;, µ, p v, v, z ) = = ˆ ẑ ˆ ẑ [ Π F irm R B ;, p v, v, z ) + Π Bank R B ;, µ, p v, v, z )] dz [ E ω) R B B z) ] ˆ ẑ dz µ ˆ R B Bz) ω) φω)dω dz. The first term expresses the welfare gain expected to be generated by the financed projects net of their opportunity cost of financing and aggregated across cost-types that are not credit rationed. The second term expresses the aggregate welfare loss expected from the costly monitoring of entrepreneurs that default on their loans. Monitoring activities result in a societal loss because they are assumed here to involve a deadweight loss of the consumption good. In a numerical example, we have compared the social welfare under the adherence to the APR vis-a-vis the violation of the APR as it was implemented under the US bankruptcy law during the 198s. The estimates of the frequency of the APR violation p v =.7 and the extent of the violation v =.6 provided by the studies mentioned in the introduction, were used in our simple numerical example. In addition, we have assumed that µ =.15, which is the value suggested by Carlstrom and Fuerst 1997). The rest of the parameters are set as follows: α = 2, β = 1, ω H = 1, R D = 1 and = 6. Under these assumptions on the parameters, we compare SW AP R RBank; B, µ, z ) to SW V iolatedap R RBank; B, µ, p v, v, z ) and find that the latter is larger. Thus, we are able to document examples under which the violation of the APR can be welfare enhancing. A more general result on the desirability of violating the APR can be obtained under the assumption that the expected returns to the bank are sufficiently high so that all projects are financed and no entrepreneur is credit rationed before and after the APR violation takes place. In that case, the violation of the Absolute Priority Rule is unambiguously welfare improving under the monopolistic banking scenario. The intuition behind this result is that the reduction in the 14

15 interest rate induced by the violation will lead to a reduction in the monitoring costs and to less deadweight losses incurred in bankruptcy proceedings. Figure 2.2) illustrates the expected net profit Π Bank R B ; z ) to a bank, its expected revenue G Bank R B ; z ) and cost R D Bz) in terms of the deposits raised under the uniform distribution assumption. The leftmost diagram shows the case of a credit-rationed entrepreneur. In this case, there is no available interest rate such that the bank can recover the cost of financing the project. If the bank expects a negative net profit, then it will choose not to finance the project. The central diagram shows the marginal entrepreneur that is given a loan. The bank expects a zero net profit from financing the marginal entrepreneur with the cutoff level z Cutoff.. The corresponding interest rate for the bank is denoted as R B z Cutoff ) in the left diagram of figure 2.3) and has been determined in equations 2.7) and 2.8). Bank's Expected Revenue/Cost/Profit R D Bz High ) Bank's Expected Revenue/Cost/Profit R D Bz Cutoff ) Bank's Expected Revenue/Cost/Profit R D Bz Low ) G Bank R B ;z High ) G Bank R B ;z Cutoff ) G Bank R B ;z Low ) R B R B R B Π Bank R B ;z High ) Π Bank R B ;z Cutoff ) Π Bank R B ;z Low ) Credit Rationed Project Marginally Financed Project Financed Project Figure 2.2: Bank s expected net profit Π Bank R B ; z ), expected revenue G Bank R B ; z ) and cost R D Bz) under various cost-types z as a function of R B. The rightmost diagram of figures 2.3) and 2.4) represents the cases of investment projects that can be financed by the bank for some values of the interest rate R B. Depending on the market structure under consideration, the interest rate can be given by the bank s zero expected profit condition or by the bank s expected profit maximization condition. The first case corresponds to perfect banking competition and the interest rate is given by RF B irmin figure 2.3). The monopoly bank charges a higher interest rate, denoted as RBank, B which is the one that maximizes its expected net profit in figure 2.3). Bank's Expected Revenue/Cost/Profit R D Bz Cutoff ) Bank's Expected Revenue/Cost/Profit R D Bz) R B G Bank R B ;z Cutoff ) R B Π Bank R B ;z Cutoff ) G Bank R B ;z) R B z Cutoff ) R B* Firm z) R B* Bank z) Π Bank R B ;z) R B Marginally Financed Project Financed Project Figure 2.3: Interest rate determination under alternative bank market structures and cost-types z. 15

16 The comparative statics results obtained in the previous sections with regards to changes in the frequency or the extent of the APR violation are roughly summarized in figure 2.4) for the case of a general cost-type z that continues to receive a loan both before and after the change in the bankruptcy law takes place. Bank's Expected Revenue/Cost/Profit R D Bz) G Bank R B ;z) G Bank New R B ;z) RFirm B*Old z) R B*New Firm z) R B*New Bank z) RBank B*Old z) Π Bank R B ;z) R B ΠNew Bank R B ;z) Figure 2.4: Effect of intensifying the APR violation on the interest rates under alternative bank market structures. An increase in the extent or the frequency of the APR violation leads to a shift of the expected revenue curve G Bank R B ; z ) and to a lefft-downward shift of the expected net profit curve Π Bank R B ; z ) which leads to an increase of the competitive interest rate RF B irm and to a reduction of the monopolistic interest rate RBank. B It is easy to infer from figure 2.3) that the left-downward shift of the expected net profit curve Π ) Bank R B ; z Cutoff would imply that the marginal entrepreneur would no longer be financed, if the APR violation were intensified. Thus, credit rationing would be expected to increase under all bank market structures. 3 Implicit Banking Collusion and the Business cycle Assume that the economy consists of N islands in each of which there exists one bank. Each island has the population characteristics that we have discussed up to now. In total, there exist a fixed number of N symmetric banks which have access to a deposit and a loan market that span all islands. The bank takes the interest rates on savings as given. The loan applicants will choose to borrow from their local bank, as long as the loan interest rate that they face in other islands is higher or equivalent 16. If any bank offers the lowest interest rate that can be found across islands, then every loan applicant from each island will choose to borrow from that bank. In the case of perfect banking competition, each bank expects a zero profit from each investment project that it decides to finance. This result is obtained in section 2.3) where the non-credit rationed entrepreneur will optimally accept an interest rate which renders binding the participation constraint of the fully competitive bank. If the N banks decide to perfectly collude and behave collectively as a monopoly, then they will charge the monopolistic interest rate to each financed entrepreneur. Loan applicants of the 16 In the case that the interest rates are equivalent, we adopt the behavioural assumption that borrowers will prefer to borrow from their local bank, despite that transportation across islands is assumed to be costless. 16

17 same cost type from different islands will then face a uniform monopolistic interest rate, and will decide to accept the monopolistic loan terms of their local bank. In this section, we introduce variation in the common productivity parameter t+1 that occurs at the beginning of the next period. Let S t denote the state of the world at time t, where S t = {L, H} i.e., L = Low, H = High). The value of the common productivity parameter t+1 S in state S and time t + 1 is known to all economic actors at the beginning of period t + 1, but remains unknown at time t. Entrepreneurs are short-lived compared to the banks. They are one-period lived agents, whereas the banks are assumed to be infinitely lived. Every bank has the same discount factor of future payoffs which is denoted as β, 1). Assume that the aggregate productivity parameter in period t + 1 is high, t+1, H in state S t+1 = H with probability q H and low, t+1, L in state S t+1 = L with probability q L i.e., t+1 H > t+1). L If all N banks agree to collude to set the same interest rate RS B Collusion for a given cost type z in period t and state S, then each symmetric bank has the following expected profit: ˆ ẑs [ S, Collusion Πj = G Bank RS B Collusion ; S, µ, p v, v, z ) R D B z) ] dz 3.1) Equation 3.1) is derived by aggregating the expected net profit for the bank from providing a loan to each type z that is not credit rationed 17. More generally, equation 3.1) expresses the expected profit per-period for each bank, in the case of collusion in the banking market. This expression can be used to determine the discounted expected profit for each bank, in the case that collusion is preserved ad infinitum: V Collusion j = t= = 1 1 β β [ t H, Collusion q H Πj [ H, Collusion qh Πj + q L Π + q L Π ] L, Collusion j ] L, Collusion j 3.2) Expression 3.2) provides the discounted expected profit for loans that will be agreed and repaid from the next period and onward, as long as tacit collusion is sustained. A complete collusive arrangement would allow banks to charge the monopolistic interest rate to each borrower. In that case, the expected discounted profit for each bank is: V Monopoly j = 1 1 β [ H, Monopoly qh Πj + q L Π ] L, Monopoly j S, Monopoly where Πj = [ ẑ S G Bank RBank; B S, µ, p v, v ) R D B z) ] dz and RBank B is the monopolistic interest rate that is set in the way that was described in section 2.4). In that section, the monopolistic interest rate was expressed as a function of the exogenous parameters of the optimization problem of the monopolistic bank: RBank B z,, µ, pv, v ) If the state is known to be S at time t, then the discounted payoff at time t from deviating from the collusive monopolistic interest rate is: 17 Projects that have a cost-type larger than ẑ S will be credit-rationed. 17

18 ˆ ẑs S, Deviation Πj = N = N Π [ G Bank R B Bank; S, µ, p v, v, z ) R D B z) ] dz S, Monopoly j A bank may deviate from the collusive monopoly outcome by slightly undercutting the rest of the banks and capturing the whole loan market for one period. In the rest of the periods, the rest of the banks will respond by charging the competitive interest rate. Having this in mind, each bank will compare its expected payoff from deviating once and receiving a zero payoff thereafter, to the case where it complies to the collusive monopolistic outcome. Under the collusive monopoly, each bank receives a fraction 1/N) of the overall monopoly banking profits N Π period. Perfect collusion will take place if: S, Deviation Πj S, Monopoly j in each S, Monopoly Πj + βv Monopoly j 3.3) When the state of the economy is H, it can be shown that the expected profit for each bank is weakly) higher than when the state of the economy is expected to be L. The reason is that each project that is financed has a lower probability of default holding other parameters constant. Thus, the expected amount from loan repayment increases, while the costs of financing the project remain the same. Since expected bank profits are higher when the state of the economy is H, then the incentive to deviate in this state is higher. Therefore, for the collusive monopoly to be sustainable for all states, we need to check whether the above collusion condition 3.3) holds for S = H: H, Deviation Πj H, Monopoly Πj + βv Monopoly j 3.4) Combining 3.2), 3.3) and 3.4) we get the following cut-off level for the discount factor above which perfect collusion takes place for all states: H, Monopoly N Πj H, Monopoly Πj + β 1 β [ H, Monopoly qh Πj + q L Π ] L, Monopoly j where β β β = q H N 1 + q L N 1 ) Π L, Monopoly j H, Monopoly Πj Having defined the threshold value of the discount factor that will lead to collusive outcomes, we can state the following propositions: Proposition 3.1. Depending on the value of the discount factor, β, we derive the following market structures: i) If β < N 1, then the banking sector is perfectly competitive. N ii) If β > β, then the banking sector is perfectly collusive and the monopolistic interest rate is sustained under all states of the economy. 3.5) 18