Peer monitoring and moral hazard in underdeveloped credit markets. Shubhashis Gangopadhyay* and Robert Lensink**

Transcription

1 eer monitoring and moral hazard in underdeveloped credit markets. Shubhashis angopadhyay* and Robert ensink** *ndia Development Foundation, ndia. **Faculty of Economics, University of roningen, The Netherlands. Corresponding author: Robert ensink. Faculty of Economics, University of roningen, O Box 800, 9700 AV roningen, The Netherlands; B.W. ensink@eco.rug.nl. Fax: ; tel: JE classification: D82, O16, O17 Keywords: Moral azard, Underdeveloped Credit Markets, eer Monitoring, Delegated Monitoring The first version of the paper was prepared when the first author was visiting the University of roningen. The SOM Research School and N.W. O. provided funding for this work. The authors bear complete responsibility for any errors. 1

2 1. ntroduction t is well known that asymmetric information between financiers and those who need financing may lead to moral hazard problems (e.g. Stiglitz and Weiss, 1981). Moral hazard problems are especially harmful for the functioning of formal credit markets in underdeveloped areas, where borrowers do not have enough (acceptable) collateral that banks may require to be pledged to avoid the negative implications of borrowers hidden actions. The lack of access to formal credit implies a loss in national output, because productive opportunities are not being utilized by a properly functioning credit market. Therefore, moral hazard problems and the resulting poor performance of underdeveloped credit markets is a cause for serious concern. Consequently, it is highly important to better understand how lending schemes can be developed that induce borrowers to be diligent. Stimulated by the widespread adoption of group lending schemes, and the success of those programs, several economists (e.g. Morduch, 1999) argue that joint liability systems with peer monitoring may help to reduce the moral hazard problem. eer monitoring means that members of a borrowing group do the monitoring for the financier and are able to affect the behavior of other members of the group. f a bank writes a contract in which borrowers are made jointly liable for the repayments of the loans, each borrower has an incentive to monitor her peer. This may provide incentives to the group members to invest in safe projects, and thus may reduce problems of moral hazard. This paper adds to the small literature on peer monitoring and moral hazard problems. There are two aims. First, by developing a group lending model with joint liability in 2

3 which peer monitoring is assumed to be costly, we show that each group member will have to undergo the monitoring costs in order to avoid that peers behave in a noncooperative fashion. eer monitoring will only solve the moral hazard problem if group members are induced to behave cooperative, which requires that all borrowers monitor each other. Moreover, peer monitoring will only avoid moral hazard if a minimum amount of deposits is pledged with the bank before the borrower is allowed to get a loan. This outcome differs fundamentally from the main implications of the well-known peer monitoring model by Stiglitz (1990), who assumes costless monitoring between peers. Second, and most importantly, we compare a peer monitoring system with an individual lending scheme with a delegated monitor in their efficiency in reducing moral hazard problems. There is a general descriptive discussion in the literature on the advantages of group loans over individual loans. Some authors clearly prefer individual loans because they are assumed to be more flexible, whereas others are in favor of group loans. For a summary of this discussion, see e.g. Conning (1999) or Morduch (1999). owever, there are almost no attempts to formally compare peer monitoring systems with delegated monitoring systems. The only exception we are aware of is Conning (2005), but his model differs fundamentally from ours. The main difference being that Conning (2005) ignores the possibility of collusion between monitors and borrowers, whereas we explicitly develop a collusion-proof incentive contract between the principal and the specialized monitor for the delegated monitoring system. We will show that even with the same monitoring technology it is not clear which system is most efficient. The system to be preferred depends on a range of parameters, such as the level of monitoring cost, the level of the deposit rate and the difference between the expected value of high and low effort. 3

4 The remainder of this paper is organized as follows. Section 2 presents the benchmark model. n our setup, a moral hazard problem arises when a financier cannot verify the effort of a borrower. Since a contract can only be based on verifiable variables, the informational asymmetry implies that the financier cannot control the action of the borrowers i.e., the effort cannot be included in the terms of the contract. A problem then arises if a high effort case will provide the best outcome for the society, while it is beneficial for the borrower to put in low effort. Out benchmark model shows that the moral hazard problem may lead to a socially inefficient outcome. Section 3 considers a group lending system with joint liability and costless peer monitoring. f costless monitoring is assumed, group lending with joint liability may be an efficient way to reduce moral hazard. owever, costless monitoring seems to be an unrealistic assumption. Therefore, Section 4 continues by examining under which parameter setting a group lending system with costly peer monitoring can prevent moral hazard and allows the credit market to function. Section 5 does the same for individual lending with a delegated monitor. n this section we will also make a comparison between the peer monitoring system and the delegated monitoring system. Section 6 discusses the relevance of our main results and makes a comparison with other existing peer monitoring models. 2 ndividual lending without monitoring We consider an underdeveloped village with N entrepreneurs, who each have one risky project in which to invest. Each entrepreneur seeks to finance her investment project of a size normalized to one. The needed funds may be borrowed from a financier, who may be a moneylender, a bank, or a microfinance institution. For 4

5 reasons of convenience, we use the term bank henceforth. The bank provides finance under a standard debt contract. The costs of raising funds from an equity market are assumed to be prohibitively high, so that we ignore equity financing. This is not unrealistic, given that we are considering small village players in underdeveloped economies that are characterized by capital markets that are still in their infancy. n line with most moral hazard models, we assume that each entrepreneur can choose between two possible effort levels, high () and low (). The entrepreneur s effort is private information, and is not verifiable. This implies that the entrepreneur s effort cannot be used as a contracting variable by the bank; in other words, the lender is not able to prove in a court of law that the borrower has neglected an assigned task. The success of the investment, on the other hand, is verifiable by outsiders so that the entrepreneur can promise to repay some fixed amount only in case of success. The order of decisions of the game we consider is as follows. n period zero the bank designs a contract and the entrepreneur accepts or rejects the contract. n the next period, the entrepreneur invests by supplying non-verifiable effort. The pay-offs for entrepreneurs and the bank will become clear in the same period, depending on the success or failure of the projects. The assumption that entrepreneurs invest one period later than designing the contract is not essential for the model, but makes the analysis better comparable to the analyses presented in Sections 3 and 4. Note that when designing the contract, the bank needs to take into account that the entrepreneur, after signing the contract, will choose the effort level that is most beneficial for her. 5

6 et Q j be the probability of success of a project undertaken with effort level j, j =,, R j be the output when a project with effort level j, j =, succeeds, r be the opportunity cost (one plus the deposit rate for a competitive bank) of the bank s resources, = Q R µ, µ = Q R and µ = µ µ. All projects yield a zero return if unsuccessful. The disutility of effort level j is represented by a cost c j, j =, and c = c c. The effort cost can be interpreted as the monetized value of the disutility of effort; thus, the entrepreneur can incur this cost even when the return from the project is zero. We make the following assumptions A.1: 0 Q < Q < 1 < A.2: A.3: R > R c < c A.4: µ c A.5: Entrepreneurs and the bank are risk neutral. A.6: The bank makes zero profits. A.2 and A.4 imply that the high effort is more profitable in expected value terms, although pay-off with low effort is higher when the project is successful. A.4 also implies that from a social point of view it would be better if all entrepreneurs put in high effort. emma 1: et 0 µ c < r Q. Then, there does not exist any standard debt contract where the bank makes non-negative profit and the entrepreneur chooses the high effort, where Q Q Q. 6

7 roof: Suppose that, contrary to hypothesis, there exists a debt contract where the entrepreneur chooses the high effort and the bank makes non-negative profit. et d be the debt claim of the bank in the debt contract. Since the bank makes no expected losses, Q d r d ( r / Q ) The entrepreneur only chooses high effort if expected payoff in case of high effort exceeds the expected payoff in case of low effort. This implies that the entrepreneur only chooses high effort if µ c Q d µ c µ c Qd d Q utting the two restrictions on d together, we need r Q c µ for the loan Q contract to ensure that entrepreneurs put in high effort. owever, this cannot be satisfied if 0 µ c < r Q. For the rest of the paper we will assume A.7: 0 µ c < r Q. This assumption is a simple one that makes moral hazard possible in our model. Observe that the second inequality in A.7 can be written as 7

8 µ c rq < µ c rq The expressions on the two sides of the inequality sign are the entrepreneurial payoffs on a debt contract that charges as interest the opportunity cost to the bank. Since both project types are risky, the actual interest charged by the bank will be such that it is greater than r. Since Q > Q, the left hand side of the inequality falls faster than the right hand side as r rises. A.7 simply says that moral hazard is an issue at all feasible rates of interest that the bank tries to charge. Under A.4 and A.7 the only viable solution is that the entrepreneur chooses low effort and that the bank breaks even on a loan to entrepreneurs with low effort. et nm the debt contract offered by the bank in the absence of a monitor and Eπ the expected pay-off of an entrepreneur with low effort level in the absence of monitoring. Then a competitive equilibrium of the credit market is obtained if nm d be (1) nm nm Q d = r d = r Q and nm nm (2) Eπ = Q ( R d ) c = µ c r et nm EΠ be the expected aggregate payoff to the N entrepreneurs in the absence of monitoring. Then, 8

9 nm (3) EΠ = N[ µ c r] Observe that, from A.4, N[ µ c r] is less than N[ µ c r], which would have been the total surplus in the system if the high effort was chosen by everybody. Thus, under the parameters in our model, moral hazard leads to a socially inefficient outcome in the credit market. 3 roup lending with costless monitoring The question we will now deal with is whether group lending can prevent moral hazard and improves on the social outcome. The model we use is similar to the one used in Section 2. Again there are N risk neutral borrowers, who need bank finance for a risky investment project. The assumptions A1-A7 apply. There are some important differences with the model in Section 2, though. First, the N risky entrepreneurs in the village have to form groups of two borrowers. The bank writes a joint liability contract for the groups. The joint liability contract is such that if one of the borrowers from a group fails, the succeeding partner not only has to pay her own debt claim, but also that of her failed partner. Moreover, before a borrower is allowed to get a loan, she has to pledge a deposit with the bank, which is a common feature in most group lending systems. n period 1 when the borrowing takes place, the deposit (including the interest on it), will be reimbursed to the borrower only if she, or her partner for her, has paid off the debt claim to the bank. We will denote this deposit amount as X. 9

10 The order of the game is as follows. n period zero the bank designs a joint-liability contract. The entrepreneurs in a group decide cooperatively to put in high or low effort and decide on accepting or rejecting the contract. f they accept, they also pledge the required deposit. When designing the contract, the bank needs to take into account that entrepreneurs in a group, after signing the contract, will choose the effort level that is most beneficial for them. We assume that monitoring is costless and that group members can prevent any deviation from the cooperative agreement by using social sanctions. This assumption is in line with Stiglitz (1990). t has far-reaching consequences, as we will show below. Before proceeding any further, we will introduce one other assumption. A.8: X r This assumption is required for consistency in the model. Recall that X is the value of the deposit put in by the entrepreneur. f we interpret the opportunity cost of the bank as the deposit rate offered by it, then we can think of original deposit, x (principal), times the interest on deposit. Thus, X as being equal to the X = x r. By assuming A.8, we are saying that x 1. Essentially, this means that the bank is not raising its resources from the entrepreneur and then lending it back to her! 10

11 et d be the debt contract under group lending. n period one, the payoff to an individual borrower j, j =, from a group of two borrowers who both agree to put in the same effort is R 2 j + X d c with probability Q j j 2 R j X d c j with probability Q j (1 Q j ) (4) + π j ( jj ) = X c j with probability (1 Q j ) Q j 0 c with probability (1 Q ) 2 j j The first part of π j is the payoff to a borrower if both partners are successful. Each gets her success revenue, is returned her deposit (or pledge) with the bank, pays off her debt and suffers the disutility cost of effort. The probability of this event is n the second case, the borrower is successful but her partner is not. ere the borrower will have to pay both her and her partner s debt obligation, and hence, the 2d. The third case is when the borrower is unsuccessful and her partner pays for her. n the fourth case, both are unsuccessful and hence, the bank forfeits their deposits. 2 Q j. et Eπ j ( jj) be the expected payoff to a borrower in a group where both put in the same effort. Then, using the probabilities given in (4), for an entrepreneur j, j =, (5) Eπ ( ) ( j jj = µ j + X d ) Q j (2 Q j ) c j 11

12 The payoff to the bank from the borrower and her partner is given by (6) 2d with probability Q 2 j 2 b d with probability Q j (1 Q j ) Π j ( jj ) = 2 d with probability (1 Q j ) Q j 2 X with probability (1 Q ) 2 j et EΠ b j ( jj) be the expected payoff to the bank from the two borrowers when both put in effort j, j =, in a group lending system. Then (7) EΠ b ( jj) 2 d Q (2 Q ) X (1 Q ) 2 j = j j + j This implies that from each entrepreneur the bank gets (8) Eπ b ( jj) d Q (2 Q ) X (1 Q ) 2 j = j j + j where Eπ b j denotes the expected payoff to the bank per borrower when both are putting in the same effort j =, in a peer monitoring system. ets consider whether moral hazard can be avoided with group lending. This will be the case if the incentive scheme with group lending is such that it is incentive compatible for each borrower to choose for the high effort level. The bank can enforce this outcome by imposing a constraint such that it will be beneficial for the 12

13 group to be diligent. n our model, requiring a minimum amount of deposits that needs to be pledged before a loan can be obtained can do this. roposition 1: Under A1-A8, and in case group members choose their effort levels cooperatively, group lending schemes will avoid moral hazard if µ c X = r Q (2 Q ) and the bank offers the debt contract A r X (1 Q ) 2 d =, where A = Q ( 2 Q ) Q (2 Q ). The bank will make Q (2 Q ) zero profits. roof: see appendix Using the value of d as given in roposition 1, the total payoff to the N entrepreneurs in the costless peer monitoring system equals (9) EΠ = N µ c r X + Observe that this is the payoff from the costless peer monitoring system. owever, there is an additional cost to the peer monitoring system. This is the requirement that the entrepreneurs must pledge some funds at the beginning (period 0) whose value becomes X at the end (period 1). f we assume that the bank offers the deposit rate r on an amount of deposit x, and that the opportunity cost to the entrepreneur of these funds is ρ, then the expected surplus in the costless peer monitoring system is 13

14 (10) ES = N µ c r x + ( r ρ ) f we compare (10) with the expression corresponding to (2), the group lending system with costless peer monitoring system is better if and only if X (11) µ c x ( ρ r) = ( ρ r) r This will always be the case, given A4, if ρ = r. owever, a major problem with small entrepreneurs, and those that peer monitoring contracts try to target are those with very little liquidity. t is, therefore, not entirely unrealistic to assume that their opportunity cost of funds will be greater than the deposit rate that they will get from the bank, or that ρ r. What (11) signifies is that those that have a very high cost of putting together liquid funds, will not be able to partake of the peer monitoring system. n other words, the costless peer monitoring system will only be more efficient than individual lending without monitoring if the opportunity cost of funds are not very high compared to the deposit rate. Alternatively, the costless monitoring system will be more efficient if the opportunity cost of funds for an individual borrower does not differ much from the opportunity cost of funds for the bank. Yet, the latter outcome entirely depends on the assumption that monitoring is costless and that social sanctions can be used to discourage each borrower to behave in a noncooperative fashion. The importance of this assumption can be clarified as follows. 14

15 Consider the following example. Denote the borrower s payoff who put in low effort, given that the other borrower puts in high effort by π i ( ij ), where i =, j =. R + X d c with probability Q Q 2 (1 ) (12) R X d c with probability Q Q ( ) + π = X c with probability (1 Q) Q 0 c with probability (1 Q)(1 Q ) Observe that (12) is similar to equation (4) and has the same explanations. Substituting for d from the statement of the roposition, and including a social sanction of S because the borrower puts in low effort, we have (13) Q Q ( ) E c r X Q Q π = µ + + S Q Q From equation (4), (14) Eπ ( ) c r X = µ + which is what the borrower will get if she put in the high effort. f Eπ ( ) > Eπ ( ) it will never pay the borrower to behave opportunistically by putting low effort. t is easy to see that this can always be guaranteed by imposing a certain level of social sanctions S. owever, if there are no social sanctions (S=0) it will be in the interest of each individual player to put in low effort, and thus to behave 15

16 in a non-cooperative fashion, as the following shows. f S=0, for the profit in (13) to be more than that in (14), we need (15) X r 1 Q µ c Q Q Q ( 1 ) t is easy to show that, given A.7, the right hand side of (15) is always greater than r. ence, given A.8, (15) will always hold and it will, therefore, always pay the borrower to deviate from the high effort. 1 4 roup lending with costly peer monitoring The previous section has shown that a group lending system with costless monitoring can solve the moral hazard problem. owever, the assumption that group members can observe each other actions without costs and thus can side-contract without costs seems unrealistic. Therefore, this section considers group lending with costly peer monitoring. n order to examine this, we use a model that is similar to the one used in Section 3. owever, we assume that each borrower in a group can only find out the effort her partner is devoting to a project against certain monitoring costs. Also in line with the previous section, we assume that the bank determines a required level of deposits to be pledged by each entrepreneur. The required level of deposits is set at a level, which ensures that the group earns more if all group members put high effort than if all group members put low effort. The entrepreneurs in a group decide jointly on whether to choose high or low effort. f they decide to choose low effort, they will not report this to the bank. n this case, they do not need to monitor each other and hence monitoring costs are zero. owever, 16

17 if they decide to put in high effort, they need to monitor each other since there is a possibility of cheating. f entrepreneurs in a group monitor each other, they are assumed to be able to force the partner to put in high effort (for instance by means of social sanctions). f entrepreneurs promise to put in high effort, the total monitoring cost per entrepreneur is assumed to be equal to m N + F, where m equals the variable monitoring costs and F the fixed monitoring costs. Naturally, m = F = 0. Since we are dealing with groups of two borrowers, each borrower monitors (and is monitored) only by one peer. Therefore, the monitoring costs per entrepreneur equal m + F, which are equal to the per loan monitoring costs. The valuation of the monitoring cost has the same interpretation as the cost of effort --- money value of the disutility from the monitoring activity. Before proceeding any further, we will introduce one additional assumption. A.9: µ c m F 0 A.9 says that the cost of monitoring is not too high. More importantly, it says that in the ideal case, the high effort is more efficient even with a monitoring cost. et d be the debt contract under peer monitoring and let E j ( jj) π be the expected payoff to a borrower in a group where both put in the same effort. Then, following (4) and (5) and adding monitoring costs, for an entrepreneur j, j =, (16) Eπ ( ) ( j jj = µ j + X d ) Q j (2 Q j ) m F c j 17

18 There are two important things to note. First, even though they are going as a pair, each has to pay the monitoring cost necessary to keep the partner honest. Thus, to ensure that the partner puts in high effort, the borrower has to monitor the partner. s this necessary? n the proof of roposition 2, we will show that it is. Second, if the two cooperatively decide to put in a mixture of high and low effort, there has to be an understanding that the two share in the costs and benefits of the agreement. We discuss the implications of these in the proof of roposition 2. n line with the derivation of (8), it is simple to show that the expected payoff to the bank from each borrower when both put in effort j, j =, in a group lending system with peer monitoring ( Eπ b j ( jj) ) equals (17) Eπ b j ( jj) = d Q j (2 Q j ) + X (1 Q j ) 2 We can now formulate the following proposition. roposition 2: Under A1-A9 group lending schemes with peer monitoring will avoid moral hazard if µ c X r m = F Q (2 Q ) and the bank offers the A debt contract d 2 r X (1 Q ) =. The bank will make zero profits. Q (2 Q ) roof: see appendix 18

19 Using the value of entrepreneurs equals d as given in roposition 2, the total payoff to the N (18) EΠ = N µ c m F r X + n line with the analysis in the previous section, the expected surplus in the peer monitoring system can be calculated (19) ES = N[ µ c m r + x ( r ρ) ] By comparing (19) with (2), the group lending system with costly peer monitoring is better if and only if X (18) µ c m F x ( ρ r) = ( r) r ρ This will again always be the case, given A9, if ρ = r. owever, as we have argued before, it is realistic to assume that the opportunity cost of funds will be greater than the deposit rate. Since monitoring costs are positive, it is also clear that the costly monitoring system is less efficient than the group lending system with costless monitoring (compare 19 with 10). 5. ndividual borrowing with a delegated monitor We continue by comparing the group lending peer monitoring system with a system where the bank hires an auditor who monitors all N borrowers in the village. 19

20 The bank wants to create an environment in which it is in the interest of the monitor to report any cheating by entrepreneurs. The problem, however, is that the auditor may be bribed by the entrepreneur. The bank knows this and tries to prevent this by giving the auditor a bonus, to be specified below, above her normal wage if she reports that an entrepreneur has put in low effort. The model is similar to the benchmark model. The assumptions A1-A9 hold. n line with the peer monitoring model we assume that an entrepreneur needs to deposit an amount x in period zero (with value X in period 1) before being able to receive a loan in period one. The superscript denotes that we are dealing with a model with incentivized monitoring. n contrast to the peer monitoring model, the bank offers individual debt contracts and an incentive contract to the auditor. The order of the game is as follows. n period zero the bank offers an incentive contract to the auditor. The bank also designs a debt contract for the entrepreneur. The entrepreneur decides on taking up the debt contract. f she accepts the debt contract, she has to put in a deposit x in the bank. n period one, the entrepreneurs borrow and invest by supplying effort that is still non-verifiable to the bank, but is verifiable by the auditor. f the entrepreneur puts in low effort, she decides whether she will try to bribe the auditor. The auditor reports to the bank. The pay-offs for entrepreneurs, the auditor and the bank will become clear. When designing the contract, the bank needs to take into account that entrepreneurs after signing the contract will choose the effort level that is most beneficial for them. 20

21 et us start by considering the bribe game. Since there can be no penalty if the borrower repays, the effect of monitoring kicks in only if the project fails. Only the auditor and the borrower know whether the effort put in is high or low. Therefore, there is the possibility that they can collude. f the borrower bribes the auditor with a bribe b she may report that the effort put in by the borrower is high, when actually the effort put in is low. To prevent this, we assume that the bank offers an incentive contract α X. So, if the auditor reports to the bank that an entrepreneur has put in the low effort, and the project fails, the auditor will get a fraction α of the deposit that is pledged by the entrepreneur. The remainder of the value of the deposit )X will ( 1 α go to the bank. The entrepreneur looses the entire deposit when she puts in low effort and the auditor reports that to the bank when the project fails. f, however, the auditor reports a high effort when the project has failed, the borrower gets back her deposit. roposition 3: f α = 1, it will not pay the entrepreneur to bribe the auditor. roof: When evaluating the payoff from a bribe b she is offered by the borrower, the auditor accepts the bribe if: (19) b αx The left-hand side of this equation gives the payoff to the auditor if the borrower bribes her. This equals b since we assume that there is no one checking on the auditor. The right hand side is the payoff to the monitor if she does not accept the bribe, but truthfully reports to the bank that the entrepreneur has put in low effort. 21

22 Recall that the borrower loses X when she puts in low effort, the projects fails and she does not bribe. f she bribes she has to pay b given by (19). n that case she does not lose X. So, if b X then the borrower is better off not paying the bribe, or colluding. ence, no bribing will take place if (20) X ( α 1) 0 So, if the bank offers an incentive contract to the auditor such that if she reports that the entrepreneur has put in low effort, she will get the entire value of the deposit pledged by the entrepreneur (i.e. α = 1), it will never pay for the entrepreneur to bribe the auditor. QED t should be noted that in our model there is nobody monitoring the auditor. The model could be extended by assuming that there is also a supervisor monitoring the auditor. n such a set-up a similar, although somewhat more complicated, no-bribing game can be derived. n an earlier version of the paper we have actually done that, but since it only complicates matters without giving more insights we have ignored this possibility here. So, now consider a contract the bank makes with each of the N entrepreneurs. t offers a loan of 1 unit and asks the auditor to monitor all borrowers. t charges an interest of d and asks for a deposit of x to be returned with value X = rx if the project succeeds, or the project fails but the borrower had put in high effort (as reported by the auditor). The auditor undertakes a per loan variable cost of a fixed cost of F / N. We introduce the following assumption αm and 22

23 A10: α 1 A10 captures the idea that variable costs of monitoring by an outside auditor are at the least equal to that of a peer monitoring system since group members probably have better information about their peers than an outside auditor. The bank pays the monitoring costs to the auditor. f the auditor detects low effort and reports it, the auditor gets the borrower s deposit X. Since the auditor s cost is covered, and because there is a bonus if she unearths low effort with default, it will always pay the auditor to carry out this activity. t is helpful to note that the main difference between the peer monitoring system and the delegated monitoring system is that with peer monitoring there is joint liability which helps to avoid low effort by entrepreneurs, whereas in the delegated monitoring system there is a contract which gives an incentive to the auditor to report low effort by any of the other entrepreneurs. f the entrepreneur puts in low effort, she will get (21) Eπ Q ( R X d ) c Q ( X d = + = µ + ) c f the low effort succeeds, the entrepreneur gets her deposit back after paying off the interest. f she fails, the auditor reports the low effort and she gets nothing. The profit of an individual borrower that puts in high effort equals: 23

24 (22) Eπ = Q ( R d + X ) + (1 Q ) X c = µ + X Qd c Note that the entrepreneur now does not loose Recall that with group lending the borrower always loses X when she puts in high effort. p X if the project fails, even if she has put in high effort. The reason for this is that with group lending borrowers monitor each other, and there is no formal incentive scheme that may induce the monitor to be truthful. So, with group lending, if the project failed, there is an incentive to always pretend that this is the result of bad luck (and not low effort). So with group lending there is no possibility to differentiate between strategic default and bad luck, whereas with a formal auditor an incentive scheme can be set up that can avoid strategic defaults. The entrepreneur will put in high effort if (23) µ + X X d Q d Q 1 Q c µ + Q µ c 1 Q X Q d c We now need to solve for d. Recall that per loan monitored the bank pays F α m + and undergoes the opportunity cost r of lending a unit. Note that we are N implicitly assuming here that the auditor does not earn the bonus from monitoring as the person she monitors has put in high effort. Thus, we focus on so-called collusionproof outcomes. 24

25 For zero profit, it will require that (24) F Q d = r + αm + N The left-hand side of (24) represents the expected debt payments from the borrower. The right-hand side gives the costs of the loans, containing the wage costs of the monitor and the opportunity cost of the bank s resources. From (24) it follows that (25) r m F / N d + α + = Q Substituting (25) in the no moral hazard constraint (23) gives (26) X r + α m + F / N µ Q c Q (1 Q) 1 Q f (26) holds, then the total profit is (27) EΠ = N µ c m F / N r X α + and the total surplus in the delegated monitoring system is (28) ES = N µ c m F / N r x α + ( r ρ) 25

26 f the opportunity costs of funds equal the deposit rate ρ = r, the delegated monitoring system leads to a higher surplus if (29) m F N m F ( ) m F ( N N ) α + / < + α 1 1/ < 0 Equation 29 points at an important difference between the peer monitoring system and the delegated monitoring system. The peer monitoring system may be more cost efficient because borrowers have better information about their peers than an outside auditor. owever, the delegated monitoring system saves on fixed monitoring costs. Yet, as we have argued before it is not unreasonable to assume that ρ > r. Assuming that (26) holds with equality, then the relative efficiency of the two systems also depend on a comparison of X and X. An additional positive effect of the delegated monitoring system then results if X X, i.e., (30) r + α m F / N µ c µ Q r c m F Q (2 Q ) Q (1 Q) 1 Q A Yet, without additional parameter restrictions it is not clear whether (30) holds and thus which system is most efficient. A closer look at (30) may gain a better insight into the working of the model. To concentrate on the difference in the systems as distinct from a possible monitoring advantage, we assume in the remainder that the monitoring technology in both systems is the same (i.e. α = 1 and N = 1). et and EΤ be the expected gain in pay-offs to an entrepreneur who puts high effort, EΤ 26

27 instead of low effort, for the peer monitoring system and the delegated monitoring system, respectively. Then (31) EΤ = Eπ ( ) E π ( ) (32) EΤ = Eπ E π et us first consider the effect of an increase in required deposits (X) on EΤ. Under peer monitoring, an increase in required deposits affects EΤ and EΤ both directly and indirectly via the debt claim. A unit increase in required deposits increases profits under high effort directly by Q (2 Q ), while with low effort it increases profits directly by only Q(2 Q ). These terms reflect the fact that, both in case of low and high effort, the entrepreneur will loose the deposit if both entrepreneurs in the group fail, which happens with probability (1 Q ) 2 j for j, j =,. n addition, the effect via the decrease in the debt claim has to be taken into account. t is simple to calculate that (33) deτ Q (2 Q ) Q(2 Q ) A = = dx Q (2 Q ) Q (2 Q ) Under the delegated monitoring system, a unit increase in required deposits leads to a unit increase in profits in case of high effort, while the increase is only Q for low effort. The reason is that with high effort a firm does not loose the deposit if a firm 27

28 fails. The debt claim is not affected under delegated monitoring since in equilibrium each entrepreneur will put in high effort. t is straightforward to show that deτ (34) = 1 Q dx t now follows that (35) deτ deτ Q [ Q (2 Q ) (2 Q ] = < 0 dx dx Q (2 Q ) where it is assumed that required deposits under both systems are equal. Equation (35) shows that the effect of an increase in required deposits on EΤ is bigger than that on EΤ. This implies that the required increase in deposits to compensate a unit decrease in excess profits in order to avoid moral hazard is smaller under delegated monitoring than under peer monitoring. Once again, the main reason for this difference is that under delegated monitoring, the entrepreneur never looses X when she puts in high effort, while she will loose X is she puts in high effort but fails under the peer monitoring system. This additional positive effect of putting in high effort under delegated monitoring as compared to peer monitoring is partly compensated by the decrease in the debt claim under the peer monitoring system, which leads to an increase in pay-offs that are higher with high effort than with low effort. Next we consider the impact of a unit increase in the debt claim on EΤ and EΤ. Under peer monitoring and delegated monitoring, respectively, the multipliers are 28

29 deτ (36) = Q(2 Q) Q (2 Q ) = A dd (37) deτ = Q Q = Q dd Since Q(1 Q) Q (1 Q ) < 0 for 0 < Q < Q < 1 it follows that deτ deτ (38) < < 0 dd dd Thus, a unit increase in the debt claim decreases profits more under peer monitoring than under delegated monitoring. The reason is that with peer monitoring the debt claim also has to be paid if the entrepreneur is successful, and her partner not. This effect of joint liability does not exist under delegated monitoring. We can now continue the analysis by considering the effects of increases in the difference in expected value with high and low effort ( µ c ), the deposit rate r and the monitoring costs. Note that for each variable in (30), given the other variables, it is possible to calculate a threshold value for which the required deposit to avoid moral hazard is the same under both systems. By calculating and comparing multipliers it can be determined whether delegated monitoring is more efficient than peer monitoring for values of these variables below or above the threshold value. We first consider monitoring costs, assuming the same monitoring technology. Under the peer monitoring system, monitoring costs do not enter the debt contract. A unit 29

30 increase in monitoring costs decreases profits in case of high effort with one dollar, whereas it does not affect profits in case of low effort. The unit decrease in profits in case of high effort has to be compensated by an increase in required deposits to avoid moral hazard. To compensate for the unit decrease in profits, required deposits needs to increase by deτ Q (2 Q ) (39) 1/ = > 1. dx A Under the delegated monitoring system, monitoring costs affect profits of firms, and consequently the total surplus, directly via the debt claim. Since the bank operates under zero profits, this increase is passed on to firms via a higher debt claim. The effect of a unit increase in the debt claim is given by (37). For the equilibrium debt claim, where firms are assumed to put in high effort, a unit increase in the monitoring costs leads to an increase in the debt claim of 1 Q. Therefore, excess profits decline by Q Q if monitoring costs increase by one unit. To compensate for this loss, required deposits have to increase by Q deτ Q (40) / = < 1 Q dx Q (1 Q) Note that a one dollar increase in monitoring costs requires a more than proportional increase in required deposits to avoid moral hazard under peer monitoring, while the minimal required increase in deposits is less than one dollar under delegated 30

31 monitoring. This implies that the delegated monitoring system will be more efficient for monitoring costs above a hypothetical threshold value of monitoring costs. Thus, ceteris paribus, the delegated monitoring system is more efficient if monitoring costs are relatively high, while the opposite holds for relatively low monitoring costs. Next we consider the difference in expected value with high and low effort ( µ c ). Under peer monitoring and delegated monitoring, a unit decrease in ( µ c ) leads to a unit decrease in excess profits. t is simple to calculate that the required increase in deposits to avoid moral hazard under peer monitoring and delegated monitoring, respectively, equal (41) Q (2 Q ) > 1 A 1 (42) > 1 (1 Q ) Since 1 Q (2 Q ) <, the required increase in deposits under delegated (1 Q) A monitoring is smaller than under peer monitoring. This implies that the delegated monitoring system is more efficient if the difference in expected value between high and low effort is relatively small. Finally, we consider the impact of a rise in the deposit rate r. Under both systems this affects excess profits via the debt claim. Under peer monitoring, a unit increase in r increases the debt claim by 1, whereas the increase of the debt claim Q (2 Q ) 31

32 equals 1 Q under delegated monitoring. The required increase in deposits under peer monitoring then equals (43) A Q (2 Q ) = 1. Q (2 Q ) A For delegated monitoring this is Q (44) < 1. Q (1 Q) Thus, for relatively high opportunity costs for the bank, the delegated monitoring system will be more efficient. 6 Discussion and comparison to other papers The analysis so far leads to several conclusions. First, a group lending system with joint liability and costless monitoring may be an efficient way to avoid moral hazard. The main assumption for this result is that borrowers in a group can costlessly write side-contracts and therefore can, for instance via social sanctions, avoid noncooperative behavior without costs. This result corresponds to the analysis by Stiglitz (1990). n line with our model, he considers a moral hazard problem where all individuals can undertake a relatively safe or a relatively risky project. e also assumes zero profits for the bank. Yet, the model by Stiglitz (1990) differs in several ways from ours. n his model, the investment projects do not have a size normalized to one and the return of a project depends on the amount of funds. Furthermore, 32

33 Stiglitz considers risk-averse entrepreneurs, whereas our model assumes risk neutrality. n the model by Stiglitz, the effect of joint liability works as follows: at a given level of loans, utility will be higher if both borrowers are successful, but utility of the successful borrower will be lower if her partner fails. This imposes an additional risk on the co-signer, which needs to be compensated by a larger loan provided by the lender. Stiglitz shows that the additional risk burden imposed on the co-signer will be compensated by an increase in loans, and hence will be welfare improving, for not too high levels of the joint liability payment. A major difference between his model and ours is that he does not assume that borrowers have to pledge a deposit with the bank before they are allowed to get a loan. n our model, the amount of deposits that has to be pledged before an entrepreneur can obtain a loan serves an important task in that it rules out collusion between borrows in a group. Our analysis, however, also shows that the amount of deposits to be pledged lowers the total social surplus if the individual opportunity costs of funds are higher than the opportunity costs of funds for the bank. This may even make the costless peer monitoring system less efficient than the individual monitoring system without monitoring. More importantly, it also implies that borrowers with a very high cost of putting together liquid funds, probably the very poor borrowers, may not be able to participate in a peer monitoring system. This is in line with reality since several authors observe that the poorest people have little access to these systems (e.g. ulme and Mosley, 1996). Second, if agents in a group can not observe their partners behavior without costs, and therefore decide not to monitor, opportunistic behavior will result. Thus even if the bank requires that each agent pledges an amount of deposits which guarantees that for 33

34 the entire group high effort is more beneficial than low effort, individual agents will decide to put low effort. The resulting equilibrium may imply that all group members put low effort. Clearly, the group lending system will then not solve the moral hazard problem. This result is comparable to hatak and uinnane (1999), who show that peer monitoring systems, in comparison to individual lending, are only better in reducing moral hazard problems if borrowers in a group act cooperatively. Third, if costly monitoring is taken into account, and all group members monitor each other, non-cooperative behavior will be avoided and thus the group lending system comes around the moral hazard problem. owever, it is still not clear that the group lending system will be more efficient than the individual lending system without monitoring due to the possibility that the opportunity costs of funds are higher that the deposit rate. f this is the case, the deposits that need to be pledged imply an additional burden that lowers the social surplus. Note also that we have assumed that cost of monitoring is not too high, such that the high effort is more efficient even with monitoring cost (see A.9). t is clear that a violation of A.9, which occurs if monitoring costs are high, will make the peer monitoring system not feasible. affont and Rey (2003) come to a similar conclusion. Using a model with a profit-maximizing monopolistic bank they show that group lending contracts are optimal as long as the cost of monitoring is not too large. t is also interesting to compare our result with two other costly monitoring models. Banerjee, Besley, and uinnane (1994) show that group lending with joint liability may better reduce moral hazard problems than individual lending without monitoring. Their model is therefore more optimistic about the benefits of group lending. owever, their model differs from ours. For instance, they assume that project risk is a continues variable, in contrast to our model where 34

35 project risk is a binary variable. More importantly, Banerjee, Besley, and uinnane (1994) assume that each group consists of one entrepreneur, and one auditor. The auditor monitors the entrepreneur and co-signs the loan, paying q to the bank if the entrepreneur fails. By assumption, the auditor does not produce. n our model, each group consists of two borrowers, who both monitor each other. Banerjee, Besley, and uinnane (1994) show that if the entrepreneur chooses a project with lower risk, income of the auditor increases since he saves q but increases due to an increase in the marginal costs of monitoring. A major difference with our model is also that the auditor makes the joint liability payment in all states of the world. n our model, the joint liability payment will not be made if the borrower-monitor fails. By determining the equilibrium project risk via maximizing profits of the auditor, Banerjee, Besley, and uinnane prove that an increase in the joint liability payment will induce lower project risk. Yet, in our view the model by Banerjee, Besley, and uinnane does not give a realistic view of how joint liability works in practice, in that they assume that there is only one borrower in the group, and that the joint liability payment is made in all states of the world. Our costly peer monitoring model can also be compared to that of Chowdury (2005). e also considers group lending with two borrowers, who are jointly liable and can monitor each other against some costs. is model differs from our model e.g. in that he assumes that the lending rate is set exogenously, whereas we assume that the lending rate (the debt contract) is set via the zero profit condition of banks. More importantly, he assumes a continues variable monitoring (in fact, the probability of monitoring) and quadratic monitoring costs. Optimizing profits sets the optimal level of monitoring. This leads to a reaction function for which the optimal level of monitoring of borrower i depends on the level of monitoring of borrower j. is model implies a reaction function of the ith borrower of mi = m j ( r), where 35

36 m i is the optimal level of monitoring of borrower i and m j is the optimal level of monitoring of borrower j. ( r) > 0 is the amount both borrowers get if they both invest in the safe project. is the income from the safe project and r is the amount to be paid to the bank. Similarly, the reaction function of the jth borrower equals m j = mi ( r). t is obvious that both functions are only compatible if m j = mi = 0. Thus, in his costly peer monitoring model the unique Nash equilibrium involves no monitoring! The result is that ordinary group lending with joint liability does not solve the moral hazard problem according to Chowdury (2005). e argues therefore that ordinary group lending with joint liability is not feasible. The moral hazard problem can only be resolved if the group lending system involves a combination of bank monitoring and joint liability or if it involves sequential financing. n our costly peer monitoring model this is not needed since it implies a unique Nash equilibrium where both borrowers monitor, and put in high effort. The main reason for this difference is that the amount of deposits to be pledged in our model guaranteed that no collusion between borrowers takes place. The required amount of deposits also ensures that if one borrower does not monitor, the other borrower still prefers to monitor (but puts in low effort). f this happens, the borrower who is not monitoring could do better if she also decides to monitor. Thus, one borrower monitoring and the other not cannot be a Nash equilibrium. Evidently, both borrowers not monitoring could not be a Nash equilibrium either, since, given the deposit that has to be pledged, it is always in the interest of one of the borrowers to deviate from the equilibrium by monitoring her partner. Therefore, the unique Nash equilibrium would involve both borrowers monitoring. Only in this situation, there is no incentive for one of the borrowers to deviate from the equilibrium. This does not happen in the model of Chowdury since he does not include a non-collusion constraint. n fact, the costly peer 36

37 monitoring model by Chowdury comes to the same conclusion than our costly peer monitoring model in which it is assumed that nobody monitors because of the high costs. Fourth, we argue that a main difference between a costly peer monitoring system and a delegated monitoring system is that with a delegated monitoring system an incentive scheme can be developed that can avoid strategic defaults, whereas with peer monitoring there is no possibility to differentiate between strategic default and bad luck. n other words, in a delegated monitoring system, the possibility of collusion between the supervisor and the supervisee can be avoided by means of an incentive contract written by the principal (the bank). We argue that this does not happen in a joint liability system. The reason is that with peer monitoring there is no formal incentive scheme so that there is an incentive to always pretend that a project failure is the result of bad luck, and not low effort. There are not many papers we are aware of that have compared the efficiency of a costly peer monitoring system with a delegated monitoring system. A recent exception is Conning (2005). The model by Conning (2005) is in many ways comparable to ours. e also uses a moral hazard model in which the bank operates under zero profits, and compares costly peer monitoring with a delegated monitoring system. n addition, he accounts for a noncollusion constraint between borrowers in a group. owever, in his model this is done via a minimum collateral requirement, whereas in our model the non-collusion is guaranteed due to a minimum level of deposits that needs to be pledged. An obvious difference between these two mechanisms is that the collateral requirement, unlike the deposit requirement, does not lead to a decrease in social surplus on account of a difference between the opportunity cost of funds and the deposit rate. More 37