A Model of Microfinance With Adverse Selection, Loan

Transcription

1 A Model of Microfinance With Adverse Selection, Loan Default, and Self-Financing 1 by Amitrajeet A. Batabyal 2 and Hamid Beladi 3 1 We thank the Editor, Calum G. Turvey, two anonymous referees, and session participants at the 2008 NARSC Annual Conference in New York City, for their helpful comments on a previous version of this paper. Batabyal acknowledges financial support from the Gosnell endowment at RIT. The usual disclaimer applies. 2 Department of Economics, Rochester Institute of Technology, 92 Lomb Memorial Drive, Rochester, NY , USA. Internet aabgsh@rit.edu 3 Department of Economics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX , USA. Internet hamid.beladi@utsa.edu 1 Electronic copy available at:

2 A Model of Microfinance With Adverse Selection, Loan Default, and Self-Financing Structured Abstract Purpose: We analyze a market for microfinance in a region of a developing nation in which all projects are either of high or low quality. There is adverse selection because only borrowers know whether their project is of high or low quality but the microfinance institutions (MFIs) do not. The MFIs are competitive, risk neutral, and they offer loan contracts specifying the amount to be repaid only if a borrower's project makes a profit. Otherwise, this borrower defaults on his contract. Design/methodology/approach: We use a game theoretic model that explicitly accounts for adverse selection and then we study the trinity of adverse selection, loan default, and self-financing. Findings: First, in the pooling equilibrium, a borrower with a low quality business project will obtain positive expected profit. In contrast, this borrower will obtain zero expected profit in the separating equilibrium. Second, for small enough values of the probability p that a business project is of high quality, MFIs will not finance any business project in the pooling equilibrium. Third, the cost of sending a signal is not too high and hence a separating equilibrium exists. Finally, under some circumstances, self-financing can be used to mitigate adverse selection related problems. Research limitations/implications: We study a model with only two types of business projects. In addition, we do not allow for repeated interactions between borrowers and MFIs. Keywords: Adverse Selection, Loan Contract, Microfinance, Self-Financing, Signaling Game JEL Codes: G210, O120, D820 2 Electronic copy available at:

3 1. Introduction Muhammad Yunus, a former economics professor at Chittagong University in Bangladesh and a subsequent winner of the Nobel Prize for peace in 2006, first began making small loans to local villagers in the 1970s. Since then, his actions have led to the creation of the remarkably successful Grameen Bank and to what some have called the microfinance revolution. 4 This revolution has not only had a significant impact on the developing countries of the world but it has also affected parts of the developed world. Specifically, Muhammad Yunus s Grameen Bank has now been duplicated in five continents. As noted by Armendariz de Aghion and Morduch (2005), Grameen Bank inspired approaches begun in Latin America have now found their way to the streets of El Paso and New York City and policy makers in China and India are now developing their own homegrown microfinance institutions (MFIs). Indeed, given the salience of the microfinance revolution, the United Nations designated 2005 as the International Year of Microcredit. Today, generally speaking, there are two views of microfinance. The first view see Robinson (2001) considers the ideas surrounding microfinance to be nothing short of revolutionary and paradigm shifting given contemporary banking practices. The second view see Morduch (1998) says that the benefits of microfinance have yet to be fully developed and tested over time. This dichotomy notwithstanding, most researchers now agree that microfinance has...shaken up the world of international development (Armendariz de Aghion and Morduch, 2005, p. 1). Given the contemporary salience and the future promise of microfinance as, inter alia, a poverty alleviating tool, researchers have studied various aspects of microfinance from a theoretical 4 The term microfinance typically refers to the provision of financial services such as small loans to poor or low income clients including consumers and the self-employed. For more on the history and the early working of the Grameen Bank, the reader should consult Yunus (2001, 2007). 3

4 and from an empirical perspective. Focusing on La Paz, Bolivia, Navajas et al. (2003) have analyzed the ways in which changes in competition between lenders have affected the terms of loan contracts and the diligence with which borrowers repay their loans. Daru et al. (2005) describe the outcome of an International Labor Organization (ILO) sponsored study designed to alleviate the plight of poor borrowers in South Asia who often have great difficulty in repaying their loans because they are bonded to their employers. McIntosh and Wydick (2005) have argued that competition between MFIs can give rise to situations in which the most impatient borrowers begin to obtain multiple loans and thereby create a negative externality that leads to less favorable equilibrium loan contracts for all borrowers. Andersen and Malchow-Moller (2006) have used a game theoretic model to show that the existence of a collateral requirement in connection with formal loans gives rise to a Nash equilibrium in which both informal and formal lenders earn higher profits. Karlan et al. (2006) have used experimental methods in Lima, Peru, to explain why MFIs have increasingly been moving away from group based lending practices. Katchova et al. (2006) point out that relative to static models, a dynamic model better explains the present experience with individual and group lending in developing nations. Karlan and Zinman (2007) have studied information asymmetries in lending by using a field experiment in South Africa. They find stronger evidence for the presence of moral hazard but weaker evidence in support of the existence of adverse selection. Simtowe et al. (2007) have used data from Malawi to conduct an empirical investigation of the salience of moral hazard in microfinance. This analysis shows that MFIs cannot rely on peer selection and pressure to reduce the incidence of moral hazard. Instead, in repeated borrowing and lending contexts, MFIs need to continuously evaluate the changing, and typically growing, financial needs of the borrowers. Finally, using a cross-country perspective, Hartarska and Nadolnyak (2008) 4

5 have studied the extent to which rating agencies have helped MFIs in raising funds. The papers discussed in the previous two paragraphs have certainly advanced our understanding of many aspects of microfinance. This notwithstanding, three points are now worth emphasizing. First, in their recent book, Armendariz de Aghion and Morduch (2005, pp ) clearly point out that loan default is an issue of considerable significance in the environments in which MFI s typically operate. Second, in this same book, Armendariz de Aghion and Morduch (2005, p. 37) contend that the task of microfinance is...to solve the information problems... stemming in part from the presence of adverse selection in the contractual relationship between MFIs and potential borrowers. In addition to the papers that we have already cited in the previous two paragraphs, researchers such as Armendariz de Aghion and Gollier (2000), Laffont and N Guessan (2000), and Hermes and Lensink (2007) have also studied adverse selection in the context of lending by MFIs. Even so, the third point we would like to make is that a key aim of these papers has been to show how adverse selection related problems can be mitigated by studying group lending with joint liability. What has received very little attention in the extant literature is the role that a particular signaling device, namely, self-financing, can play in mitigating adverse selection related problems in the context of lending by MFIs to poor borrowers. In addition, to the best of our knowledge, there are virtually no studies that compare the outcomes of the interactions between MFIs and borrowers when these borrowers are and are not able to self-finance a fraction of their business projects. Given this state of affairs, our primary objective in this paper is to analyze a theoretical model of the interaction between MFIs and poor borrowers that explicitly accounts for the trinity 5

6 of adverse selection, 5 loan default, and self-financing. A secondary objective of ours is to compare and contrast the outcomes of the interaction between MFIs and borrowers when these borrowers are and are not able to self-finance a fraction of their business projects. Specifically, we focus on a market for microfinance in a region of an arbitrary developing country in which all business projects are of either high or low quality. There is adverse selection because only borrowers know whether their business project is of high or low quality but the MFIs do not. 6 The MFIs are competitive, risk neutral, and they offer loan contracts specifying the amount to be repaid only if a borrower s business project makes a profit. Otherwise, this borrower defaults on his contract. In this setting, we undertake four tasks. First, we determine the pooling equilibrium repayment amount and the set of business projects that are financed by the MFIs. Second, we study the borrower/mfi interaction when the borrower self-finances a fraction of his business project and thereby signals this project s quality to the MFI. Third, we compute the best separating equilibrium of the signaling game between the self-financing borrower and the MFI. Finally, we compare and contrast this best separating equilibrium with the previously determined pooling equilibrium. The rest of this paper is organized as follows. Section 2 describes the theoretical framework of the paper in detail. Section 3 undertakes the foregoing paragraph s first task involving the determination of the pooling equilibrium repayment amount. Section 4 sheds light on the previous 5 In the context of this paper, adverse selection refers to a situation in which the MFIs lack good information about the riskiness of the borrowers business projects. Therefore, the MFIs are unable to discriminate against the risky borrowers. For more on adverse selection in the context of microfinance see Armendariz de Aghion and Morduch (2005) and for textbook treatments of this concept see Kreps (1990, chapter 17) and Hindriks and Myles (2006, chapter 9). 6 The problem of adverse selection arises because MFI s do not know the inherent riskiness of borrowers. As noted by Armendariz de Aghion and Morduch (2005, p. 37), some borrowers may simply be more prudent, more conservative, better insured. Others may be risk-loving, may be poorly disciplined, or may face competing claims on their funds. This situation creates a scenario in which MFIs may not be able to find an interest rate that appeals to all creditworthy borrowers and permits them to recover their expected costs. This is why, in the presence of adverse selection, less risky or more creditworthy borrowers may get shut out of the credit market. 6

7 paragraph s second task in which a borrower self-finances a fraction of his business project. Section 5 discusses the preceding paragraph s third task which involves computing the best separating equilibrium. Section 6 comments on the prior paragraph s fourth and final task which involves comparing the separating equilibrium of section 5 with the pooling equilibrium of section 3. Section 7 concludes and discusses ways in which the research described in this paper might be extended. 2. The Theoretical Framework We adapt standard adverse selection models of the sort studied by Stiglitz and Weiss (1981), Armendariz de Aghion and Morduch (2005, pp ), and Hindriks and Myles (2006, pp ) to consider a scenario in which there is adverse selection, loan default, and self-financing. To reiterate from section 1, the primary contribution of our paper is to demonstrate the value of a particular signaling device, i.e., self-financing, in reducing adverse selection related problems in the context of lending to poor borrowers by MFIs. The secondary contribution is the comparative analysis we present of the outcomes of the interaction between MFIs and borrowers both with and without self-financing of business projects. Consider a particular geographic region in an arbitrary developing country. Poor borrowers in this region are seeking financing in terms of small loans for various small scale business projects. All business projects in this region are either of high quality with probability or of low quality with complementary probability To model the adverse selection aspect of the underlying story, we suppose that only the borrowers know whether their business projects are of high or low quality. A high quality business project yields positive profit denoted by with probability and zero profit with probability Similarly, a low quality business project gives rise to positive 7

8 profit with lower probability i.e., and zero profit with a higher probability To model the fact that we are talking about very small scale business projects, we suppose that the cost of all the pertinent projects is To obtain the small loans mentioned in the previous paragraph, the borrowers have to interact with MFIs. We are using the term MFI in this paper broadly to include banks such as the Grameen Bank in Bangladesh and the SEWA Bank in India and other more general organizations such as the Rural Finance Company in Malawi and the Zambuko Trust in Zimbabwe. Following the work of McIntosh and Wydick (2005), we suppose that the MFIs in the developing country region under study are competitive and risk neutral. This means that these institutions will offer loan contracts to our borrowers that yield zero expected profit. The reader should note that even though we are assuming that the MFIs under study are competitive, we acknowledge that borrowers may have access to funds from sources other than the relevant MFIs. If such access such as informal borrowing and lending among friends and relatives exists then, from the standpoint of the MFIs, this will act as an additional source of competition and this additional competition may crowd out some lending by MFIs. A loan contract specifies a repayment amount that is to be repaid to the MFI but this repayment occurs only if a business project makes a profit. Otherwise, we suppose that a borrower defaults on his loan contract. Finally, the opportunity cost of funds to a MFI is Our first task now is to determine the pooling equilibrium repayment amount and the set of projects that are financed by the MFIs. 3. Equilibrium Repayment Amount The MFIs in our paper are risk neutral and they cannot distinguish between high and low 8

9 quality business projects. 7 This means that any particular MFI will either finance all business projects or will finance none of them. Now, from an overall standpoint, the MFIs will break even by financing all the business projects if (1) Equation (1) tells us that the repayment amount in the so called pooling equilibrium is (2) where The reader will note that the probability of loan repayment, is increasing in the proportion of high quality business projects. Now, a borrower of type will go through with a project if (3) Upon simplification, the inequality in (3) can be expressed as Now, using the value of from equation (2) in the preceding inequality, the condition specified in (3) can be written as 7 Also see footnote 3 in section 1. 9

10 (4) Because the probability of loan repayment, is increasing in the proportion of high quality business projects, MFIs will want borrowers to undertake a business project of type if the probability is high enough. Put differently, MFIs will want borrowers to complete a business project of type if the proportion of all business projects that are high quality or is large enough. This will happen if, mathematically speaking, high quality business projects satisfy and low quality business projects satisfy Therefore, in the remainder of this paper, we assume that these two conditions hold. 8 The reader will note that the above two assumptions can also be written as and as Now, let denote the solution to the equation Then, the following two points follow. First, this threshold value of the probability or is less than one. Second, all business projects will be undertaken when This is true because when this last inequality holds, we have Note that no business project whether of high or low quality will be undertaken by our borrowers when because when this strict inequality holds, we have Summarizing, what we have demonstrated thus far is the following. All business projects are undertaken by our borrowers and this happens when Conversely, no business project 8 Note that these two conditions do not involve the repayment amount will lead to negative returns after the loan has been repaid. and hence they do not imply that low quality business projects 10

11 is undertaken by these same borrowers when This last result clearly tells us that there exist circumstances in which the microfinance market essentially breaks down. This is likely to happen when the opportunity cost of funds is large relative to the profit variable and when the function is small, i.e., when the proportion of low quality business projects is relatively large. We now move on to examine the borrower/mfi interaction when the borrower self-finances a fraction of his business project and thereby signals this project s quality to the MFI. 4. Self-Financing of Business Projects We have already noted in footnote 3 in section 1 that in the presence of adverse selection, borrowers with high quality business projects may get shut out of the credit market. The analysis in section 3 provided a formal demonstration of this same point. Having said this, note that even when all business projects are undertaken by our borrowers, and this happens when the resulting outcome is a pooling equilibrium. In a sense then, the adverse selection problem remains because the repayment terms stipulated by the MFIs are identical for all borrowers. This outcome is unsatisfactory in the sense that instead of having differential repayment terms, borrowers with high quality business projects are lumped together with and treated the same way as borrowers with low quality business projects. Given this state of affairs, what we now want to study is whether borrowers with high quality business projects can credibly signal to the MFIs that their business projects are more likely to be profitable by using some sort of signaling device. The specific signaling device that we study is the act of self-financing a fraction of a business project. If this kind of signaling is not too costly and hence possible, then the resulting equilibrium will be a separating equilibrium in which the basic problem stemming from adverse selection is solved in the sense that borrowers with high quality business projects are offered repayment terms by the MFIs that are 11

12 different from the repayment terms offered by these same MFIs to borrowers with low quality business projects. Now, to fix ideas, suppose that a borrower can signal the quality of his business project to a MFI by self-financing a fraction of this project. Further, suppose that the opportunity cost of funds to a borrower is 9 In this setting, we now want to delineate the borrower s payoff as a function of the type of his business project, the loan repayment amount and the self-financing fraction In particular, we want to shed light on the properties of the indifference curve for each type of borrower in space. If a borrower self-finances a fraction of his business project and repays to the MFI for the rest of this project then his expected payoff for a business project of type is (5) Now, if we totally differentiate the expression in equation (5) with respect to the repayment amount and the self-financing fraction then we obtain the slope of the indifference curve for a type borrower. Mathematically, we get (6) 9 Note that if then we have a costly signal. 12

13 as long as In other words, the slope of the indifference curve in a relatively small (large) value of the repayment amount space is negative (positive) for Figure 1 shows the two types of Figure 1 about here negatively sloping indifference curves in space. As shown in figure 1, the direction of preference is south-westerly because from equation (5) it is clear that a borrower s expected payoff decreases as either the repayment amount or the self-financing fraction increases. 10 We see that on the downward sloping side of the indifference curve, the curve is steeper for the low quality business project relative to the high quality business project. The reader will note that this feature arises because i.e., the probability of loan repayment is smaller for the low quality business project. From this discussion it follows that the well known single crossing property of the indifference curves see figure 1 also holds. 11 This concludes our initial discussion of the borrower/mfi interaction with self-financing of business projects. We now compute the best separating equilibrium of the signaling game between the self-financing borrower and the MFI. 5. The Best Separating Equilibrium From the standpoint of a MFI, the desirable aspect of self-financing is that it permits this institution to distinguish between or separate high and low quality business projects. Therefore, in 10 See Kreps (1990, chapter 17) and Hindriks and Myles (2006, chapter 9) for textbook discussions of the shapes of indifference curves of the sort shown in figure This single crossing property is a feature of many agency theoretic models with adverse selection. In the context of our model, this property refers to a situation in which any given indifference curve for a type borrower crosses any given indifference curve for a type borrower at most once. For textbook treatments of the single crossing property, see Kreps (1990, pp ) or Varian (1992, p. 457). 13

14 a separating equilibrium, the MFIs offer separate loan contracts to self-select high and low quality business projects. Because a MFI knows the type of business project a specific borrower is presenting it with, it can offer different repayment amounts given by for From the assumption made in section 3 see the paragraph immediately after equation (4) it follows that (7) Equation (7) tells us that in a separating equilibrium only the high quality business projects are undertaken. Now, the fundamental point to note is the following. The minimum amount of selffinancing that a borrower with a high quality business project undertakes to effectively signal his type must give rise to a negative expected payoff to a borrower with a low quality business project if this borrower were to self-finance amount of his project and finance the rest from a MFI with repayment amount Put differently, must solve (8) Using the equilibrium repayment amount we get 14

15 (9) Simplifying equation (9) gives us (10) where From the above reasoning we can tell that as the marginal cost of signaling decreases and the probability increases, the critical level of self-financing has to increase. Similarly, as increases and increases, this critical level of self-financing also has to increase. The reader should understand that because the expected payoff to a low quality business project is zero, the expected payoff to a high quality business project will be positive. Having said this, we are now in a position to describe the best separating equilibrium that is the object of this section s inquiry. Specifically, in this equilibrium, a borrower with a low quality business project will not selffinance and will accept the MFI s loan contract as long as On the other hand, a borrower with a high quality business project will self-finance and accept the MFI s loan 15

16 contract as long as Finally, note that the MFI will offer a loan contract with repayment amount if and it will offer a loan contract with repayment amount if These then are the properties of the best separating equilibrium. Our final task now is to compare and contrast this best separating equilibrium with the pooling equilibrium discussed in section 3 of this paper. 6. A Comparative Exercise Some thought will convince the reader that the borrower with a low quality business project will not be better off but could be worse off in the separating equilibrium of section 5. In particular, note that for large enough values of the probability that a business project is of high quality, all business projects will be financed and with the same terms as in the pooling equilibrium described in section 3. In this pooling equilibrium, a borrower with a low quality business project will obtain positive expected profit. In contrast, this same borrower with the low quality business project will obtain zero expected profit in the separating equilibrium of section 5. For small enough values of the probability that a business project is of high quality, MFIs will not finance any business project in the pooling equilibrium of section 3. This tells us that borrowers with low quality business projects will obtain zero expected payoff in both the pooling equilibrium and in the separating equilibrium. In contrast, borrowers with high quality business projects will unambiguously prefer the separating equilibrium of section 5. The reader should now note the following two points. First, in the model of this paper, the cost of separation or, alternately, the cost of sending a signal is not too high and hence a separating equilibrium exists. This need not always be the case. In particular, if it is too costly for some 16

17 borrowers to self-finance a fraction of their business projects or, equivalently, if the cost of separation is too high, then no separating equilibrium will exist and hence it will not be possible to mitigate adverse selection related problems in the context of microfinance by using self-financing as a signaling device. Second, while it is true that, in general, borrowers with high quality business projects will prefer a separating equilibrium, if its exists, the welfare of borrowers with low quality business projects depends fundamentally on critical parameter values and, in particular, the value of the probability A contribution of our paper is to demonstrate the manner in which the welfare of borrowers with low quality business projects depends on, for instance, the value of 7. Conclusions In this concluding section, we first discuss some of the ways in which MFIs can use the results of this paper and then we suggest ways in which the research delineated in this paper might be extended. The extant literature on microfinance has shown that adverse selection related problems that plague the interactions between borrowers in developing nations and MFIs can be mitigated by using the concept of group lending. Indeed, in their recent book, Armendariz de Aghion and Morduch (2005, p. 113) refer to the idea of group lending as one of the major innovations of the microfinance movement... Even so, researchers and practitioners have now come to the conclusion that although group lending solves some problems, it often creates others. This recognition has led researchers studying lending by MFIs to look beyond the notion of group lending. In this regard, Armendariz de Aghion and Morduch (2005, p. 136) contend that analysts now ought to address the adverse selection problem by providing ways for borrowers to build up financial assets and then...base lending on [these] assets. If borrowers are allowed to build up financial assets then, over time, some of them in particular those with discipline and money 17

18 management skills will be in a position to self-finance a fraction of their business projects. This is where the analysis of our paper is pertinent. The central result of our paper is that under some circumstances, a credible signaling device such as self-financing can be used to mitigate adverse selection related problems that routinely plague interactions between poor borrowers in developing countries and MFIs. 12 Therefore, MFIs can use the results of this paper in three ways. First, consistent with the previously quoted contention of Armendariz de Aghion and Morduch (2005, p. 136) and particularly in the context of intertemporal lending relationships, MFIs ought to encourage borrowers to build up financial assets over time. This will enable a subset of the pool of borrowers to self-finance a fraction of their business projects. Second, just as some researchers have suggested that lending by MFIs can be made more efficient by making repayments public see Armendariz de Aghion and Morduch (2005, pp ) MFIs ought to make it publically known that they will look favorably upon loan requests that involve some degree of selffinancing. Finally, our analysis in this paper shows that if separation is too costly or, equivalently, if it is too costly to provide a credible signal to a MFI, then a separating equilibrium will not exist. Given this finding, it would be useful for MFIs to look for ways to make self-financing a more plausible alternative for poor borrowers. In addition to permitting the accumulation of financial assets over time, one way to do this might be to reduce the difference in the interest rate that borrowers are charged for loans and the interest they are paid on their deposits. The analysis in this paper can be extended in a number of different directions. We now 12 The focus of our paper on individual loans notwithstanding, as the Editor has noted, there is a self-financing and signaling interpretation that one can give to borrower/mfi interactions in group settings as well. Specifically, in a group lending scenario, members are sometimes expected to contribute to a savings account over several months until a threshold savings balance has been established. This savings balance can then be used to support a group loan. Because this balance is, in principle, fungible, we can think of it as a form of self-financing. In addition, the ability to build up such a balance can be interpreted as a signal from the group to a MFI. 18

19 suggest two potential extensions. First, we studied models with two types of business projects, i.e., high and low quality projects. An obvious way to extend the analysis in this paper would be to analyze a model with either types of business projects or with a continuum of business project types. Second, in the models that we examined in this paper, we said nothing about intertemporal considerations in the choice of optimal loan contracts. Given the discussion in the previous paragraph, it would be useful to analyze a game theoretic model that allows repeated interactions between borrowers and MFIs. Studies that analyze these aspects of the problem will enhance our understanding of the economics of microfinance. 19

20 R I hq I lq 1 f Figure 1 20

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