Good Intentions Pave the Way to... the Local Moneylender

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1 Good Intentions Pave the Way to... the Local Moneylender Lutz G. Arnold (corresponding author) Benedikt Booker University of Regensburg Department of Economics Regensburg, Germany Phone: Fax: Abstract Microborrowers may use usurious loans to repay a loan taken from a microfinance institution (MFI) because of having neglected the time inconsistency of optimal plans or having discounted future payoffs too strongly from the ex-post perspective. Microfinance programs should strive at preventing such consequences of bounded rationality. JEL classification: G21, D91 Key words: microfinance, hyperbolic discounting

2 1 Introduction In a widely discussed article in the Wall Street Journal, Gokhale (2009) highlights that moneylending, at very high interest rates and often using harsh methods of enforcing repayment, tends to coexist when and where microfinance (MF) flourishes. There is a debate over the correct interpretation of this observation. A critical view holds that MF fails to provide a well-functioning substitute for traditional moneylending activity. An interpretation which is more benevolent toward MF holds that demand for loans simply grows faster than the MF industry. In any case, there is some evidence to suggest that it happens quite frequently that MF borrowers turn to a moneylenders (ML) in order to meet the repayment obligations on their loans. The reply of standard economic theory is: so what? If people decide to take an MFI loan and use an ML loan to repay the former, then this reveals their preference for taking risks rather than staying inactive. Yet, as in similar contexts, this reply misses the point if borrowers have presentbiased preferences (Laibson, 1997, O Donoghue and Rabin, 1999). In that case, it may not be in the borrower s best interest to act in such a way that she ends up with an ML loan, for two different reasons. First, consider a naive borrower with a small-scale investment project who is unaware of the time inconsistency of optimal plans induced by her present bias. It may happen that she takes an MFI loan, planning to accept a penalty exerted by the MFI in case of default due to failure of the project, but then revises her plan and repays the MFI loan with a new loan from an ML, even though she would not have taken the MFI loan in the first place if she had held sophisticated (correct) beliefs about her future behavior. Second, consider a sophisticated borrower, who correctly anticipates her future actions, but interpret her present bias as an error (O Donoghue and Rabin, 2003, 187). It may happen that she takes an MFI loan and ends up with an ML loan, even though she would either accept the MFI penalty in case of failure or not take the MFI loan in the first place if she acted in line with her true preferences. So on the premise of present-biased preferences, one can argue that MFI loans drive boundedly rational borrowers to usurious MLs. The main policy implication is that the financial literacy component of MF programs should be taken very seriously and focus not only on the financial products but also on the very people using them. 2 Model The following model is used to highlight the consequences of naive or boundedly rational behavior for the investment behavior of a micro entrepreneur. There are three dates t = 0, 1, 2. At date 0, the borrower is endowed with an investment project, which requires one unit of capital. She has no 1

3 t= 0 stay inactive 0 decision about MFI loan take MFI loan, invest failure success t= 1 take ML loan, invest decision about ML loan accept MFI penalty, no ML loan p y 2 failure success failure success t= 2 P y 2R 0 y Figure 1: Decision tree equity. An MFI offers her a loan. We focus on situations in which she repays the loan with certainty, so there is no default risk, and the MFI charges no interest. The borrower decides whether to stay inactive (which yields payoff zero) or take the MFI loan and invest. The project succeeds with probability π (0 < π < 1) and fails with probability 1 π. If it succeeds, it yields payoff y (> 2) at date 1, otherwise the payoff is zero. The borrower is endowed with the same project at t = 1. If the project started at t = 0 succeeds, she repays one unit of income to the MFI, uses another unit of income to start the new project, and consumes y 2. At date 2, she consumes y or nothing, depending on whether the second project succeeds or fails. If the project started at t = 0 fails, she decides whether to default on the MFI loan or take a loan from an ML and use this loan to repay the MFI and start the new project at date 1. If she defaults on the MFI loan she faces a penalty p (> 0). We treat the gross interest on the ML loan R (> 1) as exogenous. At date 2, the borrower repays 2R and consumes y 2R (> 0) if her second project succeeds and faces a penalty P (> p) if it also fails (see Figure 1). The borrower is risk-neutral and present-biased. Let c t be the difference of consumption and the penalty taken at t (= 1, 2). When we compare naive with sophisticated decision-making in Section 3, we assume that utility is U 0 = β(δc 1 + δ 2 c 2 ) as of date 0 and U 1 = c 1 + βδc 2 as of date 2, where β < 1 and δ 1. The borrower is said to be naive if at date t (= 0, 1), she plans to take the current and future actions which maximize U t, ignoring possible time inconsistency. She is sophisticated if she maximizes utility subject to the time consistency constraint, i.e., if she solves the problem backward anticipating future optimal decisions (cf. O Donoghue and Rabin, 1999). 2

4 When we compare sophisticated with rational decision-making in Section 4, perceived utility is U 0 = c 1 + βδc 2 at date 0 and U 1 = c 1 + βδc 2 at date 1. That is, dates 0 and 1 are so close together (compared to dates 1 and 2) that there is no discounting (or, equivalently, all the action going on at dates 0 and 1 in the former model takes place at one date here). As before, the sophisticated borrower solves her utility maximization problem backward. The present bias implied by β < 1 is now interpreted as bounded rationality. The borrower s true preferences are obtained by setting β = 1. 3 Naive versus sophisticated investment behavior Suppose the borrower is naive. She plans at t = 0 to accept the MFI penalty at t = 1 if the investment project fails if, and only if, βδ 2 [(1 π)( P ) + π(y 2R)] < βδ( p). (1) Given the plan to accept the penalty, she takes the MFI loan at t = 0 if, and only if, βδ [(1 π)( p) + π(y 2)] + βδ 2 π 2 y > 0. (2) It turns out that the plan to accept the penalty is time-inconsistent and the borrower takes the ML loan in order to repay the MFI loan and invest again if, and only if, βδ [(1 π)( P ) + π(y 2R)] > p. (3) If she were sophisticated, she would anticipate her decision not to accept the MFI penalty. She would then not take the MFI loan in the first place if, and only if, [ ] βδ 2 (1 π) 2 ( P ) + (1 π)π(y 2R) + βδπ(y 2) + βδ 2 π 2 y < 0. (4) Proposition 1: Let p βδ > (1 π)p π(y 2R) > π y 2 + δπy 1 π δ Then a naive investor takes the (interest-free) MFI loan and invests at t = 0, though she would not if she were sophisticated. Proof: The inequalities in the proposition imply the validity of the inequalities in (1) (4). Under the conditions of Proposition 1, the naive borrower ends up with an ML loan because of having taken a fair MFI loan (and having had bad luck). It is easy to construct situations in 3 > p δ.

5 which the borrower would not use an ML loan in the absence of an MFI. For instance, suppose the borrower can take an ML loan at gross interest R to carry out the investment project at date 0. If it succeeds, she repays, reinvests, and consumes y R 1 at date 1 and y at date 2 if the second project also succeeds; if it fails, the penalty P applies at date 1. Then the borrower does not invest if, and only if, (1 π)p π(y 2R) > δπ 2 y π(r 1). 4 Sophisticated versus rational investment behavior Suppose the borrower is sophisticated but present-biased and there is no discounting between dates 0 and 1. Condition (3) continues to imply that she takes the ML loan if the project financed using the MFI loan fails. Consider now the case in which the sophisticated borrower does invest at date 0: [ ] βδ (1 π) 2 ( P ) + (1 π)π(y 2R) + π(y 2) + βδπ 2 y > 0. (5) If the borrower were rational, she would take the MFI penalty at date 1 if, and only if, δ [(1 π)( P ) + π(y 2R)] < p. (6) Proposition 2: Let min { p βδ, π 1 π } y 2 + βδπy > (1 π)p π(y 2R) > p βδ δ. A sophisticated investor takes the (interest-free) MFI loan at t = 0 and the ML loan at t = 1 if her project fails. If she were rational, she would either accept the MFI penalty in case of failure or not take the MFI loan in the first place. Proof: The inequalities in the proposition imply the validity of (3), (5), and (6). If π y 2 + πδy 1 π δ she takes the loan and accepts the penalty in case of failure. Otherwise, she stays inactive at t = 0. Proposition 2 deals with the question of whether a rational borrower would default on or not even take the (zero-interest) loan designed for a present-biased borrower (who does not default). Taking default into account reinforces the conclusion. To break even, the MFI has to set the contractual repayment equal to 1/π if the rational borrower defaults when her project fails. The increase in the contractual repayment weakens the condition for default in case of failure (cf. (6)). So the assertion of Proposition 2 holds true. 4 > p δ,

6 5 Conclusion From the fact that a microborrower ends up with a loan from a moneylender we must not conclude that she acted in her best interest ex ante. She might have neglected the time inconsistency of optimal plans or simply regret having discounted future payoffs too strongly. The main policy implication for MF markets is that financial literacy should be more than a buzzword in MF programs and should not focus exclusively on financial products but also on the people using them. MFIs should make borrowers envisage the consequences of failure of their projects on their future financial position and encourage them to become clear about the relative valuation of future versus current consumption. In designing their programs, MFIs should take care of the impact of the penalties they threaten to impose on borrowers decision to look for alternative sources of funds. References Gokhale, Ketaki (2009), As Microfinance Grows in India, So Do Its Rivals, The Wall Street Journal, December 15. Laibson, David (1997), Golden Eggs and Hyperbolic Discounting, Quarterly Journal of Economics 62, O Donoghue, Ted and Matthew Rabin (1999), Doing it Now or Later, American Economic Review 89, O Donoghue, Ted and Matthew Rabin (2003), Studying Optimal Paternalism, Illustrated with a Model of Sin Taxes, American Economic Review, Papers and Proceedings 93,