The trade-off between profitability and outreach in microfinance

Economic Modelling xxx (2017) 1–11

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Economic Modelling journal homepage: www.elsevier.com/locate/econmod

The trade-off between profitability and outreach in microfinance Maurizio Caserta a, Simona Monteleone b, Francesco Reito a, * a b

University of Catania, Department of Economics and Business, Italy University of Catania, Department of Education, Italy

A R T I C L E I N F O

A B S T R A C T

JEL Classificationnumbers: D81 L14

The focus of this paper is on the alleged shift of microfinance programs from targeting poor borrowers towards wealthier clients and profitability. In a simple moral-hazard setting, we determine the equilibrium financial contracts offered by a for-profit and a not-for-profit microfinance institution (MFI). We show that: i) with a forprofit MFI, mission drift does not necessarily occur if borrowers are offered a combination of individual and joint liability contracts; ii) with a not-for-profit MFI, poor individuals are never crowded out by wealthier entrepreneurs.

Keywords: Microfinance Outreach Mission drift

1. Introduction In recent years, the microfinance literature has often claimed that many microfinance institutions (MFIs) have increased their attention towards financial sustainability and profitability. Namely, there seems to be a shift, known as mission drift, from the classic outreach to poor borrowers to a new focus on (relatively) wealthier clients.1 Armendariz de Aghion and Szafarz (2011) argue that the drift is well described by the dynamics of the average loan size provided by MFIs. They relate mission drift to the increase on the loan size received by borrowers, when this increase is justified neither by cross-subsidization among different risk-type clients nor by progressive lending. The authors posit that this tendency is motivated by the profit-seeking behavior of MFIs, which can find it more attractive to lend to richer individuals who ask for larger loans. Besides, perhaps due to lack of collateral, poorer borrowers are in general served by joint liability programs, while richer borrowers often receive individual loans. This empirical evidence is discussed in Madajewicz (2003), who finds that in microfinance the proportion of group loans declines with wealth in favor of individual loans. Additional evidence is reported by Ahlin and Townsend (2007), who show that in microfinance the proportion of group lending is declining with borrowers’ wealth in favor of individual and more profitable loans.2 More to

the point, Cull et al. (2009) and Hermes et al. (2011) argue that lending to the poor entails higher transactions costs, and thus profitability can be achieved only at the expense of outreach. However, the literature is not unanimous about the emergence of mission drift in microfinance. Empirical support for the non-existence of mission drift can be found in the cross-country analysis of Mersland and Strøm (2010), and in Gonzalez-Vega et al. (1997), who show that the commercialization of BancoSol in Bolivia has not reduced the depth of outreach. Quayes (2012) even describes a positive correlation between social welfare and profitability. Frank (2008) reports some evidence that, in Latin America, regulated MFIs offer larger loans than unregulated MFIs. These larger loans can be seen as a natural evolution of microfinance practices, which should support dynamic and growing economies where entrepreneurs need to widen their business activities. She also argues that the shift towards profitability can be motivated by the need to decrease the reliance on donor funding, which is highly volatile and unpredictable. Similar results are reported by Hartarska and Nadolnyak (2007), and Kar (2013). Raihan et al. (2017) show that, although the emergence of the Microcredit Regulatory Authority in Bangladesh in 2006 has led to an increase of about 28 percent on the size of micro-loans, this has also contributed to higher capital accumulation and employment opportunities. And, clearly, the extent of outreach may also depend on

* Corresponding author. E-mail addresses: [email protected] (M. Caserta), [email protected] (S. Monteleone), [email protected] (F. Reito). 1 Banco Comportamos in Mexico started as a non-profit NGO, and is now a publicly traded for-profit MFI. Grameen Bank and ASA in Bangladesh have recently shown that it is possible to implement a sustainable and profitable business model for MFIs. In 2011, ASA, which is a donor-free institution, had a gross loan portfolio of 638.6 million USD and an average loan balance per borrower of 152.7 USD (http://www.asa.org.bd/about.html). 2 On the same topic, Cull et al. (2009), using a sample of 124 MFIs, report that individual-based institutions lend an average loan of 1220 USD, while group-based institutions (or village MFIs) lend on average 148 USD. https://doi.org/10.1016/j.econmod.2018.01.003 Received 13 July 2017; Received in revised form 20 November 2017; Accepted 3 January 2018 Available online xxxx 0264-9993/© 2018 Elsevier B.V. All rights reserved.

Please cite this article in press as: Caserta, M., et al., The trade-off between profitability and outreach in microfinance, Economic Modelling (2017), https://doi.org/10.1016/j.econmod.2018.01.003

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Table 1 Outreach and main declared mission of four major MFIs. (Source: Mix Market Report, 2009 and Grameen Foundation). MFI

Country

Grameen

Bangladesh

ASA BRI

Bangladesh Indonesia

Compartamos

Mexico

Legal Status

Outreach (%)

Main Mission

Regulated MFI NGO Regulated MFI Regulated MFI

4.43

Poverty Reduction

3.31 1.44

Income Generation Financial Services to small entrepreneurs Create Development Opportunities

Table 2 Number of Institutions by forms of incentive compatibility contracts. (Source: Mix Market Report, 2009).

No Individual Liability Individual Liability

0.55

Total

No Joint Liability

Joint Liability

Total

20 (3.0%) 259 (39.1%) 279 (42.1%)

81 (12.2%) 303 (45.7%) 384 (57.9%)

101 (15.2%) 562 (84.8%) 663 (100%)

compatible interest rate. Thus, the issue of mission drift may be independent of whether a profit motivated lender operates or not. This conclusion is similar to the one obtained by Ghosh and van Tassel (2011), with the difference that, in their paper, the entry of profit-oriented donors in the microfinance industry may force MFIs to drive more attention to profitability in order to attract external funds. In contrast, this paper does not consider the presence of donors and shows that, as long as the output produced by poor borrowers is sufficient to cover the individual or joint liability payments, more outreach does not always result in a lower portfolio return for MFIs. The theoretical model is close to Madajewicz (2011), with some significant differences in the structure and conclusions. There, lenders are in perfect competition and the financial contract is chosen by borrowers, who receive the entire surplus from trade. Borrowers may prefer joint liability contracts if they are very poor, and then shift to individual contracts whenever they accumulate the collateral needed by MFIs to break even on larger loans. Therefore, the model by Madajewicz (2011) does not refer to a mission drift, and seems to well describe the increase in average loan size due to the incentive mechanism of progressive lending. The rest of the paper is as follows. Section 2 introduces the model. Section 3 derives the equilibrium contract terms under a for-profit MFI. Section 4 discusses the case of a non-profit MFI. Section 5 summarizes the main results, suggests some policy implications, and concludes.

the specific strategy of poverty reduction chosen by MFIs. Table 1 considers four of the largest MFIs, ranked by a proxy for outreach (as a percentage of the poorest among borrowers).3 Note that, despite the large difference in the outreach parameter between Grameen Bank and Compartamos, they both share a similar mission. This paper extends the work of Caserta and Reito (2013), and proposes a simple moral-hazard model in which some individuals need outside financing to undertake their investment projects. The probability of project success depends on the unobservable effort exerted by the entrepreneur. Loans are provided by a single MFI, and we will consider the two cases of for-profit monopolistic MFI,4 and non-profit benevolent MFI. The MFI can offer two types of debt contracts: standard individual liability contracts, which are characterized by a collateral requirement; joint liability contracts, in which the MFI requires borrowers to form groups of two, and where borrowers are liable for each other's loan repayment. In the model, mission drift can occur if the MFI decides to finance investments with individual liability contracts. In this case, the MFI obtains the full-information (first-best) profit on borrowers with an endowment higher than a given collateral threshold. This implies that, if the availability of loanable funds is not large enough, poor individuals with little or no endowment may be the first ones to be excluded from the microcredit market. If, instead, joint liability contracts are offered by the MFI, the extent of mission drift depends on the borrowers' cost of exerting high effort. Specifically, if the cost is relatively low, the contract will earn the MFI the first-best profits without the need to use collateral to secure the loan. Hence, the MFI can lend to individuals irrespective of their initial wealth, and mission drift is not a concern. The MFI can also offer a combination of individual liability contracts for richer individuals, and group lending contracts for poorer individuals. The combination of individual and group lending contracts is analyzed in Navajas et al., (2003), and Burton (2011). Table 2 shows the composition of the two main types of micro-lending contracts in 663 MFIs, as reported in the MIX database. With “No Individual Liability”, we refer to all possible forms of group lending mechanisms. Note that 45.7% of MFIs offer both individual and joint liability contracts. If the effort cost is relatively high, the project output produced in case of success is not sufficient to pay both individual and joint liability under group lending. Group members are then required to post some of their endowment as collateral, and poor entrepreneurs may end up being crowded out. However, we show that, in this latter case, the collateral needed by the MFI to obtain the full-information profits is lower than that under individual liability contracts. Thus, the MFI can realize the same expected profits on loans to richer and to some of the poorer borrowers, and the extent of mission drift is lower. Another result of the paper is that mission drift is not a concern under a not-for-profit MFI. The benevolent MFI does not need any collateral on loans if its zero-profit condition can be satisfied at the incentive-

2. The setup5 Consider a simple risk-neutral, one-period economy. There is a large number of potential entrepreneurs identified by their observable endowment w 2 ½0; wMAX . Each firm has access to an investment project, whose expected return is related to the variable amount of resources invested, I, and the level of effort exerted by the entrepreneur. Specifically, the expected return is pH yH ðIÞ in case of high effort, or pL yL ðIÞ in case of low effort. With high effort the project succeeds with probability pH and yields yH ðIÞ, whereas with low effort it succeeds with pL < pH and yields yL ðIÞ < yH ðIÞ for each I. With the complementary probabilities the project fails and produces nothing. Assume that yH ðIÞ and yL ðIÞ are continuous, increasing functions of I, yH0 ðIÞ > 0, yL0 ðIÞ > 0, strictly concave, yH00 ðIÞ < 0, yL00 ðIÞ < 0, and that yH ð0Þ ¼ 0, yL ð0Þ ¼ 0. Low effort is costless, while high effort entails a cost eðIÞ, with e0 ðIÞ  0 and e00 ðIÞ  0. The justification for the increasing effort costs is that large firms may be more complex and difficult to manage than small firms. The endowment is illiquid, but can be used as collateral. Loans are provided by a single microfinance institution (MFI). We will analyze in sub-section 3.1 the case of a for-profit monopolistic MFI, and then in sub-section 3.2 the case of a non-profit benevolent MFI. The MFI can offer two alternative forms of debt contracts, individual liability and joint liability (group lending) contracts. The individual contract is a standard debt contract, ½I; RðIÞ; CðIÞ, where I is the loan size, RðIÞ is the (gross) repayment, and CðIÞ is the collateral

3

Microfinance Information Exchange, Inc. (MIX). http://www.mixmarket.org. Empirical examples of monopolistic, for-profit MFIs are reported in Armendariz de Aghion and Szafarz (2011), and de Quidt et al. (2011). Both papers also develop a theoretical model in which the MFI is monopolistic (for another theoretical paper with profit-motivated MFIs, see Guha and Roy Chowdhury, 2013). 4

5

2

A list of the symbols used in the model is given after the body of the paper.

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The entrepreneur chooses high effort iff

transferred in case of default. Under joint liability lending, borrowers form groups of two members. The group lending contract is the triple ½I; RðIÞ; DðIÞ, whereby a successful borrower must also pay DðIÞ if the other group member does not obtain a positive outcome. If the output produced in case of success is not sufficient to cover both RðIÞ and DðIÞ, the joint liability contract is the quadruple ½I; RðIÞ; CðIÞ; DðIÞ, where borrowers are required to use some additional collateral to back their loans. The MFI has imperfect information about the effort chosen by each entrepreneur and, since this choice is not contractible, we have a classic ex-ante moral-hazard problem.6 We assume that:

The contract must also satisfy the following limited liability constraints and ex-post incentive compatibility constraint,

pH yH ðIÞ  eðIÞ  I > pL yL ðIÞ  I for each I;

(A1)

CðIÞ  w;

pH RIC ðIÞ  I > pL yL ðIÞ  I; for each I:

(A2)

RðIÞ þ CðIÞ  yH ðIÞ;

pH ½yH ðIÞ  RðIÞ  ð1  pH ÞCðIÞ  eðIÞ  pL ½yL ðIÞ  RðIÞ  ð1  pL ÞCðIÞ;

or RðIÞ  ½pH yH ðIÞ  pL yL ðIÞ  eðIÞ=ðpH  pL Þ þ CðIÞ ¼ RIC ðIÞ þ CðIÞ. The participation constraint is u  w:

Assumption (A2) will become clear in the analysis that follows (for the definition of RIC ðIÞ, see the expression for the incentive compatibility constraint, IC, below). We will show that, under (A2), the MFI would never promote low effort from borrowers. However, this assumption does not imply that borrowers will never find it advantageous to choose the low-effort strategy. It is important to remark that, since yH ðIÞ > yL ðIÞ, an equity contract contingent on project returns would earn the monopolistic MFI the firstbest profit on each borrower type (see de Meza and Webb, 1987). Thus, to justify our focus on debt contracts, we follow part of the literature on costly state verification, and assume that the project return is imperfectly observable (see Besanko and Thakor, 1987). Namely, the MFI can observe at no cost whether the project succeeded or failed (the outcome of the project), but not the exact output produced (the return of the project). However, in this model, we have the additional problem that successful borrowers, who obtained yH ðIÞ with high effort, may have the incentive to report they exerted low effort and produced yL ðIÞ. We will show that such an incentive does not arise under the ex-post incentive compatibility constraint that successful borrowers, who report yL ðIÞ, must transfer all the output yL ðIÞ to the MFI. Therefore, the optimal form of financing under a for-profit MFI is the debt contract.

LLCS



ðEICÞ

π ¼ pH RðIÞ þ ð1  pH ÞCðIÞ  I;

(2)

subject to (IC), (PC), ðLLC Þ, ðLLC Þ and ðEICÞ. We assume that the MFI's opportunity cost of capital is 0. We will show that F

CðIÞ ¼

S

pL eðIÞ  pH pL ½yH ðIÞ  yL ðIÞ ¼ CFI ðIÞ pH  pL

is the collateral such that (PC) is binding, and such that the MFI is able to achieve the full-information profit. Thus, when CFI ðIÞ < w, the MFI is forced to require a collateral lower than the endowment. The collateral CFI ðIÞ is positive if eðIÞ > pH ½yH ðIÞ  yL ðIÞ ¼ eMIN ðIÞ and, throughout the paper, we will assume that eðIÞ > eMIN ðIÞ;

for each ðrelevantÞ I;

(A3)

Assumption (A3) implies that the for-profit MFI is not able to extract all the surplus from the contract without the presence of collateral. The monopolistic MFI will set the repayment at the highest possible level. Hence, in equilibrium, RðIÞ ¼ RIC ðIÞ þ minfw; CFI ðIÞg, and (2) can be rewritten as

Consider an entrepreneur with w 2 ½0; wMAX . The MFI observes w and proposes the contract ½I; RðIÞ; CðIÞ, trying to extract all possible surplus from the project.7 We first derive the equilibrium repayment and collateral, taking as given I. Then, we will endogenize the loan choice of the MFI.

π ¼ pH RIC ðIÞ þ minfw; CFI ðIÞg  I:

(2 ’)

To derive the equilibrium payoffs, we will distinguish between two sub-cases: minfw; CFI ðIÞg ¼ CFI ðIÞ; minfw; CFI ðIÞg ¼ w. i) minfw; CFI ðIÞg ¼ CFI ðIÞ If I is such that minfw; CFI ðIÞg ¼ CFI ðIÞ, the equilibrium collateral is CFI ðIÞ. So, (PC) is binding, and the payoffs are

3.1.1. Equilibrium R and C If the contract ½I; RðIÞ; CðIÞ is signed, the entrepreneur's expected payoff is for high effort; for low effort



The constraint ðLLC Þ requires that the collateral transferred in case of project failure cannot exceed the available endowment, while the constraint ðLLCS Þ that the sum paid in case of project success must be lower than the output produced. The ex-post incentive compatibility constraint, ðEICÞ, ensures that, after the realization of the project outcome, successful borrowers do not have the incentive to report they produced yL ðIÞ instead of yH ðIÞ. The contract provides that, if the borrower reports yL ðIÞ in case of positive outcome, this whole return is transferred to the MFI. From (A2), the MFI will always promote high effort and maximize

3.1. Individual liability lending

w þ pH ½yH ðIÞ  RðIÞ  ð1  pH ÞCðIÞ  eðIÞ w þ pL ½yL ðIÞ  RðIÞ  ð1  pL ÞCðIÞ

ðLLCF Þ

F

This Section derives the equilibrium financial terms and contract composition under a for-profit monopolistic MFI. The Section is as follows: sub-sections 3.1 and 3.2 present two benchmark cases of individual and joint liability equilibrium contracts; sub-section 3.3 shows the equilibrium composition of contracts chosen by the MFI.

u¼

ðPCÞ

yH ðIÞ  yL ðIÞ  yH ðIÞ  RðIÞ;

3. For-profit MFI




ðICÞ

  u ¼ w þ pH yH ðIÞ  RIC ðIÞ  CFI ðIÞ  ð1  pH ÞCFI ðIÞ  eðIÞ ¼ w;

(3)

for the firm, and

(1)





π ¼ pH RIC ðIÞ þ CFI ðIÞ þ ð1  pH ÞCFI ðIÞ  I ¼ pH yH ðIÞ  eðIÞ  I ¼ π FI ðIÞ;

(4)

6

For a similar setup, but under adverse selection, see the paper by Lahkar and Pingali (2016). 7 On the rent extraction behavior of for-profit MFIs, see, for example, de Quidt et al. (2011), and Ghosh and van Tassel (2011).

for the MFI. Therefore, if w  CFI ðIÞ, the MFI obtains the fullinformation profits.

3

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The limited liability constraint ðLLCS Þ is satisfied when R ðIÞ þ CFI ðIÞ  yH ðIÞ, or ½ð1  pL ÞeðIÞ  ð1  pH ÞpL ðyH ðIÞ  yL ðIÞÞ= ðpH  pL Þ  0. This inequality holds if eðIÞ  ð1  pH Þ pL ½yH ðIÞ  yL ðIÞ=ð1  pL Þ. And, since the right-hand side is such that ð1  pH ÞpL ½yH ðIÞ  yL ðIÞ=ð1  pL Þ < eMIN ðIÞ, this means that, under (A3), the constraint ðLLCS Þ is satisfied, and successful borrowers are always able to repay the loan out of future earnings. The ex-post incentive compatibility constraint, ðEICÞ, is also satisfied under (A3) since yH ðIÞ  yL ðIÞ  yH ðIÞ  RIC ðIÞ  CFI ðIÞ simplifies and can be rewritten as ð1  pL Þ½eðIÞ  pH ðyH ðIÞ  yL ðIÞÞ=ðpH  pL Þ  0, which holds if eðIÞ > eMIN ðIÞ.

u¼

IC




π¼

for each ðrelevantÞ I

π FI ðIÞ; for I 2 ½0; IA Þ; 4 and π ðIÞ; for I 2 ½IA ; ID :

(6)

The following Lemma characterizes the loan size chosen by the MFI. Lemma 2.

If w is such that:

1) IA < IB < IC , then I ¼ IB , the loan that maximizes π ðIÞ; 2) IB < IA < IC , then I ¼ IA , the loan such that π FI ðIÞ ¼ π ðIÞ; 3) IB < IC  IA , then I ¼ IC , the loan that maximizes π FI ðIÞ.

(3 ’)

Proof. See the Appendix. To provide graphical intuition, we consider simple Cobb-Douglas functions, yH ðIÞ ¼ H⋅I a , yL ðIÞ ¼ L⋅I a , with H > L. The project's expected return is pH H⋅I a for high effort, and pL L⋅I a for low effort, where a 2 ð0; 1Þ measures the concavity of the function. The effort function is eðIÞ ¼ e⋅I b , with e > 0 and b  1. Fig. 1a shows an example of the profit functions for the firm in (5), and the MFI in (6), in the case IB < IA < IC (in the Appendix, we show that, with Cobb-Douglas functions, IA , IB , IC , and ID exist and are unique). The parameters used are: pH ¼ 0:8, pL ¼ 0:4, H ¼ 11, L ¼ 7, a ¼ 0:5, b ¼ 2, e ¼ 2, and w ¼ 1. In the figure, both π ðIÞ ¼ pH RIC ðIÞ þ w  I and π FI ðIÞ ¼ pH yH ðIÞ  eðIÞ  I are first increasing, and then decreasing in I, when the effect of decreasing marginal productivity is high. The function CFI ðIÞ is decreasing for low levels of I (because the term e⋅I b is very small when I < 1), and then always increasing.9 Fig. 1b isolates the relevant profit functions. For all I  IA , i.e. the loan such that π FI ðIÞ ¼ π ðIÞ, we have w  CFI ðIÞ and π FI ðIÞ  π ðIÞ, so the relevant profit function for the MFI is π FI ðIÞ, and for the borrower is w. For I > IA , we have w < CFI ðIÞ and π FI ðIÞ > π ðIÞ, so the relevant functions are π ðIÞ and CFI ðIÞ. In this example, the optimal loan is IA , the MFI obtains π ¼ π ðIA Þ ¼ π FI ðIA Þ, and the borrower u ¼ CFI ðIA Þ ¼ w. In Fig. 2, the endowment is lower, w ¼ 0:2, and such that IA < IB < IC . In this case, the function π ðIÞ moves downward, while π FI ðIÞ and CFI ðIÞ remain unchanged. The MFI lends IB , the loan that maximizes π ðIÞ, and obtains π ¼ π ðIB Þ. The entrepreneur receives u ¼ CFI ðIB Þ. In Fig. 3, the endowment is w ¼ 1:75, and such that IB < IA < IC , so the loan is IC , which maximizes π FI ðIÞ. The MFI's expected profit is π ¼ π FI ðIC Þ, and the borrower's expected payoff is u ¼ w.

(4 ’)

Hence, if w < CFI ðIÞ, the entrepreneur obtains something above the opportunity cost, w, and the MFI is no longer able to extract all the surplus.8 From (A1), (4) and (4’), we have that, in equilibrium, π FI ðIÞ  π ðIÞ for each I. Note that assumption (A2) ensures that the payoff in (40 ) is higher than the full-information profits that the MFI would obtain under low effort, i.e. pL yL ðIÞ  I, even in the case in which w ¼ 0. This confirms that, under (A2), the MFI would never choose to induce low effort from borrowers. However, the profit in (4’) may be negative if w is low enough. Hence, in what follows, to restrict the analysis, we also assume that pH RIC ðIÞ  I > 0;

(5)

Again, for the case 2, if I 2 ½0; IA Þ, minfw; CFI ðIÞg ¼ CFI ðIÞ, and the MFI's profit function is π FI ðIÞ, while for the case 3, if I 2 ½IA ; ID , minfw; CFI ðIÞg ¼ w, and the function is π ðIÞ.

and

π ¼ pH RIC ðIÞ þ w  I ¼ π ðIÞ:

for I 2 ½0; IA Þ; and for I 2 ½IA ; ID 

Indeed, for the case 2 above, if I 2 ½0; IA Þ, minfw; CFI ðIÞg ¼ CFI ðIÞ, and the firm obtains w. Whereas, for the case 3, if I 2 ½IA ; ID , minfw; CFI ðIÞg ¼ w, and the payoff function is CFI ðIÞ. For the MFI, the profit function is

Remark 1. If w is large enough, the MFI can extract all surplus by means of collateral, so that the constraint ðPCÞ is binding and the ðICÞ slack. However, in the paper, we assume that the MFI first chooses to set the interest rate such that ðPCÞ is binding in order to reduce the collateral needed to be eligible for a loan. ii) minfw; CFI ðIÞg ¼ w If I is such that minfw; CFI ðIÞg ¼ w, the equilibrium collateral is w, and the payoffs are   u ¼ w þ pH yH ðIÞ  RIC ðIÞ  w  ð1  pH Þw ¼ CFI ðIÞ;

w; CFI ðIÞ;

(A4)

This assumption implies that the MFI can at least break even on borrowers with w ¼ 0. 3.1.2. Endogenous I By inspection of (4) and (4’), we distinguish the following three cases. case 1 : if I is such that w ¼ CFI ðIÞ; then π FI ðIÞ ¼ π ðIÞ; case 2 : if I is such that w > CFI ðIÞ; then π FI ðIÞ < π ðIÞ; case 3 : if I is such that w < CFI ðIÞ; then π FI ðIÞ > π ðIÞ: Besides, we denote by:

3.2. Joint liability lending

IA the loan such that w ¼ CFI ðIÞ and π FI ðIÞ ¼ π ðIÞ; IB the loan such that π ðIÞ is maximized; IC the loan such that π FI ðIÞ is maximized; ID the loan such that π ðIÞ ¼ 0 ðwith ID positiveÞ:

This sub-section derives the equilibrium contract terms and loan sizes under group lending. We assume that group members are able to observe each other's effort level (that is, whether they are working hard or not), but not the project outcome and return. This means that borrowers have a partial but not complete informational advantage over the MFI. However, we consider no peer selection or performance monitoring among borrowers, and no reporting (whistleblowing) to the MFI. As in the (adverse-selection) model of Ghatak (2000), group members are able to make side transfers to each other, for example through future

We have the following immediate result. Lemma 1. In equilibrium, IC > IB . Proof. See the Appendix. For Lemma 1, the loan that maximizes π FI ðIÞ is always larger than the loan that maximizes π ðIÞ. Thus, given the cases 1, 2 and 3 above, we can derive the equilibrium payoffs in function of I. The firm's payoff function is

9 We would obtain the same qualitative results with other types of production functions, provided they are continuous, increasing and strictly concave (the cases 1, 2, 3, and Lemmas 1 and 2 would hold).

8

In Reito (2011) the firm can strategically choose to offer the lowest possible amount of (unobservable) collateral in order to obtain a share of the surplus. 4

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Fig. 2. Case IA < IB < IC . Parameters: pH ¼ 0:8, pL ¼ 0:4, H ¼ 11, L ¼ 7, a ¼ 0:5, b ¼ 2, e ¼ 2, w ¼ 0:2.

Fig. 1. a) Profit functions for the firm and the MFI (case IB < IA < IC ). π ðIÞ ¼ pH RIC ðIÞ þ w  I ¼ pH ðpH H⋅I a  pL L⋅I a  e⋅I b Þ=ðpH  pL Þ þ w  I.π FI ðIÞ ¼ pH yH ðIÞ  eðIÞ  I ¼ pH H⋅I a  e⋅I b  I CFI ðIÞ ¼ ðpL eðIÞ  pH pL ½yH ðIÞ  yL ðIÞÞ= ðpH  pL Þ ¼ ðpL e⋅I b  pH pL ðH⋅I a  L⋅I a Þ=ðpH  pL Þ. Parameters: pH ¼ 0:8, pL ¼ 0:4, H ¼ 11, L ¼ 7, a ¼ 0:5, b ¼ 2, e ¼ 2, w ¼ 1. b) Relevant profit functions forw ¼ 1. For the MFI, the profit function is π FI ðIÞ for I  IA , and π ðIÞ for I > IA .For the borrower, the payoff function is w for I  IA , and CFI ðIÞ for I > IA .

Fig. 3. Case IB < IC < IA . Parameters: pH ¼ 0:8, pL ¼ 0:4, H ¼ 11, L ¼ 7, a ¼ 0:5, b ¼ 2, e ¼ 2, w ¼ 1:75.

In the following Lemma, we show that, if group partners choose different effort levels, the expected gain of the member who chooses low effort is strictly lower than the expected loss of the other who chooses high effort. Thus, group members are not willing to trade some of their risk characteristics in exchange for side payments, and will always choose the same effort level (high or low) .11

labor services, in-kind exchanges or out of the project output (the first two types of transfers are difficult to implement between borrowers and the MFI, but can be feasible among people who share a common context)10. Consider first the contract ½I; RðIÞ; DðIÞ. Each borrower's expected payoff, when both group members apply the same effort level, is


u¼

w þ pH pH ½yH ðIÞ  RðIÞ þ pH ð1  pH Þ½yH ðIÞ  RðIÞ  DðIÞ  eðIÞ w þ pL pL ½yL ðIÞ  RðIÞ þ pL ð1  pL Þ½yL ðIÞ  RðIÞ  DðIÞ

Lemma 3. Group members always choose the same effort level. Proof. See the Appendix.

for high effort; for low effort;

or, simplifying,
u¼

w þ pH ½yH ðIÞ  RðIÞ  pH ð1  pH ÞDðIÞ  eðIÞ for high effort; w þ pL ½yL ðIÞ  RðIÞ  pL ð1  pL ÞDðIÞ for low effort:

Incentive compatibility requires that pH ½yH ðIÞ  RðIÞ  pH ð1  pH ÞDðIÞ  eðIÞ

(7)

 pL ½yL ðIÞ  RðIÞ  pL ð1  pL ÞDðIÞ;

ðICJ Þ

or RðIÞ  R ðIÞ þ ðpH þ pL  1ÞDðIÞ. We assume that pH þ pL  1 > 0. IC

Remark 2. In the paper, we assume that, while the project return is unobservable, the project outcome is perfectly verifiable by the MFI. This

10

Ghatak (2000) presents an adverse-selection model with a lender and two types of borrowers, safe and risky. He shows that, in a group lending contract, the expected gain of a risky borrower from having a safe group partner is lower than the expected loss of a safe of having a risky. Thus, even though a risky borrower can make side transfers, these payments are not sufficient to compensate a safe partner. This means that group formation will always display positive assortative matching or risk homogeneity among borrowers.

11 The result of Lemma 1 can be interpreted as the moral hazard version of positive assortative matching in group lending.

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assumption implies that successful borrowers are unable to “take the money and run” by reporting project failure. If borrowers had the opportunity to report no output, the MFI would have to design additional or alternative incentive mechanisms to induce truthful revelation. For example, one solution may be for the MFI to ex-post monitor project returns and impose sanctions to deter strategic default. In this case, the qualitative results of the model would be essentially unchanged if the MFI's unit cost of monitoring is the same under individual or group lending, or strengthened if the MFI delegates monitoring to group members and they have a relative advantage, for example due to geographical proximity or the possibility to use moral sanctions (see Ghatak and Guinnane, 1999; Armendariz de Aghion and Gollier, 2000). Alternatively (or additionally), the MFI could use the threat of termination under sequential lending. Namely, borrowers can be excluded from future access to credit when loans are not repaid. This mechanism can be applied to both individual and group lending (see Roy Chowdhury, 2005), so the qualitative conclusions of the paper would still hold. Under group lending, each group member's participation constraint is u ¼ w þ pH ½yH ðIÞ  RðIÞ  pH ð1  pH ÞDðIÞ  eðIÞ  w:

constraint in (9) is consistent with assumption (A3). However, we need to distinguish between two cases, eðIÞ  eJ ðIÞ and eðIÞ > eJ ðIÞ, which will be presented in following two sub-sections. 3.2.1. eðIÞ  eJ ðIÞ In this case, the constraint (LLCJS ) is satisfied, and each group member can fulfill the payment in (9) without the need to use additional wealth as collateral. The equilibrium payoffs are u ¼ w; and

π ¼ pH yH ðIÞ  eðIÞ  I ¼ π FI ðIÞ:



LLCJS

ðPCJ Þ



The limited liability constraint in case of project failure defined in Section 3 for individual liability, ðLLCF Þ that is CðIÞ  w, is not applied to the contract ½I; RðIÞ; DðIÞ. The ex-post incentive compatibility constraint under group lending is yH ðIÞ  yL ðIÞ  pH ½yH ðIÞ  RðIÞ þ ð1  pH Þ½yH ðIÞ  RðIÞ  DðIÞ;

ðEICJ Þ

Remark 3. In the group lending scheme analyzed here, the equilibrium repayment is RIC þ ðpH þ pL  1ÞD > D, so we do not derive the ex-post incentive compatibility problem pointed out by Gangopadhyay et al. (2005). Namely, the incentive for group members, when R < D, to claim that both had success when one of them actually failed in order to reduce the overall group's liability.

The reason why we have an expected value on the right-hand side of ðEICJ Þ is that group members can observe neither the return, nor the outcome of their peers' projects. Thus, after the realization of output, successful borrowers must decide whether to report yH ðIÞ or yL ðIÞ to the MFI prior to knowing whether they will have to pay just the individual liability (which happens with probability pH , that is when the other group member's project succeeds), or both individual and joint liability (which happens with probability 1  pH , when the other project fails). In equilibrium, RðIÞ ¼ RIC ðIÞ þ ðpH þ pL  1ÞDðIÞ, and DðIÞ derives from the binding ðPCJ Þ,

3.2.2. Case: eðIÞ > eJ ðIÞ If eðIÞ > eJ ðIÞ, the constraint in (9) does not hold, and group members cannot repay both individual and joint liability using the output produced in case of project success. Borrowers are then required to post some collateral to be eligible for loans, and the contract is the quadruple ½I; RðIÞ; CðIÞ; DðIÞ. Under the contract, each borrower's expected payoff, when both group members apply the same effort level, is

  u ¼ w þ pH yH ðIÞ  RIC ðIÞ  ðpH þ pL  1ÞDðIÞ  pH ð1  pH ÞDðIÞ  eðIÞ ¼ w;

u ¼ w þ pH pH ½yH ðIÞ  RðIÞ þ pH ð1  pH Þ½yH ðIÞ  RðIÞ  DðIÞ  ð1  pH ÞCðIÞ  eðIÞ ¼ ¼ w þ pH ½yH ðIÞ  RðIÞ  pH ð1  pH ÞDðIÞ  ð1  pH ÞCðIÞ  eðIÞ;

eðIÞ  pH ½yH ðIÞ  yL ðIÞ : pH ðpH  pL Þ

u ¼ w þ pL pL ½yL ðIÞ  RðIÞ þ pL ð1  pL Þ½yL ðIÞ  RðIÞ  DðIÞ  ð1  pL ÞCðIÞ ¼ ¼ w þ pL ½yL ðIÞ  RðIÞ  pL ð1  pL ÞDðIÞ  ð1  pL ÞCðIÞ  eðIÞ; (13)

(8)

The joint liability payment in (8) is positive if eðIÞ > pH ½yH ðIÞ  yL ðIÞ ¼ eMIN ðIÞ, which is always true for (A3). The limited liability constraint in ðLLCJS Þ is satisfied, that is successful borrowers can pay both the individual and joint liability payment, if

if low effort is chosen. We assume that collateral is transferred to the MFI whenever a group member defaults, which happens with probability ð1  pH ÞpH þð1  pH Þð1  pH Þ ¼ 1  pH , or ð1  pL ÞpL þ ð1  pL Þð1  pL Þ ¼ 1  pL . Again, the expected loss of a borrower who applies high effort, when the other group member chooses low instead of high effort, pH ðpH  pL ÞDðIÞ, is higher than the expected gain of choosing low effort, when the other member exerts high instead of low effort, pL ðpH  pL ÞDðIÞ. So, Lemma 2 applies also to the case analyzed in this sub-section. From (12) and (13), the equilibrium incentive-compatible repayment

RIC ðIÞ þ ðpH þ pL  1ÞDðIÞ þ DðIÞ  yH ðIÞ; or eðIÞ 

p2H ½yH ðIÞ  yL ðIÞ  ¼ eJ ðIÞ: pL

Since

(12)

if high effort is exerted, or

which gives DðIÞ ¼

(11)

The payments due by a successful borrower when the other group member's project succeeds and fails are, respectively, RIC ðIÞ þ ðpH þ pL  1ÞDðIÞ, and RIC ðIÞ þ ðpH þ pL  1ÞDðIÞ þ DðIÞ. Using the equilibrium DðIÞ from (8), the ex-post incentive constraint, ðEICJ Þ, can be rewritten as eðIÞ=pH  yH ðIÞ  yL ðIÞ, which always holds under (A3). As a result, through the guarantee provided by mutual liability, the MFI is able to extract the whole project's surplus from each borrower with w 2 ½0; wMAX , irrespective of the initial wealth. Thus, if eðIÞ  eJ ðIÞ, borrowers are not required to use additional collateral under joint liability lending. The equilibrium group loan is implicitly defined by yH0 ðIÞ ¼ ½1 þ e0 ðIÞ=pH , and is equal to the individual liability loan, IC , of sub-section 3.1.

The limited liability constraint in case of success can be rewritten as RðIÞ þ DðIÞ  yH ðIÞ:

(10)

eJ ðIÞ  eMIN ðIÞ ¼ pH ðpH  pL Þ½yH ðIÞ  yL ðIÞ=pL > 0,

(9)

the

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obtains the first-best profits, π FI ðIC Þ. If the availability of loanable funds is not constrained, all entrepreneurs can be financed. If, instead, funds are limited, the MFI can randomly choose its borrowers, irrespective of their initial wealth. Thus, mission drift does not necessarily occur. When eðIÞ > eJ ðIÞ, the for-profit MFI can offer either joint liability contracts to all individuals with w 2 ½CJ ðIÞ; wMAX , or a combination12 of individual liability contracts to borrowers with w 2 ½CFI ðIÞ; wMAX , and group lending contracts to borrowers with w 2 ½CJ ðIÞ; CFI ðIÞÞ, where CFI ðIÞ > CJ ðIÞ. For all these contracts, the loan size is IC , and the MFI earns the full-information profit, π FI ðIC Þ. The MFI can also offer individual liability contracts to borrowers with w 2 ½0; CJ ðIÞÞ. In this case, the loan size is the one that maximizes π ðIÞ ¼ pH RIC ðIÞ þ w  I, that is IB , and the MFI's expected profit is π ðIB Þ < π FI ðIC Þ. Therefore, individuals with w 2 ½0; CJ ðIÞ; Þ may be the first to be excluded from the financial program if the availability of loanable funds is limited.13 We can summarize the discussion of sub-section 3.1 and 3.2 in the following.

is RðIÞ ¼ RIC ðIÞ þ CðIÞ þ ðpH þ pL  1ÞDðIÞ, where CðIÞ and DðIÞ derives from the following system of two equations: w þ pH ½yH ðIÞ  RðIÞ  pH ð1  pH ÞDðIÞ  ð1  pH ÞCðIÞ  eðIÞ ¼ w;

(14)

yH ðIÞ  RðIÞ  DðIÞ ¼ 0:

(15)

Equation (14) requires that the participation constraint, ðPCJ Þ, must be binding, and equation (15) that the net return obtained by each successful borrower, when the other group member defaults, must be equal to 0. At the equilibrium repayment, RIC ðIÞ þ CðIÞ þ ðpH þ pL  1ÞDðIÞ, the solutions of the system are: CðIÞ ¼

p2L eðIÞ  p2H pL ½yH ðIÞ  yL ðIÞ ¼ CJ ðIÞ; ðpH  pL Þ½pH ð1  pL Þ þ pL 

(16)

DðIÞ ¼

ð1  pL ÞeðIÞ  ð1  pH ÞpL ½yH ðIÞ  yL ðIÞ : ðpH  pL Þ½pH ð1  pL Þ þ pL 

(17)

Proposition 1.

The collateral CJ ðIÞ in (16) is positive when eðIÞ > eJ ðIÞ, which is true in the sub-section analyzed here. The joint liability payment in (17) is positive when eðIÞ > ð1  pH ÞpL ½yH ðIÞ  yL ðIÞ=ð1  pL Þ, which is satisfied under (A3) as eMIN ðIÞ > ð1  pH ÞpL ½yH ðIÞ  yL ðIÞ=ð1  pL Þ. In this sub-section, the ex-post incentive compatibility constraint can be rewritten as yH ðIÞ  yL ðIÞ  pH ½yH ðIÞ  RðIÞ. The reason is that, after the realization of output, successful borrowers know that, when they report yH ðIÞ and their group partners default (which happens with probability 1  pH ), their net return will be 0 from (15). The ex-post incentive compatibility constraint holds if eðIÞ  ½p2H ð1  2pL Þ þ pH pL ð1 þ pL Þ  p2L ½yH ðIÞ  yL ðIÞ=pH ð1  pL Þ, where the right-hand side is always lower than eMIN ðIÞ. So, it is always satisfied for (A3). Therefore, the MFI is again able to extract the whole project's surplus, but only on individuals with w  CJ ðIÞ. In this case, borrowers with w 2 ½CJ ðIÞ; wMAX  obtain their reservation payoff, u ¼ w, and the MFI the fullinformation profits, π ¼ π FI ðIC Þ. On the other hand, the MFI can offer individual liability contracts to borrowers with w 2 ½0; CJ ðIÞÞ. In this case, since CJ ðIÞ < CFI ðIÞ, the MFI is no longer able to obtain the full-information profits, and borrowers receive a positive surplus. On all contracts to individuals with w 2 ½0; CJ ðIÞÞ, the MFI chooses the loan size IB , that is the loan that maximizes the profit function π ðIÞ ¼ pH RIC ðIÞ þ w  I. Note that the difference between the collateral levels such that the MFI is able to realize its full-information profits under individual and joint liability lending is CFI ðIÞ  CJ ðIÞ ¼

pH pL ð1  pL ÞeðIÞ  pH ð1  pH Þp2L ½yH ðIÞ  yL ðIÞ : ðpH  pL Þ½pH ð1  pL Þ þ pL 

If:

a) eðIÞ  eJ ðIÞ, the for-profit MFI can randomly choose among individuals with w 2 ½0; wMAX , so mission drift does not necessarily occur, even when the availability of loanable funds is constrained; b) eðIÞ > eJ ðIÞ, some or all individuals with w 2 ½0; CJ ðIÞÞ can be excluded from the microfinance market, and mission drift may occur. For Proposition 1, we can conclude that mission drift is not an inevitable consequence of the profit-seeking behavior of the MFI. Fig. 4 describes the contract composition on the basis of the initial wealth, w, of individuals (in the case in which loanable funds are not constrained). 4. Not-for-profit MFI This section analyzes the case of a benevolent non-profit MFI, and shows that most of the basic results derived in Section 3 remain unchanged. We do not consider the presence of external donors and subsidies, and assume that the MFI expects to break even on each type of loan contract. We will show that, under (A4), a non-profit MFI does not need any collateral or joint liability payment to break even, and can offer individual liability loans to all types of borrowers.14 The MFI's zero-profit condition is pH RðIÞ ¼ I

ð0π CÞ

Consider an individual with w 2 ½0; wMAX . The financial contract is the couple ½I; RðIÞ and, using RðIÞ from ð0π CÞ, the incentive compatibility constraint is

(18)

The expression in (18) is positive when eðIÞ > ð1  pH ÞpL ½yH ðIÞ  yL ðIÞ=ð1  pL Þ, where ð1  pH ÞpL ½yH ðIÞ  yL ðIÞ= ð1  pL Þ < eMIN ðIÞ, so it is satisfied under (A3). Therefore, CFI ðIÞ > CJ ðIÞ for each I, and the equilibrium collateral such that the MFI obtains the full-information profits under individual liability is always larger than that under joint liability. This can have important policy implications, which will be discussed in Section 5.

    I I pH yH ðIÞ   eðIÞ  pL yL ðIÞ  ; pH pH

12 This result may explain why, in many microfinance programs, poor borrowers are served by group lending programs, whereas richer borrowers by collateralized individual liability loans. This is confirmed by the empirical evidence reported by Ahlin and Townsend (2007) for Thailand, and Hermes et al. (2011) for Eritrea. 13 For the Cobb-Douglas functions used in the description of Fig. 1, the inequality can be written as e⋅I b  p2H ðH  LÞI a =pL . If, to simplify, we consider the case in which b ¼ 1, the

3.3. Contract composition

inequality holds if I  ½p2H ðH  L=pL eÞ

From the analysis of sub-sections 3.1 and 3.2, the set of contracts offered by the for-profit MFI depends on the effort cost function, eðIÞ. There are two distinct cases to consider, eðIÞ  eJ ðIÞ and eðIÞ > eJ ðIÞ. When eðIÞ  eJ ðIÞ, the for-profit MFI can offer either joint liability contracts to all borrowers, or a combination of individual liability contracts to borrowers with w 2 ½CFI ðIÞ; wMAX , and joint liability contracts to borrowers with w 2 ½0; CFI ðIÞÞ. On all such contracts, the MFI lends IC and

1=ð1aÞ

¼ I.In the Appendix, we show that the loan

size that maximizes the MFI's full-information profits is IC ¼ ½apH H=ð1 þ eÞ1=ð1aÞ . We have that IC  bI when the effort parameter, e, is such that e  ½pH ðH  LÞ=½apL H  pH ðH  LÞ ¼ be . Thus, if e  be , the equilibrium described in the first part of Proposition 1 would always emerge. 14 This conclusion may explain the recent evolution away from collateralized loans and group lending in many microfinance programs. See, for some examples, Burton (2011) and Schicks (2007) for the case of the Grameen Bank II in Bangladesh. 7

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Fig. 4. Contract composition for each subset of ½0; wMAX . When eðIÞ  eJ ðIÞ, the MFI obtains: the first-best profits, π FI ðIC Þ, on individual liability contracts if borrowers' endowment is w 2 ½CFI ðIÞ; wMAX ; the first-best profits, π FI ðIC Þ, on joint liability contracts individuals if the endowment is w 2 ½0; wMAX . All individuals with w 2 ½0; wMAX  can receive credit and mission drift does not occur (even if the MFI's availability of loan funds is constrained). When eðIÞ > eJ ðIÞ, the MFI obtains: the first-best profits, π FI ðIC Þ, on individual liability contracts if w 2 ½CFI ðIÞ; wMAX ; the first-best profits, π FI ðIC Þ, on joint liability contracts individuals if w 2 ½CJ ðIÞ; wMAX ; the profit, π ðIB Þ < π FI ðIC Þ, on individual liability contracts if w 2 ½0; CJ ðIÞÞ. Individuals with w 2 ½0; CJ ðIÞÞ can be excluded from the credit market if loan funds are constrained.

orpH RIC ðIÞ  I, which always holds under (A4). The incentive constraint is satisfied for each w, so the borrower maximizes pH yH ðIÞ  I, and chooses I ¼ IC . The final payoffs are u ¼ w þ π FI ðIC Þ;

sufficient to cover the joint liability payments, and no collateral is required to receive loans. In this case, the MFI can earn the first-best profits on all types of borrowers, and mission drift does not necessarily occur. If the effort cost is higher than eJ ðIÞ, we show that the output produced in case of project success is not enough to pay both individual and joint liabilities, so additional collateral is needed to secure credit. In this case, if the borrower's endowment is higher than the threshold CJ ðIÞ, the MFI is again able to earn the first-best π FI ðIÞ, whereas if the endowment is lower than CJ ðIÞ, the MFI obtains π ðIÞ < π FI ðIÞ. Individuals with w < CJ ðIÞ may therefore be excluded from the microcredit market. The analysis of the for-profit MFI implies that mission drift is not necessarily a direct result of its profit-seeking nature. In the model, we also show that CJ ðIÞ < CFI ðIÞ, that is the collateral threshold such that the for-profit MFI can achieve the first-best profit under joint liability is lower than that required under individual liability. This result has the immediate policy implication that an intervention aimed at increasing financial inclusion can be less costly to implement if the MFI offers joint liability contracts. For example, a collateral subsidy, whereby the government or other institutions underwrite (part of) the collateral on joint liability loans to poor entrepreneurs, would reduce the public cost in the event of project default (for the discussion of footnote 13, mission drift is more likely to occur if the effort parameter, e, is higher than the threshold be ). If the MFI is a non-profit organization that seeks to maximize the welfare of its clients, we show that collateral is not needed as long as the incentive-compatible repayment is high enough. In this case, each type of borrower obtains the first-best payoff, π FI ðIÞ, and there is no mission drift. A fundamental assumption used throughout the paper is that the output produced and the probability of project success do not depend on the endowment of micro-borrowers. This is in line with part of the literature, which reports that there is no significant difference in the repayment rate between individual (richer) and group lending (poorer) contract schemes (see Gine and Karlan, 2009; for the Philippine microcredit market). Related to this point, Sagamba et al. (2013), in their field experiment in Burundi, find that there is no difference in the client target chosen by for-profit or non-profit MFIs officers. They show that microfinance officers are not significantly influenced by the level of poverty, and that the most relevant prerequisite for loan attribution is the quality of the investment projects. This may suggest that it is indeed possible to observe a convergence in the objectives of the two types of microcredit institutions. However, an extensive empirical literature also reports that the quality of projects and the probability of success of poor micro-entrepreneurs are often negatively affected by their limited business education and management skills. McKenzie and Woodruff (2013) posit that most micro and small firms in developing countries do not follow many of the business practices that are standard in more developed countries. For example, they report that most entrepreneurial projects are not well defined, accounting books are not properly kept, and marketing strategies are poorly implemented. Therefore, another policy implication that can be drawn from the paper is that the profitability of MFIs (whether they are for- or not-for-

(19)

and

π ¼ 0:

(20)

The analysis above applies to each borrower with w 2 ½0; wMAX , so we can state the following. Proposition 2. Under (A4), mission drift will never occur with a nonprofit MFI. The intuition behind Proposition 2 is that, as long as the MFI's zeroprofit condition is satisfied at the lowest incentive-compatible repayment, RðIÞ ¼ I=pH , each borrower is able to maximize the fullinformation profit.15 Note that, if the supply of loanable funds is limited, we cannot determine the equilibrium contract composition without specifying the social values associated to each type of borrower by the benevolent MFI. For example, we could introduce and consider alternative forms of costeffective analyses, such as the concept of return on investment in terms of poverty reduction (as discussed by Ghosh and van Tassel, 2011). It is important to stress that, though the results in terms of social welfare are equivalent to the for-profit case, borrowers pay a higher interest rate and receive a lower share of the project's surplus under a monopolistic MFI. Therefore, a relevant question, which is not discussed here, is whether or not we should care about the cost of credit in contexts where people have no regular access to formal financial markets. 5. Summary, policy implications, and conclusions This paper discusses the recent behavior of microfinance institutions to determine the theoretical conditions for the emergence of a drift from the classic outreach towards poor entrepreneurs towards profitability. The model developed in the paper analyzes individual and joint liability contracts offered by either a for-profit monopolistic MFI or a non-profit benevolent MFI. In the former case, the objective of the MFI is to maximize its expected profits. We show that, if borrowers can post a collateral higher than the threshold CFI ðIÞ, the MFI obtains the first-best profits, π FI ðIÞ, under individual liability contracts. This means that the MFI can earn lower profits on borrowers with an endowment below CFI ðIÞ. These individuals are likely to be denied credit if loanable funds are not sufficient, or if the MFI is able to obtain the full-information profits elsewhere. If the for-profit MFI offers joint liability contracts, mission drift depends on whether the borrowers' cost of high effort is lower or higher than the threshold eJ ðIÞ. If the cost is lower, the output generated by the project is

15 If the assumption in (A4) were not made, individuals would be forced to use all or part of their endowment as collateral to satisfy ð0π CÞ.

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GTZ/CEFE program, and the UNCTAD program). The authors are though skeptical about the effectiveness of these programs, and they conclude that the magnitude of their impacts has been rather small. Other studies, instead, report positive effects deriving from training programs, for borrowers and MFIs. See, for example, Bhatt and Tang (2001), who analyze the impact of business training in the USA, and the field experiments of Karlan and Valdivia (2011) in Peru, and Mano et al. (2012) in Ghana. We believe that more support should be given to such initiatives, and more attention should be paid, not only to the access of micro-entrepreneurs to financial services, but also to the issue of exit and unfinished businesses.

profit) should be made less dependent on collateral or other guarantees based on personal wealth of micro-entrepreneurs. To avoid mission drift, governments of developing countries should focus more on programs and processes that support and sustain a new culture of business, especially for very poor entrepreneurs. An improvement in the quality of projects would make lending to the poor more attractive even to profit-seeking MFIs. McKenzie and Woodruff (2013) argue that this is the reason why many microfinance institutions and non-governmental organizations offer support to micro-firms in the form of business training programs and management practices (for example, the International Labor Organization, started in 1977 and operating in over 100 countries, the

List of symbols

w pH pL I eðIÞ eMIN ðIÞ eMAX ðIÞ eJ ðIÞ yH ðIÞ yL ðIÞ RðIÞ CðIÞ RIC ðIÞ DðIÞ CFI ðIÞ CJ ðIÞ u π ðIÞ π FI ðIÞ IA IB IC ID

Borrower's endowment Probability of project success for high effort Probability of project success for low effort Investment loan Effort function Lowest effort compatible with the individual liability equilibrium Highest effort compatible with the individual liability equilibrium Highest effort compatible with the joint liability equilibrium Outcome in case of project success for high effort Outcome in case of project success for low effort Loan repayment Collateral Incentive-compatible repayment for CðIÞ ¼ 0 Joint liability payment Full-information collateral Collateral used in the joint liability contract Borrower's expected payoff MFI's expected profit MFI's expected full-information profit Loan size such that π FI ðIÞ ¼ π ðIÞ Loan size such that π ðIÞ is maximized Loan size such that π FI ðIÞ is maximized Loan size such that π ðIÞ ¼ 0

Appendix Proof of Lemma 1. The loan that maximizes π FI ðIÞ ¼ pH yH ðIÞ  eðIÞ  I is implicitly derived from yH0 ðIÞ ¼ ½1 þ e0 ðIÞ=pH . Since pH yH ðIÞ  eðIÞ > pH RIC ðIÞ under (A3), we can write π ðIÞ ¼ pH RIC ðIÞ þ w  I in (4’) as pH βyH ðIÞ þ w  eðIÞ  I, with β < 1. The loan that maximizes π ðIÞ is then defined by yH0 ðIÞ ¼ ½1 þ e0 ðIÞ=βpH . Proof of Lemma 2. 1) For all I > IA , w < CFI ðIÞ and π FI ðIÞ > π ðIÞ, and the relevant profit function for the MFI is π ðIÞ. Thus, the MFI chooses IB , the loan that maximizes π ðIÞ. 2) For I  IA , w  CFI ðIÞ and π FI ðIÞ  π ðIÞ, and the relevant profit function for the MFI is π FI ðIÞ. For I > IA , we have w < CFI ðIÞ and π FI ðIÞ > π ðIÞ, and the relevant function is π ðIÞ. Since π FI ðIÞ is increasing for all I  IA and π ðIÞ is decreasing for all I > IA , the equilibrium loan is IA , the loan such that π ðIÞ ¼ π FI ðIÞ. 3) For I < IA , the relevant profit function is π FI ðIÞ and the MFI chooses IC , the loan that maximizes π FI ðIÞ. Proof of Lemma 3. Define the expected loss of a borrower who applies high effort, when the other group member chooses low instead of high effort, as fpH ½yH ðIÞ  RðIÞ  pH ð1  pL ÞDðIÞ  eðIÞg  fpH ½yH ðIÞ  RðIÞ  pH ð1  pH ÞDðIÞ  eðIÞg ¼ ¼ pH ðpH  pL ÞDðIÞ: Define also the expected gain of a borrower who exerts low effort, when the other member chooses high instead of low effort, as fpL ½yL ðIÞ  RðIÞ  pL ð1  pH ÞDðIÞg  fpL ½yL ðIÞ  RðIÞ  pL ð1  pL ÞDðIÞg ¼ ¼ pL ðpH  pL ÞDðIÞ: Since pH ðpH  pL ÞDðIÞ > pL ðpH  pL ÞDðIÞ, the expected loss is higher than the expected gain, so members will never choose different effort levels. Characterization of equilibrium IA , IB , IC , ID . Consider the Cobb-Douglas functions, yH ðIÞ ¼ H⋅I a , yL ðIÞ ¼ L⋅I a , with H > L, and a 2 ð0; 1Þ. The effort function is eðIÞ ¼ e⋅I b , with e > 0 and b  1. 9

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To simplify the derivations, we consider the case in which b ¼ 1 (if b > 1, we would not be able to derive the solutions without specifying the production functions or assigning specific values to the parameters a and b). IA : the loan size IA derives from w ¼ CFI ðIA Þ ¼

pL e⋅IA  pH pL ðH  LÞIAa : pH  pL

If we rewrite the right-hand side of the equation above as a function of I, that is CFI ðIÞ, and take the first-order condition, we obtain pL e  apH pL ðH  LÞI a1 ¼ 0: pH  pL The turning point of the function CFI ðIÞ is I¼

1  apH ðH  LÞ 1a ¼ I0 : e

The sign of the second-order condition is að1  aÞpH pL ðH  LÞI a2 > 0; pH  pL so I0 is a minimum. The function CFI ðIÞ is first decreasing and then increasing in I. It follows that there exists a unique IA > I0 such that w ¼ CFI ðIA Þ. IB : the loan size IB is the loan that maximizes the profit function

π ðIÞ ¼ pH RIC ðIÞ þ w  I ¼ pH

ðpH H  pL LÞI a  e⋅I þ w  I: pH  pL

From the first-order condition, pH

aðpH H  pL LÞI a1  e  1 ¼ 0; pH  pL

the profit maximizing loan is I¼

1  apH ðpH H  pL LÞ 1a ¼ IB : pH ð1 þ eÞ  pL

The loan IB corresponds to a maximum as the second-order condition is að1  aÞpH ðH  LÞI a2  < 0: pH  pL Thus, the function π ðIÞ is first increasing and then decreasing in I. IC : the loan size IC is the loan that maximizes the full-information profit function,

π FI ðIÞ ¼ pH H⋅I a  e⋅I  I: The first-order condition is apH H⋅I a1  e  1 ¼ 0; and the optimal loan is I¼

1  apH H 1a ¼ IC : 1þe

The second-order condition is að1  aÞpH H⋅I a2 < 0; so IC corresponds to a maximum. ID : the loan ID is the positive loan such that π ðIÞ ¼ pH RIC ðIÞ þ w  I ¼ 0. Without specifying the parameters of the function π ðIÞ, we are not able to derive the exact value of ID . However, since π ðIÞ is continuous and first increasing and then decreasing in I, we can say there always exists a unique positive loan ID such that π ðIÞ ¼ 0 .

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