Is it better to be mixed in group lending?

• Published date: 01 February 2019
• Date: 01 February 2019
• Author: Francesco Reito
• DOI: http://doi.org/10.1111/rode.12549

REGULAR ARTICLE

Is it better to be mixed in group lending?

Francesco Reito

University of Catania, Catania, Italy

Correspondence

Francesco Reito, Department of

Economics and Business, University of

Catania, Corso Italia 55, 95100 Catania,

Italy.

Email: reito@unict.it

Abstract

This paper shows that, in a group‐lending scheme with

joint liability, a microfinance institution can achieve a

Pareto improvement by promoting negative assortative

matching among borrowers. The main results are: (i) bor-

rowers may be better off in heterogeneous groups; and

(ii) a heterogeneous group equilibrium is possible when

individual or homogeneous group equilibria do not exist.

KEYWORDS

group lending, assortative matching, Pareto improvement

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INTRODUCTION

Group lending is probably the most popular instrument used by microfinance institutions to

enforce the repayment of loans. The typical feature of this lending arrangement is that borrow-

ers are required to form groups in which all members are considered jointly liable for each

other's loan repayment. Namely, if one or more of the group members fail to repay, successful

borrowers must pay both individual and joint liability commitments. This mechanism has

drawn the attention of a growing literature on credit market imperfections, which shows that

group lending can help mitigating the problem of information asymmetry between lenders and

borrowers.

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This paper is based on the works by Van Tassel (1999) and Ghatak (1999), who argue that

group lending always leads to positive assortative matching among micro‐entrepreneurs. This

means that, in a population of potential borrowers with different risk profiles, individuals will sort

themselves into homogeneous risk groups. Low‐risk individuals would never agree to match with

high‐risk types, even if side payments among group members are possible.

In particular, this paper is based on the adverse‐selection framework of Ghatak (2000), in which

the credit market can be characterized by either underinvestment (Stiglitz & Weiss, 1981), or over-

investment (de Meza & Webb, 1987). Ghatak (2000) considers two types of potential borrowers

(safe and risky), and compares their expected utilities under homogeneous and heterogeneous

(mixed) matching. However, in this comparison, the payoffs under homogeneous and mixed

groups are based on the same financial contract offered by a microfinance institution (MFI). That

DOI: 10.1111/rode.12549

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© 2018 John Wiley & Sons Ltd wileyonlinelibrary.com/journal/rode Rev Dev Econ. 2019;23:54–71.

is, the contractual terms (individual and joint liability payments) are considered exogenous, irre-

spective of the final composition of borrowers’types within the group financed. Under these con-

ditions, the match‐payoff function is always supermodular (see Becker, 1973; Topkis, 1998), and

the assortative matching can never be negative. The present paper argues that the payoff of mixed

groups should actually be based on a different financial contract. Specifically, the MFI should offer

a menu of two different contracts, one designed for homogeneous groups, and one for mixed

groups. In each of these contracts, the MFI must break even, and so let borrowers choose the type

of partner that maximizes their expected payoff.

The two main results of the article are:

(1) Borrowers may be better off in mixed groups. This means that a MFI can achieve a Pareto

improvement, over the equilibrium characterized by positive assortative matching, by prom oting

negative matching among borrowers.

The intuition for the presence of risk heterogeneity is that, in some circumstances, safe types may be

willing to trade some of their low‐risk profile in exchange for side payments from risky partners. Mixed

matching can be explainedby the desire for an intra‐group insurance system in additionto joint liability.

This kind of insurance may operate through transfers of money, food, labor services and gifts among

group members. It is well known that credit groups can also serve the role of mutual assistance in rural

and poor environments, and empirical evidence of this self‐help behavior is reported by Carpenter and

Sadoulet (2000), Dupas and Robinson (2009) and Fafchamps and La Ferrara (2012).

Although the prevalent view is that group lending leads to homogeneous risk matching (for exam-

ple Ahlin, 2009), a number of authors report that group heterogeneity is, in some cases, the optimal

form of risk‐sharing arrangement. For example, evidence on negative matching (or at least the

absence of positive matching) can be found in Van Tassel (2000) himself, Carpenter and Sadoulet

(2000), Lensink and Mehrteab (2003), Fafchamps and Gubert (2007), and Berhabe et al. (2009).

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(2) A mixed equilibrium is possible when homogeneous equilibria do not exist, and even when

the reservation utility of borrowers is equal to zero. In the underinvestment setup of Ghatak

(2000), safe types cannot receive individual liability contracts because their expected payoff is not

sufficient to cover the average loan repayment. This is the classic adverse‐selection problem,

whereby risky types drive safe types out of the credit market. Ghatak (2000) shows that, if the pro-

ject's expected return of safe types is large enough to guarantee the presence of a joint liability

equilibrium, group lending can solve the underinvestment problem. In contrast, underinvestment

may occur under joint liability in two possible circumstances: (i) if the safe type's participation

constraint is not satisfied under group lending; (ii) if the reservation payoff of borrowers is very

low or zero (a reasonable assumption in underdeveloped contexts). This paper argues that, in such

cases, a mixed equilibrium may exist and eliminate the underinvestment problem.

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It is important to stress that the mixed equilibrium described in the model can be, in some

cases, subject to rematching of borrowers. The MFI knows the proportion of safe and risky types,

but project risk is private information of borrowers. Thus, if a mixed contract is offered, mixed

group members may have the incentive to rematch in homogeneous pairs and yet sign the mixed

contract in order to raise their payoffs.

This paper shows that negative matching can be a stable equilibrium if the MFI introduces the threat

of withdrawing the mixed contract if loan applications are not compatiblewith heterogeneous lending.

The rest of the paper is as follows. Section 2 reviews the underinvestment setup of Ghatak (2000).

Section 3 introduces the mixed lending contract. Section 4 derives the sign, positive or negative, of

the assortative matching. Section 5 derives the equilibrium contract composition and discusses the

stability of mixed matching. Section 6 shows that a mixed group equilibrium may exist when homo-

geneous group equilibria are not possible. Section 7 discusses the results and concludes.

REITO

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