The joint liability literature claims that positive assortative matching, or risk homogeneity, is always the first best solution. We examine this claim in presence of group formation costs and find that the assertion is not always true.Group Formation Costs

Prabirendra Chatterjee

Sudipta Sarangi

English

Research Papers in Economics

Enforcement with Costly Group Formation 
Prabirendra Chatterjee Sudipta Sarangi
Louisiana State University Louisiana State University
Abstract
The joint liability literature claims that positive assortative matching, or risk homogeneity, is
always the first best solution. We examine this claim in presence of group formation costs
and find that the assertion is not always true.
We would like to thank Aditi Roy, David Li and an anonymous referee for helpful suggestions. All remaining errors are ours.
Citation: Chatterjee, Prabirendra and Sudipta Sarangi, (2005) "Enforcement with Costly Group Formation." Economics
Bulletin, Vol. 15, No. 9 pp. 1−8
Submitted: June 2, 2004.  Accepted: February 13, 2005.
URL: http://www.economicsbulletin.com/2005/volume15/EB−04O10003A.pdf1. Introduction
In recent years economists have spent a considerable amount of time demonstrat-
ing the advantages of joint liability lending over individual liability lending. This
literature ﬁnds that due to the joint liability clause, members of endogeneously
formed groups know each other well and hence are able to overcome the informa-
tion asymmetry faced by the lender. Thus, the mechanism alleviates the major
problems associated with individual liability lending, resulting in high repayment
rates. For an excellent overview of theoretical and empirical work in this area we
refer the reader to Ghatak and Guinanne (1999) and Morduch (1999).
Relatively less work has been done on the issue of enforcement in group lend-
ing programs and our note focuses on this issue. Unlike the evil troika of adverse
selection, moral hazard and costly state veriﬁcation that arise due to asymmet-
ric information between lenders and borrowers, the enforcement problem occurs
primarily because of the limited ability of lenders to apply any sort of sanctions
against borrowers who do not repay.1 For example, lenders cannot force a bor-
rower to repay if she oﬃcially announces that her income is below the subsistence
level, especially if the lenders are interested in poverty alleviation. Thus there are
strong incentives for borrowers to be deliberately delinquent.
Economists argue that joint liability lending is better because a (highly) suc-
cessful borrower has the ability to repay the default amount of her unsuccessful
partner. More importantly, each borrower can monitor her partner and ensure
that the partner does not misrepresent facts. Besley and Coate (1995) from whom
this insight is derived further mention that there is also a negative eﬀect under
joint liability lending − a moderately successful borrower who does not intend to
cheat may be pushed into default by the debt burden of her partner. However,
when social ties are strong, given the possibility of sanctions from both the group,
as well as the bank, it is argued that the net eﬀect on joint liability lending is
positive. Thus, willful default is lower under joint liability lending. In this paper
we examine the enforcement problem in the group lending context by requiring
borrowers to incur group formation costs.
F o r m a t i o no fa ne ﬀective group for the purpose of borrowing through a joint
liability scheme is a costly aﬀair. Given that each group member is jointly liable
and must also be able to monitor and sanction other group members, the ties
between group members have to be very strong. We argue that forming and
1Note that clients of group lending programs are usually too impoverished to have any
collateral.
1keeping such strong ties requires costly time and eﬀort. In the context of Chicago’s
Full Circle Fund, Balkin (1993) claims it takes more than 6 to 8 months for groups
to form and explains this by noting that in a setting where potential members do
not have prior interactions, it takes considerable time for members to assess the
honesty and trustworthiness of the others. Similarly, in two of the three Chinese
programs studied by Park and Ren (2001), travel costs were a major obstacle for
group lending programs.
Further, it may be easier to form groups with some people than others, regard-
less of the risk characteristics of these individuals. This could be for reasons like
the person’s proximity in terms of the work place, language, religion, ethnicity,
or just plain neighborhood. Simply put it might be easier for me to communi-
cate with someone who speaks the same language while communicating in another
tongue will require greater eﬀort. The repayment performance of a low cost group
will diﬀer from that of a high cost group even if we assume symmetric project
outcomes for both groups. This model explains how and under what conditions
a safe-risky combination may outperform a safe-safe combination in the context
of loan repayment.
The fact that varying degree of social ties can aﬀect group formation has
been empirically documented in the literature, though its signiﬁcance has not
really been formally analyzed. A case in example is the attempt to clone the
Grameen Bank in Arkansas under the name of the Good Faith Fund.A r k a n s a s
has signiﬁcant racial and social heterogeneity as well as low population density.
Due to this members experienced diﬃculty in ﬁnding four other group members in
their vicinity. Forming groups with those who lived further away was prohibitively
expensive (Taub (1998)). Similarly, Ghatak and Guinnane (1999) note that some
of BancoSol’s lending groups were reconstituted from older Rosca groups. Van
Tassel (1999) mentions a BancoSol survey where 38 of the 40 members interviewed
knew their group members for more than 3 years. Similarly, the majority of
Grameen’s borrowers are women. One reason for this could be that in a traditional
society it is easier to form same sex groups. Wydick (1999) in the context of
Guatemala shows that groups often tend to be composed of members who are
closer professionally and these groups also have higher repayment rates. Olomola’s
(2000) study using Nigerian data ﬁnds that the degree of acquaintance within
fellow group members has a positive eﬀe c to nr e p a y m e n ts i n c ei te a s i e rf o rs u c h
groups to form and also have better interaction among the members. Similarly,
Lensink and Mehrteab (2003) who ﬁnd evidence of risk heterogeneity in Eritrea
also ﬁnd that 287 of the 351 individuals in their sample already knew each other.
2Thus we see that group formation is not a random process but occurs primarily
among individuals who have closer social ties.
The paper is organized as follows. Section 2 develops the basic model of
group lending. Section 3 formulates and analyzes the model of enforcement in
the context of group lending, and ﬁnally, in Section 4 there are some concluding
remarks.
2. A simple model of group lending
The model developed here follows Ghatak and Guinnane (1999) but introduces
two groups of borrowers. The pool of borrowers in a community either belong to
Group A or to Group B. Borrowers in both groups can either be safe or risky.
Each individual borrower thus is denoted by an ordered pair ij ∈ {A,B}×{R,S},
where the ﬁrst element describes their group membership and the second their
risk attribute with R and S being risky and safe respectively. We assume that
a borrowing group consists of two risk-averse individuals who are jointly liable
for the loan.2 S i n c et h eb o r r o w e r sa r ej o i n t l yl i a b l ew ed e n o t eb yc = r the cost
incurred by an individual if her partner’s project does not succeed, where r>0
is the repayment amount of each borrower. Therefore, a successful borrower has
to repay 2r if her partner’s project does not succed.
All borrowers engage in an economic activity using their loan. Let Y denote
the outcome of a successful project, while the value of a failed project is normalized
to zero. A safe agent of either group has the same probability of project success
which is higher than the success probability of a risky agent. Similarly, risky
agents from both group also have the same project success probability.
Next we introduce the group formation costs. We assume that it is costly to
form groups where the group formation cost (C) depends on the choice of the
partner. For simplicity we assume that agents in Group A incur a lower cost
(normalized to zero) to form a group amongst themselves. Hence CA
AR = CA
AS =0
but CA
BR = CA
BS = C>0, where the subscript denotes the partner’s identity.3
T h es a m ec o s ts t r u c t u r eh o l d sf o rm e m b e r si nG r o u pB, i.e., inter-group formation
costs are identical for all agents in the community. Relaxing this assumption will
2As in Ghatak and Guinanne (1999) relaxing this assumption does not alter results.
3This is a simple way to model the group formation costs. We are assuming that all individ-
uals in Group A for instance, live on Sesame Street and can form a group with each other very
easily. On the other hand, those in Group B live in a far away part of the village called Elm
Street and hence getting to know them is costly. This relationship is of course symmetric.
3not alter results (for more on this see Chatterjee and Sarangi (2004)).
We assume that while the lending party does not have information regarding
the risk characteristic of a borrower, this attribute is common knowledge among
the borrowers. Also, as in Ghatak and Guinanne (1999) we assume that borrow-
ers can receive loans in the future as well, and take the opportunity cost of these
loans into account when choosing to default willfully. From the above formulation
it is clear that we can have both homogeneous (same group pairings) and hetero-
geneous (A−B pairings) groups. Consequently, with group formation costs, safe
partners may not always better than risky partners, especially if the safe partner
is from a diﬀerent group.
Observation: A homogenous group may or may not be risk heterogeneous.
In other words, both safe-safe and safe-risky pairings can occur in a homogeneous
group. However, given that safe partners are always better than risky partners,
and forming of heterogeneous group is costly, heterogeneous groups, when formed,
will always be risk homogeneous.
3. Enforcement issues
A successful borrower’s project yields output Y and the participation constraint
requires that Y> r + Ck
ij. Now, a borrower will repay her loan only if the
discounted net beneﬁt of continued future access to credit denoted by FB is
greater than the gain from not repaying, i.e.,
U(Y − C
k
ij) − U(Y − C
k
ij − r) <FB (3.1)
where U(.) denotes a standard utility function. Like Ghatak and Guinnane (1999)
we assume that a borrower who defaults can never get a loan in the future. Simi-
larly it is easy to see that a borrower will choose to repay the entire loan amount
if her partner defaults only when the following condition holds:
U(Y − C
k
ij) − U(Y − C
k
ij − 2r) <FB . (3.2)
If k and i belong to the same group then Ck
ij = 0, and the analysis is identical
to Ghatak and Guinnane (1999). For every r let Y (r) denote the threshold r such
that the borrower can repay her own debt if Y ≥ Y (r) and the entire group’s debt
if Y ≥ Y (2r). There are just two possibilities here:
4(i) Y (r) <Y <Y(2r): In this instance the borrower can repay her own debt but
not her partner’s loan.
(ii) Y (r) <Y(2r) <Y: The borrower is able to repay the debts of the whole
group.
In the ﬁrst case individual liability is better, while joint liability is preferable in
the second case. Standard analysis then claims that the threat of social sanctions
under joint liability makes it unattractive for the borrowers to deliberately default
in the ﬁrst scenario. Consequently, the group structure tips the scale in favor of
joint liability lending.
With group formation costs however, we get a richer set of possibilities. If
Y (2r) <Y− C<Yall groups regardless of their composition can repay their
debts. Similarly, if Y − C<Y<Y (r), then nobody is in a position to repay
debts. We now focus on the more interesting intermediate scenarios.
• Low costs of group formation: Y (r) <Y− C<Y<Y (2r). In this
situation all agents regardless of whether they belong to a homogeneous or
heterogeneous group, can repay their own debt but will be unable to pay
for their partner’s loan.
• High costs of group formation: Y − C<Y(r) <Y <Y(2r). In this case
members of a homogeneous group can repay their own debts but not those
of their partners. Members of heterogeneous groups cannot repay even their
own loan. Recall that heterogeneous groups consist of safe-safe pairings
only, while homogeneous groups can also be risk heterogeneous. Hence with
high group formation costs, risk heterogeneity may outperform groups that
are risk homogeneous.
Of course, high group formation costs can be associated with high project
returns: Y − C<Y(r) <Y(2r) <Y. In this case the homogenous groups have
the ability to repay the loan for their partner as well. This model explains the
so-called paradoxical situation when safe-risky combinations can do better than
safe-safe combinations. We summarize this in the following proposition.
Proposition 1. In the presence of group formation costs the repayment perfor-
mance of a homogeneous group is either at par or better than that of a hetero-
geneous group. Hence, a safe-risky combination is not necessarily a second best
outcome as a homogeneous borrowing group can exhibit heterogeneity in terms
of risk characteristics.
5Finally, consider the repayment performance of both groups when group part-
ners behave cooperatively. Here the incentives of group members are aligned and
there will be no deliberate delinquency. Thus for homogeneous groups there will
be no diﬀerence between joint liability and individual liability. For a heterogenous
group, the group formation costs will shift the threshold income required for re-
payment. Hence there will be situations when the homogeneous group can repay
but the heterogeneous group cannot. Moreover, members of the heterogeneous
group would have been able to repay under individual liability since they would
avoid the group formation costs. So we conclude that with group formation costs,
risk heterogeneous pairings may be preferable to risk homogeneous pairings in the
context of loan repayment.
4. Conclusion
We reexamine the enforcement problem for group lending programs by explicitly
modeling group formation costs. Contrary to most theoretical predictions, papers
like Sadoulet and Carpenter (2001), and Lensink and Mehrteab (2001) ﬁnd risk
heterogeneity among borrowing groups in Guatemala and Eritrea respectively.
Despite the risk heterogeneity, these programs have high repayment rates. Our
paper provides an explaination for the repayment performance of such groups. We
show that a homogeneous group (which may be risk heterogeneous) always does
at least as well as a heterogeneous group: although the heterogenous group con-
sists of safe agents, it has to incur group formation costs making repayment more
diﬃcult. In other words, the lender will have to provide loans to heterogeneous
groups at lower rates to oﬀset the group formation costs. Thus we conclude that
though group formation costs do not aﬀect lending parties explicitly, since they
have a direct eﬀect on the repayment performance of borrowers, they do aﬀect
lending parties indirectly.
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7

A Grameen Bank replication: The Full Circle Fund of the Women’s Self Employment Project of Chicago, in A.N.M. Wahid (Ed.)

Can social cohesion be harnessed to repair market failures? Evidence from group lending in Gautemala,

Determinants of the smallholder loan repayment performance: Evidence from the Nigerian microﬁnance system, Working Paper,

Endogeneous matching and risk heterogeneity : Evidence on microcredit group formation in Guatemala.

Group lending under asymmetric information,

Making the adaptation across cultures and societies: A report on an attempt to clone the Grameen Bank in Southern Arkansas,

Risk behaviour and group formation in microcredit groups in Eritrea. CREDIT Working Paper,U n i v e r s i t y of Nottingham.

Enforcement with Costly Group Formation

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