Forthcoming, Review of Economic StudiesGroup Formation in Risk-Sharing ArrangementsGarance GenicotUniversity of California, IrvineDebraj RayNew York University and Instituto de An´alisis Econ´omico (CSIC)Revised July 2002.AbstractWe study informal insurance within communities, explicitly recognizing the possibilitythat subgroups of individuals may destabilize insurance arrangements among the largergroup. We therefore consider self-enforcing risk-sharing agreements that are robust notonly to single-person deviations but also to potential deviations by subgroups. However,such deviations must be credible, in the sense that the subgroup must pass exactly thesame test that we apply to the entire group; it must itself employ some self-enforcingrisk-sharing agreement. We observe that the stability of subgroups is inimical to thestability of the group as a whole. Two surprising consequences of this analysis are thatstable groups have (uniformly) bounded size, a result in sharp contrast to the individual-deviation problem, and that the degree of risk-sharing in a community is generally non-monotonic in the level of uncertainty or need for insurance in the community.We are grateful for comments by seminar participants at the University of Chicago,Princeton University, the INRA/Delta in Paris, the University of California at Irvine,the Summer Meeting of the Econometrics Society at the University of Maryland andthe NEUDC in Cornell University. We also thank two anonymous referees for usefulcomments on an earlier draft. Address all correspondence to [email protected] [email protected] IntroductionRisk is a pervasive fact of life in developing countries. As a response to the large fluctu-ations in their income, individuals — mainly in rural areas — often enter into informalinsurance or quasi-credit agreements. To be sure, such arrangements are potentiallylimited by the presence of various incentive constraints. As a first cut, it appears thatthe most important constraint arises from the fact that such agreements are not writtenon legal paper, and must therefore be designed to elicit voluntary participation. To beself-enforcing, the expected net benefits from participating in the agreement must be atany point in time larger than the one time gain from defection.1There is a growing body of literature, both theoretical and empirical, on self-enforcingrisk-sharing agreements. Some important theoretical contributions are Posner [1980],Kimball [1988], Coate and Ravallion [1993], Kocherlakota [1996], Kletzer and Wright[2000], and Ligon, Thomas and Worrall [2002].2Our starting point is the followingobservation: all these studies (and to our knowledge all existing studies) define “self-enforcing” agreements as those that are proof from defection by individual members ofthe group. As a consequence, the common practice in the literature is to define self-enforcing risk-sharing agreements as subgame perfect equilibria of a repeated game (inwhich self-insurance is always an option), and to characterize the Pareto frontier of suchequilibria. But this raises the obvious question: if a “large” group — say the villagecommunity or a particular caste or kinship group within the community — can foreseethe benefits of risk-sharing and reach an agreement, why might smaller groups not beable to do so? Why would subgroups not be able to agree to jointly defect and sharerisk among themselves? This concern implies that to be truly self-enforcing, an informalrisk-sharing agreement needs to be immune to joint deviations by subgroups. At thesame time, it seems only natural to require that deviating groups themselves satisfy thesame criterion. To be of any value — or to pose a credible threat to the group at large —a deviating coalition should also employ self-enforcing arrangements. These embeddedconstraints characterize the concept of self-enforcing risk-sharing agreements and stablecoalitions that we define in this paper.Despite their importance, issues of participation and group formation have been little1Udry [1994], in his study of rural northern Nigeria, finds this constraint to be the most importantin describing the structure of reciprocal agreements. While this does not prove that other informationalasymmetries are of second-order importance (for instance, they may limit the choice of whom to transactwith in the first place), we feel that the self-enforcement constraint represents a good first approximation.2The literature on risk-sharing without commitment in rural societies started with the suggestionsof Posner [1980] and Kimball [1988] that schemes of mutual insurance with limited commitment werepossible. In an important paper, Coate and Ravallion [1993] characterized mutual insurance arrangementswith a restriction to stationary transfers for a symmetric two-household model. A recent strand ofliterature investigates efficient dynamic contracts in the absence of commitment (Kocherlakota [1996],Ligon, Thomas and Worrall [2002], Kletzer and Wright [2000]).2discussed in the literature on informal risk-sharing. As we shall see, this criticism is notjust one of methodology, it has substantive implications. The most important of these isthat the “individual deviations” framework places no bound on group size. For instance,in a homogeneous population, the larger the group the higher the per-capita utilityfrom risk-sharing. Barring other impediments to group size, the theory implies thatany efficient agreement has to be at the level of the “community.” That is why mostempirical tests of insurance (Deaton [1992], Townsend [1994], Udry [1994], Jalan andRavallion [1999], Ligon, Thomas and Worrall [2002], Grimard [1997], and Gertler andGruber [2002]) take the unit of analysis as exogenous and study the extent of insuranceat the level of the village or even larger groups.3Of course, this is not say that grouplimits are not taken seriously. But other considerations — caste, kinship, or even theinformational decay that must ultimately affect large groups — must be brought in tocomplete the picture. One could, of course, model this in several ways: for instance, bypositing some cost of group formation which increases with the size of the group (see,e.g., Murgai et al [2002]).We abstract from all such factors. We endogenize not just the extent of insurancewithin a given groups, but the process of group formation within a community. Withoutinvoking any of the additional