Implications of Endogenous Group Formation for Efficient Risk-Sharing

This paper models the implications of endogenous group formation for efficient risk-sharing contracts in the dynamic limited commitment model.  Endogenising group formation requires that any risk-sharing arrangement is not only stable with respect to individual deviations but also with respect to deviations by sub-groups.  This requirement alters the central predictions of the dynamic limited commitment model for efficient bilateral risk-sharing.  Firstly, consumption of constrained agents depends on the previous history of shocks and the interaction of the history of shocks with the current income realizations of other constrained agents.  As a consequence, the efficient contract does not display amnesia.  Secondly, the covariance between current consumption and past income can take on negative values.  Based on the first result, we derive a formal test for the presence of endogenous group formation under limited commitment.  In addition, we show how this test can be extended to distinguish a limited commitment/perfect information environment from a full commitment/imperfect information environment empirically.