Alernative Forms for Restricted Regressions

We study the relationship between group size and the extent of risk sharing in an insurance game played over a number of periods with random idiosyncratic and aggregate shocks to income in each period. Risk sharing is attained via agents that receive a high endowment in one period making unilateral transfers to agents that receive a low endowment in that period. The complete risk sharing allocation is for all agents to place their endowments in a common pool, which is then shared equally among members of the group in every period. Theoretically, the larger the group size, the smaller the per capita dispersion in consumption and greater is the potential value of insurance. Field evidence however suggests that smaller groups do better than larger groups as far as risk sharing is concerned. Results from our experiments show that the extent of mutual insurance is significantly higher in smaller groups, though contributions to the pool are never close to what complete risk sharing requires.