Risk Sharing with (Dis)Aggregate Shocks

Abstract

In this paper we examine conditions under which optimal risk sharing may not fully insure individuals against idiosyncratic shocks to their endowments or income, even when markets are complete. We analyze the benchmark risk-sharing model, but allow for the possibility that idiosyncratic shocks can induce fluctuations in aggregate resources, affecting in this way the Pareto optimal allocation of consumption. In particular, we show that idiosyncratic shocks affect consumption under optimal risk-sharing, when endowments are drawn from a class of power law distributions or when output is produced through input supply networks with star-shape or scale-free architecture. Under these conditions, we document two important features of optimal risk sharing. First, the effect of idiosyncratic risk on consumption growth is heterogeneous, and depends on each agent’s contribution to the aggregate resource, and, second, risk sharing involves an exposure to systemic risk that is composite of the undiversified components of idiosyncratic shocks. Additionally, we show that the frequently used empirical tests of risk-sharing which ignore the distributional aspects of income and the network structure of production, may suffer from a specification bias when idiosyncratic shocks do not dissipate in the aggregate. We offer empirical evidence to show that individual consumption growth is affected by a systemic component of risk, such as, for example, the shocks to the top percentiles of the income distribution. Our results have important implications for empirical studies of risk-sharing carried out at the individual, household and national level, irrespective of the size of the reference group, be it the household, the village, or the country.