This paper analyzes the efficient design of insurance schemes in the presence of aggregate shocks and moral hazard. The population is divided into groups, the labour force in different sectors for instance. In each group, individuals are ex ante identical but are subject to idiosyncratic shocks. Without moral hazard, optimality requires (1) full insurance against idiosyncratic shocks, which gives rise to a representative agent for each group and (2) optimal sharing of macro-economic risks between these representative agents. The paper investigates what remains of this analysis when the presence of moral hazard conflicts with the full insurance of idiosyncratic shocks. In particular, how is the sharing of macro-economic risks across groups affected by the partial insurance against idiosyncratic risks? The design of unemployment insurance schemes in different economic sectors, and the design of pension annuities in an unfunded social security system are two potential applications.
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