The Irrelevance of Market Incompleteness for the Price of Aggregate Risk

In models with a large number of agents who have constant relative risk aversion (CRRA) preferences, the absence of insurance markets for idiosyncratic labour income risk has no effect on the premium for aggregate risk if the distribution of idiosyncratic risk is independent of aggregate shocks. In spite of the missing markets, a representative agent who consumes aggregate income prices the excess returns on stocks correctly. This result holds regardless of the persistence of idiosyncratic shocks, as long as they are not permanent, even when households face binding, and potentially very tight borrowing constraints. Consequently, in this class of models there is no link between the extent of self-insurance against idiosyncratic income risk and aggregate risk premia.