Consumption and Labor Supply with Partial Insurance: An Analytical Framework

We develop a model with partial insurance against idiosyncratic wage shocks to quantify risk sharing. Closed-form solutions are obtained for equilibrium allocations and for moments of the joint distribution of consumption, hours, and wages. We prove identification and demonstrate how labor supply data are informative about risk sharing. The model, estimated with US data over the period 1967–2006, implies that (i) 39 percent of permanent wage shocks pass through to consumption; (ii) the share of wage risk insured increased until the early 1980s; and (iii) preference heterogeneity is important in accounting for observed dispersion in consumption and hours.