Consumption and labor supply with partial insurance: an analytical framework

This paper studies consumption and labor supply in a model where agents have partial insurance and face risk and initial heterogeneity in wages and preferences. Equilibrium allocations and variances and covariances of wages, hours and consumption are solved for analytically. We prove that all parameters of the structural model are identified given panel data on wages and hours, and cross-sectional data on consumption. The model is estimated on US data. Second moments involving hours and consumption show that the rise in wage dispersion in the 1970s was effectively insured by households, while the rise in the 1980s was not.