Labor Supply, Aggregation and the Labor Wedge

This paper discusses the role of household heterogeneity in a model in which idiosyncratic consumption and labor income risks manifest as a distortion to the intra-temporal optimal condition of the representative agent. Aggregation over the undistorted labor-leisure condition of each household leads to a wedge between the Marginal Rate of Substitution, between consumption and leisure, (MRS) and the Marginal Product of Labor (MPL), through the lens of the representative agent model. I use household survey data to assess the properties of this aggregation wedge. I find that it is consistent with the systematic deviation between the MRS and the MPL observed in aggregate data, the so-called "Labor Wedge", for both the long-run and the business cycles. Additionally, I explore the quantitative implications of the model assuming imperfect insurability against idiosyncratic shocks. I show that cyclical changes in the distribution of household productivity and in the degree of risk sharing lead to cyclical changes in the aggregation wedge, as if the representative agent faced higher labor taxes - or was lazier- during recessions. The model also exhibits novel dynamics for labor, relative to the benchmark RBC, because of the various labor supply elasticities induced by the individual productivities and the wealth distribution.