Using Micro Data to Estimate the Intertemporal Substitution Elasticity for Labor Supply in an Implicit Contract Model

Economists have devoted substantial resources to estimating the intertemporal substitution elasticity for labor supply because this elasticity plays a crucial role in the real business cycle literature. Generally, the estimates of the elasticity have been too low to explain business cycles. Economists have responded by trying to modify real business cycle models to allow for smaller elasticities, but they have experienced mixed success at best. However, the standard intertemporal substitution model has not done well when tested, and if this model is incorrect, so will be the estimated labor supply elasticities based upon it. An equilibrium alternative to the standard intertemporal labor supply model is the implicit contract model. In this latter model firms and workers bargain over state-contingent contracts denominated in terms of consumption and hours of work. Further, the price of leisure is the marginal product of labor or the shadow wage, which differs from the observed wage. A number of studies have found that the data are compatible with an implicit contract model; in particular in Ham and Reilly (2002) we found that we could reject a separable (within period) implicit contract model but not a non-separable one. If an implicit contract model is appropriate, this is the context in which we should try to estimate the intertemporal labor supply elasticity. However this estimation is potentially quite difficult with micro data since the shadow wage (marginal product of labor) is unobserved. In this paper we first develop a procedure that allows one to estimate the intertemporal substitution elasticity in an implicit contract model from micro data. We then implement this procedure using the Panel Study of Income Dynamics (PSID) and the Consumer Expenditure Survey (CES). We obtain statistically significant elasticities of 0.9 with the PSID and 1.0 with the CES. The consistency of the estimate across the data sets is impressive given that we use different estimation approaches (micro data versus synthetic cohorts) and different consumption measures (food consumption versus total nondurable consumption) in the two data sets. These results are three times larger than existing estimates based on the standard intertemporal supply elasticity from this data set and thus offer more hope that equilibrium perspectives on the labor market are capable of tracking the data. Given that the implicit contract model is less likely to be rejected than the standard model in our work and other research, we believe that our approach should prove to be quite useful.