Estimating Intertemporal Allocation Parameters using Synthetic Residual Estimation∗

We present a novel structural estimation procedure that is based on simulating expectation errors; we refer to it as Synthetic Residual Estimation (SRE). We develop variants of the basic procedure that allow us to account for measurement error in consumption and for heterogeneity in intertemporal allocation parameters. An investigation of the small sample properties of the SRE estimator indicates that it dominates GMM estimation of both exact and approximate Euler equations in the case when we have short panels, noisy consumption data and sample of households that are sometimes liquidity constrained. An empirical application to two panels drawn from the PSID are presented. The results are very encouraging. For example, we find discount factors that are less than, but close to unity. We also find a higher discount factor for the more educated group. We find that the more educated have a higher coefficient of relative risk aversion which we interpret to indicate that the constant EIS assumption of the iso-elastic form is rejected. Finally we present results for a model that allows for heterogeneity in both the discount factor and the coefficient of realtive risk aversion within education groups. We reject strongly the homogeneity assumption and find that these parameters vary significantly within groups and they are positively correlated.