Estimating Intertemporal Allocation Parameters using Synthetic Residual Estimation

We present a novel structural estimation procedure for models of intertemporal allocation. This is based on modelling expectations errors directly; we refer to it as synthetic residual estimation (SRE). The flexibility of SRE allows 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 generalized method of moments (GMM) estimation of both exact and approximate Euler equations in the case when we have short panels and noisy consumption data. We apply SRE to two panels drawn from the Panel Study of Income Dynamics (PSID) and estimate the joint distribution of the discount factor and the elasticity of intertemporal substitution. We reject strongly homogeneity of the discount factor and the elasticity of intertemporal substitution. We find that, on average, the more educated are more patient and less willing to substitute intertemporally than the less educated. Within education strata, patience and willingness to substitute are positively correlated.