# Estimating Intertemporal Allocation Parameters using Simulated Residual Estimation

*Sule Alan* () and
*Martin Browning*

No 2003-03, CAM Working Papers from University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics

**Abstract:**
There is widespread agreement that given currently available data, we cannot accurately estimate the parameters of intertemporal allocation using GMM on Euler equations, whether they be exact or approximate. Our reading of this literature and our own results is that this is a small sample (strictly, short panel) problem. The alternative seems to be to move to full structural modelling. In the current state of the art this is cumbersome, fragile and unable to deal with significant heterogeneity. We present a novel structural estimation procedure that is based on simulating expectation errors; we refer to it as Simulated Residual Estimation (SRE). We develop variants of the basic procedure that allow us to account for measurement error in consumption, the 'news' in interest rate realisations and for heterogeneity in discount factors. 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 and noisy consumption data. An empirical application to two panels drawn from the PSID are presented. The results are very encouraging. We find that we can estimate the parameters of intertemporal allocation much more precisely than with a conventional GMM on a log-linearised model. For example, we find that the 95% confidence interval for the EIS is [0.27, 0.70] for the more educated whereas the IGMM confidence intervals are [-0.38, 0.90] and [-3.78, 6.22] for the linearized and nonlinear models respectively. Moreover, the parameter estimates seem quite reasonable. 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 CRRA 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 the discount factor within education groups. We reject strongly the homogeneity assumption and find that discount rates vary significantly within groups.

**Date:** 2003-03

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