Estimating Euler equations with noisy data: two exact GMM estimators

In this paper we exploit the specific structure of the Euler equation and develop two alternative GMM estimators that deal explicitly with measurement error. The first estimator assumes that the measurement error is log-normally distributed. The second estimator drops the distributional assumption at the cost of less precision. Our Monte Carlo results suggest that both proposed estimators perform much better than conventional alternatives based on the exact Euler equation or its log-linear approximation, especially with short panels. An empirical application to the PSID yields plausible and precise estimates of the coefficient of relative risk aversion and the discount rate. © 2008 John Wiley & Sons, Ltd