Estimating Euler Equations with Noisy Data: Two Exact GMM Estimators.

Abstract

In this paper we exploit the speci…c structure of the Euler equation and develop two alternative GMM estimators that deal explicitly with measurement error. The …rst estimator assumes that the measurement error is lognormally distributed. The second estimator drops the distribu- tional assumption and solves out for the unknown, but constant, conditional mean. 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. The empirical application of the proposed estimators yields plausible estimates of the coe¢ cient of relative risk aversion and discount rate