Estimating forward looking Euler equations with GMM estimators: an optimal instruments approach

This paper compares different methods for estimating forward-looking output and inflation Euler equations and shows that weak identification can be an issue in conventional GMM estimation. The authors propose a GMM procedure that imposes the dynamic constraints implied by the forward-looking relation on the instruments set. This “optimal instruments” procedure is more reliable than conventional GMM, and it provides a robust alternative to estimating dynamic macroeconomic relations. Empirical applications of this procedure suggest only a limited role for expectational terms.