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

We compare different methods for estimating forwardlooking output and inflation equations and show that weak identification can be an issue in conventional GMM estimation. GMM and maximum likelihood procedures that impose the dynamic constraints implied by the forwardlooking relation on the instruments set are found to be more reliable than conventional GMM. These “optimal instruments” procedures provide a robust alternative to estimating dynamic macroeconomic relations, and suggest only a limited role for expectational terms.