GMM Estimation with Non-causal Instruments*

Abstract

This note provides a warning against careless use of the generalized method of moments (GMM) with time series data. We show that if time series follow non-causal autoregressive processes, their lags are not valid instruments, and the GMM estimator is inconsistent. Moreover, endogeneity of the instruments may not be revealed by the J-test of overidentifying restrictions that may be inconsistent and has, in general, low finite-sample power. Our explicit results pertain to a simple linear regression, but they can easily be generalized. Our empirical results indicate that non-causality is quite common among economic variables, making these problems highly relevant.