This paper contributes to the GMM literature by introducing the idea of self-instrumenting target variables instead of searching for instruments that are uncorrelated with the errors, in cases where the correlation between the target variables and the errors can be derived. The advantage of the proposed approach lies in the fact that, by construction, the instruments have maximum correlation with the target variables and the problem of weak instrument is thus avoided. The proposed approach can be applied to estimation of a variety of models such as spatial and dynamic panel data models. In this paper we focus on the latter and consider both univariate and multivariate panel data models with short time dimension. Simple Bias-corrected Methods of Moments (BMM) estimators are proposed and shown to be consistent and asymptotically normal, under very general conditions on the initialization of the processes, individual-speci.c e¤ects, and error variances allowing for heteroscedasticity over time as well as cross-sectionally. Monte Carlo evidence document BMM.s good small sample performance across di¤erent experimental designs and sample sizes, including in the case of experiments where the system GMM estimators are inconsistent. We also .nd that the proposed estimator does not su¤er size distortions and has satisfactory power performance as compared to other estimators.
short-t dynamic panels GMM weak instrument problem quadratic moment conditions panel VARs Monte Carlo evidence