Two-Stage Instrumental Variable Estimation of Linear Panel Data Models with Interactive Effects

Abstract

This paper puts forward a new instrumental variables (IV) approach for linear panel data models with interactive effects in the error term and regressors. The instruments are transformed regressors and so it is not necessary to search for external instruments. The proposed method asymptotically eliminates the interactive effects in the error term and in the regressors separately in two stages. We propose a two-stage IV (2SIV) and a mean-group IV (MGIV) estimator for homogeneous and heterogeneous slope models, respectively. The asymptotic analysis for the models with homogeneous slopes reveals that: (i) the \sqrt{NT}-consistent 2SIV estimator is free from asymptotic bias that could arise due to the correlation between the regressors and the estimation error of the interactive effects; (ii) under the same set of assumptions, existing popular estimators, which eliminate interactive effects either jointly in the regressors and the error term, or only in the error term, can suffer from asymptotic bias; (iii) the proposed 2SIV estimator is asymptotically as efficient as the bias-corrected version of estimators that eliminate interactive effects jointly in the regressors and the error, whilst; (iv) the relative efficiency of the estimators that eliminate interactive effects only in the error term is indeterminate. A Monte Carlo study confirms good approximation quality of our asymptotic results and competent performance of 2SIV and MGIV in comparison with existing estimators. Furthermore, it demonstrates that the bias-corrections can be imprecise and noticeably inflate the dispersion of the estimators in finite samples.