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

This paper analyses the instrumental variables (IV) approach put forward by \citet{NorkuteEtal20}, in the context of static linear panel data models with interactive effects present in the error term and the regressors. Instruments are obtained from transformed regressors, thereby it is not necessary to search for external instruments. We consider a two-stage IV (2SIV) and a mean-group IV (MGIV) estimator for homogeneous and heterogeneous slope models, respectively. The asymptotic analysis reveals that: (i) the $\sqrt{NT}$-consistent 2SIV estimator is free from asymptotic bias that may arise due to the estimation error of the interactive effects, whilst (ii) existing estimators can suffer from asymptotic bias; (iii) the proposed 2SIV estimator is asymptotically as efficient as existing 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.