Instrumental Variable Estimation of Dynamic Linear Panel Data Models with Defactored Regressors and a Multifactor Error Structure

Abstract

This paper develops two instrumental variable (IV) estimators for dynamic panel data models with exogenous covariates and a multifactor error structure when both crosssectional and time series dimensions, N and T respectively, are large. Our approach initially projects out the common factors from the exogenous covariates of the model, and constructs instruments based on this defactored covariates. For models with homogeneous slope coe_cients, we propose a two-step IV estimator: the _rst step IV estimator is obtained using the defactored covariates as instruments. In the second step, the entire model is defactored by the extracted factors from the residuals of the _rst step estimation and subsequently obtain the _nal IV estimator. For models with heterogeneous slope coe _cients, we propose a mean-group type estimator, which is the cross-sectional average of _rst-step IV estimators of cross-section speci_c slopes. It is noteworthy that our estimators do not require us to seek for instrumental variables outside the model. Furthermore, our estimators are linear hence computationally robust and inexpensive. Moreover, they require no bias correction, and they are not subject to the small sample bias of least squares type estimators. The _nite sample performances of the proposed estimators and associated statistical tests are investigated, and the results show that the estimators and the tests perform well even for small N and T.