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

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. The main idea is to project out the common factors from the exogenous covariates of the model, and construct instruments based on defactored covariates. For models with homogeneous slope coefficients, we propose a two-step IV estimator: in the first step, the model is estimated consistently by employing defactored covariates as instruments. In the second step, the entire model is defactored based on estimated factors extracted from the residuals of the first step estimation; subsequently, an IV regression is implemented using the same instruments as in step one. For models with heterogeneous slope coefficients, we propose a mean-group type estimator, which involves averaging of first-step IV estimates of cross-section specific slopes. The proposed estimators do not need to seek for instrumental variables outside the model. Furthermore, these estimators are linear, thereby computationally robust and inexpensive. Notably, they require no bias correction. The finite 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.