A James-Stein-type adjustment to bias correction in fixed effects panel models

Abstract

This paper proposes a James-Stein-type (JS) adjustment to analytical bias correction in fixed effects panel models that suffer from the incidental parameters problem. We provide high-level conditions under which the infeasible JS adjustment leads to a higher-order MSE improvement over the bias-corrected estimator, and the former is asymptotically equivalent to the latter. To obtain a feasible JS adjustment, we propose a nonparametric bootstrap procedure to estimate the JS weighting matrix and provide conditions for its consistency. We apply the JS adjustment to two models: (1) the linear autoregressive model with fixed effects, (2) the nonlinear static fixed effects model. For each application, we employ Monte Carlo simulations which confirm the theoretical results and illustrate the finite-sample improvements due to the JS adjustment. Finally, the extension of the JS procedure to a more general class of models and other policy parameters are illustrated.