Half-Panel Jackknife Fixed Effects Estimation of Panels with Weakly Exogenous Regressor

This paper considers estimation and inference in fixed effects (FE) panel regression models with lagged dependent variables and/or other weakly exogenous (or predetermined) regressors when NN (the cross section dimension) is large relative to TT (the time series dimension). The paper first derives a general formula for the bias of the FE estimator which is a generalization of the Nickell type bias derived in the literature for the pure dynamic panel data models. It shows that in the presence of weakly exogenous regressors, inference based on the FE estimator will result in size distortions unless NN/TT is sufficiently small. To deal with the bias and size distortion of FE estimator when NN is large relative to TT, the use of half-panel Jackknife FE estimator is proposed and its asymptotic distribution is derived. It is shown that the bias of the proposed estimator is of order TT –2, and for valid inference it is only required that NN/TT3 --> 0, as NN, TT --> 00 jointly. Extensions to panel data models with time effects (TE), for balanced as well as unbalanced panels, are also provided. The theoretical results are illustrated with Monte Carlo evidence. It is shown that the FE estimator can suffer from large size distortions when NN > TT, with the proposed estimator showing little size distortions. The use of half-panel jackknife FE-TE estimator is illustrated with two empirical applications from the literature