Half-panel jackknife fixed-effects estimation of linear panels with weakly exogenous regressors

This paper considers estimation and inference in linear panel regression models with lagged dependent variables and/or other weakly exogenous regressors when N (the cross-section dimension) is large relative to T (the time series dimension). It allows for fixed and time effects (FE-TE) and derives a general formula for the bias of the FE-TE estimator which generalizes the well-known Nickell bias formula derived for the pure autoregressive dynamic panel data models. It shows that in the presence of weakly exogenous regressors inference based on the FE-TE estimator will result in size distortions unless N/T is sufficiently small. To deal with the bias and size distortion of the FE-TE estimator the use of a half-panel jackknife FE-TE estimator is considered and its asymptotic distribution is derived. It is shown that the bias of the half-panel jackknife FE-TE estimator is of order T−2, and for valid inference it is only required that N/T³→0, as N,T→∞ jointly. Extension to unbalanced panel data models is also provided. The theoretical results are illustrated with Monte Carlo evidence. It is shown that the FE-TE estimator can suffer from large size distortions when N>T, with the half-panel jackknife FE-TE estimator showing little size distortions. The use of half-panel jackknife FE-TE estimator is illustrated with two empirical applications from the literature.