Half-Panel Jackknife Fixed Effects Estimation of 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 FE-TE estimator the use of 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. Extensions 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