On bias, inconsistency, and efficiency of various estimators in dynamic panel data models

When a model for panel data includes lagged dependent explanatory variables, then the habitual estimation procedures are asymptotically valid only when the number of observations in the time dimension (T) gets large. Usually, however, such datasets have substantial sample size in the cross-section dimension (N), whereas T is often a single-digit number. Results on the asymptotic bias (N → ∞) in this situation have been published a decade ago, but, hence far, analytic small sample assessments of the actual bias have not been presented. Here we derive a formula for the bias of the Least-Squares Dummy Variable (LSDV) estimator which has a O(N−1 T−32) approximation error. In a simulation study this is found to be remarkably accurate. Due to the small variance of the LSDV estimator, which is usually much smaller than the variance of consistent (Generalized) Method of Moments estimators, a very efficient procedure results when we remove the bias from the LSDV estimator. The simulations contain results for a particular operational corrected LSDV estimation procedure which in many situations proves to be (much) more efficient than various instrumental variable type estimators.