A Reconsideration of Consistent Estimation of a Dynamic Panel Data Model in the Random Effects (Error Components) Framework

It is widely believed that the inclusion of lagged dependent variables in a panel data model necessarily renders the Random Effects (RE) estimators, based on OLS applied to the quasi-differenced variables, inconsistent. It is shown here that this belief is incorrect under the usual assumption made in this context — i.e., that the other regressors are strictly exogenous. This result follows from the fact that lagged values of the deviation of the quasi-differenced dependent variable from its mean can be written as a weighted sum of the past values of the quasi-differenced model error term, whereas these quasidifferenced errors are serially uncorrelated by construction. The RE estimators are therefore consistent. Thus, since instrumental variables methods – e.g., Arellano and Bond (1991) – clearly provide less precise estimates, the RE estimates are preferable if a Hausman test is unable to reject the null hypothesis that the parameter estimates of interest from both methods are equal.