X-Differencing and Dynamic Panel Model Estimation

This paper introduces a new estimation method for dynamic panel models with fixed effects and AR(p) idiosyncratic errors. The proposed estimator uses a novel form of systematic differencing, called X-differencing, that eliminates fixed effects and retains information and signal strength in cases where there is a root at or near unity. The resulting "panel fully aggregated" estimator (PFAE) is obtained by pooled least squares on the system of X-differenced equations. The method is simple to implement, free from bias for all parameter values, including unit root cases, and has strong asymptotic and finite sample performance characteristics that dominate other procedures, such as bias corrected least squares, GMM and system GMM methods. The asymptotic theory holds as long as the cross section (n) or time series (T) sample size is large, regardless of the n/T ratio, which makes the approach appealing for practical work. In the time series AR(1) case (n = 1), the FAE estimator has a limit distribution with smaller bias and variance than the maximum likelihood estimator (MLE) when the autoregressive coefficient is at or near unity and the same limit distribution as the MLE in the stationary case, so the advantages of the approach continue to hold for fixed and even small n. For panel data modeling purposes, a general-to-specific selection rule is suggested for choosing the lag parameter p and the procedure works in a standard manner, aiding practical implementation. The PFAE estimation method is also applicable to dynamic panel models with exogenous regressors. Some simulation results are reported giving comparisons with other dynamic panel estimation methods.