COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1747 X-Differencing and Dynamic Panel Model Estimation Chirok Han, Peter C.B. Phillips and Donggyu Sul January 2010 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. |
