COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1438

Bias in Dynamic Panel Estimation with Fixed Effects, Incidental Trends
and Cross Section Dependence

Peter C.B. Phillips
Cowles Foundation, Yale University, University of Auckland and University of York
Donggyu Sul
Department of Economics, University of Auckland

September 2003
Revised June 2004

Explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size N —> infinity. The results extend earlier work by Nickell (1981) and later authors in several directions that are relevant for practical work, including models with unit roots, deterministic trends, predetermined and exogenous regressors, and errors that may be cross sectionally dependent. The asymptotic bias is found to be so large when incidental linear trends are fitted and the time series sample size is small that it changes the sign of the autoregressive coe.cient. Another finding of interest is that, when there is cross section error dependence, the probability limit of the dynamic panel regression estimator is a random variable rather than a constant, which helps to explain the substantial variability observed in dynamic panel estimates when there is cross section dependence even in situations where N is very large. Some proposals for bias correction are suggested and finite sample performance is analyzed in simulations.

Keywords: Autoregression, Bias, Bias correction, Cross section dependence, Dynamic factors, Dynamic panel estimation, Incidental trends, Panel unit root.

JEL Classification Numbers: C33 Panel Data