A Monte Carlo evaluation of the efficiency of the PCSE estimator

Abstract

Panel data characterized by groupwise heteroscedasticity, cross-sectional correlation, and AR(1) serial correlation pose problems for econometric analyses. It is well known that the asymptotically efficient, Feasible Generalized Least Squares (FGLS) estimator (Parks) sometimes performs poorly in finite samples. In a widely cited paper, Beck and Katz (1995) claim that their estimator panel-corrected SE (PCSE) is able to produce more accurate coefficient SE without any loss in efficiency in ‘practical research situations’. This study disputes that claim. We find that the PCSE estimator is usually less efficient than Parks – and substantially so – except when the number of time periods is close to the number of cross sections.

Acknowledgements

An earlier draft of this article was presented at the University of Oklahoma, and the 11th International Conference on Panel Data. We acknowledge helpful comments from Kevin Grier, Cynthia Rogers and Aaron Smallwood.

Notes

¹ For example, in STATA, the “xtgls” options (i) “panels(heteroscedastic)”, (ii) “panels(correlated)” and (iii) “corr(ar1/psar1)” correspond to these three types of nonspherical error variance-covariance behaviors.

² The “xtpcse” procedure in STATA uses a Prais-Winsten transformation in this first stage.

³ As a result, the better performance of the PCSE estimator cannot be attributed to the “shrinkage principle” (Diebold, 2004, p. 45).

⁴ The main difference in the two regression specifications is that version 1 includes cross-sectional fixed effects, while version 2 includes both cross-sectional and time period fixed effects. To give an idea of the difference this makes for the residuals, the R² associated with the first specification usually ran around 0.60 for the US-level data, compared to R² values that were typically over 0.90 using the second specification.

⁵All the programs used for this analysis were written in SAS/IML. The formulae for the Parks and PCSE estimators were constructed to exactly match the output from STATA's “xtgls” and “xtpcse” procedures, using the (i) “panels(correlated)” and “corr(ar1)” and (ii) “correlation(ar1)” options, respectively (we note that the default cross-sectional correlation option for the “xtpcse” option is groupwise heteroscedasticity and time-invariant cross-sectional correlation).

⁶ For example, the simulations underlying the Relative Efficiency results of BK's Table 5 assume no serial correlation.