Some Monte Carlo Evidence on the Relative Efficiency of Parametric and Semiparametric EGLS Estimators.

One of the most common practical problems in statistics and econometrics is the estimation of linear regression models with heteroscedastic errors. This article reports the results of a Monte Carlo comparison of various parametric and semiparametric estimated generalized least squares (EGLS) estimators. In small-sized (20) and sometimes medium-sized (50) samples, ordinary least squares dominated the other techniques for low levels of heteroscedasticity. In medium-sized samples, correctly specified EGLS dominated with moderate and large levels of heteroscedasticity. Apart from correctly specified EGLS, a semiparametric approach generally dominated in the medium-sized samples with moderate and large amounts of heteroscedasticity. An additional result is that an incorrectly specified EGLS estimator could, in small samples, yield more precise estimates than the other EGLS techniques. For each of the feasible parametric and semiparametric techniques considered, the usual standard errors and heteroscedasticity-consistent standard errors understated the sample variability of the estimators.