Estimating the Model with Fixed and Random Effects by a Robust Method

Abstract

Regression model with fixed and random effects estimated by modified versions of the Ordinary Least Squares (OLS) is a standard tool of panel data analysis. However, it is vulnerable to the bad effects of influential observations (contamination and/or atypical observations). The paper offers robustified versions of the classical methods for this framework. The robustification is carried out by the same idea which was employed when robustifying OLS, it is the idea of weighting down the large order statistics of squared residuals. In contrast to the approach based on the M-estimators this approach does not need the studentization of residuals to reach the scale- and regression-equivariance of estimator in question. Moreover, such approach is not vulnerable with respect the inliers. The numerical study reveals the reliability of the respective algorithm. The results of this study were collected in a file which is possible to find on web, address is given below. Patterns of these results were included also into the paper. The possibility to reach nearly the full efficiency of estimation - due to the iteratively tailored weight function - in the case when there are no influential points is also demonstrated.