This paper develops robust panel estimation in the form of trimmed mean group estimation for potentially heterogenous panel regression models. It trims outlying individuals of which the sample variances of regressors are either extremely small or large. The limiting distribution of the trimmed estimator can be obtained in a similar way to the standard mean group estimator, provided the random coefficients are conditionally homoskedastic.

The authors consider two trimming methods. The first one is based on the order statistic of the sample variance of each regressor. The second one is based on the Mahalanobis depth of the sample variances of regressors. They apply them to the mean group estimation of the two-way fixed effects model with potentially heterogeneous slope parameters and to the common correlated effects regression, and they derive limiting distribution of each estimator. As an empirical illustration, the authors consider the effect of police on property crime rates using the U.S. state-level panel data.