The expression “robust regression” denotes a set of estimation techniques that are less sensitive than ordinary least squares (OLS) to the effect of possible influential observations. In its various forms, robust regression has a well established tradition in statistics (see, e.g., Maronna et al., 2006). However, apart from median regression and quantile regression in general (Koenker and Bassett, 1978), robust regression was slow to gain popularity in applied econometrics.
Over the past decade, however, a form of robust regression based on Huber’s (1964)MM-estimator was made available in popular software packages and has been increasingly used in leading research publications and in industry. Unfortunately, most practitioners who have used this estimator seem to be unaware of the fact that its properties depend on strong assumptions about the distribution of the errors.
We show that the specific MM-estimator that has become popular in applied econometrics, henceforth termed MbwMbw-estimator, is inconsistent for the parameters of the conditional mean when the errors are skewed and heteroskedastic, and provide simulation evidence on its performance.
A particular robust regression estimator has gained popularity among applied econometricians. We show that this estimator is inconsistent for the parameters of the conditional mean when the errors are skewed and heteroskedastic, and conclude that therefore its use cannot be generally recommended.
Our results show that, in typical econometric problems where the errors can be heteroskedastic and skewed, the MbwMbw-estimates are difficult to interpret and can be very misleading. Therefore, the use of the MbwMbw-estimator in econometrics cannot be generally recommended, and it certainly should not be routinely used as an alternative to OLS.