GTL regression: a linear model with skewed and thick-tailed disturbances

Abstract

A maximum likelihood estimator of a linear regression model is efficient relative to the customary Ordinary Least Squares (OLS) estimator when disturbances are skewed and/or thick-tailed. In order to model skewed and thick-tailed disturbances, we specify a highly flexible Generalized Tukey Lambda (GTL) distribution that can closely mimic many other unimodal distributions. The GTL-based maximum likelihood regression estimator is consistent and asymptotically normal. A Monte Carlo study demonstrates the potential gains of this GTL-based estimator over the OLS estimator, and as a real-life application, an analysis of speeding tickets illustrates how GTL regression might modify standard OLS estimation results. For the applied data analyst, an LM test statistic is suggested as a straightforward post-estimation diagnostic of whether the standard OLS regression approach is suitable for the data at hand. Stata do-files are provided to perform the OLS post-estimation LM test and to implement GTL regression models.