GTL Regression: A Linear Model with Skewed and Thick-Tailed Disturbances

Wim Vijverberg,Takuya Hasebe

doi:10.2139/ssrn.2578250

Abstract

If the disturbances of a linear regression model are skewed and/or thick-tailed, a maximum likelihood estimator is efficient relative to the customary Ordinary Least Squares (OLS) estimator. In this paper, we specify a highly flexible Generalized Tukey Lambda (GTL) distribution to model skewed and thick-tailed disturbances. The GTL-regression estimator is consistent and asymptotically normal. We demonstrate the potential gains of the GTL estimator over the OLS estimator in a Monte Carlo study and in five applications that are typical of applied economics research problems: log-wage equations, hedonic housing price equations, an analysis of speeding tickets, the issue of trade creation and trade diversion that result from preferential trade agreements, and the familiar CAPM model in financial economics.

Highlights

In estimating models of economic behavior, researchers pay more attention to the specification of the systematic component of the regression model than to the disturbances
The classical linear regression model is the first model novice applied econometricians are exposed to; the concept is often the Gauss-Markov theorem that states that the Ordinary Least Squares (OLS) estimator is the best linear unbiased estimator
OLS is the workhorse approach to linear regression models, to be discarded only if there is a clear violation of its basic assumptions, such as endogenous regressors

Summary

Introduction

In estimating models of economic behavior, researchers pay more attention to the specification of the systematic component of the regression model than to the disturbances. A researcher may resort to classical assumptions about the disturbances (independently and identically distributed with a zero mean and a constant finite variance), or he may choose to describe this aggregate disturbance factor with familiar tools such as heteroskedasticity, serial correlation, and ARCH and GARCH modeling. Such tools address patterns in the behavior among the disturbances. The researcher is implicitly relying on the Central Limit Theorem, assuming that many unobservables play a role and none is dominant, yielding an approximately normally distributed aggregate disturbance.

Results

Discussion

Conclusion