A Generalized Regression Specification Using the Skewed Generalized T Distribution

• Activity Number: 419
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Carter Davis* and Daniel Walton and James McDonald
• Companies: Brigham Young University and Brigham Young University and Brigham Young University
• Keywords: skewed generalized t ; parametric regression ; flexible distributions ; maximum likelihood ; skewness ; heteroskedasticity

Abstract

The standard linear regression model typically assumes that the errors are independently and identically distributed. The corresponding ordinary least squares (OLS) estimators will yield the best linear approximation of the conditional mean. If the errors are also normally distributed, then OLS will also be maximum likelihood estimators and will achieve the minimum variance of all unbiased estimators. In this paper, we relax the homoskedasticity assumption and consider an estimation framework, using the skewed generalize t (SGT) distribution, which can accommodate situations in which the conditional mean, variance and skewness of a variable of interest may vary as a function of independent variables. We explore the properties of these models and use maximum likelihood estimators (MLE) to estimate the parameters. Monte Carlo simulations are used to investigate the properties of the estimators. We also apply these methods to estimate Mincer wage equations and asset pricing models to explore the possibility of the distributional characteristics being functions of the independent variables.