Application of SGT Family Distributions in Quasi Maximum Likelihood Estimation

In the classical normal linear regression model, ordinary least squares estimators (OLS) will be consistent and achieve the Cramer-Rao lower bound for any unbiased estimators. This paper examines the impact of several other error distributions on the properties of the OLS estimators. Several different types of example data commonly available to students and researchers in economics are used to illustrate the impact of nonnormality, because, in application, the assumption of normality may not hold in empirical testing. Using maximum likelihood, I demonstrate that flexible probability density functions better model the residual distribution of different types of data, which suggests improvements in estimation accuracy. I find that this suggested increase of fit applies to almost all data types, with the scale of these likelihood improvements contingent upon data characteristics specific to individual data sets. I conclude that consideration of these distributions is essential for truly rigorous analysis and that parsimony applies when differences between estimators are not significant