"On the Econometric Modeling of Non-Linear Relationships: the Gumbel Regression Model "

Abstract

Nonlinear relashionships among random variables often come out in all fields of economics. The academic debate on how to deal with nonlinearities, from a statistical point of view, has been centered in developing new estimation methods or modifying the specification of the classic linear econometric models. Here, we propose to face this issue by deriving population regression models from conditional distributions with genuine nonlinear conditional means. Such a mathematical procedure guarantees not only a consistent derivation of the conditional mean that gives rise to a nonlinear econometric model, but also a proper analysis of the casual effects among the involved economic variables (i.e., partial effects).Finally, we exemplify the workings of this approach by specifying a nonlinear and heteroskedastic econometric model based on the Gumbel distribution.