Gini's Multiple Regressions

Abstract

Two regression methods can be interpreted as based on Gini's Mean Difference (GMD). One, the semi-parametric approach, relies on a weighted average of slopes defined between adjacent observations and the other, the minimization approach, is based on minimization of the GMD of the errors. The properties of the former approach are reviewed in a multiple regression framework. These estimators have representations that resemble the OLS estimators, and they are robust, both with respect to extreme observations and with respect to monotonic transformations. Moreover, the use of Absolute Concentration Curves enables the user to graphically investigate the monotonicity of the regression curve. The combination of the above two methods provides a tool for assessing linearity that can be applied to each independent variable individually as well as to several independent variables simultaneously without requiring replications . The semi-parametric method is illustrated using consumption data from Israel. It is shown that the linearity of the Engel curve, and therefore the 'linear expenditures system' is rejected.

Keywords: Gini's Mean Difference, Average Derivative, Linearity, Monotonicity

JEL Classification: C20, C80