Gini's Multiple Regressions Gini's Multiple Regressions

Two regression methods can be interpreted as based on Gini's mean difference (GMD). One relies on a weighted average of slopes defined between adjacent observations and the other is based on minimization of the GMD of the errors. The properties of the former approach are investigated 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. The asymptotic behavior of the estimators is derived. The combination of the 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. The 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.