Two regressions can be
interpreted as based on Gini's Mean Difference (GMD): a semiparametric approach, which relies on
weighted average of slopes defined between adjacent observations and a
minimization approach, which is based on minimization of the GMD of the residuals.
The estimators obtained by the semiparametric approach have representations
that resemble the OLS estimators. In addition they are robust with respect to
extreme observations and monotonic transformations. The estimators obtained by
the minimization approach do not have a closed form. The relationship between
the estimators obtained by the two methods is studied in this paper.
Combination of the methods provides tools for challenging the specification of
the model. In particular it provides tools for assessing the linearity of the
model. It can be applied to each explanatory variable individually and to
several explanatory variables simultaneously without requiring replications.
The semiparametric method and its relationship with the minimization approach
are illustrated using consumption data. It is shown that the linearity of the
Engel curve, and therefore the 'linear expenditures system' is not supported by