GINIREG: Stata module for Gini regression

The ginireg package supports the estimation of Gini regressions. The Gini regression has its origin in Corrado Gini's (1912) introduction of the Gini Mean Difference (GMD) as an alternative to the variance. The population GMD is defined as GMD = E{|X_i-X_j|}, i.e., the expected absolute difference between two realizations of an i.i.d. random variable. It can be shown (see Yitzhak-Schechtman 2013, p. 18) that the GMD can be equivalently defined as GMD = 4*cov(X,F(X))}, where F(X) is the population cumulative distribution function (CDF). One intuition for the Gini regression is that it replaces the standard notion of variance with the Gini notion of variance. ginireg is a routine for estimating Gini regressions. It can run standard Gini, mixed OLS/Gini, instrumental variables (IV) Gini and extended Gini regressions. The ability to mix regression methods enables finding the implicit assumptions that affect the sign or magnitude of the estimates. ginilma is a routine for plotting the Gini LMA and NLMA curves. The LMA curve is the Line of independence Minus the Absolute concentration; the NLMA curve is the Normalized LMA curve. The LMA curve enables us to see how the Gini covariance (the numerator of the Gini regression coefficient) is composed.