The Gini Instrumental Variable, or 'the Double IV Estimator'

This paper shows that both OLS and Gini regression estimators can be interpreted as weighted averages of slopes of the regression curve, where the weights are derived from the Absolute Lorenz Curve of the independent variable. The instrumental variable estimators, under both approaches, can also be viewed as weighted sums of the same slopes, with the weights being derived from the Absolute Concentration Curve of the instrument with respect to the independent variable. This interpretation enables the derivation of sufficient conditions for monotonic transformations to change the sign of the instrumental variables' estimators. These conditions should be reported because they inform the reader how robust is the conclusion with respect to the sign of the estimate. It is also shown the Gini IV is less sensitive to outliers and to monotonic transformations than the OLS, it has a built-in test for examining the validity of the IV, and that it can be used to test the sensitivity of an IV estimator to the OLS regression method