The Gini Instrumental Variable, or the "double instrumental variable" estimator

This paper puts OLS and Gini regression in a common framework by showing that the coefficients can be interpreted as weighted averages of slopes between adjacent observations, where weights are derived from the Absolute Lorenz Curve of the independent variable. Instrumental Variable (IV) estimators, under both approaches, are also put in a common framework, and viewed as weighted sums of the same slopes, with weights derived from Absolute Concentration Curve of the instrument with respect to the independent variable. This interpretation enables derivation of sufficient conditions for monotonic transformations to change the signs of the instrumental variables' estimators. These conditions inform the user how robust the conclusion with respect to the sign of the estimate really is. It is also shown that Gini-IV is less sensitive to outliers and monotonic transformations than OLS-IV, it has built-in test for examining the validity of IV, and it can be used to test the sensitivity of IV estimator to OLS regression method. The estimation is not based on a specific set of assumptions. However, different assumptions lead to proper choices of weights. In this sense, it follows the spirit of Gini (1957) of analyzing the implication of the use of different weighting schemes.