Applications of Gini Methodology in Regression Analysis

Abstract

Ordinary least squares (OLS) regression is based on the fact that the variance of a linear combination of random variables can be decomposed into the contributions of the individual variables and to the contributions of the correlations among them. The fact that one can imitate this decomposition (under certain conditions) when decomposing the GMD of a linear combination of random variables enables one to take any OLS-based econometric textbook and replicate each chapter using the GMD instead of the variance. Practically, this means doubling the number of models because every OLS econometric model can be replicated by the GMD, resulting in different estimates of the parameters. Moreover, we present via examples (Chap. 21) that the estimates can differ in sign. This means that two investigators who use the same variables, the same model, and the same data may come up with contradicting results concerning the effect of one variable on the other. The only difference between the two researchers lies in the measure of variability they use—the GMD or the variance. Needless to say that in many cases of policy decisions the debate is on the magnitude of a parameter, which is much more vulnerable than the sign and not on the sign itself. And to make life even more complicated any regression model that is estimated by the GMD can be replicated with the EG. This means moving from doubling the number of possible estimates to an infinite number of estimates.KeywordsExplanatory VariableRegression CoefficientHorizontal AxisOrdinary Little SquareQuantile RegressionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.