The Relationship between Gini's Mean Difference and the Absolute Deviation from a Quantile

9 Pages Posted: 30 Apr 2012

See all articles by Shlomo Yitzhaki

Shlomo Yitzhaki

Hebrew University of Jerusalem - Department of Economics; National Bureau of Economic Research (NBER)

Peter J. Lambert

University of Oregon - Department of Economics; CESifo (Center for Economic Studies and Ifo Institute)

Date Written: April 24, 2012

Abstract

The aim of this note is to investigate the relationship between Gini's Mean Difference (GMD), the mean absolute deviation (MAD), the least absolute deviation (LAD), and the absolute deviation from a given quantile (QUAD). The latter measures can all be interpreted as equivalents either to the GMD of a transformed distribution, or alternatively, to a between-group GMD (BGMD) measure, according to the particular partition of the data. As such they all possess properties of the GMD but each omits the intra-group variability – and, of course, they give rise to different regression techniques. It is argued that the loss of the intra-group information is too heavy a price to pay, and that the analyst using one of these techniques should justify the omission of the intra-group variability from the analysis.

Keywords: GMD, LAD, MAD, QUAD

JEL Classification: C2, C10, C58

Suggested Citation

Yitzhaki, Shlomo and Lambert, Peter J., The Relationship between Gini's Mean Difference and the Absolute Deviation from a Quantile (April 24, 2012). Available at SSRN: https://ssrn.com/abstract=2048397 or http://dx.doi.org/10.2139/ssrn.2048397

Shlomo Yitzhaki (Contact Author)

Hebrew University of Jerusalem - Department of Economics ( email )

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Jerusalem, 91905
Israel
+972 2 659 2201 (Phone)
+972 2 652 2319 (Fax)

National Bureau of Economic Research (NBER) ( email )

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Peter J. Lambert

University of Oregon - Department of Economics ( email )

Eugene, OR 97403
United States

CESifo (Center for Economic Studies and Ifo Institute)

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Munich, DE-81679
Germany

HOME PAGE: http://www.CESifo.de

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