PROGRAM FOR DAGUM’S GINI INDEX DECOMPOSITION

 

  Camilo Dagum1, Stéphane Mussard2, Françoise Seyte2, Michel Terraza2

with SOCREES’ participation

 

1UNIVERSITY of OTTAWA

2 LAMETA, UNIVERSITY of MONTPELLIER I

 


BIOGRAPHY


 

Camilo Dagum, Emeritus Professor of the University of Ottawa and Doctor Honoris Causa of the University of Montpellier I, introduced in 1997 the decomposition of the Gini index by population subgroups. This method allows you to compute overall income inequality and to break it down into within-group and between-group income inequality.

Michel Terraza is a science Professor of economics at University of Montpellier I. He applied this decomposed measure when studying the wages inequalities in the Languedoc-Roussillon region (see the bibliography). He did it in collaboration with Françoise Seyte (Associate Professor) and Stéphane Mussard (Assistant Professor).

The SOCREES© corporation, company of statistics and economic studies, made the Gini decomposition software (first version).

 

 


 

THE SOFTWARES

 


 

The softwares you can download are Excel macro. To try it, you only need income or wage panel data. You can get some here below. The programs include the decomposition of the Gini index and either the measures derived from the general entropy inequality measures such as Theil, Hirschman-Herfindahl and Bourguignon that are additively decomposable or the weakly decomposable measures such as the coefficient of variation squared and the α-Gini. Indeed, the latter can be decomposed according to the same method as the Gini index. All the information connected with the programs running is easy and available on sheet 1 of the Excel files "The softwares" and in the paragraph "THE USE" here below.

The data, at your disposal (strictly positive reals), consist of three columns. The first one concerns the codes of the individuals that give a number to each person (from 1 to n.) The modality 1 in the second column represents the USA and the modality 2 Japan. The third column deals with the growth rate of the American and Japanese real wages between 1960 and 1996. This first example is done in order to get used to the tool. 

 

 


DOWNLOAD / THE USE


 

I. Arranging the Data

Put your data in a new Excel sheet and select them as in the following table:

Individuals’ Codes

Groups

Incomes

1

1

100

2

1

90

3

1

250

102

5

50

103

5

20

 

Column 1 represents the individuals codes that give an index to each person (for instance from 1 to 103 for a sample of 103 individuals).

Column 2 deals with the different groups of the population. The individuals belonging to the same subpopulation must be put together. In the table example there are 5 groups.

Column 3 represents the wages of the individuals belonging to the groups of column 2.

 

II. Code 1: Dagum’s Gini Decomposition and the Additive Decompositions of three Generalized Entropy Inequality Indices 

To obtain the results:

1) Download the software then open the file "Dagum" in Excel ("yes" to activate the macro);

2) Download the data, open the file "donnees" in Excel, type "Alt+F8" select "Dagum.xls!CalculDagum" then "execute" and put the number of groups "2" then "OK".

3) You should obtain the following results: Download the results. Follow the theoretical decomposition to make relevant interpretations.

 

III. Code 2: the (α,β)-Decomposition

This program is a generalization of the previous one. This new version focuses only on the pair-based inequality measures that are weakly decomposable in Ebert’s (2010) sense. The (α,β)-decomposition is an adaptation of Dagum’s (1997a, 1997b) decomposition to all the weakly decomposable measures and permits to include a parameter of inequality aversion denoted by α as well as a parameter of sensibility towards transvariation β into the calculation of the various components. A first attempt of generalization had been proposed by Chameni (2011) and had been programmed by Fattouma Souissi and Pauline Mornet of the University of Montpellier 1 (LAMETA PhD students).

This new program is inspired from theoretical researches: Chameni (2006, 2011), Mussard and Terraza (2009) and Ebert (2010). Besides allowing to capture inequality aversion, the (α,β)-decomposition permits to decompose the Gini index (obtained when α=1, forall β≥1), as well as the coefficient of variation squared (when α=2, forall β≥1). So, this generalization brings out a link between the Gini index and an entropic measure [see Chameni, 2006, 2011].

Following Ebert (2010), the main axioms PC [resp. PD], PP, NM, SM are respected as far as α>0 [resp. α≥1]. Furthermore for any α≥2 the principle of strong diminishing transfers is also satisfied by such inequality measures [see Mornet, P. Zoli, C.  Mussard, S. Sadefo-Kamdem J., Seyte, F. and M. Terraza, 2013].

To apply the decomposition:

1) Download the software then open the file "(alpha, beta)-decomposition (en)" in Excel ("yes" to activate the macro);

 

 

2) Download the data, open the file "data" in Excel and copy the information in “sheet2”. Type "Alt+F8" and select:  “The_2_parameters_weak_decomposition" then "Execute".

 

Put the number of groups,

 

and your sensitivity parameters (any positive real values),

 then "OK".

3) You should obtain the following results: Download the results. Follow the theoretical papers  to make relevant interpretations.

 

References:

a)   Ebert, U. (2010), “The Decomposition of Inequality Reconsidered: Weakly Decomposable Measures”, Mathematical Social Sciences 6 (2), 94-103.

 

b)   Chameni Nembua C. (2011), “A generalisation of the Gini coefficient: Measuring economic inequality”, Mimeo.

 

c)   Mussard, S. et Terraza M. (2009), “ La décomposition du coefficient de Gini et des mesures dérivées de l'entropie : les enseignements d'une comparaison, Recherches Economiques de Louvain 75 (2), 151-181.

 

d) Chameni Nembua C. (2006),”Linking Gini to Entropy: Measuring Inequality by an interpersonal class of indices”, Economics Bulletin 4 (5), 1-9.

 

 


 

OTHER  RELATED  SOURCES


 

* You can obtain the same results more quickly than an Excel macro using a Gauss program that can contain more than 64,000 observations:

By Michele Costa, University of Bologna: Gini.g 

 

* With SAS : used in Koubi, M. Mussard, S., F. Seyte et M. Terraza (2005):

By Malik Koubi, INSEE: Gini-SAS

 

* If your incomes are composed of several income sources (wages + income taxes + transfers + etc.), you may try the GAUSS Gini multi-decomposition (a non generalized program), used in Mussard (2006):

By Stéphane Mussard: g-revenu.g

 

* If your incomes are composed of several income sources (wages + income taxes + transfers + etc.) and several partitions of groups, use the GAUSS Gini multi-decomposition in multi-levels, used in Mussard S., Pi-Alprein M.-N., Seyte F. and Terraza M. (2006):

By Stéphane Mussard: g-revenu-2.g

 

 


Contacts

mornet@lameta.univ-montp1.fr


 

 

 


 

LICENCE

 

THESE PRODUCTS ARE PROVIDED FOR FREE ON AN 'AS IS' BASIS, WITHOUT ANY WARRANTIES OR CONDITIONS. NEITHER STEPHANE MUSSARD, FRANCOISE SEYTE, MICHEL TERRAZA, PAULINE MORNET AND SOCREES, NOR THE LAMETA AND THE UNIVERSTY OF MONTPELLIER 1 SHALL HAVE ANY LIABILITY FOR ANY INDIRECT, INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES WHATSOEVER, INCLUDING, BUT NOT LIMITED TO, LOSS OF REVENUE OR PROFIT, LOST OR DAMAGED DATA OR OTHER COMMERCIAL OR ECONOMIC LOSS.