Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T12:32:22.727Z Has data issue: false hasContentIssue false
  • English
  • Français

Décompositions des mesures d’inégalité : le cas des coefficients de Gini et d’entropie

Published online by Cambridge University Press:  17 August 2016

Stéphane Mussard  and
Michel Terraza
Stéphane Mussard
Affiliation:
LAMETA, Université Montpellier I
Michel Terraza
Affiliation:
LAMETA, Université Montpellier I
Get access

Résumé

Les mesures d'inégalité du revenu rassemblent deux types d'indicateurs décomposables : les indices décomposables en sous-populations et les indices décomposables en sources de revenu. Les premiers permettent de partager l'inégalité totale en une inégalité intragroupe et une inégalité intergroupe et les seconds d'attribuer à chaque facteur de revenu (revenu du travail, revenu du capital, taxes, etc.) une part de l'inégalité totale. Dans cet article, nous examinons d'une part la construction de ces techniques et d'autre part nous relatons les débats auxquels elles ont aboutis et plus particulièrement celui de la convergence vers un emploi simultané des deux types de décomposition.

Summary

Summary

Income inequality measures involve two sub-classes of decomposable measures: those decomposed by sub-groups and those decomposed by income source. The former enables one to compute between- and within-group indices. The latter allows for gauging the inequality related to each factor of income (labour income, capital income, social taxes, etc.). The aim of this article is, on the one hand, to review the construction of the two decomposition techniques and, on the other hand, to point out the underlying debate they lead to, and particularly the convergence towards the use of a simultaneous method based on both decompositions.

Keywords

décompositionsentropieginiDecompositionsEntropyGini

JEL classification

D63: Equity, Justice, Inequality, and Other Normative Criteria and Measurement D31: Personal Income, Wealth, and Their Distributions
Type
Research Article
Information
Recherches Économiques de Louvain/ Louvain Economic Review , Volume 75 , Issue 2 , June 2009 , pp. 151 - 181
Copyright
Copyright © Université catholique de Louvain, Institut de recherches économiques et sociales 2009 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

**

CEPS/INSTEAD Luxembourg, GREDI Université de Sherbrooke, LAMETA Université de Montpellier I. Adresse: LAMETA, UFR Sciences économiques, Université de Montpellier I, Avenue de la Mer, CS 79606, 34960 Montpellier cedex 2, France, E-mail: smussard@adm.usherbrooke.ca.

***

LAMETA, Université Montpellier I, E-mail: mterraza@lameta.univ-montp1.fr

*

Cette recherche est issu d'tn projet dont les premiers résultats furent présentés à l'institut mondial pour la recherche en économie du développement de l'Université des Nations Unies (WIDER 2003). Les auteurs remercient les Professeurs Camilo Dagum, Jacques Silber et Henri Caussinus pour leurs commentaires sur une version antérieure à ce papier. La version finale de se papier s'acheva lorsque Stéphane Mussard finissait ses recherches de post-doctorat au CEPS/INSTEAD Luxembourg. L'auteur remercie le CEPS/INSTEAD, Philippe Van Kerm, et le laboratoire GREDI de l'Université de Sherbrooke dans lequel il est chercheur associé.

References

Références

Auvray, C. et Trannoy, A. (1992). Décomposition par source de l’inégalité des revenus à l’aide de la Valeur Shapley, Journées de Microéconomie Appliquée, Sfax, Tunisie.Google Scholar
Blackorby, C, Bossert, W., et Donaldson, D. (1999). Income Inequality Measurement : The Normative Approach, in : Silber, J. (éds.), Handbook of Income Inequality Measurement, Kluwer Academic Publishers, pp. 133–161.Google Scholar
Bossert, W. et Pfingsten, A.(1990). Intermediate Inequality : Concepts, Indices and Welfare Implication, Mathematical Social Science, vol. 19, pp. 117–134.10.1016/0165-4896(90)90055-CGoogle Scholar
Bourguignon, F. (1979). Decomposable Inequality Measures, Econometrica, vol. 47, pp. 901–920.Google Scholar
Chakravarty, S.R. (1999). Measuring Inequality : The Axiomatic Approach, in Silber, J. (éds.), Handbook of Income Inequality Measurement, Kluwer Academic Publishers, pp. 163–186.Google Scholar
Chameni, C. (2006). A Note on the Decomposition of the Coefficient of Variation Squared: Comparing Entropy and Dagum’s Methods, Economics Bulletin, vol. 4 (8), pp. 1–8.Google Scholar
Chantreuil, F. et Trannoy, A. (1999). Inequality Decomposition Values : The Trade-off Between Marginality and Consistency, Document de travail n°9924, THEMA.Google Scholar
Csiszár, I. (1967). Information Type Measures of Difference of Probability Distributions and Indirect Observations, Studia Scientiarum Mathe-maticarum Hungarica, vol. 2, pp. 299–318.Google Scholar
Cowell, F.A. (1980a). Generalized entropy and the Measurement of Distributional Change, European Economic Review, vol. 13, pp. 147–159.Google Scholar
Cowell, F.A. (1980b). On the Structure of Additive Inequality Measures, Review of Economics Studies, vol. 47, pp. 521–531.10.2307/2297303Google Scholar
Cowell, F.A. (1988). Inequality Decomposition : Three Bad Measures, Bulletin of Economic Research, vol. 40 (4), pp. 309–312.Google Scholar
Cressie, N. et Read, T.R.C. (1984). Multinomial Goodness-of-fit Tests, Journal of the Royal Statistical Society, Séries Β, vol. 46, pp. 440–464.Google Scholar
Dagum, C. (1959). Transvariazione fra più di due distribuzioni, in Gini, C. (éds.), Memorie di metodologia statistica, vol. 2, Libreria Goliardica: Roma.Google Scholar
Dagum, C. (1960). Teoria de la transvariacion, sus aplicaciones a la economia, Metron, vol. 20, pp. 1–206.Google Scholar
Dagum, C. (1961). Transvariacion en la hipótesis de variables aleatorias normales multidimensionales, Proceedings of the International Statistical Institute, vol. 38 (4), pp. 473–486.Google Scholar
Dagum, C. (1987). Measuring the Economic Affluence Between Populations of Income Receivers, Journal of Business and Economic Statistics, vol. 5 (1), pp. 5–12.Google Scholar
Dagum, C. (1997a). A New Approach to the Decomposition of the Gini Income Inequality Ratio, Empirical Economics, vol. 22 (4), pp. 515–531.Google Scholar
Dagum, C. (1997b). Decomposition and Interpretation of Gini and the Generalized Entropy Inequality Measures, Proceedings of the American Statistical Association, Business and Economic Statistics Section, 157th Meeting, pp. 200–205.Google Scholar
Dagum, C. (1998). Fondements de bien-être social et décomposition des mesures d’inégalité dans la répartition du revenu, Economie Appliquée, vol. 51, n°4, pp. 151–202.Google Scholar
Dalton, H. (1920). The Measurement of Inequality of Incomes, Economic Journal, vol. 30, pp. 348–361.Google Scholar
Ebert, U. (1988). On the Decomposition of Inequality : Partitions into Non-overlapping Subgroups, in Eichorn, W. (éds.), Measurement In Economics, New-York: Physica Verlag, pp. 399–412.Google Scholar
Ebert, U. (1999). Dual Decomposable Inequality Measures, Canadian Journal of Economics, vol. 32, n°l, pp. 234–46.Google Scholar
Fei, J.C.H., Ranis, G. et Kuo, S.W.Y. (1978). Growth and the Family Distribution of Income by Factor Components, Quarterly Journal of Economics, vol. 92, pp. 17–53.Google Scholar
Fields, G. (1979). Income Inequality in Urban Columbia : A decomposition Analysis, Review of Income and Wealth, vol. 25, n°3, pp. 327–341.Google Scholar
Gini, C. (1912). Variabilità e mutabilità, Memori di Metodologia Statistica I, Variabilità e Concentrazione, Libreria Eredi Virgilio Veschi: Rome, pp. 211–382.Google Scholar
Gini, C. (1916). II concetto di transvariazione e le sue prime applicazioni, Giornale degli Economisti e Rivista di Statistica, in Gini, C. (éds.) 1959, pp. 21–44.Google Scholar
Isreali, O. (2007). A Shapley-based Decomposition of the R-Square of a Linear Regression, Journal of Economie Inequality, vol. 5 (2), pp. 199–212.10.1007/s10888-006-9036-6Google Scholar
Jenkins, S.P. (1995). Accounting for Inequality Trends : Decomposition Analyses for the UK, 1971–1986, Economica, vol. 62, pp. 29–63.Google Scholar
Kolm, S-C. (1976a). Unequal Inequalities I, Journal of Economic Theory, vol. 12, pp. 416–442.Google Scholar
Kolm, S-C. (1976b). Unequal Inequalities II, Journal of Economic Theory, vol. 13, pp. 82–111.10.1016/0022-0531(76)90068-5Google Scholar
Kolm, S-C. (1999). Rational Foundations of Income Inequality Measurement, in Silber, J. (éds.), Handbook of Income Inequality Measurement, Kluwer Academic Publishers, pp. 19–94.Google Scholar
Lerman, R. et Yitzhaki, S. (1985). Income Inequalities Effects by Income Source : A New Approach and Applications to United States, Review of Economics and Statistics, vol. 67, pp. 151–156.Google Scholar
Lerman, R. et Yitzhaki, S. (1991). Income Stratification and Income Inequality, Review of Income and Wealth, vol. 37, n°3, pp. 313–329.Google Scholar
Mookherjee, D. et Shorrocks, A. (1982). A Decomposition Analysis of the Trend in UK Income Inequality, Economic Journal, vol. 92, pp. 886–902.Google Scholar
Mussard, S. (2004a). Décompositions multidimensionnelles du rapport moyen de Gini. Applications aux revenus italiens de 1989 et 2000, Thèse, Université de Montpellier I. Google Scholar
Mussard, S. (2004b). The bidimensional Decomposition of the Gini Ratio. A Case Study: Italy, Applied Economies Letters, vol. 11, pp. 503–505.Google Scholar
Mussard, S. (2006). Une nouvelle décomposition de la mesure de Gini en sources de revenu, et la décomposition en sous-populations : une réconciliation, Annales d–Economie et de Statistique, vol. 81, pp. 1–25.Google Scholar
Mussard, S. et Peypoch, N. (2006). On Multi-decomposition of the Aggregate Malmquist Productivity Index, Economics Letters, vol. 91, pp. 436–443.Google Scholar
Pyatt, G. (1976). On the Interpretation and Disaggregation of Gini Coefficients, Economic Journal, vol. 86, pp. 243–25.Google Scholar
Pyatt, G., Chen, C.-N. et Fei, J. (1980). The Distribution of Income by Factor Component, Quarterly Journal of Economics, vol. 95, n°3, pp. 451–473.Google Scholar
Rao, V.M. (1969). Two Decompositions of Concentration Ratio, Journal of the Royal Statistical Society, Série A 132, pp. 418–425.Google Scholar
Sastre, M. et Trannoy, A. (2002). Shapley Inequality Decomposition by Factor Components: Some Methodological Issues, in Moyes, P.Seidl, C. et Shorrocks, A.F. (éds.), Journal of Economics, vol. 9, supplément, pp. 51–90.Google Scholar
Sen, A.K. (1973). On Economic Inequality, Clarendon Press: Oxford.Google Scholar
Shapley, L. (1953). A Value for η-Person Games, in Kuhn, H.W. et Tucker, A.W. (éds.), Contributions to the Theory of Games, vol. 2, Princeton University Press.Google Scholar
Shorrocks, A.F. (1980). The Class of Additively Decomposable Inequality Measures, Econometrica, vol. 48, pp. 613–625.Google Scholar
Shorrocks, A.F. (1982). Inequality Decomposition by Factor Component, Econometrica, vol. 50, pp. 193–211.Google Scholar
Shorrocks, A.F. (1984). Inequality Decomposition by Factor Components and by Population Subgroups, Econometrica, vol. 53, pp. 1369–1386.10.2307/1913511Google Scholar
Shorrocks, A.F. (1988). Aggregation Issues in Inequality Measurement, in Heichhorn, W. (éds.), Measurement in Economics, New York : Physica-Verlag, pp. 429–452.Google Scholar
Shorrocks, A.F. (1999). Decomposition Procedures for Distributional Analysis: A Unified Framework Based on the Shapley Value, Mimeo, Université d’Essex.Google Scholar
Silber, J. (1989). Factor Components, Population Subgroups and the Computation of the Gini Index of Inequality, Review of Economics and Statistics, vol. 71, pp. 107–115.Google Scholar
Theil, H. (1967). Economics and Information Theory, North-Holland Publishing Company: Amsterdam.Google Scholar
Tsui, K. (1999). Multidimensional Inequality and Multidimensional Generalized Entropy Measures : An axiomatic Derivation, Social Choice and Welfare, vol. 16, pp. 145–157. Google Scholar