Components of Gini,Bonferroni,and Zenga Inequality Indexes for EU Income Data

Abstract

In this work we apply a new approach to assess contributions from factor components to income inequality. The new approach is based on the insight that most (synthetic) inequality indexes may be viewed as (weighted) averages of point inequality measures, which measure inequality between population subgroups identified by income. Assessing contributions of factor components to point inequality measures is usually an easy task, and based on these contributions it is straightforward to define contributions to the corresponding (synthetic) overall inequality indexes as well. As we shall show through an analysis of income data from Eurostat’s European Community Household Panel Survey (ECHP), the approach based on point inequality measures gives rise to readily interpretable results, which, we believe, is an advantage over other methods that have been proposed in literature.

Keywords

Inequality decomposition factor components point inequality measures synthetic inequality index

References

Antal, E., M. Langel, and Y. Tillé. 2011. “Variance Estimation of Inequality Indices in Complex Sample Designs.” In Bulletin of the International Statistical Institute Proceedings of the 58th World Statistics Congress, 21st-26th August 2011, Dublin Convention Centre, 1036-1045. Available at: http://2011.isiproceedings.org/papers/450008.pdf (accessed April 2017). ISBN: 978-90-73592-33-9.

Bonferroni, C.E. 1930. Elementi di Statistica Generale. Firenze: Seeber.

DeVergottini, M. 1940. “Sul Signicato di Alcuni Indici di Concentrazione.” Giornale degli Economisti e Annuali di Economia 2: 317-347.

Eurostat. 1996. European Community Household Panel (ECHP): Volume 1 - Survey methodology and implementation. Luxembourg: Office for Official Publications of the European Communities. ISBN: 92-827-8928-4.

Eurostat. 2002. Imputation of Income in the ECHP, PAN 164/2002-12. Eurostat.

Eurostat. 2003a. ECHP UDB Manual: Waves 1 to 8 (Survey Years 1994 to 2001), PAN 168/2003-12. Eurostat.

Eurostat. 2003b. Anonymization Criteria Applied to the Users’ Database, PAN105/2003-05. Eurostat.

Eurostat. 2003c. Construction of Weights in the ECHP, PAN 165/2003-06. Eurostat.

Eurostat. 2003d. Description of Variables: Data Dictionary, Codebook and Differences Between Countries and Waves, PAN 166/2003-12. Eurostat.

10.

Eurostat. 2003e. Construction of Variables: from ECHP Questions to UDB Variables, PAN 167/2003-12. Eurostat.

11.

Gini, C. 1914. “Sulla Misura Della Concentrazione e Della Variabilita` dei Caratteri.” In Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti. Anno Accademico 1913-1914, Tomo LXXIII - Parte Seconda.

12.

Greselin, F., L. Pasquazzi, and R. Zitikis. 2013. “Contrasting the Gini and Zenga Indices of Economic Inequality.” Journal of Applied Statistics 40(2) : 282-297. Doi: https://dx-doi-org.web.bisu.edu.cn/10.1080/02664763.2012.740627.

13.

Greselin, F., L. Pasquazzi, and R. Zitikis. 2014. “Heavy Tailed Capital Incomes: Zenga Index, Statistical Inference, and ECHP Data Analysis.” Extremes 17(1): 127-155. Doi: https://dx-doi-org.web.bisu.edu.cn/10.1007/s10687-013-0177-2.

14.

Greselin, F. and L. Pasquazzi. 2009. “Asymptotic Confidence Intervals for a New Inequality Measure.” Communications in Statistics-Simulation and Computation 38(8): 1742-1756. Doi: https://dx-doi-org.web.bisu.edu.cn/10.1080/03610910903121974.

15.

Greselin, F., L. Pasquazzi, and R. Zitikis. 2010. “Zenga’s New Index of Economic Inequality, its Estimation, and an Analysis of Incomes in Italy.” Journal of Probability and Statistics (special issue on “Actuarial and Financial Risks: Models, Statistical Inference, and Case Studies”) . Article ID 718905, 26 pages. Available at: http://www.emis.de/journals/HOA/JPS/Volume2010/718905.pdf (accessed April 2017).

16.

Greselin, F., M. Puri, and R. Zitikis. 2009. “L-Functions, Processes, and Statistics in Measuring Economic Inequality and Actuarial Risks.” Statistics and Its Interface 2(2): 227-245. Doi: https://dx-doi-org.web.bisu.edu.cn/10.4310/SII.2009.v2.n2.a13.

17.

Langel, M. and Y. Tillé. 2012. “Inference by Linearization for Zenga’s New Inequality Index: A Comparison with the Gini Index.” Metrika 75(8): 1093-1110. Doi: https://dx-doi-org.web.bisu.edu.cn/10.1007/s00184-011-0369-1.

18.

Lerman, R. and S. Yitzhaki. 1984. “A Note on the Calculation and Interpretation of the Gini Index.” Economics Letters 15(3): 363-368. Doi: https://doi.org/10.1016/0165-1765(84)90126-5.

19.

Lerman, R. and S. Yitzhaki. 1985. “Income Inequality Effects by Income Source: A New Approach and Applications to the United States.” Review of Economics and Statistics 67(1): 151-156. Available at: https://www.researchgate.net/profile/Shlomo_Yitzhaki/publication/24094305_Income_Inequality_Effects_by_Income/links/02e7e5274ff3fce713000000.pdf (accessed April 2017).

20.

Lorenz, M.O. 1905. “Methods of Measuring the Concentration of Wealth.” Publications of the American Statistical Association 9(70): 209-219. Doi: https://dx-doi-org.web.bisu.edu.cn/10.2307/2276207.

21.

Polisicchio, M. 2008. “The Continuous Random Variable with Uniform Point Inequality Measure I(p).” Statistica & Applicazioni 6(2): 137-151.

22.

Polisicchio, M. and F. Porro. 2009. “A Comparison Between the Lorenz L(p) Curve and the Zenga I(p) Curve.” Italian Journal of Applied Statistics 21(3-4): 289-301.

23.

Porro, F. 2008. “Equivalence Between the Partial Order Based on L(p) Curve and Partial Order Based on I(p) Curve.” In Atti della XLIV Riunione Scientica: Universita` della Calabria 25-27 giugno 2008. Sessione plenaria, Sessioni specializzate, Sessioni spontanee (cd), edited by CLEUP - Padova. ISBN: 9788861292284.

24.

Porro, F. 2011. “The Distribution Model with Linear Inequality Curve I(p).” Statistica & Applicazioni 9(1): 47-61.

25.

Radaelli, P. 2007. “A Subgroup Decomposition of a New Inequality Index Proposed by Zenga.” In Bulletin of the ISI 56th World Statistics Congress of the International Statistical Institute, 22nd-29th August 2007, Lisboa Congress Centre (CCL), 5151-5154. Available at: http://isi.cbs.nl/iamamember/CD7-Lisboa2007/Bulletin-ofthe-ISI-Volume-LXII-2007.pdf (accessed April 2017), ISBN: 978-972-673-992-0.

26.

Radaelli, P. 2008a. “A Subgroups Decomposition of Zenga’s Uniformity and Inequality Indexes.” Statistica & Applicazioni 6(2): 117-136.

27.

Radaelli, P. 2008b. “Decomposition of Zenga’s Inequality Measure by Subgroups.” In Atti della XLIV Riunione Scientica: Universita` della Calabria 25-27 giugno 2008. Sessione plenaria, Sessioni specializzate, Sessioni spontanee (cd), edited by CLEUP - Padova. isbn: 9788861292284.

28.

Radaelli, P. 2010. “On the Decomposition by Subgroups of the Gini Index and Zenga’s Uniformity Index and Inequality Indexes.” International Statistical Review 78(1): 81-101. Doi: https://dx-doi-org.web.bisu.edu.cn/10.1111/j.1751-5823.2010.00100.x.

29.

Radaelli, P. and M.M. Zenga. 2005. “On the Decomposition of the Gini’s Mean Difference and Concentration Ratio.” Statistica & Applicazioni 3(2): 5-24.

30.

Rao, V. 1969. “Two Decompositions of Concentration Ratio.” Journal of the Royal Statistical Society; Series A 132(3): 418-425. Doi: https://dx-doi-org.web.bisu.edu.cn/10.2307/2344120.

31.

Shorrocks, A.F. 1982. “Inequality Decomposition by Factor Components.” Econometrica 5(1): 193-212. Available at: http://www.ophi.org.uk/wp-content/uploads/ssShorrocks-1982.pdf (accessed April 2017), Doi: https://dx-doi-org.web.bisu.edu.cn/10.2307/1912537.

32.

Shorrocks, A.F. 1983. “The Impact of Income Components on the Distribution of Family Incomes.” The Quarterly Journal of Economics 98(2): 311-326. Doi: https://dx-doi-org.web.bisu.edu.cn/10.2307/1885627.

33.

Zenga, M. 2008. “An Extension of Inequality I and I(p) Curve to Non-Economic Variables.” In Atti della XLIV Riunione Scientica: Universita` della Calabria 25-27 giugno 2008. Sessione plenaria, Sessioni specializzate, Sessioni spontanee (cd), edited by CLEUP - Padova. ISBN: 9788861292284.

34.

Zenga, M.M. 1984. “Proposta per un Indice di Concentrazione Basato sui Rapport fra Quantili di Popolazione e Quantili di Reddito.” Giornale Degli Economisti e Annali di Economia 43(5-6): 301-326.

35.

Zenga, M.M. 2007a. “Inequality Curve and Inequality Index Based on the Ratios Between Lower and Upper Arithmetic Means.” Statistica & Applicazioni 5(1): 3-27.

36.

Zenga, M.M. 2007b. “Applications of a New Inequality curve and Inequality Index Based on Ratios Between Lower and Upper Arithmetic Means.” In Bulletin of the ISI 56th World Statistics Congress of the International Statistical Institute, 22nd-29th August 2007, Lisboa Congress Centre (CCL), 5167-5170. Available at: http://isi.cbs.nl/iamamember/CD7-Lisboa2007/Bulletin-of-the-ISI-Volume-LXII-2007.pdf (accessed April 2017). ISBN: 978-972-673-992-0.

37.

Zenga, M.M. 2013. “Decomposition by Sources of the Gini, Bonferroni and Zenga Inequality Indexes.” Statistica & Applicazioni 11(2): 133-161.

38.

Zenga, M.M., P. Radaelli, and M. Zenga. 2012. “Decomposition of Zenga’s Inequality Index by Sources.” Statistica & Applicazioni 10(1): 3-31.