Comparative analysis of inequality indicators: characteristics and applications

The article reveals the diversity of inequality indicators used by international research organizations and by statistical services of different countries, evaluating their advantages and disadvantages. New methodological developments in this area are also shown. The author describes a number of relatively new indicators that may be useful for measuring dynamics and structure of inequality.

Based on a comparative analysis of inequality indicators, their mathematical properties and applications, a number of recommendations for expanding the list of the indicators traditionally used to assess inequality in Russia are offered.

Keywords

inequality, Gini coefficient, decile ratio, income quintile ratio, Lorenz curve, Palma ratio, generalised entropy indicators, Theil index, mean logarithmic deviation, Atkinson index, Pietra ratio, Robin Hood index, Hoover index, Schutz indeх, McLoone index, Zenga index

Received

12.07.2019

Publication date

12.07.2019

Number of characters

42365

Cite

GOST
MLA	Salmina, А. "Comparative analysis of inequality indicators: characteristics and applications." Obshchestvo i ekonomika 7 (2019):35-58. DOI: 10.31857/S020736760005832-4
APA	Salmina А. (2019). Comparative analysis of inequality indicators: characteristics and applications. Obshchestvo i ekonomika (7), pp.35-58 DOI: 10.31857/S020736760005832-4

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1. Anand, S. and Segal, P. «The Global Distribution of Income», in (eds.) Anthony B. Atkinson and François Bourguignon // Handbook of Income Distribution, Volume 2A. Amsterdam: North-Holland. 2015. P. 937–979.

2. Arcagni A., Francesco P. On the parameters of Zenga distribution // Statistical Methods and Applications. 2013. Vol. 22. P. 285-303.

3. Arcagni A., Zenga M. Application of Zenga’s distribution to a panel survey on household incomes of European Member States // Statistica and Applicazioni. 2013. Vol. 11. P. 79-102.

4. Atkinson A. B. On the Measurement of Inequality // Journal of Economic Theory. Vol. 2. 1970. P. 244-263.

5. Bellu L.G., Liberati P. Policy Impacts on Inequality: Welfare Based Measures of Inequality – the Atkison Index // Food and Agriculture Organization of the United Nations. 2006.

6. Berti P., Rigo P. Concentration Curve and Index, Zenga's // Wiley StatsRef: Statistics Reference Online. 2014. URL: https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781118445112.stat03450 (дата обращения 01.05.2019).

7. Burkholder P. University of Texas Inequality Project. 2003. URL: http://utip.gov.utexas.edu/tutorials/intro_ineq_studies.ppt (дата обращения 01.05.2019).

8. Cobham A., Schlogl L., Sumner A. Inequality and the Tails: The Palma Proposition and Ratio Revisited // UN DESA Working Paper 143. New York: UN DESA, 2015.

9. Cowell F. Measuring inequality /Oxford University Press, Handbook of Economic Inequality // Oxford: Oxford University Press, 2009.

10. Dalton H. The measurement of the inequality of incomes // The Economic Journal. 1920. Vol. 30. P. 348-361.

11. De Maio F. Income inequality measures. // J Epidemiol Community Health. 2007. Vol. 61 (10). P. 849–852.

12. Farris F. The Gini Index and Measures of Inequality // The American Mathematical Monthly. 2010. Vol. 117, No. 10. P. 851-864.

13. Gastwirth J. Is the Gini Index of Inequality Overly Sensitive to Changes in the Middle of the Income Distribution? // Statistics and Public Policy. 2017. 4:1. P. 1-11.

14. Greselin F., Pasquazzi L., Zitikis R. Contrasting the Gini and Zenga indices of economic inequality // Journal of Applied Statistics. 2013. Vol. 40 (2). P. 282-297.

15. Greselin F., Pasquazzi L., Zitikis R. Heavy tailed capital incomes: Zenga index, statistical inference, and ECHP data analysis // Extremes. March 2014. Vol. 17, Issue 1. P. 127-155.

16. Greselin F., Pasquazzi L., Zitikis R. Zenga's New Index of Economic Inequality, Its Estimation, and an Analysis of Incomes in Italy // Journal of Probability and Statistics. Volume 2010. URL: https://www.hindawi.com/journals/jps/2010/718905/ (дата обращения 01.05.2019).

17. Greselin F., Pellegrino S., Vernizzi A. Gini versus Zenga Inequality Index: A New Approach to Measuring Tax Redistribution and Progressivity // Conference Paper. Societ`a Italiana di Economia Pubblica – SIEP, XXIX Riunione Scientifica, Universit`a degli Studi di Catania. – 21-22 September, 2017.

18. Greselin F., Zitikis R. From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective. // Econometrics. 2018. 6 (1), 4. P. 1-20.

19. Habib E. On the decomposition of the Schutz coefficient: an exact approach with an application. // Electronic Journal of Applied Statistical Analysis EJASA. 2012. Vol. 5, Issue 2. P. 187-198.

20. Hale T. The Theoretical Basics of Popular Inequality Measures // University of Texas Inequality Project. 2014. P.2. URL: https://utip.lbj.utexas.edu/tutorials.html (дата обращения 01.05.2019).

21. Haughton J., Khandker Sh. Handbook on poverty and inequality // The International Bank for Reconstruction and Development. – The World Bank. Washington, DC, 2009.

22. Hicks D. The inequality adjusted Human Development Index: a constructive proposal // World Development. 1997. Vol. 25. P. 1283-1298.

23. Ibragimov M., Ibragimov R. Heavy tails and upper-tail inequality: The case of Russia // Empirical Economics. March 2018. Vol. 54, Issue 2. P. 823–837.

24. Ibragimov M., Ibragimov R., Karimov J., Yuldasheva G. Robust Analysis of Income Inequality Dynamics in Russia: t-Statistic Based Approaches. // The wiiw Balkan Observatory. Working Paper. 2012. Vol. 105. P. 1-37.

25. Kelly A. Measuring equity in educational effectiveness research: the properties and possibilities of quantitative indicators // International Journal of Research & Method in Education. 2015. Vol. 38, № 2. P. 115-136.

26. Klasen S., Scholl N., Lahoti R., Ochmann S., Vollmer S. Inequality – worldwide trends and current debates // Courant Research Centre: Poverty, Equity and Growth – Discussion Papers, No. 209. Göttingen, 2016.

27. Langel M., Tillé Y. Inference by linearization for Zenga’s new inequality index: A comparison with the Gini index // Metrika. 2012. Vol. 75(8). P. 1093–1110.

28. Milanovic B. A simple way to calculate the Gini coefficient, and some implications // Economics Letters. 1997. 56. P. 45-49.

29. Milanovic B. Global Income Inequality in Numbers: in History and Now // Global Policy. 2013. 4 (2) P. 198-208.

30. Mussini M., Zenga M. A longitudinal decomposition of Zenga’s new inequality index // Statistica and Applicazioni. 2013. Vol. 11. P. 63-77.

31. Novokmet F., Piketty T., Zucman G. From Soviets to oligarchs: inequality and property in Russia, 1905-2016 // The Journal of Economic Inequality, Springer,Society for the Study of Economic Inequality. 2018. Vol. 16 (2). P. 189-223. URL: http://piketty.pse.ens.fr/files/NPZ2017WIDworld.pdf#page=34&zoom=100,0,177 (дата обращения 02.05.2019 г.).

32. Ostasiewicz K., Mazurek E. Comparison of the Gini and Zenga indexes using some theoretical income distributions abstract // Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management. 2013. Vol. 1. P. 37-62.

33. Palma G. Has the Income Share of the Middle and Upper-middle been Stable over Time, or Is Its Current Homogeneity across the World the Outcome of a Process of Convergence? The «Palma Ratio» Revisited / Cambridge Working Papers in Economics 1437 // Cambridge: University of Cambridge, 2014.

34. Palma G. Homogeneous middles vs. heterogeneous tails, and the end of the ‘Inverted-U’: it’s all about the share of the rich // Development and Change. January 2011. Vol. 42, No. 1. P. 87-153.

35. Pasquazzi L., Zenga M. Components of Gini, Bonferroni, and Zenga Inequality Indexes for EU Income Data // Journal of Official Statistics. 2018. Vol. 34, № 1. P. 149-180.

36. Polisicchio M., Porro F. A comparison between Lorenz L(p) curve and Zenga I(p) curve // Statistica Applicata. 2009. Vol. 21 (3-4). P. 289-301.

37. Popova D., Rudberg A. Inequality in Income and Wealth in Russia / Global Encyclopedia of Public Administration, Public Policy, and Governance. – Switzerland: Springer, 2018. P. 1-12.

38. Punt С. et al. Measure of Poverty and Inequality: A Reference Paper. // PROVIDE Project Technical Paper. Elsenburg, October 2003. No 4.

39. Pyatt G., Chen C.-N., Fei J. The Distribution of Income by Factor Components // Quarterly Journal of Economics. 1980. November. P. 451-473.

40. Radaelli P. A subgroups decomposition of Zenga’s uniformity and inequality indexes // Statistica and Applicazioni. 2008. Vol. 6 (2). P. 117-136.

41. Radaelli P. On the decomposition by subgroups of the Gini index and Zenga’s uniformity and inequality indexes // International Statistical Review. 2010. Vol. 78. P. 81-101.

42. Sen A. On Income Inequality // Oxford: Clarendon Press, 1997.

43. Stuart A., Ord K. Kendall’s Advanced Theory of Statistics. Volume 1: Distribution Theory, 6th Edition // Holder Arnold, London, 1994.

44. UN. Inequality Measurement // Development Issues № 2. – October 2015. P. 2. URL: https://www.un.org/en/development/desa/policy/wess/ wess_dev_issues/dsp_policy_02.pdf (дата обращения 01.05.2019).

45. UNDP. Human Development Report 2016: Human Development for Everyone // United Nations Development Programme. New York, 2016.

46. Van Zanden J.L., Baten J., Foldvari, P., Van Leeuwen, B. The Changing Shape of Global Inequality 1820-2000: Exploring a new dataset // Review of Income and Wealth. 2014. Vol. 60, Issue 2. P. 279-297.

47. Zenga M. Decomposition by sources of the Gini, Bonferroni and Zenga inequality indexes // Statistica & Applicazioni. 2013. Vol. 11 (2). P. 133-161.

48. Zenga M. Decomposition of Zenga’s Inequality Index by Sources // Statistica & Applicazioni. 2012. Vol. 10. P. 3-31.

49. Zenga M. Inequality curve and inequality index based on the ratios between lower and upper arithmetic means // Statistica & Applicazioni. 2007 Vol. 5. P. 3-27.

50. Zenga M., Pasquazzi L., Polisicchio M., Zenga Ma. More on M. M. Zenga’s new three-parameter distribution for non-negative variables // Statistica and Applicazioni. 2011. Vol. 9. P. 5-33.

51. Zenga M., Pasquazzi L., Zenga Ma. First applications of a new three-parameter distribution for non-negative variables // Statistica and Applicazioni. 2012. Vol. 10. P. 131-147.

52. Авраамова Е.М., Малева Т.М. О причинах воспроизводства социально-экономического неравенства: что показывает ресурсный подход? // Вопросы экономики. 2014. № 7. С. 144-160.

53. Аганбегян А.Г. Преодоление бедности и сокращение неравенства по доходам и потреблению в России // ЭКО. 2017. №9. С. 66–86.

54. Аникин В.А., Тихонова Н.Е. Бедность и неравенство в странах БРИКС: российская специфика // Общество и экономика. 2016. № 1. С. 78-115.

55. Бурдяк А.Я. Обеспеченность жильем в постсоветской России: неравенство и проблема поколений // Журнал исследований социальной политики. 2015. Т. 13, № 2. С. 273–288.

56. Григорьев Л.М. Социальное неравенство в мире – интерпретация неочевидных тенденций // Журнал Новой экономической ассоциации. 2016. №3. С. 160-169.

57. Григорьев Л.М., Павлюшина В.А. Межстрановое неравенство: динамика и проблема стадий развития // Вопросы экономики. 2018. № 7. С. 5-29.

58. Григорьев Л.М., Салмина А.А. «Структура» социального неравенства современного мира: проблемы измерения // Социологический журнал. 2013. № 3. С. 5-21.

59. Джомо К.С., Попов В.В. Долгосрочные тенденции в распределении доходов // Журнал Новой экономической ассоциации. 2016. №3. С. 146-160.

60. Зубаревич Н.В. Неравенство доходов населения: пространственная проекция // Pro et Contra. 2013. Т. 17, № 6. С. 48-60.

61. Капелюшников Р.И. Неравенство: как не примитивизировать проблему // Вопросы экономики. 2017. № 4. С. 117-139.

62. Овчарова Л.Н. и др. Динамика монетарных и немонетарных характеристик уровня жизни российских домохозяйств за годы постсоветского развития: аналитический доклад / рук. авт. колл. Л.Н. Овчарова, А.Я. Бурдяк, А.И. Пишняк, Д.О. Попова, Р.И. Попова, А.М. Рудберг // М.: Фонд «Либеральная Миссия», 2014.

63. Овчарова Л.Н., Попова Д.О., Рудберг А.М. Декомпозиция факторов неравенства доходов в современной России // Журнал новой экономической ассоциации. 2016. № 3 (31). С. 170-186. URL: http://journal.econorus.org/pdf/NEA-31.pdf (дата обращения 30.04.2019).

64. Салмина А.А. Избыточное неравенство и развитие человеческого потенциала // Доклад о человеческом развитии в Российской Федерации за 2014 год / Науч. ред.: Л.М. Григорьев, С.Н. Бобылев // М.: Аналитический центр при Правительстве Российской Федерации, 2014. Гл. 5. С. 85-105.

65. Стукаленко Е.А. Межрегиональная дифференциация доходов населения в России // Экономическое развитие стран евразийской интеграции: монография / под ред. Г.П. Литвинцевой // Новосибирск: Изд-во НГТУ, 2017. С. 102-11