Two Classical Decompositions of the Gini Index by Income Source
Interpretation of the Contribution Terms
Keywords:
decomposition, income inequality, income source, Gini indexAbstract
The natural Gini decomposition (Rao 1969) and marginal Gini decomposition (Lerman and Yitzhaki 1985) are the most common methods for revealing the contributions of various income sources to total income inequality. Nevertheless, the former method has often been criticised, with two major objections: 1) its contribution terms lack a meaningful interpretation and 2) it yields a contribution of zero for a uniformly distributed income source. Regarding Objection 1, this article shows that the contribution of an income source expresses an inequality reduction due to the marginal replacement of this source by a uniformly distributed counterfactual income. Concerning Objection 2, the article shows that the natural Gini decomposition corresponds to the absolute inequality view, according to which equal additions of income leave inequality unchanged. Analogously, it is shown that the marginal Gini decomposition corresponds to the relative inequality view. Thus, if the view of inequality under consideration is the absolute (relative) one, the researcher should use the absolute (relative) Gini index and the natural (marginal) decomposition. The article also discusses the relationships between the two decompositions by income source and various Gini index-based decompositions of the redistributive effects of the fiscal system.
References
Aaberge, R., and A. Langørgen 2006 “Measuring the benefits from public services: The effects of local government spending on the distribution of income in Norway”, Review of Income and Wealth 52(1): 61–83. doi.org/10.1111/j.1475-4991.2006.00176.x
Adams, R.H. 1994 “Non-Farm Income and Inequality in Rural Pakistan: A Decomposition Analysis”, Journal of Development Studies 31(1): 110–133. doi.org/10.1080/00220389408422350
Amarante, V. 2016 “Income Inequality in Latin America: A Factor Component Analysis”, Review of Income and Wealth 62(S1): S4–S21. doi.org/doi:10.1111/roiw.12236
Anand, S., and P. Segal 2015 “The Global Distribution of Income”, in A. B. Atkinson and F. Bourguignon (Eds.), Handbook of Income Distribution (Vol. 2, pp. 937–979). Elsevier. doi.org/10.1016/B978-0-444-59428-0.00012-6
Araar, A. 2006 “On the Decomposition of the Gini Coefficient: an Exact Approach, with an Illustration Using Cameroonian Data”, Cahier de Recherche/Working Paper 06–02, CIRPÉE Centre interuniversitaire sur le risque, les politiques économiques et lemploi.
Atkinson, A.B. 1970 “On the measurement of inequality”, Journal of Economic Theory 2(3): 244–263. doi.org/10.1016/0022-0531(70)90039-6
—–, and A. Brandolini 2004 “Global World Inequality: Absolute, Relative or Intermediate?”, In 28th General Conference of The International Association for Research in Income and Wealth, Cork, Ireland, August 22–28, 2004.
Atkinson, A.B., and A. Brandolini 2010 “On Analyzing the World Distribution of Income”, World Bank Economic Review 24(1): 1–37. doi.org/10.1093/wber/lhp020
Avram, S., H. Levy, and H. Sutherland 2014 “Income redistribution in the European Union”, IZA Journal of European Labor Studies 3(1): 22. doi.org/10.1186/2193-9012-3-22
Cancian, M., and D. Reed 1998 “Assessing the effects of wives’ earnings on family income inequality”, Review of Economics and Statistics 80(1): 73–79. doi.org/10.1162/003465398557348
Cheng, Y. 1996 “A decomposition analysis of income inequality of Chinese rural households”, China Economic Review 7(2): 155–167. doi.org/10.1016/S1043-951X(96)90006-1
Davis, B., P. Winters, G. Carletto, K. Covarrubias, E.J. Quiñones, A. Zezza, K. Stamoulis, C. Azzarri, and S. DiGiuseppe 2010 “A Cross-Country Comparison of Rural Income Generating Activities”, World Development 38(1): 48–63. doi.org/10.1016/j.worlddev.2009.01.003
Deshpande, R.S. 2015 “Simplicity Incarnate: Remembering V M Rao”, Economic and Political Weekly 50(31): 24–26. Retrieved from http://www.jstor.org/stable/24482159
Fei, J.C.H., G. Ranis, and S.W.Y Kuo 1978 “Growth and the Family Distribution of Income by Factor Components”, Quarterly Journal of Economics 92(1): 17–53. doi.org/10.2307/1885997
Fields, G.S. 1979 “Decomposing LDC inequality”, Oxford Economic Papers 31(3): 437–459. doi.org/10.1093/oxfordjournals.oep.a041458
Flückiger, Y., and J. Silber 1995 “Income Inequality Decomposition by Income Source and the Breakdown of Inequality Differences between Two Population Subgroups”, Swiss Journal of Economics and Statistics 131(4): 599–615.
Fuest, C., J. Niehues, and A. Peichl 2010 “The Redistributive Effects of Tax Benefit Systems in the Enlarged EU”, Public Finance Review 38(4): 473–500. doi.org/10.1177/1091142110373480
García-Peñalosa, C., and E. Orgiazzi 2013 “Factor Components of Inequality: A Cross-Country Study”, Review of Income and Wealth 59(4): 689–727. doi.org/10.1111/roiw.12054
Garner, T.I. 1993 “Consumer Expenditures and Inequality: An Analysis Based on Decomposition of the Gini Coefficient”, Review of Economics and Statistics 75(1): 134. doi.org/10.2307/2109636
—–, and K. Terrell 1998 “A Gini decomposition analysis of inequality in the Czech and Slovak Republics during the transition”, Economics of Transition 6(1): 23–46. doi.org/10.1111/j.1468-0351.1998.tb00035.x
Hussain, A., P. Lanjouw, and N. Stern 1994 “Income inequalities in China: Evidence from household survey data”, World Development 22(2): 1947–1957. doi.org/10.1016/0305-750X(94)90185-6
Jenkins, S.P. 1995 “Accounting for Inequality Trends: Decomposition Analyses for the UK, 1971–86”, Economica 62(245): 29–63. doi.org/10.2307/2554775
Kakwani, N.C. 1977 “Applications of Lorenz Curves in Economic Analysis”, Econometrica 45(3): 719–727. doi.org/10.2307/1911684
Kanbur, R., Y. Wang, and X. Zhang 2021 “The great Chinese inequality turnaround”, Journal of Comparative Economics 49(2): 467–482. doi.org/10.1016/j.jce.2020.10.001
Kimhi, A. 2010 “International Remittances, Domestic Remittances, and Income Inequality in the Dominican Republic”, Discussion Paper 93130, Hebrew University of Jerusalem, Department of Agricultural Economics and Management.
—– 2011 “Comment: On the Interpretation (and Misinterpretation) of Inequality Decompositions by Income Sources”, World Development 39(10): 1888–1890. doi.org/10.1016/j.worlddev.2011.08.001
Kolm, S.-C. 1969 “The Optimal Production of Social Justice”, In J. Margolis and H. Guitton (Eds.) Public Economics Palgrave Macmillan UK.
—– 1976 “Unequal inequalities. I”, Journal of Economic Theory 12(3): 416–442. doi.org/10.1016/0022-0531(76)90037-5
—– 1976 “Unequal inequalities. II”, Journal of Economic Theory 13(1): 82–111. doi.org/10.1016/0022-0531(76)90068-5
Krstic, G. 2021 “Factors Contributing to Income and Wage Inequality: Comparative Evidence from Croatia, Serbia and Slovenia”, Eastern European Economics 59(5): 423–448. doi.org/10.1080/00128775.2021.1949352
Kyzyma, I., A. Fusco, and P. Van Kerm 2022 “Distributional Change: Assessing the Contribution of Household Income Sources”, Oxford Bulletin of Economics and Statistics 84(1): 158–184. doi.org/10.1111/obes.12462
Lambert, P.J. 1985 “On the Redistributive Effect of Taxes and Benefits”, Scottish Journal of Political Economy 32(1): 39–54. doi.org/10.1111/j.1467-9485.1985.tb00786.x
—– 2001 The Distribution and Redistribution of Income Manchester: Manchester University Press.
Layard, R., and A. Zabalza 1979 “Family Income Distribution: Explanation and Policy Evaluation”, Journal of Political Economy 87(5): 133–161. doi.org/10.1086/260826
Lerman, R.I., 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. doi.org/10.2307/1928447
—– 1994 “Effect of marginal changes in income sources on US income inequality”, Public Finance Review 22(4): 403–417. doi.org/10.1177/109114219402200401
Milanovic, B. 1999 “Explaining the increase in inequality during transition”, Economics of Transition 7(2): 299–341. doi.org/10.1111/1468-0351.00016
Morduch, J., and T. Sicular 2002 “Rethinking inequality decomposition, with evidence from rural China”, Economic Journal 112(476): 93–106. doi.org/10.1111/1468-0297.0j674
Moyes, P. 1987 “A new concept of Lorenz domination”, Economics Letters 23(2): 203–207. doi.org/10.1016/0165-1765(87)90040-1
—– 1988 “A note on minimally progressive taxation and absolute income inequality”, Social Choice and Welfare 5(2–3): 227–234. doi.org/10.1007/BF00735763
Nembua, C.C. 2012 “Inequality factor decomposition under uniform additions property with applications to Cameroonian rural data”, Applied Economics Letters 19(14): 1365–1371. doi.org/10.1080/13504851.2011.629976
Paul, S. 2004 “Income sources effects on inequality”, Journal of Development Economics 73(1): 435–451. doi.org/https://doi.org/10.1016/j.jdeveco.2003.02.004
Podder, N. 1993 “The Disaggregation of the Gini Coefficient by Factor Components and Its Applications to Australia”, Review of Income and Wealth 39(1): 51–61. doi.org/10.1111/j.1475-4991.1993.tb00437.x
—–, and S. Chatterjee 2002 “Sharing the National Cake in Post Reform New Zealand: Income Inequality Trends in Terms of Income Sources”, Journal of Public Economics 86(1): 1–27. doi.org/10.1016/S0047-2727(01)00117-7
Pyatt, G., C. Chen, and J.C.H. Fei 1980 “The Distribution of Income by Factor Components”, Quarterly Journal of Economics 95(3): 451–473. doi.org/10.2307/1885088
Rao, V.M. 1969 “Two Decompositions of Concentration Ratio”, Journal of the Royal Statistical Society. Series A (General) 132(3): 418–425. doi.org/10.2307/2344120
Reardon, T., and J.E. Taylor 1996 “Agroclimatic shock, income inequality, and poverty: Evidence from Burkina Faso”, World Development 24(5): 901–914. doi.org/10.1016/0305-750X(96)00009-5
Rozelle, S. 1994 “Rural Industrialization and Increasing Inequality: Emerging Patterns in China's Reforming Economy”, Journal of Comparative Economics 19(3): 362–391. doi.org/10.1006/jcec.1994.1108
Shorrocks, A.F. 1982 “Inequality Decomposition by Factor Components”, Econometrica 50(1): 193–212. doi.org/10.2307/1912537
—– 1983 “The Impact of Income Components on the Distribution of Family Incomes”, Quarterly Journal of Economics 98(2): 311. doi.org/10.2307/1885627
—– 1988 “Aggregation Issues in Inequality Measurement”, In W. Eichhorn (Ed.) Measurement in economics: Theory and applications of economic indices (pp. 429–451). Springer Verlag. https:// doi.org/10.1007/978-3-642-52481-3_32
Stark, O., J.E. Taylor, and S. Yitzhaki 1986 “Remittances and Inequality”, Economic Journal 96(383): 722–740. doi.org/10.2307/2232987
Urban, I. 2008 “Income Redistribution in Croatia: The Role of Individual Taxes and Social Transfers Financial Theory and Practice”, Financial Theory and Practice 32(3): 387–403.
—– 2014 “Contributions of taxes and benefits to vertical and horizontal effects”, Social Choice and Welfare 42(3): 619–645. doi.org/10.1007/s00355-013-0747-x
—– 2019 “Measuring Redistributive Effects of Taxes and Benefits: Beyond the Proportionality Standard”, FinanzArchiv 75(4): 413. doi.org/10.1628/fa-2019-0008
—– 2023 “‘Mingling’ the Gini index and the mean income to rank countries by inequality and social welfare”, In S. Bandyopadhyay and J.G. Rodríguez (Eds.) Mobility and Inequality Trends (Vol. 30, pp. 139–163). Emerald Publishing Limited. doi.org/10.1108/S1049-258520230000030005
Zhou, Y. 2009 “The factors that impact income inequality of rural residents in China: Decomposing the Gini coefficient from income components”, Frontiers of Economics in China 4(4): 617. doi.org/10.1007/s11459-009-0033-0
