Abstract
We examine the effect on inequality of increasing one income, and show that for two wide classes of indices a benchmark income level or position exists, dividing upper from lower incomes, such that if a lower income is raised, inequality falls, and if an upper income is raised, inequality rises. We provide a condition on the inequality orderings implicit in two inequality indices under which the one has a lower benchmark than the other for all unequal income distributions. We go on to examine the effect on the same indices of simultaneously increasing one income and decreasing another higher up the distribution, deriving results which quantify the extent of the ‘bucket leak’ which can be tolerated without negating the beneficial inequality effect of the transfer. Our results have implications for the inequality and poverty impacts of different income growth patterns, and of redistributive programmes, leaky or not, which are briefly discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Aaberge: Characterizations of Lorenz curves and income distributions, Social Choice and Welfare 17 (2000), 639–653.
Aaberge, R.: Axiomatic characterization of the Gini coefficient and Lorenz curve orderings, Journal of Economic Theory 101 (2001), 115–132.
Atkinson, A.B.: Wealth, Income and Inequality (Second Edition), Oxford University Press 1980.
Berrebi, Z.M. and Silber, J.: Weighting income ranks and levels: A multi-parameter generalisation for absolute and relative inequality indices, Economics Letters 7 (1981), 391–397.
Bourguignon, F.: Decomposable inequality measures, Econometrica 47 (1979), 901–920.
Camacho-Cuena, E., Neugebauer, T. and Seidl, C.: Compensating justice beats leaky buckets: An experimental investigation. Economics Working Paper No. 2005–06, University of Kiel, 2005.
Chakravarty, S.R.: Extended Gini indices of inequality, International Economic Review 29 (1988), 147–156.
Chateauneuf, A., Gajdos, T. and Wilthien, P.-H.: The principle of strong diminishing transfer, Journal of Economic Theory 103 (2002), 311–332.
Chiu, W.H.: Intersecting Lorenz curves and the degree of downside inequality aversion, Mimeo, University of Manchester, 2004.
Contoyannis, P. and Forster, M.: The distribution of health and income: A theoretical framework, Journal of Health Economics 18 (1999), 605–622.
Cowell, F.A.: On the structure of additive inequality measures, Review of Economic Studies 47 (1980), 521–531.
Deaton, A. and Paxson, C.: Mortality, income, and income inequality over time in Britain and the United States. In: D. Wise (ed) Perspectives on the Economics of Aging, University of Chicago, 2004, pp. 247–280.
Donaldson, D. and Weymark, J.A.: A single parameter generalization of the Gini indices of inequality, Journal of Economic Theory 22 (1980), 67–86.
Donaldson, D. and Weymark, J.A.: Ethically flexible indices for income distributions in the continuum, Journal of Economic Theory 29 (1983), 353–358.
Duclos, J.-Y.: Social evaluation functions, economic isolation and the Suits index of progressivity, Journal of Public Economics 69 (1998), 103–121.
Duclos, J.-Y.: Gini indices and the redistribution of income, International Tax and Public Finance 7 (2000), 141–162.
Duclos, J.-Y., Jalbert, V. and Araar, A.: Classical horizontal inequality and reranking: An integrating approach, Research on Economic Inequality 10 (2003), 65–100.
Ebert, U.: Measurement of inequality: An attempt at unification and generalization, Social Choice and Welfare 5 (1988), 147–169.
Foster, J.E. and Ok, E.A.: Lorenz dominance and the variance of logarithms, Econometrica 67 (1999), 901–907.
Foster, J.E. and Székely, M.: How good is growth? Asian Development Review 18 (2000), 59–73.
Glewwe, P.: Household equivalence scales and the measurement of inequality: Transfers from the poor to the rich could decrease inequality, Journal of Public Economics 44 (1991), 211–216.
Hardy, G., Littlewood, J., and Polya, G.: Inequalities. Cambridge University Press, London, 1934.
Jenkins, S.P.: The measurement of income inequality. In: L. Osberg (ed) Economic Inequality and Poverty: International Perspectives, Sharpe, Armonk NY, 1991, pp. 3–38.
Kimball, M.S.: Precautionary saving in the small and in the large, Econometrica 58 (1990), 53–73.
Kolm S.-C.: Unequal inequalities, I and II, Journal of Economic Theory 12 (1976), 416–442 and 13 (1976), 82–111.
Lambert, P.J.: Okun’s bucket: A leak and two splashes? Journal of Economic Studies 15 (1988), 71–78.
Lambert, P.J.: The Distribution and Redistribution of Income. University Press, Manchester, UK, 2001.
Lambert, P.J. and Lanza, G.: The effect on inequality of changing one or two incomes, Economics Discussion Paper No. 2003-15, University of Oregon, 2003.
Mehran, F.: Linear measures of income inequality, Econometrica 44 (1976), 805–809.
Modica, S. and Scarsini, M.: A note of comparative downside risk aversion, Journal of Economic Theory 122 (2005), 267–271.
Mosler, K. and Muliere, P.: Inequality indices and the starshaped principle of transfers, Statistical Papers 37 (1996), 343–364.
Okun, A.M.: Equality and Efficiency: The Big Trade-Off. Brookings Institution, Washington, District of Columbia, 1975.
Pendakur, K.: Changes in Canadian family income and family consumption inequality between 1978 and 1992, Review of Income and Wealth 44 (1998), 259–283.
Pratt, J.W.: Risk aversion in the small and in the large, Econometrica 32 (1964), 122–136.
Seidl, C.: Inequality measurement and the leaky-bucket paradox, Economics Bulletin 4(6) (2001), 1–7.
Shorrocks, A.F.: The class of additively decomposable inequality measures, Econometrica 48 (1980), 613–625.
Shorrocks A.F. and Foster, J.: Transfer sensitive inequality measures, Review of Economic Studies 54 (1987), 485–497.
Wang, Y.-Q. and Tsui, K.-Y.: A new class of deprivation-based generalized Gini indices, Economic Theory 16 (2000), 363–377.
Weymark, J.A.: Generalized Gini inequality indices, Mathematical Social Sciences 1 (1981), 409–430.
Wilthien, P.-H.: Downside-mindedness. Cahiers de la MSE n o 1999.97, CERMSEM, Université Paris I Panthéon-Sorbonne, Paris, 1999.
Wolfson, M.C.: When inequalities diverge, American Economic Review (AEA Papers and Proceedings) 84 (1994), 353–358.
Yaari, M.: A controversial proposal concerning inequality measurement, Journal of Economic Theory 44 (1988), 381–397.
Yitzhaki, S.: On an extension of the Gini index, International Economic Review 24 (1983), 617–628.
Zoli, C.: Intersecting generalized Lorenz curves and the Gini index, Social Choice and Welfare 16 (1999), 183–196.
Zoli, C.: Inverse stochastic dominance, inequality measurement and Gini indices, Journal of Economics Supplement 9 (2002), 119–161
Acknowledgements
We wish to thank two anonymous referees of this journal, and Rolf Aaberge, Branko Milanovic, Henry Chiu, Valentino Dardanoni, Jean-Yves Duclos, Udo Ebert, Joan Esteban, Mike Hoy, Stephen Jenkins, Karl Mosler, Krishna Pendakur, Christian Seidl, Jacques Silber, Shlomo Yitzhaki, Buhong Zheng and Claudio Zoli for valued comments, insights and suggestions regarding the content of this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Lambert, P.J., Lanza, G. The effect on inequality of changing one or two incomes. J Econ Inequal 4, 253–277 (2006). https://doi.org/10.1007/s10888-006-9020-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10888-006-9020-1