© Stanislaw Maciej Kot. Article available under the CC BY-SA 4.0 licence
ARTICLE
ABSTRACT
This paper proposes a theoretical framework for evaluating income distributions in terms of social welfare, economic inequality, and poverty. We introduce two types of social planners: SPϵ, who have an aversion to income inequality measured by the normative parameter ϵ, and SPν, who have an aversion to rank inequality measured by the normative parameter ν. Each member of society could play the role of a social planner, which implies that there are many possible levels of ϵ and ν. We then introduce the concept of inequality-entangled SPν and SPϵ. If a randomly selected SPν has parameter νi, one can automatically find ϵi of the inequality-entangled SPϵ, and vice versa. The paper proposes a method for eliciting pairs (νi, ϵi), i = 1, 2, …, n, from empirical income distributions, and for identifying a single pair (ν*, ϵ*) representing all n pairs. Finally, we apply this framework to assess social welfare, inequality, and poverty for the 27 European Union member countries in 2021.
KEYWORDS
income distribution, social welfare, inequality, poverty, inequality aversion, European Union
REFERENCES
Aristei, D., Perugini, C., (2016). Inequality aversion in post-communist countries in the years of the crisis. Post-Communist Economies, 28(4), pp. 436–448.
Atkinson, A. B., (1970). On the measurement of inequality. Journal of Economic Theory, 2, pp. 244–263.
Bonferroni, C., (1930). Elementi di Statistica Generale. Seeber, Firenze.
Buhmann, B., Rainwater, L., Schmaus, G. and Smeeding, T. M., (1988). Equivalence scales, well-being, inequality, and poverty: sensitivity estimates across ten countries using the Luxembourg Income Study (LIS) database. Review of Income and Wealth, 34(2), pp. 115–142.
Caltech Science Exchange, (2024). What is entanglement, and why is it important? https://scienceexchange.caltech.edu/topics/quantum .
Cover, T. M., Thomas, J. A., (1991). Maximum entropy and spectral estimation. Elements of Information Theory, pp. 266–278.
Donaldson, D., Weymark, J., (1980). Aa single-parameter generalisation of Gini indices of inequality. Journal of Economic Theory, 22, pp. 67–86.
Duclos, J. Y., (2000). Gini indices and the redistribution of income. International Tax and Public Finance, 7(2), pp. 141–162.
Evans, D., (2005). The elasticity of marginal utility of consumption: Estimates for 20 OECD countries. Fiscal Studies, 26, pp. 197–224.
Facco, E., Fracas, F., (2022). De Rerum (Incerta) Natura: A Tentative Approach to the Concept of “Quantum-like". Symmetry, 14(3), p. 480. https://doi.org/10.3390/sym14030480
Foster, J. E., Shorrocks, A. F., (1991). Subgroup consistent poverty indices. Econometrica, pp. 687–709.
Foster, J., Greer, J. and Thorbecke, E., (1984). A class of decomposable poverty measures. Econometrica, 52(3), pp. 761–766.
Harsanyi, J. C., (1980). Essays on ethics, social behavior, and scientific explanation. Theory and Decision Library, Vol. 12, Kluwer Academic Publishers Group, Dordrecht, Holland.
Kakwani, N. C., (1980). Income inequality and poverty. World Bank, New York.
Kolm, S. C., (1969). The optimal production of social justice. In Margolis, J. & Guitton, H. (Eds.). Public Economics: An Analysis of Public Production and Consumption and their Relations to the Private Sectors. Macmillan, London, pp. 145–200.
Kot, S. M., (2020). Estimating the parameter of inequality aversion on the basis of a parametric distribution of incomes. Equilibrium. Quarterly Journal of Economics and Economic Policy, 15(3), pp. 391–417.
Kot, S. M., (2022). Estimating aversion to rank inequality underlying selected Italian indices of income inequality. Statistica & Applicazioni, 10(1), pp. 1–13.
Kot, S. M., Paradowski, P. R., (2024a). The equally distributed equivalent income as the upper limit of poverty lines. LIS Working Papers Series, No. 885. Luxemburg: LIS. https://www.lisdatacenter.org/wps/liswps/885.pdf.
Kot, S. M., Paradowski, P. R., (2024b). A consistent assessment of social welfare by two methodologies. The theory and evidence from the Luxembourg Income Study database. GUT Working Paper Series A (Economics, Management, Statistics), No 1/2024(72). https://cdn.files.pg.edu.pl/zie/Strona%20polska/Nauka/Publikacje/Working%20Papers/WP_GUTFME_A_72_Kot_Paradowski.pdf.
Lambert, P. J., (2001). The Distribution and Redistribution of Income. Manchester University Press, Manchester, UK.
Lambert, P. J., Millimet, D. L. and Slottje, D., (2003). Inequality aversion and the natural rate of subjective inequality. Journal of Public Economics, 87, pp. 1061–1090.
Layard, R., Mayraz, G. and Nickell, S., (2008). The marginal utility of income. Journal of Public Economics, 92, 1846–1857.
McDonald, J. B., (1984). Some generalised functions for the size distribution of income. Econometrica, 52(3), pp. 647–665.
Okun, A. M., (1975). Equality and Efficiency: The Big Trade-Off. Brookings Institution, Washington DC.
Orrell, D., (2024). Quantum economics and physics. Quantum Economics and Finance, 1(2), pp. 95–102.
Pietra, G., (1915). Delle relazioni fra indici di variabilita note I e II, Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, 74 (2), pp. 775–804.
Richter, W. F., (1983). From ability to pay to concept of equal sacrifice. Journal of Public Economics, 20(2), pp. 211–229.
Sen, A., (1973). On Economic Inequality. Clarendon Press, Oxford.
Vitaliano, D. F., (1977). The tax sacrifice rules under alternative definitions of progressivity. Public Finance Quarterly, 5(4), pp. 489–494.
Yitzhaki, S., (1983). On an extension of the Gini inequality index. International Economic Review, 24(3), pp. 617–628.
Young, H. P., (1987). Progressive taxation and the equal sacrifice principle. Journal of Public Economics, 32(2), pp. 203–214.
Young, H. P., (1990). Progressive taxation and equal sacrifice. American Economic Review, 80, pp. 253–266.
Zenga, M., (2007). Inequality curve and inequality index based on the ratio between Lower and upper arithmetic means. Statistica & Applicazioni, 1, pp. 3–27.