The “Deciles Implied Inequality Indices” for Expressing Income Distribution and Measuring Public Financial Burden of Equalization Policies

  • Bijan Bidabad Professor, Economics and Chief Islamic Banking Advisor, Bank Melli, Iran
Keywords: Income distribution, Inequality Index, Lorenz curve, Public Finance, Equalization Policy.

Abstract

Different ways have been proposed to measure income inequality; there is no best way to calculate the inequality index that expresses income distribution as it is. Popular inequality indices provide information about some points on the distribution function and analyze the inequality of income without reference to the amount of the budget needed to improve the income distribution. In this paper, we propose a set of “Deciles Implied Inequality Indices”. By using this index, we can show how much transfer payment is needed as a redistribution policy to achieve a desired income distribution consistent with the perceived economic goals of the society. That is, we try to find a fiscal-compensation-based index for reducing inequality. By using “Deciles Implied Inequality Indices”, we may measure how much income (tax and subsidy) may be redistributed to reach the targeted income distribution policy.

References

Atkinson A. B. (1970) On the measurement of inequality, Journal of Economic Theory 1970; 2: 244-263.

Bidabad, Bijan; Behrouz Bidabad (2019), Functional form for estimating the Lorenz curve. American Finance & Banking Review, 4(1), 17-21.

https://www.cribfb.com/journal/index.php/amfbr/article/view/286

http://www.bidabad.com/doc/functional-form-lorenz.pdf

http://www.bidabad.com/doc/functional-form-lorenz.pptx

Bidabad Bijan (1989a) “Discrete and continuous L1 norm regressions, proposition of discrete approximation algorithms and continuous smoothing of concentration surface”, Ph.D. thesis, Islamic Azad University, Tehran, Iran.

Bidabad Bijan (1989b) “Discrete and continuous L1 norm regressions, proposition of discrete approximation algorithms and continuous smoothing of concentration surface”, Ph.D. thesis, Islamic Azad University, Tehran, Iran. Persian translation.

Bidabad, Bijan (2019) Continuous L1 norm estimation of Lorenz curve. Bangladesh Journal of Multidisciplinary Scientific Research, Vol. 1, no. 1, PP. 41-49.

http://www.bidabad.com/doc/l1-articl4.pdf

https://www.cribfb.com/journal/index.php/BJMSR/article/view/314

Bidabad, Bijan (2019) Estimating Lorenz curve for Iran by using continuous L1 norm estimation, International Journal of Marketing Research Innovation, 3(1), 11-21.

https://www.cribfb.com/journal/index.php/ijmri/article/view/322

http://www.bidabad.com/doc/iraninc-l1.pdf

Bidabad, Bijan (2019) USA Income distribution counter-business-cyclical trend (Estimating Lorenz curve using continuous L1 norm estimation). First meeting of the Society for the Study of Economic Inequality (ECINEQ), Palma de Mallorca, Spain, July 20-22, 2005.

http://www.bidabad.com/doc/estimating-lorenz-us.pdf

Bidabad, Bijan, Hamid Shahrestani (2010) An implied inequality index using L1 norm estimation of Lorenz curve. Global Conference on Business and Finance Proceedings. Mercedes Jalbert, managing editor, ISSN 1931-0285 CD, ISSN 1941-9589 Online, Volume 3, Number 2, 2008, The Institute for Business and Finance Research, Ramada Plaza Herradura, San Jose, Costa Rica, May 28-31, 2008, pp. 148-163. Global Journal of Business Research, Vol. 4, No. 1, 2010, pp.29-45.

http://www.bidabad.com/doc/L1-Implied-inequality-index-4.pdf

Cowell F.A. (1977) Measuring Inequality. Oxford: Philip Allan.

Cramer J.S. (1973) Empirical econometrics. North-Holland, Amsterdam.

Gupta, M.R. (1984) Functional forms for estimating the Lorenz curve, Econometrica, 52, 1313-1314

Kakwani, N.C. (1980) Income inequality and poverty, New York, Oxford University Press.

Kakwani, N.C. (1980) Functional forms for estimating the Lorenz curve: a reply, Econometrica, 48, 1063-64.

Kakwani, N.C. & Podder, N (1976) Efficient estimation of the Lorenz curve and associated inequality measures from grouped observations. Econometrica 44, 137-148.

Kendall, M. & Stuart, A. (1977) The advanced theory of statistics, Vol.1, Charles Griffin & Co., London.

Mills, Jeffrey & Sourush, A. (1997)Statistical Inference via Bootstrapping for Measures of Inequality, Journal of Applied Economics,12:133-150.

Rasche, R.H., Gaffney, J., Koo, A.Y.C. & Obst, N. (1980) Functional forms for estimating the Lorenz curve, Econometrica, 48, 1061-1062.

Salem, A.B.Z. & Mount, T.D. (1974) A convenient descriptive model of income distribution: the gamma density, Econometrica, 42, 1115-1127.

Sen A. (1973) On Economic Inequality. Oxford: Oxford University Press.

Singh, S.K. & Maddala, G.S. (1976) A function for the size distribution of income, Econometrica, 44, 963-970.

Slottje, D.J. (1989) The structure of earnings and the measurement of income inequality in the U.S., North-Holland Publishing Company, Amsterdam.

Taguchi, T. (1972a) On the two-dimensional concentration surface and extensions of concentration coefficient and Pareto distribution to the two-dimensional case-I, Annals of the Inst. of Stat. Math., 24(2), 355-381.

Taguchi, T. (1972b) On the two-dimensional concentration surface and extensions of concentration coefficient and Pareto distribution to the two-dimensional case-II, Annals of the Inst. of Stat. Math., 24(3), 599-619.

Taguchi, T. (1972c) Concentration polyhedron, two-dimensional concentration coefficient for discrete type distribution and some new correlation coefficients etc., The Inst. of Stat. Math., 77-115.

Taguchi, T. (1973) On the two-dimensional concentration surface and extensions of concentration coefficient and Pareto distribution to the two-dimensional case-III, Annals of the Inst. of Stat. Math., 25(1), 215-237.

Taguchi T. (1974) On Fechner's thesis and statistics with norm p, Ann. of the Inst. of Stat. Math., 26(2), 175-193.

Taguchi, T. (1978) On a generalization of Gaussian distribution, Ann. of the Inst. of Stat. Math., 30(2), A, 211-242.

Taguchi, T. (1981) On a multiple Gini's coefficient and some concentrative regressions, Metron, Vol. XXXIX (1-2), 5-98.

Theil H. (1967) Economic and Information Theory, Amsterdam: North Holland, 1967.

Xu, Kuan (2004). How has the literature on Gini’s index evolved in the past 80 years?, http://economics.dal.ca/RePEc/dal/wprarch/howgini.pdf

Published
2019-07-06
How to Cite
Bidabad, B. (2019). The “Deciles Implied Inequality Indices” for Expressing Income Distribution and Measuring Public Financial Burden of Equalization Policies. American Economic & Social Review, 5(2), 12-20. https://doi.org/10.46281/aesr.v5i2.347
Section
Research Paper/Theoretical Paper/Review Paper/Short Communication Paper