Estimating the parameter of inequality aversion on the basis of a parametric distribution of incomes

Authors

DOI:

https://doi.org/10.24136/eq.2020.018

Keywords:

income inequality, inequality aversion, estimation, income distribution

Abstract

Research background: In applied welfare economics, the constant relative inequality aversion function is routinely used as the model of a social decisionmaker?s or a society?s preferences over income distributions. This function is entirely determined by the parameter, ?, of inequality aversion. However, there is no authoritative answer to the question of what the range of ? an analyst should select for empirical work.

Purpose of the article: The aim of this paper is elaborating the method of deriving ? from a parametric distribution of disposable incomes.

Methods: We assume that households? disposable incomes obey the generalised beta distribution of the second kind GB2(a,b,p,q). We have proved that, under this assumption, the social welfare function exists if and only if ? belongs to (0,ap+1) interval. The midpoint ?mid of this interval specifies the inequality aversion of the median social-decisionmaker.

Findings & Value added: The maximum likelihood estimator of ?mid has been developed. Inequality aversion for Poland 1998?2015 has been estimated. If inequality is calculated on the basis of disposable incomes, the standard inequality?development relationship might be complemented by inequality aversion. The ?augmented? inequality?development relationship reveals new phenomena; for instance, the stage of economic development might matter when assessing the impact of inequality aversion on income inequality.

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References

Aghion, P., & Bolton, P. (1997). A theory of trickle-down growth and development. Review of Economic Studies, 64(2). doi: 10.2307/2971707.

DOI: https://doi.org/10.2307/2971707
View in Google Scholar

Aitchison, J., & Brown, J. A. C. (1956). The lognormal distribution. Cambridge: Cambridge University Press.
View in Google Scholar

Amiel, Y., Cowell, F., & Slottje, D. (2004). Why do people violate the transfer principle? evidence from educational sample surveys. Research on Economic Inequality, 11.

DOI: https://doi.org/10.1016/S1049-2585(04)11001-6
View in Google Scholar

Amiel, Y., Creedy, J., & Hurn, S. (1999). Measuring attitudes towards inequality. Scandinavian Journal of Economics, 101(1). doi: 10.1111/1467-9442.00142.

DOI: https://doi.org/10.1111/1467-9442.00142
View in Google Scholar

Aristei, D., & Perugini, C. (2016). Inequality aversion in post-communist countries in the years of the crisis. Post-Communist Economies, 28(4). doi: 10.1080/14631377.2016.1224053.

DOI: https://doi.org/10.1080/14631377.2016.1224053
View in Google Scholar

Aroian, L. A., Taneja, V. S., & Cornwell, L. W. (1978). Mathematical forms of the distribution of the product of two normal variables. Communications in Statistics - Theory and Methodology, A72.

DOI: https://doi.org/10.1080/03610927808827610
View in Google Scholar

Atkinson, A. (1970). On the measurement of economic inequality. Journal of Economic Theory, 2(3). doi: 10.1016/0022-0531(70)90039-6.

DOI: https://doi.org/10.1016/0022-0531(70)90039-6
View in Google Scholar

Atkinson, A. B. (1980). Wealth, income and inequality. Oxford: Oxford University Press.
View in Google Scholar

Bandourian, R., McDonald, J. B., & Turley, R. S. (2003). A comparison of parametric models of income distribution across countries and years. Estadistica 55.

DOI: https://doi.org/10.2139/ssrn.324900
View in Google Scholar

Beckman, S. R., Formbyand, J. P., Smith, W. J. (2004). Efficiency, equity and democracy: experimental evidence on Okun’s leaky bucket. In F. Cowell (Ed.). Inequality, welfare and income distribution: experimental approaches. Amsterdam: Emerald Group Publishing Limited.
View in Google Scholar

Brazauskas, V. (2002). Fisher information matrix for the Feller–Pareto distribution. Statistics & Probability Letters, 59(2). doi: 10.1016/S0167-7152(02)00143-8.

DOI: https://doi.org/10.1016/S0167-7152(02)00143-8
View in Google Scholar

Burr, I. W. (1942). Cumulative frequency functions. Annals of Mathematical Statistics, 13.

DOI: https://doi.org/10.1214/aoms/1177731607
View in Google Scholar

Carlsson, F., Daruvala, D., & Johansson-Stenman, O. (2005). Are people inequality-averse or just risk-averse? Economica, 72. doi: 10.1111/j.0013-0427.2005. 00421.x.

DOI: https://doi.org/10.1111/j.0013-0427.2005.00421.x
View in Google Scholar

Chernoff, H., & Lehmann, E. L. (1954). The use of maximum-likelihood estimates in χ2 test for goodness of fit. Annals of Mathematical Statistics, 25(3). doi: 10.1214/aoms/1177728726.

DOI: https://doi.org/10.1214/aoms/1177728726
View in Google Scholar

Clark, A. E., & D'Ambrosio, C. (2015). Attitudes to income inequality: experimental and survey evidence. In A. B. Atkinson & F. Bourguignon (Eds.). Handbook of income distribution. Amsterdam: Elsevier.

DOI: https://doi.org/10.1016/B978-0-444-59428-0.00014-X
View in Google Scholar

Cover, T. M., & Thomas, J. A. (1991). Elements of information theory. New York: Wiley.
View in Google Scholar

Cowell, F., & Gardiner, K. (1999). Welfare weights. STICERD. London School of Economics.
View in Google Scholar

Cui, G., Yu, X., Iommelli, S., & Kong, L. (2016). Exact distribution for the product of two correlated Gaussian random variables. IEEE Signal Processing Letters, 23. doi: 10.1109/LSP.2016.2614539.

DOI: https://doi.org/10.1109/LSP.2016.2614539
View in Google Scholar

D’Agostino, R .D., & Stephens, M.A. (1986). Goodness-of-fit techniques. New York and Basel: Marcel Dekker Inc.
View in Google Scholar

Dagum, C. (1977). A new model of personal income distribution: Specification and estimation. Economie Appliquée, 30.

DOI: https://doi.org/10.3406/ecoap.1977.4213
View in Google Scholar

Dahan, M., Tsiddon, D. (1998). Demographic transition, income distribution, and economic growth. Journal of Economic Growth, 3(1). doi: 10.1023/A:10097 69930916.

DOI: https://doi.org/10.1023/A:1009769930916
View in Google Scholar

Fisk, P. R. (1961). The graduation of income distribution. Econometrica, 29.

DOI: https://doi.org/10.2307/1909287
View in Google Scholar

Fisz, M. (1967). Probability theory and mathematical statistics. New York: Wiley,
View in Google Scholar

Frisch, R. (1959). A complete system for computing all direct and cross-demand elasticities in a model with many sectors. Econometrica, 27.

DOI: https://doi.org/10.2307/1909441
View in Google Scholar

Galor, O., & Tsiddon, D. (1996). Income distribution and growth: the Kuznets hypothesis revisited. Economica, 3.

DOI: https://doi.org/10.2307/2554811
View in Google Scholar

Gouveia, M., & Strauss, R. P. (1994). Effective federal individual income tax functions: an exploratory empirical analysis. National Tax Journal, 47.

DOI: https://doi.org/10.1086/NTJ41789070
View in Google Scholar

Harvey, J. (2003). A note on the `natural rate of subjective inequality' hypothesis and the approximate relationship between the Gini coefficient and the Atkinson index. Journal of Public Economics, 89. doi: 10.1016/j.jpubeco.2004.05.002.

DOI: https://doi.org/10.1016/j.jpubeco.2004.05.002
View in Google Scholar

Hoffmann, R. (2001). Effect of the rise of a person’s income on inequality. Brazilian Review of Econometrics, 21. doi: 10.12660/bre.v21n22001.2751.

DOI: https://doi.org/10.12660/bre.v21n22001.2751
View in Google Scholar

Jenkins, S. P. (2007). gb2fit: Stata module to fit Generalized Beta of the Second Kind distribution by maximum likelihood. Statistical Software Components Archive, S456823.
View in Google Scholar

Jenkins, S. P. (2007). Inequality and the GB2 income distribution. ENCINEQ working paper, 73.

DOI: https://doi.org/10.2139/ssrn.997260
View in Google Scholar

Kleiber, C. (1997). The existence of population inequality measures. Economics Letters, 57. doi: 10.1016/S0165-1765(97)81877-0 .

DOI: https://doi.org/10.1016/S0165-1765(97)81877-0
View in Google Scholar

Kleiber, C., & Kotz, S. (2003). Statistical size distributions in economics and actuarial sciences. Hoboken, NJ.: Wiley,

DOI: https://doi.org/10.1002/0471457175
View in Google Scholar

Kolm, S. Ch. (1969). The optimal production of social justice. In J. Margolis & H. Guitton, H. (Eds.). Public economics. London and New York: Macmillan.

DOI: https://doi.org/10.1007/978-1-349-15294-0_7
View in Google Scholar

Kot, S. M.(2009). The boundaries for inequality aversion and certain measures of income inequality. Prace i Materiały Wydziału Zarządzania Uniwersytetu Gdańskiego, 4/2.
View in Google Scholar

Kot, S. M. (2012). Towards the stochastic paradigm of welfare economics. Cracow: Impuls.
View in Google Scholar

Kot, S. M. (2017). Estimating inequality aversion from subjective assessments of the just noticeable differences in welfare. Equilibrium. Quarterly Journal of Economics and Economic Policy, 12(1). doi: 10.24136/eq.v12i1.7.

DOI: https://doi.org/10.24136/eq.v12i1.7
View in Google Scholar

Kuznets, S. (1955). Economic growth and income inequality. American Economic Review, 45.
View in Google Scholar

Lambert, P. J. (2001). The distribution and redistribution of income: a mathematical analysis. Manchester: Manchester University Press.
View in Google Scholar

Lambert, P. J., & Lanza, G. (2006). The effect on inequality of changing one or two incomes. Journal of Economic Inequality, 4(3). doi: 10.1007/s10888-006-9020-1.

DOI: https://doi.org/10.1007/s10888-006-9020-1
View in Google Scholar

Lambert, P. J., Millimet, D. L., & Slottje, D. (2003). Inequality aversion and the natural rate of subjective inequality. Journal of Public Economics, 87. doi: 10.1016/S0047-2727(00)00171-7.

DOI: https://doi.org/10.1016/S0047-2727(00)00171-7
View in Google Scholar

Lambert, P. J., & Naughton, H. T. (2009). The equal absolute sacrifice principle revisited. Journal of Economic Surveys, 23. doi: 10.1111/j.1467-6419.2008. 00564.x.

DOI: https://doi.org/10.1111/j.1467-6419.2008.00564.x
View in Google Scholar

Lerner, A. P. (1944). The economics of control. London: Macmillan.
View in Google Scholar

Levitt, S. D., & List, A. J. (2007). What do laboratory experiments measuring social preferences reveal about the real world? Journal of Economic Perspectives, 21. doi: 10.1257/jep.21.2.153.

DOI: https://doi.org/10.1257/jep.21.2.153
View in Google Scholar

McDonald, J. B. (1984). Some generalized functions for the size distribution of income. Econometrica, 52. doi: 10.2307/1913469.

DOI: https://doi.org/10.2307/1913469
View in Google Scholar

Mitra, T., & Ok, E. A. (1996). Personal income taxation and the principle of equal sacrifice revisited. International Economic Review, 37. doi:10.2307/2527317.

DOI: https://doi.org/10.2307/2527317
View in Google Scholar

Okun, A. M. (1975). Equality and efficiency. Washington, DC: Brookings Institution.

DOI: https://doi.org/10.2307/2534103
View in Google Scholar

Pirttilä, J., & Uusitalo, R. (2007). Leaky bucket in the real world: estimating inequality aversion using survey data. CESifo working paper, 2026.

DOI: https://doi.org/10.2139/ssrn.996559
View in Google Scholar

Pratt, J. W. (1964). Risk aversion in the small and in the large. Econometrica 32.

DOI: https://doi.org/10.2307/1913738
View in Google Scholar

Richter, W. F. (1983). From ability to pay to concept of equal sacrifice. Journal of Public Economics, 20.

DOI: https://doi.org/10.1016/0047-2727(83)90011-7
View in Google Scholar

Robinson, S. (1976). A note on the u hypothesis relating income inequality and economic development. American Economic Review, 66.
View in Google Scholar

Sarabia, J. M., & Azpitarte, F. (2012). On the relationship between objective and subjective inequality indices and the natural rate of subjective inequality. ECINEQ working papers, 248
View in Google Scholar

Sen, A. (1973). On economic inequality. Oxford: Clarendon Press.

DOI: https://doi.org/10.1093/0198281935.001.0001
View in Google Scholar

Sen, A. (1978). Ethical measurement of inequality: some difficulties. In W. Krelle & A/F. Shorrocks (Eds.). Personal income distribution. Amsterdam: North-Holland.
View in Google Scholar

Sheshinski, E.(1972). Relation between a social welfare function and the Gini index of income inequality. Journal of Economic Theory, 4. doi: 10.1016/0022-0531(72)90167-6.

DOI: https://doi.org/10.1016/0022-0531(72)90167-6
View in Google Scholar

Singh S. K., & Maddala, G. S. (1976). A function of size distribution of income. Econometrica, 44.

DOI: https://doi.org/10.2307/1911538
View in Google Scholar

Stern, N. (1977). The marginal valuation of income. In M. J. Artis & A. R. Nobay (Eds.). Essays in economic analysis. Cambridge: Cambridge University Press.
View in Google Scholar

Tuominen, E. (2015). Reversal of the Kuznets curve. Study on the inequality–development relation using top income shares data. WIDER Working Paper 2015/036.

DOI: https://doi.org/10.35188/UNU-WIDER/2015/921-3
View in Google Scholar

Vitaliano, D. F. (1977). The tax sacrifice rules under alternative definitions of progressivity. Public Finance Quarterly, 5.

DOI: https://doi.org/10.1177/109114217700500406
View in Google Scholar

Ware, R., & Lad, F. (2003). Approximating the distribution for sums of products of normal variables. Technical Report. The University of Queensland.
View in Google Scholar

World Bank (2017). World Development Indicators 2017. Washington, DC: World Bank.

DOI: https://doi.org/10.1596/26447
View in Google Scholar

Young, H. P. (1987). Progressive taxation and the equal sacrifice principle. Journal of Public Economics, 32. doi: 10.1016/0047-2727(87)90012-0.

DOI: https://doi.org/10.1016/0047-2727(87)90012-0
View in Google Scholar

Young, H. P. (1990). Progressive taxation and equal sacrifice. American Economic Review, 80.
View in Google Scholar

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Published

2020-09-07

How to Cite

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), 391–417. https://doi.org/10.24136/eq.2020.018

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