The atlas of inequality aversion: theory and empirical evidence on 55 countries from the Luxembourg Income Study database
DOI:
https://doi.org/10.24136/eq.2022.010Keywords:
inequality aversion, Atkinson Index, income distribution, inequality, utility functionAbstract
Research background: In the distributive analysis, the constant relative inequality aversion utility function is a standard tool for ethical judgements of income distributions. The sole parameter ? of this function expresses a society?s aversion to inequality. However, the profession has not committed to the range of ?. When assessing inequality and other welfare characteristics, analysts assume an arbitrary level of ?, common to all countries and years. This assumption seems unjustified.
Purpose of the article: This paper aims to estimate the parameter ? for each country and year individually using datasets from the Luxembourg Income Study Database in all available years, which dates back to the 1970s.
Methods: We utilise the method of estimating ?, which assumes the generalised beta of the second kind distribution of incomes. The estimator of ? is derived from the mathematical condition of the existence of the social welfare function.
Findings & value added: We have elaborated an ?atlas? of 388 estimates of ? for 55 countries across time. Inequality aversion is country-year specific, with a minimum of 0.97 and a maximum of 3.8. Ninety per cent of all estimates are less than 2.5. Inequality aversion is negatively correlated with income inequality, but it is independent of economic development. Thus, inequality aversion appears as an additional dimension of the classical inequality-development relationship. This article contributes to solving a fundamental problem of Welfare Economics: directly measuring the social utility of income (welfare) function. The estimates of ? for 55 countries imply a complete knowledge of these countries' constant relative inequality aversion utility functions.
Downloads
References
Amiel, Y., Creedy, J., & Hurn, S. (1999). Measuring attitudes towards inequality. Scandinavian Journal of Economics, 101, 83?96. doi: 10.1111/1467-9442.001 42.
DOI: https://doi.org/10.1111/1467-9442.00142
View in Google Scholar
Aristei, D., & Perugini, C. (2010). Preferences for redistribution and inequality in well-being across European Countries: a multidimensional approach. Journal of Policy Modeling, 32, 176?195. doi: 10.1016/j.jpolmod.2010.02.001.
DOI: https://doi.org/10.1016/j.jpolmod.2010.02.001
View in Google Scholar
Aristei, D., & Perugini, C. (2016). Inequality aversion in postcommunist countries in the years of the crisis. Post-Communist Economies, 28(4), 436?448. doi: 10.1080/14631377.2016.1224053.
DOI: https://doi.org/10.1080/14631377.2016.1224053
View in Google Scholar
Atkinson, A. B., Rainwater, L., & Smeeding, T. (1995). Income distribution in OECD Countries. Social Policy Studies, 18.
DOI: https://doi.org/10.1017/CBO9780511559396.004
View in Google Scholar
Atkinson, A. B. (1970). On the measurement of inequality. Journal of Economic Theory, 2(3), 244?263. doi: 10.1016/0022-0531(70)90039-6.
DOI: https://doi.org/10.1016/0022-0531(70)90039-6
View in Google Scholar
Attanasio, O. P., & Browning, M. (1995). Consumption over the life cycle and over the business cycle. American Economic Review, 85, 1118?1137.
View in Google Scholar
Bandourian, R., McDonald, J. B., & Turley, R. S. (2003). A comparison of para-metric models of income distribution across countries and years, Estadistica, 55, 135-152.
DOI: https://doi.org/10.2139/ssrn.324900
View in Google Scholar
Berg, A., Ostry, J. D., Tsangarides, C. G., & Yakhshilikov, Y. (2018). Redistribution, inequality, and growth: new evidence. Journal of Economic Growth, 3, 259?305. doi: 10.1007/s10887-017-9150-2.
DOI: https://doi.org/10.1007/s10887-017-9150-2
View in Google Scholar
Blundell, R., Browning, M., & Meghir, C. (1994). Consumer demand and the life-cycle allocation of household expenditures. Review of Economic Studies, 61, 57?80. doi: 10.2307/2297877.
DOI: https://doi.org/10.2307/2297877
View in Google Scholar
Bourguignon, F., & Spadaro, A. (2012). Tax-benefit revealed social preferences. Journal of Economic Inequality, 10, 75-108. doi: 10.1007/s10888-010-9153-0.
DOI: https://doi.org/10.1007/s10888-010-9153-0
View in Google Scholar
Brazauskas, V. (2002). Fisher information matrix for the Feller?Pareto distribution. Statistics & Probability Letters, 59, 159?167. doi: 10.1016/S0167-7152(02)001 43-8.
DOI: https://doi.org/10.1016/S0167-7152(02)00143-8
View in Google Scholar
Burkhauser, R. V., Butler, J. S., Feng, S., & Houtenville, A. (2004). Long-term trends in earnings inequality: what the CPS can tell us. Economics Letters 82, 295-299. doi: 10.1016/j.econlet.2003.08.011.
DOI: https://doi.org/10.1016/j.econlet.2003.08.011
View in Google Scholar
Burkhauser, R.V., Feng, S., & Jenkins, S. (2007). Using the P90/P10 ratio to meas-ure US inequality trends with Current Population Survey data: a view from inside the Census Bureau vaults. Colchester, UK: Institute for Social and Eco-nomic Research, University of Essex.
DOI: https://doi.org/10.2139/ssrn.998222
View in Google Scholar
Chotikapanich, D., Griffiths, W. E., Hajargasht, G., Karunarathne, W., & Prasada Rao, D. S. (2018). Using the GB2 income distribution. Econometrics, 6(2), 21 doi: 10.3390/econometrics6020021.
DOI: https://doi.org/10.3390/econometrics6020021
View in Google Scholar
Clark, A.E., & D?Ambrosio, C. (2015). Attitudes to income inequality: experi-mental and survey evidence. In A. B. Atkinson & F. Bourguignon (Eds.). Handbook of income distribution. Elsevier, 1147?1208. doi: 1016/B978-0-444-59428-0.00014-X.
DOI: https://doi.org/10.1016/B978-0-444-59428-0.00014-X
View in Google Scholar
Costa-Font, J., F., & Cowell, F. (2019). Incorporating inequality aversion in health-care priority setting. Social Justice Research, 32, 172?185. doi: 10.1007/s1121 1-019-00328-6.
DOI: https://doi.org/10.1007/s11211-019-00328-6
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
Dagum, C. (1977). A new model of personal income distribution: specification and estimation. Economie Appliquée, 30, 413-437.
DOI: https://doi.org/10.3406/ecoap.1977.4213
View in Google Scholar
Eriksson, K. H. (2005). Censoring and top-coding in LIS data. LIS Technical Work-ing Paper Series, 4.
View in Google Scholar
Evans, D. J. (2005). The elasticity of marginal utility of consumption: estimates for 20 OECD Countries. Fiscal Studies, 26(2), 197?224. doi: 10.1111/j.1475-5890 .2005.00010.x.
DOI: https://doi.org/10.1111/j.1475-5890.2005.00010.x
View in Google Scholar
Feng, S., Burkhauser, R. V., & Butler, J. S. (2006). Levels and long-term trends in earnings inequality: overcoming current population survey censoring problems using the GB2 distribution. Journal of Business and Economic Statistics, 24(1), 57?62. doi: 10.1198/073500105000000144.
DOI: https://doi.org/10.1198/073500105000000144
View in Google Scholar
Fisk, P. R. (1961). The graduation of income distribution. Econometrica, 29, 171?184. doi: 10.2307/1909287.
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, 177?196. doi: 10.2307/1909441.
DOI: https://doi.org/10.2307/1909441
View in Google Scholar
Graf, M., & Nedyalkova, D. (2010). GB2: Generalized Beta distribution of the decond kind: properties, likelihood, estimation. R package version 1.0. Re-trieved from http://cran.r-project.org/web/packages/GB2/index.html.
View in Google Scholar
Groom, B., & Pr, D. M. (2019). New estimates of the elasticity of marginal utility for the UK. Environmental and Resource Economics, 72(4), 1155?1182. doi: 10.1007/s10640-018-0242-z
DOI: https://doi.org/10.1007/s10640-018-0242-z
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. Retrieved from http://ideas.repec.org/c/boc/bocode/s4568 23.html.
View in Google Scholar
Johnson, N. L., Kotz, S., & Balakrishnan, N. (1994). Continuous univariate distri-butions. New York: Willey.
View in Google Scholar
Kleiber, C., & Kotz, S. (2003). Statistical size distributions in economics and actu-arial sciences, Hoboken, New Jersey: Wiley.
DOI: https://doi.org/10.1002/0471457175
View in Google Scholar
Kolm, S. C. (1969). The optimal production of social justice. In J. Margolis & H. Guitton (Eds.). Public economics: an analysis of public production and con-sumption and their relations to the private sectors. London: Macmillan, 145?200.
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, 11(1), 123?146. doi: 10.24136/eq.v12i1.7.
DOI: https://doi.org/10.24136/eq.v12i1.7
View in Google Scholar
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. doi: 10.24136/eq.2020.018.
DOI: https://doi.org/10.24136/eq.2020.018
View in Google Scholar
Kuznets, S. (1955). Economic growth and income inequality. American Economic Review, 45(1), 1?28.
View in Google Scholar
Lambert, P. J., & Naughton, H. P. (2009). The equal absolute sacrifice principle revisited. Journal of Economic Surveys, 23(2), 328?349. 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
Lambert, P. J., Millimet, D. L., & Slottje, D. (2003). Inequality aversion and the natural rate of subjective inequality. Journal of Public Economics, 87, 1061?1090. 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. (2001). Income distribution and redistribution. Manchester and New York: Manchester University Press.
View in Google Scholar
Larrimore, J., Burkhauser, R. V., Feng, S., & Zayatz, L. (2008). Consistent cell means for topcoded incomes in the public use March CPS (1976-2007). NBER Working Paper, 13941.
DOI: https://doi.org/10.3386/w13941
View in Google Scholar
Layard, R., Mayraz, G., & Nickell, S. (2008). The marginal utility of income. Jour-nal of Public Economics, 92, 1846?1857. doi: 10.1016/j.jpubeco.2008.01. 007.
DOI: https://doi.org/10.1016/j.jpubeco.2008.01.007
View in Google Scholar
Luxembourg Income Study (LIS) Database (2020). Luxembourg: LIS. Retrieved from http://www.lisdatacenter.org.
View in Google Scholar
McDonald, J. B. (1984). Some generalised functions for the size distribution of income. Econometrica, 52, 647?663. doi: 10.2307/1913469.
DOI: https://doi.org/10.2307/1913469
View in Google Scholar
McDonald, J. B., & Xu, Y. J. (1995). A generalisation of the beta distribution with applications. Journal of Econometrics, 66(1-2), 427?428. doi: 10.1016/0304-4076(94)01612-4.
DOI: https://doi.org/10.1016/0304-4076(94)01680-X
View in Google Scholar
Mirrlees, J. A. (1971). An exploration in the theory of optimum income taxation. Review of Economic Studies, 38, 175?208.
DOI: https://doi.org/10.2307/2296779
View in Google Scholar
Mitra, T., & Ok, E. A. (1996). Personal income taxation and the principle of equal sacrifice revisited. International Economic Review, 37, 925?948. doi: 10.2307 /2527317.
DOI: https://doi.org/10.2307/2527317
View in Google Scholar
Ok, E. A. (1995). On the principle of equal sacrifice in income taxation. Journal of Public Economics, 58, 453?467. doi: 10.1016/0047-2727(94)01481-3.
DOI: https://doi.org/10.1016/0047-2727(94)01481-3
View in Google Scholar
Okun, A. M. (1975). Equality and efficiency. Washington: Brookings Institution.
DOI: https://doi.org/10.2307/2534103
View in Google Scholar
Pareto, V. (1897). Cours d?Economie Politique. Lausanne: Ed. Rouge.
View in Google Scholar
Piketty, T. (2014). Capital in the 21st century. Cambridge, Massachusetts Har-vard University Press.
View in Google Scholar
Pirttilä, J., & Uusitalo, R. (2007). Leaky bucket in the real world: estimating ine-quality aversion using survey data. CESifo Working Paper, 2026.
View in Google Scholar
Ravallion, M. (2015). The Luxembourg income study. Journal of Economic Inequality, 13, 527?547. doi: 10.1007/s10888-015-9298-y.
DOI: https://doi.org/10.1007/s10888-015-9298-y
View in Google Scholar
Richter, W. F. (1983). From ability to pay to concept of equal sacrifice. Journal of Public Economics, 20, 211?229. doi: 10.1016/0047-2727(83)90011-7.
DOI: https://doi.org/10.1016/0047-2727(83)90011-7
View in Google Scholar
Schlör, H., Fischer, W., & Hake, J. F. (2012). Measuring social welfare, energy and inequality in Germany. Applied Energy, 97, 135?142.
DOI: https://doi.org/10.1016/j.apenergy.2012.01.036
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
Sheshinski, E. (1972). Relation between a social welfare function and the Gini index of income inequality. Journal of Economic Theory, 4, 98?100.
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, 963?973.
DOI: https://doi.org/10.2307/1911538
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 pro-gressivity. Public Finance Quarterly, 5, 489?494,
DOI: https://doi.org/10.1177/109114217700500406
View in Google Scholar
Young, H. P. (1987). Progressive taxation and the equal sacrifice principle. Journal of Public Economics, 32, 203?214.
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, 253?266.
View in Google Scholar
