# Estimating inequality aversion from subjective assessments of the just noticeable differences in welfare

## Main Article Content

## Abstract

Research background: In Economics, the concept of inequality aversion corresponds with the concept of risk aversion in the literature on making decision under uncertainty. The risk aversion is estimated on the basis of subjective reactions of people to various lottery prospects. In Economics, however, an efficient method of estimating inequality aversion has not been developed yet.

Purpose of the article: The main aim of this paper is to develop the method of estimating inequality aversion.

Methods: The method is based on two income thresholds which are subjectively assessed by surveyed respondents. Given the level of household income, just noticeable worsening of household welfare is perceived below the first threshold, whereas just noticeable improvement of household welfare is perceived above the second threshold. The thresholds make possible effective calculations of the parameter of the Arrow-Pratt’s constant inequality aversion utility function. In this way, an individual utility of income becomes an empirically observable economic phenomenon.

Findings and Value added: In this paper, two theorems are proved which provide the guidance on how to identify a proper version of the above function. The proposed method is tested on the basis of statistical data from the archival survey conducted among Polish households in 1999. The statistical analysis of those data reveals the appearance of convex utility functions as well as concave ones. Nevertheless, the prevailing part of the Polish society exhibited inequality aversion in the year 1999. Another result of this paper is that inequality aversion diminishes as income increases.

## Article Details

*Equilibrium. Quarterly Journal of Economics and Economic Policy*,

*12*(1), 123-146. https://doi.org/https://doi.org/10.24136/eq.v12i1.7

## References

Barro, R. J., & Sala-i-Martin, X. (2004). Economic growth. Cambridge, MA, London: The MIT Press.

Cass, D. (1965). Optimum growth in an aggregate model of capital accumulation. Review of Economic Studies, 32(3).

Colasanto, D., Kapteyn, A., & van der Gaag, J. (1984). Two subjective definitions of poverty: results from the Wisconsin basic needs study. Journal of Human Resources, 28(1).

Creedy, J. (1998). Measuring welfare changes and tax burdens. Cheltenhamn UK, Northampton, MA USA: Edward Elgar Publishing Limited.

Danziger, S. J., van der Gaag, Taussing, M., & Smolensky, E. (1984). The direct measurement of welfare levels: how much does it cost to make ends meet? Review of Economics and Statistics, 66(3).

De Vos, K., & Garner, T. (1991). An evaluation of subjective poverty definitions: comparing results from the U.S. and the Netherlands. Review of Income and Wealth, 37(3).

Dubnoff, S. (1979). Experiments in the use of survey data for the measurement of income minima. Working Papers, Center for Survey Research, Boston: University of Massachusetts,.

Hagenaars, A. J. M. (1986). The perception of poverty. Amsterdam: North-Holland Publishing Company.

Jensen, J. L. W. V. (1906). Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Mathematica 30(1). doi:10.1007/BF02418571.

Kapteyn, A., & van Praag, B. M. S. (1976). A new approach to the construction of family equivalence scales. European Economic Review, 7(4).

Kapteyn, A., Koreman, P., & Willemse, R. (1988). Some methodological issues in the implementation of subjective poverty definitions. Journal of Human Resources, 23(2).

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

Koopmans, T. (1965). On the concept of optimal economic growth. In The econometric approach to development planning. Amsterdam, North-Holland.

Kot, S. M. (1996-1997). The Cracow poverty line. Folia Oeconomica Cracoviensia. 39-40.

Kot, S. M. (2000). Ekonometryczne modele dobrobytu. Warszawa-Kraków: PWN

Kot, S. M. (2012). Ku stochastycznemu paradygmatowi ekonomii dobrobytu. Kraków: Impuls.

Lerner, A. P. (1944). The economics of control. London: Macmillan.

Levy, M., & Levy, H. (2001). Testing for risk aversion: a stochastic dominance approach. Economics Letters, 71(2).

LiCalzi, M., & Sorato, A. (2006). The Pearson system of utility functions. European Journal of Operational Research, 172(2).

Moyes, P. (2012). Comparisons of heterogeneous distributions and dominance criteria. Journal of Economic Theory, 147(4). doi: 10.1016/j.jet2011.12.001.

Pratt, J. W. (1964). Risk aversion in the small and large. Econometrica, 32(1/2).

Ramsey, F. (1928). A mathematical theory of savings. Economic Journal, 38(152).

Ravallion, M. (2011). On multidimensional indices of poverty. Journal of Economic Inequality, 9(2).

Ravallion, M. (2012). Poverty lines across the world. In P. N. Jefferson (Ed.). Oxford handbook of the economics of poverty. Oxford: Oxford University Press.

Ravallion, M., & Lokshin, M. (2002). Self-rated economic welfare in Russia. European Economic Review, 46(8).

Roemer, J. E. (1996). Theories of distributive justice. Cambridge, Massachusetts: Harvard University Press.

Rudin, W. (1976). Principles of mathematical analysis. New York: McGraw-Hill, Inc.

Seidl, C. (1994). How sensible is the Leyden individual welfare function of income? European Economic Review, 38(8).

Sen, A. K., & Foster, J. (1997). On economic inequality. Expanded edition, Oxford: Clarendon Press.

Stevens, S. S. (1986). Psychophysics. Introduction to its perceptual, neural, and social prospects. New Brunswick (U.S.A) and Oxford: Transaction, Inc.

Thistle, P. D. (1997). Generalized probabilistic egalitarism. Mimeo, University of Nevada at Las Vegas.

Van Praag, B. M. S., & Kapteyn, A. (1994). How sensible is the Leyden individual welfare function of income? A reply. European Economic Review, 38(9).

Vaughan, D. R. (1984). Using subjective assessments of income to estimate family equivalence scales: a report on work in progress. Proceedings of the Social Statistics Section, American Statistical Association.Version I.