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The impact of taxes and transfer payments on the distribution of income: A parametric comparison


The Luxembourg Income Study data is used to explore the impact of taxes and transfer payments on the distribution of income across 13 countries for different years. The five-parameter generalized beta distribution and 10 of its special cases are considered as models for the size distribution of income. Maximum likelihood methods are used to estimate the model with corresponding measures of goodness of fit and inequality reported. These results identify the best-fitting two-, three-, and four-parameter models as well as describe the inter-temporal patterns of inequality corresponding to earnings, total income, and disposable income. A general pattern of increasing inequality is observed for almost all countries considered along with significantly different distributional impacts of taxes and transfer payments across countries.

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  1. 1.

    Aitchinson, J., Brown, J.A.C.: The Lognormal Distribution with Special Reference to Its Uses in Economics. Cambridge University Press, Cambridge (1969)

    Google Scholar 

  2. 2.

    Altig, D., Calstrom, C.T.: Marginal tax rates and income inequality in a Life-Cycle Model. Am. Econ. Rev. 89, 1197–1215 (1999)

    Article  Google Scholar 

  3. 3.

    Ammon, O.: Die Gesellschaftsordnung Und Ihre Naturlichen Grundlagen. (Jena 1895)

  4. 4.

    Amoroso, L.: Ricerche Intorno alla Curva dei Redditi, Annali di Matematica. Pura ed Applicata, Series 4–21. 2, 123–157 (1924–1925)

    Article  Google Scholar 

  5. 5.

    Auten, G., Carroll, R.: The effect of income taxes on household income. Rev. Econ. Stat. 81, 681–693 (1999)

    Article  Google Scholar 

  6. 6.

    Bartels, C.P.A., Van Metele, H.: Alternative Probability Density Functions of Income. Vrije University Amsterdam: Research memorandum 29 (1975)

  7. 7.

    Bandourian, R., McDonald, J.B., Turley R.S.: A comparison of parametric models of income distribution across countries and over time. Estad. 55, 135–152 (2003)

    Google Scholar 

  8. 8.

    Bordley, R.F., McDonald, J.B., Mantrala, A.: Something new, something old: Parametric models for the size distribution of income. J. Income Distrib. 6, 91–103 (1996)

    Google Scholar 

  9. 9.

    Bound, J., Johnson G.: Changes in the structure of wage in the 1980’s: An evaluation of alternative explanations. Am. Econ. Rev. 82, 371–392 (1992)

    Google Scholar 

  10. 10.

    Card, D., Lemieux T.: Can falling supply explain the rising return to college for younger men? A cohort-based analysis. Q. J. Econ. 116, 705–746 (2001)

    Article  Google Scholar 

  11. 11.

    Cox, D.R., Hinckley, D.V.: Theoretical Statistics. Chapman and Hall, London (1974)

    Google Scholar 

  12. 12.

    Dagum, C.: A new model for personal income distribution: specification and estimation. Econ. Appl. 30, 413–437 (1977)

    Google Scholar 

  13. 13.

    Dagum, C.: Gini ratio. In: The New Palgrave: A dictionary of Economics, vol I, ed by Eatwell, J., Murray, M. and Peter, N. (1988)

  14. 14.

    Dinardo, J., Fortrin, N.M., Lemieux T.: Labor market institutions and the distribution of wages, 1973–1992: A semiparametric approach. Econometrica 64, 1001–1004 (1996)

    Article  Google Scholar 

  15. 15.

    Ervik, R.: The redistributive aim of social policy. A comparative analysis of taxes. In: Tax Expenditure Transfers and Direct Transfers in Eight Countries. LIS Working Paper Series 1884, Luxembourg (1998)

  16. 16.

    Foster, M.: Trend and driving factors in income distribution and poverty in the OECDF Area. Labour Market and Social Policy Occasional Papers, no. 42 OECD, Paris (2000)

  17. 17.

    Gibrat, R.: Les Inegalites Economiques. Sirey, Paris (1931)

    Google Scholar 

  18. 18.

    Gini, C.: Variabilita’ e mutabilita. Studio Economico-Giuridici, Universita di Cagliari. 3:2a. Reprinted in C. Gini (1955), 211–382 (1912)

  19. 19.

    Gottschalk, P., Smeeding, T.M: Cross-national comparisons of earnings and income inequality. J. Econ. Lit. 35, 633–687 (1997)

    Google Scholar 

  20. 20.

    Gottschalk, P., Smeeding, T.M.: Empirical evidence on income inequality in industrialized countries. In: Atkinson, A.B., Bourgigon, F. (eds.) Handbook of Income Distribution, vol. 1, pp. 262–307. Elsevier–North Holland Publishers, New York (2000)

    Google Scholar 

  21. 21.

    Israelsen, D., McDonald, J.B.: Measurement error and the distribution of income. J. Income Distrib. 12, 21–31 (2003)

    Google Scholar 

  22. 22.

    Katz, L.F., Murphy, K.M.: Changes in relative wages, 1963–1987: Supply and demand factors. Q. J. Econ. 107, 35–78 (1992)

    Article  Google Scholar 

  23. 23.

    McDonald, J.B.: Some issues associated with the measurement of income inequality. In: Taille, C., Patil, G.P., Balderssari, B. (eds.) Statistical Distributions in Scientific Work, vol. 6, pp 161–179. Reidel, Boston (1981)

    Google Scholar 

  24. 24.

    McDonald, J.B.: Some generalized functions for the size distribution of income. Econometrica 52, 647–663 (1984)

    Article  Google Scholar 

  25. 25.

    McDonald, J.B., Xu, Y.J.: A generalization of the beta distribution with applications. J. Econ. 66, 133–152. Errata 69, 427–428 (1995)

    Google Scholar 

  26. 26.

    Murphy, K., Welch, F.: The structure of wages. Q. J. Econ. 107, 285–326 (1992)

    Article  Google Scholar 

  27. 27.

    Parker, S.C.: The generalized beta as a model for the distribution of earnings. Econ. Lett. 62, 197–200 (1999)

    Article  Google Scholar 

  28. 28.

    Rainville, E.D.: Special Functions. MacMillan, New York (1960)

    Google Scholar 

  29. 29.

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

    Article  Google Scholar 

  30. 30.

    Sarabia, J.M., E. Castillo, Slottje, D.J.: Lorenz ordering between McDonald’s generalized functions of the income size distribution. Econ. Lett. 2002, 265–270 (2002)

    Article  Google Scholar 

  31. 31.

    Singh, S.K., Maddala, G.S.: A function for the size distribution of incomes. Econometrica 44, 963–970 (1976)

    Article  Google Scholar 

  32. 32.

    Taille, C.: Lorenz ordering within the generalized gamma family of income distributions. In: Taille, C., Patil, G.P., Balderssari, B. (eds.) Statistical Distributions in Scientific Work, vol. 6, pp. 181–192. Reidel, Boston (1981)

    Google Scholar 

  33. 33.

    Thurow, L.C.: Analyzing the American income distribution. Papers and Proceedings, Am. Econ. Assoc. 60, 261–269 (1970)

  34. 34.

    Topel, R.J.: Regional labor markets and the determinants of wage inequality. Am. Econ. Rev. 84, 17–22 (1994)

    Google Scholar 

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Correspondence to James B. McDonald.

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Dastrup, S.R., Hartshorn, R. & McDonald, J.B. The impact of taxes and transfer payments on the distribution of income: A parametric comparison. J Econ Inequal 5, 353–369 (2007).

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Key words

  • distribution of income
  • Gini coefficient
  • generalized beta
  • Dagum
  • Singh–Madalla