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Bayesian Assessment of Lorenz and Stochastic Dominance in Income Distributions

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  • Duangkamon Chotikapanich
  • William E. Griffiths

Abstract

Hypothesis tests for dominance in income distributions has received considerable attention in recent literature. See, for example, Barrett and Donald (2003), Davidson and Duclos (2000) and references therein. Such tests are useful for assessing progress towards eliminating poverty and for evaluating the effectiveness of various policy initiatives directed towards welfare improvement. To date the focus in the literature has been on sampling theory tests. Such tests can be set up in various ways, with dominance as the null or alternative hypothesis, and with dominance in either direction (X dominates Y or Y dominates X). The result of a test is expressed as rejection of, or failure to reject, a null hypothesis. In this paper we develop and apply Bayesian methods of inference to problems of Lorenz and stochastic dominance. The result from a comparison of two income distributions is reported in terms of the posterior probabilities for each of the three possible outcomes: (a) X dominates Y, (b) Y dominates X, and (c) neither X nor Y is dominant. Reporting results about uncertain outcomes in terms of probabilities has the advantage of being more informative than a simple reject / do-not-reject outcome. Whether a probability is sufficiently high or low for a policy maker to take a particular action is then a decision for that policy maker. The methodology is applied to data for Canada from the Family Expenditure Survey for the years 1978 and 1986. We assess the likelihood of dominance from one time period to the next. Two alternative assumptions are made about the income distributions –Dagum and Singh-Maddala – and in each case the posterior probability of dominance is given by the proportion of times a relevant parameter inequality is satisfied by the posterior observations generated by Markov chain Monte Carlo.

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Bibliographic Info

Paper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 960.

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Length: 36 pages
Date of creation: 2006
Date of revision:
Handle: RePEc:mlb:wpaper:960

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Keywords: Bayesian; Income Distributions; Lorenz;

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References

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  1. Chotikapanich, D. & Griffiths, W.E. & Rao, D.S.P., 2001. "Averaging Income Distributions," Department of Economics - Working Papers Series 798, The University of Melbourne.
  2. Y.K. Tse & Xibin Zhang, 2003. "A Monte Carlo Investigation of Some Tests for Stochastic Dominance," Monash Econometrics and Business Statistics Working Papers 7/03, Monash University, Department of Econometrics and Business Statistics.
  3. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 133-152.
  4. Linton, Oliver & Maasoumi, Esfandiar & Whang, Yoon-Jae, 2003. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," SFB 373 Discussion Papers 2003,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  5. DAVIDSON, Russell & DUCLOS, Jean-Yves, 1995. "Statistical Inference for the Measurement of the Incidences of Taxes and Transfers," Cahiers de recherche 9521, Université Laval - Département d'économique.
  6. Klonner, Stefan, 2000. "The first-order stochastic dominance ordering of the Singh-Maddala distribution," Economics Letters, Elsevier, vol. 69(2), pages 123-128, November.
  7. Valentino Dardanoni & Antonio Forcina, 1999. "Inference for Lorenz curve orderings," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 49-75.
  8. Barrett, Garry F. & Donald, Stephen G., 2009. "Statistical Inference with Generalized Gini Indices of Inequality, Poverty, and Welfare," Journal of Business & Economic Statistics, American Statistical Association, vol. 27, pages 1-17.
  9. Kleiber, Christian, 1996. "Dagum vs. Singh-Maddala income distributions," Economics Letters, Elsevier, vol. 53(3), pages 265-268, December.
  10. Stephen G. Donald & Garry F. Barrett, 2004. "Consistent Nonparametric Tests for Lorenz Dominance," Econometric Society 2004 Australasian Meetings 321, Econometric Society.
  11. Hasegawa, Hikaru & Kozumi, Hideo, 2003. "Estimation of Lorenz curves: a Bayesian nonparametric approach," Journal of Econometrics, Elsevier, vol. 115(2), pages 277-291, August.
  12. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
  13. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-93, September.
  14. Griffiths, William E & Chotikapanich, Duangkamon, 1997. "Bayesian Methodology for Imposing Inequality Constraints on a Linear Expenditure System with Demographic Factors," Australian Economic Papers, Wiley Blackwell, vol. 36(69), pages 321-41, December.
  15. Frank A Cowell, 1996. "Estimation of Inequality Indices," STICERD - Distributional Analysis Research Programme Papers 25, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  16. Duangkamon Chotikapanich & John Creedy, 2004. "The Atkinson Inequality Measure and its Sampling Properties: Bayesian and Classical Approaches," Australian Economic Papers, Wiley Blackwell, vol. 43(3), pages 302-314, 09.
  17. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
  18. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-63, May.
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Cited by:
  1. Duangkamon Chotikapanich & William E Griffiths, 2008. "Estimating Income Distributions Using a Mixture of Gamma Densities," Department of Economics - Working Papers Series 1034, The University of Melbourne.

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