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Bayesian Assessment of Lorenz and Stochastic Dominance in Income Distributions

Author

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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.

Suggested Citation

  • Duangkamon Chotikapanich & William E. Griffiths, 2006. "Bayesian Assessment of Lorenz and Stochastic Dominance in Income Distributions," Department of Economics - Working Papers Series 960, The University of Melbourne.
  • Handle: RePEc:mlb:wpaper:960
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    File URL: http://www.economics.unimelb.edu.au/downloads/wpapers-06/960.pdf
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    References listed on IDEAS

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    1. 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.
    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. 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 321-341, December.
    4. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2005. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 735-765.
    5. Russell Davidson & Jean-Yves Duclos, 1997. "Statistical Inference for the Measurement of the Incidence of Taxes and Transfers," Econometrica, Econometric Society, vol. 65(6), pages 1453-1466, November.
    6. 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.
    7. 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.
    8. William E. Griffiths & Duangkamon Chotikapanich & D. S. Prasada Rao, 2005. "Averaging Income Distributions," Bulletin of Economic Research, Wiley Blackwell, vol. 57(4), pages 347-367, October.
    9. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
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    11. Garry F. Barrett & Stephen G. Donald & Debopam Bhattacharya, 2014. "Consistent Nonparametric Tests for Lorenz Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 1-13, January.
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    14. Kleiber, Christian, 1996. "Dagum vs. Singh-Maddala income distributions," Economics Letters, Elsevier, vol. 53(3), pages 265-268, December.
    15. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-1193, September.
    16. Klonner, Stefan, 2000. "The first-order stochastic dominance ordering of the Singh-Maddala distribution," Economics Letters, Elsevier, vol. 69(2), pages 123-128, November.
    17. 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.
    18. 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, September.
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    Cited by:

    1. Kleiber, Christian, 2007. "A Guide to the Dagum Distributions," Working papers 2007/23, Faculty of Business and Economics - University of Basel.
    2. 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.
    3. repec:eee:ecolet:v:162:y:2018:i:c:p:76-80 is not listed on IDEAS
    4. David Lander & David Gunawan & William E. Griffiths & Duangkamon Chotikapanich, 2016. "Bayesian Assessment of Lorenz and Stochastic Dominance Using a Mixture of Gamma Densities," Department of Economics - Working Papers Series 2023, The University of Melbourne.
    5. David Lander & David Gunawan & William Griffiths & Duangkamon Chotikapanich, 2017. "Bayesian Assessment of Lorenz and Stochastic Dominance," Department of Economics - Working Papers Series 2029, The University of Melbourne.
    6. David Lander & David Gunawan & William Griffiths & Duangkamon Chotikapanich, 2017. "Bayesian assessment of Lorenz and stochastic dominance," Monash Econometrics and Business Statistics Working Papers 15/17, Monash University, Department of Econometrics and Business Statistics.

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    Keywords

    Bayesian; Income Distributions; Lorenz;

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