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Bayesian Inference for TIP curves: An Application to Child Poverty in Germany

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Abstract

TIP curves are cumulative poverty gap curves used for representing the three different aspects of poverty: incidence, intensity and inequality. The paper provides Bayesian inference for TIP curves, linking their expression to a parametric representation of the income distribution using a mixture of lognormal densities. We treat specifically the question of zero-inflated income data and survey weights, which are two important issues in survey analysis. The advantage of the Bayesian approach is that it takes into account all the information contained in the sample and that it provides small sample confidence intervals and tests for TIP dominance. We apply our methodology to evaluate the evolution of child poverty in Germany after 2002, providing thus an update the portrait of child poverty in Germany given in Corak et al. 2008.

Suggested Citation

  • Edwin Fourrier-Nicolai & Michel Lubrano, 2017. "Bayesian Inference for TIP curves: An Application to Child Poverty in Germany," AMSE Working Papers 1710, Aix-Marseille School of Economics, Marseille, France.
  • Handle: RePEc:aim:wpaimx:1710
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    References listed on IDEAS

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    1. Goebel, Jan & Kuchler, Birgit, 2003. "Incidence and Intensity of Smoothed Income Poverty in European Countries," EconStor Open Access Articles, ZBW - German National Library of Economics, pages 357-369.
    2. Russell Davidson & Jean-Yves Duclos, 2013. "Testing for Restricted Stochastic Dominance," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 84-125, January.
    3. Miles Corak & Michael Fertig & Marcus Tamm, 2008. "A Portrait Of Child Poverty In Germany," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 54(4), pages 547-571, December.
    4. Cowell, Frank, 2011. "Measuring Inequality," OUP Catalogue, Oxford University Press, edition 3, number 9780199594047.
    5. Flachaire, Emmanuel & Núñez, Olivier, 2003. "Estimation of income distribution and detection of subpopulations: an explanatory model," DES - Working Papers. Statistics and Econometrics. WS ws030201, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Coral del Río & Javier Ruiz-Castillo, 2001. "TIPs for poverty analysis. The case of Spain, 1980-81 to 1990-91," Investigaciones Economicas, Fundación SEPI, vol. 25(1), pages 63-91, January.
    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. Flachaire, Emmanuel & Nunez, Olivier, 2007. "Estimation of the income distribution and detection of subpopulations: An explanatory model," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3368-3380, April.
    9. Bradbury,Bruce & Jenkins,Stephen P. & Micklewright,John (ed.), 2001. "The Dynamics of Child Poverty in Industrialised Countries," Cambridge Books, Cambridge University Press, number 9780521803106, May.
    10. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-764, July.
    11. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    12. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    13. Gordon Anderson & Maria Pittau & Roberto Zelli, 2014. "Poverty status probability: a new approach to measuring poverty and the progress of the poor," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 12(4), pages 469-488, December.
    14. Stephen P. Jenkins & Christian Schluter, 2003. "Why Are Child Poverty Rates Higher in Britain than in Germany?: A Longitudinal Perspective," Journal of Human Resources, University of Wisconsin Press, vol. 38(2).
    15. Joan R. Rodgers & John L. Rodgers, 1993. "Chronic Poverty in the United States," Journal of Human Resources, University of Wisconsin Press, vol. 28(1), pages 25-54.
    16. Yitzhaki, Shlomo, 1982. "Stochastic Dominance, Mean Variance, and Gini's Mean Difference," American Economic Review, American Economic Association, vol. 72(1), pages 178-185, March.
    17. Jenkins, Stephen P & Lambert, Peter J, 1997. "Three 'I's of Poverty Curves, with an Analysis of UK Poverty Trends," Oxford Economic Papers, Oxford University Press, vol. 49(3), pages 317-327, July.
    18. Kaur, Amarjot & Prakasa Rao, B.L.S. & Singh, Harshinder, 1994. "Testing for Second-Order Stochastic Dominance of Two Distributions," Econometric Theory, Cambridge University Press, vol. 10(05), pages 849-866, December.
    19. Levy, Haim & Kroll, Yoram, 1976. "Stochastic Dominance with Riskless Assets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 11(05), pages 743-777, December.
    20. Bishop, John A & Chakraborti, S & Thistle, Paul D, 1989. "Asymptotically Distribution-Free Statistical Inference for Generalized Lorenz Curves," The Review of Economics and Statistics, MIT Press, vol. 71(4), pages 725-727, November.
    21. Bradbury,Bruce & Jenkins,Stephen P. & Micklewright,John (ed.), 2001. "The Dynamics of Child Poverty in Industrialised Countries," Cambridge Books, Cambridge University Press, number 9780521004923, May.
    22. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 723-735.
    23. Bram Thuysbaert, 2008. "Inference for the measurement of poverty in the presence of a stochastic weighting variable," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(1), pages 33-55, March.
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    More about this item

    Keywords

    Bayesian inference; mixture model; survey weights; zero-inflated model; poverty; Inequality;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty
    • I38 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Government Programs; Provision and Effects of Welfare Programs

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