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Multidimensional Poverty Frontiers: Parametric Aggregators Based on Nonparametric Distributions

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  • Esfandiar Maasoumi
  • Jeffrey S. Racine

Abstract

We propose a new technique for the estimation of multidimensional evaluation functions. Technical advances allow nonparametric inference on the joint distribution of continuous and discrete indicators of well-being, such as income and health, conditional on joint values of other continuous and discrete attributes, such as education and geographical groupings. In a multiattribute setting, "quantiles" are "frontiers" that define equivalent sets of covariate values. We identify these frontiers nonparametrically at first. Then we suggest "parametrically equivalent" characterizations of these frontiers that reveal likely, but different, weights for and substitutions between different attributes for different groups, and at different quantiles. These estimated parametric functionals are "ideal" in a certain sense which we make clear. They correspond directly to measures of aggregate well-being popularized in the earliest multidimensional inequality measures in Maasoumi (1986). This new approach resolves a classic problem of assigning weights to dimensions of well-being, as well as empirically incorporating the key component in multidimensional analysis, the relationship between the attributes. It introduces a new way to robust estimation of "quantile frontiers", allowing "complete" assessments, such as multidimensional poverty measurements. We discover massive heterogeneity in individual evaluation functions. This leads us to perform robust, weak uniform rankings as afforded by nonparametric tests for stochastic dominance. A demonstration is provided based on the Indonesian data analyzed for multidimensional poverty in Maasoumi & Lugo (2008).

Suggested Citation

  • Esfandiar Maasoumi & Jeffrey S. Racine, 2013. "Multidimensional Poverty Frontiers: Parametric Aggregators Based on Nonparametric Distributions," Department of Economics Working Papers 2013-07, McMaster University.
  • Handle: RePEc:mcm:deptwp:2013-07
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    File URL: http://socserv.mcmaster.ca/econ/rsrch/papers/archive/2013-07.pdf
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    1. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, number 9780521715348, December.
    2. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    3. Jean-Yves Duclos & David E. Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Poverty Comparisons," Economic Journal, Royal Economic Society, vol. 116(514), pages 943-968, October.
    4. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Oxford University Press, vol. 49(2), pages 183-201.
    5. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
    6. Maasoumi, Esfandiar & Lugo, Maria, 2006. "The Information Basis of Multivariate Poverty Assessments," Departmental Working Papers 0603, Southern Methodist University, Department of Economics.
    7. Anand, Paul & Krishnakumar, Jaya & Tran, Ngoc Bich, 2011. "Measuring welfare: Latent variable models for happiness and capabilities in the presence of unobservable heterogeneity," Journal of Public Economics, Elsevier, pages 205-215.
    8. Koen Decancq & María Ana Lugo, 2013. "Weights in Multidimensional Indices of Wellbeing: An Overview," Econometric Reviews, Taylor & Francis Journals, pages 7-34.
    9. François Bourguignon & Satya Chakravarty, 2003. "The Measurement of Multidimensional Poverty," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(1), pages 25-49, April.
    10. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355, June.
    11. Jean-Yves Duclos & David E. Sahn & Stephen D. Younger, 2010. "Partial Multidimensional Inequality Orderings," Cahiers de recherche 1003, CIRPEE.
    12. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    13. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-997, July.
    14. Gries, Thomas & Naudé, Wim, 2011. "Entrepreneurship and human development: A capability approach," Journal of Public Economics, Elsevier, vol. 95(3), pages 216-224.
    15. Maasoumi, Esfandiar, 1989. "Continuously distributed attributes and measures of multivariate inequality," Journal of Econometrics, Elsevier, vol. 42(1), pages 131-144, September.
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