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A Solution to Aggregation and an Application to Multidimensional "Well-being" Frontiers

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  • Esfandiar Maasoumi
  • Jeffrey S. Racine

Abstract

We propose a new technique for identification and estimation of aggregation functions in multidimensional evaluations and multiple indicator settings. These functions may represent "latent" objects. They occur in many different contexts, for instance in propensity scores, multivariate measures of well-being and the related analysis of inequality and poverty, and in equivalence scales. 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 weights for, and substitutions between, different attributes for different groups, and at different quantiles. These estimated parametric functionals are "ideal" aggregators 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 multiple indicators such as dimensions of well-being, as well as empirically incorporating the key component in multidimensional analysis, the relationship between the indicators. It introduces a new way for robust estimation of "quantile frontiers," allowing "complete" assessments, such as multidimensional poverty measurements. In our substantive application, we discover extensive heterogeneity in individual evaluation functions. This leads us to perform robust, weak uniform rankings as afforded by tests for multivariate stochastic dominance. A demonstration is provided based on the Indonesian data analyzed for multidimensional poverty in Maasoumi & Lugo (2008).

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Paper provided by Department of Economics, Emory University (Atlanta) in its series Emory Economics with number 1306.

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Date of creation: Aug 2013
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Handle: RePEc:emo:wp2003:1306

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  1. Koen Decancq & María Ana Lugo, 2013. "Weights in Multidimensional Indices of Wellbeing: An Overview," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 7-34, January.
  2. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2003. "Consistent testing for stochastic dominance under general sampling schemes," LSE Research Online Documents on Economics 2208, London School of Economics and Political Science, LSE Library.
  3. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, number 9780521887427.
  4. Duclos, Jean-Yves & Sahn, David E. & Younger, Stephen D., 2011. "Partial multidimensional inequality orderings," Journal of Public Economics, Elsevier, vol. 95(3), pages 225-238.
  5. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-97, July.
  6. Esfandiar Maasoumi & Maria Ana Lugo, 2008. "The Information Basis of Multivariate Poverty Assessments," Emory Economics 0804, Department of Economics, Emory University (Atlanta).
  7. Bourguignon, F. & Chakravarty, S.R., 1998. "The Measurement of Multidimensional Poverty," DELTA Working Papers 98-12, DELTA (Ecole normale supérieure).
  8. Maasoumi, Esfandiar, 1989. "Continuously distributed attributes and measures of multivariate inequality," Journal of Econometrics, Elsevier, vol. 42(1), pages 131-144, September.
  9. Atkinson, Anthony B & Bourguignon, Francois, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Wiley Blackwell, vol. 49(2), pages 183-201, April.
  10. Duclos, Jean-Yves & Sahn, David & Younger, Stephen D., 2001. "Robust Multidimensional Poverty Comparisons," Cahiers de recherche 0115, Université Laval - Département d'économique.
  11. 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.
  12. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  13. 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.
  14. Tristen Hayfield & Jeffrey S. Racine, . "Nonparametric Econometrics: The np Package," Journal of Statistical Software, American Statistical Association, vol. 27(i05).
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