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Partial Identification of Poverty Measures with Contaminated Data

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Abstract

Much of the statistical analysis for poverty measurement regards the data employed to estimate poverty statistics as error-free observations. However, it is amply recognized that surveys responses are not perfectly reliable and that the quality of the data is often poor, especially for developing countries. Robust estimation addresses this problem by searching for poverty measures that are not highly sensitive to errors in the data. However, given the assumptions of robust estimation, the rationale for point estimation is not apparent. In the present study we tackle the problem by implementing a different strategy. Since a particular poverty measure is not point identified under the assumptions of robust estimation and some outcomes that are possible ex ante are ruled out ex post, we apply a fully non-parametric method to show that for the family of additively separable poverty measures it is possible to find identification regions under very mild assumptions. We investigate the sensitivity of the bounds of these identification regions to contamination for the class of Pa poverty measures, showing that there exists an a-ordering for the elasticities of these bounds with respect to the amount of contamination. We apply two conceptually different confidence intervals for partially identified poverty measures: the first type of confidence interval covers the entire identification region, while the other covers each element of the identification region with fixed probability. The methodology developed in the paper is applied to analyze rural poverty in Mexico

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