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Empirical Likelihood for Robust Poverty Comparisons

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  • Tabri, Rami V.

Abstract

Robust rankings of poverty are ones that do not rely on a single poverty measure with a single poverty line. Mathematically, such robust rankings of two populations specifies a continuum of unconditional moment inequality constraints. If these constraints could be imposed in estimation then a statistical test can be performed using an empirical likelihood-ratio (ELR) test, which is a nonparametric version of the likelihood-ratio test in parametric inference. While these constraints cannot be imposed exactly, we show that these can be imposed approximately with the approximation disappearing asymptotically. We then propose a bootstrap test procedure that implements the resulting approximate ELR test. The paper derives the asymptotic properties of this test, presents Monte Carlo experiments that show improved power compared to existing tests such as that of Linton et al. (2010), and provides an empirical illustration to Canadian income distribution data. More generally, the bootstrap test procedure provides a uniformly asymptotically valid nonparametric test of a continuum of unconditional moment inequality constraints. The proofs exploit the fact that the constrained optimization problem is a concave semi-infinite programming optimization problem.

Suggested Citation

  • Tabri, Rami V., 2015. "Empirical Likelihood for Robust Poverty Comparisons," Working Papers 2015-02, University of Sydney, School of Economics, revised May 2015.
    • Handle: RePEc:syd:wpaper:2015-02
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    Cited by:

    1. David Lander & David Gunawan & William Griffiths & Duangkamon Chotikapanich, 2020. "Bayesian assessment of Lorenz and stochastic dominance," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(2), pages 767-799, May.
    2. Lok, Thomas M. & Tabri, Rami V., 2015. "An Improved Bootstrap Test For Restricted Stochastic Dominance," Working Papers 2015-15, University of Sydney, School of Economics, revised Aug 2019.
    3. 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.

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    Keywords

    Empirical Likelihood; Robust Poverty Comparison; Continuum of Moment Inequality Con-straints; Bootstrap;
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