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Asymptotic Versus Bootstrap Inference for Inequality Indices of the Cumulative Distribution Function

Author

Listed:
  • Ramses Abul Naga

    (Business School, University of Aberdeen, Old Aberdeen AB24 3UE, UK)

  • Christopher Stapenhurst

    (Department of Economics, University of Edinburgh, Edinburgh EH8 9AB, UK)

  • Gaston Yalonetzky

    (Business School, University of Leeds, Leeds LS2 9JT, UK)

Abstract

We examine the performance of asymptotic inference as well as bootstrap tests for the Alphabeta and Kobus–Miłoś family of inequality indices for ordered response data. We use Monte Carlo experiments to compare the empirical size and statistical power of asymptotic inference and the Studentized bootstrap test. In a broad variety of settings, both tests are found to have similar rejection probabilities of true null hypotheses, and similar power. Nonetheless, the asymptotic test remains correctly sized in the presence of certain types of severe class imbalances exhibiting very low or very high levels of inequality, whereas the bootstrap test becomes somewhat oversized in these extreme settings.

Suggested Citation

  • Ramses Abul Naga & Christopher Stapenhurst & Gaston Yalonetzky, 2020. "Asymptotic Versus Bootstrap Inference for Inequality Indices of the Cumulative Distribution Function," Econometrics, MDPI, vol. 8(1), pages 1-15, February.
    • Handle: RePEc:gam:jecnmx:v:8:y:2020:i:1:p:8-:d:325486
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    References listed on IDEAS

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    1. Abul Naga, Ramses H. & Stapenhurst, Christopher, 2015. "Estimation of inequality indices of the cumulative distribution function," Economics Letters, Elsevier, vol. 130(C), pages 109-112.
    2. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
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    5. Davidson, Russell & Flachaire, Emmanuel, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," Journal of Econometrics, Elsevier, vol. 141(1), pages 141-166, November.
    6. Kobus, Martyna & Miłoś, Piotr, 2012. "Inequality decomposition by population subgroups for ordinal data," Journal of Health Economics, Elsevier, vol. 31(1), pages 15-21.
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    11. Gaston Yalonetzky, 2013. "Stochastic Dominance with Ordinal Variables: Conditions and a Test," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 126-163, January.
    12. Russell Davidson, 2007. "Bootstrapping Econometric Models," Departmental Working Papers 2007-13, McGill University, Department of Economics.
    13. Jones, Andrew M. & Rice, Nigel & Robone, Silvana & Dias, Pedro Rosa, 2011. "Inequality and polarisation in health systems' responsiveness: A cross-country analysis," Journal of Health Economics, Elsevier, vol. 30(4), pages 616-625, July.
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    Cited by:

    1. Ramses H. Abul Naga & Christopher Stapenhurst & Gaston Yalonetzky, 2024. "Inferring inequality: Testing for median-preserving spreads in ordinal data," Econometric Reviews, Taylor & Francis Journals, vol. 43(2-4), pages 156-174, April.
    2. Kobus, Martyna & Kurek, Radosław, 2023. "Measuring inequality in the joint distribution of socioeconomic status and health," Economics Letters, Elsevier, vol. 226(C).

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