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

Ramses Abul Naga* (Corresponding Author), Christopher Stapenhurst, Gaston Yalonetzky

*Corresponding author for this work

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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.
Original languageEnglish
Article number8
Number of pages15
Issue number1
Publication statusPublished - 26 Feb 2020

Bibliographical note

Funding: This research received no external funding.
Acknowledgments: We are grateful to three anonymous referees, Karim Abadir, Martin Biewen and Emmanuel Flachaire for helpful comments and suggestions. The paper was written in part while Abul Naga was a visitor at Aix-Marseille University. The author wishes to thank the Iméra Institute of Advanced Studies and the Aix-Marseille School of Economics for their hospitality.

Author Contributions: Conceptualization, R.A.N., C.S. and G.Y.; methodology, R.A.N., C.S. and G.Y.; software, R.A.N., C.S. and G.Y.; formal analysis, R.A.N., C.S. and G.Y.; writing–original draft preparation, R.A.N., C.S. and G.Y.; writing–review and editing, R.A.N., C.S. and G.Y.; visualization, R.A.N., C.S. and G.Y. All authors have read and agreed to the published version of the manuscript.


  • measurement of inequality
  • ordered response data
  • multinomial sampling
  • large sample distributions
  • ; Studentized bootstrap tests
  • Monte Carlo experiments
  • Large sample distributions
  • Measurement of inequality
  • Ordered response data
  • Studentized bootstrap tests
  • Monte carlo experiments
  • Multinomial sampling


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