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

Ramses Abul Naga; Christopher Stapenhurst; Gaston Yalonetzky

doi:10.3390/econometrics8010008

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

Economics

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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.

Original language	English
Article number	8
Number of pages	15
Journal	Econometrics
Volume	8
Issue number	1
DOIs	https://doi.org/10.3390/econometrics8010008
Publication status	Published - 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.

Keywords

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

UN SDGs

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Cite this

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title = "Asymptotic Versus Bootstrap Inference for Inequality Indices of the Cumulative Distribution Function",

abstract = "We examine the performance of asymptotic inference as well as bootstrap tests for the Alphabeta and Kobus–Mi{\l}o{\'s} 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. ",

keywords = "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",

author = "{Abul Naga}, Ramses and Christopher Stapenhurst and Gaston Yalonetzky",

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 Im{\'e}ra 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. ",

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

Abstract

Bibliographical note

Keywords

UN SDGs

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