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Confidence Sets for Inequality Measures: Fieller-Type Methods

Jean-Marie Dufour 1 Emmanuel Flachaire 2 Lynda Khalaf Abdallah Zalghout
1 McGill University = Université McGill [Montréal, Canada]
2 AMSE - Aix-Marseille Sciences Economiques
Abstract : Asymptotic and bootstrap inference methods for inequality indices are for the most part unreliable due to the complex empirical features of the underlying distributions. In this paper, we introduce a Fieller-type method for the Theil Index and assess its finite-sample properties by a Monte Carlo simulation study. The fact that almost all inequality indices can be written as a ratio of functions of moments and that a Fieller-type method does not suffer from weak identification as the denominator approaches zero, makes it an appealing alternative to the available inference methods. Our simulation results exhibit several cases where a Fieller-type method improves coverage. This occurs in particular when the Data Generating Process (DGP) follows a finite mixture of distributions, which reflects irregularities arising from low observations (close to zero) as opposed to large (right-tail) observations. Designs that forgo the interconnected effects of both boundaries provide possibly misleading finite-sample evidence. This suggests a useful prescription for simulation studies in this literature.
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https://hal-amu.archives-ouvertes.fr/hal-01986513
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Submitted on : Friday, January 18, 2019 - 6:19:27 PM
Last modification on : Wednesday, November 3, 2021 - 9:43:48 AM

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  • HAL Id : hal-01986513, version 1

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UNIV-AMU | CNRS | EHESS | EC-MARSEILLE | AMSE

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Jean-Marie Dufour, Emmanuel Flachaire, Lynda Khalaf, Abdallah Zalghout. Confidence Sets for Inequality Measures: Fieller-Type Methods. Productivity and Inequality, Springer International Publishing, pp.143-155, 2018, 978-3-319-68678-3. ⟨hal-01986513⟩

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