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Confidence Sets for Inequality Measures: Fieller-Type Methods

In: Productivity and Inequality

Author

Listed:
  • Jean-Marie Dufour

    (McGill University, Centre interuniversitaire de recherche en analyse des organisations (CIRANO), and Centre interuniversitaire de recherche en économie quantitative (CIREQ))

  • Emmanuel Flachaire

    (Aix-Marseille Université)

  • Lynda Khalaf

    (Centre interuniversitaire de recherche en économie quantitative (CIREQ), Carleton University
    Université Laval)

  • Abdallah Zalghout

    (Carleton University)

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.

Suggested Citation

  • Jean-Marie Dufour & Emmanuel Flachaire & Lynda Khalaf & Abdallah Zalghout, 2018. "Confidence Sets for Inequality Measures: Fieller-Type Methods," Springer Proceedings in Business and Economics, in: William H. Greene & Lynda Khalaf & Paul Makdissi & Robin C. Sickles & Michael Veall & Marcel-Cristia (ed.), Productivity and Inequality, pages 143-155, Springer.
    • Handle: RePEc:spr:prbchp:978-3-319-68678-3_6
    DOI: 10.1007/978-3-319-68678-3_6
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    Cited by:

    1. Jean-Marie Dufour & Emmanuel Flachaire & Lynda Khalaf & Abdallah Zalghout, 2020. "Identification-robust Inequality Analysis," CIRANO Working Papers 2020s-23, CIRANO.

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