Confidence Sets for Inequality Measures: Fieller-Type Methods

Jean-Marie Dufour (), Emmanuel Flachaire, Lynda Khalaf and Abdallah Zalghout ()
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Jean-Marie Dufour: McGill University, Centre interuniversitaire de recherche en analyse des organisations (CIRANO), and Centre interuniversitaire de recherche en économie quantitative (CIREQ)
Abdallah Zalghout: Carleton University

A chapter in Productivity and Inequality, 2018, pp 143-155 from Springer

Abstract: 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.

Keywords: Inequality measures; Fieller-type confidence set; Delta method; Singh-Maddala distribution; Gamma distribution; Mixture (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/978-3-319-68678-3_6

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