Edgeworth expansions and normalizing transforms for inequality measures

Christian Schluter and Kees Jan van Garderen ()

Journal of Econometrics, 2009, vol. 150, issue 1, pages 16-29

Abstract: Finite sample distributions of studentized inequality measures differ substantially from their asymptotic normal distribution in terms of location and skewness. We study these aspects formally by deriving the second-order expansion of the first and third cumulant of the studentized inequality measure. We state distribution-free expressions for the bias and skewness coefficients. In the second part we improve over first-order theory by deriving Edgeworth expansions and normalizing transforms. These normalizing transforms are designed to eliminate the second-order term in the distributional expansion of the studentized transform and converge to the Gaussian limit at rate O(n-1). This leads to improved confidence intervals and applying a subsequent bootstrap leads to a further improvement to order O(n-3/2). We illustrate our procedure with an application to regional inequality measurement in Côte d'Ivoire.

Keywords: Generalized; Entropy; inequality; measures; Higher-; order; expansions; Normalizing; transformations (search for similar items in EconPapers)
Date: 2009

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Persistent link: http://EconPapers.repec.org/RePEc:eee:econom:v:150:y:2009:i:1:p:16-29

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