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Edgeworth expansions and normalizing transforms for inequality measures

Edgeworth expansions and normalizing transforms for inequality measures
Edgeworth expansions and normalizing transforms for inequality measures
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.
generalized entropy inequality measures, higher- order expansions, normalizing transformations
0304-4076
16-29
Schluter, Christian
ae043254-4cc4-48aa-abad-56a36554de2b
van Garderen, Kees Jan
f43a122c-19b8-4ba8-a6c9-18815a37a32e
Schluter, Christian
ae043254-4cc4-48aa-abad-56a36554de2b
van Garderen, Kees Jan
f43a122c-19b8-4ba8-a6c9-18815a37a32e

Schluter, Christian and van Garderen, Kees Jan (2009) Edgeworth expansions and normalizing transforms for inequality measures. Journal of Econometrics, 150 (1), 16-29. (doi:10.1016/j.jeconom.2008.12.022).

Record type: Article

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.

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Published date: May 2009
Keywords: generalized entropy inequality measures, higher- order expansions, normalizing transformations
Organisations: Economics

Identifiers

Local EPrints ID: 153067
URI: http://eprints.soton.ac.uk/id/eprint/153067
ISSN: 0304-4076
PURE UUID: b3368575-b9bc-4c82-be4e-f12b3cffe94d

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Date deposited: 18 May 2010 11:04
Last modified: 14 Mar 2024 01:26

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Author: Kees Jan van Garderen

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