K.J. van Garderen
- Edgeworth expansions and normalizing transforms for inequality measures
- Journal of Econometrics
- Volume | Issue number
- 150 | 1
- Pages (from-to)
- Number of pages
- Document type
- Faculty of Economics and Business (FEB)
- Amsterdam School of Economics Research Institute (ASE-RI)
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
JEL classification codes: C10; C14; D31; D63; I32
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