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 procedureÂ with an application to regional inequality measurement in Côte d'Ivoire.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Frank Cowell, 1998.
"Measurement of inequality,"
LSE Research Online Documents on Economics
2084, London School of Economics and Political Science, LSE Library.
- Davidson, R. & Duclos, J.Y., 1995.
"Statistical Inference for the Measurement of the Incidence of Taxes and Transfers,"
9521, Laval - Recherche en Politique Economique.
- Russell Davidson & Jean-Yves Duclos, 1997. "Statistical Inference for the Measurement of the Incidence of Taxes and Transfers," Econometrica, Econometric Society, vol. 65(6), pages 1453-1466, November.
- Davidson, R. & Duclos, J.Y., 1995. "Statistical Inference for the Measurement of the Incidence of Taxes and Transfers," G.R.E.Q.A.M. 95a30, Universite Aix-Marseille III.
- DAVIDSON, Russell & DUCLOS, Jean-Yves, 1995. "Statistical Inference for the Measurement of the Incidences of Taxes and Transfers," Cahiers de recherche 9521, Université Laval - Département d'économique.
- Russell Davidson & Emmanuel Flachaire, 2007.
"Asymptotic and bootstrap inference for inequality and poverty measures,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
- Davidson, Russell & Flachaire, Emmanuel, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," Journal of Econometrics, Elsevier, vol. 141(1), pages 141-166, November.
- Russell Davidson & Emmanuel Flachaire, 2006. "Asymptotic And Bootstrap Inference For Inequality And Poverty Measures," Departmental Working Papers 2005-06, McGill University, Department of Economics.
- Russell Davidson & Emmanuel Flachaire, 2004. "Asymptotic and bootstrap inference for inequality and poverty measures," Cahiers de la Maison des Sciences Economiques v04100, Université Panthéon-Sorbonne (Paris 1).
- Jeffrey A. Mills & Sourushe Zandvakili, 1999.
"Statistical Inference via Bootstrapping for Measures of Inequality,"
- Mills, Jeffrey A & Zandvakili, Sourushe, 1997. "Statistical Inference via Bootstrapping for Measures of Inequality," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(2), pages 133-50, March-Apr.
- Marsh, Patrick, 2004. "Transformations For Multivariate Statistics," Econometric Theory, Cambridge University Press, vol. 20(05), pages 963-987, October.
- Schluter, Christian & Trede, Mark, 2002. "Tails of Lorenz curves," Journal of Econometrics, Elsevier, vol. 109(1), pages 151-166, July.
- Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
- Thistle, Paul D, 1990. "Large Sample Properties of Two Inequality Indices," Econometrica, Econometric Society, vol. 58(3), pages 725-28, May.
- Kloek, Teun & van Dijk, Herman K., 1978. "Efficient estimation of income distribution parameters," Journal of Econometrics, Elsevier, vol. 8(1), pages 61-74, August.
- McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-63, May.
- Frank A. Cowell, 1980. "On the Structure of Additive Inequality Measures," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 521-531.
- Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-70, September.
- Cowell, Frank A., 1989. "Sampling variance and decomposable inequality measures," Journal of Econometrics, Elsevier, vol. 42(1), pages 27-41, September.
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:150:y:2009:i:1:p:16-29. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.