IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Reliable inference for the GINI Index

  • Russell Davidson

    ()

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579, CIREG - Centre interuniversitaire de recherche en économie quantitative - Université de Montréal, Department of Economics, McGill University - McGill University)

Although attention has been given to obtaining reliable standard errors for the plugin estimator of the Gini index, all standard errors suggested until now are either complicated or quite unreliable. An approximation is derived for the estimator by which it is expressed as a sum of IID random variables. This approximation allows us to develop a reliable standard error that is simple to compute. A simple but effective bias correction is also derived. The quality of inference based on the approximation is checked in a number of simulation experiments, and is found to be very good unless the tail of the underlying distribution is heavy. Bootstrap methods are presented which alleviate this problem except in cases in which the variance is very large or fails to exist. Similar methods can be used to find reliable standard errors of other indices which are not simply linear functionals of the distribution function, such as Sen's poverty index and its modification known as the Sen-Shorrocks-Thon index.

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.

File URL: http://halshs.archives-ouvertes.fr/docs/00/44/35/53/PDF/DT2009-37.pdf
Download Restriction: no

Paper provided by HAL in its series Working Papers with number halshs-00443553.

as
in new window

Length:
Date of creation: 30 Dec 2009
Date of revision:
Handle: RePEc:hal:wpaper:halshs-00443553
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00443553/en/
Contact details of provider: Web page: http://hal.archives-ouvertes.fr/

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.:

as in new window
  1. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
  2. Tomson Ogwang, 2006. "A Cautionary Note on Estimating the Standard Error of the Gini Index of Inequality: Comment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(3), pages 391-393, 06.
  3. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-30, September.
  4. David E. A. Giles, 2002. "Calculating a Standard Error for the Gini Coefficient: Some Further Results," Econometrics Working Papers 0202, Department of Economics, University of Victoria.
  5. Bishop, John A & Formby, John P & Zheng, Buhong, 1997. "Statistical Inference and the Sen Index of Poverty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(2), pages 381-87, May.
  6. Tomson Ogwang, 2004. "Calculating a Standard Error for the Gini Coefficient: Some Further Results: Reply," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(3), pages 435-437, 07.
  7. Sandstrom, Arne & Wretman, Jan H & Walden, Bertil, 1988. "Variance Estimators of the Gini Coefficient--Probability Sampling," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 113-19, January.
  8. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
  9. Bhattacharya, Debopam, 2007. "Inference on inequality from household survey data," Journal of Econometrics, Elsevier, vol. 137(2), pages 674-707, April.
  10. David E. A. Giles, 2006. "A Cautionary Note on Estimating the Standard Error of the Gini Index of Inequality: Comment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(3), pages 395-396, 06.
  11. Jeffrey A. Mills & Sourushe Zandvakili, 1999. "Statistical Inference via Bootstrapping for Measures of Inequality," Macroeconomics 9902003, EconWPA.
  12. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March.
  13. Reza Modarres & Joseph L. Gastwirth, 2006. "A Cautionary Note on Estimating the Standard Error of the Gini Index of Inequality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(3), pages 385-390, 06.
  14. George Deltas, 2003. "The Small-Sample Bias of the Gini Coefficient: Results and Implications for Empirical Research," The Review of Economics and Statistics, MIT Press, vol. 85(1), pages 226-234, February.
  15. Ogwang, Tomson, 2000. " A Convenient Method of Computing the Gini Index and Its Standard Error," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(1), pages 123-29, February.
  16. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
  17. Kuan Xu, 2007. "U-Statistics and Their Asymptotic Results for Some Inequality and Poverty Measures," Econometric Reviews, Taylor & Francis Journals, vol. 26(5), pages 567-577.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:halshs-00443553. 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: (CCSD)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.