Advanced Search
MyIDEAS: Login to save this paper or follow this series

Reliable Inference For The Gini Index

Contents:

Author Info

  • 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)

Abstract

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-Thonindex.

Download Info

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/00/35/38/56/PDF/2007-23.pdf
Download Restriction: no

Bibliographic Info

Paper provided by HAL in its series Working Papers with number halshs-00353856.

as in new window
Length:
Date of creation: 01 Nov 2007
Date of revision:
Handle: RePEc:hal:wpaper:halshs-00353856

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00353856/en/
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/

Related research

Keywords: Gini index; delta method; asymptotic inference; jackknife; boot-strap;

Other versions of this item:

References

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. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, Econometric Society, vol. 63(5), pages 1225-30, September.
  2. Russell Davidson & James G. MacKinnon, 2001. "Bootstrap Tests: How Many Bootstraps?," Working Papers, Queen's University, Department of Economics 1036, Queen's University, Department of Economics.
  3. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, Econometric Society, vol. 44(2), pages 219-31, March.
  4. 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.
  5. Bhattacharya, Debopam, 2007. "Inference on inequality from household survey data," Journal of Econometrics, Elsevier, Elsevier, vol. 137(2), pages 674-707, April.
  6. David E. A. Giles, 2002. "Calculating a Standard Error for the Gini Coefficient: Some Further Results," Econometrics Working Papers, Department of Economics, University of Victoria 0202, Department of Economics, University of Victoria.
  7. 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.
  8. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198281931, October.
  9. Sandstrom, Arne & Wretman, Jan H & Walden, Bertil, 1988. "Variance Estimators of the Gini Coefficient--Probability Sampling," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 6(1), pages 113-19, January.
  10. Kuan Xu, 2007. "U-Statistics and Their Asymptotic Results for Some Inequality and Poverty Measures," Department of Economics at Dalhousie University working papers archive, Dalhousie, Department of Economics senletters5, Dalhousie, Department of Economics.
  11. 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.
  12. Jeffrey A. Mills & Sourushe Zandvakili, 1999. "Statistical Inference via Bootstrapping for Measures of Inequality," Macroeconomics, EconWPA 9902003, EconWPA.
  13. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(2), pages 381-87, May.
  14. 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.
  15. 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.
  16. 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.
  17. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, Elsevier, vol. 22(1), pages 67-86, February.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Judith A. Clarke & Nilanjana Roy, 2010. "On Statistical Inference for Inequality Measures Calculated from Complex Survey Data," Econometrics Working Papers, Department of Economics, University of Victoria 1002, Department of Economics, University of Victoria.
  2. Stéphane Mussard & Patrick Richard, 2012. "Linking Yitzhaki's and Dagum's Gini decompositions," Applied Economics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 44(23), pages 2997-3010, August.
  3. Luis Fernando Gamboa & Andrés García-Suaza & Jesús Otero, 2010. "Statistical inference for testing Gini Coefficients: An application for Colombia," ENSAYOS SOBRE POLÍTICA ECONÓMICA, BANCO DE LA REPÚBLICA - ESPE, BANCO DE LA REPÚBLICA - ESPE.
  4. Thomas Demuynck, 2012. "An (almost) unbiased estimator for the S-Gini index," Journal of Economic Inequality, Springer, Springer, vol. 10(1), pages 109-126, March.
  5. Russell Davidson, 2010. "An Agnostic Look at Bayesian Statistics and Econometrics," Review of Economic Analysis, Rimini Centre for Economic Analysis, Rimini Centre for Economic Analysis, vol. 2(2), pages 153-168, June.
  6. Alina Jędrzejczak, 2012. "Estimation of Concentration Measures and Their Standard Errors for Income Distributions in Poland," International Advances in Economic Research, Springer, Springer, vol. 18(3), pages 287-297, August.
  7. William E. Griffiths and Gholamreza Hajargasht, 2012. "GMM Estimation of Mixtures from Grouped Data:," Department of Economics - Working Papers Series, The University of Melbourne 1148, The University of Melbourne.
  8. Judith A. Clarke & Ahmed A. Hoque, 2014. "On Variance Estimation for a Gini Coefficient Estimator Obtained from Complex Survey Data," Econometrics Working Papers, Department of Economics, University of Victoria 1401, Department of Economics, University of Victoria.

Lists

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

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:halshs-00353856. 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.