IDEAS home Printed from https://ideas.repec.org/a/vrs/offsta/v36y2020i2p237-249n2.html
   My bibliography  Save this article

Confidence Intervals of Gini Coefficient Under Unequal Probability Sampling

Author

Listed:
  • Berger Yves G.

    (University of Southampton, Southampton, SO17 1BJ, UK.)

  • Balay İklim Gedik

    (Ankara Yıldırım Beyazıt University, Esenboga Külliyesi Faculty of Business, Esenboğa, Ankara, 06760, Turkey.)

Abstract

We propose an estimator for the Gini coefficient, based on a ratio of means. We show how bootstrap and empirical likelihood can be combined to construct confidence intervals. Our simulation study shows the estimator proposed is usually less biased than customary estimators. The observed coverages of the empirical likelihood confidence interval proposed are also closer to the nominal value.

Suggested Citation

  • Berger Yves G. & Balay İklim Gedik, 2020. "Confidence Intervals of Gini Coefficient Under Unequal Probability Sampling," Journal of Official Statistics, Sciendo, vol. 36(2), pages 237-249, June.
    • Handle: RePEc:vrs:offsta:v:36:y:2020:i:2:p:237-249:n:2
    DOI: 10.2478/jos-2020-0013
    as

    Download full text from publisher

    File URL: https://doi.org/10.2478/jos-2020-0013
    Download Restriction: no
    File URL: https://libkey.io/10.2478/jos-2020-0013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Thibault Gajdos & John Weymark, 2005. "Multidimensional generalized Gini indices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 471-496, October.
    2. Giovanni Maria Giorgi & Chiara Gigliarano, 2017. "The Gini Concentration Index: A Review Of The Inference Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 31(4), pages 1130-1148, September.
    3. Yitzhaki, Shlomo, 1991. "Calculating Jackknife Variance Estimators for Parameters of the Gini Method," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(2), pages 235-239, April.
    4. 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 113-119, January.
    5. 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 133-150, March-Apr.
    6. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 723-735.
    7. 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, June.
    8. W. Sendler, 1979. "On statistical inference in concentration measurement," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 26(1), pages 109-122, December.
    9. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    10. Tomson Ogwang, 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 123-129, February.
    11. Elias Karagiannis & Milorad Kovacevic', 2000. "A Method to Calculate the Jackknife Variance Estimator For the Gini Coefficient," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(1), pages 119-122, February.
    12. repec:bla:obuest:v:62:y:2000:i:1:p:119-22 is not listed on IDEAS
    13. Bhattacharya, Debopam, 2007. "Inference on inequality from household survey data," Journal of Econometrics, Elsevier, vol. 137(2), pages 674-707, April.
    14. Qin, Yongsong & Rao, J.N.K. & Wu, Changbao, 2010. "Empirical likelihood confidence intervals for the Gini measure of income inequality," Economic Modelling, Elsevier, vol. 27(6), pages 1429-1435, November.
    15. Matti Langel & Yves Tillé, 2013. "Variance estimation of the Gini index: revisiting a result several times published," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(2), pages 521-540, 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


    Cited by:

    1. Ziqing Dong & Yves Tillé & Giovanni M. Giorgi & Alessio Guandalini, 2021. "Linearization and variance estimation of the Bonferroni inequality index," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 1008-1029, July.
    2. Encarnación Álvarez-Verdejo & Pablo J. Moya-Fernández & Juan F. Muñoz-Rosas, 2021. "Single Imputation Methods and Confidence Intervals for the Gini Index," Mathematics, MDPI, vol. 9(24), pages 1-20, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Judith A. Clarke & Ahmed A. Hoque, 2014. "On Variance Estimation for a Gini Coefficient Estimator Obtained from Complex Survey Data," Econometrics Working Papers 1401, Department of Economics, University of Victoria.
    2. Wang, Dongliang & Zhao, Yichuan & Gilmore, Dirk W., 2016. "Jackknife empirical likelihood confidence interval for the Gini index," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 289-295.
    3. Xiaofeng Lv & Gupeng Zhang & Guangyu Ren, 2017. "Gini index estimation for lifetime data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 275-304, April.
    4. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 2017. "Bootstrap-calibrated empirical likelihood confidence intervals for the difference between two Gini indexes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(2), pages 195-216, June.
    5. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 2017. "Bootstrap-calibrated empirical likelihood confidence intervals for the difference between two Gini indexes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(2), pages 195-216, June.
    6. Encarnación Álvarez-Verdejo & Pablo J. Moya-Fernández & Juan F. Muñoz-Rosas, 2021. "Single Imputation Methods and Confidence Intervals for the Gini Index," Mathematics, MDPI, vol. 9(24), pages 1-20, December.
    7. Karoly, Lynn & Schröder, Carsten, 2015. "Fast methods for jackknifing inequality indices," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 37(1), pages 125-138.
    8. Mazzi Gian Luigi & Mitchell James & Carausu Florabela, 2021. "Measuring and Communicating the Uncertainty in Official Economic Statistics," Journal of Official Statistics, Sciendo, vol. 37(2), pages 289-316, June.
    9. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    10. 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.
    11. David E. A. Giles, 2004. "Calculating a Standard Error for the Gini Coefficient: Some Further Results," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(3), pages 425-433, July.
    12. Lingsheng Meng & Binzhen Wu & Zhaoguo Zhan, 2016. "Linear regression with an estimated regressor: applications to aggregate indicators of economic development," Empirical Economics, Springer, vol. 50(2), pages 299-316, March.
    13. Ilaria Benedetti & Federico Crescenzi & Tiziana Laureti, 2020. "Measuring Uncertainty for Poverty Indicators at Regional Level: The Case of Mediterranean Countries," Sustainability, MDPI, vol. 12(19), pages 1-19, October.
    14. Ogwang Tomson, 2014. "A Convenient Method of Decomposing the Gini Index by Population Subgroups," Journal of Official Statistics, Sciendo, vol. 30(1), pages 91-105, March.
    15. Pier Luigi Conti & Alberto Iorio & Alessio Guandalini & Daniela Marella & Paola Vicard & Vincenzina Vitale, 2020. "On the estimation of the Lorenz curve under complex sampling designs," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 1-24, March.
    16. Qin, Yongsong & Rao, J.N.K. & Wu, Changbao, 2010. "Empirical likelihood confidence intervals for the Gini measure of income inequality," Economic Modelling, Elsevier, vol. 27(6), pages 1429-1435, November.
    17. Bhargab Chattopadhyay & Shyamal Krishna De, 2016. "Estimation of Gini Index within Pre-Specified Error Bound," Econometrics, MDPI, vol. 4(3), pages 1-12, June.
    18. Timothy Patrick Moran, 2006. "Statistical Inference for Measures of Inequality With a Cross-National Bootstrap Application," Sociological Methods & Research, , vol. 34(3), pages 296-333, February.
    19. Wang, Zheng-Xin & Jv, Yue-Qi, 2023. "Revisiting income inequality among households: New evidence from the Chinese Household Income Project," China Economic Review, Elsevier, vol. 81(C).
    20. Silvia De Nicol`o & Maria Rosaria Ferrante & Silvia Pacei, 2021. "Mind the Income Gap: Bias Correction of Inequality Estimators in Small-Sized Samples," Papers 2107.08950, arXiv.org, revised May 2023.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vrs:offsta:v:36:y:2020:i:2:p:237-249:n:2. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.sciendo.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.