IDEAS home Printed from https://ideas.repec.org/a/bla/obuest/v66y2004i3p425-433.html
   My bibliography  Save this article

Calculating a Standard Error for the Gini Coefficient: Some Further Results

Author

Listed:
  • David E. A. Giles

Abstract

Several authors have suggested using the jackknife technique to approximate a standard error for the Gini coefficient. It has also been shown that the Gini measure can be obtained simply from an artificial ordinary least square (OLS) regression based on the data and their ranks. We show that obtaining an exact analytical expression for the standard error is actually a trivial matter. Further, by extending the regression framework to one involving seemingly unrelated regressions (SUR), several interesting hypotheses regarding the sensitivity of the Gini coefficient to changes in the data are readily tested in a formal manner.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:obuest:v:66:y:2004:i:3:p:425-433
    DOI: 10.1111/j.1468-0084.2004.00086.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1468-0084.2004.00086.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1468-0084.2004.00086.x?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Clements, Kenneth W & Izan, H Y, 1987. "The Measurement of Inflation: A Stochastic Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(3), pages 339-350, July.
    2. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    3. Lerman, Robert I. & Yitzhaki, Shlomo, 1984. "A note on the calculation and interpretation of the Gini index," Economics Letters, Elsevier, vol. 15(3-4), pages 363-368.
    4. 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.
    5. repec:bla:obuest:v:62:y:2000:i:1:p:119-22 is not listed on IDEAS
    6. Shalit, Haim, 1985. "Calculating the Gini Index of Inequality for Individual Data," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 47(2), pages 185-189, May.
    7. Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-465, May.
    8. 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.
    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, vol. 6(1), pages 113-119, January.
    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:123-29 is not listed on IDEAS
    13. Paul Crompton, 2000. "Extending the stochastic approach to index numbers," Applied Economics Letters, Taylor & Francis Journals, vol. 7(6), pages 367-371.
    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. Bowden, Roger J., 2016. "Giving Gini direction: An asymmetry metric for economic disadvantage," Economics Letters, Elsevier, vol. 138(C), pages 96-99.
    2. 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.
    3. Shirmohammadli, Abdolmatin & Louen, Conny & Vallée, Dirk, 2016. "Exploring mobility equity in a society undergoing changes in travel behavior: A case study of Aachen, Germany," Transport Policy, Elsevier, vol. 46(C), pages 32-39.
    4. 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.
    5. Gordon Anderson & Maria Grazia Pittau & Roberto Zelli & Jasmin Thomas, 2018. "Income Inequality, Cohesiveness and Commonality in the Euro Area: A Semi-Parametric Boundary-Free Analysis," Econometrics, MDPI, vol. 6(2), pages 1-20, March.
    6. 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.
    7. David (David Patrick) Madden, 2012. "Methods for studying dominance and inequality in population health," Working Papers 201205, School of Economics, University College Dublin.
    8. El-Osta, Hisham S. & Morehart, Mitchell J., 2009. "Welfare Decomposition in the Context of the Life Cycle of Farm Operators: What Does a National Survey Reveal?," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 38(2), pages 1-17, October.
    9. Yu, Jian & Shi, Xunpeng & Cheong, Tsun Se, 2021. "Distribution dynamics of China's household consumption upgrading," Structural Change and Economic Dynamics, Elsevier, vol. 58(C), pages 193-203.
    10. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    11. Oriol Aspachs & Ruben Durante & Alberto Graziano & Josep Mestres & Marta Reynal-Querol & Jose G Montalvo, 2021. "Tracking the impact of COVID-19 on economic inequality at high frequency," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-14, March.
    12. Lubrano, Michel & Ndoye, Abdoul Aziz Junior, 2016. "Income inequality decomposition using a finite mixture of log-normal distributions: A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 830-846.
    13. Parola, Francesco & Veenstra, Albert W., 2008. "The spatial coverage of shipping lines and container terminal operators," Journal of Transport Geography, Elsevier, vol. 16(4), pages 292-299.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    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. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Carsten Schröder & Yolanda Golan & Shlomo Yitzhaki, 2014. "Inequality and the time structure of earnings: evidence from Germany," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 12(3), pages 393-409, September.
    11. Kenneth W. Clements & H. Y. Izan & Yihui Lan, 2009. "A Stochastic Measure of International Competitiveness," International Review of Finance, International Review of Finance Ltd., vol. 9(1‐2), pages 51-81, March.
    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. Akli Berri, 2009. "Transport consumption inequalities and redistributive effects of taxes: A repeated cross-sectional evaluation on French household data," Working Papers 145, ECINEQ, Society for the Study of Economic Inequality.
    14. Heshmati, Almas, 2004. "Data Issues and Databases Used in Analysis of Growth, Poverty and Economic Inequality," IZA Discussion Papers 1263, Institute of Labor Economics (IZA).
    15. 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.
    16. 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.
    17. Ansgar Belke & Robert Czudaj, 2010. "Is Euro Area Money Demand (Still) Stable? Cointegrated VAR Versus Single Equation Techniques," Applied Economics Quarterly (formerly: Konjunkturpolitik), Duncker & Humblot, Berlin, vol. 56(4), pages 285-315.
    18. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
    19. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    20. Barham, Bradford & Boucher, Stephen, 1998. "Migration, remittances, and inequality: estimating the net effects of migration on income distribution," Journal of Development Economics, Elsevier, vol. 55(2), pages 307-331, April.

    More about this item

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being

    Statistics

    Access and download statistics

    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:bla:obuest:v:66:y:2004:i:3:p:425-433. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/sfeixuk.html .

    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.