IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v36y2021i3d10.1007_s00180-021-01082-7.html
   My bibliography  Save this article

A new computational approach for estimation of the Gini index based on grouped data

Author

Listed:
  • Tatjana Miljkovic

    (Miami University)

  • Ying-Ju Chen

    (University of Dayton)

Abstract

Many government agencies still rely on the grouped data as the main source of information for calculation of the Gini index. Previous research showed that the Gini index based on the grouped data suffers the first and second-order correction bias compared to the Gini index computed based on the individual data. Since the accuracy of the estimated correction bias is subject to many underlying assumptions, we propose a new method and name it D-Gini, which reduces the bias in Gini coefficient based on grouped data. We investigate the performance of the D-Gini method on an open-ended tail interval of the income distribution. The results of our simulation study showed that our method is very effective in minimizing the first and second order-bias in the Gini index and outperforms other methods previously used for the bias-correction of the Gini index based on grouped data. Three data sets are used to illustrate the application of this method.

Suggested Citation

  • Tatjana Miljkovic & Ying-Ju Chen, 2021. "A new computational approach for estimation of the Gini index based on grouped data," Computational Statistics, Springer, vol. 36(3), pages 2289-2311, September.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:3:d:10.1007_s00180-021-01082-7
    DOI: 10.1007/s00180-021-01082-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-021-01082-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-021-01082-7?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tom Van Ourti & Philip Clarke, 2011. "A Simple Correction to Remove the Bias of the Gini Coefficient due to Grouping," The Review of Economics and Statistics, MIT Press, vol. 93(3), pages 982-994, August.
    2. Genya Kobayashi & Kazuhiko Kakamu, 2019. "Approximate Bayesian computation for Lorenz curves from grouped data," Computational Statistics, Springer, vol. 34(1), pages 253-279, March.
    3. Aaberge, Rolf & Mogstad, Magne & Peragine, Vito, 2011. "Measuring long-term inequality of opportunity," Journal of Public Economics, Elsevier, vol. 95(3), pages 193-204.
    4. Bound, John & Brown, Charles & Mathiowetz, Nancy, 2001. "Measurement error in survey data," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 59, pages 3705-3843, Elsevier.
    5. Yves Tillé & Matti Langel, 2012. "Histogram-Based Interpolation of the Lorenz Curve and Gini Index for Grouped Data," The American Statistician, Taylor & Francis Journals, vol. 66(4), pages 225-231, November.
    6. Cowell, Frank, 2011. "Measuring Inequality," OUP Catalogue, Oxford University Press, edition 3, number 9780199594047.
    7. Schenker, Nathaniel & Raghunathan, Trivellore E. & Chiu, Pei-Lu & Makuc, Diane M. & Zhang, Guangyu & Cohen, Alan J., 2006. "Multiple Imputation of Missing Income Data in the National Health Interview Survey," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 924-933, September.
    8. 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.
    9. Esmaiel Abounoori & Patrick McCloughan, 2003. "A simple way to calculate the Gini Coefficient for grouped as well as ungrouped data," Applied Economics Letters, Taylor & Francis Journals, vol. 10(8), pages 505-509.
    10. H. Schneeweiss & J. Komlos & A. Ahmad, 2010. "Symmetric and asymmetric rounding: a review and some new results," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(3), pages 247-271, September.
    11. Wodon, Quentin & Yitzhaki, Shlomo, 2003. "The effect of using grouped data on the estimation of the Gini income elasticity," Economics Letters, Elsevier, vol. 78(2), pages 153-159, February.
    12. Milanovic, Branko, 1994. "The Gini-Type Functions: An Alternative Derivation," Bulletin of Economic Research, Wiley Blackwell, vol. 46(1), pages 81-90, January.
    13. Merritt Lyon & Li C. Cheung & Joseph L. Gastwirth, 2016. "The Advantages of Using Group Means in Estimating the Lorenz Curve and Gini Index From Grouped Data," The American Statistician, Taylor & Francis Journals, vol. 70(1), pages 25-32, February.
    14. Fabrizi, Enrico & Trivisano, Carlo, 2016. "Small area estimation of the Gini concentration coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 223-234.
    15. Lerman, Robert I. & Yitzhaki, Shlomo, 1989. "Improving the accuracy of estimates of Gini coefficients," Journal of Econometrics, Elsevier, vol. 42(1), pages 43-47, September.
    16. Drechsler, Jörg & Kiesl, Hans, 2014. "Beat the heap - an imputation strategy for valid inferences from rounded income data," IAB-Discussion Paper 201402, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany].
    17. Frank A. Cowell & Fatemeh Mehta, 1982. "The Estimation and Interpolation of Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 273-290.
    18. Kakwani, Nanak & Wagstaff, Adam & van Doorslaer, Eddy, 1997. "Socioeconomic inequalities in health: Measurement, computation, and statistical inference," Journal of Econometrics, Elsevier, vol. 77(1), pages 87-103, March.
    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. Marcin Wroński, 2023. "Income distribution in Warsaw in the 1830s," European Review of Economic History, European Historical Economics Society, vol. 27(4), pages 581-605.

    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. 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.
    2. Clarke, Philip & Van Ourti, Tom, 2010. "Calculating the concentration index when income is grouped," Journal of Health Economics, Elsevier, vol. 29(1), pages 151-157, January.
    3. Tom Van Ourti & Philip Clarke, 2008. "The Bias of the Gini Coefficient due to Grouping," Tinbergen Institute Discussion Papers 08-095/3, Tinbergen Institute.
    4. Souche, Stéphanie & Mercier, Aurélie & Ovtracht, Nicolas, 2015. "Income and access inequalities of a cordon pricing," Research in Transportation Economics, Elsevier, vol. 51(C), pages 20-30.
    5. Stéphanie Souche & Aurelie Mercier & Nicolas Ovtracht, 2016. "The impacts of urban pricing on social and spatial inequalities: The case study of Lyon (France)," Urban Studies, Urban Studies Journal Limited, vol. 53(2), pages 373-399, February.
    6. Hodler, Roland & Srisuma, Sorawoot & Vesperoni, Alberto & Zurlinden, Noémie, 2020. "Measuring ethnic stratification and its effect on trust in Africa," Journal of Development Economics, Elsevier, vol. 146(C).
    7. Burauel, Patrick & Caliendo, Marco & Grabka, Markus M. & Obst, Cosima & Preuss, Malte & Schröder, Carsten & Shupe, Cortnie, 2020. "The Impact of the German Minimum Wage on Individual Wages and Monthly Earnings," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 240(2/3), pages 201-231.
    8. Amlan Majumder & Takayoshi Kusago, 2013. "A discreet approach to study the distribution-free downward biases of Gini coefficient and the methods of correction in cases of small observations," Working Papers 298, ECINEQ, Society for the Study of Economic Inequality.
    9. Speidel, Matthias & Drechsler, Jörg & Jolani, Shahab, 2018. "R package hmi: a convenient tool for hierarchical multiple imputation and beyond," IAB-Discussion Paper 201816, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany].
    10. Shweta Bahl & Ajay Sharma, 2021. "Education–Occupation Mismatch and Dispersion in Returns to Education: Evidence from India," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 153(1), pages 251-298, January.
    11. Miguel A. Márquez & Elena Lasarte & Marcelo Lufin, 2019. "The Role of Neighborhood in the Analysis of Spatial Economic Inequality," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 141(1), pages 245-273, January.
    12. Loi, Andrea & Matta, Stefano, 2021. "Minimal entropy and uniqueness of price equilibria in a pure exchange economy," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    13. Hai Zhong, 2010. "The impact of missing data in the estimation of concentration index: a potential source of bias," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 11(3), pages 255-266, June.
    14. Alvaredo, Facundo & Cogneau, Denis & Piketty, Thomas, 2021. "Income inequality under colonial rule. Evidence from French Algeria, Cameroon, Tunisia, and Vietnam and comparisons with British colonies 1920–1960," Journal of Development Economics, Elsevier, vol. 152(C).
    15. Ceren Baysan & Marshall Burke & Felipe González & Solomon Hsiang & Edward Miguel, 2018. "Economic and Non-Economic Factors in Violence: Evidence from Organized Crime, Suicides and Climate in Mexico," NBER Working Papers 24897, National Bureau of Economic Research, Inc.
    16. Yonatan Berman, 2022. "The Long-Run Evolution of Absolute Intergenerational Mobility," American Economic Journal: Applied Economics, American Economic Association, vol. 14(3), pages 61-83, July.
    17. Amlan Majumder & Takayoshi Kusago, 2021. "A consistency check of the World Income Inequality Database in favour of common readers," SN Business & Economics, Springer, vol. 1(7), pages 1-17, July.
    18. Bhuller, Manudeep & Mogstad, Magne & Salvanes, Kjell G., 2011. "Life-Cycle Bias and the Returns to Schooling in Current and Lifetime Earnings," IZA Discussion Papers 5788, Institute of Labor Economics (IZA).
    19. ERREYGERS, Guido & CLARKE, Philip & VAN OURTI, Tom, 2010. "Mirror, mirror, on the wall, who in this land is fairest of all? Revisiting the extended concentration index," Working Papers 2010015, University of Antwerp, Faculty of Business and Economics.
    20. Andrew Leigh, 2005. "Deriving Long‐Run Inequality Series from Tax Data," The Economic Record, The Economic Society of Australia, vol. 81(s1), pages 58-70, August.

    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:spr:compst:v:36:y:2021:i:3:d:10.1007_s00180-021-01082-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.