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Small area estimation of the Gini concentration coefficient

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  • Fabrizi, Enrico
  • Trivisano, Carlo

Abstract

The Gini coefficient is a popular concentration measure often used in the analysis of economic inequality. Estimates of this index for small regions may be useful to properly represent inequalities within local communities. However, the small area estimation for the Gini coefficient has not been thoroughly investigated. A method based on area level models, thereby avoiding the assumption of the availability of Census data at the micro level, is proposed. A modified design based estimator for the coefficient with reduced small sample bias is suggested as input for the small area model, while a hierarchical Beta mixed regression model is introduced to combine survey data and auxiliary information. The methodology is illustrated by means of an example based on Italian data from the European Union Survey on Income and Living Conditions.

Suggested Citation

  • Fabrizi, Enrico & Trivisano, Carlo, 2016. "Small area estimation of the Gini concentration coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 223-234.
    • Handle: RePEc:eee:csdana:v:99:y:2016:i:c:p:223-234
    DOI: 10.1016/j.csda.2016.01.010
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    1. Alessandro Tarozzi & Angus Deaton, 2009. "Using Census and Survey Data to Estimate Poverty and Inequality for Small Areas," The Review of Economics and Statistics, MIT Press, vol. 91(4), pages 773-792, November.
    2. Emma Sarno, 1998. "A variance stabilizing transformation for the Gini concentration ratio," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 7(1), pages 77-91, April.
    3. Chris Elbers & Jean O. Lanjouw & Peter Lanjouw, 2003. "Micro--Level Estimation of Poverty and Inequality," Econometrica, Econometric Society, vol. 71(1), pages 355-364, January.
    4. VAN KERM Philippe, 2007. "Extreme incomes and the estimation of poverty and inequality indicators from EU-SILC," IRISS Working Paper Series 2007-01, IRISS at CEPS/INSTEAD.
    5. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    6. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    7. Cristiano Perugini & Gaetano Martino, 2008. "Income Inequality Within European Regions: Determinants And Effects On Growth," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 54(3), pages 373-406, September.
    8. Nguyen Viet Cuong & Tran Ngoc Truong & Roy Van Der Weide, 2010. "Poverty and Inequality Maps in Rural Vietnam: An Application of Small Area Estimation," Asian Economic Journal, East Asian Economic Association, vol. 24(4), pages 355-390, December.
    9. Figueroa-Zúñiga, Jorge I. & Arellano-Valle, Reinaldo B. & Ferrari, Silvia L.P., 2013. "Mixed beta regression: A Bayesian perspective," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 137-147.
    10. Alfons, Andreas & Templ, Matthias, 2013. "Estimation of Social Exclusion Indicators from Complex Surveys: The R Package laeken," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i15).
    11. George J. Borjas & Richard B. Freeman & Lawrence F. Katz, 1992. "On the Labor Market Effects of Immigration and Trade," NBER Chapters, in: Immigration and the Work Force: Economic Consequences for the United States and Source Areas, pages 213-244, National Bureau of Economic Research, Inc.
    12. Fabrizi, Enrico & Ferrante, Maria Rosaria & Pacei, Silvia & Trivisano, Carlo, 2011. "Hierarchical Bayes multivariate estimation of poverty rates based on increasing thresholds for small domains," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1736-1747, April.
    13. Cowell, F.A., 2000. "Measurement of inequality," Handbook of Income Distribution, in: A.B. Atkinson & F. Bourguignon (ed.), Handbook of Income Distribution, edition 1, volume 1, chapter 2, pages 87-166, Elsevier.
    14. Andreas Alfons & Matthias Templ & Peter Filzmoser, 2013. "Robust estimation of economic indicators from survey samples based on Pareto tail modelling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(2), pages 271-286, March.
    15. Demombynes, Gabriel & Ozler, Berk, 2005. "Crime and local inequality in South Africa," Journal of Development Economics, Elsevier, vol. 76(2), pages 265-292, April.
    16. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    17. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    18. Vandewalle, B. & Beirlant, J. & Christmann, A. & Hubert, M., 2007. "A robust estimator for the tail index of Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6252-6268, August.
    19. Cuong, Nguyen Viet & Truong, Tran Ngoc & van der Weide, Roy, 2010. "Poverty and inequality maps for rural Vietnam: an application of small area estimation," Policy Research Working Paper Series 5443, The World Bank.
    20. Alfons, Andreas & Templ, Matthias & Filzmoser, Peter, 2010. "An Object-Oriented Framework for Statistical Simulation: The R Package simFrame," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 37(i03).
    21. 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.
    22. 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.
    23. da-Silva, C.Q. & Migon, H.S. & Correia, L.T., 2011. "Dynamic Bayesian beta models," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2074-2089, June.
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    3. 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.
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    9. Natalia Rojas‐Perilla & Sören Pannier & Timo Schmid & Nikos Tzavidis, 2020. "Data‐driven transformations in small area estimation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 121-148, January.
    10. Nikos Tzavidis & Li‐Chun Zhang & Angela Luna & Timo Schmid & Natalia Rojas‐Perilla, 2018. "From start to finish: a framework for the production of small area official statistics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 927-979, October.
    11. Rojas-Perilla, Natalia & Pannier, Sören & Schmid, Timo & Tzavidis, Nikos, 2017. "Data-driven transformations in small area estimation," Discussion Papers 2017/30, Free University Berlin, School of Business & Economics.
    12. Isabel Molina & Paul Corral & Minh Nguyen, 2022. "Estimation of poverty and inequality in small areas: review and discussion," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1143-1166, December.
    13. Aldo Gardini & Enrico Fabrizi & Carlo Trivisano, 2022. "Poverty and inequality mapping based on a unit‐level log‐normal mixture model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 2073-2096, October.
    14. Natascha Hainbach & Christoph Halbmeier & Timo Schmid & Carsten Schröder, 2019. "A Practical Guide for the Computation of Domain-Level Estimates with the Socio-Economic Panel (and Other Household Surveys)," SOEPpapers on Multidisciplinary Panel Data Research 1055, DIW Berlin, The German Socio-Economic Panel (SOEP).

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