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Mind the Income Gap: Bias Correction of Inequality Estimators in Small-Sized Samples

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  • Silvia De Nicol`o
  • Maria Rosaria Ferrante
  • Silvia Pacei

Abstract

Income inequality estimators are biased in small samples, leading generally to an underestimation. This aspect deserves particular attention when estimating inequality in small domains and performing small area estimation at the area level. We propose a bias correction framework for a large class of inequality measures comprising the Gini Index, the Generalized Entropy and the Atkinson index families by accounting for complex survey designs. The proposed methodology does not require any parametric assumption on income distribution, being very flexible. Design-based performance evaluation of our proposal has been carried out using EU-SILC data, their results show a noticeable bias reduction for all the measures. Lastly, an illustrative example of application in small area estimation confirms that ignoring ex-ante bias correction determines model misspecification.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2107.08950
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    1. Davidson, Russell & Flachaire, Emmanuel, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," Journal of Econometrics, Elsevier, vol. 141(1), pages 141-166, November.
    2. Lidia Ceriani & Paolo Verme, 2015. "Individual Diversity and the Gini Decomposition," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 121(3), pages 637-646, April.
    3. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    4. Thistle, Paul D, 1990. "Large Sample Properties of Two Inequality Indices," Econometrica, Econometric Society, vol. 58(3), pages 725-728, May.
    5. 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.
    6. Mark Finkelstein & Howard G. Tucker & Jerry Alan Veeh, 2006. "Pareto Tail Index Estimation Revisited," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(1), pages 1-10.
    7. 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.
    8. Barndorff-Nielsen, O. E. & Jørgensen, B., 1991. "Some parametric models on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 106-116, October.
    9. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    10. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    11. Cowell, Frank A & Victoria-Feser, Maria-Pia, 1996. "Robustness Properties of Inequality Measures," Econometrica, Econometric Society, vol. 64(1), pages 77-101, January.
    12. 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.
    13. 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.
    14. Enrico Fabrizi & Maria Rosaria Ferrante & Carlo Trivisano, 2020. "A functional approach to small area estimation of the relative median poverty gap," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1273-1291, June.
    15. Fabrizi, Enrico & Trivisano, Carlo, 2016. "Small area estimation of the Gini concentration coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 223-234.
    16. Michał Brzeziński, 2013. "Robust estimation of the Pareto index: A Monte Carlo Analysis," Working Papers 2013-32, Faculty of Economic Sciences, University of Warsaw.
    17. David E. Giles, 2005. "The Bias of Inequality Measures in Very Small Samples: Some Analytic Results," Econometrics Working Papers 0514, Department of Economics, University of Victoria.
    18. 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.
    19. Bruffaerts, Christopher & Verardi, Vincenzo & Vermandele, Catherine, 2014. "A generalized boxplot for skewed and heavy-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 110-117.
    20. Patrícia L. Espinheira & Alisson Oliveira Silva, 2020. "Residual and influence analysis to a general class of simplex regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 523-552, June.
    21. Martin Biewen & Stephen P. Jenkins, 2006. "Variance Estimation for Generalized Entropy and Atkinson Inequality Indices: the Complex Survey Data Case," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(3), pages 371-383, June.
    22. 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.
    23. Schluter, Christian & van Garderen, Kees Jan, 2009. "Edgeworth expansions and normalizing transforms for inequality measures," Journal of Econometrics, Elsevier, vol. 150(1), pages 16-29, May.
    24. Riccardo De Santis & Lucio Barabesi & Gianni Betti, 2020. "Variance estimation techniques for poverty and inequality measures from complex surveys: a simulation study," Department of Economics University of Siena 829, Department of Economics, University of Siena.
    25. Breunig, Robert, 2001. "An almost unbiased estimator of the coefficient of variation," Economics Letters, Elsevier, vol. 70(1), pages 15-19, January.
    26. Biewen, Martin, 2002. "Bootstrap inference for inequality, mobility and poverty measurement," Journal of Econometrics, Elsevier, vol. 108(2), pages 317-342, June.
    27. 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).
    28. 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.
    29. 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.
    30. Monique Graf & Desislava Nedyalkova, 2014. "Modeling of Income and Indicators of Poverty and Social Exclusion Using the Generalized Beta Distribution of the Second Kind," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 60(4), pages 821-842, December.
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