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Variance Estimation for Generalized Entropy and Atkinson Inequality Indices: the Complex Survey Data Case


  • Martin Biewen
  • Stephen P. Jenkins


We derive the sampling variances of generalized entropy and Atkinson indices when estimated from complex survey data, and show how they can be calculated straightforwardly using widely available software. We also show that, when the same approach is used to derive variance formulae for the independent and identically distributed case, it leads to estimators that are simpler than those proposed before. Both cases are illustrated with a comparison of income inequality in Britain and Germany. Copyright 2006 Blackwell Publishing Ltd.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:obuest:v:68:y:2006:i:3:p:371-383

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    References listed on IDEAS

    1. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
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    Cited by:

    1. Stephen P. Jenkins & John Micklewright, 2007. "New Directions in the Analysis of Inequality and Poverty," Discussion Papers of DIW Berlin 700, DIW Berlin, German Institute for Economic Research.
    2. Peter Warr & Sitthiroth Rasphone & Jayant Menon, 2015. "Two Decades of Declining Poverty Despite Rising Inequality in Laos," Departmental Working Papers 2015-13, The Australian National University, Arndt-Corden Department of Economics.
    3. Jenkins, Stephen P. & Burkhauser, Richard V. & Feng, Shuaizhang & Larrimore, Jeff, 2009. "Measuring inequality using censored data: a multiple imputation approach," ISER Working Paper Series 2009-04, Institute for Social and Economic Research.
    4. Stéphane Mussard & Pi Alperin María Noel, 2006. "Measuring Significance of Inequalities with Heterogeneous Groups and Income Sources," Cahiers de recherche 06-13, Departement d'Economique de l'École de gestion à l'Université de Sherbrooke.
    5. 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.
    6. Judith Clarke & Nilanjana Roy, 2012. "On statistical inference for inequality measures calculated from complex survey data," Empirical Economics, Springer, vol. 43(2), pages 499-524, October.
    7. Ligon, Ethan A., 2010. "Measuring Risk by Looking at Changes in Inequality: vulnerability in Ecuador," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt8vj75725, Department of Agricultural & Resource Economics, UC Berkeley.
    8. 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.
    9. Tim Goedemé, 2013. "How much Confidence can we have in EU-SILC? Complex Sample Designs and the Standard Error of the Europe 2020 Poverty Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 110(1), pages 89-110, January.
    10. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    11. Yi Tao & Kizito Henry & Qinpei Zou & Xiaoni Zhong, 2014. "Methods for measuring horizontal equity in health resource allocation: a comparative study," Health Economics Review, Springer, vol. 4(1), pages 1-10, December.
    12. Francesco Caracciolo & Fabio Gaetano Santeramo, 2013. "Price Trends and Income Inequalities: Will Sub-Saharan Africa Reduce the Gap?," African Development Review, African Development Bank, vol. 25(1), pages 42-54, March.
    13. Orsetta Causa & Mikkel Hermansen & Nicolas Ruiz, 2016. "The Distributional Impact of Structural Reforms," OECD Economics Department Working Papers 1342, OECD Publishing.
    14. Tim Goedemé & Karel Van den Bosch & Lina Salanauskaite & Gerlinde Verbist, 2013. "Testing the Statistical Significance of Microsimulation Results: Often Easier than You Think. A Technical Note," ImPRovE Working Papers 13/10, Herman Deleeck Centre for Social Policy, University of Antwerp.

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