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On Statistical Inference for Inequality Measures Calculated from Complex Survey Data

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Abstract

We examine inference for Generalized Entropy and Atkinson inequality measures with complex survey data, using Wald statistics with variance-covariance matrices estimated from a linearization approximation method. Testing the equality of two or more inequality measures, including sub-group decomposition indices and group shares, are covered. We illustrate with Indian data from three surveys, examining pre-school children’s height, an anthropometric measure that can indicate long-term malnutrition. Sampling involved an urban/rural stratification with clustering before selection of households. We compare the linearization complex survey outcomes with those from an incorrect independently and identically distributed (iid) assumption and a bootstrap that accounts for the survey design. For our samples, the results from the easy to implement linearization method and the more computationally burdensome bootstrap are in close agreement. This finding is of interest to applied researchers, as bootstrapping is currently the method that is most commonly used for undertaking statistical inference in this literature.

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Bibliographic Info

Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 1002.

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Length: 35 pages
Date of creation: 23 Aug 2010
Date of revision:
Handle: RePEc:vic:vicewp:1002

Note: ISSN 1485-6441
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Keywords: Complex survey; inequality; generalized entropy; Atkinson; decomposition; linearization;

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  1. Russell Davidson & Emmanuel Flachaire, 2004. "Asymptotic and bootstrap inference for inequality and poverty measures," Cahiers de la Maison des Sciences Economiques v04100, Université Panthéon-Sorbonne (Paris 1).
  2. Alessandro Tarozzi & Aprajit Mahajan, 2007. "Child Nutrition in India in the Nineties," Economic Development and Cultural Change, University of Chicago Press, vol. 55, pages 441-486.
  3. Bhattacharya, Debopam, 2005. "Asymptotic inference from multi-stage samples," Journal of Econometrics, Elsevier, vol. 126(1), pages 145-171, May.
  4. Moradi, Alexander & Baten, Joerg, 2005. "Inequality in Sub-Saharan Africa: New Data and New Insights from Anthropometric Estimates," World Development, Elsevier, vol. 33(8), pages 1233-1265, August.
  5. 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, 06.
  6. David Gray & Jeffrey Mills & Sourushe Zandvakili, 2003. "Immigration, Assimilation and Inequality of Income Distribution in Canada," University of Cincinnati, Economics Working Papers Series 2003-01, University of Cincinnati, Department of Economics.
  7. Russell Davidson, 2007. "Reliable Inference For The Gini Index," Working Papers halshs-00353856, HAL.
  8. Jean-Marie Dufour & Jan F. Kiviet, 1998. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Econometrica, Econometric Society, vol. 66(1), pages 79-104, January.
  9. Bhattacharya, Debopam, 2007. "Inference on inequality from household survey data," Journal of Econometrics, Elsevier, vol. 137(2), pages 674-707, April.
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  11. Pradhan, Menno & Sahn, David E. & Younger, Stephen D., 2003. "Decomposing world health inequality," Journal of Health Economics, Elsevier, vol. 22(2), pages 271-293, March.
  12. Jeffrey A. Mills & Sourushe Zandvakili, 1999. "Statistical Inference via Bootstrapping for Measures of Inequality," Macroeconomics 9902003, EconWPA.
  13. Biewen, Martin, 2002. "Bootstrap inference for inequality, mobility and poverty measurement," Journal of Econometrics, Elsevier, vol. 108(2), pages 317-342, June.
  14. Jeffrey Mills & Sourushe Zandvakili, 2004. "Analysis of gender-based family income inequality in Canada," Applied Economics Letters, Taylor and Francis Journals, vol. 11(8), pages 469-472.
  15. Menno Pradhan & David E. Sahn & Stephen D. Younger, 2001. "Decomposing World Health Inequality," Tinbergen Institute Discussion Papers 01-091/2, Tinbergen Institute.
  16. Barrett, Garry F & Crossley, Thomas F & Worswick, Christopher, 2000. "Consumption and Income Inequality in Australia," The Economic Record, The Economic Society of Australia, vol. 76(233), pages 116-38, June.
  17. David Gray & Jeffrey A. Mills & Sourushe Zandvakili, 2003. "Statistical analysis of inequality with decompositions: the Canadian experience," Empirical Economics, Springer, vol. 28(2), pages 291-302, 04.
  18. Christian Schluter & Mark Trede, 2002. "Statistical Inference for Inequality and Poverty Measurement with Dependent Data," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 493-508, May.
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Blog mentions

As found by EconAcademics.org, the blog aggregator for Economics research:
  1. Complex Survey Data in Econometrics
    by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-05-18 19:14:00

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