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On Statistical Inference for Inequality Measures Calculated from Complex Survey Data

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 rather than the d-method. Testing the equivalence 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 children’s height-for-age, 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 iid assumption and a bootstrap that accounts for the survey design. For our samples, the results from the easy to implement linearization method and more computationally burdensome bootstrap are in close agreement.

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Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0904.

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Length: 38 pages
Date of creation: 15 Jun 2009
Date of revision:
Handle: RePEc:vic:vicewp:0904
Note: ISSN 1485-6441
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Web page: http://web.uvic.ca/econ

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  1. Cowell, Frank A & Jenkins, Stephen P, 1995. "How Much Inequality Can We Explain? A Methodology and an Application to the United States," Economic Journal, Royal Economic Society, vol. 105(429), pages 421-30, March.
  2. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
  3. Russell Davidson & Emmanuel Flachaire, 2006. "Asymptotic And Bootstrap Inference For Inequality And Poverty Measures," Departmental Working Papers 2005-06, McGill University, Department of Economics.
  4. Casilda Lasso de la Vega & Ana Urrutia, 2008. "The ‘Extended’ Atkinson family: The class of multiplicatively decomposable inequality measures, and some new graphical procedures for analysts," Journal of Economic Inequality, Springer, vol. 6(2), pages 211-225, June.
  5. David E. Sahn & Stephen D. Younger, 2006. "Changes in inequality and poverty in Latin America: Looking beyond income to health and education," Journal of Applied Economics, Universidad del CEMA, vol. 0, pages 215-234, November.
  6. Garry Barrett & Thomas Crossley & Christopher Worswick, 1999. "Consumption and Income Inequality in Australia," CEPR Discussion Papers 404, Centre for Economic Policy Research, Research School of Economics, Australian National University.
  7. Van de gaer, Dirk & Funnell, Nicola & McCarthy, Tom, 1999. "Statistical inference for two measures of inequality when incomes are correlated," Economics Letters, Elsevier, vol. 64(3), pages 295-300, September.
  8. Mills, Jeffrey A & Zandvakili, Sourushe, 1997. "Statistical Inference via Bootstrapping for Measures of Inequality," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(2), pages 133-50, March-Apr.
  9. Wen-Hao Chen & Jean-Yves Duclos, 2011. "Testing for poverty dominance: an application to Canada," Canadian Journal of Economics, Canadian Economics Association, vol. 44(3), pages 781-803, August.
  10. Charles Blackorby & David Donaldson & Maria Auersperg, 1981. "A New Procedure for the Measurement of Inequality within and among Population Subgroups," Canadian Journal of Economics, Canadian Economics Association, vol. 14(4), pages 665-85, November.
  11. 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.
  12. Bhattacharya, Debopam, 2005. "Asymptotic inference from multi-stage samples," Journal of Econometrics, Elsevier, vol. 126(1), pages 145-171, May.
  13. 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.
  14. 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.
  15. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  16. Griffiths, Paula & Matthews, Zoë & Hinde, Andrew, 2002. "Gender, family, and the nutritional status of children in three culturally contrasting states of India," Social Science & Medicine, Elsevier, vol. 55(5), pages 775-790, September.
  17. 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.
  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.
  19. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Cahiers de recherche 9547, Universite de Montreal, Departement de sciences economiques.
  20. 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.
  21. repec:dgr:uvatin:20010091 is not listed on IDEAS
  22. Russell Davidson & James G. MacKinnon, 2001. "Bootstrap Tests: How Many Bootstraps?," Working Papers 1036, Queen's University, Department of Economics.
  23. 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.
  24. Atkinson, A-B, 1996. "Bringing Income Distribution in from the Cold," Economics Papers 117, Economics Group, Nuffield College, University of Oxford.
  25. Cowell, Frank A., 1989. "Sampling variance and decomposable inequality measures," Journal of Econometrics, Elsevier, vol. 42(1), pages 27-41, September.
  26. Cowell, Frank A, 1980. "On the Structure of Additive Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 47(3), pages 521-31, April.
  27. Biewen, Martin, 2002. "Bootstrap inference for inequality, mobility and poverty measurement," Journal of Econometrics, Elsevier, vol. 108(2), pages 317-342, June.
  28. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
  29. Jeffrey Mills & Sourushe Zandvakili, 2004. "Analysis of gender-based family income inequality in Canada," Applied Economics Letters, Taylor & Francis Journals, vol. 11(8), pages 469-472.
  30. Bhattacharya, Debopam, 2007. "Inference on inequality from household survey data," Journal of Econometrics, Elsevier, vol. 137(2), pages 674-707, April.
  31. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  32. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-85, November.
  33. James E. Foster & Artyom A. Shneyerov, 1999. "A general class of additively decomposable inequality measures," Economic Theory, Springer, vol. 14(1), pages 89-111.
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