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Estimation of normal mixtures in a nested error model with an application to small area estimation of poverty and inequality

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  • Elbers, Chris
  • van der Weide, Roy

Abstract

This paper proposes a method for estimating distribution functions that are associated with the nested errors in linear mixed models. The estimator incorporates Empirical Bayes prediction while making minimal assumptions about the shape of the error distributions. The application presented in this paper is the small area estimation of poverty and inequality, although this denotes by no means the only application. Monte-Carlo simulations show that estimates of poverty and inequality can be severely biased when the non-normality of the errors is ignored. The bias can be as high as 2 to 3 percent on a poverty rate of 20 to 30 percent. Most of this bias is resolved when using the proposed estimator. The approach is applicable to both survey-to-census and survey-to-survey prediction.

Suggested Citation

  • Elbers, Chris & van der Weide, Roy, 2014. "Estimation of normal mixtures in a nested error model with an application to small area estimation of poverty and inequality," Policy Research Working Paper Series 6962, The World Bank.
    • Handle: RePEc:wbk:wbrwps:6962
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    1. Anders Skrondal & Sophia Rabe‐Hesketh, 2009. "Prediction in multilevel generalized linear models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(3), pages 659-687, June.
    2. Elbers, Chris & Fujii, Tomoki & Lanjouw, Peter & Ozler, Berk & Yin, Wesley, 2007. "Poverty alleviation through geographic targeting: How much does disaggregation help?," Journal of Development Economics, Elsevier, vol. 83(1), pages 198-213, May.
    3. Christian Kleiber, 2008. "A Guide to the Dagum Distributions," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 6, pages 97-117, Springer.
    4. Demombynes, Gabriel & Ozler, Berk, 2005. "Crime and local inequality in South Africa," Journal of Development Economics, Elsevier, vol. 76(2), pages 265-292, April.
    5. 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.
    6. Tomoki Fujii, 2010. "Micro-Level Estimation of Child Undernutrition Indicators in Cambodia," The World Bank Economic Review, World Bank, vol. 24(3), pages 520-553, December.
    7. Araujo, M. Caridad & Ferreira, Francisco H.G. & Lanjouw, Peter & Özler, Berk, 2008. "Local inequality and project choice: Theory and evidence from Ecuador," Journal of Public Economics, Elsevier, vol. 92(5-6), pages 1022-1046, June.
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    Cited by:

    1. María Guadarrama & Isabel Molina & J. N. K. Rao, 2016. "A Comparison Of Small Area Estimation Methods For Poverty Mapping," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 41-66, March.
    2. Gianni Betti & Ruzhdie Bici & Laura Neri & Thomas Pave Sohnesen & Ledia Thomo, 2018. "Local Poverty and Inequality in Albania," Eastern European Economics, Taylor & Francis Journals, vol. 56(3), pages 223-245, May.
    3. Thomas Pave Sohnesen & Alemayehu Azeze Ambel & Peter Fisker & Colin Andrews & Qaiser Khan, 2017. "Small area estimation of child undernutrition in Ethiopian woredas," PLOS ONE, Public Library of Science, vol. 12(4), pages 1-17, April.
    4. 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.
    5. Pave Sohnesen,Thomas & Ambel,Alemayehu A. & Fisker,Peter Simonsen & Andrews,Colin & Khan,Qaiser M., 2016. "Small area estimation of child malnutrition in Ethiopian woredas," Policy Research Working Paper Series 7581, The World Bank.
    6. Imam, M. F. & Islam, Mohammad Amirul & Alam, M. A. & Hossain, M. Jamal. & Das, Sumonkanti, 2020. "Small Area Estimation Of Poverty In Rural Bangladesh," Bangladesh Journal of Agricultural Economics, Bangladesh Agricultural University, vol. 40(1&2), February.
    7. Marchetti Stefano & Tzavidis Nikos, 2021. "Robust Estimation of the Theil Index and the Gini Coeffient for Small Areas," Journal of Official Statistics, Sciendo, vol. 37(4), pages 955-979, December.
    8. 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.
    9. van der Weide, Roy & Blankespoor, Brian & Elbers, Chris & Lanjouw, Peter, 2024. "How accurate is a poverty map based on remote sensing data? An application to Malawi," Journal of Development Economics, Elsevier, vol. 171(C).
    10. Agne Bikauskaite & Isabel Molina & Domingo Morales, 2022. "Multivariate mixture model for small area estimation of poverty indicators," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 724-755, December.
    11. repec:csb:stintr:v:17:y:2016:i:1:p:41-66 is not listed on IDEAS
    12. Dhiraj Sharma & Tara Vishwanath & Brian Blankespoor & Nandini Krishnan, 2015. "Where are Iraq’s Poor?," World Bank Publications - Reports 22351, The World Bank Group.
    13. Charlotte Articus & Jan Pablo Burgard, 2014. "A Finite Mixture Fay Herriot-type model for estimating regional rental prices in Germany," Research Papers in Economics 2014-14, University of Trier, Department of Economics.
    14. van der Weide, Roy, 2014. "GLS estimation and empirical bayes prediction for linear mixed models with Heteroskedasticity and sampling weights : a background study for the POVMAP project," Policy Research Working Paper Series 7028, The World Bank.
    15. World Bank Group, 2016. "Knowledge Externalities from Poverty Mapping in the European Union," World Bank Publications - Reports 23905, The World Bank Group.

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    Keywords

    Statistical&Mathematical Sciences; Econometrics; Achieving Shared Growth; Inequality; Economic Theory&Research;
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