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Small area estimation on poverty indicators

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  • Molina, Isabel
  • Rao, J.N.K.

Abstract

We propose to estimate non-linear small area population quantities by using Empirical Best (EB) estimators based on a nested error model. EB estimators are obtained by Monte Carlo approximation. We focus on poverty indicators as particular non-linear quantities of interest, but the proposed methodology is applicable to general non-linear quantities. Small sample properties of EB estimators are analyzed by model-based and design-based simulation studies. Results show large reductions in mean squared error relative to direct estimators and estimators obtained by simulated censuses. An application is also given to estimate poverty incidences and poverty gaps in Spanish provinces by sex with mean squared errors estimated by parametric bootstrap. In the Spanish data, results show a significant reduction in coefficient of variation of the proposed EB estimators over direct estimators for most domains.

Suggested Citation

  • Molina, Isabel & Rao, J.N.K., 2009. "Small area estimation on poverty indicators," DES - Working Papers. Statistics and Econometrics. WS ws091505, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws091505
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    References listed on IDEAS

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    1. Alessandro Tarozzi & Angus Deaton, 2009. "Using Census and Survey Data to Estimate Poverty and Inequality for Small Areas," The Review of Economics and Statistics, MIT Press, vol. 91(4), pages 773-792, November.
    2. 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.
    3. Francesca Ballini & Gianni Betti & Samuel Carrette & Laura Neri, 2009. "Poverty and inequality mapping in the Commonwealth of Dominica," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 0(Special i), pages 123-162.
    4. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    5. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238, April.
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    Cited by:

    1. Corral Rodas,Paul Andres & Kastelic,Kristen Himelein & Mcgee,Kevin Robert & Molina,Isabel, 2021. "A Map of the Poor or a Poor Map ?," Policy Research Working Paper Series 9620, The World Bank.
    2. 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.
    3. repec:csb:stintr:v:17:y:2016:i:1:p:41-66 is not listed on IDEAS
    4. Stachurski Tomasz, 2021. "Small area quantile estimation based on distribution function using linear mixed models," Economics and Business Review, Sciendo, vol. 7(2), pages 97-114, June.
    5. Molina, Isabel, 2022. "Disaggregating data in household surveys: Using small area estimation methodologies," Estudios Estadísticos 48107, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    6. Guadarrama María & Molina Isabel & Rao J. N. K., 2016. "A Comparison of Small Area Estimation Methods for Poverty Mapping," Statistics in Transition New Series, Statistics Poland, vol. 17(1), pages 41-66, March.
    7. Paul Corral & Kristen Himelein & Kevin McGee & Isabel Molina, 2021. "A Map of the Poor or a Poor Map?," Mathematics, MDPI, vol. 9(21), pages 1-40, November.
    8. Kevin Dayaratna & Jesse Crosson & Chandler Hubbard, 2022. "Closed Form Bayesian Inferences for Binary Logistic Regression with Applications to American Voter Turnout," Stats, MDPI, vol. 5(4), pages 1-21, November.
    9. Guadarrama Sanz, Maria & Rao, J. N. K., 2015. "A Comparison of Small Area Estimation Methods for Poverty Mapping," DES - Working Papers. Statistics and Econometrics. WS ws1505, Universidad Carlos III de Madrid. Departamento de Estadística.

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    Empirical best estimator;

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