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Small area estimation on poverty indicators

Author

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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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    Citations

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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. 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.
    4. Monica Robayo-Abril & Britta Rude, 2023. "Poverty Mapping in El Salvador," World Bank Publications - Reports 39424, The World Bank Group.
    5. Corral Rodas,Paul Andres & Henderson,Heath Linn & Segovia Juarez,Sandra Carolina, 2023. "Poverty Mapping in the Age of Machine Learning," Policy Research Working Paper Series 10429, The World Bank.
    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. 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.
    8. 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.
    9. repec:csb:stintr:v:17:y:2016:i:1:p:41-66 is not listed on IDEAS
    10. repec:ecr:col027:48107 is not listed on IDEAS
    11. Peralta,Isabel Molina, 2024. "Frontiers in Small Area Estimation Research: Application to Welfare Indicators," Policy Research Working Paper Series 10828, The World Bank.
    12. 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.
    13. Hector Najera, 2026. "A Bayesian Approach for Valid and Credible Inferences on the 2010–2020 Changes in Multidimensional Poverty in Mexico at Municipal Level," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 181(1), pages 1-31, January.
    14. Guadarrama Sanz, Maria & Molina Peralta, Isabel & 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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