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Pull Your Small Area Estimates up by the Bootstraps

Author

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  • Corral Rodas,Paul Andres
  • Molina,Isabel
  • Nguyen,Minh Cong
Abstract
After almost two decades of poverty maps produced by the World Bank and multiple advances in the literature, this paper presents a methodological update to the World Bank's toolkit for small area estimation. The paper reviews the computational procedures of the current methods used by the World Bank: the traditional approach by Elbers, Lanjouw and Lanjouw (2003) and the Empirical Best/Bayes (EB) addition introduced by Van der Weide (2014). The addition extends the EB procedure of Molina and Rao (2010) by considering heteroscedasticity and includes survey weights, but uses a different bootstrap approach, here referred to as clustered bootstrap. Simulation experiments comparing these methods to the original EB approach of Molina and Rao (2010) provide empirical evidence of the shortcomings of the clustered bootstrap approach, which yields biased point estimates. The main contributions of this paper are then two: 1) to adapt the original Monte Carlo simulation procedure of Molina and Rao (2010) for the approximation of the extended EB estimators that include heteroscedasticity and survey weights as in Van der Weide (2014); and 2) to adapt the parametric bootstrap approach for mean squared error (MSE) estimation considered by Molina and Rao (2010), and proposed originally by González-Manteiga et al. (2008), to these extended EB estimators. Simulation experiments illustrate that the revised Monte Carlo simulation method yields estimators that are considerably less biased and more efficient in terms of MSE than those obtained from the clustered bootstrap approach, and that the parametric bootstrap MSE estimators are in line with the true MSEs under realistic scenarios.

Suggested Citation

  • Corral Rodas,Paul Andres & Molina,Isabel & Nguyen,Minh Cong, 2020. "Pull Your Small Area Estimates up by the Bootstraps," Policy Research Working Paper Series 9256, The World Bank.
    • Handle: RePEc:wbk:wbrwps:9256
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    References listed on IDEAS

    as
    1. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    2. 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.
    3. Elbers, Chris & Lanjouw, Jean O. & Lanjouw, Peter, 2002. "Micro-level estimation of welfare," Policy Research Working Paper Series 2911, The World Bank.
    4. Guadarrama, María & Molina, Isabel & Rao, J.N.K., 2018. "Small area estimation of general parameters under complex sampling designs," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 20-40.
    5. 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.
    6. Yolanda Marhuenda & Isabel Molina & Domingo Morales & J. N. K. Rao, 2017. "Poverty mapping in small areas under a twofold nested error regression model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1111-1136, October.
    7. Sumonkanti Das & Ray Chambers, 2017. "Robust mean‐squared error estimation for poverty estimates based on the method of Elbers, Lanjouw and Lanjouw," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1137-1161, October.
    8. Gabriel Demombynes & Chris Elbers & Jean O. Lanjouw & Peter Lanjouw & Johan A. Mistiaen & Berk Özler, 2002. "Producing an Improved Geographic Profile of Poverty: Methodology and Evidence from Three Developing Countries," WIDER Working Paper Series DP2002-39, World Institute for Development Economic Research (UNU-WIDER).
    9. Nguyen,Minh Cong & Corral Rodas,Paul Andres & Azevedo,Joao Pedro Wagner De & Zhao,Qinghua, 2018. "sae : A Stata Package for Unit Level Small Area Estimation," Policy Research Working Paper Series 8630, The World Bank.
    10. Gabriel DEMOMBYNES & Chris ELBERS & Jean O. LANJOUW & Peter LANJOUW, 2008. "How Good is a Map? Putting Small Area Estimation to the Test," Rivista Internazionale di Scienze Sociali, Vita e Pensiero, Pubblicazioni dell'Universita' Cattolica del Sacro Cuore, vol. 116(4), pages 465-493.
    11. Molina, Isabel, 2019. "Desagregación de datos en encuestas de hogares: metodologías de estimación en áreas pequeñas," Estudios Estadísticos 44214, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    12. Mamadou S. Diallo & J. N. K. Rao, 2018. "Small area estimation of complex parameters under unit‐level models with skew‐normal errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(4), pages 1092-1116, December.
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    Cited by:

    1. Gianni Betti & Vasco Molini & Dan Pavelesku, 2023. "Using poverty maps to improve the design of household surveys: the evidence from Tunisia," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(5), pages 1641-1657, December.
    2. Balgobin Nandram, 2021. "A Bayesian Approach to Linking a Survey and a Census via Small Areas," Stats, MDPI, vol. 4(2), pages 1-20, June.
    3. Molina Isabel, 2020. "Discussion of “Small area estimation: its evolution in five decades”, by Malay Ghosh," Statistics in Transition New Series, Statistics Poland, vol. 21(4), pages 40-44, August.
    4. Masaki,Takaaki & Newhouse,David Locke & Silwal,Ani Rudra & Bedada,Adane & Engstrom,Ryan, 2020. "Small Area Estimation of Non-Monetary Poverty with Geospatial Data," Policy Research Working Paper Series 9383, The World Bank.
    5. Isabel Molina, 2020. "Discussion of "Small area estimation: its evolution in five decades", by Malay Ghosh," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 40-44, August.

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