Publication: Pull Your Small Area Estimates Up by the Bootstraps
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2021-05-08
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0094-9655
Date
2022-01-14
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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 institution: the traditional ELL approach and the Empirical Best (EB) addition introduced to imitate the original EB procedure of Molina and Rao [Small area estimation of poverty indicators. Canadian J Stat. 2010;38(3):369–385], including heteroskedasticity and survey weights, but using a different bootstrap approach, here referred to as clustered bootstrap. Simulation experiments provide empirical evidence of the shortcomings of the clustered bootstrap approach, which yields biased and noisier point estimates. The document presents an update to the World Bank’s EB implementation by considering the original EB procedures for point and noise estimation, extended for complex designs and heteroscedasticity. Simulation experiments illustrate that the revised methods yield considerably less biased and more efficient estimators than those obtained from the clustered bootstrap approach.
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Publication Pull Your Small Area Estimates Up by the Bootstraps(World Bank, Washington, DC, 2020-05)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.Publication A Map of the Poor or a Poor Map?(World Bank, Washington, DC, 2021-04)This paper evaluates the performance of different small area estimation methods using model and design-based simulation experiments. Design-based simulation experiments are carried out using the Mexican Intra Censal survey as a census of roughly 3.9 million households from which 500 samples are drawn using a two-stage selection procedure similar to that of Living Standards Measurement Study surveys. Several unit-level methods are considered as well as a method that combines unit and area level information, which has been proposed as an alternative when the available census data is outdated. The findings show the importance of selecting a proper model and data transformation so that the model assumptions hold. A proper data transformation can lead to a considerable improvement in mean squared errors. The results from design-based validation show that all small area estimation methods represent an improvement, in terms of mean squared errors, over direct estimates. However, methods that model unit level welfare using only area level information suffer from considerable bias. Because the magnitude and direction of the bias are unknown ex ante, methods that rely only on aggregated covariates should be used with caution, but they may be an alternative to traditional area level models when these are not applicable.Publication How Good a Map? Putting Small Area Estimation to the Test(World Bank, Washington, DC, 2007-03)The authors examine the performance of small area welfare estimation. The method combines census and survey data to produce spatially disaggregated poverty and inequality estimates. To test the method, they compare predicted welfare indicators for a set of target populations with their true values. They construct target populations using actual data from a census of households in a set of rural Mexican communities. They examine estimates along three criteria: accuracy of confidence intervals, bias, and correlation with true values. The authors find that while point estimates are very stable, the precision of the estimates varies with alternative simulation methods. While the original approach of numerical gradient estimation yields standard errors that seem appropriate, some computationally less-intensive simulation procedures yield confidence intervals that are slightly too narrow. The precision of estimates is shown to diminish markedly if unobserved location effects at the village level are not well captured in underlying consumption models. With well specified models there is only slight evidence of bias, but the authors show that bias increases if underlying models fail to capture latent location effects. Correlations between estimated and true welfare at the local level are highest for mean expenditure and poverty measures and lower for inequality measures.Publication SAE - A Stata Package for Unit Level Small Area Estimation(World Bank, Washington, DC, 2018-10)This paper presents a new family of Stata functions devoted to small area estimation. Small area methods attempt to solve low representativeness of surveys within areas, or the lack of data for specific areas/sub-populations. This is accomplished by incorporating information from outside sources. Such target data sets are becoming increasingly available and can take the form of a traditional population census, but also large scale administrative records from tax administrations, or geospatial information produced using remote sensing. The strength of these target data sets is their granularity on the subpopulations of interest, however, in many cases they lack the ability to collect analytically relevant variables such as welfare or caloric intake. The family of functions introduced follow a modular design to have the flexibility with which these can be expanded in the future. This can be accomplished by the authors and/or other collaborators from the Stata community. Thus far, a major limitation of such analysis in Stata has been the large size of target data sets. The package introduces new mata functions and a plugin used to circumvent memory limitations that inevitably arise when working with big data. From an estimation perspective, the paper starts by implementing a methodology that has been widely used for the production of several poverty maps.Publication Frontiers in Small Area Estimation Research(Washington, DC: World Bank, 2024-06-28)This paper reviews the main methods for small area estimation of welfare indicators. It begins by discussing the importance of small area estimation methods for producing reliable disaggregated estimates. It mentions the baseline papers and describes the contents of the different sections. Basic direct estimators obtained from area-specific survey data are described first, followed by simple indirect methods, which include synthetic procedures that do not account for the area effects and composite estimators obtained as a composition (or weighted average) of a synthetic and a direct estimator. The previous estimators are design-based, meaning that their properties are assessed under the sampling replication mechanism, without assuming any model to be true. The paper then turns to proper model-based estimators that assume an explicit model. These models allow obtaining optimal small area estimators when the assumed model holds. The first type of models, referred to as area-level models, use only aggregated data at the area level to fit the model. However, unit-level survey data were previously used to calculate the direct estimators, which act as response variables in the most common area-level models. The paper then switches to unit-level models, describing first the usual estimators for area means, and then moving to general area indicators. Semi-parametric, non-parametric, and machine learning procedures are described in a separate section, although many of the procedures are applicable only to area means. Based on the previous material, the paper identifies gaps or potential limitations in existing procedures from a practitioner’s perspective, which could potentially be addressed through research over the next three to five years.
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