Small area estimation of general parameters with application to poverty indicators: A hierarchical Bayes approach

Abstract

Poverty maps are used to aid important political decisions such as allocation of development funds by governments and international organizations. Those decisions should be based on the most accurate poverty figures. However, often reliable poverty figures are not available at fine geographical levels or for particular risk population subgroups due to the sample size limitation of current national surveys. These surveys cannot cover adequately all the desired areas or population subgroups and, therefore, models relating the different areas are needed to "borrow strength" from area to area. In particular, the Spanish Survey on Income and Living Conditions (SILC) produces national poverty estimates but cannot provide poverty estimates by Spanish provinces due to the poor precision of direct estimates, which use only the province specific data. It also raises the ethical question of whether poverty is more severe for women than for men in a given province. We develop a hierarchical Bayes (HB) approach for poverty mapping in Spanish provinces by gender that overcomes the small province sample size problem of the SILC. The proposed approach has a wide scope of application because it can be used to estimate general nonlinear parameters. We use a Bayesian version of the nested error regression model in which Markov chain Monte Carlo procedures and the convergence monitoring therein are avoided. A simulation study reveals good frequentist properties of the HB approach. The resulting poverty maps indicate that poverty, both in frequency and intensity, is localized mostly in the southern and western provinces and it is more acute for women than for men in most of the provinces.

A Comparison of Small Area Estimation Methods for Poverty Mapping

“…• EB and HB methods are expected to give practically the same point estimates, see Molina, Nandram and Rao (2014). Thus, the proposed HB method has good frequentist properties.…”

“…Moreover, to obtain the parametric bootstrap MSE estimator, the Monte Carlo approximation needs to be repeated for each bootstrap replicate. Seeking for a computationally more efficient approach, Molina, Nandram and Rao (2014) developed the alternative HB method for estimation of complex non-linear parameters. This approach does not require the use of bootstrap for MSE estimation because it provides samples from the posterior distribution, from which posterior variances play the role of MSEs, and any other useful posterior summary can be easily obtained.…”

“…, π 3 have known forms, but not π 4 . However, since ρ is in a closed interval from (0, 1), we can generate values from π 4 using a grid method, for more details see Molina, Nandram and Rao (2014). Samples from θ = (u , β , σ 2 e , ρ) can then be generated directly from the posterior distribution in (17), avoiding the use of Markov Chain Monte Carlo (MCMC) methods.…”

“…We consider the same model-based simulation setup as in Molina, Nandram and Rao (2014), where data are generated at the unit level following the nested error model (9). However, here we will also include FH estimators derived from the FH area level model obtained using the area means of the auxiliary variables as covariates.…”

“…Here we review the main small area estimation methods for poverty mapping. In particular, we consider direct estimation, the Fay-Herriot area level model, the method of Elbers, Lanjouw and Lanjouw (2003) used by the World Bank, the empirical Best/Bayes (EB) method of Molina and Rao (2010) and its extension, the Census EB, and finally the hierarchical Bayes proposal of Molina, Nandram and Rao (2014). We put ourselves in the point of view of a practitioner and discuss, as objectively as possible, the benefits and drawbacks of each method, illustrating some of them through simulation studies.…”