Demand for reliable statistics at a local area (small area) level has greatly increased in recent years. Traditional area-specific estimators based on probability samples are not adequate because of small sample size or even zero sample size in a local area. As a result, methods based on models linking the areas are widely used. World Bank focused on estimating poverty measures, in particular poverty incidence and poverty gap called FGT measures, using a simulated census method, called ELL, based on a one-fold nested error model for a suitable transformation of the welfare variable. Modified ELL methods leading to significant gain in efficiency over ELL also have been proposed under the one-fold model. An advantage of ELL and modified ELL methods is that distributional assumptions on the random effects in the model are not needed. In this paper, we extend ELL and modified ELL to two-fold nested error models to estimate poverty indicators for areas (say a state) and subareas (say counties within a state). Our simulation results indicate that the modified ELL estimators lead to large efficiency gains over ELL at the area level and subarea level. Further, modified ELL method retaining both area and subarea estimated effects in the model (called MELL2) performs significantly better in terms of mean squared error (MSE) for sampled subareas than the modified ELL retaining only estimated area effect in the model (called MELL1).

翻译：近年来，对局部区域（小区域）层面可靠统计量的需求大幅增加。基于概率抽样的传统区域特定估计方法因局部区域样本量较小甚至为零而效果欠佳。因此，基于区域关联模型的估计方法被广泛采用。世界银行重点通过模拟普查方法（即ELL方法）估计贫困测度指标（特别是贫困发生率和贫困缺口，即FGT指标），该方法基于对福利变量进行适当变换后的单重嵌套误差模型。在单重模型框架下，已提出在效率上显著优于ELL的改进ELL方法。ELL及改进ELL方法的优势在于无需对模型中的随机效应设定分布假设。本文我们将ELL及改进ELL方法扩展至两重嵌套误差模型，以估计区域（如州）和子区域（如州内县）的贫困指标。模拟结果表明，改进ELL估计量在区域层面和子区域层面均较ELL方法带来巨大效率提升。此外，在模型中对区域和子区域估计效应均予以保留的改进ELL方法（记为MELL2），针对有样本子区域其均方误差（MSE）表现显著优于仅保留区域估计效应的改进ELL方法（记为MELL1）。