Many countries measure poverty based only on income or consumption. However, there is a growing awareness of measuring poverty through multiple dimensions that captures a more reasonable status of poverty. Estimating poverty measure(s) for small geographical areas, commonly referred to as poverty mapping, is challenging due to small or no sample for the small areas. While there is a huge literature available on unidimensional poverty mapping, only a limited effort has been made to address special challenges that arise only in the multidimensional poverty mapping. For example, in multidimensional poverty mapping, a new problem arises involving estimation of relative contributions of different dimensions to overall poverty for small areas. This problem has been grossly ignored in the small area estimation (SAE) literature. We address this issue using a multivariate hierarchical model implemented via a Bayesian method. Moreover, we demonstrate how a multidimensional poverty composite measure can be estimated for small areas. In this paper, we demonstrate our proposed methodology using a survey data specially designed by one of us for multidimensional poverty mapping. This paper adds a new direction to poverty mapping literature.

翻译：许多国家仅依据收入或消费来衡量贫困。然而，通过多维度衡量贫困以更合理地反映贫困状况的意识日益增强。由于小区域样本量小或缺乏样本，估算小地理区域（通常称为贫困制图）的贫困指标具有挑战性。尽管关于单维贫困制图的文献浩如烟海，但针对多维贫困制图中特有挑战的研究却十分有限。例如，在多维贫困制图中，出现了一个新问题：如何估算不同维度对小区域总体贫困的相对贡献。这一问题在小区域估计（SAE）文献中一直被严重忽视。我们通过贝叶斯方法实现多元层次模型来解决该问题。此外，我们展示了如何估算小区域的多维贫困综合指标。本文使用由作者之一专门为多维贫困制图设计的调查数据来演示所提出的方法。本研究为贫困制图文献开辟了新的方向。