Bayesian Methods Applied to Small Area Estimation for Establishment Statistics

Abstract

Establishment survey data is frequently used to estimate population level characteristics of organizations rather than individuals. For large domains of interest, direct survey estimates may fare well; however, when interest lies in domains that contain relatively few samples, direct survey estimates are inefficient, leading to the need for small area models. These models rely on various dependencies within the data in order to “borrow information,” leading to more precise estimates. Dependencies may include covariates, spatial dependence, temporal dependence, multivariate relationships, or in the case of establishment surveys specifically, dependence on industry classification. Bayesian hierarchical modeling provides a natural foundation for modeling sources of dependence, and thus also a natural framework for small area estimation of establishment statistics. Within this Bayesian framework, there are two separate overarching modeling approaches. The first approach is to use area-level models, which treat the direct survey estimates as the response, and then “smooth” these estimates through the modeling hierarchy. In contrast, unit-level models, which do not consider the direct estimates, instead, model the sampled units directly. There are positive and negative trade-offs under both approaches and, in this work, we give an overview of various Bayesian methods that fall under both categories. In addition, based on the 2007 Survey of Business Owners (SBO) administered by the U.S. Census Bureau, we conduct an empirical simulation study as well as a data analysis that compare a subset of the methods introduced.