Using American Community Survey Data to Improve Estimates from Smaller US Surveys Through Bivariate Small Area Estimation Models

We demonstrate the potential for borrowing strength from estimates from the American Community Survey (ACS), the largest US household survey, to improve estimates from smaller US household surveys. We do this using simple bivariate area-level models to exploit strong relationships between population characteristics estimated by the smaller surveys and ACS estimates of the same, or closely related, quantities. We illustrate this idea with two applications. The first shows impressive variance reductions for state estimates of health insurance coverage from the National Health Interview Survey when modeling these jointly with corresponding ACS estimates. The second application shows impressive variance reductions in ACS one-year county estimates of poverty of school-aged children from modeling these jointly with previous ACS five-year county estimates of school-age poverty. Simple theoretical calculations show how the amount of variance reduction depends on characteristics of the underlying data. In our applications, we examine three alternative bivariate models, starting with a simple bivariate Gaussian model. Since our applications involve modeling proportions, we also examine a bivariate binomial logit normal model, and an unmatched model that combines the Gaussian sampling model with the bivariate logit normal model for the population proportions. Given the strong relationships between the population characteristics estimated by the smaller surveys and the corresponding ACS estimates, and the low levels of sampling error in the ACS estimates, the models achieve large variance reductions even without using regression covariates drawn from auxiliary data sources.