A Bayesian Zero-One Inated Beta Model for Estimating Poverty in U.S. Counties

We propose and evaluate a Bayesian beta regression model for U.S. county poverty rates. Such a rate model could be an improvement to the U.S. Census Bureau’s current small-area poverty approach of linearly modeling the logarithm of poverty levels. For small areas, some of which may have estimates of no poverty or all poverty, a zero-one inated rate model can usefully account for estimated rates of 0 or 1. Using Bayesian computation techniques, we estimate the parameters of a zero-one inated beta regression model. We compare the results to the Census Bureau’s current small-area model for county poverty estimation. The Small Area Income and Poverty Estimates (SAIPE) program at the U.S. Census Bureau uses small area estimation techniques to create model-based estimates of selected poverty and income statistics. The estimates are intended to be more timely than direct estimates from the decennial census or ve-year American Community Survey (ACS), as well as more precise and stable than single-year ACS direct estimates for small areas. In this paper, we are concerned with estimating the number of related poor children aged 5-17 in U.S. counties. These estimates are provided to the Department of Education and used for allocating federal funding to local programs. In 1998 a panel of the National Research Council studied alternative county models. In its report, the panel deems the county model to be at \the heart of the estimation procedure that develops estimates of school-age children in poverty to allocate federal funds under Title I of the Elementary and Secondary Education Act for education programs to aid disadvantaged children. The existing county-level approach is based on a Fay-Herriot ‘log-level’ model, i.e. a model on the natural log of the number of related poor children in each area. The model combines single-year ACS direct estimates with regression predictors from administrative data records including Internal Revenue Service (IRS) tax data and Supplemental Nutrition Assistance Program (SNAP) (‘food stamp’) data. This Fay-Herriot model is described in more detail on the Small Area Income and Poverty Estimates website (U.S. Census Bureau, 2010). The current SAIPE model is tractable and well-established, but it is worth considering alternative models that may have advantages over the current approach. In particular, some counties have ACS direct estimates of zero related children in poverty. Since log(0) is undened, these counties must be dropped from the estimation procedure, with a resulting loss of information and eciency.