Models for Small Area Estimation for Census Tracts

This study examines issues of Small Area Estimation (SAE) that are raised by reliance on the American Community Survey (ACS), which reports tract-level data based on much smaller samples than the decennial census long-form that it replaced. We demonstrate the problem using a 100% transcription of microdata from the 1940 census. By drawing many samples from two major cities, we confirm a known pattern: random samples yield unbiased point estimates of means or proportions, but estimates based on smaller samples have larger average errors in measurement and greater risk of large error. Sampling variability also inflates estimates of measures of variation across areas (reflecting segregation or spatial inequality). This variation is at the heart of much contemporary spatial analysis (Sampson 2012). We then evaluate possible solutions. For point estimates, we examine three Bayesian models, all of which reduce sampling variation, and we encourage use of such models to correct ACS small area estimates. However, the corrected estimates cannot be used to calculate estimates of variation, because smoothing toward local or grand means artificially reduces variation. We note that there are potential Bayesian approaches to this problem, and we demonstrate an efficacious alternative that uses the original sample data.