Using the t-distribution in Small Area Estimation : An Application to SAIPE State Poverty Models

The Census Bureau’s Small Area Income and Poverty Estimates (SAIPE) program produces state age-group (0-4, 5-17, 18-64, 65+) poverty ratio estimates from Bayesian treatment (Bell 1999) of a Fay-Herriot model (Fay and Herriot 1979) applied to direct state poverty ratio estimates from the Current Population Survey (CPS) Annual Social and Economic Supplement (ASEC, formerly known as the CPS March income supplement). The models borrow information from regression variables related to poverty that are constructed from administrative records data, as well as age group poverty ratio estimates from the previous decennial census. Estimates are identified by the “income year” (IY), which refers to the year for which income is reported in the ASEC. Since 2001, the CPS ASEC sample size has been about 100,000 households. Further information is available on the SAIPE web site at www.census.gov/hhes/www/saipe/index.html. For simplicity, in what follows we shorten references to “CPS ASEC” to just “CPS.” In recent years supplementary surveys for the American Community Survey (ACS) have also provided state poverty estimates. The ACS asks essentially the same questions as previous decennial census long form surveys, and is replacing the long form, but with the data collection spread continuously throughout the decade. The supplementary surveys have had sample sizes of about 800,000 addresses, significantly larger than the CPS. Further information on the ACS may be found at www.census.gov/acs/www/. The ACS procedures for collecting income data differ from those of the CPS. ACS collects income data continuously with a reference period of the pre-