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The Census Bureau’s Small Area Income and Poverty Estimates Program (SAIPE) produces model-based poverty estimates at the county and state level. SAIPE uses Fay-Herriot (1979) models with dependent variables obtained from direct survey poverty estimates (currently obtained from ACS, but prior to 2005 obtained from CPS), and regression predictor variables derived from tabulations of IRS tax data, SNAP (Supplemental Nutrition Assistance Program, formerly food stamps) program data, and previous census estimates (since 2000, these have been the Census 2000 long form estimates). Although the latter have consistently been important predictors in the state and county models, as time advances and the Census 2000 poverty estimates become further removed from the production year, questions arise about their continued value in the model, and particularly about whether they might be somehow replaced in the model by ACS estimates for previous years. At the county level this would suggest consideration be given to replacing Census 2000 estimates with ACS 5-year estimates formed from data for the 5 years preceding the production year (because the only estimates published for all counties are 5-year estimates.) At the state level, the Census 2000 estimates could be replaced by single-year ACS estimates for the year immediately preceding the production year.
In using previous census poverty estimates to define regression variables, SAIPE has ignored the fact that these are survey estimates obtained from the long form and so contain sampling error. At the state level, the sampling errors of the Census 2000 long form estimates used by SAIPE are essentially negligible and can be ignored. This is less true at the county level, however, particularly for small counties. Furthermore, in considering the replacement in the model of previous census estimates with previous ACS estimates, this issue becomes more pressing, as the ACS sampling variances are higher. We illustrate this point in the report. When a predictor variable, such as Census 2000 long form data or previous ACS data, contains nonnegligible sampling error, a bivariate Fay-Herriot model with that predictor as a second dependent variable, can account for that uncertainty. We take that approach in this study, using bivariate models in which “current year” ACS estimates define one of the dependent variables, and either Census 2000 estimates or previous ACS estimates define the second dependent variable. We then compare prediction error variances (posterior variances) from these models to assess which predictor variable—Census 2000 estimates or previous ACS estimates—yields the lowest prediction error variances for the current year. We do this for models at the state and county level for which ACS single-year estimates for 2009 provide the current year estimates. We also obtain county model results with ACS single-year estimates for 2010 providing the current year estimates.
There are two general conclusions from our study. One is that the differences in prediction error variances depending on which data define the second dependent variable are generally not large. The second conclusion is that, among the three candidates, prediction error variances from using ACS multi-year estimates from previous years as the second dependent variable were in some cases lower, and were generally not higher, than those from the other two candidate models. This suggests that replacing the univariate Fay-Herriot models that use Census 2000 estimates to define regression predictor variables with bivariate Fay-Herriot models that use previous 5-year ACS estimates as the second dependent variable may yield improvements as we move further away from Census 2000, and this change is unlikely to do worse.
Elizabeth T. Huang and William R. Bell. (2012). An Empirical Study on Using Previous American Community Survey Data Versus Census 2000 Data in SAIPE Models for Poverty Estimates. Center for Statistical Research & Methodology Research Report Series (Statistics #2012-04). U.S. Census Bureau. Available online at <http://www.census.gov/srd/papers/pdf/rrs2012-04.pdf>.
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