Methodological Change - Bayesian approach for state model estimation:
In 1995 and prior income years, the state poverty ratio and median income models were fitted to the CPS data by maximum likelihood (ML), and the resulting fitted models were used to develop Empirical Bayes (EB) "shrinkage" estimates of the true poverty ratios and corresponding error variances for the estimates. A key parameter used in the model fitting is the model error variance. This parameter, together with the state sampling error variances (which are estimated separately by fitting a sampling error model to direct CPS variance estimates), determines the weights given to the direct CPS estimates and to the regression predictions in the EB shrinkage estimates. The model and sampling error variances also determine the error variance of the shrinkage estimates. For all the age group poverty ratios, ML estimated the model error variance to be zero for many of the previous years, though this was not the case for median income. Statistical estimates of variance components by ML and some other methods can be zero; for EB shrinkage, however, this result has the unreasonable consequences that (1) no weight is then given to the direct CPS estimate in the EB shrinkage, and (2) the estimated error variances of the shrinkage estimates are likely to underestimate the true variances, resulting in confidence intervals that are too narrow.
To address the problems caused by estimates of zero for the model error variance, we switched to a Bayesian approach for treatment of the state models. This approach is described in "Accounting for Uncertainty About Variances In Small Area Estimation" (Bell 1999) in the Published Papers section of this web site. The Bayesian approach always leads to a positive estimate of the model error variance. In practical terms, the Bayesian predictions of the true poverty ratios and of median income tend not to differ very much from the corresponding EB estimates, but the Bayesian prediction error variances are substantially larger than the estimated variances for the EB estimates. The fact that the Bayesian approach leads to larger estimated variances than those for the EB approach does not mean that the true variances for the Bayesian approach are larger than those for EB. In fact, the differences between the Bayesian and EB estimated variances are most likely due to the estimated EB variances significantly underestimating the true EB variances. If anything, the true variances for the poverty ratio estimates should be slightly lower for the Bayesian approach than for the EB approach.
For median income, the switch to the Bayesian approach was not motivated by a need to deal with zero estimates of model error variance, since that problem does not occur for median income. Rather, it was done partly for consistency with the treatment of the poverty ratio models, and partly to address understatement of error variances in previous EB estimates of median income. This variance understatement was due to ignoring the variance contribution arising from having to estimate the model error variance parameter. This variance contribution is easily handled in the Bayesian approach; alternatively, it can be addressed for EB by augmenting the naive EB variance estimates used previously by an approximate correction term (Datta and Lahiri 2000). Both approaches yield mostly similar results for median income, though the variances from the Bayesian approach tend to be slightly larger, and are significantly larger in some cases.
Model Change - County model CPS sampling variance function:
In the county model we modified the equation for calculating the CPS sampling error variance to better match the distribution of the errors. This change improves the characterization of the estimated uncertainty of the poverty estimates, which were presented as confidence intervals, and improves the statistical models' description of the data. This change is based on research which is documented in Technical Report #1 and Technical Report #4 which can be found in the Technical Reports section of this web site.
Variable Definition Changes:
For the state food stamp variable, the method of adjusting for disaster food stamp issuance was changed. In 1995, the adjustment to remove increases in the number of recipients due to issuance of "disaster relief" food stamps was based on data supplied by USDA. For 1996 revised and 1997, we instead adjusted for receipt of disaster relief stamps using time series modeling. This change has minor effects on the actual food stamp variable constructed (which divides 12-month average adjusted recipients by population), but was made for two reasons. First, for some disasters the number of disaster relief food stamp recipients had to be approximated because the available data gave only the number of recipient households. Second, the adjustment based soley on USDA data on issuance of disaster relief food stamps left significant outliers in many of the affected months, suggesting that this adjustment was inadequate. One reason for this could be that some people who would otherwise receive regular food stamps instead apply for disaster relief stamps, and for our purposes this unknown number of persons should not be subtracted from the total number of food stamp participants. This change affects the county model because each state's county food stamp participation numbers are raked to the state total food stamp participation number.
In the state model that estimates poverty for people age 65 and over we modified the Supplemental Security Income (SSI) variable. For the 1996 revised and 1997 estimates we used an average of the four month estimates (March, June, September and December) of the number of recipients "Age 65 and over" receiving SSI payments as reported by the Social Security Administration. In previous years we used a one month (December) estimate of the number of "Aged" recipients. We switched to using "Age 65 and over" because this variable includes all people who are over "Age 65 and over" received SSI payments whereas the "Aged" variable only included people who received SSI payments because they were over age 65, excluding people who were now over 65 but received them prior to turning 65 for another reason (such as a disability). We had not used the "Age 65 and over" variable in previous years because it was not available. We switched to an average of four months rather than a single-month data point to minimize the effects of monthly changes in recipients. Although we believe the new definition of SSI participants makes more sense for our models, the new and old variables are in fact very closely related, and comparisons of model fit with income year 1996 and 1997 data showed almost no difference between use of the old and new variables.
Bell, William R. (1999), "Accounting for Uncertainty About Variances in Small Area Estimation," Bulletin of the International Statistical Institute, 52nd Session, Helsinki, 1999. Datta, Gauri S. and Lahiri, Partha (2000), "A Unified Measure of Uncertainty of Estimated Best Linear Unbiased Predictors in Small-Area Estimation Problems," Statistica Sinica, 10, 613-628.