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Small Area Income & Poverty EstimatesModel-based Estimates for States, Counties, & School Districts |
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The 1999 state and county estimates of poverty and income were released in October 2002. For an overview of the changes in methodology between this release and the previous release see Estimation Procedure Changes.
Several features of the 1999 state estimates should be noted.Bayesian Estimation Techniques. The models SAIPE used to estimate 1999 income and poverty at the state level employ both direct survey-based estimates of 1999 income and poverty from the March 2000 CPS and regression predictions of income and poverty based on administrative records and Census 2000 data. We combine the regression predictions with the direct sample estimates using Bayesian techniques. The Bayesian techniques weight the contribution of the two components (regression predictions and direct estimates) on the basis of their relative precision.
The regression model used to develop the regression predictions is postulated for the true, unobserved poverty ratios or median income, but it is fitted to the CPS direct estimates allowing for the sampling error in the data. If the variance of the error term in this regression model (the model error variance) were known, then the Bayesian estimate for each state would be a weighted average (shrinkage estimate) of the state's regression prediction and direct CPS estimate. The two weights in this average add to 1.0, with the weight on the direct estimate computed as the model error variance divided by the total variance (model error variance plus sampling error variance). In this average, the larger the sampling variance of a direct sample estimate, the smaller its contribution to the shrinkage estimate, and the larger the contribution from the regression prediction. Since the model error variance is unknown, the Bayesian approach averages the shrinkage estimates computed over a plausible range of values of the model error variance, weighting the results for each of these values according to the posterior (conditional on the data) probability distribution of the model error variance developed from the Bayesian calculations. The result is generally very close to what one gets by estimating the model error variance by the mean of its posterior distribution and computing the corresponding shrinkage estimate. Technical details of the Bayesian approach are discussed in the paper, "Accounting for Uncertainty About Variances In Small Area Estimation," (Bell 1999) in the Published Papers section of this web site.
Prior Distribution for Regression Parameters. Bayesian estimation requires that a "prior probability distribution" be specified for the model parameters to reflect what we know about them prior to fitting the model to the data. In past years we used a noninformative prior that conveyed no useful prior information - the prior distribution was simply a constant over all parameter values. For 1999, however, we specified an informative prior distribution for the regression coefficients of the administrative records predictors in the poverty ratio models. (We still used a noninformative, constant prior for the other model parameters.) We made this change because of the unique status of the census poverty ratio estimates when they refer to the same year as the CPS estimates being modeled rather than to an earlier year. Since the 2000 census and 2000 CPS both estimated poverty for 1999, albeit with differences in regard to sampling and nonsampling errors, there is reason to expect the administrative records regression variables in the CPS models to be much less relevant in 1999 than in other, non-census years. Empirical verification of this came from model fits to 1990 CPS poverty ratio estimates for IY 1989 using 1990 census data in the model: the fits showed the coefficients on the administrative records variables to be statistically insignificant for all age groups. To reflect our prior knowledge that the administrative records variables should be less relevant for 1999 than for non-census years, and that in fact for 1999 they may not be useful at all, we used a prior distribution for their regression coefficients that had mean zero and had variance determined in a manner we thought to be "conservative" in the sense of avoiding placing too much confidence in the prior.
Results from the poverty ratio model fits for IY 1989 were used in developing the prior variances of the administrative records variables' regression coefficients. In fact, we simply took the variance matrix of these coefficients from the fitted model and multiplied it by 4 to reflect additional uncertainty about how these results from 1989 would translate to 1999. This doubled the standard deviations of these parameters from the 1989 model fits to reflect a relatively mild amount of prior information ("conservative assumptions.")
The use of the informative prior reduced the uncertainty about the corresponding regression coefficients in the 1999 poverty ratio models. It thus yielded small reductions in the state prediction error variances, and hence slightly narrower confidence intervals for the true poverty ratios. The prior had very minor effects on the point estimates.
We did not use an informative prior distribution for the coefficient of the administrative records variable (IRS median adjusted gross income) in the 1999 CPS median income model, because in the median income model we fit for IY 1989, we found the IRS variable to be statistically significant, even with the census data in the model. The same result also held in the 1999 median income model.
Poverty Ratios and Numbers of Poor People. Deriving state-level estimates of the numbers of poor people of various ages involves two steps. The first step is to apply the Bayesian estimation techniques applied to CPS direct state estimates of "poverty ratios." The second step is to multiply the resulting model-based poverty ratio estimates by corresponding demographic population estimates to convert the results to estimates of the numbers of poor people of various ages.
The poverty ratios used as the dependent variables in the regression models have the CPS direct-estimated number poor of the given age in the numerator and the CPS direct-estimated noninstitutional population of the given ages in the denominator. These "poverty ratios" differ from official poverty rates which would use the CPS estimated poverty universes of the given age as the denominators. (For a discussion of the differences between the noninstitutional population and the poverty universe see Denominators for Model-Based State and County Poverty Rates).
We use CPS estimated numbers in both the numerator and denominator of the poverty ratios because positive correlation between the two estimates generally makes the resulting poverty ratio estimate more precise than one obtained with a CPS estimated numerator and a demographic population estimate in the denominator. We multiply the model-based poverty ratio estimates by demographic population estimates, however, because the demographic estimates are deemed more reliable than CPS direct population estimates, which contain substantial sampling error for most states. The CPS controls survey weights only to estimates of the population age 16 and over at the state level, and we are making estimates for more specific age groups.
While we have multiplied model-based poverty ratio estimates by population estimates at the state level, we have not addressed the county-level estimation in the same way, because the estimates of the populations of counties by age are likely to be much less stable than the state population estimates, and little is known about their error structure. Thus, for counties, we directly model (logarithms of) CPS estimates of the number of poor people.
Controlling to the National Estimates. After converting the Bayesian estimates of poverty ratios to state estimates of numbers of poor, we control these estimates to the direct national estimate of number poor based on the CPS. We do not control estimates of state median household income to the national median because the estimation model does not produce the entire household income distribution, which would be required to do so.
Using Estimates from Census 2000 in the Models. The Census 2000 estimates provide regression predictor variables for each of the age-specific poverty ratio models and the median income model. The specific variables are documented below. The models use the actual census estimates, rather than "census residuals" as was generally done in previous years. However, since 1999 is a census year, the models using census estimates as a regression variable are equivalent or nearly equivalent to models using census residuals for the purpose of developing model-based estimates of poverty ratios or median income. For further discussion of this point see Estimation Procedure Changes for the 1999 Estimates on this web site.
The Poverty Ratio Models
The model of 1999 state poverty ratios employs the following predictors:
Note the population estimates for other years use July 1, demographic population estimates in the denominators. For 1999 estimates we use Census 2000, which represents April 1, 2000 population.
For further information on these variables, go to Information about Data Inputs.
The dependent variable is the 1999 state estimate of the ratio of the number poor for the relevant age group to the noninstitutional population of that age with both the numerator and denominator estimated from the March 2000 CPS.
Estimating the Total Number of Poor People.
We derive the estimate of the total number of poor people in a state by summing the separate model-based estimates of the number of poor people by age (not limited to related children). The age groups with separate models were 1) people under 5 years of age, 2) people age 5 to 17 years, 3) people age 18 to 64 years, and 4) people age 65 years and over.
The Model For Median Household Income
The regression model for the 1999 median household income for states has the following predictor variables:
The dependent variable is the direct estimate of median household income in 1999 from the March 2000 CPS.