Small Area Income & Poverty Estimates  Model-based Estimates for States, Counties, & School Districts

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2005 State-Level Estimation Details

For an overview of the changes in methodology between the 2005 and 2004 estimates, see Estimation Procedure Changes. The major change discussed there involves the switch to using data from the American Community Survey (ACS) as the basis for the SAIPE estimates, replacing the data from the Current Population Survey (CPS) Annual Social and Economic Supplement (ASEC) that was used in previous years.

Several features of the state estimates should be noted.

• Bayesian estimation techniques are applied to the Small Area Income and Poverty Estimates (SAIPE) program's models to combine regression predictions with direct estimates from the ACS in a way that varies the importance given to the direct ACS estimates from state to state depending upon their reliability.
• The SAIPE program multiplies model-based estimates of state poverty ratios by demographic estimates of state populations to provide estimates of the numbers of people in poverty in each state for various age groups.
• The SAIPE program controls the state estimates of the number of people in poverty so that their total agrees with the direct ACS national estimate.
• The SAIPE program state models use data from the prior census (2000) to form a predictor variable in the regression models in one of two ways. The models either use the Census 2000 estimates directly, or use residuals from auxiliary cross-sectional regressions done with the Census 2000 estimates.
• Because the Department of Education requires estimates of the number of "related children age 5 to 17 in families in poverty", and not all children 5 to 17 are "related children", there are two sets of equations for children ages 5 to 17.
• The SAIPE program estimates the total number of people in poverty as the sum of estimates derived from a set of four age-specific equations.

A brief discussion of these features follows along with a presentation of the specific models used.

Bayesian Estimation Techniques
The models the SAIPE program uses to estimate income and poverty at the state level employ both direct survey-based estimates of income and poverty from the ACS 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. This is done separately for each year.

The regression models used to develop the regression predictions are postulated for the true, unobserved poverty ratios and median income, but they are fitted to the ACS direct estimates allowing for the sampling errors in the data. If the variance of the error term in a given regression model (the model error variance) was known, then the Bayesian estimate for each state would be a weighted average (shrinkage estimate) of the state's regression prediction and direct ACS 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 Publications section of this web site.

Note that with the ACS data the sampling error variances for many states are sufficiently low that the direct ACS estimate effectively gets most of the weight. This contrasts with the situation in previous years when SAIPE used data from the CPS ASEC, whose sampling error variances tended to be much larger than the estimated model error variance. The models for the CPS ASEC data led to most of the weight being put on the regression predictions.

Poverty Ratios and Numbers of People in Poverty
Deriving state-level estimates of the numbers of people in poverty of various ages involves two steps. The first step is to apply the models and Bayesian estimation techniques to the ACS 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 people in poverty of various ages.

The poverty ratios used as the dependent variables in the regression models have the ACS direct-estimated number of people in poverty of the given age group in the numerator, and the ACS direct-estimated household population of the given age group in the denominator. These "poverty ratios" differ slightly from official poverty rates, which would use the ACS direct-estimated poverty universes of the given age as the denominators. For a discussion of the differences between the household population and the poverty universe see Denominators for State and County Poverty Rates.

The ACS direct state household population estimates are generally very close to the demographic state population estimates used to multiply the model-based poverty ratio estimates, particularly for larger states and for the broader SAIPE age groups (i.e., 18-64 versus 0-4). This is due to the use of substate demographic population estimates for detailed age groups as controls in the determination of the ACS final tabulation weights. Differences between the ACS and demographic state population estimates for the age groups used by SAIPE arise due to collapsing over these age groups that occurs in the application of the population controls for some areas. The ACS and demographic estimates of total population (all ages) will generally agree, however. For a discussion of the use of population controls in the ACS weighting, see Section 11.4 of the report on Design and Methodology: American Community Survey [PDF 7.8M]. (Note: The 2005 ACS, and the demographic population estimates just mentioned, refer to the household population, whereas published Census Bureau population estimates refer to the larger resident population, which includes both the household and group quarters population.)

Controlling to the National Estimates
After converting the Bayesian estimates of poverty ratios to state estimates of numbers of people in poverty, we control these estimates to the direct national estimate of number people in poverty based on the ACS. 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 prior census results appear in some form in each of the models. In the model for the ACS 2005 poverty ratios of people age 65 and over, the 65 and over poverty ratio from Census 2000 is used as a predictor. For all the other models, the use of the prior census data is somewhat more complex.

For each of the poverty ratios for ages 0-4, 5-17, and 18-64, and for median household income, we first estimated a cross-sectional model for 1999, using the Census 2000 state estimates as the dependent variable and the 1999 values of the administrative data as predictor variables. The residuals from these cross-sectional regressions reflect the extent to which the model based only on the administrative data predictors either overestimates or underestimates poverty for each state, as measured by the census. We used the residuals from these cross-sectional regressions as predictors in the models for the ACS 2005 data.

The Poverty Ratio Models

The dependent variable is the direct state estimate of the ratio of the number of people in poverty for the relevant age group to the household population of that age with both the numerator and denominator estimated from the 2005 ACS.

The models of state poverty ratios employ the following predictor variables:

• an intercept term.
• the 2004 "tax return poverty rate" for the age group. The numerator of this rate is defined as the number of exemptions entered on returns for which the adjusted gross income falls below the official poverty threshold for a family of the size implied by the number of exemptions on the return. For the age 5-17 and 65 and over poverty ratio models, we use the number of exemptions for children in poverty and the number of exemptions for people over 65 in poverty, respectively, in the numerator. For the other age groups, we use the number of exemptions of all persons under age 65 in poverty in the numerator. The denominator of this rate is the 2005 demographic estimate of the state population for the age group corresponding to that used in the numerator, except for 5-17 for which the denominator is the total state child exemptions for 2004.
• the 2004 "nonfiler rate". For the ages 0-4, 5-17, and 18-64 poverty ratio models, this is defined as the difference between the estimated population under age 65 and the number of exemptions under age 65, expressed as a percentage of the population under age 65. For the age 65 and over poverty ratio model, this is defined as the difference between the estimated population age 65 and over and the number of age exemptions, expressed as a percentage of the population age 65 and over. Note that this variable, as well as the "tax return poverty rate" variable, do not refer specifically to the age group being modeled, except in the 65 and over model.
• the food stamp participation rate -- the adjusted, monthly average number of participants of all ages in the food stamp program over the 12 months July 2004 - June 2005 as a proportion of the total population. This variable is used for the 0-4, 5-17, and 18-64 models.
• the 2004 Supplemental Security Income (SSI) recipiency rate. This is defined as the 12-month average number of state SSI recipients age 65 years and over for 2004 divided by the 2005 demographic estimate of the state population of that age. This variable is used only for the 65 and over model.
• the Census 2000 65 and over poverty ratios for 1999 (for the 65 and over poverty ratio model) or (for the other age groups) the residuals from a regression of the Census 2000 poverty ratios for 1999 for the relevant age group on the 1999 values of the above variables.

For further information on these variables, go to Information about Data Inputs.

Estimating the Total Number of People in Poverty.

We derive the estimate of the total number of people in poverty in a state by summing the separate model-based estimates of the number of people in poverty 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 dependent variable is the direct state estimate of median household income from the 2005 ACS.

The regression model for the state median household income has the following predictor variables:

• an intercept term.
• the 2004 state median adjusted gross income derived from IRS tax returns.
• residuals from a regression of the Census 2000 state median household income (for income year 1999) on the intercept term and the 1999 IRS median income.

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Page Last Modified: January 09, 2008