For an overview of the changes in methodology between this release and the 2003 release see Estimation Procedure Changes.

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 Annual Social and Economic Supplement (ASEC) of the Current Population Survey (CPS) in a way that varies the importance given to the direct CPS ASEC estimates from state to state depending upon their reliability.
- The SAIPE program multiplies model-based estimates of poverty ratios by demographic estimates of the population to provide estimates of the numbers of people in poverty.
- The SAIPE program controls the state estimates of the number of people in poverty so that the total agrees with the direct CPS ASEC national estimates.
- 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 CPS ASEC 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 CPS ASEC 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 CPS ASEC 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.

**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 CPS ASEC 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 CPS ASEC direct-estimated number of people in poverty of the given age in the numerator and the CPS ASEC direct-estimated noninstitutional population of the given ages in the denominator. These "poverty ratios" differ from official poverty rates, which would use the CPS ASEC 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 ASEC 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 ASEC 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 ASEC direct population estimates, which contain substantial sampling error for most states. The CPS ASEC controls survey weights only to reproduce estimates of the population age 0-18 and 19 and over at the state level, and we are making estimates for more specific age groups.

**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 CPS ASEC. 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 poverty ratios of
people age 65 and over in 2004, 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 2004.

From 2000 to 2003 we used Census 2000 estimates, not census residuals, as predictors in all our models. The switch to census residuals for most of the 2004 models was made because statistical comparisons of the two alternative models for 2004 favored use of census residuals (for all but the 65 and over poverty ratios). For further discussion see Estimation Procedure Changes.

**The Poverty Ratio Models**

The dependent variable is the 2004 state estimate of the ratio of the number of people in poverty for the relevant age group to the noninstitutional population of that age with both the numerator and denominator estimated from the 2005 CPS ASEC.

The model of state poverty ratios employs the following predictors:

- 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 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 estimate of median household income in 2004 from the 2005 CPS ASEC.

The regression model for the 2004 median household income for states 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.

Source: U.S. Census Bureau | Small Area Income and Poverty Estimates |
Last Revised:
April 29, 2013