For an overview of the changes in methodology between this release and the 2005 release see Estimation Procedure Changes. One change of note discussed there is that, starting in 2009, estimates of poverty for ages 5-17 for the District of Columbia (DC) are obtained from the county model, instead of the state model. For poverty of the other age groups and for median household income, estimates for DC are still obtained from the state model.

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 (American Community Survey) 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 these state estimates of the number of people in poverty so that their total across states 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 direct ACS 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. This is the Bayesian estimate used by SAIPE. It is generally very close to what one would get 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.

Note that for many states the sampling error variances of the direct ACS estimates are sufficiently low that in the Bayesian estimation the direct ACS estimate effectively gets most of the weight. Thus, for large states the Bayesian estimates are very close to the direct ACS estimates. For small states the Bayesian estimates potentially differ more from the direct ACS estimates (when the regression prediction for a state differs materially from its direct ACS estimate.)

**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 direct ACS 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 direct ACS-estimated number of people in poverty of the given age group in the numerator, and (approximately) the direct ACS-estimated poverty universe (those persons for whom the survey would determine if they are in poverty or not in poverty) of the given age group in the denominator. For ages 18-64 and 65 and over the denominator actually is the estimated "poverty universe" for the age groups, so these ratios are true "poverty rates." For ages 0-4 and 5-17 the denominators differ slightly from the estimated poverty universes, so the "poverty ratios" differ slightly from official poverty rates. For further discussion of this, see Denominators for Model-Based State and County Poverty Rates.)

For each age group the model-based poverty ratio estimates are multiplied by corresponding demographic state population estimates (adjusted to estimate the poverty universe for ages 18-64 and 65 and over, and the slightly different concept used for ages 0-4 and 5-17). These demographic estimates are generally very close to the denominators of the direct ACS estimated state poverty ratios, particularly for larger states and for the broader SAIPE age groups (i.e., 18-64 as opposed to 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 11.5 of the report on Design and Methodology: American Community Survey. (Note: Since the poverty universe is a subset of the total population, the demographic estimates of the poverty universe are slightly smaller than published Census Bureau population estimates which are for the total resident 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 models for the ACS 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 2006 - 2009 data.

**The Poverty Ratio Models**

For concreteness we describe the poverty ratio models used for 2009. Completely analogous comments apply to the models used for 2006 – 2008, but with the variables shifted back appropriately in time (except for the Census 2000 estimates and Census 2000 residuals, which remain the same).

The dependent variable is the estimated state poverty ratio, with both the numerator and denominator estimated from the 2009 ACS.

The models of state poverty ratios employ an intercept term and the following predictor variables calculated for each state:

- the 2008 "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 the tax return poverty rate is the 2009 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 2008.
- the 2008 "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 and the "tax return poverty rate" variable, do not refer specifically to the age group being modeled, except in the 65 and over model.
- the SNAP participation rate (formerly known as the Food Stamp Program participation rate)-- the adjusted, monthly average number of participants of all ages receiving SNAP benefits over the 12 months July 2008 - June 2009 as a proportion of the total population. This variable is used for the 0-4, 5-17, and 18-64 models.
- the 2008 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 2008 divided by the 2009 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**

For the 2009 estimates the dependent variable is the direct state estimate of median household income from the 2009 ACS.

The 2009 regression model for state median household income employs an intercept term and the following predictor variables calculated for each state:

- the 2008 state median adjusted gross income (AGI) 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.

The analogous model is used for the 2006-2008 state median household income estimates, with the variables shifted back appropriately in time.

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