- SAIPE combines estimates from the regression with estimates from the Current Population survey (CPS) in a way that varies the importance of the CPS estimates from state to state depending upon their reliability.
- SAIPE multiplies estimates of poverty ratios by estimates of the population to provide estimates of the numbers of poor people.
- SAIPE controls the state estimates of the number of poor people so that the total agrees with the CPS national estimates.
- SAIPE represents the prior census (1990) with residuals from auxiliary cross-sectional regressions.
- 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 under age 18 are "related children," there are two sets of equations for children ages 5 to 17.
- SAIPE estimates the total number of poor people as the sum of estimates from a set of age-specific equations.

*Empirical Bayes Techniques.*
The models SAIPE uses to estimate 1995 income and poverty at the
state level employ both direct survey-based estimates of 1995 income and poverty from the
March 1996 CPS and regression predictions of income and poverty based on administrative and
census data. We combine the regression predictions with the direct sample estimates using
Empirical Bayes (EB) techniques. The EB techniques weight the contribution of the two
components (regression predictions and direct estimates) on the basis of their relative precision.

The EB or "shrinkage" estimates are the weighted averages of the model predictions and the direct sample estimates. In the case of poverty, we combine estimates of ratios. The two weights for each state add to 1.0 and the weight on the model prediction is computed as the sampling variance divided by the total variance (sampling plus lack-of-fit) of the direct estimate. Using this technique, the larger the sampling variance of a direct sample estimate, the smaller its contribution to the model estimate, and the larger the contribution from the prediction equation.

*Poverty Ratios and Numbers of Poor People.*
In deriving state-level estimates of the numbers
of poor people of various ages, we use regression equations with poverty ratios for those ages as
the dependent variables. We multiply regression predictions from these equations by estimates of
the noninstitutional population of the appropriate ages to obtain modeled estimates of the
numbers of poor people. We multiply the direct CPS estimates of poverty ratios by the same
population estimates to convert them to direct (i.e., survey-based) estimates of numbers of poor
people.

The poverty ratios used in the state-level models are not the official poverty rates because we use the noninstitutional population as the denominator rather than the poverty universe (for a discussion of poverty universe differences, see Denominators for Model-Based State and County Poverty Rates). For related children in families, we use ratios of the number of related children in families in poverty to the number of children in the noninstitutional population. We use these poverty ratios because of the difficulty of deriving estimates of the size of the poverty universe and the number of related children in families.

We derive the estimates of the noninstitutional population by age from the U.S. Census Bureau's annual intercensal population estimates for states. We use these estimates, instead of the estimates of population obtained directly from the CPS, because 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 poverty ratio estimates by population estimates at the state level, we have not employed the county-level estimates in the same roles, because the estimates of the populations of counties by age are likely to be much less stable than state estimates, and little is known about their uncertainty.

*Controlling to the National Estimates.*
Completing the shrinkage estimates does not
produce the final state estimates. After converting the shrinkage estimates of poverty ratios to
estimates of numbers of poor, the last step in the process is controlling the model-based state
estimates of the number of poor people to the direct national estimate of numbers 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.

*Representing the Prior Census in the Poverty Rate Models.*
The prior census results appear
in some form in each of the age-specific models of poverty. In the models for poor people age 65
and over in 1995, the poverty rate for that age group in the 1990 census is a predictor. For all
other age groups, the representation of the prior census is somewhat more complex.

For each of the age groups 0-4, 5-17, and 18-64, we estimated a cross-sectional model for 1989, using the 1990 census poverty rate for the age group as the dependent variable and the census year values of the administrative data as predictors. The residuals from these cross-sectional regressions identify states in which the selected predictors either overestimate or underestimate poverty, as measured by the census. We used the residuals from the 1990 cross-sectional regression as predictors of poverty in 1995.

*Estimating the Total Number of Poor People.*
We derived the estimate of the total number of poor people in a state
by summing 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. Summing state-level
estimates from separate models for these groups produces superior estimates of
the total relative to a single state-level model for the total number of poor.

**The Model for the Number of Poor People Ages 5 to 17**

The model of 1995 state poverty ratios for related children age 5 to 17 years in families in poverty employs the following predictors:

- the 1995 "tax return poverty rate" for children -- the percentage of child 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;
- the 1995 "nonfiler rate" for people under age 65 -- 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;
- the 1995 food stamp recipiency rate -- average number of participants of all ages per month in the food stamp program as a proportion of the total population;
- residuals from a regression of the 1990 census poverty rates for 1989 for all people 5 to 17 years of age on the 1989 values of these three variables; and
- an intercept term.

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

The dependent variable is the 1995 state estimates of the ratio of poor related children age 5 to 17 years to the noninstitutional population of that age from the 1996 March CPS.

The residuals from the 1990 census identify states in which the selected predictors tend to either overestimate or underestimate poverty, as measured by the census. Note that only this independent variable refers to the group age 5 to 17 years.

To derive the 5 to 17 year old component of the total number of poor in 1995, we estimate an equation with the same independent variables using the 1995 state estimates of the ratio of the number of poor children age 5 to 17 (related and unrelated) to the noninstitutional population age 5 to 17 as the dependent variable.

We average the predicted ratio for each state with the CPS direct sample estimates using Empirical Bayes techniques, and transform the results into estimated numbers of poor by multiplying them by the appropriate estimate of the noninstitutional population (see the discussion of poverty rates and numbers of poor above in this section). Finally, we ratio-adjust the estimated numbers for each state to the CPS national estimate.

**The Model for the Number of Poor People under Age 5**

The model of 1995 state poverty ratios for people under age 5 employs the following predictors:

- the 1995 "tax return poverty rate" for people under age 65 years -- the number of exemptions under age 65 years which are 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 divided by the population for that age group;
- the 1995 "nonfiler rate" for people under age 65 -- 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;
- the 1995 food stamp recipiency rate -- average number of participants of all ages per month in the food stamp program as a proportion of the total population;
- residuals from a regression of the 1990 census poverty rates for 1989 for all people under age 5 years on the 1989 values of these three variables; and
- an intercept term.

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

The dependent variable is the 1995 state estimates of the ratio of the number of poor children under 5 years to the noninstitutional population of that age from the March 1996 CPS. Note that only the residuals from the previous census refer precisely to the target age group. We average the predicted rates with the CPS direct sample estimates using Empirical Bayes techniques, and transform the results into estimated numbers of poor by multiplying them by the appropriate estimate of each state's noninstitutional population. Finally, we ratio-adjust the estimated numbers for each state to the CPS national estimate.

**The Model for the Number of Poor People Ages 18-64**

The model of 1995 state poverty ratios for people age 18 to 64 years employs the same predictors as the model for people under age 5, except that the 1990 census residuals are specific to people 18 to 64 years of age instead of children under age 5. The dependent variable is the 1995 state estimate of the ratio of the number of poor people age 18-64 to the population of that age from the March 1996 CPS.

**The Model for the Number of Poor People Age 65 and over**

The equations for people age 65 and over are slightly different from those above. We have more appropriate predictors because we can separate the tax exemptions for people age 65 years and over and because we have data from the Supplemental Security Income program for people this age. In addition, the poverty rate for people age 65 and over from the prior census is a better predictor for this age group than the regression residuals we have employed for other age groups. The predictors of 1995 state poverty rates for people age 65 and over are:

- the 1995 "tax return poverty rate" for people age 65 years and over -- the number of exemptions age 65 years and over which are 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 divided by the population for that age group;
- the 1995 "nonfiler rate" for people age 65 and over -- the difference between the estimated population age 65 and over and the number of exemptions age 65 and over, expressed as a percentage of the population age 65 and over;
- the 1995 Supplemental Security Income recipiency rate -- the number of recipients age 65 years and over divided by the population of that age;
- the poverty rate for people age 65 years and over from the 1990 census; and
- an intercept term.

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

The dependent variable is the CPS estimates of 1995 state poverty rates for people age 65 and over. We average the predicted rates with the CPS direct sample estimates using Empirical Bayes techniques, and transform the results into estimated numbers of poor by multiplying them by the appropriate estimate of each state's noninstitutional population. Finally, we ratio-adjust the estimated numbers for each state to the CPS national estimate.

**The Model for the Total Number of Poor People**

We derived 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. Summing state-level estimates from separate models for these groups produces superior estimates of the total relative to a single state-level model for the total number of poor.

**The Model For Median Household Income**

The regression model for the 1995 median household income for states has the following predictor variables:

- the 1989 median household income derived from the 1990 census; and
- the 1989 median household income derived from the 1990 census adjusted by the ratio of the median 1995 adjusted gross income to the median 1989 adjusted gross income from tax returns.

The dependent variable is the direct estimate of median household income in 1995 from the March 1996 CPS. We average the model estimates with the direct sample estimates from the March CPS using Empirical Bayes techniques. We do not ratio-adjust the state medians to the CPS estimate of the national median. Unlike estimates of poverty ratios, estimates of state-level medians cannot be averaged to get a national median.

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