# Small Area Income and Poverty Estimates

## 1993 State-Level Estimation Details

The 1993 state and county estimates were originally released in April of 1997. Revisions in the 1993 estimates were made in January of 1998. The following documentation outlines our estimation procedure for the modified estimates.

There are several complexities of our 1993 state estimates to keep in mind.
• SAIPE combines estimates from the regression with estimates from the 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 demographic estimates of the population to provide estimates of the numbers of poor people.
• SAIPE controls the state estimates of the number of poor people to the CPS national totals.
• 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 persons under age 18 are "related children," there are two sets of equations for persons under five years and two sets for persons 5-to-17.
• SAIPE estimates the total number of poor people as the sum of estimates from a set of age-specific equations.
A brief discussion of these features follows. The models are then presented.

Empirical Bayes Techniques. The models SAIPE uses to estimate 1993 income and poverty at the state level employ both direct sample-based estimates of 1993 income and poverty from the March 1994 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 empirical Bayes or "shrinkage" estimates are the weighted averages of the model predictions and the direct sample estimates. In the case of poverty, estimates of "ratios" are combined. 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. (To see the discussion of poverty universe differences, go to 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 or 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 state population estimates. We use these estimates, instead of the estimates of population one could obtain directly from the CPS, because at the state level the CPS controls survey weights only to estimates of population age 16 years and over, and we are making estimates for more specific age groups.

While we have multiplied population estimates by poverty ratio estimates at the state level, we have not employed the county-level estimates in the same roles, because the demographic 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. Completion of the shrinkage estimators 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 to control the model-based state estimates of the number of poor people to the direct national estimate of numbers based on the Current Population Survey. 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. Similarly, we control the model-based county poverty estimates to the model-based state estimates, but not their estimated median incomes.

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 1993, 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, a cross-sectional model was estimated 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. (We use census poverty rates for all children because in the census, there is no distinction between related and all children 0-4 in families and the effect for 5-17 was much less than for the CPS.) The residuals from these cross-sectional regressions identify states in which the selected predictors either overestimate or underestimate poverty, as measured by the census. The residuals from the 1990 cross-sectional regression are used as predictors of poverty in 1993. Residuals from similar 1980 cross-sectional regressions are used as predictors of poverty in 1989, when model-based estimates for that year are required.

Estimating the Total Number of Poor People. The estimate of the total number of poor people in a state was derived by summing separate model-based estimates of the number of poor by age, here not limited to related children. The age groups modeled separately were 1) people under 5 years, 2) people 5-to-17 years, 3) people 18-to-64 years, and 4) people 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 Poverty Models

People 5-to-17 years of age. The model of 1993 state poverty ratios for related children age 5-to-17 years employs the following predictors:

• The 1993 "tax return poverty rate" for child exemptions -- 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 1993 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 1993 food stamp recipiency rate -- participants, of all ages, in the food stamp program for one month 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.
• An intercept term.

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

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.

The coefficients in this equation are estimated using 1994 March CPS state estimates of the ratio of poor related children age 5-to-17 years to the noninstitutional population age 5-to-17 years for income year 1993 as the dependent variable.

To derive the 5-to-17 year old component of the total number of poor in 1993, an equation with the same independent variables is estimated using the 1993 state estimates of the ratio of poor to noninstitutional population age 5-to-17 as the dependent variable.

In each case the predicted ratios are averaged with the CPS direct sample estimates using Empirical Bayes techniques, and the results transformed 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, the estimated numbers for each state are ratio-adjusted to the CPS national estimate.

Children under age 5. The model of 1993 state poverty ratios for children under age 5 employs the following predictors:

• The 1993 "tax return poverty rate" for exemptions under age 65 years -- the percentage 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.
• The 1993 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 1993 food stamp recipiency rate -- participants, of all ages, in the food stamp program for one month 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.
• An intercept term.

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

The coefficients in this equation are estimated using the 1994 March CPS state estimates of the ratio of the number of poor children under 5 years to the institutional population of that age as the dependent variable. Note that only the residuals from the previous census refer to precisely the target age group. The predicted rates are averaged with the CPS direct sample estimates using Empirical Bayes techniques, and the results transformed into estimated numbers of poor by multiplying them by the appropriate estimate of each state's noninstitutional population. Finally, the estimated numbers for each state are ratio-adjusted to the CPS national estimate.

People 18-64. The model of 1993 state poverty ratios for persons age 18-to-64 years employs the same predictors, except that the 1990 Census residuals are specific to persons 18-to-64 instead of persons under 5 years.

People 65 and over. The equations for people age 65 and over are slightly different from those above. We have predictors more precisely tied to the target age group, both because we can separate tax exemptions into those over and under age 65 and because we have data from an income program specifically targeted to persons this age. In addition it turns out that the poverty rate for persons 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 1993 state poverty rates for people age 65 and over are:

• The 1993 "tax return poverty rate" for exemptions age 65 years and over -- the percentage 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.
• The 1993 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 1993 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.
• An intercept term.

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

The coefficients of this equation were estimated using the CPS estimates of 1993 state poverty rates for people age 65 and over as the dependent variable. The predicted rates are averaged with the CPS direct sample estimates using Empirical Bayes techniques, and the results transformed into estimated numbers of poor by multiplying them by the appropriate estimate of each state's noninstitutional population. Finally, the estimated numbers for each state are ratio-adjusted to the CPS national estimate.

Total 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 1993 median household income for states has the following predictor variables:

• The 1989 median household income derived from the 1990 Census
• The 1989 median household income derived from the 1990 Census adjusted by the ratio of 1993 median adjusted gross income for all tax returns to 1989 median adjusted gross income for all tax returns.

The dependent variable is the direct estimate of median household income in 1993 from the March 1994 CPS. The model estimates are averaged with the direct sample estimates from the March CPS using Empirical Bayes techniques. The state medians are not ratio-adjusted to the CPS estimate of the national median, because unlike estimates of state numbers, the median for the nation offers no strong constraint on the state medians.

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