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Small Area Income and Poverty Estimates

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1998 State-Level Estimation Details

The 1998 state estimates of poverty and income were released in August 2001. The 1998 county estimates of poverty and income were released in November 2001. For an overview of the changes in methodology between this release and the previous release see Estimation Procedure Changes.

Several features of the 1998 state estimates should be noted.
  • SAIPE models combine estimates from the regression with direct estimates from the Current Population Survey (CPS) in a way that varies the importance given to the direct CPS estimates from state to state depending upon their reliability.
  • SAIPE multiplies model-based 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 so that the total agrees with the direct CPS national estimates.
  • SAIPE uses data from the prior census (1990) in the regression models in the form of residuals from auxiliary cross-sectional regressions done with Census data.
  • 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.
  • SAIPE estimates the total number of poor people as the sum of estimates derived from a set of four age-specific equations.
A brief discussion of these features follows. The models are then presented.

Bayesian Estimation Techniques. The models SAIPE used to estimate 1998 income and poverty at the state level employ both direct survey-based estimates of 1998 income and poverty from the March 1999 CPS and regression predictions of income and poverty based on administrative records and prior (1990) census 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.

The regression model used to develop the regression predictions is postulated for the true, unobserved poverty ratios or median income, but it is fitted to the CPS direct estimates allowing for the sampling error in the data. If the variance of the error term in this regression model (the model error variance) were known, then the Bayesian estimate for each state would be a weighted average (shrinkage estimate) of the state's regression prediction and direct CPS 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 Poor People. Deriving state-level estimates of the numbers of poor people of various ages involves two steps. The first step is the use of the Bayesian estimation techniques just discussed, which are applied to CPS 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 poor people of various ages.

The poverty ratios used as the dependent variables in the regression models have the CPS direct estimated number poor of the given age in the numerator and the CPS direct estimated noninstitutional population of the given ages in the denominator. These "poverty ratios" differ from official poverty rates which would use the CPS 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 these poverty ratios instead of poverty rates because of the difficulty of constructing demographic estimates of the poverty universes.

We use CPS 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 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 demographics estimates are deemed more reliable than CPS direct population estimates, which contain substantial sampling error for most states. 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 model-based poverty ratio estimates by population estimates at the state level, we have not addressed the county-level estimation in the same way, because the estimates of the populations of counties by age are likely to be much less stable than the state population estimates, and little is known about their error structure. Thus, for counties, we directly model (logarithms of) CPS estimates of the number of poor people.

Controlling to the National Estimates. After converting the Bayesian estimates of poverty ratios to state estimates of numbers of poor, we control these estimates to the direct national estimate of number poor 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.

Using Estimates from the Prior Census in the Models. The prior census estimates are used to construct regression predictor variables for each of the age-specific poverty ratio models and the median income model. For the 1998 poverty ratio models (for all age groups) and median income, the prior census estimates determine census residuals that are used as regression predictor variables in the models. These census residuals are obtained by fitting a cross-sectional model for 1989, using the 1990 census estimated age group poverty ratio (median household income) as the dependent variable and the 1989 values of the regression predictors from the administrative data plus an intercept term, as the independent variables. The residuals from these cross-sectional regressions identify states in which the selected predictors tend to either overestimate or underestimate poverty, as measured by the census.

The Poverty Ratio Models

The model of 1998 state poverty ratios employs the following predictors.

  • an intercept term.
  • the 1998 "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 models, we use poor child exemptions and poor age exemptions, respectively, in the numerator. For the other age groups, we use poor exemptions of all persons under age 65. The denominator of this rate is the July 1, 1999 demographic state population estimate 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.
  • the 1998 "nonfiler rate". 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 all except the 65 and over model. For the 65 and over model we use estimates of the population over age 65 and the number of age exemptions.
  • the 1998 Supplemental Security Income recipiency rate. Defined as the 12-month average number of state SSI recipients age 65 years and over for 1998 divided by the state population of that age estimated for July 1, 1999. This variable is used only for the 65 and over model.
  • residuals from a regression of the 1990 census poverty ratios for 1989 for the relevant age group on the 1989 values of the above variables. Note that this is the only predictor variable that refers specifically to the age groups being modeled.

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

The dependent variable is the 1998 state estimate of the ratio of the number poor for the relevant age group to the noninstitutional population of that age both estimated from the March 1999 CPS.

Estimating the Total Number of Poor People.

We derive 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.

The Model For Median Household Income

The regression model for the 1998 median household income for states has the following predictor variables:

  • an intercept term.
  • the median gross income derived from IRS tax returns.
  • residuals from a regression of the 1990 census state median household income(for income year 1989) on the intercept term and the 1989 IRS median income.

The dependent variable is the direct estimate of median household income in 1998 from the March 1999 CPS.


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