# Small Area Income and Poverty Estimates

## 1999 County-Level Estimation Details

The 1999 state and county estimates of poverty and income were released in October 2002. For an overview of the changes in methodology between this release and the previous release see Estimation Procedure Changes.

Here are some points to consider about the 1999 estimates of poverty for counties:
• We estimate a regression model which predicts the number of poor persons using three-year average of county-level observations from the March Current Population Survey (CPS) as the dependent variable, and administrative records and census data as the predictors. Although we use only the approximately 1,200 counties with CPS sample cases to estimate the equation, we make regression "predictions" for all 3,141 counties.
• The model is multiplicative; that is, we model the number of poor as the product of a series of predictors which are numbers (not rates) and have unknown errors. When estimating the coefficients in the model, we take logarithms of the dependent and all independent variables. While we may omit reference to logs, all variables in the county regression models for numbers of poor are logarithmic.
• The estimates for different counties are of different reliability because of the size of the CPS sample in them. Our estimates take this factor into account.
• To use the information contained in the direct estimates for the 1,200 counties in the CPS, we combine the regression predictions with these direct estimates using Empirical Bayes (or "shrinkage") techniques. The Empirical Bayes (EB) techniques weight the contribution of the two components (regression and direct estimates) based on their relative precision.
• We control the estimates for the counties of a given state to sum to the independently derived state estimate (which in turn sum to the official national estimate).
• We provide a confidence interval, which represents uncertainty from both sampling and from modeling, for each estimate.

Using counties in the CPS sample. Our use of the CPS implicitly assumes that the counties in the survey sample are representative of those not selected, but this need not be the case. The CPS sample is designed to represent each state's population and only incidentally represents counties. The characteristics of some counties guarantee that they are included, e.g., most counties in large metropolitan areas and counties with large populations. More generally, while all counties have a nonzero probability of being included in the sample, some have higher probabilities than others. Further, the probability of selecting a county may be related to its income and poverty level. On the other hand, comparison of regression equations based on census data for counties in the CPS sample and equations based on all counties indicate remarkably similar results, providing some assurance that the CPS counties are largely representative of all counties.

The survey weights used in estimation at the national level are not appropriate for county-level estimates. The CPS sample design selects some primary sampling units (usually a county or group of counties) to represent a set of counties in the same stratum. The sum of the weights for sample households from such a county estimates the total population of the entire set of counties it represents. Because we want each county in the CPS sample to stand for itself, we have adjusted the weights to make each county self-representing.

Estimation of the model equation. CPS sampling variances are not constant over all counties. We avoid giving observations with larger variances (a great deal of uncertainty) the same influence on the regression as observations with smaller variances (less uncertainty) by, in effect, weighting each observation by the inverse of its uncertainty. Representing this uncertainty requires recognizing that it arises from two sources:

• uncertainty about where the estimates lie relative to the true values for each county (sampling error), and
• uncertainty about where the true county values lie with respect to the regression surface (lack of fit).

To estimate the lack-of-fit component, we estimate our model using the Census 2000 data and assume that the lack-of-fit component of residual variance is the same when the same model is fit to the CPS and to the census. Since we have separate estimates of sampling variance for each observation in Census 2000, we use them to estimate the unknown lack-of-fit component with a maximum likelihood procedure (see "Chapter 8: Accuracy of the Data" in Census 2000, STF3 documentation). (7.4M)

Next we fit a regression equation to the CPS data. We assume the sampling variance of the log of the number of poor is inversely proportional to the sample size (in households) and the lack-of-fit variance is the same as that estimated in the census regression. We estimate the CPS regression parameters and the two components of the CPS variance with a maximum likelihood procedure.

Combining model and direct survey estimates. Final estimates are weighted averages of the model predictions and the direct CPS estimates, where they exist. The two weights for each county add to 1.0, and we compute the weight on the model prediction as the sampling variance divided by the total variance (sampling plus lack-of-fit) of the direct estimate. With this technique, the larger the sampling variance of the direct estimate, the smaller its contribution and the larger the contribution from the prediction model. These weights are commonly referred to as "shrinkage weights," and the final estimates as "shrinkage" or "Empirical Bayes" estimates. For counties not in the CPS sample, the weight on the model's predictions is one and the weight on the direct survey estimate is zero.

Controlling to State Estimates.The last steps in the production process are transforming the county estimates from the log scale to estimates of numbers and controlling them to the independently derived state estimates. We make a simple ratio adjustment to the county-level estimates to ensure that they sum to the state totals. We control model-based estimates at the state level to the national level direct estimates derived from the March 2000 CPS. We adjust the estimated standard errors of the county estimates to reflect this additional level of control.

We do not control estimates of county median household income to the state medians because the estimation model does not produce the entire household income distribution, which would be required to do so.

Standard Errors and Confidence Intervals. One goal of our small area estimation work is providing estimates of the uncertainty surrounding the estimates of the numbers of poor. The census and model-based estimates shown in the tables are accompanied by their 90-percent confidence intervals. These intervals were constructed from estimated standard errors.

For the model-based estimates, the standard error depends mainly on the uncertainty about the model and the CPS sampling variance. While the variance of the shrinkage weights could also be a significant component of uncertainty about our estimates (if sizeable and ignored, we would be underestimating the standard errors), our research indicates that its contribution is negligible.

For the census, we derive the standard errors from a set of generalized variance functions that reflects the nature of the census sample design for the long form questionnaire (for further information, see Quantifying Uncertainty in State and County Estimates).

The Model for Total Number of Poor People

The model is multiplicative; that is, we model the number of poor as the product of a series of predictors that are numbers (not rates), and we model the unknown errors. To estimate the coefficients in the model, we take logarithms of the dependent and all independent variables. Our choice of a multiplicative model is motivated, in part, by the fact that the distribution of the number of poor has a huge range -- from zero in some counties to more than a million in the largest county (with a mean of 10,000), based on the 1990 census -- and the distribution is highly skewed. Taking the logarithm of all variables makes their distributions more centered and symmetrical and has the effect of diminishing the otherwise inordinate influence of large counties on the coefficient estimates. Another advantage of a multiplicative model is that it makes it plausible to maintain that the (unobserved) errors for every county, no matter how large or small, are drawn from the same distribution.

The predictor variables in the regression model used to estimate the total number of poor people by county for income year 1999 are:

• the log of the number of 1999 tax return exemptions (all ages) on returns whose adjusted gross income falls below the official poverty threshold for a family of the size implied by the number of exemptions on the form;
• the log of the number of food stamp recipients in July 1999;
• the log of the estimated total resident population as of April 1, 2000;
• the log of the total number of 1999 tax return exemptions; and
• the log of the Census 2000 estimate of the total number of poor.

Note the population estimates for other years use July 1, demographic population estimates as a predictor variable. For the 1999 estimates we use census 2000, which represents April 1, 2000 population.

For further information on these variables see Information about Data Inputs.

The dependent variable is the log of the total number of poor in each county as measured by the three-year average of values from the March CPS for 1999, 2000, and 2001. We combine the regression predictions, in the log scale, with the logs of the direct CPS sample estimates, and then transform the results into estimates of the numbers of poor. Finally, we control the estimates to the independent estimates of state totals.

The Model for the Number of Related Children Ages 5 to 17 in Families in Poverty

The estimation model for related children age 5 to 17 in poverty parallels that for all people in poverty in structure. There are five predictor variables:

• the log of the number of 1999 child exemptions claimed on tax returns whose adjusted gross income falls below the official poverty threshold for a family of the size implied by the number of exemptions on the form;
• the log of the number of food stamp recipients in July 1999;
• the log of the estimated resident population under age 18 as of April 1, 2000;
• the log of the total number of child exemptions indicated on 1999 tax returns; and
• the log of the Census 2000 estimate of the number of poor related children age 5 to 17.

Note the population estimates for other years use July 1, demographic population estimates as a predictor variable. For the 1999 estimates we use census 2000, which represents April 1, 2000 population.

For further information on these variables see Information about Data Inputs.

The dependent variable is the log of the number of poor related children age 5 to 17 in each county as measured by the three-year weighted average of the March CPS for 1999, 2000, and 2001. We combine the regression predictions, in the log scale, with the logs of the direct CPS sample estimates, and then transform the results into estimates of the numbers of poor. Finally, we control the estimates to the independent estimates of state totals.

The Model for the Number of Poor People Under Age 18

The estimation model for poor people under age 18 in poverty is quite similar. There are five predictor variables:

• the log of the number of 1999 child exemptions indicated on tax returns whose adjusted gross income falls below the official poverty threshold for a family of the size implied by the number of exemptions on the form;
• the log of the number of food stamp recipients in July 1999;
• the log of the estimated resident population under age 18 as of April 1, 2000;
• the log of the total number of child exemptions indicated on 1999 tax returns; and
• the log of the Census 2000 estimate of the number of poor persons under age 18.

Note the population estimates for other years use July 1, demographic population estimates as a predictor variable. For the 1999 estimates we use census 2000, which represents April 1, 2000 population.

For further information on these variables see Information about Data Inputs.

The dependent variable is the log of the number of poor people under age 18 in each county as measured by the three-year weighted average of the March CPS for 1999, 2000, and 2001. We combine the regression predictions, in the log scale, with the logs of the direct CPS sample estimates, and then transform the results into estimates of the numbers of poor. Finally, we control the estimates to the independent estimates of state totals.

The Model for Median Household Income

Like the model for total number of poor, the model for median household income is multiplicative. A consequence of the multiplicative form and the model performing well relative to the direct CPS estimates of median household income is that the standard errors of the estimates are proportional to the point estimates. In other words, the unobserved errors associated with wealthy counties are larger than the unobserved errors in poor counties. To estimate the model, we take logarithms of the dependent and all independent variables; i.e., the model is linear in logarithms. However, we report median household income in the linear scale and, as a result, the confidence intervals are asymmetric. The predictor variables in the regression model used to generate the estimate for 1999 county median household income are:

• the log of the Census 2000 estimate of county median household income;
• the log of the median adjusted gross income from 1999 tax returns;
• the log of the proportion of the 1999 Bureau of Economic Analysis (BEA) estimate of total personal income derived from government transfers;
• the log of the growth of BEA total personal income since 1989; and
• the log of the "nonfiler" rate.

We define the nonfiler rate as the ratio of estimated total population minus total exemptions claimed on IRS tax returns to estimated total population. For further information on these variables see Information about Data Inputs.

The dependent variable is the log of county median household income interpolated with three years of March CPS surveys given in 1999, 2000, and 2001. We adjust the March 1999 and 2001 CPS surveys to express incomes in 1999 dollars before computing median household income.

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