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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology (2000)

Chapter: Appendix C: County Model Comparisons with 1990 Census Estimates

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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×

APPENDIX

C

County Model Comparisons with 1990 Census Estimates

An external evaluation of alternative models for producing county estimates of poor school-age children can be carried out by comparing the county estimates obtained from each model for 1989 with 1900 census estimates of related children 5-17 who were poor in 1989. Although this evaluation is not ideal, it serves as a valuable tool for model assessment.

Chapter 6 reports the results of such an evaluation for four candidate models and four procedures that rely more heavily on estimates from the 1980 census. This appendix supplements the material in Chapter 6 in two ways. First, it provides additional results for the four models and four procedures examined in Chapter 6. Second, it provides evaluation results for the six single-equation models that were considered in the first round of evaluations.

EVALUATION MEASURES

Four measures are used for the evaluations in Chapter 6 and in this appendix. Two are overall measures of the differences between the county estimates from a model (or procedure) and the census, and two are measures for categories of counties. The four measures are defined as follows:

  1. Average absolute difference: the sum over all counties of the absolute (unsigned) difference between the model estimate of poor school-age children and the 1990 census estimate for each county, divided by the number of counties (3,141), or

    ∑(|YmodeliYcensusi|) / n .

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
  1. Average proportional absolute difference: the sum over all counties of the absolute difference between the model estimate of poor school-age children and the 1990 census estimate as a proportion of the census estimate for each county, divided by the number of counties,1 or

    ∑[(|YmodeliYcensusi |) / Ycensusi ] / n.

  2. Category algebraic difference: the sum for all counties (i) in a category (j) of the algebraic (signed) difference between the model estimate of poor school-age children and the 1990 census estimate for each county in the category, divided by the sum of the census estimates for the counties in the category, or

    i (YmodelijYcensusij) / ∑iYcensusij .

  3. Category average proportional algebraic difference: the sum for all counties (i) in a category (j) of the algebraic difference between the model estimate of poor school-age children and the 1990 census estimate as a proportion of the census estimate for each county in the category, divided by the number of counties in the category, or

    i [(Ymodelij− Ycensusij) / Ycensusij ] / nj .

Measure (1) expresses overall absolute model-census differences in terms of numbers of poor school-age children; measure (2) expresses overall absolute model-census differences in terms of percentage errors for counties. Similarly, for categories of counties, measure (3) expresses model-census differences in terms of numbers of poor school-age children, while measure (4) expresses model-census differences in terms of percentage errors for counties. The two kinds of category differences are algebraic (not absolute) measures, in which positive differences offset negative differences.

For measures (3) and (4), the counties are grouped into categories of the following characteristics: census geographic division; metropolitan status of county; population size in 1990; population growth from 1980 to 1990; percentage of poor school-age children in the 1980 census; percentage of Hispanic population in 1990; percentage of black population in 1990; persistent poverty from 1960 to 1990 for rural counties; economic type for rural counties; percentage of group quarters residents in 1990; whether the county had households in the CPS sample; and percentage change from 1980 to 1990 in the proportion of poor school-age children.2Table C-1 and Table C-2 show the number of counties in each category.

1  

An analogous measure, shown in Table 6-3, is the average proportional absolute difference in estimated proportions of poor school-age children.

2  

The characteristic of percentage change in the proportion of poor school-age children from 1980 to 1990 was not included in the first round of evaluations.

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×

TABLE C-1 Comparison of Model Estimates and Other Procedures with 1990 Census County Estimates of the Number of Poor School-Age Children in 1989: Algebraic Difference by Category of County (in percent)

   

Model

Other Procedures

   

Log No. Under 21

Log No. Under 18

Log Rate Under 21

Log Rate Under 18

Stable Shares

Stable Shares in State

Stable Rates in State

Average of Census and (a)

Category

Countiesa (Number)

(a)

(b)

(c)

(d)

(i)

(ii)

(iii)

(iv)

Census Divisionb

New England

67

−2.9

−2.9

−2.9

−2.9

35.9

−2.9

−2.9

7.8

Middle Atlantic

150

−2.8

−2.8

−2.8

−2.8

27.1

−2.8

−2.8

4.4

East North Central

437

−0.2

−0.2

−0.2

−0.2

−2.8

−0.2

−0.2

−5.6

West North Central

618

1.7

1.7

1.7

1.7

−1.8

1.7

1.7

−2.1

South Atlantic

591

0.5

0.5

0.5

0.5

14.8

0.5

0.5

8.1

East South Central

364

−4.5

−4.5

−4.5

−4.5

14.1

−4.5

−4.5

2.1

West South Central

470

−2.7

−2.7

−2.7

−2.7

−18.1

−2.7

−2.7

−6.3

Mountain

281

4.3

4.3

4.3

4.3

−23.2

4.3

4.3

−3.1

Pacific

163

6.5

6.5

6.5

6.5

−21.3

6.5

6.5

0.2

Metropolitan Status

Central county of metropolitan area

493

2.4

1.6

−0.1

−0.5

−1.6

−0.6

−0.4

0.4

Other metropolitan

254

−6.6

−5.0

5.1

6.3

3.2

−6.1

10.1

3.4

Nonmetropolitan

2,394

−4.2

−2.8

−0.3

0.4

3.3

1.8

−0.5

−1.4

1990 Population Size

under 7,500

525

−9.0

−2.3

−1.9

2.3

16.5

23.0

9.4

1.3

7,500-14,999

630

−4.4

0.5

2.5

5.5

10.9

10.7

4.4

2.2

15,000-24,999

524

−5.1

−2.6

0.3

1.9

6.2

3.4

0.0

−0.6

25,000-49,999

620

−4.2

−2.9

0.6

1.3

2.4

−0.2

−0.3

−1.3

50,000-99,999

384

−3.5

−5.1

−1.2

−2.3

−2.5

−4.8

−2.5

−3.3

100,000-249,999

259

−1.8

−4.4

−1.8

−3.5

−4.9

−5.9

−2.9

−3.3

250,000 or more

199

3.3

3.2

0.5

0.5

−0.6

0.8

0.8

1.8

1980 to 1990 Population Growth

Decrease of more than 10.0%

444

−1.9

0.6

−3.4

−1.9

9.1

9.9

−3.1

−3.4

Decrease 0.1-10.0%

972

−0.6

−0.5

−1.9

−1.8

7.5

0.7

−4.6

−2.7

0.0-4.9%

547

−2.8

−2.8

−3.2

−3.1

11.0

−2.3

−3.3

−0.2

5.0-14.9%

620

0.0

−1.0

0.2

−0.6

6.1

0.2

1.7

2.1

15.0-24.9%

260

7.7

5.8

5.5

4.6

−12.8

4.4

3.5

2.4

25.0% or more

292

−4.0

−1.4

1.7

3.1

−21.2

−6.8

7.2

1.0

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
This page in the original is blank.
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
   

Model

Other Procedures

   

Log No. Under 21

Log No. Under 18

Log Rate Under 21

Log Rate Under 18

Stable Shares

Stable Shares in State

Stable Rates in State

Average of Census and (a)

Category

Countiesa (Number)

(a)

(b)

(c)

(d)

(i)

(ii)

(iii)

(iv)

Percent Poor School-Age Children, 1980

Less than 9.4%

516

−4.0

−4.5

0.0

0.2

2.4

0.8

5.1

−1.1

9.4-11.6%

524

−0.5

−1.0

−1.6

−1.8

−9.9

−4.0

−1.9

−3.6

11.7-14.1%

530

3.6

2.3

1.8

1.0

−4.2

1.8

0.7

0.2

14.2-17.2%

523

0.9

1.2

−1.2

−1.4

−5.0

−3.0

−5.3

−1.8

17.3-22.3%

519

1.8

1.7

0.3

−0.1

10.7

1.9

−0.1

4.2

22.4-53.0%

523

−2.2

0.8

1.3

2.8

12.3

4.1

1.8

4.1

Percent Hispanic, 1990

0.0-0.9%

1,770

−3.4

−3.3

−1.6

−1.5

10.7

−0.6

−1.4

0.2

1.0-4.9%

847

0.5

0.1

0.4

0.1

0.2

0.1

1.1

−0.4

5.0-9.9%

193

−1.4

−0.6

−1.1

−0.8

6.7

1.2

1.4

1.7

10.0-24.9%

181

2.2

1.8

0.7

0.5

−5.7

1.7

1.3

0.1

25.0-98.0%

150

3.9

4.6

2.2

2.7

−16.8

−1.2

−1.3

−0.4

Percent Black, 1990

0.0-0.9%

1,446

−1.2

0.3

3.9

4.9

−3.7

3.9

6.0

−0.5

1.0-4.9%

615

−0.7

−2.0

1.3

0.5

−6.3

−1.6

−0.4

−2.9

5.0-9.9%

294

−2.9

−2.5

−0.7

−0.6

−8.4

−2.3

2.2

−1.8

10.0-24.9%

381

2.0

1.2

−1.0

−1.3

−2.6

−0.7

−2.1

0.2

25.0-87.0%

405

1.0

1.7

−1.8

−1.4

16.5

1.2

−2.4

3.7

Persistent Rural Poverty, 1960-1990c

Rural, not poor

1,740

−4.0

−3.7

−1.2

−1.0

0.1

0.2

−1.4

−3.4

Rural, poor

535

−5.0

−2.1

0.7

2.1

9.8

5.4

0.1

1.2

Not classified

866

1.7

1.2

0.3

0.0

−1.2

−0.7

0.4

0.7

Economic Type, Rural Countiesc

Farming

556

−5.5

−2.5

−1.6

0.7

13.2

18.0

7.9

1.1

Mining

146

−10.7

−5.1

−6.3

−3.6

−8.9

−6.6

−13.1

−10.6

Manufacturing

506

−6.2

−5.9

−1.7

−1.0

12.1

0.8

−1.1

−0.2

Government

243

2.1

−1.3

6.3

3.2

−0.9

4.6

4.1

0.0

Services

323

−3.9

−3.0

−1.8

−1.2

−5.8

−4.0

−3.4

−4.3

Nonspecialized

484

−3.7

−1.0

−0.1

1.4

2.2

1.6

−2.0

−1.5

Not classified

883

1.7

1.2

0.3

0.0

−1.2

−0.7

0.4

0.7

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
This page in the original is blank.
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
   

Model

Other Procedures

   

Log No. Under 21

Log No. Under 18

Log Rate Under 21

Log Rate Under 18

Stable Shares

Stable Shares in State

Stable Rates in State

Average of Census and (a)

Category

Countiesa (Number)

(a)

(b)

(c)

(d)

(i)

(ii)

(iii)

(iv)

Percent Group Quarters Residents, 1990

Less than 1.0%

545

−6.7

−2.7

2.0

4.7

−1.4

−0.9

3.7

0.3

1.0-4.9%

2,187

0.3

0.7

−0.3

0.1

−0.4

0.3

−0.1

0.1

5.0-9.9%

299

2.3

−4.4

0.5

−5.2

7.8

−1.4

−2.8

−0.8

10.0-41.0%

110

14.2

−3.2

7.4

−7.5

1.8

−0.9

−1.4

−2.2

Status in CPS, 1989-1991

In CPS sample

1,028

1.4

1.0

−0.2

−0.5

−0.6

−0.7

−0.4

0.5

In CPS, no poor children 5-17

246

−2.6

−1.9

7.3

7.8

10.0

3.7

12.0

5.9

Not in CPS sample

1,867

−4.1

−2.8

−0.1

0.6

0.6

2.3

−0.3

−2.3

Change in Poverty Rate for School-Age Children, 1980-1990

Decrease of more than 3.0%

536

7.5

10.4

16.2

18.1

51.6

30.1

32.8

30.0

Decrease 0.1-3.0%

649

2.1

1.9

3.1

2.9

29.2

8.0

9.8

12.1

0.0-0.9%

272

−2.6

−0.8

−0.4

0.5

4.3

−0.9

3.3

3.1

1.0-3.4%

621

3.8

2.2

3.4

2.6

−5.1

3.7

3.4

0.2

3.5-6.4%

532

−1.2

−2.4

−3.8

−4.3

−14.3

−7.7

−9.5

−8.3

6.5-38.0%

523

−7.2

−5.2

−8.7

−7.8

−25.2

−14.2

−16.5

−14.5

NOTES: The census estimates are controlled to the CPS national estimate for 1989. The algebraic difference by category is the sum for all counties in a category of the algebraic (signed) difference between the model estimate of poor school-age children and the 1990 census estimate for each county, divided by the sum of the census estimates for all counties in the category. See Chapter 6 text for definitions of models.

a3,141 counties are assigned to a category for most characteristics; 3,135 counties are assigned to a category for 1980-1990 population growth and 1980 percentage poor school-age children; 3,133 counties are assigned to a category for 1980-1990 percentage change in poverty rate for school-age children.

bCensus division states: New England: Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut Middle Atlantic: New York, New Jersey, Pennsylvania East North Central: Ohio, Indiana, Illinois, Michigan, Wisconsin West North Central: Missouri, Minnesota, Iowa, North Dakota, South Dakota, Nebraska, Kansas South Atlantic: Delaware, Maryland, District of Columbia, Virginia, West Virginia, North Carolina, South Carolina, Georgia, Florida East South Central: Kentucky, Tennessee, Alabama, Mississippi West South Central: Arkansas, Louisiana, Oklahoma, Texas Mountain: Montana, Idaho, Wyoming, Colorado, New Mexico, Arizona, Utah, Nevada Pacific: Washington, Oregon, California, Alaska, Hawaii

cThe Economic Research Service, U.S. Department of Agriculture, classifies rural counties by 1960-1990 poverty status and economic type. Counties not classified are urban counties and rural counties for which a classification could not be made.

SOURCE: Data from U.S. Census Bureau.

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
This page in the original is blank.
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×

TABLE C-2 Comparison of Model Estimates and Other Procedurees with 1990 Census County Estimates of the Number of Poor School-Age Children in 1989: Average Proportional Algebraic Difference for Counties in Each Category (in percent)

   

Model

Other Procedures

   

Log No. Under 21

Log No. Under 18

Log Rate Under 21

Log Rate Under 18

Stable Shares

Stable Shares in State

Stable Rates in State

Average of Census and (a)

Category

Counties (Number)

(a)

(b)

(c)

(d)

(i)

(ii)

(iii)

(iv)

Census Division

New England

67

4.1

4.5

6.6

7.1

45.6

7.0

8.6

20.2

Middle Atlantic

150

−5.9

−8.4

0.7

−1.0

28.8

−0.2

3.1

3.6

East North Central

437

−3.6

−3.0

2.5

3.0

0.6

3.5

5.8

−4.6

West North Central

618

−3.1

−0.6

0.5

2.3

18.7

21.0

15.9

3.7

South Atlantic

591

1.2

2.5

8.9

9.8

28.6

10.2

11.9

14.5

East South Central

364

−4.6

−3.0

0.5

1.3

19.5

0.4

0.3

5.0

West South Central

470

−7.6

−4.6

−4.0

−2.3

−6.4

8.8

−0.2

−5.5

Mountain

281

0.6

5.4

7.2

10.4

−3.4

30.5

22.6

2.6

Pacific

163

10.2

13.6

17.8

20.2

−9.6

23.9

20.6

7.5

Metropolitan Status

Central county of metropolitan area

493

0.6

−2.0

1.0

−0.6

4.2

−0.2

2.2

0.8

Other metropolitan

254

−3.6

−0.8

11.6

13.7

16.2

7.0

20.9

11.7

Nonmetropolitan

2,394

−2.6

0.2

2.9

4.7

13.2

15.0

9.9

3.6

1990 Population Size

under 7,500

525

−5.9

1.6

2.6

7.6

30.3

42.0

25.9

9.2

7,500-14,999

630

−1.0

3.0

5.7

8.4

16.3

17.5

12.2

6.1

15,000-24,999

524

−3.2

−1.8

2.1

3.2

9.0

6.8

4.5

1.1

25,000-49,999

620

−1.5

−0.7

4.2

4.6

6.0

3.1

5.3

2.2

50,000-99,999

384

−1.4

−3.3

2.5

1.2

3.1

−1.7

3.3

0.8

100,000-249,999

259

−0.7

−3.4

1.5

−0.3

2.4

−2.5

2.8

0.8

250,000 or more

199

1.0

0.4

1.3

1.1

7.9

2.9

6.5

4.5

1980 to 1990 Population Growth

Decrease of more than 10.0%

444

−5.2

−1.0

−1.2

2.0

29.0

36.9

17.5

3.7

Decrease 0.1-10.0%

972

−3.3

−2.2

0.1

0.9

11.6

10.1

3.0

−0.8

0.0-4.9%

547

−1.3

0.4

4.0

5.0

11.7

7.5

5.2

3.3

5.0-14.9%

620

−0.7

0.0

4.7

5.0

9.9

6.1

8.7

4.8

15.0-24.9%

260

4.0

3.8

10.6

10.1

8.7

8.7

16.0

10.4

25.0% or more

292

−4.1

2.3

9.8

14.0

−4.0

4.3

23.8

12.6

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
This page in the original is blank.
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
   

Model

Other Procedures

   

Log No. Under 21

Log No. Under 18

Log Rate Under 21

Log Rate Under 18

Stable Shares

Stable Shares in State

Stable Rates in State

Average of Census and (a)

Category

Counties (Number)

(a)

(b)

(c)

(d)

(i)

(ii)

(iii)

(iv)

Percent Poor School-Age Children, 1980

Less than 9.4%

516

−4.1

−3.0

3.7

5.2

1.9

2.9

8.1

−0.4

9.4-11.6%

524

−1.7

−0.2

2.4

3.6

3.5

6.0

6.1

0.6

11.7-14.1%

530

−2.0

−1.2

1.4

2.0

5.6

8.3

6.2

0.5

14.2-17.2%

523

−0.3

0.8

3.9

4.7

15.6

17.0

13.6

6.0

17.3-22.3%

519

−2.6

−1.2

1.9

2.6

17.0

15.1

9.8

5.1

22.4-53.0%

523

−2.3

3.2

6.3

9.3

28.7

22.4

13.6

11.1

Percent Hispanic, 1990

0.0-0.9%

1,770

−3.2

−1.4

2.6

3.9

20.7

12.1

10.2

5.4

1.0-4.9%

847

1.0

3.1

7.1

8.3

4.7

10.4

11.0

4.5

5.0-9.9%

193

−0.6

0.7

2.2

3.3

−0.6

15.4

10.2

1.0

10.0-24.9%

181

−5.7

−3.0

−2.9

−1.2

−7.1

14.8

5.1

−3.5

25.0-98.0%

150

−6.2

−3.3

−2.2

−0.3

−10.0

11.7

−1.2

−5.8

Percent Black, 1990

0.0-0.9%

1,446

−2.4

1.4

4.0

6.7

12.7

19.9

15.9

4.1

1.0-4.9%

615

−1.4

−2.1

3.1

2.4

5.3

5.1

3.8

0.3

5.0-9.9%

294

−2.4

−2.4

2.6

2.6

5.7

3.2

4.9

2.4

10.0-24.9%

381

−0.7

0.6

4.7

5.4

13.8

5.9

8.0

8.0

25.0-87.0%

405

−3.8

−2.7

0.0

0.9

23.1

6.2

0.5

5.3

Persistent Rural Poverty, 1960-1990

Rural, not poor

1,740

−2.6

0.0

2.3

4.1

12.5

16.4

11.4

3.0

Rural, poor

535

−3.7

0.3

3.5

5.5

16.2

12.0

4.0

4.4

Not classified

866

−0.4

−1.1

5.2

4.8

8.6

3.0

9.3

5.1

Economic Type, Rural Counties

Farming

556

−5.2

0.3

0.3

4.2

29.0

37.3

22.6

7.5

Mining

146

−8.6

−1.2

−1.7

2.2

−2.4

11.9

3.3

−4.0

Manufacturing

506

−3.8

−2.2

2.6

3.9

17.3

7.0

5.1

4.0

Government

243

5.8

5.1

11.8

10.5

5.8

12.1

9.3

5.0

Services

323

−2.1

−0.4

1.6

2.7

2.6

6.4

5.9

0.4

Nonspecialized

484

−2.8

−0.1

1.9

3.7

6.8

7.1

3.7

0.8

Not classified

883

−0.1

−0.8

5.4

5.1

8.8

3.5

9.6

5.3

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
This page in the original is blank.
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
   

Model

Other Procedures

   

Log No. Under 21

Log No. Under 18

Log Rate Under 21

Log Rate Under 18

Stable Shares

Stable Shares in State

Stable Rates in State

Average of Census and (a)

Category

Counties (Number)

(a)

(b)

(c)

(d)

(i)

(ii)

(iii)

(iv)

Percent Group Quarters Residents, 1990

Less than 1.0%

545

−5.7

2.5

6.1

11.4

16.4

17.6

15.8

8.4

1.0-4.9%

2,187

−3.1

−0.6

1.7

3.7

11.3

11.2

8.6

3.0

5.0-9.9%

299

5.2

−0.6

6.7

1.7

11.5

9.6

6.7

3.0

10.0-41.0%

110

13.8

−5.0

11.5

−3.9

7.7

6.4

5.0

−0.7

Status in CPS, 1989-1991

In CPS sample

1,028

−0.9

−1.3

1.9

1.7

7.9

2.8

4.4

2.7

In CPS, no poor children 5-17

246

−1.3

1.0

9.9

11.6

20.5

11.2

19.0

11.3

Not in CPS sample

1,867

−3.0

0.2

3.1

5.2

13.2

17.2

11.2

3.5

Change in Poverty Rate for School-Age Children, 1980-1990

Decrease of more than 3.0%

536

12.5

19.1

25.6

30.0

71.8

65.8

61.7

41.4

Decrease 0.1-3.0%

649

2.0

3.6

9.2

10.3

28.1

19.2

20.6

13.9

0.0-0.9%

272

−0.9

−0.1

4.9

5.4

9.5

9.8

9.3

3.5

1.0-3.4%

621

−3.7

−4.0

−0.3

−0.4

−0.9

1.9

0.1

−4.2

3.5-6.4%

532

−7.8

−7.7

−6.3

−6.2

−13.4

−8.2

−12.4

−12.6

6.5-38.0%

523

−15.5

−12.9

−13.8

−12.3

−26.5

−18.6

−23.7

−20.9

NOTE: See Notes to Table C-1.

SOURCE: Data from U.S. Census Bureau.

COMPARISONS FOR CANDIDATE MODELS AND OTHER ESTIMATION PROCEDURES

The four candidate models considered in Chapter 6 have the following designations: (a) log number model (under 21); (b) log number model (under 18); (c) log rate model (under 21); and (d) log rate model (under 18).3 The four other

3  

The estimates from the four candidate models and the models considered in the first round of evaluations, listed below, are the final estimates for all counties, after the initial estimates from the county regression model are combined in a “shrinkage procedure” with direct CPS estimates for those counties with households in the CPS sample and raked for consistency with the estimates from the state model; see Chapter 4.

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×

procedures (see Chapter 6) are designated as follows: (i) stable shares; (ii) stable shares within state; (iii) stable rates within state (with conversion); and (iv) average of 1980 census estimates and estimates for 1989 from the log number (under 21) model (a).

Table 6-3 presents the overall measures of average absolute difference (measure 1) and average proportional absolute difference (measure 2) between the estimates from the four candidate models and four procedures and the estimates from the census. Table 6-4 presents the category algebraic differences (measure 3) for the four candidate models and procedures (i) and (iv). Table C-1 is identical to Table 6-4 except that it also includes results for procedures (ii) and (iii). Table C-2 presents the category average proportional algebraic differences

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×

for the four candidate models and the four procedures. For reasons given in Chapter 6, the 1990 census estimates used in these comparisons are ratio-adjusted by a constant factor to equal the CPS national estimate of poor school-age children in 1989.

The findings from these evaluations are discussed in Chapter 6. The additional detail in Table C-1 and Table C-2 is presented without commentary.

COMPARISONS FOR THE SINGLE-EQUATION MODELS CONSIDERED IN THE FIRST ROUND OF EVALUATIONS

Six single-equation models were considered in the first round of evaluations (see Chapter 5). For this appendix these models are labeled as follows: (C.1) log number model (under 21) (model (a) of the candidate models); (C.2) log number model (under 18) (model (b) of the candidate models); (C.3) log number model (under 21) with fixed state effects; (C.4) log rate model (under 21) (model (c) of the candidate models); (C.5) rate model (under 21, variables not transformed); and (C.6) hybrid log rate-number model (under 21).4 Also included are comparisons for a variant of each of the three rate models—C.4a, C.5a, and C.6a, respectively—in which 1990 census population figures instead of estimates from the Census Bureau's population estimates program are used to convert the estimated proportions of poor school-age children from each rate model to estimated numbers.

For the first round of evaluations the census estimates were not ratio-adjusted to make the census national estimate of poor school-age children in 1989 equal to the corresponding CPS total for 1989, unlike the situation with the evaluations of the candidate models and other procedures described above. Thus, the results of the first round of evaluations given in Table C-3, Table C-4 and Table C-5 cannot be directly compared with those for the later round. However, knowing that the ratio-adjustment increased the census estimates by about 5 percent, it could be possible to make some rough comparisons.

Overall Differences

Table C-3 presents the average absolute difference (measure 1) and the average proportional absolute difference (measure 2) between model estimates and 1990 census estimates of the number of poor school-age children in 1989 for the six single-equation models, C.1-C.6, that were included in the first round of county model evaluations. It also shows the two absolute difference measures for the variant of the three rate models, C.4a, C.5a, and C.6a, in which 1990 census population figures instead of estimates from the Census Bureau's population

4  

The “under 21” designation is retained in the discussion only for the log number model, C.1, to distinguish it from model C.2.

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×

TABLE C-3 Comparison of First-Round Model Estimates with 1990 Census County Estimates of the Number of Poor School-Age Children in 1989

Model

Average Absolute Difference

Average Proportional Absolute Difference, in Percent

C.1

Log number model (under 21)

284

15.7

C.2

Log number model (under 18)

284

17.1

C.3

Log number model (under 21), with fixed state effects

289

17.4

C.4

Log rate model (under 21), rates converted to numbers with 1990 population estimates

285

18.9

C.4a

Log rate model (under 21), rates converted to numbers with 1990 census estimates

263

17.9

C.5

Rate model (under 21), untransformed, rates converted to numbers with 1990 population estimates

325

20.0

C.5a

Rate model (under 21), untransformed, rates converted to numbers with 1990 census estimates

299

18.8

C.6

Hybrid log rate-number model (under 21), rates converted to numbers with 1990 population estimates

298

17.1

C.6a

Hybrid log rate-number model (under 21), rates converted to numbers with 1990 census estimates

270

15.3

NOTE: See text for definitions of models and measures.

SOURCE: Data from U.S. Census Bureau.

estimates program are used to convert estimated proportions to estimated numbers of poor school-age children.

For models C.1, C.2, C.3, C.4, C.5, and C.6, the average absolute difference ranges from 284 to 325, or 11-13 percent of the average number of poor school-age children per county for 1989 (about 2,500 children). For these six models, the average proportional absolute difference ranges from 15.7 to 20.0 percent. The log number (under 21) model (C.1) performs best; it has the lowest average proportional absolute difference and is tied with the log number (under 18) model

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×

(C.2) for the lowest average absolute difference. The rate model (D.5) performs worst; it has the largest differences on both measures.

Because the 1990 census estimates used in the comparisons for models C.1-C.6 are not ratio-adjusted to the CPS national estimate of poor school-age children in 1989, the absolute difference measures in Table C-3 are about 5 percent higher than they would be if the ratio-adjustment had been made.5 For an evaluation of overall differences, controlling the 1990 census estimates to the CPS national estimate does not affect comparisons across models. However, for evaluation of category differences, there could be an effect.

Use of 1990 Population Estimates

For rate models, it is necessary to use population estimates of the number of school-age children to convert estimated proportions to estimated numbers of poor school-age children. The population estimates themselves differ from 1990 census figures (see Chapter 8). The use of 1990 population estimates instead of 1990 census figures to convert estimated proportions from the three rate models to estimated numbers increases the average absolute difference in the estimated number of poor school-age children by 8-10 percent and increases the average proportional absolute difference by about 6 percent for the log rate and rate models and 12 percent for the hybrid log rate-number model. (Compare the measures in Table C-3 for model C.4 and C.4a, for C.5 and C.5a, and for C.6 and C.6a.)

Differences by Categories of Counties

Table C-4 and Table C-5 (on pages 214-225) show the category algebraic differences (measure 3) and the category average proportional algebraic differences (measure 4), respectively, between model estimates and 1990 census estimates of the number of poor school-age children in 1989 for the six single-equation models that were considered in the first round of county model evaluations and the variant of the three rate models. The discussion considers models C.1-C.6.

Census Division The category algebraic differences in the predicted number of poor school-age children categorized by census division (measure 3, Table C-4) are the same for all of the models because they are raked to the same set of state estimates. They vary widely by census division. In particular, all of the models overpredict the number of poor school-age children for counties in the Mountain Division and, especially, the Pacific Division relative to other counties.

5  

Comparing Table C-3 and Table 6-3, the average absolute differences for models C.1, C.2, and C.4 from Table C-3 are 4 to 6 percent higher than the corresponding differences for models (a), (b), and (c) from Table 6-3; the average proportional absolute differences are 2 to 8 percent higher.

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×

The proportional category differences (measure 4, Table C-5) vary even more widely across divisions than do the category differences. For the Pacific Division, the proportional category difference is 1.3 to 2 times the category difference (16-26% versus 12%), indicating that the overprediction is more pronounced for smaller counties than larger counties in that geographic area.6 Further investigation is required to determine the reasons for the variations across divisions, which could include sampling variability in the CPS for 1989 or a specification problem in the state model (see Chapter 6).

Metropolitan Status The category differences and proportional category differences in the predicted number of poor school-age children vary somewhat for counties categorized by metropolitan status. There is no consistent pattern across models: for example, the log number (under 21) model (C.1) overpredicts the number of poor school-age children in central counties of metropolitan areas relative to other counties, while the log rate model (C.4) overpredicts the number of poor school-age children in “other metropolitan” counties relative to central counties or counties in nonmetropolitan areas.

1990 Population Size The category differences in the predicted number of poor school-age children (Table C-4) show a systematic tendency for the log number (under 21) model (C.1) and the hybrid log rate-number model (C.6) to overpredict the number of poor school-age children for larger size counties relative to smaller size counties. The proportional category differences ( Table C-5) show somewhat less variation. A statistical test established that the variations in the proportional differences for categories of counties classified by population size were significant for model C.6, but not for model C.1. However, the test used was not sensitive to monotonic patterns—for example, an increasing rate of overprediction by county size. (The test was not performed for the category differences, measure 3.)

Population Growth from 1980-1990 The category differences and proportional category differences in the predicted number of poor school-age children show a tendency for most models to overpredict the number of poor school-age children in counties with larger rates of population increase from 1980 to 1990 relative to counties with smaller increases or with decreases. 7 However, the extent of overprediction does not increase monotonically. In particular, most

6  

The proportional category differences differ somewhat across models because they are calculated relative to each county's 1990 census estimated number of poor school-age children before being summed.

7  

A statistical test established that the variations in the proportional category differences for categories of counties classified by population growth rate were significant for three of the four models tested: C.1, C.2, and C.3, but not C.6.

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×

models underpredict the number of poor school-age children for counties with the largest population increases (25% or more) relative to counties with the next largest increases (15-25%). In contrast to the pattern shown by other models, the log number model with fixed state effects (C.3) tends to overpredict the number of poor school-age children for counties that experienced a large population decrease relative to other counties.

Percentage of Poor School-Age Children, 1980 Census The category differences and proportional category differences in the predicted number of poor school-age children show relatively little variation for most models for counties categorized by their proportion of poor school-age children in 1979. The exception is the log number model with fixed state effects (C.3), which overpredicts the number of poor school-age children for counties that had a higher proportion of such children in 1979 relative to counties with a lower proportion. The variation in the proportional category differences (Table C-5) for counties defined by their 1979 proportion of poor school-age children is statistically significant for this model.

Percentage of Hispanic Population in 1990 The category differences in the predicted number of poor school-age children (Table C-4) show a tendency for most models to overpredict the number of poor school-age children for counties with larger proportions of Hispanics relative to other counties. This pattern is particularly pronounced for the log number (under 21 and under 18) models (C.1, C.2). The proportional category differences (Table C-5) tend to show the opposite pattern, in which the number of poor school-age children is overpredicted for counties with smaller proportions of Hispanics relative to other counties. The variations in the proportional category differences for counties characterized by percentage of Hispanic population are statistically significant for all models with this pattern that were tested. The differences in the patterns for the two measures may occur because the models behave differently for small counties with many Hispanics (primarily rural border counties) than for large counties (cities).

Percentage of Black Population in 1990 The category differences in the predicted number of poor school-age children (Table C-4) show a slight tendency for the log rate and rate models (C.4, C.5) to overpredict the number of poor school-age children for counties with smaller proportions of blacks relative to other counties. The proportional category differences (Table C-5) show little variation for any of the models for counties characterized by percentage of black population in 1990.

Persistent Rural Poverty, 1960-1990 The category differences in the predicted number of poor school-age children (Table C-4) vary little for most mod-

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×

els for counties characterized as rural and persistently poor, rural and not persistently poor, and not classified (urban counties and rural counties for which a classification could not be made). However, the log number (under 21) model (C.1) underpredicts the number of poor school-age children for rural counties relative to not classified counties. Also, the hybrid log rate-number model (C.6) underpredicts the number of poor school-age children for rural counties, whether or not they are persistently poor, relative to not classified counties. This pattern, which appears for both category difference measures, is statistically significant for the proportional category difference measure (Table C-5).

Economic Type, Rural Counties The category differences and proportional category differences in the predicted number of poor school-age children vary for all models for rural counties categorized by their principal economic activity. In particular, all of the models overpredict the number of poor school-age children in rural counties that have a large government presence relative to other types of rural counties.

Percentage of Group Quarters Residents in 1990 The category differences and proportional category differences in the predicted number of poor school-age children show that the log number (under 21) model (C.1), log number model with fixed state effects (C.3), and log rate model (C.4) tend to overpredict the number of poor school-age children in counties with larger percentages of group quarters residents relative to other counties. The pattern is particularly strong for model C.1. As discussed in Chapter 6, the replacement of the population under age 21 as a predictor variable in model C.1 by the population under 18 in model C.2 removed this pattern.

Status in CPS, 1989-1991 The category differences and proportional category differences in the predicted number of poor school-age children are similar in most models for counties categorized by their representation in the CPS sample. The log rate model (C.4) overpredicts the number of poor school-age children in counties with CPS sampled households, none of which contain poor school-age children (and thereby are excluded from the sample for estimating the model),8 relative to other counties. The hybrid log rate-number model (C.6) somewhat overpredicts the number of poor school-age children in counties with CPS sampled households relative to counties with no CPS sampled households.

8  

The only model that uses these counties in the estimation is the rate model for which the variables are untransformed (C.5).

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×

TABLE C-4 Comparison of First-Round Model Estimates with 1990 Census County Estimates of the Number of Poor School-Age Children in 1989: Algebraic Difference by Category of County (in percent)

 

Model

 

Log Number Under 21

Log Number Under 18

Log Number Under 21, Fixed State Effects

Log Rate Under 21

Rate Under 21

Log Hybrid Rate-Number Under 21

Category

C.1

C.2

C.3

C.4

C.4a

C.5

C.5a

C.6

C.6a

Census Divisiona

New England

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

1.9

Middle Atlantic

2.0

2.0

2.0

2.0

2.0

2.0

2.0

2.0

2.0

East North Central

4.7

4.7

4.7

4.7

4.7

4.7

4.7

4.7

4.7

West North Central

6.8

6.8

6.8

6.8

6.8

6.8

6.8

6.8

6.8

South Atlantic

5.5

5.5

5.5

5.5

5.5

5.5

5.5

5.5

5.5

East South Central

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

0.3

West South Central

2.1

2.1

2.1

2.1

2.1

2.1

2.1

2.1

2.1

Mountain

9.4

9.4

9.4

9.4

9.4

9.4

9.4

9.4

9.4

Pacific

11.8

11.8

11.8

11.8

11.8

11.8

11.8

11.8

11.8

Metropolitan Status

Central county of metropolitan area

7.4

6.7

6.6

4.8

4.5

4.8

4.5

7.7

7.4

Other metropolitan

−2.0

−0.3

−3.9

10.2

7.5

9.7

7.0

2.5

−0.1

Nonmetropolitan

0.5

2.0

2.8

4.6

5.8

4.6

5.8

−0.9

0.2

1990 Population Size

under 7,500

−4.5

2.5

4.7

3.0

4.4

5.6

7.2

−6.6

−5.3

7,500-14,999

0.4

5.5

6.0

7.6

8.6

7.7

8.7

−0.9

0.0

15,000-24,999

−0.4

2.3

2.8

5.3

6.4

5.2

6.3

−1.5

−0.4

25,000-49,999

0.5

1.8

1.9

5.6

6.1

5.5

6.0

0.3

0.7

50,000-99,999

1.2

−0.4

−0.1

3.6

3.9

3.8

4.0

0.3

0.6

100,000-249,999

3.1

0.4

1.1

3.0

3.1

1.7

1.8

2.1

2.2

250,000 or more

8.4

8.3

7.9

5.5

5.0

5.7

5.3

9.2

8.8

1980 to 1990 Population Growth

Decrease of more than 10.0%

3.0

5.6

9.0

1.3

1.9

2.4

3.0

2.4

3.0

Decrease 0.1-10.0%

4.3

4.4

5.9

2.9

3.0

3.1

3.2

3.9

4.0

0.0-4.9%

2.0

2.0

2.5

1.6

2.3

1.2

1.9

1.3

2.0

5.0-14.9%

5.0

3.8

3.8

5.2

5.1

5.6

5.6

4.2

4.2

15.0-24.9%

13.1

11.1

10.9

10.7

9.9

10.9

10.0

12.6

11.7

25.0% or more

0.7

3.5

−0.5

6.7

6.6

5.8

5.6

4.1

3.9

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
This page in the original is blank.
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
 

Model

 

Log Number Under 21

Log Number Under 18

Log Number Under 21, Fixed State Effects

Log Rate Under 21

Rate Under 21

Log Hybrid Rate-Number Under 21

Category

C.1

C.2

C.3

C.4

C.4a

C.5

C.5a

C.6

C.6a

Percent Poor School-Age Children, 1980

Less than 9.4%

0.8

0.2

−1.0

4.9

1.7

5.6

2.3

5.6

2.3

9.4-11.6%

4.4

3.9

3.3

3.2

3.0

4.4

4.2

5.6

5.3

11.7-14.1%

8.8

7.3

7.0

6.8

6.9

6.2

6.4

7.5

7.6

14.2-17.2%

5.8

6.2

5.2

3.7

6.7

2.8

5.7

2.7

5.7

17.3-22.3%

6.8

6.7

8.5

5.3

5.8

4.4

4.8

5.0

5.6

22.4-53.0%

2.6

5.7

7.7

6.3

6.8

6.2

6.7

2.1

2.7

Percent Hispanic, 1990

0.0-0.9%

1.4

1.4

2.3

3.3

3.1

3.1

3.0

1.6

1.4

1.0-4.9%

5.5

5.0

4.7

5.4

5.1

5.1

4.8

5.6

5.3

5.0-9.9%

3.5

4.3

3.3

3.8

3.4

5.0

4.7

4.4

3.9

10.0-24.9%

7.3

6.8

7.4

5.7

5.1

7.2

6.4

8.2

7.6

25.0-98.0%

9.0

9.8

8.5

7.2

8.9

5.9

7.7

6.9

8.6

Percent Black, 1990

0.0-0.9%

3.6

5.2

5.3

9.0

9.1

8.6

8.7

4.3

4.3

1.0-4.9%

4.2

2.8

2.9

6.3

5.6

6.9

6.1

4.8

4.0

5.0-9.9%

1.9

2.4

1.5

4.2

3.6

4.1

3.6

4.3

3.6

10.0-24.9%

7.0

6.2

5.7

3.9

3.8

3.9

3.8

6.5

6.3

25.0-87.0%

6.0

6.7

7.9

3.1

4.2

2.9

4.1

4.2

5.5

Persistent Rural Poverty, 1960-1990b

Rural, not poor

0.8

1.0

1.4

3.6

5.4

3.6

5.3

−1.1

0.5

Rural, poor

−0.3

2.7

5.2

5.7

5.9

5.7

5.8

−1.4

−1.2

Not classified

6.7

6.2

5.8

5.2

4.8

5.2

4.8

7.2

6.9

Economic Type,Rural Countiesb

Farming

−0.8

2.4

7.0

3.3

5.2

5.0

6.9

−3.9

−2.1

Mining

−6.3

−0.4

−4.0

−1.7

1.5

−1.4

1.8

−6.0

−3.1

Manufacturing

−1.6

−1.2

0.4

3.2

3.1

3.4

3.3

−1.5

−1.7

Government

7.2

3.6

8.7

11.6

11.7

9.7

9.7

1.9

2.0

Services

0.8

1.8

1.1

3.1

4.8

3.1

4.8

−0.5

1.2

Nonspecialized

1.0

3.9

3.4

4.8

6.8

4.4

6.3

−0.4

1.4

Not classified

6.7

6.2

5.8

5.2

4.8

5.3

4.8

7.3

6.9

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
This page in the original is blank.
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
 

Model

 

Log Number Under 21

Log Number Under 18

Log Number Under 21, Fixed State Effects

Log Rate Under 21

Rate Under 21

Log Hybrid Rate-Number Under 21

Category

C.1

C.2

C.3

C.4

C.4a

C.5

C.5a

C.6

C.6a

Percent Group Quarters Residents, 1990

Less than 1.0%

−2.1

2.1

−0.5

7.0

4.9

8.9

6.7

2.7

0.6

1.0-4.9%

5.2

5.7

5.4

4.6

4.6

4.7

4.7

5.7

5.7

5.0-9.9%

7.4

0.3

5.0

5.5

7.3

4.0

5.8

0.3

2.0

10.0-41.0%

19.9

1.6

11.9

12.7

17.4

5.0

9.3

0.6

4.7

Status in CPS, 1989-1991

In CPS sample

6.4

5.9

5.8

4.7

4.4

5.3

5.0

6.8

6.6

In CPS, no poor children 5-17

2.2

3.0

0.8

12.6

10.2

−1.0

−2.9

5.3

3.0

Not in CPS sample

0.6

2.0

2.8

4.8

6.2

5.0

6.3

−1.4

−0.1

NOTES: See text for definitions of models and measures. 3,141 counties are assigned to a category for most characteristics; 3,135 counties are assigned to a category for 1980-1990 population growth and 1980 percentage of poor school-age children; 3,133 counties are assigned to a category for 1980-1990 percentage change in poverty rate for school-age children; see Table C-1 for number of counties in each category.

aCensus division states:

New England: Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut

Middle Atlantic: New York, New Jersey, Pennsylvania

East North Central: Ohio, Indiana, Illinois, Michigan, Wisconsin

West North Central: Missouri, Minnesota, Iowa, North Dakota, South Dakota, Nebraska, Kansas

South Atlantic: Delaware, Maryland, District of Columbia, Virginia, West Virginia, North Carolina, South Carolina, Georgia, Florida

East South Central: Kentucky, Tennessee, Alabama, Mississippi West South Central: Arkansas, Louisiana, Oklahoma, Texas

Mountain: Montana, Idaho, Wyoming, Colorado, New Mexico, Arizona, Utah, Nevada

Pacific: Washington, Oregon, California, Alaska, Hawaii

bThe Economic Research Service, U.S. Department of Agriculture, classifies rural counties by 1960-1990 poverty status and economic type. Counties not classified are urban counties and rural counties for which a classification could not be made.

SOURCE: Data from U.S. Census Bureau.

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
This page in the original is blank.
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×

TABLE C-5 Comparison of First-Round Model Estimates with 1990 Census County Estimates of the Number of Poor School-Age Children in 1989: Average Proportional Algebraic Difference for Counties in Each Category (in percent)

 

Model

 

Log Number Under 21

Log Number Under 18

Log Number Under 21, Fixed State Effects

Log Rate Under 21

Rate Under 21

Log Hybrid Rate-Number Under 21

Category

C.1

C.2

C.3

C.4

C.4a

C.5

C.5a

C.6

C.6a

Census Division

New England

9.3

9.7

8.1

11.9

13.1

10.9

12.2

8.3

9.4

Middle Atlantic

−1.2

−3.9

−3.5

5.7

4.1

4.2

2.8

−1.2

−2.6

East North Central

1.2

1.8

2.2

7.5

8.5

6.4

7.4

−0.1

0.7

West North Central

1.7

4.4

7.4

5.4

7.3

6.1

8.0

−0.2

1.6

South Atlantic

6.2

7.6

8.1

14.3

12.6

14.5

12.8

7.7

6.1

East South Central

0.1

1.8

0.9

5.4

4.8

5.3

4.6

0.7

0.0

West South Central

−3.0

0.1

0.2

0.7

3.3

1.8

4.3

−6.7

−4.4

Mountain

5.6

10.6

12.2

12.5

14.6

17.0

19.3

3.9

5.7

Pacific

15.6

19.2

19.2

23.7

23.8

25.6

25.8

15.6

15.7

Metropolitan Status

Central county of metropolitan area

5.6

2.9

3.5

6.0

4.9

5.0

4.0

6.1

4.9

Other metropolitan

1.1

4.1

−0.1

17.1

13.3

16.1

12.4

6.8

3.4

Nonmetropolitan

2.2

5.1

6.5

7.9

9.4

9.0

10.5

0.3

1.6

1990 Population Size

under 7,500

−1.3

6.6

9.9

7.7

9.2

12.7

14.2

−3.5

−2.3

7,500-14,999

3.9

8.1

9.3

10.9

12.3

11.5

12.8

2.2

3.4

15,000-24,999

1.6

3.0

4.2

7.2

8.2

6.9

8.0

0.1

1.1

25,000-49,999

3.4

4.2

3.7

9.3

10.1

8.8

9.6

2.8

3.5

50,000-99,999

3.4

1.5

1.0

7.5

7.3

7.3

7.0

3.1

2.8

100,000-249,999

4.2

1.4

1.4

6.6

6.0

3.3

2.9

4.0

3.4

250,000 or more

5.9

5.4

5.0

6.3

4.4

7.3

5.5

8.7

6.9

1980 to 1990 Population Growth

Decrease of more than 10.0%

−0.5

3.9

10.5

3.7

3.9

7.9

8.0

−1.7

−1.5

Decrease 0.1-10.0%

1.5

2.6

5.5

5.0

6.4

5.4

6.8

−0.7

0.6

0.0-4.9%

3.6

5.3

5.1

9.2

9.9

8.2

8.9

2.7

3.4

5.0-14.9%

4.2

4.9

4.1

9.9

10.2

9.6

10.0

3.4

3.6

15.0-24.9%

9.2

9.0

7.5

16.0

15.6

15.6

15.2

8.0

7.6

25.0% or more

0.7

7.3

−0.3

15.2

15.7

16.2

16.9

3.9

4.1

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
This page in the original is blank.
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
 

Model

 

Log Number Under 21

Log Number Under 18

Log Number Under 21, Fixed State Effects

Log Rate Under 21

Rate Under 21

Log Hybrid Rate-Number Under 21

Category

C.1

C.2

C.3

C.4

C.4a

C.5

C.5a

C.6

C.6a

Percent Poor School-Age Children, 1980

Less than 9.4%

0.6

1.8

−1.3

8.9

7.5

7.2

5.9

3.8

2.5

9.4-11.6%

3.2

4.8

3.5

7.5

9.0

8.5

10.2

2.3

3.7

11.7-14.1%

2.9

3.6

4.3

6.4

7.7

7.3

8.6

0.9

2.2

14.2-17.2%

4.6

5.8

8.1

9.1

11.1

10.2

12.3

1.4

3.2

17.3-22.3%

2.2

3.7

6.9

7.0

8.1

7.5

8.6

−0.6

0.4

22.4-53.0%

2.5

8.3

11.2

11.5

10.6

13.0

11.0

2.4

1.5

Percent Hispanic, 1990

0.0-0.9%

1.6

3.5

5.1

7.7

7.6

8.4

8.2

1.5

1.4

1.0-4.9%

6.0

8.2

6.7

12.4

12.9

12.1

12.7

5.6

6.1

5.0-9.9%

4.3

5.7

6.4

7.2

10.0

9.3

12.4

0.6

3.0

10.0-24.9%

−1.1

1.8

3.1

1.9

5.4

3.3

6.9

−6.0

−2.9

25.0-98.0%

−1.5

1.5

4.7

2.6

7.4

3.8

8.7

−7.7

−3.5

Percent Black, 1990

0.0-0.9%

2.4

6.5

7.3

9.2

10.4

10.4

11.7

1.5

2.6

1.0-4.9%

3.5

2.8

3.5

8.2

8.7

8.0

8.7

2.0

2.4

5.0-9.9%

2.4

2.4

1.8

7.7

6.6

7.9

6.9

3.1

2.1

10.0-24.9%

4.2

5.6

4.5

9.9

9.8

9.0

9.0

3.9

3.7

25.0-87.0%

0.9

2.1

5.6

5.0

5.4

5.9

6.2

−1.0

−0.5

Persistent Rural Poverty, 1960-1990

Rural, not poor

2.2

4.9

6.1

7.3

9.4

8.7

10.8

0.1

1.9

Rural, poor

1.0

5.3

7.7

8.6

8.3

8.4

8.1

0.0

−0.2

Not classified

4.5

3.8

2.9

10.3

8.7

9.7

8.2

6.0

4.5

Economic Type, Rural Counties

Farming

−0.5

5.3

9.9

5.3

7.6

9.3

11.6

−3.5

−1.3

Mining

−4.1

3.7

0.7

3.1

8.6

4.5

10.3

−6.7

−2.0

Manufacturing

1.0

2.7

3.5

7.6

7.6

7.5

7.4

1.2

1.1

Government

11.0

10.3

13.2

17.3

17.2

15.0

14.8

7.2

7.0

Services

2.7

4.5

4.3

6.6

8.2

7.9

9.6

0.8

2.3

Nonspecialized

2.0

4.9

4.8

7.0

8.7

6.9

8.6

0.3

2.0

Not classified

4.8

4.1

3.3

10.6

9.0

10.1

8.6

6.3

4.8

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
This page in the original is blank.
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
 

Model

 

Log Number Under 21

Log Number Under 18

Log Number Under 21, Fixed State Effects

Log Rate Under 21

Rate Under 21

Log Hybrid Rate-Number Under 21

Category

C.1

C.2

C.3

C.4

C.4a

C.5

C.5a

C.6

C.6a

Percent Group Quarters Residents, 1990

Less than 1.0%

−1.1

7.5

3.8

11.3

10.7

13.7

13.2

1.8

1.1

1.0-4.9%

1.7

4.3

5.0

6.7

7.4

7.4

8.1

1.5

2.1

5.0-9.9%

10.4

4.3

9.5

11.9

14.2

11.3

13.5

3.3

5.3

10.0-41.0%

19.4

−0.3

12.4

17.0

19.0

9.9

11.8

2.0

3.8

Status in CPS, 1989-1991

In CPS sample

4.0

3.6

3.9

7.0

6.6

8.9

8.6

4.3

3.9

In CPS, no poor children 5-17

3.6

6.0

3.1

15.4

13.9

4.6

3.5

5.8

4.5

Not in CPS sample

1.8

5.1

6.7

8.2

9.7

9.5

11.0

−0.3

1.1

NOTE: See notes to Table C-4.

SOURCE: Data from U.S. Census Bureau.

Summary of Category Differences

Three of the eleven characteristics examined show no pronounced patterns of overprediction or underprediction of the number of poor school-age children for any of the models:

  • percentage of poor school-age children from the 1980 census;

  • percentage of black population in 1990; and

  • persistent rural poverty from 1960 to 1990.

Four characteristics show patterns for all or all but one model in which some categories of counties are over(under)predicted relative to other counties:

  • census geographic division;

  • percentage of change in population from 1980 to 1990 (population growth);

  • percentage of Hispanic population in 1990; and

  • economic type, for rural counties.

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×

The remaining four characteristics exhibit mixed patterns, in which some models give evidence of over(under)prediction for counties in some categories and other models do not:

  • metropolitan status of county;

  • 1990 population size;

  • percentage of group quarters residents in 1990; and

  • status in CPS sample.

Of these four characteristics, over(under)prediction for those models in which it occurs is most pronounced for population size and percentage of group quarters residents.

Overall, there is no clearly best or worst model in terms of differences from the 1990 census estimates for categories of counties. Each model exhibits strengths and weaknesses (keeping in mind that the analysis is based on a single evaluation). On balance, the log number (under 18) model (C.2) performs somewhat better than the other models.

Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
Page 205
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
Page 206
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Page 219
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Page 220
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Page 221
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
Page 222
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
×
Page 223
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Page 224
Suggested Citation:"Appendix C: County Model Comparisons with 1990 Census Estimates." National Research Council. 2000. Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. Washington, DC: The National Academies Press. doi: 10.17226/10046.
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Page 225
Next: Appendix D: Use of School Lunch Data in New York State for the Estimation of School-Age Children in Poverty: An Analysis »
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The Panel on Estimates of Poverty for Small Geographic Areas was established by the Committee on National Statistics at the National Research Council in response to the Improving America's Schools Act of 1994. That act charged the U.S. Census Bureau to produce updated estimates of poor school-age children every two years for the nation's more than 3,000 counties and 14,000 school districts. The act also charged the panel with determining the appropriateness and reliability of the Bureau's estimates for use in the allocation of more than $7 billion of Title I funds each year for educationally disadvantaged children.

The panel's charge was both a major one and one with immovable deadlines. The panel had to evaluate the Census Bureau's work on a very tight schedule in order to meet legal requirements for allocation of Title I funds. As it turned out, the panel produced three interim reports: the first one evaluated county-level estimates of poor school-age children in 1993, the second one assessed a revised set of 1993 county estimates; and the third one covered both county- and school district-level estimates of poor school-age children in 1995. This volume combines and updates these three reports into a single reference volume.

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