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 .



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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology 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: 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 ∑(|Ymodel i − Ycensus i|) / n .

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology 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 ∑[(|Ymodel i − Ycensus i |) / Ycensus i ] / n. 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 (Ymodel ij −Ycensus ij) / ∑i Ycensus ij . 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 [(Ymodel ij − Ycensus ij) / Ycensus ij ] / 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.2 Table 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.

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

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

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology     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.

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

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

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

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology   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.

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

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

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology   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.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology 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.