APPENDIX
B Population Estimates
The Census Bureau has long had an active program of using demographic analysis to develop updated estimates of total population and population by age for various levels of geography, such as states, counties, and cities. The Census Bureau's state and county models of school-age children who were poor in 1993 use state and county postcensal population estimates for age groups as of July 1994. These estimates were developed within the framework of the Census Bureau's population estimates program (Long, 1993).1
TOTAL POPULATION ESTIMATES
Total population estimates are developed by the component method of demographic analysis. In general, the component method starts from an area's population in the previous census. That number is then updated by the net demographic change—adding births and international immigration and subtracting deaths and emigration. The final component, internal migration or migration to and from other parts of the United States, is currently estimated from administrative records. No adjustments are made to the population estimates to allow for the estimated net population undercount in the census.
Postcensal county estimates of total population are produced by the component method: (1) the numbers of births and deaths are based on reported vital statistics for each county; (2) reports of the Immigration and Naturalization Service are used to estimate net immigration from abroad; and (3) administrative records are used to estimate net migration among counties. Net migration of people under 65 years of age is estimated for each county from a year-to-year match of IRS federal income tax returns; for people aged 65 and over, net migration is estimated for each county from the change in Medicare enrollment (Bureau of the Census, 1995). Estimates are developed separately for household and group quarters populations.
The county population totals are summed for each state to provide estimates of the total population of each state. All county and state population totals are then adjusted to sum to independently derived estimates of the total U.S. population. The county estimates are also reviewed locally under the Census Bureau's Federal-State Cooperative Population Estimates (FSCPE) program.
Operationally, the county total population estimates are the sum of the estimates for four groups:
-
Household population under age 65 (HHP<65);
-
Household population age 65 and over (HHP65+);
-
Group quarters population under age 65 (GQ<65); and
-
Group quarters population age 65 and over (GQ65+).
HHP<65
The estimates for HHP<65 use a component method for year t to measure change in each component of population change during the 12-month period preceding the estimate date, as follows::
(1)
NI is natural increase (births and deaths for people under age 65), which is estimated from a combination of vital statistics data from the National Center for Health Statistics (NCHS) and the FSCPE. Each of these sources has some problems. The FSCPE does not include all states, and the NCHS data exhibit some peculiarities (e.g., birth records are not always properly assigned to place of residence in such areas as Washington, D.C., in which births often occur in hospitals that are not in the county of residence, and in areas with military bases).
NMIG, net internal migration, is estimated from data on IRS tax returns matched year to year on the basis of the Social Security number of the filer. A migration rate is developed from the number of exemptions on the matched tax returns [(inmigrants-outmigrants) / (nonmigrants + outmigrants)], and this rate is applied to the migration base [HHP<65 t-1 + 1/2(NI + NETMOVE)-AGE].
Coverage of the IRS data (i.e., the proportion of exemptions to estimated population) varies across counties, as do matching rates.
NETMOVE is nondomestic net movements, mainly international immigration and emigration. It is estimated with a variety of data, and the totals generally are small. Legal immigrants and refugees (about 800,000 per year nationwide) are assigned to a county of residence on the basis of Immigration and Naturalization Service data about their intended place of residence although they may not reside at the indicated place. Undocumented immigrants (estimated at 225,000 annually) are assigned to a county on the basis of the 1990 census distribution of the foreign born population. Estimates are also made of emigrants (about 195,000 per year). Net inmigrants from Puerto Rico (only about 7,000 annually because there is almost an equal number of outmigrants each year) used to be estimated from passenger traffic data from the San Juan airport. However, this method became increasingly untenable, and the current procedure uses estimates of migration of Puerto Ricans to the rest of the world, which include an assumption of the U.S. share. The U.S. share is allocated to counties on the basis of 1990 census data on place of residence. Estimates of the net movement in and out of the country of military and federal civilian and military dependents are based on data from the Department of Defense (DoD) and the Office of Personnel Management. County station strength data from DoD, which are used to allocate military personnel to counties, are modified in some locations (e.g., the Washington, D.C., area).
Lastly, AGE is an estimate of the number of persons in the county who aged from 64 to 65 during the year.
Except for internal migration, all components are controlled to national totals.
HHP65+
The estimates for HHP65+ use a component method in which:
(2)
NI65+ is natural increase (decrease) of persons aging into the cohort (AGE in the first equation) minus deaths in the population aged 65 and over.
NMIG65+ is internal migration, which is estimated from Medicare enrollment data. A migration rate is estimated as [(actual Medicare enrollment t-1 - expected Medicare enrollment) / actual enrollmentt-1]. Expected Medicare enrollment is [actual enrollmentt-1 + (NI65 + t-1 × the 1990 Medicare coverage ratio)].2 The estimated migration rate is then applied to the migration base, HHP65 + t-1 + 1/2(NIt-1 + NETMOVEt-1).
NETMOVE65+ is other net movements (legal immigrants, undocumented immigrants, refugees, emigrants, net entrants from Puerto Rico).
GQ<65 and GQ65+
Group quarters population for both age groups (GQ<65 and GQ65+) is estimated as the 1990 census group quarters population plus the difference between the current group quarters report (GQR) minus the 1990 GQR figure. The GQR is compiled annually from data obtained from the FSCPE, DoD, Veterans Administration, and colleges by type of group quarters: correctional facility, juvenile facility, nursing home, other institutional, college, military quarters, other noninstitutional.
ESTIMATES BY AGE
Estimates by age are prepared separately, but within the framework of the total population estimates for states and counties.
County age estimates are prepared in a two-step procedure. In the first step, estimates of total county population are developed as described above. Separately, estimates of state populations by single years of age, sex, race, and Hispanic origin are developed. The state age estimates (which are controlled to the state total population estimates) use a component method in which migration rates by age for people under age 65 are derived from school enrollment data (Bureau of the Census, 1987).
In the second step, the county age estimates are developed by using a raking-ratio adjustment of the estimates from the previous census. In this approach, the beginning matrix of counts for each county by age, sex, race, and Hispanic origin from the previous census is simultaneously adjusted to agree with the postcensal estimate of the total county population and the postcensal estimates for the applicable state by age, sex, race, and Hispanic origin (Sink, 1996).3
This procedure assumes that the age distribution of each county within a state changes in the same manner as that state's age distribution. Errors in the county estimates of an age group can arise from errors in this assumption, errors in the derivation of the state estimates of age groups, and errors in the derivation of the county estimates of total population.
USE OF POSTCENSAL POPULATION ESTIMATES
The process for estimating school-age children in poverty at the county level in 1993 and the Title I allocation formulas for using those estimates require population totals by age in a noncensus year. For estimating numbers of poor school-age children, the Census Bureau's county model uses population estimates for the population under age 18 in 1994, and the state model uses population estimates for the population under age 65 and the noninstitutionalized population aged 5-17 in 1994. Estimates for the noninstitutionalized population are developed by subtracting administrative record counts of institutionalized people in the relevant age groups from the demographic estimates developed as described above.
As required by the Title I legislation, the Census Bureau provided to the Department of Education estimates of total children aged 5-17 for counties as of July 1994 to use as denominators in calculating county proportions of poor school-age children to use in the Title I allocations. (The numerators are the Census Bureau's estimates of the number of related school-age children in each county who were poor in 1993, developed as described in Chapter 2, with the addition by the Department of Education of estimates for several other groups of children, such as those in foster care, as specified by the legislation.)
EVALUATION OF COUNTY AGE ESTIMATES
The Census Bureau maintains an ongoing program to develop and review the performance of its population estimates, including evaluating the estimates at 10-year intervals by comparing them with decennial census figures. These comparisons are not complete measures of the accuracy and precision of the population estimates because the standard (i.e., the decennial census) itself is flawed, notably from net population undercount, which varies by age group across time and place (see Robinson et al., 1993).
To evaluate the county age estimates developed with the current raking-ratio procedure, the Census Bureau raked the 1980 census county age figures to the 1990 estimates of county total population and state population by age. The resulting 1990 county age estimates were compared with the 1990 census county age figures, which were assumed to be the true values in each case.
Tables B-1 to B-8 show the average proportional algebraic difference and the average proportional absolute difference, expressed as percents, between the 1990 county population estimates for people aged 5-17, developed by raking the 1980 census estimates as described above, and the 1990 census figures. Following Census Bureau terminology, these difference measures are termed mean alge-
braic (i.e., signed) percent error and mean absolute percent error. 4 The two measures are shown for all counties and for counties grouped into categories for the following characteristics: population size in 1990; population growth from 1980 to 1990; percent black and other nonwhite population in 1990; percent Hispanic population in 1990; percent poor population in 1990; percent group quarters residents in 1990; census division; and metropolitan status. Also shown are the percentage of counties with negative errors (underpredictions relative to the census) and the number of counties with more than a 20 percent negative or positive error.
FINDINGS
The overall mean absolute percent error in the 1990 county estimates of people aged 5-17 is 6.3 percent (shown in Table B-l).5 By comparison, for 1990 county estimates of total population, prepared using the Census Bureau's current estimation procedure, it is 3.6 percent (Davis, 1994).
The mean absolute percent errors do not seem to be concentrated in any particular types of counties (Tables B-2 to B-8). However, as would be expected, the smallest counties (those with populations under 2,500) have errors running at twice the overall average: 12.4 percent, compared with 6.3 percent overall (see Table B-1).
There may be a systematic prediction bias by county population size (Table B-l). The mean algebraic percent error is negative for counties in the smaller population size groups (except for those under 2,500 with a 0.0 value) and positive for counties in the larger population size groups. The percentage of counties with negative prediction errors generally increases as county population size decreases. Overall, the mean algebraic percent error is-0.4.
Nonmetropolitan counties also have a negative mean algebraic percent error (see Table B-8), with 60 percent of these counties having negative prediction errors, which is consistent with the pattern of negative prediction errors for smaller counties. Negative mean algebraic percent errors also characterize counties with negative or lower rates of population growth (Table B-2); with lower percent black and other nonwhite population (Table B-3); with average or higher than average percent Hispanic population (Table B-4); with smaller percent poor popu-
lation (Table B-5); with higher percent group quarters residents (Table B-6); and for counties in the Mountain, Pacific, North Central (East and West), and New England Divisions (Table B-7).
The 72 counties with mean algebraic percent errors of greater than 20 percent, whether positive (36 counties) or negative (36 counties), do not have any common features except that they are almost all nonmetropolitan counties and generally have smaller populations. There are, however, a few counties with populations of 50,000 or more and many counties with populations of 10,000 or more that have large prediction errors. Most of the large errors are between 20 and 30 percent.
An issue in examining the mean algebraic percent errors in the 1990 county estimates of children aged 5-17 for categories of counties (see Tables B-1 through B-8) is whether the patterns observed for example, the tendency for smaller (larger)-sized counties to have negative (positive) prediction errors—are statistically significant, suggesting the possibility of a systematic bias. Tests of significance were conducted to determine whether there is evidence of possible bias with respect to the characteristics in Tables B-1 to B-8. Since most of these characteristics have ordered categories, a test of a linear trend was conducted using the Abelson-Tukey test procedure (Abelson and Tukey, 1963). Because the number of degrees of freedom is large, the test statistic has essentially a normal distribution under the null hypothesis of no trend. The categories for census division do not have an ordering, so a one-way analysis of variance was performed for that characteristic.
The test results suggest the possibility of some bias associated with the estimates of children aged 5-17 for several categories of counties: county population size, percent black and other nonwhite population, percent Hispanic population, percent group quarters residents, metropolitan status, and census division. However, the results are not conclusive given that there is only a single year—1990—for which it is possible to evaluate the estimates by comparison with figures from the census or another source.
TABLE B-1 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Population Size in 1990
|
|
|
|
|
|
|
Counties with More Than 20 Percent Error (Number) |
|
Population Size, 1990 |
Counties (Number)a |
Mean Algebraic Percent Errorb |
Mean Absolute Percent Errorb |
Percentage of Counties with Negative Errors |
- |
+ |
||
All |
3,140 |
-0.4 |
(8.7) |
6.3 |
(6.1) |
56.2 |
36 |
36 |
1,000,000 and over |
30 |
1.5 |
(6.5) |
5.2 |
(4.1) |
46.7 |
0 |
0 |
500,000 to 1,000,000 |
67 |
1.7 |
(5.1) |
4.4 |
(3.2) |
29.9 |
0 |
0 |
100,000 to 500,000 |
361 |
0.9 |
(5.9) |
4.6 |
(3.8) |
50.4 |
0 |
I |
50,000 to 100,000 |
384 |
0.6 |
(7.3) |
5.6 |
(4.7) |
51.3 |
2 |
2 |
10,000 to 50,000 |
1,543 |
-0.5 |
(7.7) |
6.0 |
(4.8) |
56.9 |
10 |
12 |
5,000 to 10,000 |
457 |
-1.5 |
(9.0) |
7.2 |
(5.6) |
61.7 |
6 |
8 |
2,500 to 5,000 |
180 |
-3.2 |
(10.5) |
8.4 |
(7.0) |
67.2 |
8 |
3 |
Less than 2,500 |
118 |
0.0 |
(21.2) |
12.4 |
(17.2) |
59.0 |
10 |
10 |
a Excludes Kalawayo County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. b Standard deviations are in parentheses. |
TABLE B-2 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Growth Rate, 1980-1990
|
|
|
|
|
|
|
Counties with More Than 20 Percent Error (Number) |
|
Growth Rate, 1980-1990 |
Counties (Number)a |
Mean Algebraic Percent Errorb |
Mean Absolute Percent Errorb |
Percentage of Counties with Negative Errors |
- |
+ |
||
All |
3,140 |
-0.4 |
(8.7) |
6.3 |
(6.1) |
56.2 |
36 |
36 |
Decrease of 5% or more |
834 |
-0.7 |
(10.1) |
6.7 |
(7.5) |
58.4 |
12 |
14 |
-5% to 0% |
595 |
-1.0 |
(7.8) |
5.8 |
(5.3) |
60.7 |
1 |
4 |
0 to 5% |
583 |
-0.4 |
(7.8) |
5.9 |
(5.0) |
55.8 |
7 |
5 |
5 to 10% |
386 |
-0.1 |
(7.7) |
5.7 |
(5.1) |
57.5 |
2 |
4 |
10 to 15% |
208 |
0.6 |
(7.5) |
6.1 |
(4.5) |
49.0 |
2 |
0 |
15 to 25% |
247 |
0.3 |
(9.0) |
6.7 |
(6.0) |
51.8 |
3 |
3 |
25% and over |
287 |
-0.2 |
(10.0) |
7.5 |
(6.5) |
48.4 |
9 |
6 |
a Excludes Kalawayo County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. b Standard deviations are in parentheses. |
TABLE B-3 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Percent Black and Other Nonwhite Population, 1990
|
|
|
|
|
|
|
Counties with More Than 20 Percent Error (Number) |
|
Percent Black and Other Nonwhite, 1990 |
Counties (Number)a |
Mean Algebraic Percent Errorb |
Mean Absolute Percent Errorb |
Percentage of Counties with Negative Errors |
- |
+ |
||
All |
3,140 |
-0.4 |
(8.7) |
6.3 |
(6.1) |
56.2 |
36 |
36 |
Less than 0.5% |
304 |
-0.7 |
(13.1) |
7.4 |
(10.8) |
61.6 |
9 |
7 |
0.5 to 1.0% |
405 |
-2.1 |
(8.3) |
6.1 |
(6.0) |
67.2 |
3 |
5 |
1.0 to 2.0% |
468 |
-1.6 |
(8.4) |
6.8 |
(5.2) |
62.4 |
5 |
5 |
2.0 to 5.0% |
550 |
-1.0 |
(7.8) |
6.2 |
(4.8) |
58.6 |
4 |
3 |
5.0 to 15.0% |
641 |
0.3 |
(8.2) |
6.3 |
(5.3) |
49.1 |
9 |
7 |
15.0 to 40.0% |
546 |
0.8 |
(7.6) |
5.7 |
(5.1) |
48.7 |
3 |
3 |
40.0% and over |
226 |
1.6 |
(8.0) |
6.1 |
(5.5) |
48.5 |
3 |
6 |
a Excludes Kalawayo County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. b Standard deviations are in parentheses. |
TABLE B-4 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Percent Hispanic Population, 1990
|
|
|
|
|
|
|
Counties with More Than 20 Percent Error (Number) |
|
Percent Hispanic, 1990 |
Counties (Number)a |
Mean Algebraic Percent Errorb |
Mean Absolute Percent Errorb |
Percentage of Counties with Negative Errors |
- |
+ |
||
All |
3,140 |
-0.4 |
(8.7) |
6.3 |
(6.1) |
56.2 |
36 |
36 |
Less than 0.5% |
983 |
0.7 |
(9.2) |
6.1 |
(6.9) |
52.9 |
5 |
13 |
0.5 to 1.0% |
760 |
0.2 |
(7.0) |
5.5 |
(4.3) |
52.5 |
4 |
3 |
1.0 to 2.0% |
485 |
-0.1 |
(8.3) |
6.5 |
(5.2) |
56.1 |
3 |
10 |
2.0 to 5.0% |
385 |
-1.4 |
(8.8) |
6.5 |
(6.2) |
60.3 |
7 |
3 |
5.0 to 15.0% |
291 |
-3.2 |
(9.8) |
7.5 |
(7.0) |
63.4 |
11 |
4 |
15.0 to 40.0% |
162 |
-3.8 |
(10.4) |
8.4 |
(7.3) |
70.4 |
5 |
3 |
40.0% and over |
74 |
-1.0 |
(8.1) |
6.5 |
(4.9) |
56.8 |
1 |
0 |
a Excludes Kalawayo County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. b Standard deviations are in parentheses. |
TABLE B-5 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Percent Poor Population, 1990
|
|
|
|
|
|
|
Counties with More Than 20 Percent Error (Number) |
|
Percent Poor, 1990 |
Counties (Number)a |
Mean Algebraic Percent Errorb |
Mean Absolute Percent Errorb |
Percentage of Counties with Negative Errors |
- |
+ |
||
All |
3,140 |
-0.4 |
(8.7) |
6.3 |
(6.1) |
56.2 |
36 |
36 |
None |
50 |
-1.5 |
(8.2) |
7.0 |
(4.4) |
58.0 |
0 |
0 |
Less than 5% |
253 |
1.8 |
(13.9) |
7.3 |
(11.9) |
45.5 |
11 |
6 |
5 to 10% |
1,046 |
-1.4 |
(7.7) |
6.0 |
(5.1) |
62.1 |
8 |
8 |
10 to 15% |
929 |
-1.1 |
(8.4) |
6.7 |
(5.2) |
58.3 |
13 |
8 |
15 to 25% |
688 |
0.9 |
(8.2) |
6.1 |
(5.6) |
50.0 |
2 |
11 |
25 to 40% |
157 |
0.8 |
(7.0) |
5.4 |
(4.4) |
49.7 |
2 |
1 |
40% and over |
17 |
3.1 |
(11.4) |
8.9 |
(7.5) |
35.3 |
0 |
2 |
a Excludes Kalawayo County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. b Standard deviations are in parentheses. |
TABLE B-6 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Percent Group Quarters Residents, 1990
|
|
|
|
|
|
|
Counties with More Than 20 Percent Error (Number) |
|
Percent Group Quarters, 1990 |
Counties (Number)a |
Mean Algebraic Percent Errorb |
Mean Absolute Percent Errorb |
Percentage of Counties with Negative Errors |
- |
+ |
||
All |
3,140 |
-0.4 |
(8.7) |
6.3 |
(6.1) |
56.2 |
36 |
36 |
Less than 0.5% |
175 |
1.0 |
(17.3) |
9.9 |
(14.2) |
50.6 |
9 |
11 |
0.5 to 1.0% |
372 |
1.4 |
(8.1) |
6.4 |
(5.2) |
43.0 |
6 |
4 |
1.0 to 1.5% |
636 |
0.6 |
(7.6) |
5.9 |
(4.7) |
49.7 |
4 |
3 |
1.5 to 2.0% |
591 |
-0.3 |
(7.4) |
5.7 |
(4.6) |
55.3 |
1 |
3 |
2.5 to 3.0% |
535 |
-1.8 |
(8.3) |
6.3 |
(5.7) |
64.7 |
7 |
5 |
3.0 to 5.0% |
431 |
-0.9 |
(7.0) |
5.5 |
(4.4) |
60.8 |
1 |
4 |
5.0% and over |
400 |
-2.1 |
(9.0) |
7.1 |
(5.9) |
66.1 |
8 |
6 |
a Excludes Kalawayo County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. b Standard deviations are in parentheses. |
TABLE B-7 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Census Division
|
|
|
|
|
|
|
Counties with More Than 20 Percent Error (Number) |
|
Census Division |
Counties (Number)a |
Mean Algebraic Percent Errorb |
Mean Absolute Percent Errorb |
Percentage of Counties with Negative Errors |
- |
+ |
||
All |
3,140 |
-0.4 |
(8.7) |
6.3 |
(6.1) |
56.2 |
36 |
36 |
New England |
67 |
-1.2 |
(5.3) |
4.1 |
(3.6) |
62.7 |
1 |
0 |
Middle Atlantic |
150 |
0.6 |
(5.2) |
4.1 |
(3.3) |
54.0 |
0 |
0 |
East North Central |
437 |
-1.4 |
(5.7) |
4.7 |
(3.5) |
64.5 |
0 |
0 |
West North Central |
618 |
-3.0 |
(7.5) |
6.4 |
(5.0) |
72.0 |
4 |
5 |
South Atlantic |
591 |
2.4 |
(8.3) |
6.5 |
(5.7) |
39.6 |
7 |
7 |
East South Central |
364 |
2.9 |
(7.2) |
6.0 |
(5.0) |
37.4 |
0 |
7 |
West South Central |
470 |
-0.4 |
(9.6) |
7.0 |
(6.5) |
50.9 |
9 |
8 |
Mountain |
281 |
-2.8 |
(14.1) |
9.0 |
(11.2) |
68.7 |
10 |
7 |
Pacific |
161 |
-2.5 |
(7.9) |
6.5 |
(5.1) |
68.5 |
5 |
2 |
a Excludes Kalawayo County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. b Standard deviations are in parentheses. |
TABLE B-8 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Metropolitan Status, 1990
|
|
|
|
|
|
|
Counties with More Than 20 Percent Error (Number) |
|
Metropolitan Status, 1990 |
Counties (Number)a |
Mean Algebraic Percent Errorb |
Mean Absolute Percent Errorb |
Percentage of Counties with Negative Errors |
- |
+ |
||
All |
3,140 |
-0.4 |
(8.7) |
6.3 |
(6.1) |
56.2 |
36 |
36 |
Nonmetropolitan |
2,393 |
-1.2 |
(9.0) |
6.5 |
(6.3) |
60.0 |
34 |
26 |
Metropolitan |
747 |
1.9 |
(7.2) |
5.6 |
(4.9) |
43.9 |
2 |
10 |
a Excludes Kalawayo County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. b Standard deviations are in parentheses. |