Monthly Labor Review October 2003 3

Evaulation of Labor Force Projections

T he Bureau of Labor Statistics (BLS) has

made labor force projections since the late

1950s. Data for these projections are based

on age, sex, race and Hispanic origin. Beginning

in 1968, BLS has reviewed and evaluated past

labor force projections to determine closeness to

the actual figures. Such evaluations help both

individuals making projections and those using

the projections to understand the sources of error

and the accuracy of specific components.

BLS projected the 2000 labor force at five different

times, roughly 2 years apart. Of these 5 projections,

3 had errors of a million or less; the most extreme

errors ranged 1.5 percent above or below the actual

2000 labor force of 140.9 million. The growth rate of

the labor force is crucial to the BLS employment

projections program. The error in the growth rate

varied by a tenth of a percentage point above or

below the actual growth rate for the periods over

which the projection was made. At the same time,

projections of the civilian noninstitutional

population were uniformly low. Thus, the labor force

participation rate projections were generally too

high.

Until recently, BLS projections focused on

years divisible by five, so evaluations took place

at 5-year intervals. This article is an evaluation of

the BLS labor force projections to 2000. Beginning

in 1986 and continuing to 1994, BLS prepared five

projections either to 2000 or through 2000.1

 This

article examines the difference between the

projections and the labor force as estimated in

the Current Population Survey (CPS) using

weights from the 1990 census. The differences,

or errors, are calculated by sex for detailed age

Howard N Fullerton Jr.

formerly

was a senior

demographic

statistician in the

Office

of Occupational

Statistics and

Employment

Projections, Bureau of

Labor Statistics.

BLS labor force participation rates were

high and census population projections were

low, resulting in relatively accurate

labor force projections to 2000

Evaluating the BLS labor force

projections to 2000

Howard N Fullerton Jr. groups of the white, black, Asian and other, and

Hispanic origin population and labor force. (These

earlier projections did not have as much age detail

for Hispanics as for the other groups.) Each of the

five projections to 2000 had three alternatives: high,

moderate, and low. This analysis, for the most part,

focuses on the middle or “moderate” growth projection in each series. Where appropriate, the

accuracy of the five 2000 projections are compared

with evaluations of BLS projections to 1985, 1990,

and 1995. Each of the projections is identified by

the year from which the projection was made (1986,

1988, 1990, 1992, and 1994).2

One of the challenges in evaluating projections

is that the estimates for 2000 are not strictly

comparable with the data projected. For example,

after the 1990 census, extensive changes to the CPS

were implemented in 1994. These changes included

an adjustment for the undercount, as well as

changes in the questions asked. The latter resulted

in a greater proportion of women and older persons

being counted in the labor force. It is not possible

to quantify the effect of these improvements in the

survey, so it is not possible to know how much

they affect projection accuracy. However, it is clear

that projections made before 1994 did not anticipate

the effects of the redesign and that projections

made after 1994 did not immediately incorporate all

the changes.

Another challenge in evaluation is that no one

measure of error or quality satisfies all users of

the labor force projections. Some use the total

labor forceor even the growth rate of the labor

forcenot needing any of the components. For

many users, some part of the labor force is vital,
Evaluation of Labor Force Projections

4 Monthly Labor Review October 2003

for example, youth workers or older workers. Others use the

projected labor force participation rates to conduct market

research or to project State populations. Another group of users

focus on the distribution of the labor force by race and sex.

Still another challenge is that there are two sources of

possible error in projecting the labor force: the projected

population and the projected labor force participation rates.

It would be helpful to know how these series combine to

produce the errors in the labor force projections.

This article first examines the error in the aggregate labor

force, both in the levels and in the growth rates. It then

examines errors in the projection of the population and errors

in labor force participation rates. Finally, this article analyzes

labor force errors, including issues of distribution and levels

among demographic groups.

Aggregate 2000 projections

Evaluation of the aggregate 2000 labor force projections

reveals that the overall errors were greatest in 1986 and 1990;

except for these 2 years, the errors were less than 1 percent.

The following tabulation shows the projections to 2000 (in

millions), and the numerical and percent error made in each

year the projections were based:

Projection for 2000 Historical Projected Actual Error

1986 ......................... 2.2 1.2 1.3 –0.1

1988 ......................... 2.0 1.2 1.2 .0

1990 ......................... 1.6 1.3 1.1 .1

1992 ......................... 1.5 1.3 1.2 .1

1994 ......................... 1.2 1.1 1.2 –.1

The error in the annual growth rate from 1988 was actually

0.02 percent. For four other projections, the error in the annual

growth rate was either –0.1 or 0.1. For individuals using the

projections to forecast either employment or economic growth,

this level of error would be minor. For growth rates, BLS projected

variously that the rate of growth would slow significantly from

past rates of growth (by a full percentage point in the 1986

projection) to not much different from past rates of growth (by a

tenth of a point in the 1994 projection). Except for the 1994

projection, when BLS projected a decrease in the growth rate and

the labor force continued to grow at past rates, the change was

in the correct direction and the error in the growth rate was less

than the projected change in the growth rate.

Population projections

BLS labor force projections are prepared using the incidence

method: the labor force participation rates by age, sex, race, or

Hispanic origin are multiplied by comparable projections of the

population, prepared by the Census Bureau.3 BLS adjusts the

resident population, provided by the Census Bureau, to get

figures of the civilian, noninstitutional population. Although

errors were made in making this adjustment, they are not

considered to be sufficiently large to incorporate into this

analysis. Some sense of the size of this type of error may be

garnered by seeing how the errors in the adjusted population

varies for the first two labor force projections. For the projection

from 1994, the projected population also was adjusted for the

1990 undercount, as the CPS itself was so adjusted.

Population projections have three components: births,

deaths, and net immigration. Each of these may be a source of

error, as well as the initial population from which the projection

is made. Because these projections spanned a period of less

than 16 years, errors in births did not affect the size or

composition of the labor force. Although it is true that there

were fewer deaths than projected, most of those extended lives

occurred at older ages when persons are less likely to be in the

labor force. The source of the discrepancy must be net

immigration either over the projection or as part of the estimate

of the base year population. If so, then errors would be larger

for Hispanics and Asian and others. The Census Bureau

prepares its own evaluation of their population projections;

this article examines only the population projections as they

affect the size and composition of the labor force.4

Projection for 2000 Labor

 made from— force Error

Millions Percent

1986 ............................. 138.8 –2.1 -1.5

1988 ............................. 141.1 .3 .2

1990 ............................. 142.9 2.0 1.5

1992 ............................. 141.8 1.0 .7

1994 ............................. 140.0 –.9 –.6

Actual:

2000 ............................. 140.9 ... ...

The error information in the tabulation indicates that the short,

versus long time-span does not seem to be a factor in improving

the accuracy of labor force projections. A similar conclusion

would be inferred from earlier analyses. (The first three

projections also were evaluated for 1995. The overall errors were

greatest in 1986 and 1990; for the other years, the errors were

less than 1 percent. It is interesting to note that the numerical

errors are less for 2000 than those for 1995 with the 1988 and 1990

projections. It is possible for a projection to improve with age.)

For some users, the absolute error or the percent error is not

relevant, but the error in the growth rate is. The following

tabulation displays the historic growth rate for the civilian labor

force, the projected annual growth rate, the actual growth rate,

and the error in the growth rate. All three rates in a row are

measured over the same number of years. The historic rate is

calculated over the same number of years before the date of

the projection, as 2000 is after the date of the projection:

 made in— rate rate rate
Monthly Labor Review October 2003 5

Error for the population projections. For the past decade,

population growth has accounted for more labor force growth

than has the labor force participation rate change. Thus, the

accuracy of population projections should be crucial to the

accuracy of the labor force projections. The following

tabulation shows the 2000 projections for the civilian,

noninstitutional population aged 16, and the errors associated

with the total population projections:

Projections for 2000 Total Error

 made in—

 Millions Percent

1986 ............................. 204.7 –5.0 –2.4

1988 ............................. 204.6 –5.1 –2.4

1990 ............................. 208.0 –1.7 –.8

1992 ............................. 208.0 –1.7 –.8

1994 ............................. 208.8 –.9 –.4

Actual

2000 ............................. 209.7 ... ...

Unlike the labor force projection, all the population

projections were low. Unlike the labor force projections, the

population projections show steady improvement. The

difference between the percent errors in the first tabulation

(page 4) and this one indicate that BLS made offsetting errors

in labor force participation rates, reducing the errors in the

aggregate labor force. The following tabulation presents

hypothetical labor force projections using the projected

population and the actual 2000 labor force participation rates:

Projections for 2000 Total Error Difference Percent

 made in— (in from actual error

millions) error

1986 ......................... 136.9 –3.9 –1.8 –2.8

1988 ......................... 136.8 –4.0 –4.3 –2.9

1990 ......................... 139.5 –1.3 –3.4 –1.0

1992 ......................... 139.2 –1.6 –2.6 –1.9

1994 ......................... 140.4 –.5 .4 –.3

The numerical errors made in this hypothetical projection

are less than those for the population (previous tabulation).

Except for the projection from 1994, these projections would

have a larger error than the projections that were made: the

labor force would have been even smaller. The percent errors

for these hypothetical labor force projections were different

from those for the population projection and, except for 1994,

the percent errors for the hypothetical labor force projections

were greater.

Errors by sex, race and Hispanic origin, and age in the

population projections. To trace errors in the population

projection, the mean absolute percent error (hereinafter referred

to as “mean error”) may be calculated at differing levels of

aggregation. Table 1 provides the mean errors for several of

the various aggregations (in percent). The mean error for

aggregate population is the absolute value of the percent

error. The mean error for men and women considered separately

averages to the aggregate mean error, so they are not displayed

in this table. When mean errors are calculated for the three

race and one Hispanic origin groups, they are larger than the

aggregate error, but the relative standing of the various

projections does not change. The errors made when projecting

by race offset each other. Therefore, the projection with all race/

ethnicity groups separated out is more accurate than that implied

by the error associated with any single race/ethnicity grouping.

When sex and race are considered together, the mean errors are

lower than the error associated with race alone for the first two

projections and about the same as those for the last three

projections of the population. Finally, accounting for age, sex,

and race results in a larger aggregate error than any of the other

groupings considered. Examination of the detailed projections

does not indicate that using more aggregated age groups would

have increased the accuracy of the overall projections.

The population of both men and women were underprojected.

A closer examination reveals that the difference was greater for

men than for women through the projection from 1990. The first

two projections had markedly larger projection errors than the

last three. That the error was larger for men than for women

reflects the greater tendency for men to be undocumented

immigrants, thus, it is likely that the errors attributed to

underestimates of undocumented workers decreased because

population projection errors reduced as time passed. All five

projections correctly projected that there would be substantially

more women than men in the 16 and older population.

For all five labor force projections (three population

projections), the size of the white population was underprojected.

As whites made up 84 percent of the population in 2000, they

should also account for most of the error. Generally, however, it is

easier to measure and project large groups. For all the projections,

the errors for the white labor force projections were less than 84

percent of the error. Except for the projection from 1990, whites

accounted for more than half of the projection error.

Two population groups would be expected to be hard to

project: Asians and others and Hispanics. Both groups have

high immigration, are fairly heterogeneous, and are relatively

small. Asians and others accounted for 5 percent of the 16 and

older population in 2000, but for each of the projections, the first

population projection, they accounted for 27 percent of the error.

For the next population projection, their numerical error slightly

exceeded the error for whites. For the fifth population projection,

the errors were much smaller, accounting for 16 percent of error.

However, their projected population was higher than actual,

unlike the other three groups.

Hispanics may be of any race, however, more than 90 percent

are white. Thus, errors in projecting the numbers of Hispanics
Evaluation of Labor Force Projections

6 Monthly Labor Review October 2003

carry into the number of whites. It should be no surprise that the

Hispanic population is difficult to project accurately because

Hispanics have high immigration rates and it is estimated they

are a large component of undocumented immigration. Hispanics

accounted for 11 percent of the 16 and older population in 2000.

Errors in their population projection accounted for 38 percent of

the error from 1986 and 37 percent of the projections from 1988.

For the labor force projection from 1990, which used the same

population projection for Hispanics as the previous two, the

error was the same size (1.9 million low), but it now exceeded the

total population error (1.7 million low). This projection was not

based on the 1990 census. The 1992 and 1994 projections were

the relative size of the projection errors decreased. Even so, the

error in the number of Hispanics exceeded that for whites in the

projection from 1992. The dynamic changes in the Hispanic

population are reflected in the difficulties of projecting this

group.

For the first two population projections (first three labor

force projections), the black population had relatively small

errors—less than their share of the population, which is 12

percent. This population group, though growing faster than

the overall population, has demonstrated a consistent path

of growth. The black population was the most accurately

projected group in the projections from 1994. For the projection from 1992 the error was much larger, and accounted

for 30 percent of total error. For the projection from 1994,

although the size of the numerical error was smallest of the

five (because the total error was by far the smallest), the

black’s share of the projection error was larger than their share

of the population.

Errors by age, sex, and race or Hispanic origin in the

population projections. For each of the five population

projections, there are 108 errors to examine at the level of age,

sex, race or Hispanic origin. Table 2 provides summary

information about the depth and dispersion of the errors, in

thousands. It indicates that the population was underprojected.

The middle, half-way points, or medians are negative. For the

first population projection, three-quarters of the population

errors were negative. It is apparent from the three lines of error

dispersion that the more recent projections had a smaller range

of errors. Indeed, the ranges of errors dropped by a third. The

decrease in dispersion is larger that the change in the medians

of the errors.

Which groups had the lowest underprojection? For the

projections from 1986 through 1992, it was white men ages 20

to 24. For the projection from 1994, it was Hispanic women

ages 25 to 34. (The error for this group of women was always

in the lowest one-eighth.) White men ages 20 to 24 consist of

a large group with a large absolute error, but their relative

errors are smaller. The relative errors for Hispanic women ages

25 to 34 are larger than those for white men ages 20 to 24.

Hispanic men ages 20 to 24 also have large errors—absolute

and relative—for the 1986 population projections. Nevertheless,

errors in projecting the size of the 20- to-24 and 25- to-34-year

old Hispanic population also affected projecting the size of

the white population of the same age.

Which groups were the most overprojected? This varied

by year. For the 1986 population projection, it was white men

ages 50 to 54. For the 1988 population projection, it was white

men ages 30 to 34, followed by white men, 35 to 39. For the

1994 projection, Asian and other women ages 50 to 54 were

the most overprojected group. Again, white men are a large

group and the source of a large error. Also for the 1994

projection, Asian and others were overprojected as a group.

White men’s age groups were over- and underprojected, by

large amounts, but the population of older white men was

uniformly overprojected.

At this point, it is clear that the population projections

were too low; given that the aggregate labor force projections

were much more accurate, it is easy to infer that the projected

labor force participation rates must be too high. It is not clear

what effect the errors in the population projections had on

the distribution of the labor force by race or sex. That question

must be answered after examining the labor force participation

rate projections.

Mean errors for various aggregations,

projections for 2000 made in 1986–94

[In percent]

 Projection for 2000 made in–

1986 1988 1990 1992 1994

Aggregate error ....................... 2.4 2.4 0.8 0.8 0.4

Mean error for—

Race ...................................... 6.4 6.4 4.3 3.5 1.5

Sex and race ......................... 5.5 5.6 4.2 3.4 1.5

Sex, race, and age ............... 7.6 7.7 6.3 4.1 3.6

Category

Table 1.

Table 2. Summary of depth and dispersion of errors in

 projections for 2000 made in 1986–94

[In thousands]

 Category 1986 1988 1990 1992 1994

 Depth

Lowest ............................. –965 –958 –622 –495 –273

Lowest one-eighth ........... –167 –167 –114 –106 –53

Lowest quarter ................. –100 –108 –56 –44 –25

Half (median) .................... –36 –36 –22 –6 –10

Highest quarters .............. –1 –1 23 16 8

Highest eighth .................. 41 41 53 33 24

Highest ............................. 136 137 226 195 75

 Dispersion

Inner 50 percent .............. 100 107 78 59 33

Inner 75 percent .............. 208 208 167 139 76

Range ............................... 1,101 1,095 848 691 348
Monthly Labor Review October 2003 7

Labor force participation rates

Aggregate measures of labor force participation. What BLS

brings to the labor force projection process is its projection of

labor force participation rates. Although the population

projections currently account for most of projected labor force

change, study of the errors made in projecting the labor force

participation rates is important also.

Four of the five labor force participation rate projections had

the aggregate labor force participation higher than the actual. As

table 3 indicates, the aggregate labor force rate has yet to reach

68 percent, though three of the projections anticipated that this

would happen by 2000. Given that 2000 was the last year in a

sequence of high economic growth, it is significant that the

projected labor force rates were higher than the actual. From the

projection made in 1988 up to 1994 the error in the aggregate

labor force participation rate decreased for each projection.

However, the 1986 projection was the second most accurate.

Comparing women and men, it is clear that men’s rates were

more accurately projected than those of women. All the

projected participation rates for women were high. As the

labor force rates of men change more slowly than those of

women, it is easier to accurately project their labor force

participation rate. This slower rate of change for male rates

may be ending at the older ages. A variety of incentives exist

that could result in higher labor force participation rates for

retirement age men. These include a change in the normal

retirement age under Social Security, and a switch from defined

benefit to defined contribution retirement plans.

Sex and race or Hispanic origin. Mean absolute percent

errors may be calculated also for the labor force participation

rates. For the aggregate error, they are the absolute value of

the relative errors. (See table 4.) Errors by gender provide little

additional information beyond that for aggregate error—the

greatest difference from the aggregate error occurs with the

projection from 1994, which had the rate for women too high

and that for men too low—because there is no reward for

offsetting errors. The mean absolute percent error for race

indicates that the worst projection was the one from 1994.

Labor force rates for the four race and Hispanic origin groups

shows that the percentage point error for 1994 was zero for

whites—their best projection—but that the projection from

1994 was by far the worst for blacks, Asians and others, and

Hispanics. The mean absolute percent errors were not weighted

by size of group. Whites were 83 percent of the 2000 labor force,

so that for weighted measures of error, the most accurate year for

the overall labor force would be the most accurate year for whites.

For the mean absolute percent error by race and gender, the

projection from 1988 was least accurate. It was not the case that

a good projection for men implied a good projection for women,

but certainly the converse was not true. (The correlation of men

and women’s errors is 0.33.) When the age structure is also

considered, then the projection from 1986 had the greatest mean

absolute percent error. The projection for this year also had the

greatest numerical error. Both the population and the labor force

participation projections contributed to this error in the 1986

projection, with the population too low and the participation too

high.

The labor force participation rate projections from 1994 had

the lowest error for whites, but had the worst errors for other

race groups. Because whites make up the majority of the labor

force, the 1994 projection had the lowest error in labor force

participation rates. By contrast, the 1986 projection had large

errors in both the population and labor force participation

rate projections.

Age, sex, and race or Hispanic origin. Overall, there are 108

labor force participation rate projection errors to examine. Table 5

summarizes the cumulative errors for those categories, ranked

from most negative to most positive. The aggregate labor force

participation rates were too high in 4 of the 5 projections; the

median of the errors of the age-sex-race or Hispanic origin

participation rates were closer to zero than the errors of the

aggregate, with the exception of the most recent projection. If the

thesis is that the labor force participation rates were too high to

offset population projections that were too low, then 4

projections of the 5 fit that mold. This information is also

Total Men Women

1986 ............... 67.8 0.6 74.7 0.0 61.5 1.3

1988 ............... 69.0 1.8 75.9 1.2 62.6 2.4

1990 ............... 68.7 1.5 76.0 1.3 62.0 1.8

1992 ............... 68.2 1.0 75.3 .6 61.6 1.4

1994 ............... 67.0 –.2 74.0 –.7 60.6 .4

Actual ............ 67.2 ... 74.7 ... 60.2 ...

 Projections

 for 2000

 made in— Percent

Error (in

 percent-

 age

 points)

Error (in

percent-

 age

 points )

Percent

Error (in

percent-

 age

 points)

Percent

Projections of the 2000 labor force participation

rate, by sex and percentage point errors, 1986–

1994, and actual

Table 3.

 Projections for 2000 made in—

1986 1988 1990 1992 1994

Aggregate error ........... 0.9 2.7 2.3 1.5 0.3

Mean error for–

Sex ........................... 1.1 2.8 2.4 1.6 .8

Race ......................... 1.2 1.9 .9 .8 3.1

Sex and race ............ 4.4 5.9 2.8 2.1 3.0

Sex, race, and age .. 14.5 9.8 5.7 6.2 5.1

Category

Table 4. Mean errors for various aggregations of the

projections for 2000, by sex, race, and age

[In percent]
Evaluation of Labor Force Projections

8 Monthly Labor Review October 2003

available in chart 1 (top panel), which has box-and-whisker

plots for the five projections. (See box on page 10.)

One desirable characteristic of the projections as a

sequence would be that the dispersion of the errors would be

less for the more recent projections. The measures of

dispersion in table 5 (bottom) and chart 1 (top panel) indicate

that this was taking place until the 1994 projection. That the

most accurate projection is not the most recent made seems

to be a characteristic of labor force projections, this also

happened with the projections to 1990 and 1995.

Which groups had the worst labor force participation rate

projection error? The following tabulation illustrates the

answer to this question for each projection.

Projection Most Most

 from— overprojected underprojected

1986 .......... Black men 18 and 19 Asian and other men 60 and 61

1988 .......... Black men 18 and 19 Asian and other men 65 to 69

1990 .......... Asian and other 

women 16 and 17 Hispanic women 45 to 54

1992 .......... Black men 60 and 61 Black women 25 to 29

1994 .......... Asian and other

women 50 to 54 Hispanic men 60 to 64

The pattern here implies that small groups are hard to

project. For half the groups, 2 years of errors occur. With

the exception of black women 25 to 29, the remaining

groups are small.

“Were some age groups harder to project than others?” To

examine this question, chart 1 (middle panel) presents boxand-whisker plots of the errors by age-sex-race/Hispanic

origin groups. (We have six projection errors for white women

ages 20 to 24, six for black women of the same age, and so on.)

Although the median of the errors by projection year are near

zero, except for the 1994 projection, the data by age indicate

that there was significant variation in the errors by age. For

the 25- to-54-age group, which exhibits the highest labor

force participation rates, the median of the errors were

either high or near zero, giving the source of the high

aggregate labor force participation rates. For the older ages,

the median of the errors was below zero. For these age

groups for which there is now great interest in their pattern

of labor force participation, there was a consistent pattern

of labor force participation projections that were too low.

Labor force participation rates for older men increased from

1985 to 1990, then decreased until 1994 and have increased

since then. These changes did not start at the same time

for all groups of older men. Starting with the 1996 labor

force projections, BLS has projected this change in trend.

(It was among the first to do so.)

According to the box-and-whisker plots of labor force

participation rates by age group (chart 1, middle panel), it

is clear that the age groups younger than 60 were

overprojected. The labor force participation rates for

groups older than 60 were uniformly underprojected. Some

age groups were harder to project than others. The two

age groups with the largest boxes were those 18 and 19

and 65 to 69. The latter group had the most extreme errors.

However, the extreme errors for those 65 to 69 were high—

for Asian and other men in the 1986 projection and Asian

and other women in the 1988 projection.

Labor force

At this point, it is clear that the labor force participation

rate projections were, as a group, too high. However, the

aggregate labor force was fairly accurately projected. As

new labor force projections were reviewed within BLS, the

reviewers have an independent estimate of the aggregate

labor force and employment, which contributes to a more

accurate overall labor force. In the face of low population

projections, labor force participation rates were increased,

resulting in an accurate projection of the labor force.

Sex and race or Hispanic origin. Historically, BLS labor

force projections have been characterized as having

projected labor force levels too high for men and too low

for women. However, for 3 of the 5 projections in this

evaluation, the projected labor force for men was lower

than the actual. For women, all of the projected labor force

levels were higher than the actual. Thus, the traditional

view of BLS labor force projections is now wrong. For the

two projections with the largest overall error, the male labor

force was off by 2.2 million in 1986; women’s labor force

was off by 1.4 million in 1990. In the projection with least

overall error, men and women’s errors offset. In any case,

there does not seem to be a pattern of projecting labor

force better for one gender than the other.

Summary of errors in the components of the

labor force participation rates, for 5 years of the

2000 projection

Error 1986 1988 1990 1992 1994

 Depth

Lowest ................. –16.9 –9.8 –8.5 –9.0 –10.6

Lowest eighth ...... –5.8 –3.5 –2.6 –3.4 –4.9

Lowest quarter .... –3.1 –2.1 –1.8 –1.3 –3.6

Half (median) ....... –.1 .6 .6 .4 –1.6

Highest quarter ... 3.1 3.5 2.3 1.8 .3

Highest eighth ..... 6.6 6.1 4.3 3.4 1.7

Highest ................ 12.4 11.1 8.3 7.6 7.1

 Dispersion

Inner 50 percent ... 6.1 5.6 4.1 3.1 3.9

Table 5.
Monthly Labor Review October 2003 9

Chart 1. Errors in 2000 for participation rates and labor force, by selected categories

 10

 5

 0

 –5

–10

–15

 10

 5

 0

 –5

–10

–15

1986 1988 1990 1992 1994

Percent Participation rate error by projection Percent

Participation rate error by age group

 10

 5

 0

 –5

–10

–15

16–17 20–24 30–34 40–44 50–54 60–61 65–69 75 and

 older

Percent

 10

 5

 0

–5

–10

–15

Percent

–50

16–17 20–24 30–34 40–44 50–54 60–61 65–69 75 and

 older

 50

–50

0 0

50

Thousands Labor force error by age group Thousands
Evaluation of Labor Force Projections

10 Monthly Labor Review October 2003

Summary of errors in the components of the

labor force for 5 years of the 2000 projection

Error 1986 1988 1990 1992 1994

 Depth

Lowest ................. –518 –543 –372 –326 –290

Lowest eighth ...... –244 –140 –118 –97 –100

Lowest quarter .... –93 –75 –62 –43 –59

Half (median) ....... –-16 –14 –4 –6 –13

Highest quarter ... 0 9 21 13 4

Highest eighth ..... 39 55 97 61 26

Highest ................ 712 772 563 765 230

 Dispersion

Inner 50 percent ... 94 84 84 55 64

Inner 75 percent ... 282 195 215 158 126

Range .................. 1,230 1,315 935 1,091 520

Table 6.

Aggregate error ........ 1.5 0.2 1.5 0.7 0.6

Mean absolute

percent errors for—

Sex ........................ 1.4 1.5 1.5 .7 .8

Race ..................... 6.2 5.9 4.7 3.9 3.4

Sex and race ......... 6.3 5.6 5.5 4.0 4.1

Sex, race, and age ... 15.4 12.3 9.1 7.5 8.5

The first row of the tabulation substantiates the information

from this section’s overview. Once gender is taken into account,

the 1988 projection error increases. The 1988 projection had a

highly accurate projection of the level, but the labor force level

was too low for men and too high for women. The accuracy of

overall projections is the result of offsetting errors. The other

four projections did not have large offsetting errors by sex. The

more detailed measures reveal where the errors were made. Thus,

taking race and Hispanic origin into account increases the error

because less of the offset is concealed. In the 1988 and 1990

projections, the projected white labor force was too large,

compared with those of the black and Asian and other groups,

for which the labor force was projected too low. The 1994

projection accurately projected the white labor force, but that

for blacks was almost a million low. For all the projections,

Hispanics were underprojected, by substantial amounts.

Taking race and gender into account, the error in the 1994

projection rises because the accuracy of the white labor force

level is due to sizable offsetting errors in the labor force levels

of men and women. Once age, sex, race (and Hispanic origin)

are taken into account, the errors increase, as offsetting errors

of having some ages too high and others too low are taken

into account. This shows the pattern of error decreasing from

the 1986 projection to the 1992 projection, then increasing for

the 1994 projection. However, the accuracy of the overall labor

force was obtained through offsetting errors.

Age, sex, or race and Hispanic origin. Table 6 summarizes the

cumulative errors for 108 categories of the labor force, ranked

from most negative to most positive. The median of the individual

errors are all small, but negative. The low quartiles or hinges are

all negative and the high hinges are all positive—the errors are

grouped around zero. The innerquartile range decreased from

the 1986 projection to the 1992 projection, before a slight increase

for the 1994 projection. However, the range and the inner 75

percent show a decrease through 1994. The errors for the 1994

projection were systematic, but not large.

The white population and labor force is significantly larger

than the black, Hispanic, or Asian and other population and

labor forces. Thus, the largest numerical errors are in white

groups. For the 1986 through 1992 projections, the group with

the largest overprojection was white women ages 35 to 39.

For the 1994 projection, white women ages 40 to 44 had the

greatest error. By comparison, for the first four projections,

white men ages 20 to 24 were underprojected the most. For

the 1994 projection, Hispanic men ages 25 to 34 were the group

most underprojected.

The older labor force had the greatest relative errors. The

labor force for these ages is small, so a modest numerical error

 Box-and-whisker plots

“A boxplot is a way to look at the overall shape of a set of

data. The central box shows the data between the ‘hinges’

(roughly quartiles), with the median respresented by a line.

‘Whiskers’ go out to the extremes of the data, and very

extreme points are shown by themselves.” See W. N.

Venables and B. D. Ripley, Modern Applied Statistics with

S-PLUS, 2nd edition (New York, Springer, 1997), p.172.

The goal of box and whisker plotting is to examine

distributions; in this case, the distribution of errors. The

errors are centered on zero (that is, they have a median near

zero). We would like them to be tightly distributed around

zero. That means that the two quartiles would be near zero

and the remaining errors would be near the upper and lower

quartiles (the vertical lines would be short). We would like

no outliers, however, they do exist in this analysis, and

provide an interesting discussion.

The heavy white line in each box is the median. The

upper and lower edges of the box are the quartiles or hinges.

The horizontal lines above and below the box indicate the

maximum and minimum values.

1986 1988 1990 1992 1994

The following tabulation shows mean absolute percent errors for various aggregations:

[In thousands]

Projection for 2000 made in—
Monthly Labor Review October 2003 11

yields a large relative error. (See chart 1, bottom panel for

relative errors by age group.) For those age groups with high

labor force participation, the relative errors had a median of

zero and the errors were closely grouped around the median.

The labor force participation rate projections at the older ages,

which were too low for older men, had negative median errors

and wide dispersion around the median. Thus, the greatest

errors in the labor force were at ages with modest impact on

the size of the labor force.5

Distribution

For some users, the size and growth rate of the labor force is

unimportant; the concern is for the distribution between men

and women, among the various race and ethnic groups, or

among the various age groups. The text tabulation (page 10)

presents the index of dissimilarity comparing the projections

to the 2000 actual, by various levels of aggregation.

 Projection for 2000 made in—

 Index of dissimilarity 1986 1988 1990 1992 1994

 by—

Sex ........................................ 0.7 0.8 0.3 0.3 0.4

Race ..................................... .6 .8 .7 .5 .6

Race and sex ........................ 1.3 1.5 1.0 .9 .9

Race, sex, and age .................. 3.3 2.6 2.0 1.9 1.3

The index of dissimilarity may be interpreted as the amount

the one distribution has to change to be like another. In these

cases, it records how much the projected distribution has to

change to be like the actual 2000 labor force distribution. Thus,

the 1986 projection would have had to change by 0.7 of a

percentage point to reflect the actual distribution of the labor

force between men and women. The projections were also quite

good in reflecting the actual composition of the labor force by

race. Taking race and gender into account, there is a higher

index of dissimilarity (or greater error) than when considering

race or only sex.However, in the worst year, 1988, the distribution

would have only needed to change by 1.5 percentage points.

Once race, sex, and age are all taken into account, the indexes

increase again; however, they improve with time, as the worst

year, 1986, is 3.3 percent and the best year, 1994, is 1.3 percent.

Even though the older labor force was underprojected, the age

composition of the labor force was fairly well projected.

Alternatives and confidence intervals

For each of the five labor force projections, BLS prepared three

alternatives (low moderate and high). This analysis focuses on

the middle or moderate alternative because BLS presents the

middle alternative in its presentations. However, a user could

High and low alternatives of the labor force for 5 years

of the 2000 projection

Labor force Participation Labor force Participation

(thousands) rate (thousands) rate

1986 .................... 141.1 68.0 134.5 65.7

1988 .................... 146.8 70.7 137.7 67.3

1990 .................... 156.2 71.5 141.8 66.1

1992 .................... 156.5 70.1 147.3 67.3

1994 .................... 153.4 68.7 143.6 65.5

 Actual

1994 .................... 140.9 67.2 140.9 67.2

Projection for

2000 made

in—

Table 7.

High alternative Low alternative

THE PROCESS OF REVIEWING labor force projections helps

provide a picture of the strengths and weaknesses of the BLS

labor force projections model. Over time, this allows for

improvements in that model. Faced with population

projections that were too low, BLS made subtle adjustments in

the labor force participation rate for the labor force ages 30 to

64, resulting in somewhat high aggregate labor force

participation rates. For users of the labor force projections

who needed projections of the size of the total labor force or

of its growth rate, this projection would have served them

well. For users of projected labor force participation rates, the

problem was with projections for older workers, whose rates

were too low. 

reasonably expect the 2000 labor force to be between the low and

high alternatives.

Unlike projections for earlier years, some of these alternative

projections did not cover the actual. (See table 7.) Only the

 projections prepared in 1986 bracketed or covered both the actual

2000 labor force and the participation rate. Given the

characteristics of the projections with the labor force levels more

accurately projected than the labor force participation rates, one

would expect that the labor force projections would cover the

actual and the labor force participation rates would not. For three

of the projections, the low alternative labor force was higher than

the 2000 actual. This happened for only two of the labor force

participation rate projections. The 1992 projection was the only

one to have neither the labor force or participation rate confidence

interval cover the actual. Every possible combination of covering

and not covering occurred among the five projections.

Evaluations of projections to earlier years indicated that the actual

labor force projection was covered by the alternatives.

Notes

1

 Howard N Fullerton, Jr., “Labor force projections: 1986 to 2000,”

Monthly Labor Review, September 1987, pp. 19–29. Reprinted with

additional detail in Projections 2000, BLS Bulletin 2302, March 1988.

Howard N Fullerton, Jr., “New labor force projections, spanning 1988

to 2000,” Monthly Labor Review, November 1989, pp. 3–12.
Evaluation of Labor Force Projections

12 Monthly Labor Review October 2003

Reprinted with additional detail in Outlook 2000, BLS Bulletin 2352,

April 1990. Howard N Fullerton, Jr., “Labor force projections: the

baby boom moves on,” Monthly Labor Review, November 1991, pp.

31–44. Reprinted with additional detail in Outlook 1990–2005, BLS

Bulletin 2402, May 1992. Howard N Fullerton, Jr., “Another look at

the labor force,” Monthly Labor Review, November 1993, pp. 31–40.

Reprinted with additional detail in The American Work Force: 1992–

2005, BLS Bulletin 2452, April 1994. Howard N Fullerton, Jr., “The

2005 labor force: growing, but slowly,” Monthly Labor Review,

November 1995, pp. 29–44.

2

 Howard N Fullerton, Jr., “Evaluating the 1995 BLS labor force

projections,” Proceedings of the Section on Government Statistics

and Section on Social Statistics (Alexandria, VA, American Statistical

Association, 1997), pp. 394–99; Howard N, Fullerton, Jr., “An

evaluation of labor force projections to 1990,” Monthly Labor Review,

August 1992, pp. 3–14; Howard N, Fullerton, Jr., “An evaluation of

labor force projections to 1985,” Monthly Labor Review, November

1988, pp. 7–17; Howard N, Fullerton, Jr., “How accurate were the

1980 labor force projections?,” Monthly Labor Review, July 1982, pp.

15–21; Paul M. Ryscavage, “BLS labor force projections: a review of

methods and results,” Monthly Labor Review, April 1979, pp. 15–22;

and Marc Rosenblum, “On the accuracy of labor force projections,”

Monthly Labor Review, October 1972, pp. 22–29.

3

 Projections of the Population of the United States by Age, Sex and

Race: 1987 to 2080, Current Population Reports, Series P–25, no.

1018 (Bureau of the Census, 1989). Projections of the Population of

the United States by Age, Sex and Race: 1993 to 2050, Current

Population Reports, Series P–25, No. 1104 (Bureau of the Census,

1993). Projections of the Population of the United States by Age, Sex

and Race: 1995 to 2050, Current Population Reports, Series P–25, no.

1130 (Bureau of the Census, 1995).

4

 Tammany Mulder, “Accuracy of the U.S. Census Bureau National

Population Projections and Their Respective Components of Change,”

Population Division Working Paper No. 50 (Bureau of the Census,

forthcoming).

5

 This is confirmed if a box and whisker chart of the errors in

thousands is examined. If a user were particularly interested in the

labor force participation of older workers or the size of their labor

force, this set of projections would have been relatively unhelpful.
Monthly Labor Review October 2003 13