COMPOSITE WEIGHTS FOR THE CURRENT POPULATION SURVEY

Janice Lent, Stephen Miller, Bureau of Labor Statistics; Patrick Cantwell, Bureau of the Census

Janice Lent, Bureau of Labor Statistics, 2 Massachusetts Ave. N.E., Washington, DC 20212

1. Introduction. Each month, the Bureau of

Labor Statistics (BLS) publishes labor force estimates

for the U.S. resident population and a variety of its

demographic subgroups, e.g., teenagers, Hispanics.

Published figures include estimated numbers of persons

employed, unemployed, and not in the labor force, as

well as relevant rates such as unemployment rates.

These statistics are computed using data from the

Current Population Survey (CPS), a monthly

household survey the Census Bureau conducts for the

BLS.

The CPS sample is a two-stage probability sample

of housing units, covering the entire U.S. Each new

sample unit remains in the sample for four months,

leaves the sample for eight months, and then re-enters

for another four months. One quarter of the sample is

new (or re-entering) each month, while half of each

month's sample comes from the sample for the same

calendar month one year earlier. This "four-eightfour" sample rotation scheme results in positive

correlation between CPS estimates from different

months, improving measures of change over time. The

positive correlation is further increased by composite

estimation.

Composite estimation is the last in a series of

estimation steps performed on CPS data, prior to

seasonal adjustment. Unlike weighting techniques,

composite estimation does not affect CPS micro data;

composite estimates are computed using estimated

totals from the various rotation groupsgroups of

respondents who enter the sample together. Since the

composite estimates incorporate information from

several months' data, users cannot compute composite

estimates from only one month's micro data.

In this paper, we present a method of computing

composite weights for the CPSmicro data weights

that incorporate the effect of composite estimation.

Data users would compute composite estimates by

simply adding these weights, using only one month's

CPS data. This method, suggested by Fuller (1990),

also allows us to tailor the composite estimatorby

varying coefficientsto the correlation structures of

major labor force categories, thus improving reliability.

Section 2 provides a brief overview of current CPS

estimation procedures, including composite estimation.

In Section 3, we describe the process of selecting

compositing coefficients for different labor force

categories. Section 4 contains results of an empirical

study of two variants of Fuller's composite weighting

method, as applied to CPS data.

2. Current CPS Estimation Procedures. For

each person in the monthly CPS sample, the Census

Bureau calculates a weighta rough estimate of the

number of actual persons the sample person represents.

Computing the weights involves several steps: initial

weights reflect probabilities of selection for the sample;

these "base weights" are then adjusted upward to

account for the occupied sample households not

interviewed. Two types of ratio adjustments are then

applied. The final ratio adjustment, a raking process,

ensures that the sample weights for important

population subgroups sum to population estimates that

nearly equal independently derived population

estimates for those groups. Our methods of computing

composite weights, which we discuss in Section 4,

closely resemble the current CPS raking ratio

adjustment.

2.1. The CPS Raking Ratio Adjustment.

Because demographic characteristics, such as age, race,

and area of residence, are correlated with labor force

status, CPS estimates should reflect the distributions of

these traits in the population. Accordingly, the Census

Bureau adjusts weights for CPS sample persons aged

16 or over to agree with three sets of population

estimates: population by state, by age/sex/ethnicity

group, and by age/sex/race group. (Only two

ethnicities, Hispanic and non-Hispanic, are considered

in the adjustment.) These population estimates, often

called raking "controls," are based on the most recent

decennial census, corrected to account for changes

since the census time. Because the composite

estimation step follows ratio adjustment and reweights

the data according to sample rotation group, the raking

is performed separately within each of these groups.

For a description of the actual raking process, see

Current Population Survey: Design and Methodology,

p. 59 (Technical Paper 40, U.S. Bureau of the Census,

1977).

2.2. The CPS Composite Estimator. Each

monthly CPS sample comprises eight rotation groups,

which are distinguished by the number of monthly

interviews they have completed. A separate set of

labor force estimates may be computed from each

rotation group's data. We use the notation of Cantwell

and Ernst (1993): for i = 1,...,8, let xh,i be a labor force

estimator of total (e.g., total unemployed) for month h,
computed using data from the ith rotation group. That

is, xh,i is eight times the sum of the sample weights,

after raking, of respondents in the specified labor force

category who completed their ith interview in month h.

Then Y x h = ∑i= h i

1

8 1

8

,

 is the CPS ratio estimator for the

labor force category.

The CPS composite estimate for a given labor

force characteristic is based on a weighted average of

two estimates for the same characteristic: (1) the CPS

ratio estimate and (2) the previous month's composite

estimate plus an estimate of change since the previous

month. Because of the "four-eight-four" sample

rotation pattern, six of the eight rotation groups in the

sample for month h-1 remain in sample for month h.

Thus for i ∈ S, where S = {2,3,4,6,7,8}, positive

correlation between xh,i and xh-1,i-1 serves to reduce the

variance of estimates of change computed from these

figures. So the change in the labor force characteristic

since the previous month is estimated here by

Δh h i h i

i S

= x − x − −

∈

∑

1

6

, 1, 1

c h.

In addition to the weighted average of the two

estimates described above, the CPS composite estimate

incorporates an adjustment which reduces variance

while at the same time partially correcting for bias

associated with time in sample. Results of past

research have indicated that, for estimates of total

unemployed, E(xh,1) significantly exceeds E(Yh). (See

Bailar 1975.) While the causes of the time-in-sample

bias are unknown, Breau and Ernst (1983) found that

adding a bias adjustment term to the composite

estimator reduced both the variance and the time-insample bias of CPS estimates. The current bias

adjustment term is based on the quantity

bh h i

i S

h i

i S

= x − x

R

S

T

U

V

∉ ∈ W

∑ ∑

1

8

1

3

, ,

,

which serves to reweight the estimates from the various

rotation groups, assigning slightly more weight to data

from persons completing their first or fifth interviews

in month h. Note that if all the xh,i's had the same

mean, βh would have mean zero.

Incorporating both the weighted average and the

bias adjustment term, the CPS composite estimator

takes the form

Yh K Yh K Yh h A h

" "

= − + + + ,

−

1 1

a f c Δ h b

where A and K are constant parameters between zero

and one. The CPS composite estimator is often called

an "AK estimator," because it involves these constant

coefficients. Currently, the estimator is applied with A

= .2 and K = .4 for all labor force categories. These

values are approximately optimal for monthly

estimates of unemployment level.

Optimal values of A and K for monthly labor force

totals, however, depend both on the time-in-sample

bias pattern and on the correlation structure of the

labor force estimates across time. Since these vary by

labor force categoryestimates for employed, for

example, are more strongly correlated than those for

unemployedoptimal values for the compositing

coefficients also vary. Moreover, in January 1994, a

new questionnaire and data collection method were

introduced in the CPS; these may affect the time-insample bias. Estimating the new bias pattern will

require data from several months following January

1994.

Due to differences in the correlation structures of

CPS estimates, using different A and K parameters for

different labor force categories would improve

accuracy. At the same time, however, varying the

coefficients could render some estimates inconsistent

with one another. By definition, for example, the

civilian labor force comprises persons who are either

employed or unemployed. Use of different compositing

coefficients for these three categories could result in

estimates of total employed and total unemployed that

fail to sum to the estimated level of the civilian labor

force. Also, as discussed above, CPS population

estimates must reflect the population distributions of

certain demographic traits, as estimated through the

decennial census. Widely varying compositing

coefficients could alter the distributions of these traits

in CPS sample population estimates computed as sums

of composited labor force estimates.

The "composite weighting" approach, suggested by

Fuller (1990), eliminates the problem of inconsistent

estimates by introducing a second raking ratio

adjustment, similar to the one now used in the CPS.

This time, however, the composite estimated labor

force totals would take the place of population

estimates, forcing the resulting person weights within

each labor force category to sum to the composite

estimate. The actual raking could be performed in a

variety of ways, as discussed in Section 4.

3. Selecting Compositing Coefficients for Labor

Force Categories. In this research we apply different

pairs of A,K compositing parameters for measuring

different characteristics. The choice of values for A

and K, however, is still not obvious. A pair which

works well for estimating monthly level may not

perform as well when estimating month-to-month

change or annual average.

For evaluating the proposed technique, we selected

A = .3 and K = .4 when estimating the number of

people unemployed, and A = .4 and K = .7 for the
number employed. Each of these pairs represents a

compromise across the important measurements.

It should be noted that the methods and results

presented in this paper apply to AK estimators. As has

been observed by Breau and Ernst (1983) and Gurney

and Daly (1965), estimators which allow more general

coefficients can effect further reductions in the

variances, especially when measuring annual average.

The accompanying biases, however, may be larger in

these cases.

3.1. Criteria for Selecting the Coefficients. For

any labor force characteristic, the estimates for

different months from the same rotation group are

correlated because of their common respondents. If xh,i

and xh-r,j represent estimators from the same rotation

group r months apart, the values are correlated as a

function of r. When measuring the number of people

unemployed, previous studies (Breau and Ernst 1983;

Adam and Fuller 1992) yield correlations of about .50

when r is 1, decreasing to about .20 when r is 15.

Corresponding values for the number of employed are

considerably larger, dropping from about .80 to under

.60 over fifteen months. In our study, we used

correlations slightly smoothed from those obtained in

the given references.

Estimates for the different characteristics also

exhibit different patterns of bias across the eight

months in sample. For this study, however, we

selected the A,K pairs based on comparisons of

variance rather than mean squared error. CPS monthin-sample bias patterns have probably changed since

January 1994, when a new questionnaire was

introduced and laptop computers replaced paper and

pencil in the data collection process. It will be a while

before good estimates of the new bias patterns are

available.

For any labor force characteristic, we must

consider three measurements when choosing the

parameters A and K: monthly level, month-to-month

change, and annual average. The importance of the

first two is not in question. But annual average is

critical for many state CPS estimates. Of the 50 states

and the District of Columbia, 40 do not have samples

large enough to meet reliability requirements on a

monthly basis. For these smaller states, the annual

average for labor force characteristics is a key measure.

A cursory look at the form of the AK estimator in

Section 2.2 shows that changing K gives conflicting

results: while increasing K can help reduce the

variance of month-to-month change, it generally

amplifies the variance of annual average.

The choice of coefficients to use came down to

computing three variances for each A,K pair and

comparing the sets across all A,K pairs. As no one pair

yielded the smallest variances for all three

measurements, a compromise was necessary.

3.2 The Selections. Though the variance

formulas required for selecting optimal parameters A

and K are found in Cantwell (1990), solving for

optimal A and K would be a formidable task. We

therefore computed variances for all combinations of A

and K equal to 0,.1,.2,...,.9. Except at the extremes (A

and K near 0 or .9), the variances do not change

rapidly with changing A and K.

For estimating the number of people unemployed,

we selected A = .3 and K = .4. This pair is optimal,

among the 100 pairs observed, for measuring monthly

level; it is close to optimal when measuring month-tomonth change and annual average. A similar situation

arises when we estimate the number of people

employed. The optimal pair for measuring monthly

level, A = .4 and K = .7, fares well for all three

measures. So for estimating unemployed and

employed, the selections which minimize the variances

of monthly levels are good compromise choices.

4. Computing CPS Composite Weights. The

first step in Fuller's method of computing composite

weights is to compute the composite estimates which

will serve as "controls" in the raking adjustment. The

raking process we apply will differ slightly according

to the level of the controls. We consider two basic

approaches:

1. Compute composite labor force estimates only for

the nation as a whole. We will refer to the

resulting composite weights as national composite

weights.

2. Compute separate composite estimates for each of

the demographic subgroups represented in the CPS

raking ratio adjustment. We will call the resulting

weights marginal composite weights.

In our empirical study of these alternatives, we

consider only data from respondents aged sixteen or

older.

In the first approach, we composite the national

estimates for two labor force categoriesemployed and

unemployedusing values of A and K selected

specifically for each category, as described in the

previous section. The civilian labor force, by

definition, comprises persons falling into one of these

two categories; thus the sum of the composite estimates

for employed and unemployed is a reasonable estimate

of the number of people in the civilian labor force. An

estimate of the number of people not in the labor force

may then be obtained by subtracting this estimate from

the national population control. The raking procedure

that follows is identical to the CPS raking ratio
adjustment, except a fourth dimension of raking is

added: raking to the national composite labor force

estimates.

The second approach requires computing

composite estimates for the three main labor force

categories within each demographic group used in the

raking ratio adjustment. The method used to compute

the composite estimates is analogous to the one used at

the national level. The three-dimensional reraking

process, however, must be carried out separately for

each labor force category; it proceeds just as the

current raking ratio adjustment, but the composite

estimates for the given category take the place of the

population controls.

Since replicate weights, computed by generalized

replication (see Fay 1989) were available for 1987 CPS

data, we used these weights to compute composite

replicate weights by the two methods mentioned above.

From the composite replicate weights we estimated the

variances of labor force estimates computed from each

set of composite weights.

4.1. Raking to National Composite Estimates.

We performed the four-dimensional raking adjustment

using national composite estimates on CPS data from

April through December, 1987. Typical adjustment

factors used in this method fell very close to 1.0:

compositing appeared to have little effect on the

national labor force estimates. This seemed reasonable

because, as explained above, the composite estimator is

based on a weighted average of two estimators. When

the sample is large, as in the case of the national

estimates, the variances of both estimators are

relatively low, so the difference between estimates

obtained from them is usually slight. The difference

between national CPS ratio estimates and composite

estimates is correspondingly small, resulting in

adjustment factors close to 1.0.

Since the bias patterns of CPS estimates have

probably changed due to the new data collection

method, we used the coefficients of variation (CV's) to

evaluate the accuracy of labor force estimates computed

from the national composite weights. The CV's of

subnational estimates computed from the national

composite weights consistently exceeded those of the

optimal composite estimates. For employment levels

and estimated numbers of people not in the labor force,

differences in the CV's for the two sets of estimates

were especially marked. We used the estimated CV's

for the eleven largest states to test the significance of

the loss of reliability that would result from using the

national composite weights. Because of the positive

correlation of the estimates across months, we

averaged the nine monthly estimates of CV for each

state and each estimation method (optimal composite

and national composite weights). We then computed a

ratio of CV's for each state, dividing the average CV

for the national composite weight estimates by that for

the optimal composite estimates. T-tests performed on

the state CV ratios for each labor force category gave

the results shown in Table 1. The null hypothesis

that the ratios have a mean of oneis equivalent to the

assumption of no significant difference in the

reliability of optimal composite estimates and estimates

computed from the national composite weights. As

indicated by the p-values, all the t-statistics are

significant at the 0.05 level, implying that the

reliability lost by use of the national composite weights

is significant.

Table 1. Results of T-test for State CV Ratios

EMP UE NILF

Mean CV Ratio 1.1155 1.0165 1.1146

t-statistic 9.0212 2.9715 8.6360

p-value 0.0001 0.0140 0.0001

4.2. Raking to Composite Estimates by

Demographic Group. Because of the reliability

problems with the national composite weights, we also

computed marginal composite weights for 1987 data.

As mentioned, producing marginal composite weights

requires a separate raking process for each of the three

main labor force categories (employed, unemployed,

and not in the labor force). For estimates of

employment level, none of the demographic groups

used in the CPS raking adjustment proved too small to

support reasonable composite estimates. Six iterations

of raking were sufficient to virtually reproduce the

optimal composite estimates for all states and

demographic groups as sums of marginal composite

weights. The marginal composite weights thus

outperformed the national composite weights for

monthly subnational estimates of employment level.

Producing marginal composite weights for the

unemployed category, however, proved more

problematic. Unemployed sample persons for some of

the age/sex/race groups used in the raking adjustment

notably those including mainly persons of retirement

ageoften numbered in the single digits; in some data

months, we had no unemployed sample for some of

these older groups. In these cases, the composite

estimates of unemployment level occasionally strayed

below zero. We also observed small sample counts for

some Hispanic age/sex groups used in the ratio

adjustment, indicating the possibility of negative

composite estimates, though none actually occurred in

the data we analyzed.
Table 2. Cells Collapsed in Computation of Marginal

 Composite Weights: Unemployed

Age

Cells

Average

Sample

Count

Collapsed

Cells

White 60-62 33.9

Male 63-64 12.0 White

65-67 9.0 Male

68-69 4.8 60+

70-74 6.2

75+ 2.8

White 60-62 21.2

Female 63-64 8.4 White

65-67 7.0 Female

68-69 3.0 60+

70-74 4.0

75+ 2.6

Black 45-49 18.4

Male 50-54 12.6 Black

55-59 9.0 Male

60-64 7.7 45+

65+ 2.6

Black 45-49 21.3

Female 50-54 11.3 Black

55-59 8.1 Female

60-64 4.4 45+

65+ 2.1

Other 16-44 90.4 Other

Male 45+ 18.1 Male 16+

Other 16-44 68.1 Other

Female 45+ 9.7 Fem. 16+

Hispanic 30-49 66.4 Hispanic

Male 50+ 21.2 Male 30+

Hispanic 30-49 50.7 Hispanic

Female 50+ 11.4 Fem. 30+

Demographic cells with unusually high or low

sample population estimatesusually due to low

sample countsare routinely collapsed with other cells

in the CPS raking ratio adjustment. The collapsing

algorithm, however, results in different collapsing

patterns for different months (and even for different

rotation groups in the same month). Since computing

marginal composite weights requires compositing

estimates across months, varying cell definitions from

month to month would complicate implementation

considerably. We chose instead to seek one set of

permanent cell definitions which would (1) ensure

sufficient sample in each cell to provide reasonable

composite estimates and (2) result in minimal loss of

reliability in the labor force estimates computed from

the marginal composite weights.

Our collapsing of cells was based on sample

counts: to provide reasonable composite estimates, we

wanted at least ten sample persons per cell. Since

sample counts vary from month to month, it seemed

desirable to collapse cells whose sample counts rarely

exceeded a dozen, even if the counts for these cells

never fell below ten for the 1987 data months we

analyzed. Given the loss of reliability that resulted

from using national composite weights, however, we

were also concerned that too much collapsing might

increase the CV's of labor force estimates computed

from the marginal composite weights.

We computed marginal composite weights for

1987 unemployment data (April through December)

using several alternative collapsing plans, which

involved different lower bounds for the average sample

count or for the minimum sample count obtained from

our nine data months. Estimated CV's of the resulting

unemployment totals indicated that collapsing the

smaller cells had little effect on the reliability of

estimates computed from the composite weights. Table

2 shows the average sample counts for the smaller

age/sex/ethnicity cells and age/sex/race cells and

indicates the collapsing pattern we found most

desirable. Since it involved collapsing all cells whose

minimum sample counts fell below twelve, we were

confident that it would ensure sufficient sample to

provide reasonable composite estimates for all cells.

For certain cells, collapsing was clearly necessary:

unemployment estimates for the older age groups

considered in the age/sex/race adjustment consistently

suffered from low sample counts. In cases where the

need for collapsing was disputable, however, we

performed statistical tests to determine whether or not

the collapsing would significantly increase the CV's of

estimates computed from the composite weights. For

demographic groups affected by such collapsing, we

considered the ratio of the CV of the unemployment

estimate computed from the marginal composite

weights to the CV of the corresponding optimal

composite estimate. Let
r

CV X

CV X

m

o

=

$

$

,

e j

e j

where

$Xm = an unemployment estimate computed

 from marginal composite weights ;

and

$Xo = the corresponding optimal composite

 estimate of unemployment .

For each data month i, i = 1,...,9, we computed r$i, an

estimate of r, for each of several demographic groups.

We used these nine observations to test the hypothesis

that the effect of the cell collapsing shown in Table 2

did not significantly affect the reliability of important

unemployment estimates computed from the marginal

composite weights. That is, we tested

H0: r = 1,

for each demographic group.

The results of the t-tests for the collapsing of age

cells in the "other races" category are shown in Table

3. Due to positive correlation between the estimated

CV ratios for different months, the t-statistics are

conservative in the sense that they support rejection

more often than the usual nominal level (under no

correlation) would indicate. Since none of the test

statistics are significant, the effect of the cell collapsing

on the CV's of the estimates is negligible. Thus the

collapsing of age cells within each sex group in the

"other races" category appears appropriate: all the pvalues in Table 3 are too high to allow rejection of H0

.

Table 3. Tests for Loss of Reliability Due to

Collapsing Age/Sex/Race Cells: Unemployed

Mean

r$i

t-stat. p-value

Other Male 16-44 1.0088 1.0091 0.3425

Other Male 45+ 1.0315 0.8916 0.3986

Other Fem. 16-44 1.0098 0.8726 0.4083

Other Fem. 45+ 0.9474 -1.2009 0.2641

5. Summary. We can improve reliability of CPS

labor force estimates by using different AK

compositing coefficients for different labor force

categories. To ensure that estimated labor force totals

equal the sums of their estimated components, Fuller

(1990) suggested incorporating the effect of composite

estimation into CPS micro data weights through a

procedure similar to the raking ratio adjustment now

used in the CPS. Composite estimates may then be

computed as sums of these composite weights.

In our research on computing CPS composite

weights, we consider two possible methods, each based

on a ratio adjustment applied to the micro data weights

to force the weights in a given labor force category to

sum to a composite estimate. The methods differ in

that the composite estimates used as "controls" in the

ratio adjustment are computed at a different level for

each method. The first methodcomputing composite

estimates at the national levelappears to result in

subnational estimates whose reliability falls

significantly below that of the optimal AK composite

estimates. In the second method, we compute

composite estimates for each demographic group

represented in the current CPS raking ratio adjustment

and then perform a separate raking adjustment for each

labor force category. Though some collapsing of

demographic groups is needed to allow implementation

for the unemployed category, this method provides

labor force estimates for states and important

demographic subgroups that virtually equal the

corresponding optimal AK composite estimates.

REFERENCES

[1] Adam, A. and Fuller, W. (1992). "Covariances of Estimators for

the Current Population Survey," Proceedings of the Section on

Survey Research Methods, American Statistical Association, p.

586-591.

[2] Bailar, B. (1975). "The Effects of Rotation Group Bias on

Estimates from Panel Surveys," Journal of the American

Statistical Association, 70, p. 23-30.

[3] Breau, P. and Ernst, L. (1983). "Alternative Estimators to the

Current Composite Estimator," Proceedings of the Section on

Survey Research Methods, American Statistical Association, p.

397-402.

[4] Cantwell, P. (1990). "Variance Formulae for Composite

Estimators in Rotation Designs," Survey Methodology, 16, p.

153-163.

[5] Cantwell, P. and Ernst, L. (1993). "Short Term Changes to the

CPS Composite Estimator in January 1994," Proceedings of the

Section on Survey Research Methods, American Statistical

Association, p. 724-729.

[6] Fay, R. (1989). "Theory and Application of Replicate Weighting

for Variance Calculations," Proceedings of the Section on Survey

Research Methods, American Statistical Association, p. 212-

217.

[7] Fuller, W. (1990). "Analysis of Repeated Surveys," Survey

Methodology, 16, p. 167-180.

[8] Gurney, M. and Daly, J. (1965). "A Multivariate Approach to

Estimation in Periodic Sample Surveys," Proceedings of the

Social Statistics Section, American Statistical Association, p.

242-257.

Acknowledgments: The authors gratefully

acknowledge the contributions of the following people:

Lawrence Ernst, who provided the initial inspiration

for this project; Robert Fay and Elizabeth Huang, who

reviewed the paper; and Athar Malik, who provided

computer programming support.
Note: Any opinions expressed in this paper are those of the authors and

do not constitute policy of the Bureau of Labor Statistics or the Bureau

of the Census.