CPS BRIDGE TEAM TECHNICAL REPORT 1

What Would the Unemployment Rate Have Been Had the Redesigned Current Population

Survey Been in Place from September 1992 to December 1993 ? :

A Measurement Error Analysis

Prepared by

Stephen M. Miller

For the CPS Bridge Team

February 4, 1994

Revised March 3, 1994
i

Executive Summary of

CPS BRIDGE TEAM TECHNICAL REPORT 1

What Would the Unemployment Rate Have Been Had the Redesigned Current Population

Survey Been in Place from September 1992 to December 1993 ? :

A Measurement Error Analysis

February 1994

The official monthly labor force estimates from January 1994 onwards will be based on

data from a comprehensively redesigned Current Population Survey (CPS). The redesign

incorporates changes in the basic questionnaire and collection methodology. In addition,

these estimates will be constructed using 1990-Census-based population controls rather

than 1980-Census-based population controls.

To better understand the effect of the CPS redesign on published estimates, a Parallel

Survey, intended to provide annual average labor force estimates, was conducted from

July 1992 to December 1993 using a separate monthly sample of households

approximately one-fifth the size of the regular CPS sample. Because of the small sample

size, monthly estimates from the Parallel Survey are highly variable.

To help analysts interpret the 1994 monthly CPS estimates, the CPS Bridge team has

modeled the Parallel Survey estimates from September 1992 through December 1993 for

the purposes of producing more accurate estimates of what the CPS might have looked

like during that period had the redesigned CPS been in place. The modeling has used only

data from the Parallel Survey and the CPS and yields monthly estimates with

approximately one-half the sampling variability of the monthly Parallel Survey estimates,

but still about twice the variance of the regular CPS estimates. While the model estimates

are less variable than the monthly estimates from the Parallel Survey, it should be noted

that, because not all design differences could be taken into account, the model estimates

may not provide a completely accurate picture of what the estimates from the redesigned

CPS would have looked like during that period. The model estimates were seasonally

adjusted with factors computed under the old CPS, so not all seasonality may be

accounted for.

Several seasonally adjusted national unemployment rate series are shown below. The CPS

1980 weighted estimates are the official seasonally adjusted rates as originally published.

The CPS 1990 weighted estimates show the effect on the original CPS estimates of

switching to the 1990 Census adjusted population controls. The change to 1990

weighting results in a 0.1 increase in the unemployment rate over the 1980 weighted

estimates. The model estimates are our estimates of what the unemployment rate would

have been had the redesigned survey been in place. They are uniformly higher than both

of the CPS estimates, averaging 0.6 higher than the 1980 weighted estimates over the

period. All three series show a decline in the unemployment rate of more than a

percentage point between September 1992 and December 1993.
ii

Seasonally Adjusted Unemployment Rates

Date

CPS 1980

weighting

CPS 1990

weighting Model

1992: Sep. 7.5 7.6 8.3

 Oct. 7.3 7.4 7.9

 Nov. 7.3 7.4 8.0

 Dec. 7.3 7.4 7.9

1993: Jan. 7.1 7.2 7.7

 Feb. 7.0 7.1 7.5

 Mar. 7.0 7.1 7.4

 Apr. 7.0 7.1 7.4

 May. 6.9 7.0 7.5

 Jun. 6.9 7.0 7.6

 Jul. 6.8 6.9 7.6

 Aug. 6.7 6.8 7.5

 Sep. 6.7 6.7 7.3

 Oct. 6.7 6.8 7.3

 Nov. 6.5 6.6 7.2

 Dec. 6.4 6.5 7.0

Seasonally Adjusted Unemployment Rates 

6

6.5

7

7.5

8

8.5

Sep92Oct92Nov92Dec92Jan93Feb93Mar93Apr93May93Jun93Jul93Aug93Sep93Oct93Nov93Dec93

Model

CPS 1990 weighting

CPS 1980 weighting
iii

Contents

Twelve labor force series are modeled and used to construct unemployment rates for the

period September 1992 to December 1993 which are comparable to the rates that will be

produced from the redesigned CPS starting in January 1994. This report, which is the

product of joint work between the Bureau of Labor Statistics and the Bureau of the

Census, is laid out as follows. The Background section provides an introduction to the

parallel survey used to evaluate the effect on annual average labor force estimates using

the new questionnaire and collection procedures, as well as a discussion of the problems

inherent in trying to develop an historical time series comparable to the estimates from the

redesigned CPS. The Summary of Statistical Methodology section provides an overview

of the methods used to produce the comparable series. The Presentation of Selected

Labor Force Series section provides a summary of the comparable data to the official

CPS data published during the same period. Finally, two Appendices provide additional

details about the statistical modeling used.

Acknowledgments

The CPS Bridge Team consists of Chester E. Bowie, Shail J. Butani, Lawrence S.

Cahoon, Cathryn S. Dippo, Robert E. Fay, Donna L. Kostanich, Elizabeth A. Martin,

Stephen M. Miller, Anne E. Polivka, and N. Clyde Tucker. Other participants in the

team's work included Katharine Abraham, Jack Bregger, Mick Couper, Thomas Plewes,

and Jennifer Rothgeb. Outside consultants included Wayne Fuller, and Robert Groves.

This report was prepared by Stephen Miller, who also was responsible for the modeling.

Robert Fay computed variances for the Parallel Survey, and also provided CPS estimates

for September 1992. Additional assistance was provided by Ken Robertson, Athar Malik,

Ed Robison, and Janice Lent.
- 1 -

Background

Current Population Survey (CPS)

The Current Population Survey (CPS) is a national survey of approximately 60,000

households which provides a monthly picture of the nation's labor force characteristics.

The CPS began in 1940, and the questionnaire has remained essentially unchanged since

the last redesign in 1967. The current redesign takes into account changes which have

taken place in the workforce and structure of American society, and takes advantage of

improvements in survey methodology, such as computer-assisted data collection and

questionnaire methods based on the theories of cognitive psychology. Further discussion

of the changes in CPS can be found in the September 1993 issue of the Monthly Labor

Review.

In addition to the questionnaire and mode of collection changes, new weights will be used

to derive estimates from the sample. Starting in January 1994, the 1990-undercountadjusted census population counts will be used. We will refer to this as 90 weighting.

The data used in this report are all based upon 90 weighting unless otherwise stated. (The

old weights were based on the 1980 Census of Population.)

Parallel Survey

In order to better understand the effects of the CPS redesign changes upon published

estimates, BLS sponsored a Parallel Survey conducted from July 1992 to December 1993

by the Census Bureau. Using a monthly sample of approximately 12,000 households, the

design of the Parallel Survey sample was a national stratified multistage probability sample

which yields unbiased estimates for the nation as a whole. In contrast, the CPS sample has

a State-based design which yields unbiased estimates for States and the Nation. In this

report, we will utilize data for September 1992 through December 1993. The data

collected during the initial two months, July and August of 1992, were not used due to

startup effects in the Parallel Survey.

Polivka (1994) provides annual average estimates from the Parallel Survey. Annual

averages give our best overall understanding about the differences between the redesigned

CPS and the CPS prior to January 1994. These have been used as the basis of comparison

because their sampling errors are much lower than those of the monthly Parallel Survey
- 2 -

estimates, and their use eliminates the need for seasonally adjusting the data. However, to

interpret 1994 monthly estimates in comparison to 1993, analysts need comparable

monthly estimates, both on a seasonally adjusted and unadjusted basis. Providing these

estimates is a formidable task because of the many design differences between the CPS

and the Parallel Survey. In this report, we present a set of estimates which attempt to

account for some, but not all, of these differences. The major design differences are

summarized in table 1.
- 3 -

Table 1. Design Features of CPS and the Parallel Survey (PS) from Sep. 92 - Dec. 93.

CPS PS

SAMPLING DESIGN

 Type of Design State-Based National

 Number of sample primary sampling units (PSU) 729 283

 Number of geographic areas in sample PSU's 1,973 579

 Monthly sample size (occupied housing units) 58,900 12,000

 Post-stratification 600 cells

Plus States

559 cells

NO States

 Composite estimation Yes No

 Standard Error of Monthly Unemployment Rate 0.11 0.25

 Standard Error of Annual Avg. Unemployment Rate 0.07 0.16

COLLECTION PROCEDURES

 Mode of collection PAPI, CATI CAPI, CATI

 % Centralized CATI 9% 18%

 % True Month-in-Sample in September 1992 100% 50%

 % True Month-in-Sample in October 1992 100% 50%

 % True Month-in-Sample in November 1992 100% 50%

 % True Month-in-Sample in December 1992 100% 50%

 % True Month-in-Sample in January 1993 100% 54%

 % True Month-in-Sample in February 1993 100% 58%

 % True Month-in-Sample in March 1993 100% 64%

 % True Month-in-Sample in April 1993 100% 76%

 % True Month-in-Sample in May 1993 100% 78%

 % True Month-in-Sample in June 1993 100% 86%

 % True Month-in-Sample in July 1993 100% 93%

 % True Month-in-Sample in August 1993 100% 97%

 % True Month-in-Sample in September 1993 100% 100%

 % True Month-in-Sample in October 1993 100% 100%

 % True Month-in-Sample in November 1993 100% 100%

 % True Month-in-Sample in December 1993 100% 100%
- 4 -

The model-based estimates presented in this report take into account differences between

the CPS and Parallel Survey in sampling error and population controls but do not account

for differences in post-stratification procedures, sample rotation, rotation group bias

patterns, composite estimation, percent CATI, and seasonal patterns in monthly estimates.

A brief discussion of the implications for the model-based estimates of these latter

differences follows. For an in-depth discussion of the differences in sampling design

between CPS and the Parallel Survey, see Kostanich and Cahoon (1994).

Poststratification

Poststratification is a statistical procedure used to ensure, among other things, that

estimates aggregate to known population totals. In the CPS, estimates are controlled to

match State totals. Estimates from the Parallel Survey were not controlled to match State

totals. In addition, because of the small sample size of the Parallel Survey, more

collapsing of race and ethnicity cells had to be done than is the case under regular CPS.

Sample rotation

The CPS uses a 4-8-4 rotation sampling scheme which means that households are

interviewed for 4 consecutive months, not interviewed for 8 months, and then interviewed

for 4 additional months before being permanently dropped from the sample. Each month,

a new panel or rotation group is introduced, replacing the panel which received its 8th

interview the previous month. Thus, each month 1/8 of the total sample is being

interviewed for the 1st, 2nd, ..., and 8th time. This particular sampling scheme attempts to

balance respondent burden with improved estimates of month-to-month and year-to-year

change. (In any given month, 75 percent of the interviewed households were interviewed

in the previous month and 50 percent were interviewed in the same month in the previous

year.) Historically, it has been shown that, for a given month, the expected value of the

estimated unemployment rate from each of the 8 rotation groups is different. For

example, the estimated unemployment rate for the month-in-sample 1 (MIS1) panel is, on

average, 7.4 percent higher than the estimated rate based on the month-in-sample 2

(MIS2) panel and 8.8 percent higher than the estimated rate based on the month-in-sample

8 panel. The estimated unemployment rate from the CPS for MIS1 through MIS4

combined is, on average, 4.3 percent higher than for MIS5 through MIS8. Although this

basic 4-8-4 rotation scheme was used in the Parallel Survey, it takes 16 months to

completely phase in this type of design, and the first month in which 1/8 of the sample
- 5 -

received its 8th interview was September 1993. Thus, if the rotation group bias pattern

under the old methodology were to hold true under the new methodology, we might

expect estimates from the Parallel Survey to be higher than they would have been if the

sample had been fully phased in before September 1992.

Rotation Group Bias Patterns

A major change in the redesigned CPS questionnaire is the inclusion of questions each

month to determine if persons not in the labor force are discouraged workers. In the "old"

CPS, from January 1970 through December 1993, questions for determining discouragedworker status were asked only of MIS4 and MIS8 households. Between January 1967

and December 1969, these questions had been asked of MIS1 and MIS5 households.

When the discouraged worker questions were moved from MIS1 and MIS5 to MIS4 and

MIS8, the rotation group bias patterns changed dramatically. Thus, we expect the

rotation group bias pattern for the new CPS to be different from the old. Because of the

small sample sizes in the Parallel Survey and the incomplete rotation phase-in, we cannot

estimate what the new pattern is. On the other hand, for the parallel testing period,

monthly estimates based only on true MIS1 households were 4 percent higher than for

true MIS2 to MIS4 combined, as compared to a 3 percent difference in CPS, providing

some evidence that there was a change.

Composite Estimation

The CPS estimates are computed each month using a composite estimator to increase the

accuracy of both the monthly estimates and the estimates of month-to-month changes.

The composite estimator is a weighted linear combination of two estimates for the current

month. One is based on data from the entire sample for the current month; the other

derives from the previous month's composite estimate plus an estimate of over-the-month

change from the 75% of the sample interviewed in both months. The particular form of

the composite estimator was chosen based upon the rotation group bias patterns found

under the old CPS methodology. Since, as mentioned earlier, we do not have accurate

estimates of the rotation group bias pattern for the new methodology, we cannot modify

the form of the composite estimator. To avoid mixing January 1994 estimates based on

the new methodology by using December 1993 estimates based on the old methodology,

the estimate for January will not be composited. The composite estimator will be restarted

in early 1994. There will be an effect due to starting up the composite estimator, but we
- 6 -

are unable to predict the exact effect. Because of the problems inherent in the sample

rotation pattern for the Parallel Survey mentioned above, the model estimates reported in

the present paper were developed based upon noncomposited Parallel Survey data.

Centralized CATI Percentage

The percentage of centralized computer-assisted telephone interviewing (CATI) was 18

percent in the Parallel Survey and 9 percent in the CPS. The redesigned CPS will have

approximately 13 percent centralized CATI in January 1994, and this will increase to 18

percent sometime in 1994. For information on the implications of these differences on

estimates see Kostanich and Cahoon (1994).

Seasonal Adjustment

The method used by BLS for seasonal adjustment is X-11 ARIMA, with seasonal factors

reestimated every 6 months. The most recent set of factors was estimated in December

1993. For the seasonally adjusted estimates in this report, we used these most recent

seasonal factors computed using data from the CPS through December 1993 based upon

1980 weighting. It was not possible to compute accurate seasonal factors from the

Parallel Survey, since it usually requires at least 5 years of data to produce good monthly

factors. The factors obtained from CPS data through December 1993 are the factors that

will be used starting in January 1994 to adjust the redesigned CPS. BLS will monitor the

seasonally adjusted estimates from the redesigned CPS to look for possible changes in

seasonal patterns.

Summary of Statistical Methodology

The modeling effort reported here looked at the 12 basic series that, when aggregated,

comprise the civilian labor force. These are listed in table 2.
- 7 -

Table 2. The 12 modeled series

1

2

3

4

5

6

7

8

9

10

11

12

Agricultural employment, women 16-19

Agricultural employment, men 16-19

Agricultural employment, women 20+

Agricultural employment, men 20+

Nonagricultural employment, women 16-19

Nonagricultural employment, men 16-19

Nonagricultural employment, women 20+

Nonagricultural employment, men 20+

Unemployment, women 16-19

Unemployment, men 16-19

Unemployment, women 20+

Unemployment, men 20+

Since the civilian noninstitutional population is known, having estimates of these 12 series

makes it possible to compute estimates of those not in the labor force by subtraction. A

large number of rate series then can be computed. Our approach was to produce modeled

monthly unadjusted estimates for each of the 12 series and then use the standard seasonal

adjustment procedure for each of the 12 series individually. Once the model estimates

were computed, estimates for those not in the labor force were obtained by subtraction.

The remaining series were then used to produce seasonally adjusted unemployment rates,

employment-to-population ratios, and labor force participation rates.

The importance of decreasing the variability of the monthly estimates from the Parallel

Survey can be seen from table 3. The first column represents the average over the 16-

month period, September 1992 to December 1993, of the ratios of the variance of the

monthly Parallel Survey estimates to the variance of the monthly CPS estimates. The

column labeled Model gives the average, over the same 16 months, of the ratios of the

variance of the monthly model estimates to the variance of the monthly CPS estimates.
- 8 -

Table 3. Ratio of Parallel Survey and Model variance to CPS variance

PS Model

Agricultural Employment

 Women 16-19 5.1 1.4

 Men 16-19 5.8 1.7

 Women 20+ 6.4 3.8

 Men 20+ 3.8 2.3

Nonagricultural Employment

 Women 16-19 3.5 1.5

 Men 16-19 3.7 1.3

 Women 20+ 5.1 2.5

 Men 20+ 4.4 2.2

Unemployment

 Women 16-19 4.3 1.2

 Men 16-19 4.1 2.0

 Women 20+ 4.6 2.5

 Men 20+ 4.3 1.5

The average of the ratios in the first column is about 4.5, which is close to the ratio of the

sample size of CPS to the Parallel Survey. In order to improve the monthly estimates of

each of these 12 series, modeling was done for each series separately.

There are many different methods that could have been used to improve the monthly

Parallel Survey estimates. Our approach, which may be improved upon at a later time, is

described below. All of the modeling was done on non-seasonally adjusted data. Let

(1) Yt = Observed monthly CPS estimate under the old method

yt = True monthly CPS value under the old method

and let

(2) Y y e t = t + t

where et is the CPS sampling error, and t = 1,K,T , where T = 16. Also, let
- 9 -

(3) Xt = Observed monthly Parallel Survey estimate under the new method

xt = True monthly Parallel Survey value under the new method

and let

(4) X x u t = t + t

where ut is the Parallel Survey sampling error. We will make the assumption that

(5) y x t = b0 +b1 t

which says that the true values have a linear structural relationship. Our goal is to

estimate the true value xt for each of the 16 months. The estimates of the xt are what we

refer to as the model estimates. The model parameters b0 and b1 allow the CPS

observation to contribute to the monthly estimate. In effect, the model uses both the CPS

and Parallel Survey estimate to give an improved monthly estimate. By using information

from both the CPS and the Parallel survey, the model is able to reduce the variance of the

monthly estimate as defined under the Parallel Survey. The reduction in variance can be

seen in the column labeled Model in table 3. On average, over all 12 characteristics, the

models produced a 57 percent decrease in the variance relative to the variance of the

monthly Parallel Survey estimates. It should be noted, however, that the variance of the

model is still greater than the variance of the monthly CPS estimate by about a factor of

two.

In addition to estimating the model parameters and the monthly estimates xt for each of

the 16 months, we computed two test statistics. The first was a 

statistic G

2

cG

2

 tests the hypothesis that the model, as given in equation

cG

2

 suggest that the model is deficient,

cG

2

 measures how much unexplained variability remains in the data apart from that

The construction and properties of cG

2

 are discussed more fully in the appendix, but under

the null hypothesis that the model specified in equation (5) is adequate, cG

2

approximately distributed as a chi-square random variable on 14 degrees of freedom.
- 10 -

The second test statistic was a structural relation test statistic cS

2

. This statistic tests the

null hypothesis H0 0 1:b = 0, b = 1, which implies that there is no difference between the

true values as measured under CPS and the Parallel Survey. Large values of the test

statistic cS

2

Survey are measuring different true values. There are other structural relationship tests

one might also consider, but that selected seems a natural one. The construction and

cS

2

 are discussed more fully in the appendix, but under the null hypothesis cS

2

is approximately distributed as a chi-square random variable on 2 degrees of freedom.

4 in terms of the two tests just discussed. Table 4 lists the actual test statistics along with

p

underlying hypotheses. For example, a small p

hypothesis, while a large p

hypothesis. Values of 0.05 and 0.10 are often used as references when judging the sizes

of -values; when a p

to be significant at the 0.05 level of significance. Small p

of-fit statistics G

2

 indicate that the model is inadequate, i.e., that the relationship in

equation (5) does not adequately explain the observed variation in the data apart from

sampling variability. Small p-values for the structural relationship test indicate that the

model cannot be further simplified to one where CPS and the Parallel Survey are

estimating the same underlying true value.
- 11 -

Table 4. Summary of model fitting for the 12 labor force characteristics.

Model

goodness-of-fit

Structural

relationship test

cG

2

p-value cS

2

-value

Agricultural Employment

10.60 0.72 0.27

 Men 16-19 0.27 2.21

 Women 20+ 7.72 18.22 0.00

23.28 0.06 0.10

Nonagricultural Employment

19.32 0.15 0.08

 Men 16-19 0.83 1.32

 Women 20+ 19.48 1.95 0.38

12.88 0.54 0.26

Unemployment

8.96 0.83 0.00

 Men 16-19 0.64 8.17

 Women 20+ 10.31 64.99 0.00

11.95 0.61 0.19

None of the goodness-of-fit statistics in table 4 indicate substantial model failure. On the

the underlying true values between CPS and the Parallel Survey, in particular those for the

unemployed adult women, unemployed teenage women and adult women employed in

groups, except adult men, are significantly different.

Appendix 1 presents detailed graphs of the model estimates for each of the 12 series, in

data and the model estimates over time. The modeled estimates produce a smoother

monthly series than the Parallel Survey, but one aspect of the model estimates needs to be

average of the Parallel Survey estimates over the same 16 months. The model estimates

seem to underestimate employment in agriculture, in particular, and slightly underestimate
- 12 -

total employment. Because total unemployment also was slightly underestimated, this did

not have a noticeable effect on the reported unemployment rate estimate, but may have

had a slight effect on the employment-to-population ratios and labor force participation

rates presented in the next section. These last two rates may be slightly underestimated,

on average. Since our main concern in this report was with producing unemployment rate

estimates, estimation procedures that would have produced higher levels of employment

were not investigated. Other estimation procedures may be studied in the future.

Table 5. Ratio of 16 Month Averages of

Model Estimates to Parallel Survey Estimates

Ratio of

Averages

Agricultural Employment

 Women 16-19 0.794

 Men 16-19 0.889

 Women 20+ 0.979

 Men 20+ 0.932

Nonagricultural Employment

 Women 16-19 0.993

 Men 16-19 1.003

 Women 20+ 0.999

 Men 20+ 1.000

Unemployment

 Women 16-19 0.996

 Men 16-19 1.004

 Women 20+ 0.999

 Men 20+ 0.997
13

In this section, we present graphs and tables portraying seasonally adjusted and unadjusted

model estimates, along with estimates from the CPS. The first two graphs show total

from the model and from the CPS under both 90 weighting 80 weighting. The next

are followed by six tables, each formatted similarly to table A-33 from the monthly

Employment and Earnings 

seasonally adjusted model estimates, and table 6, the unadjusted estimates. Table 7 gives

the seasonally adjusted composited CPS estimates based upon , with

compositing beginning in October 1992, and table 8 gives the unadjusted estimates. Table

80 weighted data,

The following abbreviations are used in all of the tables:

LFPR

EPR Employment to population ratio

Unemployment rate
- -

Seasonally Adjusted Unemployment Rates 

5

5.5

6

6.5

7

7.5

8

8.5

9

Sep92Oct92Nov92Dec92Jan93Feb93Mar93Apr93May93Jun93Jul93Aug93Sep93Oct93Nov93Dec93

Model

CPS 1990 weighting

CPS 1980 weighting

Unadjusted Unemployment Rates 

5

5.5

6

6.5

7

7.5

8

8.5

9

Sep92Oct92Nov92Dec92Jan93Feb93Mar93Apr93May93Jun93Jul93Aug93Sep93Oct93Nov93Dec93

Model

CPS 1990 weighting

CPS 1980 weighting
- 15 -

Seasonally Adjusted Unemployment Rates for Men 

5

5.5

6

6.5

7

7.5

8

8.5

9

Sep92Oct92Nov92Dec92Jan93Feb93Mar93Apr93May93Jun93Jul93Aug93Sep93Oct93Nov93Dec93

Model

CPS 1990 weighting

CPS 1980 weighting

Unadjusted Unemployment Rates for Men 

5

5.5

6

6.5

7

7.5

8

8.5

9

Sep92Oct92Nov92Dec92Jan93Feb93Mar93Apr93May93Jun93Jul93Aug93Sep93Oct93Nov93Dec93

Model

CPS 1990 weighting

CPS 1980 weighting
- 16 -

Seasonally Adjusted Unemployment Rates for Women 

5

5.5

6

6.5

7

7.5

8

8.5

9

Sep92Oct92Nov92Dec92Jan93Feb93Mar93Apr93May93Jun93Jul93Aug93Sep93Oct93Nov93Dec93

Model

CPS 1990 weighting

CPS 1980 weighting

Unadjusted Unemployment Rates for Women 

5

5.5

6

6.5

7

7.5

8

8.5

9

Sep92Oct92Nov92Dec92Jan93Feb93Mar93Apr93May93Jun93Jul93Aug93Sep93Oct93Nov93Dec93

Model

CPS 1990 weighting

CPS 1980 weighting
- 17 -

Table 5. Seasonally Adjusted Model Estimates (Based on 90 weighting)

 SEP92 OCT92 NOV92 DEC92 JAN93 FEB93 MAR93 APR93 MAY93 JUN93 JUL93 AUG93 SEP93 OCT93 NOV93 DEC93

Total

LFPR 67.2 66.7 66.8 66.7

EPR 61.6 61.4 61.5 61.4

UER 8.3 7.9 8.0 7.9

Men 16+

LFPR 75.7 75.4 75.2 75.0

EPR 69.4 69.2 69.2 69.2

UER 8.3 8.2 8.0 7.8

Men 20+

LFPR 77.3 77.2 77.0 76.7

EPR 71.5 71.4 71.3 71.3

UER 7.5 7.5 7.3 7.1

Women 16+

LFPR 59.4 58.7 59.0 59.0

EPR 54.5 54.3 54.4 54.3

UER 8.3 7.6 7.9 8.0

Women 20+

LFPR 59.9 59.3 59.4 59.5

EPR 55.4 55.2 55.3 55.2

UER 7.6 6.9 7.0 7.2

Teens 16-19

LFPR 54.7 52.7 53.5 53.8

EPR 42.8 42.4 42.5 42.9

UER 21.6 19.6 20.6 20.3

 66.7 66.6 66.5 66.5 66.7 66.8 66.8 66.8 66.5 66.7 66.7 66.5

 61.6 61.6 61.6 61.6 61.7 61.7 61.7 61.8 61.7 61.8 61.9 61.9

 7.7 7.5 7.4 7.4 7.5 7.6 7.6 7.5 7.3 7.3 7.2 7.0

 74.7 74.8 74.9 74.9 75.1 75.1 75.0 75.0 74.8 75.0 74.9 74.9

 69.3 69.3 69.3 69.2 69.4 69.2 69.2 69.2 69.2 69.3 69.5 69.5

 7.3 7.3 7.5 7.6 7.7 8.0 7.8 7.7 7.6 7.6 7.3 7.1

 76.3 76.3 76.4 76.5 76.7 76.7 76.7 76.8 76.7 76.9 76.7 76.6

 71.4 71.3 71.3 71.3 71.4 71.4 71.4 71.5 71.3 71.5 71.7 71.7

 6.5 6.5 6.7 6.8 6.9 6.9 6.9 6.9 6.9 6.9 6.6 6.4

 59.3 59.0 58.8 58.9 58.9 59.0 59.2 59.3 58.8 58.9 59.0 58.9

 54.5 54.5 54.5 54.6 54.6 54.8 54.9 54.9 54.7 54.9 54.9 54.9

 8.1 7.6 7.3 7.3 7.4 7.1 7.3 7.3 7.0 6.9 7.0 6.8

 59.8 59.5 59.3 59.3 59.3 59.5 59.6 59.7 59.2 59.3 59.4 59.3

 55.4 55.4 55.5 55.5 55.5 55.6 55.6 55.8 55.6 55.6 55.7 55.7

 7.3 6.8 6.4 6.4 6.5 6.4 6.7 6.5 6.2 6.1 6.2 5.9

 54.3 54.4 54.1 53.9 54.2 54.8 54.3 53.7 53.0 53.6 53.6 53.4

 43.1 43.1 42.6 42.6 42.9 42.6 43.3 43.0 43.0 43.2 43.3 43.0

 20.7 20.8 21.1 21.0 20.8 22.1 20.2 19.9 18.9 19.4 19.3 19.4

Table 6. Unadjusted Model Estimates (Based on 90 weighting)

 SEP92 OCT92 NOV92 DEC92 JAN93 FEB93 MAR93 APR93 MAY93 JUN93 JUL93 AUG93 SEP93 OCT93 NOV93 DEC93

Total

LFPR 67.1 66.6 66.6 66.4

EPR 61.7 61.7 61.6 61.4

UER 8.0 7.4 7.6 7.5

Men 16+

LFPR 75.5 75.1 74.8 74.5

EPR 69.8 69.6 69.1 68.8

UER 7.5 7.3 7.6 7.6

Men 20+

LFPR 77.3 77.0 76.7 76.5

EPR 72.1 71.9 71.4 71.1

UER 6.7 6.7 6.9 7.0

Women 16+

LFPR 59.3 58.9 59.1 59.0

EPR 54.2 54.5 54.7 54.6

UER 8.6 7.5 7.6 7.4

Women 20+

LFPR 60.0 59.6 59.7 59.6

EPR 55.3 55.5 55.7 55.6

UER 7.8 6.8 6.7 6.7

Teens 16-19

LFPR 52.2 50.6 51.3 50.8

EPR 40.9 40.7 40.7 41.3

UER 21.7 19.5 20.6 18.8

 66.1 66.1 66.1 66.0 66.6 67.7 67.9 67.4 66.4 66.6 66.6 66.3

 60.5 60.7 61.0 61.2 61.7 62.4 62.7 62.5 61.7 62.0 62.0 61.9

 8.4 8.1 7.7 7.3 7.3 7.8 7.7 7.3 7.0 6.8 6.8 6.6

 74.0 74.2 74.4 74.3 75.0 76.4 76.6 75.9 74.7 74.8 74.6 74.4

 67.7 67.9 68.2 68.6 69.4 70.3 70.8 70.6 69.6 69.7 69.5 69.2

 8.5 8.5 8.3 7.6 7.5 7.9 7.5 7.0 6.8 6.8 6.8 6.9

 76.0 76.1 76.2 76.2 76.7 77.2 77.3 77.1 76.7 76.8 76.5 76.4

 70.1 70.2 70.5 70.9 71.6 72.2 72.2 72.2 71.9 72.0 71.8 71.5

 7.8 7.7 7.5 6.9 6.7 6.6 6.5 6.3 6.2 6.2 6.2 6.3

 58.8 58.7 58.5 58.4 58.8 59.7 60.0 59.6 58.7 59.1 59.2 58.9

 53.9 54.1 54.3 54.4 54.6 55.2 55.3 55.0 54.5 55.0 55.2 55.2

 8.3 7.7 7.1 6.8 7.1 7.6 7.9 7.7 7.1 6.9 6.8 6.2

 59.6 59.3 59.2 59.1 59.3 59.6 59.6 59.5 59.3 59.5 59.7 59.4

 55.1 55.2 55.5 55.5 55.7 55.7 55.3 55.3 55.5 55.9 56.1 56.1

 7.6 6.9 6.2 6.0 6.2 6.6 7.1 7.1 6.4 6.0 6.0 5.6

 49.2 50.0 49.8 49.5 52.4 63.1 67.1 60.9 50.7 51.5 51.5 50.5

 38.5 39.0 38.7 39.3 41.1 47.5 54.0 50.7 41.2 41.5 41.6 41.6

 21.7 22.1 22.3 20.6 21.7 24.6 19.5 16.7 18.8 19.3 19.2 17.7
- 18 -

Table 7. Seasonally Adjusted CPS 90 weighted Estimates (Composited beginning with October 1992)

 SEP92 OCT92 NOV92 DEC92 JAN93 FEB93 MAR93 APR93 MAY93 JUN93 JUL93 AUG93 SEP93 OCT93 NOV93 DEC93

Total

LFPR 66.5 66.2 66.4 66.3

EPR 61.5 61.4 61.4 61.4

UER 7.6 7.4 7.4 7.4

Men 16+

LFPR 76.0 75.7 75.7 75.6

EPR 70.0 69.8 69.8 69.8

UER 7.9 7.8 7.8 7.6

Men 20+

LFPR 77.7 77.6 77.5 77.4

EPR 72.3 72.0 72.1 72.1

UER 7.0 7.1 7.0 6.9

Women 16+

LFPR 57.8 57.5 57.8 57.8

EPR 53.6 53.6 53.7 53.7

UER 7.2 6.8 7.0 7.2

Women 20+

LFPR 58.4 58.2 58.4 58.5

EPR 54.6 54.6 54.8 54.7

UER 6.5 6.2 6.3 6.5

Teens 16-19

LFPR 52.3 50.4 51.3 51.6

EPR 41.4 41.1 40.9 41.5

UER 21.0 18.4 20.4 19.5

 66.2 66.2 66.2 66.2 66.4 66.4 66.4 66.4 66.2 66.4 66.4 66.4

 61.4 61.5 61.5 61.5 61.7 61.7 61.8 61.9 61.7 61.9 62.0 62.1

 7.2 7.1 7.1 7.1 7.0 7.0 6.9 6.8 6.7 6.8 6.6 6.5

 75.4 75.5 75.5 75.5 75.6 75.6 75.6 75.6 75.2 75.4 75.2 75.2

 69.8 69.9 69.9 69.9 70.1 70.0 70.1 70.2 69.9 70.1 70.2 70.2

 7.3 7.4 7.5 7.4 7.3 7.3 7.3 7.2 7.0 7.0 6.7 6.6

 77.2 77.2 77.3 77.2 77.4 77.3 77.4 77.4 77.1 77.3 77.1 77.1

 72.1 72.1 72.0 72.2 72.3 72.3 72.3 72.4 72.2 72.4 72.5 72.5

 6.6 6.6 6.8 6.6 6.5 6.5 6.5 6.4 6.3 6.3 5.9 5.9

 57.7 57.7 57.6 57.6 57.9 57.9 57.9 57.9 57.9 58.1 58.2 58.3

 53.6 53.8 53.8 53.8 54.0 54.1 54.1 54.2 54.2 54.3 54.4 54.6

 7.1 6.8 6.5 6.7 6.7 6.7 6.5 6.4 6.4 6.5 6.5 6.3

 58.3 58.3 58.2 58.3 58.4 58.5 58.4 58.5 58.5 58.7 58.8 58.9

 54.6 54.7 54.9 54.7 55.0 55.0 55.0 55.2 55.1 55.2 55.4 55.5

 6.4 6.1 5.8 6.1 6.0 6.0 5.9 5.8 5.8 5.9 5.8 5.7

 51.2 51.8 51.4 51.5 52.3 51.7 52.2 51.8 51.1 51.0 51.1 50.8

 41.1 41.6 41.3 41.1 41.9 41.6 42.6 42.4 41.9 41.4 41.8 41.8

 19.7 19.7 19.6 20.3 19.9 19.6 18.4 18.3 17.9 18.8 18.3 17.7

Table 8. Unadjusted CPS 90 weighted Estimates (Composited beginning with October 1992)

 SEP92 OCT92 NOV92 DEC92 JAN93 FEB93 MAR93 APR93 MAY93 JUN93 JUL93 AUG93 SEP93 OCT93 NOV93 DEC93

Total

LFPR 66.4 66.2 66.2 66.1

EPR 61.6 61.6 61.5 61.4

UER 7.3 6.9 7.1 7.1

Men 16+

LFPR 75.9 75.4 75.3 75.1

EPR 70.5 70.2 69.8 69.5

UER 7.1 7.0 7.4 7.5

Men 20+

LFPR 77.8 77.5 77.3 77.1

EPR 72.9 72.6 72.2 71.9

UER 6.3 6.4 6.6 6.8

Women 16+

LFPR 57.7 57.7 57.9 57.8

EPR 53.4 53.8 54.0 54.0

UER 7.4 6.8 6.7 6.6

Women 20+

LFPR 58.5 58.5 58.7 58.6

EPR 54.5 55.0 55.2 55.0

UER 6.7 6.1 6.0 6.1

Teens 16-19

LFPR 49.9 48.3 49.1 48.6

EPR 39.4 39.4 39.1 39.9

UER 20.9 18.3 20.5 17.9

 65.6 65.8 65.8 65.6 66.3 67.3 67.5 67.0 66.1 66.4 66.3 66.2

 60.3 60.6 60.9 61.1 61.7 62.4 62.8 62.6 61.8 62.1 62.1 62.1

 8.0 7.8 7.4 6.9 6.8 7.2 7.0 6.6 6.4 6.4 6.2 6.1

 74.6 74.9 75.1 74.8 75.5 76.8 77.2 76.5 75.1 75.2 74.9 74.7

 68.2 68.4 68.8 69.3 70.1 71.2 71.8 71.6 70.4 70.4 70.2 69.9

 8.6 8.6 8.3 7.4 7.1 7.3 7.0 6.5 6.3 6.3 6.3 6.4

 76.8 77.0 77.1 76.9 77.4 77.9 78.0 77.7 77.1 77.3 76.9 76.8

 70.8 71.0 71.3 71.8 72.5 73.1 73.2 73.2 72.8 73.0 72.7 72.4

 7.9 7.9 7.6 6.7 6.3 6.2 6.1 5.9 5.6 5.6 5.6 5.8

 57.3 57.4 57.3 57.2 57.8 58.5 58.6 58.2 57.7 58.2 58.4 58.3

 53.1 53.4 53.7 53.6 54.0 54.4 54.5 54.3 53.9 54.4 54.7 54.9

 7.3 6.9 6.3 6.3 6.5 7.1 7.0 6.8 6.6 6.5 6.2 5.8

 58.2 58.2 58.2 58.1 58.4 58.7 58.3 58.4 58.5 58.9 59.1 59.1

 54.3 54.5 54.9 54.8 55.1 55.1 54.7 54.7 55.0 55.5 55.8 55.9

 6.6 6.2 5.7 5.7 5.7 6.1 6.3 6.3 6.0 5.8 5.6 5.3

 46.2 47.5 47.1 47.0 50.5 60.2 65.1 59.1 48.8 49.0 49.1 48.0

 36.6 37.5 37.4 37.8 40.1 46.6 53.3 50.2 40.1 39.8 40.2 40.4

 20.7 21.0 20.6 19.7 20.8 22.6 18.1 15.1 17.7 18.7 18.2 15.8
- 19 -

Table 9. Seasonally Adjusted CPS 80 weighted Estimates (Composited beginning with October 1992)

 SEP92 OCT92 NOV92 DEC92 JAN93 FEB93 MAR93 APR93 MAY93 JUN93 JUL93 AUG93 SEP93 OCT93 NOV93 DEC93

Total

LFPR 66.4 66.1 66.2 66.2

EPR 61.4 61.3 61.4 61.4

UER 7.5 7.3 7.3 7.3

Men 16+

LFPR 75.8 75.4 75.5 75.3

EPR 69.9 69.6 69.7 69.7

UER 7.8 7.7 7.7 7.5

Men 20+

LFPR 77.4 77.2 77.2 77.0

EPR 72.0 71.8 71.8 71.8

UER 7.0 7.1 6.9 6.8

Women 16+

LFPR 57.8 57.5 57.7 57.8

EPR 53.7 53.6 53.7 53.7

UER 7.1 6.7 6.9 7.1

Women 20+

LFPR 58.3 58.2 58.3 58.4

EPR 54.6 54.6 54.7 54.6

UER 6.4 6.1 6.2 6.4

Teens 16-19

LFPR 52.5 50.5 51.4 51.7

EPR 41.5 41.2 41.0 41.6

UER 20.9 18.4 20.3 19.5

 66.0 66.1 66.0 66.1 66.2 66.2 66.2 66.2 66.0 66.2 66.2 66.3

 61.3 61.4 61.4 61.4 61.6 61.6 61.7 61.7 61.6 61.8 61.9 62.0

 7.1 7.0 7.0 7.0 6.9 6.9 6.8 6.7 6.7 6.7 6.5 6.4

 75.1 75.3 75.3 75.3 75.4 75.3 75.3 75.3 74.9 75.1 75.0 75.0

 69.7 69.8 69.7 69.7 69.9 69.8 69.9 70.0 69.7 69.9 70.0 70.1

 7.2 7.3 7.4 7.3 7.2 7.2 7.2 7.1 6.9 6.9 6.6 6.5

 76.8 76.9 76.9 76.9 77.0 77.0 77.0 77.0 76.7 77.0 76.8 76.8

 71.9 71.8 71.8 71.9 72.1 72.0 72.0 72.1 71.9 72.2 72.3 72.3

 6.5 6.6 6.7 6.5 6.5 6.5 6.5 6.4 6.3 6.2 5.9 5.8

 57.7 57.7 57.6 57.6 57.9 57.8 57.8 57.9 57.9 58.1 58.2 58.3

 53.7 53.8 53.9 53.8 54.0 54.1 54.1 54.2 54.2 54.3 54.5 54.7

 7.0 6.7 6.4 6.6 6.6 6.6 6.4 6.3 6.3 6.4 6.4 6.2

 58.3 58.2 58.2 58.2 58.3 58.4 58.3 58.5 58.4 58.6 58.7 58.9

 54.6 54.7 54.8 54.7 54.9 55.0 55.0 55.1 55.0 55.2 55.4 55.5

 6.3 6.0 5.7 6.0 5.9 5.9 5.8 5.7 5.8 5.8 5.7 5.7

 51.4 52.0 51.5 51.7 52.4 51.5 51.8 51.6 51.2 51.1 51.2 50.9

 41.3 41.8 41.5 41.2 42.1 41.5 42.2 42.1 42.0 41.4 41.8 41.9

 19.6 19.6 19.5 20.3 19.8 19.5 18.4 18.4 17.9 18.9 18.3 17.8

Table 10. Unadjusted CPS 80 weighted (Composited beginning with October 1992)

 SEP92 OCT92 NOV92 DEC92 JAN93 FEB93 MAR93 APR93 MAY93 JUN93 JUL93 AUG93 SEP93 OCT93 NOV93 DEC93

Total

LFPR 66.2 66.0 66.1 65.9

EPR 61.5 61.6 61.5 61.3

UER 7.2 6.8 7.0 7.0

Men 16+

LFPR 75.6 75.2 75.1 74.8

EPR 70.3 70.0 69.6 69.3

UER 7.0 6.9 7.3 7.3

Men 20+

LFPR 77.4 77.1 76.9 76.7

EPR 72.6 72.3 71.9 71.6

UER 6.2 6.3 6.5 6.7

Women 16+

LFPR 57.6 57.6 57.9 57.8

EPR 53.4 53.8 54.0 54.0

UER 7.3 6.6 6.6 6.5

Women 20+

LFPR 58.4 58.5 58.6 58.5

EPR 54.5 54.9 55.2 55.0

UER 6.6 6.0 5.9 6.0

Teens 16-19

LFPR 49.9 48.3 49.1 48.6

EPR 39.5 39.5 39.1 40.0

UER 20.9 18.2 20.4 17.8

 65.4 65.6 65.7 65.5 66.1 67.1 67.3 66.8 65.9 66.2 66.1 66.0

 60.3 60.6 60.8 61.0 61.7 62.3 62.7 62.4 61.7 62.0 62.1 62.0

 7.9 7.7 7.3 6.8 6.7 7.1 6.9 6.5 6.4 6.3 6.1 6.0

 74.4 74.7 74.8 74.6 75.2 76.5 76.9 76.3 74.8 74.9 74.6 74.4

 68.1 68.3 68.7 69.1 70.0 71.0 71.6 71.3 70.2 70.3 70.0 69.7

 8.5 8.5 8.2 7.4 7.0 7.2 6.9 6.4 6.2 6.2 6.2 6.3

 76.5 76.7 76.8 76.6 77.1 77.6 77.6 77.4 76.8 77.0 76.6 76.5

 70.5 70.7 71.0 71.5 72.3 72.8 72.9 72.9 72.5 72.7 72.4 72.1

 7.8 7.8 7.5 6.6 6.2 6.2 6.1 5.8 5.6 5.6 5.5 5.8

 57.2 57.3 57.3 57.2 57.8 58.5 58.5 58.1 57.7 58.2 58.3 58.3

 53.1 53.4 53.7 53.6 54.1 54.4 54.5 54.3 54.0 54.5 54.8 55.0

 7.2 6.8 6.2 6.2 6.4 7.0 6.9 6.7 6.5 6.4 6.1 5.7

 58.1 58.1 58.1 58.0 58.3 58.6 58.2 58.3 58.4 58.9 59.0 59.0

 54.3 54.5 54.9 54.7 55.1 55.0 54.6 54.7 55.0 55.5 55.8 55.9

 6.6 6.2 5.6 5.6 5.6 6.0 6.2 6.2 5.9 5.7 5.5 5.3

 46.2 47.4 47.1 47.1 50.6 60.3 65.3 59.2 48.7 48.9 49.1 48.0

 36.7 37.5 37.4 37.8 40.1 46.7 53.5 50.2 40.1 39.8 40.2 40.4

 20.6 20.9 20.5 19.7 20.7 22.5 18.1 15.1 17.7 18.7 18.1 15.7
- 20 -

Appendix 1 Modeled Series Graphs

The following 6 pages present further modeling results. Each page contains four plots.

The two plots on the left are for teenagers, and the two plots on the right are for adults.

In both cases, the top plot is a scatter plot of the monthly data for both the Parallel Survey

and CPS for the particular characteristic being represented. The gray line is a 45 degree

reference line, and the solid black line is the estimated structural relationship as

represented in equation (5). The bottom graph is a set of time series for the 16 months

from September 1992 to December 1993. The solid black line is the CPS, the dashed line

is the Parallel Survey, and the gray line is the model. Dots represent monthly estimates in

all these series. The upper and lower gray lines (without dots) are the upper and lower

bounds of an approximate 90% prediction confidence bound around the monthly model

estimates. The prediction intervals form a range where we would have expected the

observed CPS to have fallen (approximately 90% of the time) had the new methodology

and weighting been used during that period. The prediction intervals account for the

variance in estimating the true monthly values, as well as the variance in the monthly CPS

sampling error. This is discussed more fully in Appendix 2. In all cases, the data are

reported in thousands.
- 21 -

Figure 1. Agricultural Employment, Women.
- 22 -

Figure 2. Agricultural Employment, Men.
- 23 -

Figure 3. Non Agricultural Employment, Women.
- 24 -

Figure 4. Non Agricultural Employment, Men.
- 25 -

Figure 5. Unemployment, Women.
- 26 -

Figure 6. Unemployment, Men.
- 27 -

Appendix 2 Details of Statistical Methods

As described earlier, we modeled each of the twelve labor force series separately. We will

describe the common procedure used for each below.

(A1) Yt = Observed monthly CPS estimate under the old method

yt = True monthly CPS value under the old method

and let

(A2) Y y e t = t + t

where et is the CPS sampling error, and t = 1,K,T , where T = 16. Also, let

(A3) Xt = Observed monthly Parallel Survey estimate under the new method

xt = True monthly Parallel Survey value under the new method

and let

(A4) X x u t = t + t

where ut is the Parallel Survey sampling error. We will make the assumption that

(A5) y x t = b0 +b1 t

which says that the true values are linearly structurally related. If we write

(A6) e′ = e e 1 16 b,K, g

u′ = u1 u16 b,K, g

then we can write our next assumption as

(A7)

e

u

0

0

0

0

ee

uu

F

H

GI

KJ FH

GI

KJF

H

G I F

H

G KJ

I ~ N , KJ

Σ

Σ

.
- 28 -

We have estimates of both Σee and Σuu, which we will consider as known and fixed for

the purposes of estimation. The estimate of Σ ee was based upon generalized variance

function estimates and correlations obtained from previous research on the CPS. The

estimate of Σuu was computed directly by replication using Robert Fay's program VPLX.

We treated the unknown parameters of the problem as

(A8) q = b b

′

0 1 1 16 b, , x ,K, x g

where we treated the xt

q by weighted nonlinear least squares. Second, use those

estimates in a one-step Gauss Newton estimation to get the final estimates, as well as

estimates of variance. We next describe the actual estimation of the model parameters and

estimated true values in more detail.

STEP 1 Initial estimates.

Let Zt = Yt Xt

′ b, g and εt t t =be ,ug for t = 1,K,16. Also let

(A9) Σ ε εεtt t

eett

uutt

≡ =F

H

G I Vlq KJ

s

s

0

0

.

Let

(A10) mZZ = Z Z Z Z

′

−

−

=

15 ∑

1

1

a 16 ftct hct h

Σεε•• Σεε

=

•

••

= = H16 ∑ G KJ

0

0

1

1

16 f tt

t

ee

uu

s

where Z = Z

−

=

16 ∑

1

1

a 16

t

t

 . We estimated the parameters b0 and 1 by methods described in

Fuller (1987). Let $

l be the smallest root of the determinental equation

(A11) mZZ − l Σεε•• = 0
- 29 -

and let α$ = $ , $

′ ba1 a 2g be the generalized eigenvector associated with $

l which satisfies

(A12) m 0 ZZ − •• =

$

l Σ α$ e εε j .

Define

(A13) $b a$ a$

1 2 1

1

= −

−

$ $ b0 = Y − Xb1

$

$ $ $

xt = eett + uutt uutt Yt − + eettXt

−

s b1s s b b s

2

1 e j 1e 0j for t = 1,K,16.

Call the initial estimates

(A14) $ $

,

$ θ , $ , , $

1

0 1 1 16

af=e j′

b b x K x .

STEP 2 Weighted Nonlinear Estimation.

Define the function

(A15) G Y x X x eett t t uutt t t

t aθf= ∑=

s

−1 b− b0 − b1 g2

+ s

−1 b− g2

1

16

.

Let $θa2f be the solution to the minimization of Gaθf, obtained by using $θa1f as an initial

estimates. There is an alternative formulation of this step. Define

(A16) H eett uutt Yt Xt

t aβf= ∑=

cs + b1

2

s h−1b− b0 −b1 g2

1

16

and let %β be the minimizer of Haβf, and let

(A17) %

% % %

xt = eett + uutt uutt Yt − + eettXt

−

s b1s s b b s

2

1 e j 1e 0j for t = 1,K,16.
- 30 -

Then, $θa2f is equal to %,

% b b , % , , %

0 1 1 16 e x K x j′

. It turns out, in general, that if Σεεtt is constant

over t, then the estimates in Step 1 and Step 2 give the same result.

STEP 3 One-Step Gauss Newton Estimation

Define

(A18) Z

Y

X

=F

H

GI

KJ

Y =

′

Y1 Y16 b,K, g

X =

′

X1 X16 b,K, g

f

1 x

x

aθf=F+

H

G I

KJ

b0 b1

F

f

θ

θ af

θ

=

¶af

¶

and let

(A19) w = Z− f

$θea2fj

V

0

0

ee

uu

=F

H

G I

KJ

Σ

Σ

% $ $ $ δ = ′ θ θ ′ θ

−

−

−

F V F F V w

2 1 2

1 eafjeafjea2fj1

$ $ % θ θ δ a3f= a2f+

where $θa3f is the final estimate. The approximate distribution of $θa3f is given by
- 31 -

(A20) $θ ~ θ, θ θ

3 1 af NeF′afV

− Faf−1j

and we estimated the variance of $θa3f by

(A21) V$ $ $ $ θ F θ V F θ

3 3 1 3 oaf af af 1 t= ′ej− ej−

.

When we speak of the approximate distribution, we refer to an approximation as variances

of the survey errors get small. This definition of asymptotics implies that the estimators

obtained in each of the first two steps are consistent estimators of θ , and that the final

estimator in Step 3 is efficient in the sense that they have the same limiting distribution as

the maximum likelihood estimator of θ .

From now on, we drop the superscript and refer to the final estimates as $θ , as well as the

components of $θ . Note that the resulting estimates x$ = $ , , $

′

x x b1 K 16g are the estimates of

the true (but unobservable) value under the New CPS definition, and $Vlx$q is an estimate

of the covariance matrix of the estimates, where $Vlx$q is to lower 16 ×16 sub matrix of

V$ $θoa3ft given above. The estimates x$ = $ , , $

′

x x b1 K 16g can also be thought of as a predictor

of what the observed CPS might have been under the New CPS definition, and we can use

(A22) $V x$lq+ Σee

as an estimator of the covariance matrix of the prediction errors, where we used the

covariance matrix Σee , the covariance matrix of the CPS sampling errors, in (A7). These

prediction error variances were used to construct the prediction confidence intervals in

Figures 1-6.

In addition, we computed the goodness-of-fit statistic

(A23) cG q q

2 1

= −

′

−

− Z f V Z f ee$j ee$j

which is approximately distributed as a chi-square random variable with 14 degrees-offreedom
- 32 -

In addition, we computed a structural relationship test, which tested the hypothesis

H0 0 1:b = 0, b = 1, which says that there is no difference in the true values as defined under

the Parallel Survey and CPS. The test statistic used is

(A24) cS

2 1

= −

′

−

$ $ − $ $ eβ bjV {β

}eβ bj

which is approximately distributed as a chi-squared random variable with 2 degrees-offreedom under the null hypothesis, where V$ ${β

} is the upper 2 × 2 sub matrix of V$ $θoa3ft

given above, and b =

′ a0,1f.
- 33 -

References

Fuller, Wayne A. (1987). Measurement Error Models. John Wiley.

Kostanich, Donna L. and Cohoon, Lawrence S. (1994). Effect of Design Differences

Between the Parallel Survey and New CPS. CPS Bridge Team Technical Report 3.

Bureau of Labor Statistics, Washington DC.

Polivka, Anne E. (1994) Comparisons of Labor Force Estimates for the Parallel Survey

and the Current CPS. Overlap Analysis Team Technical Report 1. Bureau of

Labor Statistics, Washington DC.