Predicting the National Unemployment Rate that the "Old" CPS Would Have Produced

Richard Tiller and Michael Welch, Bureau of Labor Statistics

Richard Tiller, Bureau of Labor Statistics, Room 4985, 2 Mass. Ave., N.E., Washington, DC 20212-0001

KEY WORDS: Time series forecasting, Structural Models

Abstract: In January 1994, the introduction of the redesigned Current Population Survey (CPS) questionnaire and

automation of collection procedures was expected to affect most labor force estimates. To help evaluate the change

in the unemployment rate attributed to these revisions, time series models were used to extrapolate the pre- 1994

series to predict the unemployment rate estimates for 1994.

I. Introduction

Beginning with January 1994 data, the Current

Population Survey (CPS) introduced new data

collection procedures and population controls based on

the 1990 census, adjusted for census undercount.

These new procedures may result in substantial

changes in many labor force series, including the

national unemployment rate. In order to address the

issue of comparability between the "old" and "new"

series for various groups of data users, time series

models were developed by the Bureau of Labor

Statistics to predict what the national unemployment

rate would be during the early months of 1994 under

the "old" CPS data collection procedures and

population controls based on the 1980 census.

The model uses the historical relationships between

CPS data and unemployment insurance claims for the

CPS reference week and employment from the Current

Employment Statistics Survey (the BLS payroll survey

of business establishments). The model was fitted to

data from January 1976 through December 1993, the

last month for which official estimates were made

using the "old" data collection procedures. As soon as

data are validated from the new parallel survey, which

will use the "old" CPS methods, these data will be

incorporated into a model to estimate what the

monthly unemployment rate would have been had the

"old" survey been continued. The new model and

sample-based estimates then may replace the

projections described in this paper.

This report discusses background of the CPS; gives a

brief description of the data used in the models;

presents the model and examines test statistics relevant

to assessing its performance; predicts the

unemployment rate, not seasonally adjusted, that

would have been produced had the "old" survey been

continued in 1994; describes the methods used to

seasonally adjust the model-based prediction; and

offers caveats concerning the predictions. Additional

technical detail is provided in the complete paper.

II. Background

The CPS is a monthly probability sample survey of

about 60,000 households, conducted by the Bureau of

the Census for the Bureau of Labor Statistics (BLS).

Beginning with the January 1994 interview, the CPS is

conducted using a new questionnaire in a completely

computer-assisted environment. The Bureau of the

Census and the BLS tested the new procedures for 18

months (July 1992 - December 1993) on a separate,

national-based probability sample of 12,000

households. The results of this parallel survey indicate

that the CPS annual average unemployment rate would

have been 0.5 percentage point higher in 1993 if the

new approach had been used. Additionally, the

introduction of 1990-based population controls raises

the unemployment rate 0.1 percentage point more than

that obtained from 1980-based population controls.

Additional effects due to design differences are

discussed in Kostanich and Cahoon1.

To better understand the differences between the "old"

and "new" methodology, we are switching the old CPS

procedures to the parallel survey sample of 12,000

households (here in after "new parallel survey"). In

other words, in January 1994, the CPS sample of

60,000 households began using the "new" methods,

and the parallel survey sample of 12,000 households

began using the "old" methods. Due to operational

constraints, it was not possible to avoid this switchover with its possible attendant effects on respondents

and interviewers.

Although data are being collected using both the old

and new collection methods, the official labor force

estimates are based on the CPS using the new

methods. We cannot provide the public with an

immediate source of comparison between the "new"
and "old" labor force estimates because the reliability

of data from the new parallel survey may be low

during the initial months, due to nonsampling errors

associated with the start-up period that are beyond our

control. As an interim measure, we developed a

structural time series model to predict what the

monthly national unemployment rate would have been

had the "old" CPS been continued. This paper outlines

the research conducted jointly by the BLS, the Bureau

of the Census, and consultants from Iowa State

University to develop this prediction.

III. Description of data

The data used for modeling the unemployment rate

cover the period January 1976 through December

1993. These data consist of estimates of the civilian

noninstitutional population and the unemployment rate

from the CPS, estimates of employment from the

Current Employment Statistics (CES) survey, and

unemployment insurance continued claims counts

provided by the Employment and Training

Administration. The CPS and CES data are official

BLS estimates obtained from the Bureau's LABSTAT

database. Data are not seasonally adjusted, and levels

are rounded to the nearest thousand.

The CPS data are composited and based on 1980

population controls. The CES data are final

benchmarked up to March 1992, first benchmarked for

the period April 1992 through April 1993, third closing

for the period May 1993 through November 1993, and

second closing for December 1993. Although the most

recent CES data are subject to further revision, for the

sake of consistency, we will not use data reflecting

future revisions to reestimate our model. The

unemployment insurance claims counts are the total

number of regular state unemployment insurance

claims filed during the week that includes the CPS

reference week. These do not include claims paid

under the Emergency Unemployment Compensation

Act or earlier extended benefits provisions.

IV. The prediction model

A number of different time series models were fit to

CPS unemployment rate data for the period January

1976 through December 1993 for a total of 216

observations. The alternatives considered were

structural time series models with explanatory

variables2, multiple regression with autocorrelated

disturbances3, and univariate ARIMA models4. (See

the appendix for more details.) A structural time

series model was selected as the preferred model

because of its goodness of fit to the historical data,

forecasting performance, and ease of explanation.

The structural model is essentially a multiple

regression that includes a trend and seasonal

component and two explanatory variables as

regressors. This model differs from the usual

regression model in that the trend and seasonal

components do not have a fixed functional form over

the entire sample period but rather are allowed to vary

smoothly over time. The model is given by

Yt = mt + b1CLRt + b2CESEPt + St + et ,

where

Yt = CPS unemployment rate for month t,

mt = time varying trend term,

CLRt = 100(UIt/CESEMt),

CESEPt = 100(CESEMt/POPt),

UIt = unemployment insurance claims,

CESEMt = employment level from the CES,

 

POPt = civilian noninstitutional population,

b1, b2 = fixed regression coefficients,

St = the seasonal component, and

et = a random disturbance (noise) term.

The two explanatory variables used in the model are

the ratio of worker claims for unemployment insurance

benefits to CES employment (CLR) and the ratio of

CES employment to the estimated civilian

noninstitutional population (CESEP).

The CLR and CESEP variables are included in the

model because they are strongly correlated with the

CPS unemployment rate, and are readily available on a

timely basis. However, the variables do not explain a

significant amount of variation in the CPS rate. A

complete explanation would require a complex model

with many variables. As an alternative to such a

complex model, we add stochastic trend and seasonal
components to capture both long-run movements and

seasonal variation in the CPS unemployment rate that

are not accounted for by the two regressors (CLR and

CESEP). Note that in this model the seasonal

component reflects the seasonal pattern in the

unemployment rate not accounted for by the

explanatory variables and thus it is not suitable for

seasonally adjusting the unemployment rate.

The trend component, mt

, or time varying intercept, is

represented as a nonstationary autoregressive process

(random walk). That is, its current value is equal to its

previous period value plus a random disturbance.

Thus, the trend will change very smoothly over time,

shifting up or down, with no persistent directional

change. The magnitude of the change is determined

by the variance of the disturbance term. Similarly, the

seasonal component is specified as a nonstationary

process consisting of the sum of six trigonometric

terms with seasonal periodicities. Each of these

components contains a random disturbance with a

common variance. This allows the amplitude and

phase of the seasonal pattern to change slowly over

time, where the degree of change depends upon the

size of the disturbance variance.

The effect of specifying the trend and seasonal

components in the fashion just described is to discount

past observations in the computation of these

components. Thus, data from the 1990's are assumed

to be more relevant for predicting the trend and

seasonal components in 1994 than are data from the

1970's. The degree of discounting depends upon the

size of the variances of the trend and seasonal

components. These variances are determined

empirically.

Table 1 presents the values of the estimated

coefficients and t-ratios for the two explanatory

variables, and monthly estimates of the trend and

seasonal components for 1993. The trend has a large

positive value, but is offset by multiplying the CESEP

variable by its negative coefficient.

In the initial model estimation, the seasonal pattern

was estimated to vary smoothly over time. A closer

examination, as suggested by Wayne Fuller of Iowa

State University, revealed that most of the change in

the seasonal component was occurring in May and

June, months when teenagers have a strong influence

on labor force movements. There has been a secular

decline in the relative size of this teenager group,

which might explain the observed changes in the

seasonal pattern. To test this possibility, a seasonal

change variable for May and June expressed as a

function of the percent of 16 to 19-year-olds to total

population was introduced. When this variable was

added to the model, the variance in the residual

seasonal component was reduced to zero. While this

had little effect on the final predictions, it did reduce

the standard deviation of the prediction error by 15

percent.

The lower part of Table 1 presents evaluative

statistics. The standardized one-step ahead prediction

errors generated from the model were tested for

autocorrelation, non-normality, and increasing

variance over the 1993 sample period. The Q statistic

is the portmanteau test for autocorrelations in the

prediction errors up to 24 lags. This statistic has an

asymptotic chi-squared distribution with 24 degrees of

freedom. A value of about 40 or more would indicate

significant autocorrelations. The normality test can be

compared to a chi-square distribution with two degrees

of freedom. A value higher than about six would

indicate lack of normality. The variance test checks

for larger prediction errors in the last third of the

sample relative to the first third. This test statistic has

an F distribution. The root mean square error (RMSE)

is the standard deviation of the one-step-ahead

prediction errors computed over the last year of the

sample period. This statistic measures how well

model predictions compare to actual observations.

None of the diagnostics in table 1 suggests that the

model is inappropriate.

Three alternative coefficients of determination ( R

2

,

RD

2

, and Rs

2

) are shown as measures of goodness of

fit. The conventional R

2

 is 1 minus the sum of

squared prediction errors to the sum of squared

deviations of the unemployment rate observations

about the mean. It shows how much of the variation in

the series is explained by the full set of model

variables, including the time-varying intercept and the

seasonal factors. The RD

2

 measure indicates how

much of the variation in the first difference of the

series can be explained by the model. The RS

2

measure is even more stringent; it represents the share

of the residual variation explained by the model after

taking first differences and then subtracting seasonal

means. This measure is considerably lower than the

value for R

2

. Nevertheless, the model makes a

relatively large contribution to explaining the variation

in the unemployment rate that remains even after trend
and seasonal movements have been factored out of the

series.

Table 1. Model Estimates and Evaluative Statistics

Coefficients/components

(T-ratios in absolute value)

CESEP1 CLR2

-0.47 (6.9) 0.56 (7.3)

Trend (1993) Seasonal (1993)

Jan 32.58 (8.1) -0.09 (1.5)

Feb 32.61 (8.1) -0.09 (1.6)

Mar 32.53 (8.1) -0.20 (4.6)

Apr 32.48 (8.0) -0.35 (10.9)

May 32.40 (8.0) 0.08 (1.3)

Jun 32.40 (8.0) 0.46 (14.7)

Jul 32.31 (8.0) 0.07 (2.1)

Aug 32.20 (8.0) -0.10 (2.5)

Sep 32.12 (7.9) 0.13 (2.8)

Oct 32.09 (7.9) 0.08 (1.9)

Nov 31.98 (7.9) 0.14 (3.4)

Dec 31.94 (7.9) -0.12 (2.9)

Evaluative statistics

Q 12.83

Normality 1.04

Variance Test 1.20

Rmse 0.17

R

2 0.98

RD

2 0.85

Rs

2 0.31

Predictions

Table 2 presents the official unemployment rate

estimates for 1993 with associated standard errors and

90 percent confidence intervals together with the

predicted values for January through October 1994,

their standard errors, and 90-percent confidence

prediction intervals. The standard errors are

computed from the model. The prediction intervals

will become longer as the prediction period is

extended.

The predicted rate is seasonally adjusted by using the

implicit seasonal factors derived from the official rate

estimates (discussed in detail later in this report).

Approximate confidence intervals for the seasonally

adjusted estimates are computed using the standard

errors for the unadjusted data.

V. Seasonal adjustment procedure

The seasonally adjusted national unemployment rate

from the CPS is produced by aggregating 12

independently adjusted series. The component series

are: agricultural employment, nonagricultural

employment, and unemployment, each for four sexage groups (men 20 years and older; women 20 years

and older; men 16 to 19 years; and women 16 to 19

years). Eight of these series are seasonally adjusted

using multiplicative adjustment factors; the remaining

four -- nonagricultural men and women aged 16 to 19

years, and unemployed men and women aged 16 to 19

years use additive adjustment

factors.

The seasonal adjustment factors are generated using

X-11 ARIMA software, and the factors for 1994 are

given in the January 1994 issue of Employment and

Earnings. Each of the 12 series is separately adjusted

for seasonal variation. The series then are added to

derive seasonally adjusted aggregate figures. The

seasonally adjusted unemployment estimate is a sum

of four seasonally adjusted unemployment

components. The seasonally adjusted figure for the

civilian labor force is a sum of eight seasonally

adjusted civilian employment components and four

seasonally adjusted unemployment components. The

overall unemployment rate is derived by dividing the

estimate of unemployment by the estimate of the

civilian labor force.

The modeling described here yields an estimate of the

unemployment rate, not seasonally adjusted. A

seasonally adjusted rate was calculated by multiplying

the unadjusted rate estimate by the ratio of the official

January 1994 adjusted rate to the official January 1994

unadjusted rate. This approach seemed reasonable

because analysis indicated that monthly differences

between CPS and initial parallel survey unemployment

rates were not affected by seasonal adjustment.

The official CPS unemployment rate, seasonally

adjusted, for January 1994 is 6.7 percent, and the not

seasonally adjusted unemployment rate is 7.3 percent.

The ratio of the seasonally adjusted rate to the not

seasonally adjusted one is, therefore, 0.9178. To

obtain the seasonally adjusted prediction of the

January 1994 unemployment rate that would have

been produced by the "old" CPS methods, we multiply

the not seasonally adjusted prediction of 6.9 percent by

0.9178. This gives us a seasonally adjusted prediction

of 6.3 percent for January 1994.
VI. Caveats

It is important to note that the predicted estimates are

based on historical relationships that may or may not

carry over into the future. Specifically, it should be

noted that no concurrent CPS data are used in the

model to reflect the old CPS questionnaire and data

collection methodology. This means that disturbances

to the economy in early 1994 will not be reflected in

the predictions, except as captured by the explanatory

variables. In view of this, the predictions should be

interpreted with caution, especially when the period is

extended beyond January. As soon as data from the

new parallel survey that replicates the "old" CPS

methods have been validated, they will be

incorporated into a model to estimate what the

monthly unemployment rate would have been had the

"old" survey been continued. These model and sample

based estimates will then replace the projections

described in the present report. Production of these

estimates will continue, as we seek to help users better

understand the relationship between the new, official

series and the data derived from the "old" CPS.

APPENDIX: Description of the Modeling Methods

Three different approaches to time series models were

used to estimate alternative forecasts of the CPS

unemployment rate in 1994. These methods are based

on the structural modeling approach1; autoregressiveintegrated-moving-average (ARIMA) models2; and

multiple regression models. The structural model

provided the best alternative to satisfying the objective

of multi-period forecasting with explanatory variables.

This appendix provides further technical detail on the

structural modeling method and then briefly addresses

the regression model and ARIMA approaches

considered.

Structural modeling with explanatory variables. This

approach, as exemplified in the work of A.C. Harvey3,

explicitly models components known to exist in a time

series, such as trends, seasonals, and irregulars. In

univariate form, these models are closely related to

ARIMA models, but do not include as wide a class of

models as the

G.E.P. Box-G.M. Jenkins approach4. When

explanatory variables are added to this model, it is

similar to a regression model. The general form of the

model used in our application is described below.

Let

Yt = mt + btXt + St + et ,

where Yt is the observed unemployment rate at time t; 

μt

 is a time varying intercept or trend term; βt is a

(1xk) row vector of time-varying coefficients; Xt is a

column vector of explanatory (regressor) variables at

time t; St is a seasonal component; and εt

 is an error

term.

The time-varying trend is represented by a locally

smooth linear trend with a random level, μt

, and slope, 

γ

t. . This is expressed as

 

m m g u

g g u

t t t t

t t t

= + +

= +

− −

−

1 1

1

*

,

where ut and ut

*

are independent white noise terms

with zero expectations and variances s u s u

2

 and *

2

.

Similarly, the regression coefficient vector is

described by

bt = bt−1 + xt ,

where ξt

 is a white noise vector with zero expectation

and covariance matrix Diag(s s x1 x

2 2

,..,

k

).

The seasonal component is modeled by

 St Sjt

j

=

=

∑

1

6

 ,

where

S S S

S S S

p p

jt j j t j j t s

jt j j t j j t s

j j

j

j

= + +

= − + +

= =

− −

− −

−

cos( ) sin( ) ,

sin( ) cos( ) ,

, { , , , , . , },

, ,

*

*

, ,

* *

w w z

w w z

w p

1 1

1 1

1

2 12 6 4 3 2 4 2

 

and the zsj

 and zsj

*

are independent white noise

disturbances with zero means and constant variance.

This model provides, as a special case, the standard

time series regression model in which the intercept and

regression coefficients are fixed and the seasonal

component is represented by monthly dummy

variables. The role of the time varying intercept is to

capture long run variation in the unemployment rate
that is not reflected in the explanatory variables.

Similarly, the purpose of the seasonal component is to

account for seasonal movements in the rate that can

not be fully explained by the regressor variables.

Seasonal movements are allowed to slowly change in

magnitude over the sample period. The error term, εt

,

accounts for survey measurement error and can be

modeled by a stationary process. For national data,

the relative variance of the CPS survey errors are small

enough so that the autocorrelation structure can be

ignored; thus we let εt be a zero mean, white noise

process with variance s e

2

 . Additionally, we assume

that all disturbance terms in the model are normally

distributed.

In our application, we used two explanatory variables

in the model. These are CESEMt , employment

estimated by the Current Employment Statistics

survey; UI t, worker claims for unemployment

insurance benefits; and POPt, representing the

civilian noninstitutional population, 16 years and over.

These variables are defined below.

CESEPt = 100(CESEMt/POPt)

CLRt = 100(UIt/CESEMt)

Two models were fitted. One model includes both

variables, and the other includes only the CLR

variable. For parameter estimation and signal

extraction, the models were expressed in state space

form. The parameters were estimated based on a

maximum likelihood procedure, using the Kalman

filter to estimate the likelihood function. Given the

parameters of the system, the Kalman filter was used

to optimally decompose a sample observation into its

signal and noise components5.

Regression models with autoregressive disturbances.

In this approach, multiple regression models with

autocorrelated errors are formulated as follows6.

Yt Xt t

t i t i

i

p

t

= +

= − +

=

∑

b e

e q e u

1

These models were estimated in both level and

difference form. Variables used in the model are as

follows:

RMPY7 = (POPt)

-1Y7 - 3559(POPt

)

-1

RMPY6 = (POPt

)

-1Y6 - 50416(POPt

)

-1

Y7 = Unemployment insurance claims

Y6 = CES employment

POP = Civilian population 16+

CPSUER = CPS unemployment rate

DR = First difference of CPS

unemployment rate

RMDIF = Lag(RMPY7 - .5RMPY6)

MMDINT = [RMPY7 - 0.46RMPY6 +

0.43RMDIF][POP]

-1[POP - POP ]

POP = mean of POP

TREND = 1

0 375 122 1

+

−

−

e

{ . (t )}

The level model contained RMPY7, RMPY6, RMDIF,

MDINT, TREND, 11 seasonal dummies, and 11 crossproduct terms of TREND with the seasonal dummies.

The difference model contained DRMPY7, DRMPY6,

DRMDIF, 11 seasonal dummies, and the 11 season-byTREND cross product terms. The notable features of

these regression models were the inclusion of the

TREND variable, estimated from fitting a logistic

function to the unadjusted unemployment rate and the

detrending of several variables. An additional

variable, the proportion of teenagers 16 and older in

the civilian noninstitutional population was included in

the difference model to account for changing

seasonality in May and June. Other auxiliary variables

were tried in the regression model, but did not improve

the model fit; these variables included the help-wanted

index and number of hours worked in the

manufacturing sector.

ARIMA models

ARIMA modeling is one of the most frequently used

approaches to short term forecasting7. These models

allow for a wide variety of potential forecast functions

for extrapolating a time series from its own past.

However, because forecasts are required for up to the

first 5 months of 1994, the ARIMA univariate model

has limited application, as the forecasts standard errors

for this type of model increase considerably as the

forecast period is extended.

With multi-period forecasting, models that use related

series (when the values of those series are available

during the forecast period) are preferred because their

forecast errors are likely to be smaller. However,

ARIMA models are useful benchmarks for

comparison, because they often produce high quality

forecasts over the first few periods of the forecast

range. ARIMA models that were useful for one-stepahead forecasts were the (3,1,0)(0,1,1)12 and the

(0,2,2)(0,1,1)12.
Endnotes

1. D. L. Kostanich, and L. S. Cahoon, "Effect of

Design Differences Between the Parallel Survey

and New CPS," CPS Bridge Team Technical

Report 3, (Bureau of Labor Statistics, 1994).

2. A. C. Harvey, Forecasting, Structural Time Series

Models and the Kalman Filter (Cambridge,

Cambridge University Press, 1989).

3. W. A. Fuller, Introduction to Statistical Time Series

(New York, Wiley, 1976).

4. G. E. P. Box, and G. M. Jenkins, Time Series

Analysis: Forecasting and Control (San Francisco,

Holden-Day, 1976).
Table 2. Official and Predicted Unemployment Rates

 Based on the old CPS Design

January 1993 - October 1994

Seasonally adjusted

Month

Not seasonally

adjusted

Standard

error*

Unemployment

rate

90% Confidence interval

lower upper

Official

 January 93 7.9 0.12 7.1 6.9 7.3

 February 7.7 0.12 7.0 6.8 7.2

 March 7.3 0.12 7.0 6.8 7.2

 April 6.8 0.11 7.0 6.8 7.2

 May 6.7 0.11 6.9 6.8 7.1

 June 7.1 0.11 6.9 6.8 7.1

 July 6.9 0.11 6.8 6.6 7.0

 August 6.5 0.11 6.7 6.6 6.9

 September 6.4 0.11 6.7 6.5 6.9

 October 6.3 0.11 6.7 6.5 6.9

 November 6.1 0.10 6.5 6.3 6.6

 December 6.0 0.10 6.4 6.2 6.6

Predicted

 January 94 6.9 0.17 6.3 6.0 6.6

 February 7.0 0.20 6.4 6.1 6.7

 March 6.6 0.22 6.3 5.9 6.7

 April 5.9 0.24 6.1 5.7 6.5

 May 6.0 0.26 6.1 5.7 6.5

 June 6.1 0.28 5.9 5.4 6.3

 July 6.1 0.29 6.0 5.5 6.4

 August 5.8 0.31 6.0 5.5 6.5

 September 5.6 0.32 5.9 5.4 6.5

 October 5.5 0.34 5.9 5.3 6.4

*Standard errors are based on rates that are not seasonally adjusted and are used to construct the

confidence intervals.