BLS WORKING PAPERS

U.S. DEPARTMENT OF LABOR

Bureau of Labor Statistics

 

OFFICE OF COMPENSATION AND

WORKING CONDITIONS

Cyclical Aggregation Bias

Michael K. Lettau

Working Paper 311

April 1998

 

The views expressed in this paper are solely the authors’ and do not necessarily reflect those of the U.S. Bureau of

Labor Statistics or the U.S. Department of Labor.
Cyclical Aggregation Bias

Michael K. Lettau

April 1998

Abstract

The paper estimates the aggregation bias in compensation per hour for the United

States, where aggregation bias is defined as the difference over the business cycle

between compensation in the typical job and average compensation in the labor market.

It compares the Employment Cost Index with the Employer Cost for Employee

Compensation, both of which are calculated using the same data from a panel survey of

jobs. The results suggest that the aggregation bias is countercyclical, so compensation in

the typical job is more procyclical than average compensation in the labor market.

The views expressed in this paper are those of the author and do not necessary

reflect the policies of the U. S. Bureau of Labor Statistics or the views of other BLS staff

members.

Michael K. Lettau

Office of Compensation and Working Conditions

Bureau of Labor Statistics, mail stop 4130 PSB

2 Massachusetts Avenue NE

Washington, DC 20212

Phone: (202) 606-7396

Fax: (202) 606-6310

lettau_m@bls.gov
I. Introduction

Previous studies of the wage rate over the business cycle define aggregation bias

as the difference between the cyclical movement of the wage rate for a typical worker

and the average wage rate in the labor market. Average wage measures may

misrepresent the movement of the typical worker’s wage because the composition of

workers changes over the cycle. Previous studies therefore create a panel of continuously

employed workers to calculate a wage series that is uncontaminated by changes in the

labor force. They disagree as to the sign and magnitude of the aggregation bias, although

the preponderance of the evidence suggests it is countercyclical. That is, the typical

worker’s wage rate is more procyclical than the average wage rate in the labor market.

See Abrahams and Haltiwanger (1995) for a review of the literature.

For their uncontaminated series, previous studies focus primarily on holding the

set of workers constant over the cycle. Holding the job situation of workers constant

receives at most secondary consideration. Bils (1985) finds that wage rates of young men

are strongly procyclical for workers who change employers. However, his estimate is

much smaller in magnitude and not statistically significant for young men who remain

with the same employer. In contrast, Solon, Barsky, and Parker (1994) report that wage

rates are only slightly less procyclical for prime-aged male workers who remain with the

same employer than for all prime-aged male workers.

This paper also compares the cyclical movement of an average compensation

series with a compensation series that is not contaminated by changes in the composition

of the labor force. It compares the Employer Cost for Employee Compensation (ECEC)

with the Employment Cost Index (ECI), both of which are calculated using data from the
2

National Compensation Survey (NCS) of the U. S. Bureau of Labor Statistics (BLS).

Because the NCS is a panel survey of jobs rather than individuals, the ECI focuses on

holding the detailed job situation constant over time, not the individual worker.

Therefore, this paper addresses a somewhat difference question from previous studies.

How does the cyclical movement of average compensation in the labor market compare

to the movement of compensation in the typical job?1

Other unique aspects of the paper are the following. The ECI and ECEC are

based on the same micro data from the NCS. They differ only in the way these micro

data are aggregated. Therefore, they provide an opportunity to compare two widelyreported compensation series that use the same concepts and data collection procedures.

Moreover, the NCS is specifically designed and replenished to produce an

uncontaminated series that continually represents private and state and local government

workers. Further advantages are that the data are collected quarterly, which corresponds

more closely to a business cycle frequency than annual measures. Also, the ECI and

ECEC report employer costs for fringe benefits as well as wages and salaries. Finally,

the data are collected from establishments rather than households, so they may be subject

to less measurement error.

The paper is organized as follows. The next section describes the National

Compensation Survey and how the ECI and ECEC are calculated. The third section

presents the empirical results. The results suggest that the aggregation bias is

countercyclical, so compensation in the typical job moves more procyclically than

average compensation in the labor market. The final section summarizes.

 

1

 Wilson (1996) and Solon, Whatley, and Stevens (1997) each use data from two firm to estimate the

cyclicality of wage rates for workers who remain in the same job and workers who remain with the same
3

II. Description of ECI and ECEC

The NCS is a quarterly survey of jobs within establishments. Like all index

number programs, the ECI must define a good that it can price from one quarter to the

next. Jobs in the NCS for purposes of the ECI and ECEC are chosen as follows. For

each establishment in the survey, a small number of workers are chosen randomly from

an employee list. The establishment is then asked which jobs the chosen employees hold.

The job refers to the most detailed job classification recognized by the establishment.

These jobs become the units of observation, and the NCS collects average data among the

workers in the job. Thus, relative to other index number programs at the BLS, the ECI

largely defers to the supplier of its data, the establishment, to define what is considered

the same good over time. The jobs are scheduled to remain in the NCS for roughly four

to five years. See the BLS Handbook of Methods (1997) for a complete description of

the NCS.

The ECI is reported as an index number, with a base period arbitrarily defined as

100. The ECEC is reported in dollars and cents. They use the same micro data in their

calculation. They just aggregate the micro data differently. This paper interprets their

log difference as the aggregation bias. Let the ECI for quarter t equal It and let the ECEC

for quarter t equal Wt. Their log difference equals the following.

[1] ln(I ) ln(W ) K ln( E w ) ln( E w )it

i

it

ECI

it

i

t − t = o + ∑ ib − ∑

The K0 term depends on the quarter in which the ECI is defined to equal 100, but it does

not vary with t otherwise.

 

firm but switch jobs.
4

Interpretation of the right-hand side of equation [1] as the aggregation bias

requires an explanation of how the ECI and ECEC are calculated. The labor market is

divided into categories of labor, which are defined by the cross-section of approximately

70 industry and ten occupation groups. The i in equation [1] is the subscript for the

categories. The ECI and the ECEC are both calculated in two steps. First, compensation

is estimated for each category. Second, the categories are aggregated into the overall

estimate. Both steps differ between the ECI and ECEC.

The ECI, which is designed to remove quarter-to-quarter changes in the

composition of jobs, calculates compensation for each category of labor using an

updating procedure.

[2] w w rit

ECI

it 1

ECI

it = − ×

The variable rit equals average compensation in quarter t divided by average

compensation in quarter t-1 among jobs from category i in the sample for both t and t-1.

Thus, the ECI does not estimate compensation for category i in quarter t by simply

averaging compensation among jobs from the category currently in the sample. Instead,

it updates compensation for quarter t-1 by the growth in compensation between t-1 and t

among a set of matched jobs. Similarly, the category’s compensation in t+1 equals

compensation in t updated by the set of jobs matched between t and t+1, etc.

Because the sample is constantly being replenished, jobs matched between t-1 and

t will not equal jobs matched between t and t+1, etc. However, the updating procedure

ensures that the level of compensation in jobs entering the sample is never compared to

the level of compensation in jobs they replace. Consequently, if the distribution of jobs

in the labor market is moving toward lower-paying jobs, but the growth rate in
5

compensation is the same for all jobs, the ECI will reflect the constant growth rate. It

will not pick up the trend toward lower-compensation jobs, even though jobs entering the

sample tend to have lower compensation than the jobs they replace. The ECI is designed

specifically to chain out such changes in the distribution of the jobs.

In contrast, the ECEC uses no updating procedure. The ECEC simply uses

average compensation among jobs from category i currently in the sample to estimate the

category’s compensation, which is the numerator for the updating ratio in equation [2].

Therefore, the ECEC will reflect a trend in the labor market toward lower or higherpaying jobs.

The second step for both the ECI and the ECEC is to combine the estimates for

the categories of labor into the overall measure. Again, the ECI and ECEC handle the

step differently. The ECI continues to focus on removing composition changes, so the

categories are aggregated using a fixed set of employment weights from a base period,

represented by the Eib terms in equation [1]. In contrast, the ECEC uses current

employment shares for the categories of labor, represented by Eit in equation [1].

III. Empirical Results

Previous studies on the cyclicality of wage rates generally proceed as follows.

They first deflate the average wage series and the uncontaminated series using a price

index. They then regress the deflated series separately on a measure of the business

cycle. The difference in the coefficient estimates for the cyclical measure estimates the

aggregation bias. In contrast, this paper estimates the aggregation bias directly. The log

difference between the ECI and the ECEC is regressed on the unemployment rate, which
6

is used as the measure of the cycle. The coefficient for the unemployment rate gives the

estimate of the aggregation bias. Estimating the aggregation bias directly has the

advantage that any aggregate price index used to deflate both the ECI and ECEC will

cancel out of equation [1]. Thus, the relationship between their log difference and the

unemployment rate can be interpreted as the aggregation bias in average real

compensation as well as average nominal compensation, without the need to introduce a

price index into the estimation.

For the empirical exercises, the ECI and ECEC series begin in March 1986 and

run through December 1997, although March 1986 is defined as 100 for the ECI, so the

sample effectively begins in June 1986. The ECEC was first published in 1987, but the

BLS recently reported estimates for 1986.2

 The BLS publishes the ECEC for March

quarters only, but this paper calculates ECEC estimates for all quarters using the same

procedure. In June 1986, the ECI began using the 1980 Census for the fixed employment

weights, as represented by Eib in equation [1]. In March 1995, the ECI switched to the

1990 Occupation Employment Survey (OES). However, this paper continues to use the

1980 Census weights to avoid a slight break in series. The results are very similar when

the 1990 OES weights are used for the fixed weights throughout the period. Although the

NCS also collects data for workers in state and local government, the results are restricted

to workers in private industries.

The results presented are mainly coefficient estimates for the unemployment rate

from the following regression.

− = α + α + α + δ t + β t + εt εt = ρεt + νt

2

t t o 1 2 [3] ln(I ) ln(W ) t t 'S U ;

 

2

 See Schwenk (1997).
7

The St terms are dummy variables for June, September, and December, so the log

difference between the ECI and the ECEC is regressed on the unemployment rate Ut, a

quadratic time trend, and seasonal dummy variables. The error term is assumed to follow

first-order autocorrelation.

As background, Chart 1 shows the log difference between the ECI and ECEC for

wages and salaries, benefits, and total compensation. Total compensation equals the sum

of wages and salaries and benefits. The log difference is set to zero in March 1986 for

each of the three series. The ECI grew relative to the ECEC for all of them, although the

differential increased the most for benefits. From March 1986 through December 1997,

the ECI grew by 49, 68, and 54 percent for wages and salaries, benefits, and total

compensation, respectively, while the ECEC grew by 39, 41, and 39 percent.

 Superimposed on the right-hand axis of Chart 1 is the unemployment rate. The

unemployment rate series is for private wage and salary workers in all nonagricultural

industries except private households, because it matches the scope of the NCS most

closely. The unemployment rate declines from the beginning of the period through the

end of the 1980s. It then increases to the trough of the business cycle at the end of 1991

and the beginning of 1992. The unemployment rate declines steadily after 1992.

Lettau, Loewenstein, and Cushner (1997) documents the dominant feature in

Chart 1, the divergent growth between the ECI and the ECEC, which suggests a shift

toward lower-compensation jobs. Here, the focus is on the business cycle. As specified

in equation [3], if an expansion in the labor market augments the shift toward lowercompensation jobs beyond the time trend, the aggregation bias is countercyclial.
8

Conversely, if an expansion offsets the longer-term trend, the aggregation bias is

procyclical.

The top third of Table 1 shows estimates of the unemployment rate coefficient in

equation [3] for workers from all private industries. The columns present separate results

for wages and salaries, benefits, and total compensation. For all three dependent

variables, the coefficient estimate for the unemployment rate is negative, although it is

not statistically significant for benefits. The negative estimates suggest the aggregation

bias is countercyclical, so compensation in the typical private job is more procyclical than

average compensation among private workers.

Chart 2 makes the negative comovement between the aggregation bias and the

business cycle more transparent. It plots the residuals of the log difference between the

ECI and ECEC and the unemployment rate from regressions on the quadratic time trend

and the seasonal dummy variables. The residuals for the log difference clearly tend to be

above zero when the residuals for the unemployment rate are below zero, and vice versa.

One exception is during the recession of the early 1990s, when the residual for the

unemployment rate becomes positive a few quarters before the residual for the log

difference becomes negative. However, due to some details of the ECEC calculation, the

aggregation bias might be expected to lag the unemployment rate by at least a quarter or

two. It is actually somewhat surprising how contemporaneous their comovement is. The

next section explores these details of the ECEC more fully.

One way to gauge the magnitude of the coefficient estimates for the

unemployment rate is to compare them to the time trend. The countercyclical

aggregation bias implies that a contraction in the labor market partially offsets the trend
9

toward lower-compensation jobs. Between June 1986 and September 1997, the median

unemployment rate is 5.9, while the maximum is 8.4. For wages and salaries, an increase

in the unemployment rate from 5.9 to 8.4 reduces the expected log difference between the

ECI and the ECEC by 0.01. Equation [3] specifies the time trend as quadratic, but

evaluated at the median for the period, the estimated time trend must be multiplied by 8.1

quarters to equal 0.01. Thus, for wages and salaries, an increase unemployment rate from

the median to the maximum offsets about two years of the trend shift toward lowercompensation jobs.

For benefits and total compensation, the estimates for the unemployment rate

coefficients are smaller in magnitude relative to their time trends. For total

compensation, an increase in the unemployment rate from 5.9 to 8.4 offsets about five

quarters of the trend shift toward lower-compensation jobs. For benefits, where the

coefficient estimate is not statistically significant, the same increase in the unemployment

rate offsets only about two and a half quarters of the time trend. The shorter offset period

for benefits is due at least in part to the stronger trend in the shift toward lowercompensation jobs.

To summarize the results so far, after controlling for trend and seasonal effects,

the aggregation bias is countercyclical, at least for wages and salaries. Thus, movement

in the average compensation in the labor market tends to understate the procyclical

movement of compensation for the typical job.

Panel effects in the ECEC

The analysis so far ignores details of the calculation of the ECEC that potentially

affect the results. As mentioned above, jobs in the NCS sample are scheduled to remain
10

for four to five years after they enter the calculation of the ECI and the ECEC. This

design suits the ECI. The BLS introduced the ECEC as a byproduct of the ECI because

data users wanted a level series in addition to the index series. Ideally, for purposes of

the ECEC, the entire sample would be replenished each quarter. However, the average

overlap for the set of jobs matched between t-1 and t and between t and t+1 was 91

percent for June 1986 through December 1997, so the sample is replenished slowly. At

the lower level of aggregation, compensation for each industry-occupation category

differs between the ECI and the ECEC only to the degree to which the sample is

replenished. Therefore, a general trend in the labor market toward lower-compensation

jobs may show up as cyclical movement if the replenishment scheme of the NCS

corresponds to the business cycle.

Three extensions to the initial results attempt to control for this. First, separate

results are presented for goods-producing and service-producing industries. Second,

direct measures of the replenishment scheme are included in the regressions as control

variables. Third, the ECEC series are replaced by experimental ECEC series, which

attempt to remove panel effects due to sample replacement.

Until recently, the NCS used an industry rotation system. Each quarter, a group

of two-digit industries was chosen to have its sample replaced. All establishments from

these industries left the sample and replacement establishments entered the sample.

Therefore, any split by industry group produces two samples with quite different time

patterns for their replenishment. The bottom two-thirds of Table 1 shows results

separately for goods-producing industries, which are mining, construction, and

manufacturing, and service-producing industries, which are the balance of industries.
11

This split is not on the theoretic grounds that these are separate labor markets or that the

aggregation bias is larger for one industry group than the other. It is merely to compare

two groups with different replenishment schedules. The groups are not equal in size. In

September 1997, service-producing industries contained about three-quarters of

employment, while goods-producing industries contained one-quarter. Also, the

unemployment rate now corresponds to the relevant industry group.

Splitting the sample by industry group has a large effect on the estimate of the

aggregation bias. For the goods-producing industries, the coefficient estimates for the

unemployment rate are small in magnitude and not statistically significant. In contrast,

for service-producing industries, the coefficient estimates for wages and salaries and total

compensation remain statistically significant, and they become larger in magnitude.

Chart 3 shows the residuals after the regression on the time trend and the seasonal

variables for wages and salaries in service-producing industries. As in Chart 2, the

negative comovement between the residuals for the log difference and the unemployment

rate is apparent. In fact, removing the goods-producing industries strengthens the

countercyclical movement of the aggregation bias.

A second test for the effect of the sample replenishment on the results is to

include a direct measure of the replenishment scheme in the regressions as a control

variable. The variable used is the average time in the NCS among quotes in the quarter’s

sample. The percent of overlap between matched jobs from one quarter to the next was

also tried, but the time-in-sample variable seems more appropriate. The log difference

between the ECI and the ECEC is a cumulative measure of the divergence in the two
12

series. Correspondingly, the average time in sample for the jobs is a cumulative measure

of the replenishment scheme.

Chart 4 demonstrates the effect of including the time-in-sample variable. It shows

two sets of residuals for the log difference between the ECI and ECEC for benefits in

goods-producing industries. The first set is from a regression on the quadratic time trend

and the seasonal variables, which determines the statistically insignificant coefficient

estimate in the middle of Table 1. The second set is from the same regression, but with

the average time in the NCS for the quarter’s sample added an explanatory variable. The

residuals without the time-in-sample variable reveal when the manufacturing industries

had their sample replenished, at the end of 1989 and again in 1994. They show a

sawtooth pattern, which is expected for the detrended difference between two series that

differ only because jobs entering the sample have lower compensation than the jobs they

replace. However, including the time-in-sample variables removes the sawtooth pattern.

In fact, the residuals start to show a bit of the cyclical pattern. With the time-in-survey

variable included in equation [3], the coefficient estimate for benefits in goods-producing

industries becomes statistically significant at –0.0032 with a standard error of 0.0014.

For service-producing industries, including the time-in-sample variable has little effect on

the estimates for the unemployment rate coefficient.

The final test for the effect of replenishment uses experimental ECEC series,

which attempt to lessen the panel effects. The update procedure in equation [2] requires a

job to be in the NCS at least one quarter before it enters the calculation of the ECI.

Because the ECEC uses the same production sample as the ECI, jobs enter its calculation
13

with at least a one-quarter lag.3 Therefore, the first experimental ECEC introduces jobs

into its calculation more quickly than the published estimates. However, the estimates

for the unemployment rate coefficients do not change much.

A more radical experimental ECEC uses the quarter of overlap between exiting

and replacement quotes to smooth the transition to the replacement quotes. Assume that,

after accounting for sampling variation, the difference in compensation between the

incoming and outgoing jobs in the overlap quarter represents bias that has accumulated in

the outgoing panel. Assume further that this bias accumulates at a constant rate as the

panel ages. Compensation in previous quarters can then be adjusted by the bias estimate.

This adjustment smoothes the transition to the replacement jobs, and it also helps to

account for the lack of representativeness of the sample due to its infrequent

replenishment.

Table 2 shows estimates for the unemployment rate coefficient after this

experimental ECEC replaces the standard ECEC. Because the adjustment for the bias

becomes available only after the jobs rotate out of the sample, the time period runs only

through June 1994. Even though the time period is shorter, the standard errors for the

coefficient estimates are smaller than in Table 1, which likely results from the smoother

ECEC series. Consequently, the coefficient estimates when the log difference in benefits

is the dependent variable become statistically significant. For wages and salaries, the

magnitude of the coefficient estimates is smaller in Table 2 than Table 1. However, this

 

3

 Beginning in March 1996, the production samples for the ECI and ECEC have differed slightly. Their

difference is due primarily to a treatment of suppression codes. It is not due to a faster introduction of jobs

into the calculation of the ECEC. This paper replicates the ECI and ECEC estimates using programs

written by the Compensation Research Group of the Office of Compensation and Working Conditions at

the BLS. The production samples for these replications are identical.
14

is due in part to the different time period. When the sample is restricted to the shorter

time period, the estimates using the standard ECEC are more similar.

 In summary, although the structure of the ECI sample scheme is not ideal for the

calculation of the ECEC, panel effects do not seem to drive the finding of a

countercyclical aggregation bias. Both incorporating direct measures of the

replenishment scheme and using the experimental ECEC series tends to strengthen, rather

than weaken, the evidence for a countercyclical bias.

Results using the average hourly earnings from the CES

Perhaps the best-known average wage series the BLS produces is the average

hourly earnings series from the Current Employment Survey (CES) program. The results

comparing the ECI and ECEC therefore raise the question of whether a countercyclical

aggregation bias also results from comparing the ECI and the CES.

The ECI must be modified to match the scope and concepts of the CES. When

the log difference between the modified ECI and average hourly earnings from the CES

is the dependent variable in equation [3], the estimate for the unemployment rate

coefficient is actually positive and marginally significant at twelve percent. However, the

positive correlation is due to a mechanical difference between how the two series account

for overtime. The NCS collects overtime hours for a job only when it enters the survey.

Overtime hours are held constant in subsequent quarters. Consequently, the update

procedure in equation [2] ensures that the modified ECI for wages and salaries plus

overtime is virtually identical to the ECI for wages and salaries.
15

Separate regression results for industry groups demonstrate the effect of the

collection of overtime. For nonsupervisory workers in service-producing industries, the

coefficient estimate for the unemployment rate is negative, though not statistically

significant. In contrast, for production workers in manufacturing industries, where

overtime hours are more prevalent, the corresponding coefficient estimate for the

unemployment rate is positive and statistically significant.

The procyclical estimate of the aggregation bias for production workers in

manufacturing is due entirely to the procyclicality of overtime hours in the CES. When

the dependent variable in equation [3] is the log difference between the ECI for wages

and salaries and straight-time hourly earnings from the CES, the estimate for the

unemployment rate coefficient is not statistically significant and very close to zero.

Thus, the procyclical movement of overtime hours in the CES drives the procyclical

estimate for the aggregation bias. There is no additional evidence for either a procyclical

or a countercyclical aggregation bias. However, it may be too much to expect two

surveys with disparate methods of data collection to show more than a long-run

correspondence. Abrahams, Spletzer, and Stewart (1998) describes the calculation of

average hourly earnings from the CES.

IV. Summary

This paper defines aggregation bias as the difference over the business cycle

between compensation in the typical job and average compensation in the labor market.

It compares the Employment Cost Index with the Employer Cost for Employee

Compensation, both of which are based on the same micro data from the National
16

Compensation Survey. The results suggest that the aggregation bias is countercyclical, so

compensation in the typical job is more procyclical than average compensation in the

labor market.
17

References

Abraham, Katharine G. and John C. Haltiwanger. "Real Wages and the Business Cycle."

Journal of Economic Literature, vol. 33 no. 3, September 1995: 1215-1264.

Abraham, Katharine G., James Spletzer, and Jay Stewart. "Divergent Trends in

Alternative Wage Series," forthcoming in Labor Statistics Measurement Issues,

Haltiwanger, Manser, and Topel eds., University of Chicago Press, 1998.

Bils, Mark. "Real Wages over the Business Cycle: Evidence from Panel Data." Journal

of Political Economy, vol. 93 no. 4, 1985: 666-689.

Lettau, Michael K., Mark A. Loewenstein, and Aaron T. Cushner. "Explaining the

Differential Growth Rates of the ECI and the ECEC." Compensation and

Working Conditions, vol. 2 no. 2, Summer 1997: 15-23.

Manser, Marilyn E. "Real Wages Over the Business Cycle: Estimates Using A FixedWeight Wage Index." BLS Working Paper no. 187, June 1988.

Schwenk, Albert E. "Measuring Trends in the Structure and Levels of Employer Costs

for Employee Compensation." Compensation and Working Conditions, vol. 2 no.

2, Summer 1997: 3-14.

Solon, Gary, Robert Barsky, and Jonathon A. Parker. "Measuring the Cyclicality of Real

Wages: How Important is Composition Bias?" Quarterly Journal of Economics,

vol. 109 no. 1, February 1994: 1-25.

Solon, Gary, Warren Whatley, and Ann Huff Stevens. "Wage Changes and Intrafirm Job

Mobility Over the Business Cycle: Two Case Studies." Industrial and Labor

Relations Review, vol. 50 no. 3, April 1997: 402-415.

U.S. Bureau of Labor Statistics. BLS Handbook of Methods, U.S. Department of Labor,

Bulletin 2490, April 1997.

Wilson, Beth Anne. "Movements of Wages Over the Business Cycle: An Intra-Firm

View." Manuscript, Federal Reserve Board, December 1996.
18

Table 1

Regression Results for Log Difference between the ECI and the ECEC

Coefficient Estimates for the Unemployment rate

Wages and Salaries Benefits Compensation

workers in all private industries

unemployment rate -0.0040**

(0.0013)

-0.0034

(0.0028)

-0.0034**

(0.0016)

autocorrelation of residual 0.52 0.63 0.63

number of quarters 47 47 47

workers in goods-producing industries

unemployment rate -0.0009

(0.0018)

-0.0022

(0.0029)

-0.0013

(0.0020)

autocorrelation of residual 0.70 0.61 0.66

number of quarters 47 47 47

workers in service-producing industries

unemployment rate -0.0078**

(0.0016)

-0.0050

(0.0039)

-0.0068**

(0.0020)

autocorrelation of residual 0.39 0.58 0.52

number of quarters 47 47 47

Standard errors are in parentheses; * indicates statistical significance at 10%; ** indicates statistical

significance at 5%. All regressions also include a quadratic time trend and seasonal dummy variables.
19

Table 2

Regression Results for Log Difference between the ECI and the

Experimental ECEC

Coefficient Estimates for the Unemployment rate

Wages and Salaries Benefits Compensation

workers in all private industries

unemployment rate -0.0021**

(0.0009)

-0.0036**

(0.0010)

-0.0025**

(0.0008)

autocorrelation of residual 0.40 0.32 0.32

number of quarters 33 33 33

workers in goods-producing industries

unemployment rate -0.0005

(0.0006)

-0.0019**

(0.0005)

-0.0011**

(0.0004)

autocorrelation of residual 0.32 -0.04 0.07

number of quarters 33 33 33

workers in service-producing industries

unemployment rate -0.0044**

(0.0015)

-0.0075**

(0.0020)

-0.0050**

(0.0014)

autocorrelation of residual 0.42 0.44 0.44

number of quarters 33 33 33

Standard errors are in parentheses; * indicates statistical significance at 10%; ** indicates statistical

significance at 5%. All regressions also include a quadratic time trend and seasonal dummy variables.
20

Chart 1

Unemployment Rate and Log Difference Between ECI and ECEC

Workers in All Private Industries

0

0.080.060.040.02

0.1

0.180.160.140.12

0.2

Jun-86

Dec-86

Jun-87

Dec-87

Jun-88

Dec-88

Jun-89

Dec-89

Jun-90

Dec-90

Jun-91

Dec-91

Jun-92

Dec-92

Jun-93

Dec-93

Jun-94

Dec-94

Jun-95

Dec-95

Jun-96

Dec-96

Jun-97

Dec-97

quarter

log difference

98.587.576.565.554.54

unemployment rate

wages and salaries benefits compensation unemployment rate
21

Chart 2

Unemployment Rate and Log Difference Between ECI and ECEC

Workers in All Private Industries

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

Jun-86

Dec-86

Jun-87

Dec-87

Jun-88

Dec-88

Jun-89

Dec-89

Jun-90

Dec-90

Jun-91

Dec-91

Jun-92

Dec-92

Jun-93

Dec-93

Jun-94

Dec-94

Jun-95

Dec-95

Jun-96

Dec-96

Jun-97

Dec-97

quarter

detrended log difference

21.510.50-0.5-1-1.5-2

detrended unempl. rate

wages and salaries unemployment rate
22

Chart 3

Unemployment Rate and Log Difference Between ECI and ECEC

Workers in Service-Producing Industries

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

Jun-86

Dec-86

Jun-87

Dec-87

Jun-88

Dec-88

Jun-89

Dec-89

Jun-90

Dec-90

Jun-91

Dec-91

Jun-92

Dec-92

Jun-93

Dec-93

Jun-94

Dec-94

Jun-95

Dec-95

Jun-96

Dec-96

Jun-97

Dec-97

quarter

detrended log difference

1.510.50-0.5-1-1.5

detrended unempl. rate

wages and salaries unemployment rate
23

Chart 4

Detrended Log Difference Between ECI and ECEC

Workers in Goods-Producing Industries

-0.01-0.02-0.03-0.04

0

0.040.030.020.01

Jun-86

Dec-86

Jun-87

Dec-87

Jun-88

Dec-88

Jun-89

Dec-89

Jun-90

Dec-90

Jun-91

Dec-91

Jun-92

Dec-92

Jun-93

Dec-93

Jun-94

Dec-94

Jun-95

Dec-95

Jun-96

Dec-96

Jun-97

Dec-97

quarter

detrended log difference

benefits benefits (average time in NCS included)