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ESTIMATES OF YEAR-TO-YEAR CHANGE IN COSTS PER HOUR

WORKED FROM THE EMPLOYER COSTS FOR EMPLOYEE

COMPENSATION SURVEY

INTRODUCTION

The Bureau of Labor Statistics (BLS) annually publishes cost level estimates for

employee pay and benefits, known as the Employer Costs for Employee Compensation

(ECEC). These cost levels are derived from the Employment Cost Index (ECI), a

quarterly measure of the rate of change in employee compensation. Unlike the ECI, which

is a Laspeyres, fixed-weight index that eliminates the effects of employment shifts over

time among major occupational groups and industries, the ECEC cost level estimates

reflect current employment distributions.

This article presents, for the first time, estimates of year-to-year change in the

ECEC costs-per-hour-worked of the components of compensation for private industry

workers, by industry division and occupational group, and the corresponding standard

errors, together with an analysis of the change estimates and how they compare to ECI

12-month percent change and associated standard errors. This article also includes a brief

review of the ECEC estimation methodology and sample design, along with an

explanation of the balanced-repeated replication method of standard error computation

which was used with the ECEC change estimates.

ECEC cost levels measure average compensation levels, whereas ECI indexes

measure average change in compensation costs. The ECI was specifically intended to

track the rate of change of wages and benefit costs, but some have tried using annual

changes in the ECEC, which provides information on actual cost levels for each

component of compensation, to accomplish the same goal. As expected, changes in

ECEC estimates vary from the ECI estimates of change for the same period, due to

different estimation methodology. Over the past decade, ECEC wage and benefit levels

have generally grown at a slower rate than ECI wage and benefit indices.

METHODOLOGY AND SAMPLE DESIGN

Both the Employment Cost Index and Employer Costs for Employee

Compensation share compensation data obtained from a single sample of establishments.

BLS economists obtain wage and benefit information quarterly from each establishment in

the ECI survey sample. In order to measure compensation trends uninfluenced by

employment shifts among occupational groups and industries, the Bureau calculates the

ECI with fixed employment weights, which since December 1994, have been the 1990

employment counts from the BLS’s Occupational Employment Survey. (From June 1986

through December 1994, employment counts from the 1980 Census of Population were

used.) In addition to employment weights, the ECI uses sample weights (the weight of the

establishment occupation in the sample) which reflect both employment in each
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establishment occupation and the probability of selection of the occupation within the

establishment.

These sample weights are the product of the reciprocal of the probability of

selection of the sample establishment, the sampling interval used in the occupational

selection, and a nonresponse adjustment factor. The sample weights are used to obtain

estimates within a fixed employment weighting cell, while the fixed employment weights

(described above) are used for estimation across these cells.

The ECI covers all occupations within the private economy (excluding farms,

households, and the self-employed) and the public sector (excluding the Federal

Government). In March 1996, the ECI sample included about 17,000 occupations within

4,100 firms in the private sector and about 5,000 occupations within nearly 900

establishments in State and local governments.

Establishment sample

BLS statisticians draw the sample of ECI establishments on a probability basis by

industry from State unemployment insurance and supplementary files. Industry

classification, based on the 1987 Standard Industrial Classification (SIC), as defined by the

U.S. Office of Management and Budget, is usually categorized at the 2-digit SIC level.

The probability of selection is proportionate to an establishment’s relative employment

size within the industry.

After 4 to 5 years of ECI data collection, BLS statisticians replace the industry

sample in order to reduce the burden on respondents and to keep the sample frame as

current as possible. Total sample replacement is gradual, with a set of industries replaced

each calendar quarter. The design of this rotation scheme is such that, in absence of

typical nonsampling errors, such as those produced by nonresponse, the subsample of

quotes with data for both the current and prior quarters properly represents all

occupations covered by ECI. In addition, for industries not replaced in a given year, BLS

statisticians select a sample of newly-created establishments (birth quotes) to represent

establishments that have come into existence since the date of the industry sample frame.

In 1996, the BLS Statistical Methods Group introduced a new cross-industry sample

replenishment scheme for the ECI, instead of industry-by-industry. Unlike previously,

when there was no geographical clustering, this new ECI design is primary sample unit

(PSU) based, grouped according to metropolitan statistical areas and non-metropolitan

counties.

Occupational sample

Sampling occupations at the most narrowly-defined level in each establishment

follows the drawing of the industry sample of establishments for the ECI survey. As is the

case with establishment sampling, sample selection for occupations within establishments

is on a probability-proportionate-to-employment basis.

During the initial personal visit to collect wage and benefit data, a BLS

representative samples occupations. The field economist targets a specific number

(depending on establishment employment) of narrowly-defined occupations, with the

probability of occupational selection proportionate to the occupational employment size

within the establishment. Since June 1986, the ECI survey utilized the occupational
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definitions used in 1980 Census, based on the Standard Occupational Classification (SOC)

system.

The sample weight of a selected occupation is constant during the entire time that

it remains in the ECI sample. Thus, ECI estimates for a given period do not strictly reflect

the current employment of that period. At the same time, between twenty and twenty-five

percent of the ECI sample is replenished every year.

Computing cost levels

Prior to computing the average cost level estimates at aggregate levels, it is

necessary to convert wages and salaries to a straight-time hourly rate, and benefit costs to

the cost per hour worked.

Cost level estimation at aggregate levels involves the application of a separate

adjustment factor to the ECI sample weights in each industry, in order to force the

estimates of employment in the industry to agree with the independent counts. These

counts are derived from BLS Current Employment Statistics (CES) data. The numerator

of this factor is the CES employment count in the industry, and the denominator is the ECI

estimate of this employment using the sample weights (prior to this adjustment). Adjusted

weights, used to compute cost level estimates, are the product of multiplying the

adjustment factor with the sample weights for each industry. This adjustment process is

referred to as benchmarking.

The formula for the estimated cost level for total compensation, wages and

salaries, or benefits for a domain D such as major industrial division or major occupational

group, denoted X$

 is:

X$ = 

( )

( )

i q i q

i q

W Y

W

i q D

i q D

, ,

,

( , )

( , )

∈

∈

∑

∑

where:

Wi,q is the adjusted weight for the qth quote in the ith establishment.

Yi,q

 is the mean compensation, wages and salaries, or benefits for the qth quote in the ith

establishment.

Computing the index

A standard Laspeyres fixed-employment-weighted index, the ECI wage index is

the weighted average of the cumulative wage changes within each cell (generally a major

occupational group in a 2-digit SIC industry), with base-period wage bills as the fixed

weights for each cell. The base-period wage bill is the fixed employment weights from the

Census multiplied by the sample-weighted average wage in the base period of June 1989.

Index computation for benefits and total compensation proceeds similarly. The formula

for the index for quarter t, denoted I

t,

 is:
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I

t

 = 

( )

( )

o i t i

o i

W M

W

, ,

,

∑

∑

 * 100

where:

Mt,i = Mt-1,i * Rt,i, and is the cumulative average wage change in the ith cell from time 0

(base period) to time t (current quarter).

Rt,i is the ratio of the current-quarter weighted average wage in the cell to the priorquarter weighted average wage in the cell, both calculated using matched

establishment/occupation wage quotations. The weights applied are the sample weights.

Wo,i is the estimated base-period (June 1989) wage bill for the ith cell. The wage bill is

the average wage of workers in the cell, estimated from the June 1989 ECI, multiplied by

the number of workers represented by the cell (the census weight).

Reliability of the estimates

The method used for computing the standard errors for both the 12-month percent

change in the ECI and the ECEC cost levels change is called "balanced-repeated

replication." This involves the division of each industry sample into a number of variance

strata, and then the further division of each sample in every variance stratum into halfsamples. Replication of cost level or percent change estimates 64 times follows, using

data from one half-sample from each stratum, instead of the data from both half-samples.

Each of the 64 replicates has a different combination of half samples. Subtracting the 64

prior year replicates from the 64 current year replicates yields the 64 year-to-year change

replicates. Then, calculation of the standard error (the square root of the variance) is

possible for the year-to-year change using the 64 change replicates.

The formula used for estimating the variances, VAR ( X$

), and in turn the standard

errors, for change in cost levels is:

VAR( X$

) = ( )

2

1

64

64 i

x xo

i

∑ −

=

where:

xo is the full sample change in level estimate for some characteristic; and

xi is the ith half-sample change in level estimate for the same characteristic.

The formula used for estimating the variances, and in turn the standard errors, for

the index percent changes is:

VAR t o

s o

I

I

,

,

















 = 

2

1

64

64 t i

s i

t o

s o

I

I

I

i I

,

,

,

,

−













 ∑ 

=

where:
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t o

s o

I

I

,

,

is the change in the index for some characteristic from time s to time t calculated

using the full sample; and

t i

s i

I

I

,

,

 is the change in the index for the same characteristic from time s to time t calculated

using the ith balanced half-sample.

RESULTS

Table 1 shows ECEC year-to-year changes in private industry total compensation,

wages and salaries, and benefit costs, and associated standard errors. Between March

1995 and March 1996, total compensation increased 40 cents, with a standard error of 9

cents, to a level of $17.49. In percentage terms, as summarized in Table 4, total

compensation grew 2.3 percent, with a standard error of 0.5 percent. During the same

period, wages and salaries increased 2.7 percent and benefits 1.2 percent, and both of

these estimates had a standard error of 0.6 percent. The difference between the percent

increase in wages and benefits is significant at the 0.1 level of significance, but not at the

.05 level of significance.

In addition to comparing estimates of 12-month change, we computed long term

change estimates. Because there is no overlap in the samples which are more than 5 years

apart, the covariance term in the formula for the variance of the difference of estimates at

least that far apart is zero. This allows using the square root of the sum of the two

variance estimates of the cost levels to estimate the standard error of change. The relative

errors of the levels of cost estimates are published in the yearly bulletin Employment Cost

Indexes and Levels, 1975-1996. This is in contrast to the variances for the 12-month

changes which are computed as described in the previous section in order to incorporate

the covariance term.

The ten-year change, ending in March 1996, in total compensation was $4.07 with

a standard error of 23 cents. For total benefits, the ten year change was $1.31 with a

standard error of 8 cents, while for wages and salaries the change was $2.75 with a

standard error of 16 cents. In percentage terms, benefits grew faster than wages and

salaries, 36.5 percent and 28 .0 percent respectively, with the difference significant at the

.05 level of significance.

Table 2 and Table 3 show ECEC year-to-year change in employer costs per hour

worked for employee compensation and their corresponding standard errors by major

industrial division and major occupational group respectively. The March 1995-March

1996 change in total compensation costs for the individual goods-producing industries

ranged numerically from $.21 to $.89. The corresponding changes in the serviceproducing industries ranged numerically from $.22 to $1.20. Despite that numerically

there is a large range among the individual industries, one cannot draw any meaningful

statistical conclusions about these differences, even at the .1 level of significance.

Likewise, for individual white-collar, blue-collar, and service occupations, cost level
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changes for total compensation ranged numerically from -$.01 to $1.00. Again, we did

not detect any significant differences among each of the individual occupational groups.

We also compared in broader terms the aggregate goods-producing industry to the

aggregate service-producing industry over the most recent one year period and the

aggregate white-collar, blue-collar and service occupations. Unfortunately, we have not

computed the standard error for these aggregate groupings using the approach described

in the previous section and were forced to calculate the standard error for the change as

the square root of the sum of the variance estimates of the cost levels, which tends to

overestimate the standard error because it does not subtract out the effect of the

covariance term. We found that for the year ending March 1996, the goods-producing

industry division increased $.52 with a standard error of $.57, while service-producing

cost levels increased $.40 with a standard error of $.25. The aggregate white-collar, blue

collar, and service occupations increased $.60, $.35 and $.22, respectively, with standard

error of $.40, $.32, and $.14, respectively. Neither the differences between these

aggregate industries nor among these aggregate occupational groups were statistically

significant, even at the .1 level of significance.

However, over a 10-year period, such comparisons do yield differences that are

statistically significant. Total compensation costs for the goods-producing industry grew

$5.41 for the 10-year period ending in March 1996, while service-producing cost levels

increased $3.87, with standard errors of $.49 and $.25, respectively. For the same period,

white-collar workers total compensation increased $5.54, while that of blue-collar workers

increased $3.61 and service workers increased $2.18, with the three corresponding

standard errors, $.39, $.28 and $.14 respectively. At the .05 level of significance, the

increase in compensation for goods-producing industries was significantly larger than for

service-producing industries. While, as ascertained by a multiple comparisons test, the

increase for white-collar workers was larger than that for blue-collar workers, which in

turn was larger than that for service workers.

ECEC and ECI Compensation Levels and Trends

Over the period, March 1986-96, private industry compensation costs rose 40.5

percent as measured by the ECI and 30.3 percent as measured by the change in cost levels,

with standard errors of 2.2 and 1.9, respectively. The growth in wages and salaries

amounted to 35.2 and 28.0 percent, for the ECI and cost levels, with standard errors of

2.9 and 1.9, respectively, while benefits rose 54.9 and 36.5 percent with standard errors of

2.2 and 2.4, respectively. In annual terms, these increases correspond to an annual growth

rate of 3.1 for wages and salaries, and 4.5 percent benefits for the ECI indices, while the

annual growth rate for the ECEC levels was 2.5 percent for wages and salaries, and 3.2

percent for benefits. The differences in percent change between the ECI and the ECEC for

compensation, wages and salaries, and benefits were all significant at the .05 level of

significance.

Table 4 shows trends in compensation of private industry workers, measured by

12-month dollar changes and percent changes in the ECEC and percent changes in the

ECI and their corresponding standard errors. Although these differences between the ECI

and ECEC are significant over the long term, they are not significant over the 12-month

period from March 1995-1996. For example, from March 1995 to March 1996, the
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ECEC compensation costs increased 2.3 percent, with a standard error on the difference

of 0.51 percent. The ECI 12-month percent change ending in March 1996 was 2.7

percent, with a standard error on the difference of 0.27 percent

Various factors have been suggested to explain this divergent behavior of the ECI

and the ECEC, including differences in the way the two measures are constructed, the sets

of weights used, and the way the data are linked from quarter to quarter. A key difference

between the ECEC and the ECI is the issue of matched quotes. When computing

quarterly change, the ECI only uses quotes for which data were collected in two

consecutive quarters. The ECEC on the other hand, estimates levels using quotes in the

sample for a particular quarter only. Because about one-fifth of the sample is replaced

each year, approximately 20 percent of the quotes in the sample one year are not in the

sample the following year. Hence, there is not a perfect overlap in quotes used in

estimating 12-month change.

Lettau, Lowenstein, and Cushner in “Explaining the Differential Growth Rates in

the ECI and ECEC”, analyze the two main steps in the calculation of the ECI and ECEC.

Step 1, combining all of the job quotes within a given cell to obtain a cell average, yields

different estimates for ECI and ECEC, particularly due to the matched quote issue

described above. This is because incoming jobs have tended to offer lower wages and

benefits than outgoing jobs, and the increases in ECEC level estimates would therefore be

expected to be lower than the annual ECI change. The same authors in “Sample

Replacement in the ECI” conclude that about half of the difference between the wages of

incoming and outgoing jobs can be explained by differences in these jobs’ observable

characteristics, that is establishment size, unionization, and work schedule (part-time/fulltime).

Step 2, combining cell means to obtain final estimates, involves fixed weights for

the ECI, while the ECEC uses CES weights. By isolating the two steps in the process,

they determined that at least one-third of the divergence of the ECI and ECEC is

attributable to differences in the way the job quotes are aggregated to obtain the cell

means, and at least one-third is attributable to differences in the way cell means are

aggregated.

Finally, the answer to the question about which survey, the ECEC or the ECI, is

appropriate for measuring the rate of change must be determined by the needs of the user.

If a user prefers a measure of change, which maintains fixed employment distribution by

industry and occupation group, the ECI provides an appropriate measure. Conversely, if

the user wants the survey which measure rates of change accounting for changes in the

employment distribution, the ECEC is more appropriate. However, if the user desires an

estimate of change which both keeps the employment distribution fixed by industry and

occupation group, but incorporates change arising from new jobs in the same weighting

cell, then an estimator would have to be developed, which does Step 1 above using the

ECEC approach and Step 2 using the ECI approach.

Any opinions expressed in this paper are those of the author and do not constitute

policy of the Bureau of Labor Statistics.
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References

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, Summer 1997, pp. 15-23.

Lettau, Michael K., Mark A. Loewenstein, and Aaron T. Cushner, “Is the ECI Sensitive to

the Method of Aggregation?,” Compensation Research and Program Development Group

Working Paper, 1996.

Lettau, Michael K. and Mark A. Loewenstein, “Sample Replacement in the ECI,”

Compensation Research and Program Development Group Working Paper, 1996.

Miller, Rich, “Employment Cost Index Under Scrutiny Ahead of Federal Open Market

Committee,” Reuters Financial Report, May 19, 1997.

Nathan, Felicia “Analyzing Employers’ Costs for Wages, Salaries, and Benefits,” Monthly

Labor Review, October 1987, pp. 3-11.

O’Connor, Karen and Wong, William, “Measuring the Precision of the Employment Cost

Index,” Monthly Labor Review, March 1989, pp. 29-36.

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

for Employee Compensation,” Compensation and Working Conditions, Summer 1997,

pp. 3-13.

Schwenk, Albert E., “Introducing new weights for the Employment Cost Index,” Monthly

Labor Review, June 1985, pp. 22-27.

Schwenk, Albert E., “Introducing 1990 Weights for the Employment Cost Index,”

Compensation and Working Conditions, June 1995, pp. 1-5.

Sheifer, Victor, “Employment Cost Index: a measure of change in the ‘price of labor’.”

Monthly Labor Review, July 1975, pp. 3-12.

Wood, G. Donald, “Estimation Procedures for the Employment Cost Index,” Monthly

Labor Review, May 1982, pp. 40-42.

U.S. Department of Labor, Bureau of Labor Statistics, “Employment Cost Index,”

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Bulletin 2239, 1986.
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