17 Compensation and Working Conditions Spring 1998

Analyzing Year-to-Year

Changes in Employer

Costs for Employee

Compensation

BLS recently completed research on the significance of differences

in the year-to-year change in employer costs for employee compensation among compensation components, occupational groups,

and industries. It also looked at the significance of those differences as compared to change measured by the Employment Cost

Index.

BY MARTHA A.C. W ALKER

AND BRUCE J. BERGMAN

Martha A.C. Walker is a mathematical statistician in the Statistical Methods Group, Bureau

of Labor Statistics. Telephone (202) 606-6138.

She presented these findings in August 1997 at

the annual American Statistical Association

Joint Statistical Meeting.

Bruce J. Bergman is an economist in the Office

of Compensation and Working Conditions, Bureau of Labor Statistics. Telephone (202) 606-

6179.

The Employer Costs for Em

ployee Compensation (ECEC)

Survey provides estimates of

pay and benefits costs levels, whereas

the Employment Cost Index (ECI)

measures the rate of change in employee compensation. Recent studies

have addressed why measured changes

in ECEC estimates, published annually, frequently differ from ECI

changes, published quarterly, but until now, measures of the statistical significance of year-to-year changes in

ECEC estimates were unavailable.

Derived from the ECI data source,

ECEC cost level estimates reflect current employment distributions. This

contrasts with the ECI, a Laspeyres,

fixed-weight index, that eliminates the

effects of employment shifts over time

among major occupational groups and

industries. For the 10-year period ending in March 1996, total compensation increased by 30.3 percent as measured by change in the ECEC and 40.5

percent as measured by the ECI.

To help explain this difference, the

BLS Statistical Methods Group calculated standard errors1 on estimates of

year-to-year change in the ECEC

costs-per-hour-worked of the components of compensation for private industry workers, by selected industrial

divisions and occupational groups.

With the use of these data, it is now

possible to analyze differences among

published change estimates and how

they compare to annual changes in the

ECI.

The results, as summarized in table

1, indicate that differing levels of

change among industrial and occupational groups in the ECEC from March

1995 to March 1996 usually were not

statistically significant.2 Over the long

term, however, differences were significant. This pattern held for compensation components, selected industries, and occupational groups.

Methodology

The method used for computing the

standard errors for the 12-month percent change in the ECI and the ECEC

cost levels is called “balanced-repeated

replication.” This approach allows the

covariance term due to the overlap in

samples to be efficiently incorporated.
 Compensation and Working Conditions Spring 1998 18

The first step of the process is to collapse sampling strata into a number

of variance strata. This is followed by

dividing each industry sample in every variance stratum into half-samples.

Data from one half-sample from

each stratum, instead of data from both

half-samples, are then used to calculate replicate samples for each estimate. For ECEC levels data, there is

replication of estimates 64 times. Each

of the 64 replicates has a different combination of half samples. The standard error is then calculated by taking

the square root of the average variance

for the 64 replicates.

The standard error for ECEC yearto-year change is computed similarly.

After calculating replicate samples for

each year’s estimates, the 64 prior-year

replicates are subtracted from the 64

current-year replicates to yield 64 yearto-year change replicates. Then, the

standard error of the year-to-year

change is calculated by taking the

square root of the average variance for

the 64 change replicates.

The formula used for estimating the

variances, VAR ( X$ ), and in turn the

standard error 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

error 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:

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.

Trends in components of compensation

Table 2 shows ECEC year-to-year

cost changes in private industry total

compensation, wages and salaries, and

benefits, and associated standard errors. Between March 1995 and March

1996, as summarized in table 3, total

compensation increased $0.40, with a

standard error of $0.09, to a level of

$17.49.

Note that using table 2, the 1996

level estimate of $17.49 minus the

1995 level estimate of $17.10 yields

$0.39. Due to the way each estimated

replicate is subtracted, several rounding differences of $0.01 occur in the

estimates.

Table 3 also summarizes the 95-

percent confidence intervals which

aid in determining statistical significance. These data can be used to

determine if wage and salary costs

increased faster than benefit costs.

The 95-percent confidence interval

for wages and salaries does not overlap with the 95-percent confidence

interval for benefits, thus the higher

increase in wage cost levels is statistically significant.

Along with the level data in table 3

is a summary of the percent change

data. The percent change is calculated

using the replicates by dividing the

current year level estimate by the prior

year estimate and then subtracting one.

Table 3 shows that the percent change

translates into overlapping the 95-percent confidence intervals for both

wages and salaries and for benefits.

Thus, the difference between the percent increases is not statistically significant with 95 percent confidence.

It is necessary to determine at what

confidence level the differences are statistically significant. The following

calculations demonstrate that the differences are statistically significant at

the 0.1 level.

To compute the 95-percent statistical significance:

Cumulative normal distribution

value, d = 1.96

variance = standard deviation

squared

Table 1. Tests of significance, comparisons using year-to-year change in the ECEC

ECEC components of compensation

 Wages compared to benefits1 NO YES YES YES

ECEC occupational groups

 White collar compared to blue collar2 NO NO YES YES

ECEC industry divisions

 Goods producing compared to

 service producing2 NO NO YES YES

ECEC compensation compared

 to ECI compensation1 NO NO YES YES

Level of significance

Data comparison 1995-96 change 1987-96 change

0.05 0.1 0.05 0.1

1 For this comparison, the balanced-repeated

replication method was used to compute the

standard error of the 1995-96 change, and the

square root of the sum of two variance estimates

for the 1987-96 change.

2

 For this comparison, the square root of the

sum of two variance estimates was used to

compute standard errors for both the 1995-96

change and the 1987-96 change.
19 Compensation and Working Conditions Spring 1998

Table 3. ECEC changes in total compensation, wages and salaries, and benefits, private industry workers, year ending March 1996

Total compensation...................................................... 0.40 0.09 0.23 0.57 2.3 0.5 1.3 3.3

 Wages and salaries ................................................. 0.34 0.07 0.21 0.47 2.8 0.6 1.6 3.9

 Benefits ................................................................... 0.06 0.03 0.00 0.12 1.3 0.6 0.1 2.5

Level change Percent change

95-percent

confidence interval

95-percent

confidence interval 1995-96

change

Standard

error

Lower Lower Upper Upper

Standard

error

1995-96

change

Compensation component

Table 2. Trends in compensation for private industry workers, measured by changes in Employer

Costs for Employee Compensation and the Employment Cost Index, March 1986-96

Survey and

compensation component

Year ending March

1987 1988 1989 1990 1991 1992 1993 1994 1995 1996

ECEC

Total compensation:

Cost level ...................... $13.42 $13.79 $14.28 $14.96 $15.40 $16.14 $16.70 $17.08 $17.10 $17.49

12-month dollar change ........ .18 .36 .48 .69 .43 .73 .56 .38 .02 .40

Standard error .................. .21 .14 .08 .11 .09 .12 .09 .08 .14 .09

12-month percent change ..... 1.3 2.7 3.5 4.8 2.9 4.8 3.5 2.3 .1 2.3

Standard error .................. 1.6 1.1 .6 .8 .6 .8 .5 .5 .8 .5

 Wages and salaries:

Cost level ...................... $9.83 $10.02 $10.38 $10.84 $11.14 $11.58 $11.90 $12.14 $12.25 $12.58

12-month dollar change ........ .16 .19 .35 .47 .29 .45 .32 .24 .11 .34

Standard error .................. .16 .11 .06 .08 .06 .08 .07 .06 .10 .07

12-month percent change ..... 1.7 2.0 3.5 4.5 2.7 4.0 2.7 2.0 .9 2.8

Standard error .................. 1.7 1.2 .6 .8 .6 .7 .6 .5 .8 .6

 Benefits:

Cost level ...................... $3.60 $3.77 $3.90 $4.13 $4.27 $4.55 $4.80 $4.94 $4.85 $4.91

12-month dollar change ........ .01 .17 .13 .23 .14 .29 .25 .14 -.09 .06

Standard error .................. .06 .04 .03 .04 .03 .04 .03 .03 .05 .03

12-month percent change ..... .4 4.8 3.5 5.8 3.3 6.7 5.4 3.0 -1.9 1.3

Standard error .................. 1.6 1.0 .7 1.0 .8 1.0 .6 .6 .9 .6

ECI

Total compensation:

Index level .................... 91.0 94.5 98.8 103.9 108.5 113.1 117.1 121.0 124.5 127.9

12-month percent change ..... 3.2 3.8 4.6 5.2 4.4 4.2 3.5 3.3 2.9 2.7

Standard error .................. .3 .2 .3 .2 .2 .2 .3 .2 .2 .3

 Wages and salaries:

Index level .................... 92.0 95.0 99.0 103.2 107.3 110.9 113.9 117.2 120.6 124.4

12-month percent change ..... 3.1 3.3 4.2 4.2 4.0 3.4 2.7 2.9 2.9 3.2

Standard error .................. .4 .2 .4 .3 .2 .3 .3 .2 .3 .4

 Benefits:

Index level .................... 88.2 93.4 98.4 105.5 111.6 118.6 125.2 130.7 134.5 136.6

12-month percent change ..... 2.8 5.9 5.4 7.2 5.8 6.3 5.6 4.4 2.9 1.6

Standard error .................. .3 .3 .2 .3 .4 .2 .3 .3 .4 .3

NOTE: Cost levels are in current dollars. Index levels and change

unadjusted for seasonality, and reflect a base of June 1989=100.

Several rounding differences of $0.01 exist among the dollar

changes as a result of the estimation method used.
 Compensation and Working Conditions Spring 1998 20

If |x-y| > 1.96*(standard

deviation of x-y) then statement is

valid,

xi = 2.8; SE = 0.6; variance of

x = 0.6*0.6 = 0.36

yi = 1.3; SE = 0.6; variance of y

= 0.6*0.6 = 0.36

standard deviation of x-y =

0.8485

|x-y| > 1.96*(standard deviation

of x-y)

2.8–1.3 > 1.96*(0.8485)

1.5 > 1.663

Therefore, the statement that the

percentage increase in wage cost levels is greater than that of benefits is

not valid at the .05 level of significance.

However, at the 90-percent confidence level, d-value is 1.645

|x-y| > 1.645*(standard deviation of x-y)

2.8–1.3 > 1.645*(0.8485)

1.5 > 1.396

Therefore, the statement is valid at

the 0.1 level of significance.

In percentage terms, from March

1995 to March 1996, total compensation grew 2.3 percent, with a standard

error of 0.5 percent. During the same

period, wages and salaries increased

2.8 percent and benefits 1.3 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.

These results differ from similar

comparisons for the 10-year period

ending in March 1996, as summarized

in table 4. For comparisons which are

more than 5 years apart, there is no

overlap in the samples. Thus, the balanced-repeated replication method of

variance estimation is not required. In

other words, the covariance term in the

formula for the variance of the difference of estimates, at least 5 years 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.3

The 10-year change, for the period

ending in March 1996, in total compensation was $4.07 with a standard

error of $0.23. For benefits, the 10-

year change was $1.31, with a standard error of $0.08; for wages and salaries, the change was $2.75, with a

standard error of $0.16. 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 5 shows ECEC year-to-year

percentage change among specific

benefit categories and corresponding

standard error. Year-to-year change

in health insurance was significantly

higher than life insurance from 1991

to 1994. There was no significant difference, however, between life and

health insurance for the years ending

March 1995 and 1996.

Trends among industry divisions

and occupational groups

Table 6 shows ECEC year-to-year

changes in employer costs-per-hourworked for employee compensation

and corresponding standard error by

major industrial division and major

occupational group. Table 7 shows that

the March 1995-96 change in total

compensation costs for the individual

goods-producing divisions ranged numerically from $0.21 to $0.89. The

corresponding changes in the serviceproducing divisions ranged numerically from $0.22 to $1.20.

The 95-percent confidence interval

for each estimate is calculated as follows:

x d ikxi ± σ2

where, i = 1, ..., k

σ xi

2

 = variance of xi

dk = 1.96 when comparing

two estimates, i.e., k = 2

dk = multiplication factor

which is provided in the table

below for values of k from 3

to 20.4

k dk

3 2.39

4 2.50

5 2.58

6 2.64

7 2.69

8 2.73

9 2.77

10 2.81

11 2.84

12 2.87

13 2.89

14 2.91

15 2.94

16 2.96

17 2.97

18 2.99

19 3.01

20 3.02

Although there is a large numeric

range among the individual industrial

divisions, no meaningful statistical

conclusions about these differences can

be drawn, even at the 0.1 level of significance. Likewise, white-collar,

blue-collar, and service occupational

groups show cost level changes for

Table 4. ECEC changes in total compensation, wages and salaries, and benefits, private industry, 10 years ending March 1996

Total compensation...................................................... 4.07 0.23 3.62 4.52 30.3 1.9 26.5 34.0

 Wages and salaries ................................................. 2.75 0.16 2.43 3.07 28.0 1.9 24.2 31.7

 Benefits ................................................................... 1.31 0.08 1.16 1.46 36.5 2.4 31.9 41.1

95-percent

confidence interval

Lower Upper

Standard

error

1987-96

change

Level change Percent change

95-percent

confidence interval

Lower Upper

1987-96

change

Standard

error

Compensation component
21 Compensation and Working Conditions Spring 1998

Table 5. Estimates of year-to-year percent change in employer costs-per-hour-worked for employee benefits, private

industry, and corresponding standard errors, 1986-96

Paid benefit

1986-87 1987-88 1988-89 1989-90 1990-91

Percent

change

Standard

 error

Percent

change

Standard

 error

Percent

change

Standard

 error

Percent

change

Standard

 error

Percent

change

Standard

 error

Leave ....................................... 0.5 2.8 4.4 1.3 3.2 0.9 2.4 1.2 2.3 1.2

Vacation ................................ 1.4 3.3 4.0 1.2 3.1 1.1 2.3 1.3 2.0 1.3

Holiday .................................. -1.9 2.7 4.1 1.3 3.0 1.0 2.0 1.2 2.6 1.2

Sick leave ............................. 2.3 3.8 5.1 2.0 2.8 1.6 1.8 2.2 2.7 1.6

Other leave ........................... 6.7 5.7 10.7 3.5 5.9 4.3 8.8 3.0 3.3 3.2

Supplemental pay ................... 5.7 2.0 3.7 2.5 2.9 2.0 9.6 4.0 -3.5 3.1

Premium pay ........................ -1.0 2.2 5.8 1.9 2.1 2.0 -3.6 2.6 4.2 1.7

Shift pay ................................ -3.8 5.8 10.1 4.2 14.3 4.5 -3.5 3.4 7.3 2.2

Nonproduction bonuses ........ 20.7 5.9 -1.3 5.8 -.1 4.2 34.8 10.8 -15.0 6.3

Insurance1 ............................... -1.6 1.9 7.9 1.3 9.4 1.2 8.0 1.4 9.3 1.3

Life ........................................ ––––––––––

Health ................................... ––––––––––

Sickness and accident2 ........ ––––––––––

Retirement and savings ......... -4.1 2.9 -6.1 2.2 -6.3 1.5 7.0 2.5 -2.1 1.9

Pensions3 ............................. -4.7 2.9 -8.9 2.4 -10.6 1.6 5.6 3.1 -3.8 2.0

Savings and thrift3 ................ .2 9.4 12.8 3.9 17.7 3.0 12.4 5.4 4.4 3.6

Legally required benefits4 ..... 2.2 1.1 7.7 .8 4.0 .6 6.1 .7 3.7 .5

Social Security ...................... 1.4 1.3 7.8 .8 3.9 .5 6.4 .7 3.4 .5

Federal unemployment

insurance ............................ 5.0 1.2 7.1 1.2 -6.3 .9 .8 .6 -.2 .9

1991-92 1992-93 1993-94 1994-95 1995-96

Percent

change

Standard

 error

Percent

change

Standard

 error

Percent

change

Standard

 error

Percent

change

Standard

 error

Percent

change

Standard

 error

Leave ....................................... 4.2 1.4 1.0 0.8 0.4 0.9 -1.6 1.4 2.2 0.7

Vacation ................................ 3.0 1.9 .6 .9 .6 .8 -1.2 1.7 3.0 1.1

Holiday .................................. 4.5 1.2 2.3 .8 .6 1.0 -1.4 1.3 1.3 .6

Sick leave ............................. 6.4 1.9 1.1 1.8 -1.6 1.3 -2.3 1.9 .7 1.3

Other leave ........................... 8.8 4.6 -2.9 2.0 1.0 2.9 -6.4 2.7 6.2 3.0

Supplemental pay ................... 8.8 2.6 9.6 1.7 4.2 2.1 6.4 3.6 4.8 2.6

Premium pay ........................ 4.7 2.0 1.9 1.3 1.2 1.4 .4 2.8 5.0 1.7

Shift pay ................................ 3.3 2.4 2.1 4.4 6.3 3.6 -1.4 3.7 1.9 2.8

Nonproduction bonuses ........ 16.3 6.4 21.2 4.2 6.7 5.0 14.1 7.8 5.3 4.9

Insurance1 ............................... 10.9 1.5 7.1 1.0 3.1 1.0 -6.6 1.2 -1.2 .8

Life ........................................ 2.4 2.1 .8 1.6 -3.0 1.3 -4.4 1.7 .1 1.6

Health ................................... 11.4 1.5 7.4 1.0 3.7 1.0 -6.6 1.3 -2.3 .9

Sickness and accident2 ........ 9.0 3.3 6.9 1.8 -3.0 2.9 -7.6 2.5 – –

Retirement and savings ......... 4.6 3.4 5.0 2.0 6.8 1.8 -.4 2.1 5.9 1.9

Pensions3 ............................. 5.4 4.1 4.5 2.7 7.4 2.0 ––––

Savings and thrift3 ................ 1.4 5.2 7.0 2.7 4.5 2.4 ––––

Legally required benefits4 ..... 5.4 .7 5.1 .5 3.3 .6 -.5 .7 .0 .6

Social Security ...................... 4.1 .6 2.9 .5 2.6 .5 1.0 .6 -17.9 .3

Federal unemployment

insurance ............................ 3.9 1.2 -3.0 1.2 .2 .6 1.2 .6 -5.0 .6

See footnotes at end of table.
 Compensation and Working Conditions Spring 1998 22

Table 5. Estimates of year-to-year percent change in employer costs-per-hour-worked for employee benefits, private

industry, and corresponding standard errors, 1986-96 — Continued

Paid benefit

1986-87 1987-88 1988-89 1989-90 1990-91

Percent

change

Standard

 error

Percent

change

Standard

 error

Percent

change

Standard

 error

Percent

change

Standard

 error

Percent

change

Standard

 error

Legally required benefits4

State unemployment

insurance ............................ -4.2 1.8 -2.9 1.5 -5.5 1.6 -13.8 1.8 -2.7 1.8

Workers’ compensation ........ 9.6 2.5 13.7 2.2 11.6 2.0 14.7 2.1 6.6 1.7

Other benefits5 ........................ -4.8 6.6 19.8 6.2 -15.0 5.4 -25.7 8.3 4.2 5.5

1991-92 1992-93 1993-94 1994-95 1995-96

Percent

change

Standard

 error

Percent

change

Standard

 error

Percent

change

Standard

 error

Percent

change

Standard

 error

Percent

change

Standard

 error

Legally required benefits4

State unemployment

insurance ............................ 8.6 2.0 15.5 1.4 9.5 1.4 -3.1 1.7 -3.4 1.4

Workers’ compensation ........ 9.2 2.5 9.3 1.7 4.0 2.0 -3.3 1.8 .7 1.6

Other benefits5 ........................ 40.1 8.7 103.8 36.0 -3.2 8.5 -26.4 15.6 -7.9 6.5

1 Individual insurance benefit cost estimates were first published for 1991

data. 2 Until 1996, long-term disability insurance was included in the category of

sickness and accident insurance. 3 Discontinued in 1994. The pension and savings and thrift categories were

replaced by defined benefit and defined contribution plans categories beginning

in 1995. Although these old and new categories are not comparable with each

other, the overall category of retirement and savings is comparable.

4 Prior to 1996, railroad retirement and unemployment insurance benefits

were included with the legally required benefits category. Since then, railroad

benefit costs have been reclassified into the benefits that match their intended

purpose (Social Security, retirement and savings, sickness and accident

insurance, and state unemployment insurance). 5 Includes severance pay and supplemental unemployment benefits.

NOTE: Cost levels change and standard error are percentages. Dashes

indicate data unavailable.

total compensation that ranged numerically from -$0.01 to $1.00. (See

table 8.) Again, there are no significant differences among the individual

occupational groups.

Furthermore, for March 1995-96,

broader comparisons5 of the overall

goods-producing sector with the service-producing sector yielded similar

results, as did comparisons of whitecollar, blue-collar, and service occupational groups.

For the year ending March 1996,

total compensation costs in the goodsproducing sector increased $0.52 with

a standard error of $0.57, while the

service-producing sector cost levels

increased $0.40 with a standard error

of $0.25. The aggregate white-collar,

blue-collar, and service occupational

groups increased $0.60, $0.35 and

$0.21, respectively, with standard errors of $0.40, $0.32, and $0.09, respectively. None of these differences between aggregate industries or

aggregate occupational groups were

statistically significant, even at the 0.1

level of significance.

However, over a 10-year period, as

shown in tables 9 and 10, such comparisons do yield differences that are

statistically significant. Total compensation costs for the goods-producing

sector grew $5.41 for the 10-year period ending in March 1996, while the

service-producing sector cost levels

increased $3.87, with standard errors

of $0.49 and $0.25, respectively. For

the same period, total compensation

costs for white-collar workers increased $5.54, while that of blue-collar workers increased $3.61 and that

of service workers increased $2.18,

with standard errors of, $0.39, $0.28

and $0.14, respectively. At the .05

level of significance, the increase in

compensation for goods-producing

industrial divisions was significantly

larger than for the service-producing

divisions. As ascertained by a multiple comparisons test, the increase for

white-collar workers was larger than

the increase for blue-collar workers,

which in turn was larger than the increase for service workers.

ECEC trends compared to the

ECI

Table 11 shows that, over the period March 1987-96, private industry
23 Compensation and Working Conditions Spring 1998

Table 6. Estimates of year-to-year change in employer costs-per-hour-worked for employee compensation by industry

division and occupational group, private industry, and corresponding standard errors, 1986-96

Industry division

and occupational group

1986-87 1987-88 1988-89 1989-90 1990-91

Change Standard

 error Change Standard error Change Standard error Change Standard error Change Standard error

All private industry ......................... $0.18 $0.21 $0.36 $0.14 $0.48 $0.08 $0.69 $0.11 $0.43 $0.09

Goods-producing industries

Construction ............................. .86 .19 -.15 1.10 .48 .23 .74 .26 .90 .30

Manufacturing

Durables ............................... .20 .08 .70 .11 .98 .30 .13 .46 1.04 .13

Nondurables ......................... .25 .16 .83 .08 .78 .05 .50 .70 .76 .12

Service-producing industries

Transportation and public

 utilities ...................................... .37 .20 .26 .38 -.30 .61 1.28 .20 .61 .31

Wholesale trade ........................ -.25 .76 .58 .16 .78 .21 .99 .29 -.41 .85

Retail trade ............................... .03 .11 .16 .17 .10 .16 .42 .06 .28 .05

Finance, insurance, and real

estate ...................................... 1.16 .62 -.49 1.26 1.12 .15 .91 .16 1.00 .26

Services .................................... .10 .67 .62 .12 .46 .11 .98 .19 .26 .22

White-collar occupations

Professional and technical ........ .11 .73 1.04 .24 .94 .25 1.47 .35 .52 .34

Executive, administrative, and

managerial .............................. 1.60 .70 -.09 .68 1.49 .33 1.39 .58 1.53 .52

Sales ......................................... -.59 .47 -.20 .36 .52 .22 .75 .26 .75 .31

Administrative support .............. .64 .26 .58 .08 .50 .10 .60 .10 .54 .12

1991-92 1992-93 1993-94 1994-95 1995-96

Change Standard

 error Change Standard error Change Standard error Change Standard error Change Standard error

All private industry ......................... $0.73 $0.12 $0.56 $0.09 $0.38 $0.08 $0.02 $0.14 $0.40 $0.09

Goods-producing industries

Construction ............................. .57 1.00 .80 .21 .88 .22 .44 .29 .56 .26

Manufacturing

Durables ............................... 1.18 .12 1.11 .18 .59 .11 -.18 .63 .21 .22

Nondurables ......................... .75 .14 .65 .14 .67 .14 -.43 .86 .89 .34

Service-producing industries

Transportation and public

 utilities ...................................... .83 .36 1.16 .20 .51 .21 -1.33 .58 .98 .30

Wholesale trade ........................ .59 .18 .45 .21 .30 .16 .19 .85 .44 .22

Retail trade ............................... .26 .08 .21 .09 -.10 .17 .14 .13 .22 .09

Finance, insurance, and real

estate ...................................... .92 .26 .31 .76 .76 .51 .37 .27 1.20 .20

Services .................................... .89 .32 .75 .18 .45 .15 .13 .16 .27 .21

White-collar occupations

Professional and technical ........ 1.41 .68 1.93 .42 .53 .20 .53 .42 1.00 .49

Executive, administrative, and

managerial .............................. 1.27 .85 1.02 .49 .69 .62 1.30 .72 .70 .48

Sales ......................................... .37 .17 .05 .16 .50 .24 -.19 .31 .71 .17

Administrative support .............. .52 .24 .45 .10 .51 .14 -.01 .14 .28 .12

See footnotes at end of table.
 Compensation and Working Conditions Spring 1998 24

Table 7. ECEC changes in total compensation, by private industry division, year ending March 1996 - multiple

comparison (k=8, d=2.73)

Goods producing ............................................................ 0.52 0.57 -0.59 1.63

 Construction ................................................................. 0.56 0.26 -0.16 1.28

 Durable manufacturing .................................................. 0.21 0.22 -0.40 0.82

 Nondurable manufacturing ............................................ 0.89 0.34 -0.03 1.81

Service producing ........................................................... 0.40 0.25 -0.09 0.89

 Transportation and public utilities .................................. 0.98 0.30 0.16 1.80

 Wholesale trade ............................................................ 0.44 0.22 -0.17 1.05

 Retail trade ................................................................... 0.22 0.09 -0.04 0.48

 Finance, insurance, and real estate .............................. 1.20 0.20 0.65 1.75

 Services ....................................................................... 0.27 0.21 -0.30 0.84

Division

Current dollars

1995-96

change

Standard

error

95-percent confidence interval

Lower Upper

Table 6. Estimates of year-to-year change in employer costs-per-hour-worked for employee compensation by industry

division and occupational group, private industry, and corresponding standard errors, 1986-96 — Continued

Industry division

and occupational group

1986-87 1987-88 1988-89 1989-90 1990-91

Change Standard

 error Change Standard error Change Standard error Change Standard error Change Standard error

Blue-collar occupations

Precision production, craft, and

 repair ..................................... $0.19 $0.30 $0.48 $0.40 $0.37 $0.18 $0.65 $0.23 $0.90 $0.20

Machine operators,

assemblers, and inspectors .... .72 .15 .51 .08 .63 .18 -.09 .31 .75 .17

Transportation and material

movement ............................... .15 .38 .57 .20 .66 .42 .35 .35 .15 .39

Handlers, equipment cleaners,

helpers, and laborers .............. -.88 .21 .33 .24 .37 .19 .10 .20 .33 .15

Service occupations ................... -.16 .21 .33 .07 .40 .11 .49 .10 .16 .10

1991-92 1992-93 1993-94 1994-95 1995-96

Change Standard

 error Change Standard error Change Standard error Change Standard error Change Standard error

Blue-collar occupations

Precision production, craft, and

 repair ..................................... $1.05 $0.38 $0.75 $0.18 $0.69 $0.21 $-0.04 $0.29 $0.42 $0.21

Machine operators,

assemblers, and inspectors .... .74 .18 .52 .13 .54 .16 -.82 .38 .26 .25

Transportation and material

movement ............................... .58 .33 .25 .17 .68 .37 -.11 .48 -.01 .28

Handlers, equipment cleaners,

helpers, and laborers .............. .46 .24 .38 .11 .18 .16 -.34 .30 .45 .15

Service occupations ................... .62 .12 .11 .09 -.16 .14 .01 .07 .21 .08

NOTE: Cost change and standard error are in current dollars.
25 Compensation and Working Conditions Spring 1998

employer compensation costs rose 40.5

percent as measured by the ECI and

30.3 percent as measured by the

change in ECEC 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 the ECEC, 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 percent for wages and salaries,

and 4.5 for 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. As table 11 shows, the differences in percent change for the 10-

year period between the ECI and the

ECEC for compensation, wages and

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

Table 2 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 the corresponding standard errors. Although

differences between the ECI and

ECEC are significant over the long

term, they are not significant over the

12-month period, March 1995-96.

(See table 12.) For example, ECEC

compensation costs increased 2.3 percent over the period with a standard

error on the difference of 0.5 percent.

The ECI 12-month percent change for

the same period was 2.7 percent with

a standard error on the difference of

0.3 percent.

Various factors have been suggested

to explain the 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 two 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

20 percent of the sample is replaced

each year, a number 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 Cushner6

analyzed differences in the two main

steps involved 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 (mean),

yields different estimates for ECI and

ECEC, mostly 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. In another paper,

Lettau and Lowenstein7 concluded

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/full-time).

Step 2, combining cell means to

obtain final estimates, involves fixed

weights for the ECI, while the ECEC

uses Current Employment Statistics

Survey weights. By isolating the two

steps in the process, Lettau,

Lowenstein, and Cushner 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 measure, the ECEC or the

ECI, is appropriate for determining the

rate of change must be determined by

the needs of the user. If a user prefers

a measure of change that maintains

fixed employment distribution by industry and occupation group, the ECI

provides an appropriate measure.

Conversely, if the user wants the survey that measures 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 applies the

ECEC approach for step 1 and the ECI

approach for step 2.

Table 8. ECEC changes in total compensation, by private industry occupational group,

year ending March 1996 - multiple comparison (k=9, d=2.77)

White collar ............................................. 0.60 0.40 -0.18 1.38

 Professional and technical .................... 1.00 0.49 -0.37 2.37

 Executive, administrative and

 managerial .......................................... 0.70 0.48 -0.64 2.04

 Sales .................................................... 0.71 0.17 0.25 1.17

 Administrative support .......................... 0.28 0.12 -0.05 0.61

Blue collar ............................................... 0.35 0.32 -0.28 0.98

 Precision production, craft, and repair .. 0.42 0.21 -0.16 1.00

 Machine operators, assemblers,

 and inspectors .................................... 0.26 0.25 -0.44 0.96

 Transportation and material movement . -0.01 0.28 -0.77 0.75

 Handlers, equipment cleaners,

 helpers, and laborers .......................... 0.45 0.15 0.03 0.87

Service occupations ............................... 0.21 0.09 -0.03 0.45

Current dollars

95-percent

confidence interval Occupational group 1995-96

change

Standard

error Lower Upper
 Compensation and Working Conditions Spring 1998 26

Table 9. ECEC changes in total compensation, by private industry division, 10 years ending March 1996 - multiple

comparison (k=8, d=2.73)

Goods producing ............................................................ 5.41 0.49 4.45 6.37

 Construction ................................................................. 5.22 1.11 2.20 8.24

 Durable manufacturing.................................................. 5.75 0.66 3.95 7.57

 Nondurable manufacturing ............................................ 5.16 0.98 2.45 7.83

Service producing ........................................................... 3.87 0.25 3.38 4.36

 Transportation and public utilities .................................. 3.98 0.70 2.07 5.89

 Wholesale trade ............................................................ 3.89 0.82 1.65 6.13

 Retail trade ................................................................... 1.69 0.24 1.03 2.35

 Finance, insurance, and real estate .............................. 6.10 0.56 4.56 7.64

 Services ....................................................................... 4.84 0.38 3.80 5.88

Table 10. ECEC changes in total compensation, by private industry occupational group, 10 years ending March

1996 - multiple comparison (k=9, d=2.77)

White collar ..................................................................... 5.54 0.39 4.78 6.30

 Professional and technical ............................................ 9.38 0.78 7.23 11.53

 Executive, administrative and managerial ..................... 9.31 1.08 6.33 12.29

 Sales ............................................................................ 3.27 0.34 2.32 4.22

 Administrative support .................................................. 3.99 0.25 3.29 4.69

Blue collar ....................................................................... 3.61 0.28 3.06 4.16

 Precision production, craft, and repair .......................... 5.27 0.48 3.93 6.61

 Machine operators, assemblers, and inspectors .......... 3.04 0.42 1.87 4.21

 Transportation and material movement ......................... 3.13 0.64 1.37 4.89

 Handlers, equipment cleaners, helpers, and laborers ... 2.26 0.43 1.07 3.45

Service occupations ....................................................... 2.18 0.14 1.79 2.57

Table 11. ECEC/ECI changes in total compensation, wages and salaries, and benefits, private industry, 10 years

ending March 1996

 Total compensation ......................................................... 40.5 2.2 30.3 1.9 10.2 2.9

 Wages and salaries ..................................................... 35.2 2.9 28.0 1.9 7.2 3.5

 Benefits ....................................................................... 54.9 2.2 36.5 2.4 18.5 3.2

95-percent confidence interval

Current dollars

Lower

1987-96

change

Standard

error

Division

Upper

Percent change

ECI ECEC ECI-ECEC

Change

1987-96

Standard

error

Standard

error

Standard

error Change

1987-96

Change

1987-96

Compensation component

Current dollars

95-percent confidence interval

Lower Upper

1987-96

change

Standard

error

Occupational group
27 Compensation and Working Conditions Spring 1998

Trends in the ECEC and the ECI

This article supplements two articles from the Summer 1997 issue of Compensation

and Working Conditions which focused on trends in the ECI and ECEC. “Measuring

Trends in the Structure and Levels for Employer Costs for Employee Compensation,” by

Albert E. Schwenk, discussed trends in the distribution of employer costs among compensation components at different points in time. “Explaining the Differential Growth Rates

of the ECI and the ECEC,” by Michael K. Lettau, Mark A. Loewenstein, and Aaron T.

Cushner, examined how differences in the construction of these measures contribute to

differing trends. This article adds another dimension to the discussion, by explaining how

to use newly-published standard error data to analyze differences in year-to-year changes.

For a more complete discussion of the scope of and the methods used in the ECI and

ECEC series, see BLS Handbook of Methods, Bulletin 2490, Bureau of Labor Statistics,

April 1997, pp. 57-65; G. Donald Wood, Jr., “Estimation Procedures for the Employment

Cost Index,” Monthly Labor Review, May 1982, pp. 40-42; and Karen O’Conor and

William Wong, “Measuring the Precision of the Employment Cost Index,” Monthly Labor

Review, March 1989, pp. 29-36.

1

 The standard error is a measure of the precision of the estimate. A 95-percent confidence

interval is centered around a sample estimate and

includes all values within 2 times the estimate’s

standard error. If all possible samples were selected to estimate the population value, the confidence interval from each sample would include

the true population value approximately 95 percent of the time. See Albert E. Schwenk, “Measuring Trends in the Structure and Levels of Employer Costs for Employee Compensation,” Appendix, “Measuring the Precision of Cost Level

Changes,” Compensation and Working Conditions, Summer 1997, p. 14.

2

 Statistical statements may be evaluated using different significance levels, otherwise known

as alpha levels. The .05 alpha level corresponds

to the 95-percent confidence interval, the level

usually used to measure the precision of an estimate.3

 To compute standard errors using this approach, relative errors, published in the bulletin

Employment Cost Indexes and Levels, 1975-1995,

were used. Relative error is the standard error expressed as a percent of a cost level estimate. 4

 These multiplication factors are used to compare, for example, an occupational group (or industry) to an occupational group comprised of two

or more other occupational groups. Such multiple comparisons involve using a higher cumulative normal distribution d-value to determine the

confidence interval. For a more complete discussion of testing various types of statistical statements, see Lawrence R. Ernst and Chester H.

Ponikowski, “Statistical Review of Press Releases

and Bulletins,” Internal Memorandum, Statistical

Methods Group, Bureau of Labor Statistics, December 1996. 5

 For these aggregate categories, it was necessary to compute the standard error as the square

root of the sum of the variance estimates of the

cost levels. This approach, which tends to overestimate the standard error because it does not subtract the effect of the covariance term, had to be

used because of resource limitations. 6

 See Michael K. Lettau, 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. 7

 See Michael K. Lettau and Mark A.

Loewenstein, “Sample Replacement in the ECI,”

Compensation Research and Program Development Group Working Paper, 1996.

Table 12. ECEC/ECI changes in total compensation, wages and salaries, and benefits, private industry, year

ending March 1996

Total compensation.......................................................... 2.7 0.3 2.3 0.5 0.4 0.6

 Wages and salaries ..................................................... 3.2 0.4 2.8 0.6 0.5 0.7

 Benefits ....................................................................... 1.6 0.3 1.3 0.6 0.3 0.7

Percent change

Standard

error

Standard

error

Standard

error

Change

1995-96

Change

1995-96

Change

1995-96

ECI ECEC ECI-ECEC Compensation component

—ENDNOTES—