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Chapter 8.
National Compensation Measures
Computations
The following section describes in detail the method used to compute each of the major NCS products.
Wage estimates
For the NCS wage products, the following estimates are calculated and published for specific areas of interest: Mean annual wages, mean weekly wages, mean hourly wages, total employment, and hourly wage percentiles. Areas of interest include geographical area by industry and by occupational group.
The formula used for calculating mean annual wages, mean weekly wages, and mean hourly wages uses the individual weight of the sampled occupation, the individual rates in the sampled occupations, and the number of weeks worked per year. Since 1996, the calculation of average hourly wage also has included the number of hours paid.
The following estimation formulas are used for computing mean wages, total employment, and hourly wage percentiles for the NCS.
(1) Mean annual wage
(2) Mean weekly wage
(3) Mean hourly wage
(4) Total Employment
(5) Hourly Wage Percentile. The p-th percentile is that
hourly wage rate Yql such that the resulting weighted annual hours figure paid less than Yql is less than p percent of the total weighted annual hours paid, and the weighted annual hours paid more than Yql is less than (100 - p) percent of the
total weighted annual hours paid
where
Subscript D is the domain of interest
(e.g., occupation x level, occupational group x level),
Subscript q is the quote, and l is the wage record,
Yql is the annual wage rate in formula (1), the weekly
wage rate in formula (2), and the hourly wage rate in formula (3) of
a particular worker or group of workers in a particular quote,
Xql is the number of workers for a particular wage rate,
Hq is the number of weekly hours paid for a particular
worker, which is assumed to be the same for each worker in a quote,
(NOTE: Weekly hours paid is used only when computing average hourly
wage.)
Aq is the number of annual weeks worked for a particular worker, which is assumed to be the same for each worker in a quote, and
Wq is the individual weight. The individual weight is calculated by dividing the final quote weight by the number of employees in the quote. The final quote weight for local area occupational wage estimates is a product of the reciprocal of the probability of selecting the establishment given the set of sample areas; a correction factor to adjust for cases in which data are collected for a different number of employees than data should be collected for; the establishment nonresponse adjustment factor; the occupational nonresponse adjustment factor; and the probability selection of occupation interval, which is the number of eligible employees divided by the number of occupational selections. For national and census division estimates, the final quote weights are a product of the same type of factors and one additional factor, the reciprocal of the probability of selecting the sample area in which the establishment is located. The benchmark factors are aggregated for geographical areas, census divisions, and national wage computations. The individual weight contains an additional factor to account for changes in the employment distribution.
Employment Cost Index
The ECI is a Laspeyres index. The basic computational framework for the ECI is the standard formula for an index number with fixed weights, as modified by the special statistical conditions that apply to the ECI. This discussion focuses on the ECI measures of wage changes, but indexes of changes in compensation and benefits are calculated in essentially the same fashion.
Method. An index for the ECI is a weighted average of the cumulative average wage changes from a specified base-period wage.
A formula for It, the index at quarter t, is presented. This formula assumes that the index series is based at 100 for t = 0. Currently, the index is based at 100 for December 2005; so It should be divided by the original index value for December 2005 to obtain the value of the index at quarter t with this base.
where
W(t-1)i , Wti are the wage bill for cell i for quarter t-1 computed at quarter t and the wage bill for cell i at quarter t, computed at quarter t, respectively.
A cell is defined by private or government sector, industry, and occupational group. The wage bill is the weighted average hourly wage of workers in the cell times the number of workers represented by the cell (the fixed employment weight). The fixed weights used in the index calculation for March 2006 to the present are based primarily on 2002 employment from the BLS Occupational Employment Survey (OES). From March 1995 through December 2005, the 1990 OES employment counts were used.
Now
Wti = W(t-1)i *Rti (1)
where Rti is the ratio of the current-quarter weighted average wage in the cell to the prior-quarter weighted average wage in the cell, both calculated in the current quarter using matched establishment/occupation wage quotations—that is, quotes with usable data in both quarters. The weights applied are the sample quote weights described in the previous section.
As for W(t-1)i , note the wage bill for the cell for quarter t-1 was originally calculated at quarter t-1 using (1) with t and t-1 replaced by t-1 and t-2, respectively. At quarter t the wage bill for quarter t-1 remains the same, except if quarter t is the once a decade t-1 quarter in which the fixed employment weights are changed, such as March 1995 and March 2006. In this latter case, the wage bill for quarter t-1 is recomputed at quarter t as the product of the new fixed employment for the cell and the mean wage for the cell at quarter t-1 calculated from the ECI sample.
The index computation for a quarter involves five principal steps:
- Establishment sample quote weights are applied to the average occupational hourly wage in every estab- lishment that has both current- and prior-quarter wage information. These data are used to calculate a weight ed average wage for each cell (that is, occupational group within industry) for the current and prior sur- vey periods.
- The ratio of current-quarter to prior-quarter weighted average wage is then calculated for each cell.
- This ratio for each cell is multiplied by the wage bill for the cell from the prior quarter. The product is the current-quarter wage bill.
- Both the current-quarter and previous-quarter wage bills are then summed over all cells within the scope of the index. For example, for the manufacturing in - dex, the wage bills would be summed across all cells in manufacturing.
- The summed current-quarter wage bill is divided by the summed previous-quarter wage bill. The result is the quarterly change in the index. This quarterly change is multiplied by the previous quarter’s index value to obtain the current quarter’s index value.
The computations for the occupational and industry groups follow the same procedures as those for the overall indexes except for summation. For example, for an index for a broad occupational group, the wage bills are summed across all cells that are a subset of that occupational group, with indexes for industry groups calculated analogously.
Computation procedures for the regional, union or nonunion, and metropolitan or nonmetropolitan measures of change differ from those of the national indexes because the sample is not large enough to hold constant the wage bills at that level of detail. For these subseries, each quarter the prevailing distribution in the sample (for example, between union and nonunion within each ownership/industry/occupation cell) is used to apportion the prior-quarter wage bill in that cell (for example, between the union and nonunion series). The portion of the wage bill assigned to the union sector is then moved by the percentage change in the union wages in the cell, and similarly for the nonunion sector. Therefore, the relative employment of the union sector in each cell is not held constant over time. Since the weights of the region, the union, and metropolitan area subcells are allowed to vary over time, the indexes for these series are not strictly comparable to those for the aggregate, industry, and occupation series.
Seasonal adjustment. Over the course of a year, the rate of wage-and-benefit cost changes is affected by events that follow a more or less regular pattern. For example, ECI 3-month rates of change for wage-and-benefit costs in State and local governments, which include State and local education as a substantial part, show larger rates of increase in September, reflecting new contracts associated with the beginning of new school sessions.
Adjusting for these seasonal patterns makes it easier to observe the cyclical and other nonseasonal movements in the series. When evaluating changes in a seasonally adjusted series, it is important to note that seasonal adjustment is an approximation based on past experience. Seasonally adjusted estimates have a broader margin of possible error than the original data on which they are based because they are subject to errors associated with seasonal factor estimation, in addition to sampling and nonsampling errors.
Seasonal adjustment is performed using the X-12 ARIMA program developed by the time series staff in the Statistical Research Division of the Census Bureau, U.S. Department of Commerce. The X-12 ARIMA program includes enhancements to the X-11 Variant of Census Method II seasonal adjustment program, as well as the X-11 ARIMA program developed by Statistics Canada.
At the beginning of each calendar year, seasonal adjustment factors are calculated for use during the coming year. The seasonal factors for the coming year are published on the BLS Web site. Revisions of seasonally adjusted indexes and 3-month percent changes for the most recent 5 years also are published on that Web site.
ECI series are seasonally adjusted using either direct or indirect methods. In the direct method, an original or unadjusted index is divided by its seasonal factor. In the indirect method (also called composite seasonal adjustment), the seasonally adjusted index is calculated as a weighted sum of seasonally adjusted index components.
Employer Costs for Employee Compensation estimates
ECEC estimates are shown as costs per hour worked for total compensation (wages and benefits), expressed both as dollar amounts and as percentages of compensation. ECEC estimates are computed for various costs, c, including wages, individual benefits, combinations of benefits, total benefits, and total compensation (total wages plus total benefits). The formula for  , the mean hourly cost c for domain D, is
where
D is the domain of interest,
W'qis the final quote weight for quote q, calculated as in the description of the final quote weight in the section on the calculation of wage levels, with one additional factor to account for changes in the employment distribution, and
Ycq is the mean hourly cost c for quote q
In addition, PcD, the mean hourly cost c as a percentage of total compensation, is calculated as
where
 is the mean hourly cost for total compensation for domain D.
Benefit Incidence and Provisions Estimates
NCS provides information on the incidence and detailed provisions of employee benefit plans.
Incidence, which refers to the number or percentage of employees that receive a benefit plan or specific benefit feature, is measured in two ways—access and participation. Employees are considered as having access to a benefit plan if it is available for their use or will be once a service requirement has been met. Access is determined on an occupational basis within an establishment; either all employees or no employees in an occupation in an establishment have the benefit available to them. Participation refers to the proportion of employees who are actually enrolled in the plan.
Access. The formula for Ad, the percentage of employees with access to a benefit area such as life insurance, for domain D is
where
D is the domain of interest,
W'q calculated as described in the previous section on the calculation of ECEC estimates, and
Xq is 1 if the quote has access to the benefit being estimated, and 0 otherwise.
Participation. The formula for ID,
the percentage of employees participating in a benefit area such as medical care, for domain D is
where
D is the domain of interest,
W'q is the final quote weight for
quote q, calculated as described in the previous section on the calculation of ECEC estimates, and
Pqj is the percentage of workers in quote q participating in plan j.
Other estimates of incidence, such as the percentage of participants in a benefit area or subset of a benefit area, can be computed in a similar manner, in which the base includes only those workers who participate in the benefit. For example, to calculate the percentage of medical insurance participants in domain D participating in indemnity plans, a ratio is calculated such that the denominator is the same as the numerator of the previous formula, and the numerator is of the same form except that the summation is restricted to those participants in indemnity plans.
Average (Means). The formula for
 , the average flat monthly employee contribution for medical insurance for domain D, is
where
D is the domain of interest,
W'q is the final quote weight for quote q, calculated as described in the previous section on the calculation of ECEC estimates,
Yqj is the average monthly employee contribution for plan j in quote q, and
Pqj is the percentage of workers in quote q participating in plan j.
Other means, such as the average annual deductible for medical insurance, can be calculated using a similar formula. In all cases, the averages include only those workers with the provision.
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Bureau of Labor Statistics
