Chapter 2.
Employment, Hours, and Earnings from the Establishment Survey

Estimating Procedures

Employment
Employment estimates are made at what is termed the basic estimating cell level, and are aggregated upward to broader levels of industry detail by simple addition. Basic cells are defined by industry (usually at the five- or six-digit NAICS level). Within the construction industry, stratification by geographic region also is used.

To obtain all-employee estimates for a basic estimating cell, the following five steps are necessary:

1. A total employment figure (benchmark) is obtained for the basic estimating cell as of a specified month (March).
2. For each report, employment is multiplied by the sample selection weight to obtain weighted employment for the months for which estimates are being made and for the previous month.
3. For each cell, the ratio of the weighted all employees sample total in 1 month to that in the preceding month (termed the weighted link-relative) is computed for sample establishments that reported for both months.
4. Beginning with the benchmark month, the all-employee estimate for each month is obtained by multiplying the all-employee estimate for the previous month by the weighted link-relative for the current month.
5. Add a net birth/death estimate from the model described below.

The following example illustrates how the estimating procedure is applied in preparing a series. Assume that the estimate for all employees for a given cell was 50,000 in July. The sample, comprising 60 establishments that reported for both months, had weighted employment of 25,000 in July and 26,000 in August, a 4-percent increase. The net birth/death estimate for August equals 100. To derive the August estimate, the ratio of weighted sample employment for August to that for July is applied to the July estimate:

This procedure, known as the weighted link-relative technique, is efficient in that it takes advantage of a reliable, complete count of employment and of the high correlation between levels of employment in successive months in identical establishments.

Business birth and death modeling. A net birth/death factor is added to national employment estimates to produce the monthly published estimates. Regular updating of the CES sample frame with information from the UI universe files helps to keep the CES survey current with respect to employment change due to business births and deaths. The timeliest UI universe files available however, always will be a minimum of 9 months out of date. Thus, the CES survey cannot rely on regular frame maintenance alone to provide estimates of the employment effects of business births and deaths. BLS utilizes a model-based approach for this component.

While both the business birth and business death portions of total employment are generally significant, the net contribution is relatively small and stable. To account for this net birth/death portion of total employment, BLS has an estimation procedure with two components. The first component uses business deaths to impute employment for business births. The second component is an ARIMA time-series model designed to estimate the residual net birth/death employment not accounted for by the imputation.

The imputation component is incorporated in the weighted link-relative estimation procedure by simply not reflecting sample units going out of business, but imputing to them the same trend as the other firms in the sample. The ARIMA time-series model estimates the residual net business birth/death employment that is not accounted for by imputation. The historical time series used to create and test the ARIMA model was derived from the UI universe micro-level database and reflects the actual residual net of births and deaths over the past 5 years. The net birth/death model component figures are unique to each month and exhibit a seasonal pattern that can result in negative adjustments in some months.

Production and nonsupervisory workers. To obtain estimates of production (or construction or nonsupervisory) worker employment, the ratio of weighted production workers to the weighted all employees in the sample is assumed to equal the same ratio in the universe. The current month’s production worker ratio is thus estimated and then multiplied by the all-employee estimate. The weighted difference- link and taper formula, described in the section on hours and earnings, is used to estimate the current month’s production worker ratio. This formula adds the change in the matched sample’s production worker ratio (the weighted difference link) to the prior month’s estimate, which has been slightly modified to reflect changes in the sample composition (the taper). An analogous method is used to estimate the number of women workers.

The estimates for each type of series (all employees, production workers, and women workers) for individual basic estimating cells are summed to obtain corresponding totals for broader industry sectors.

Hours and earnings
Independent benchmarks are not available for the hours and earnings series; consequently, the levels derive directly from the CES weighted-sample averages.

Average weekly hours and average hourly earnings. Before hours and earnings sample averages or estimates are calculated, production workers and aggregate hours and payrolls must be multiplied by sample weights both for the month for which estimates are being made and for the prior month. To obtain average weekly hours for a basic estimating cell, the sum of reported worker hours for the establishments classified in the cell is divided by the total number of production workers reported for the same establishments. In computing average hourly earnings, the reported payroll is divided by the reported worker hours for the same establishments.

Sample averages of average weekly hours and average hourly earnings are first modified at the basic estimating-cell level through the use of a wedging technique designed to compensate for month-to-month changes in the sample of reporting establishments (weighted difference-link and taper).

For example, unmodified sample averages for the current month, ,are obtained from aggregates from a matched sample of establishments reporting for both the current month and the previous month. Similarly, unmodified sample averages for the previous month, x_p, are calculated from the same matched sample. The expression x_c-x_p denotes the change between the 2 months.

The other component of the weighted difference-link and taper formula is the estimate of average hourly earnings for the previous month, X_p. Because the panel of establishments reporting in the sample is not completely fixed from month to month, X_p and x_p may differ. An estimate for the current month, X_c, is obtained by using both pieces of information:

The procedure reflected in this formula has the following advantages: (1) It uses matched sample data; (2) it tapers the estimate toward the sample average for the previous month of the current matched sample (x_p) before applying the current month’s change; and (3) it promotes continuity by heavily favoring the estimate for the previous month (X_p) when applying the numerical factors.

Average weekly hours and average hourly earnings for industries and groups above the basic estimating cell level are weighted averages of the figures for component cells. The average weekly hours for each basic estimating cell are multiplied by the corresponding estimate of the number of production workers to derive aggregate worker hours. Payroll aggregates are the product of the aggregate worker hours and average hourly earnings. The payroll and worker-hour aggregates for industry groups and divisions are the sums of the aggregates for the component industries.

Average weekly hours for industry groups are obtained by dividing the worker-hour aggregates by the corresponding production worker estimates. Average hourly earnings for industry groups are computed by dividing the payroll aggregates by the worker-hour aggregates. This method is equivalent to weighting average weekly hours by the estimated number of production workers in the universe and weighting average hourly earnings by the estimated worker hours for the universe.

For all levels, from basic estimating cells to supersectors and higher aggregates, average weekly earnings are computed by multiplying average hourly earnings by average weekly hours.

Overtime hours. Average weekly overtime hours are estimated in basically the same way as average weekly hours. Overtime worker-hour sample averages are used in the computations in place of the sample averages for total worker hours. The sample totals for production workers used in the computations are those for the reports containing overtime worker hours (including those reporting zero overtime hours) as well as production workers, total payroll, and total worker hours. The wedging technique and the summary level estimating technique for the overtime hours estimation also are comparable to those used to estimate average weekly hours.

Average hourly and weekly earnings in 1982 dollars. Average hourly and weekly earnings are computed and published in terms of 1982 dollars to give an approximate measure of changes in “real” average earnings (earnings in constant dollars). These series are computed by dividing the average hourly and weekly earnings (in current dollars) for a given month by the BLS Consumer Price Index for Urban Wage Earners and Clerical Workers (CPI-W) (1982 = 100) for the same month.

Average hourly earnings, excluding overtime, for the manufacturing supersector. These estimates are computed by dividing the total production worker payroll for an industry group by the sum of the total production worker hours and one-half of the total overtime worker hours, which is equivalent to the payroll divided by straight-time hours. This method excludes overtime earnings at an assumed rate of 1 1/2 times the straight-time rates; no further adjustment is made for other premium payment provisions.

Indexes of aggregate weekly hours and payrolls. These indexes are prepared by dividing the current month’s aggregates by the annual average aggregate for 2002. The hours aggregates are the product of average weekly hours and production, construction, or nonsupervisory worker employment; the payroll aggregates are the product of the hours aggregates and average hourly earnings.

Indexes of diffusion of employment changes. These indexes measure the dispersion among industries of the change in employment over the specified timespan. The overall indexes are calculated from seasonally adjusted employment series for four-digit NAICS-coded industries. The diffusion indexes for private nonfarm payroll employment are based on estimates for 278 industries, while the manufacturing indexes are based on estimates for 84 industries. Each component series is assigned a value of 0, 50, or 100 percent, depending on whether its employment showed a decrease, no change, or an increase over a given period. The average (mean) value is then calculated, and this percent is the diffusion index number. The reference point for interpreting the diffusion indexes is 50 percent, the value that indicates that the same number of component industries have increased in employment as have decreased. The direction and distance of the index number from the 50 percent reference point indicate whether growing (above 50) or declining (below 50) industries predominate and by what magnitude. The margin between the percentage of industries that increased and the percentage that decreased employment equals twice the difference between the index number and 50 percent.

Seasonally adjusted series
Many economic statistics reflect a regularly recurring seasonal movement that can be measured from past experience. By eliminating that part of the change attributable to the normal seasonal variation, it is possible to observe the cyclical and other nonseasonal movements in these series. Seasonally adjusted series are published regularly for selected employment, hours, and earnings series. CES published 146 seasonally adjusted employment series in 2003.

X-12 ARIMA software, developed by the U.S. Census Bureau, is used to seasonally adjust CES data on a concurrent basis. Using special features of X-12 ARIMA, adjustments are made to remove the effect of the variable number of weeks between surveys from month to month (about 1 month in 3 has a 5-week instead of a 4-week interval) and to remove the effect of the variable number of work days in the reference month, to adjust for moving holidays, and to adjust for the variations in the number of election poll workers in November from year to year.

CES processes concurrent seasonal adjustment on a monthly basis using the latest estimates of employment, hours, and earnings. Seasonally adjusted employment series for broader industry groups are obtained by summing the seasonally adjusted data for the component industries. Seasonally adjusted hours and earnings averages for broader level industry groups are weighted averages of the seasonally adjusted component series.

Next: Data Presentation