Adjusting for Calendar Related Fluctuations in Average Weekly
Hours and Average Hourly Earnings Series
This is a research paper done in April 1998. It was not
updated to reflect the June 5, 1998 release of benchmarked
estimates. The benchmarked estimates incorporate the methodology
used to produce the experimental series discussed in this
article.
Over the past several months the Bureau of
Labor Statistics (BLS) has conducted research into potential
distortions in published over-the-month changes in the average
weekly hours and average hourly earnings series from the Current
Employment Statistics (CES) program. Researchers both within BLS
and from outside organizations have noted the presence of
fluctuations in the series that are correlated with the number of
weekdays, or standard workdays, in a month. Specifically,
research has demonstrated that both the hours and the earnings
series consistently evidence stronger growth in shorter months
(20 or 21 weekdays) than in longer months (22 or 23 weekdays).
This paper provides a discussion of the issue, results from BLS
research to date, and plans for corrective action to be
implemented in June 1998, with the release of annual benchmark
revisions.
Background - The CES program is a sample
survey of nearly 400,000 business establishments nationwide,
which provides monthly estimates of nonfarm payroll jobs and the
hours and earnings of workers. The reference period for
respondents reporting to the survey is the pay period including
the 12th of the month. For a majority of sample
respondents this equates to the week including the 12th,
but establishments that pay workers on other frequencies —
biweekly, semi-monthly, or monthly — report payroll and hours
data for their specific pay periods. These non-weekly data must
be converted to a weekly equivalent in order to be used in the
average weekly hours (AWH) and average hourly earnings (AHE)
estimate calculations. Because there are a variable number of
workdays across calendar months for semi-monthly and monthly
respondents, the initial investigation of the calendar-related
fluctuations focused on the reporting and processing of these
data.
An initial review of hours and payroll data from semi-monthly
and monthly respondents indicated that both response error and
processing error associated with these reports likely underlay
the calendar-related spikes observed in the series. Response
error can arise from sample respondents reporting a fixed number
of total hours for workers regardless of the length of the
reference month, while the CES conversion process assumes the
hours reporting will be variable. For example, for a semi-monthly
reporter, the conversion process assumes that more hours will be
reported for an 11-day pay period than for a 10-day pay period
and the conversion factor is varied accordingly. (The standard
semi-monthly pay period runs from the 1st through the
15th of a month, and always has either 10 or 11
weekdays.) Specifically, the conversion to a weekly equivalent
takes 45% of the total hours reported in an 11-day pay period (5
days/11 days) and 50% of the hours reported in a 10-day pay
period (5 days/10 days). If a respondent reports the same fixed
number of hours in both 10 and 11 day payroll periods, the
conversion process will introduce an artificial spike up in the
AWH series in shorter months that will be reversed in longer
months. A constant level of hours reporting most likely occurs
when employees are salaried rather than paid by the hour, as
employers are less likely to keep actual detailed hours records
for these employees.
While the aforementioned response error can affect AWH series,
a separate processing error affects the AHE series. For
respondents with salaried workers who do report
hours correctly, i.e., vary them according to the length of the
month, different conversion factors should be applied to payroll
and hours. CES processing systems do not currently allow for
this. Using the semi-monthly example again, and assuming that
employees receive 1/24 of their annual pay on each pay date, a
fixed factor of .46 is appropriate for payroll (24 pay dates/52
weeks), while the hours factor should be .45 in 11-day months and
.50 in 10-day months. In fact the current processing system uses
the hours conversion factor for both fields, resulting in upward
spikes in AHE in short months and reversals in long months. This
happens because payroll is reduced too little in short months;
the conversion takes 50% instead of 46% of the total payroll in
converting to a weekly equivalent. In longer months, the
reduction is slightly in error in the other direction; the
conversion takes 45% of total payroll as the weekly equivalent as
compared with the correct 46%. These initial hypotheses were
further examined and tested as described below.
Research and Results - Four avenues of
research were pursued to further pinpoint the scope and sources
of the distortion in the weekly hours and earnings series, and to
identify possible solutions. The research activities and results
are briefly summarized below:
Time Series Modeling A time series
technique known as REGARIMA modeling was used to identify,
measure, and remove the length-of-pay period effect for the
publication level seasonally adjusted AWH and AHE series.
REGARIMA modeling combines standard regression analysis, which
measures correlations among two or more variables, with ARIMA
modeling, which describes and predicts the behavior of a data
series based on its own past history. REGARIMA modeling currently
is used in the CES seasonal adjustment process to mitigate a
different calendar effect, the varying number of weeks between
surveys (the 4- versus 5-week effect).
In this current context, the correlations of interest are
between the number of weekdays in a month and the AHE and AWH
levels. Models were fit to all publication-level series, with a
variable specified to denote a longer versus a shorter month. The
regression coefficients produced by the REGARIMA models provided
an estimate of the average magnitude of variation in the AWH and
AHE series attributable to the length-of-pay period effect. The
coefficients then were used to adjust the raw CES data to remove
the effect, prior to application of standard CES seasonal
adjustment methodology.
The length-of-pay period variable proved significant for
explaining AWH movements in all the service-producing major
industry divisions, as measured by standard regession
diagnostics. For AHE, the length-of-pay period variable was
significant for 3 major industry divisions: wholesale trade,
finance, insurance and real estate, and services.
Application of REGARIMA models yielded seasonally adjusted
series that are considerably smoother than the currently
published series, especially for AWH. The improvement for AHE was
not as pronounced. See Charts 1 and Chart 2 for
the finance, insurance and real estate industry as an example.
This division showed the most significant improvement from the
modeling.
The overall modeling results correspond with the hypothesis
that calendar-related spikes are traceable to semi-monthly and
monthly reports, as these types of reports are far more prevalent
in the service-producing than the goods-producing industries, as
shown in table 1 below:
Table 1
Percentage Distribution of CES Sample Reports
by Length of Pay Period
Industry |
Weekly and Biweekly |
Semi-monthly and Monthly |
|
|
|
Total Private |
82% |
18% |
Mining |
78 |
22 |
Construction |
94 |
6 |
Manufacturing |
93 |
7 |
Transportation and public
utilities |
81 |
19 |
Wholesale trade |
80 |
20 |
Retail trade |
85 |
15 |
Finance, insurance and real
estate |
64 |
36 |
Services |
75 |
25 |
Microdata Screening and Estimate Simulations-
In order to provide confirmation that the semi-monthly and
monthly reports are the source of calendar-related fluctuations,
estimates were simulated excluding all semi-monthly and monthly
reports. Additional estimate simulations were completed after
attempting to identify and screen out the problematic reports,
i.e., those affected by response or processing error.
Simulated AWH and AHE series produced without any semi-monthly
or monthly reports appeared to be free of the calendar-related
spikes found in the published series. These simulations then
helped confirm that the calendar-related spikes are in fact
caused by the semi-monthly and monthly reports. One other notable
result from the AHE simulation is that deleting all the
semi-monthly and monthly reports lowered the level of the series.
A review of the average earnings by type of payroll confirmed
that those on semi-monthly and monthly payrolls were on average
higher paid than those on weekly and biweekly payrolls. Thus,
deleting all semi-monthly and monthly reports biased the series
downward.
Screening tests were developed separately for hours and
payroll data as a method for more precisely identifying
problematic reports. To test for response error in hours
reporting, AWH means were computed separately for shorter months
and longer months and then tested for a statistically significant
difference between them. The reasoning for this test is that if a
respondent is reporting fixed hours the means of weekly hours
will differ systematically with the number of workdays in the
month because of the distortion introduced by the variable
conversion factor. For example, if a semi-monthly respondent
always reports as if there is a 10-day month, the AWH mean for
10-day months may be near 40 hours (factor of .50 * reported
hours of 80) and for 11-day months near 36 hours (factor of .45 *
reported hours of 80). Respondents whose data reflect this type
of pattern are flagged by the test as the presumed source of the
spikes in the AWH series.
As expected, very small percentages of the weekly and biweekly
reports were flagged by the equal means test, while nearly half
of the semi-monthly reports and over 20% of the monthly reports
were. When a simulated series was produced with these flagged
reports deleted, the calendar related spikes were mitigated but
not completely eliminated.
To identify reports that may be the source of the AHE spikes,
a related screening test was developed. This test sought to
identify respondents who were reporting hours that vary
appropriately with the number of days in a month (i.e., were not
flagged by the hours equal means test above) and also were
reporting fixed payroll figures, such that using the same
conversion factors for both payroll and hours is problematic. To
implement this test, average pay per worker (payroll/number of
production workers) was calculated separately for shorter and
longer months. The interpretation of the results is analogous to
that for the hours test above. If a respondent reports a fixed
payroll across months, the report will be flagged by the equal
means test because of the fluctuations introduced by the variable
conversion factors. Thus respondents who are identified as having
equal means across months for hours but unequal means for payroll
are presumed to be the source of the AHE spikes. The percentages
of CES reports that meet these criteria was only 3.8% overall,
but 12.8% of semi-monthly reports and 6.8% of monthly reports are
flagged by this test. When the AHE estimates were simulated
without the flagged reports, the fluctuations were slightly
dampened but not eliminated.
Respondent Recontact As an independent
effort to confirm conclusions from the microdata examination and
the REGARIMA modeling, a sample of 100 monthly and semi-monthly
respondents was selected and edit reconciliation call backs made
to the employers to inquire about their hours and earnings
reporting practices.
Key findings from the callbacks relate to the availability of
payroll and hours records used as a basis for CES reporting.
Respondents report using actual hours figures over 90% of the
time to compile data for their hourly paid workers. By contrast
actual hours were available only 12% of the time for salaried
workers. When actual hours figures were not available, they were
estimated, usually according to some fixed formula or by using a
constant value, e.g., always reporting 80 hours per employee for
a semi-monthly pay period. When asked if the number of hours they
reported would vary with the number of weekdays in a month, about
80% of respondents said yes for the hourly paid workers; they
answered yes only 20% of the time for the salaried workers. The
absence of actual records for hours data helps explain the high
incidence of apparent response error for AWH, as the estimation
methods used by respondents often do not take into account the
varying number of weekdays in a month.
The result of asking the same questions for payroll rather
than hours indicates a much higher percentage of respondents have
actual payroll records available for salaried workers as compared
with hours data for that group: about 50% have actual payroll
data as compared with the 12% who have actual hours data. Nearly
90% of respondents had actual payroll data for hourly paid
workers.
Another important finding from the respondent recontact effort
was that among those surveyed, most had both hourly paid and
salaried workers combined in their report. This argues for
collecting hourly and salaried worker payrolls as two separate
figures in the CES program in order to handle payroll and hours
conversions properly. Currently a single total payroll and total
hours figure are collected. Separate reporting generally appears
to be feasible from the respondents point of view
77% of the respondents with both types of payrolls said they
could provide separate payroll figures for hourly and salaried
workers.
The results of the respondent recontact effort also were
cross-tabulated against results from the equal means screening
tests. In about 70% of the cases, the recontact produced the
expected answer from the respondent given the equal means test
results for AWH. For AHE, the results between the equal means
test and the respondent recontact were more disparate. Only about
60% of the time did the screening test results and respondent
information correspond.
Summary and Implementation Plans - All of the
research efforts confirmed that monthly and semi-monthly reports
and their treatment in the CES processing systems are the source
for calendar-related spikes in hours and earnings series. Tests
designed to edit out problematic reports do not provide a
satisfactory resolution of the problem for two reasons. First,
the results of the tests could not be consistently validated with
respondents own explanations of how their data were
developed and secondly, simulations did not consistently show a
significant improvement for the AHE series from deleting those
reports flagged by the screening tests.
Utilizing REGARIMA models to identify and control for the
calendar-related spikes now present in the AWH and AHE series
provides a more viable solution. The observed problems in the
hours and earnings series can be effectively eliminated in the
seasonally adjusted AWH and AHE series by the application of the
models for appropriate industry series. BLS will implement a
REGARIMA-based length-of-pay period adjustment with the
introduction of CES national benchmark revisions in June.
Specifically, the adjustment will be implemented as follows:
- All division level AWH series in the service-producing
sector will be adjusted: transportation and public
utilities, wholesale trade, retail trade, finance,
insurance and real estate, and services.
- The division level AHE series for wholesale trade,
finance, insurance and real estate, and services will be
adjusted.
- The series to which the length-of-pay period adjustment
is applied will not be subject to the 4- versus 5-week
adjustment, as the modeling cannot support the number of
variables that would be required in the regression
equation to make both adjustments. Because the 4- vs
5-week models show only marginal significance in the
service-producing industries their replacement with the
length-of-pay period adjustment is a viable trade-off.
The 4- versus 5- week adjustment is most significant in
manufacturing hours and earnings series; it will continue
to be applied there and in other divisions not affected
by the length-of-pay period variable.
- The total private hours and earnings series are formed
from a weighted average of component series and thus will
be affected by the length-of-pay period adjustment at
lower levels. The research results from applying the
REGARIMA smoothing techniques are shown on Tables 2 and 3
for the total private AWH and AHE series. The hours series effects
range from zero to +0.4 of an hour on the
over-the-month changes. The earnings series
effects range from zero to +4 cents on the
over-the-month changes.
- The affected series will be adjusted from 1989 forward.
There is no statistically significant correlation
measured between series movements and length-of-pay
period prior to that point.
- Revised hours and earnings data incorporating the
REGARIMA adjustments for length-of-pay period will be
published with the release of CES national benchmark
revisions and the May Employment Situation news release
on June 5, 1998. The 6-months of projected seasonal
factors published for May through October 1998 also will
include this refinement.
Effect on Analysis Implementation of
the REGARIMA-based smoothing techniques will eliminate a
significant source of non-economic volatility in the CES hours
and earnings series, thereby improving the month-to-month
measurement of underlying economic trends. A recent example of
this occurs for the months of November and December 1997. As
shown on table 2 the published over-the-month change for AWH for
November (a short month) was +0.3 hour. This was reversed in
December (a long month) with an over-the-month change of -0.2
hour. When the series is adjusted for the length-of-pay period
effect, it shows less volatility. The November over-the-month
change is 0.1 hour while the over-the-month change for
December is zero, indicating there was little actual change in
AWH over those months.
An analogous observation can be made for AHE for November and
December 1997. As shown on table 3, the published over-the-month
change for November was +8 cents, followed by an over-the-month
change of zero for December. With adjustment for the
length-of-pay period effect the over-the-month changes are +4
cents for November and +2 cents for December, figures more
reflective of the actual underlying earnings trend.
Further Research and Longer Term Corrective Action -
While application of the REGARIMA models will improve measurement
of the seasonally adjusted over-the-month change it will not
correct the underlying microdata response and processing errors,
nor correct the not seasonally adjusted series. BLS will continue
to research and plan for longer term corrective actions in these
areas as part of the comprehensive concepts review and sample
redesign efforts now underway. Further research and review will
include:
- modification to existing processing systems to apply
differing length-of-pay period conversion factors to
hours and payroll data when appropriate;
- re-examination of procedures for collecting hours figures
for salaried workers when hard information may not be
available from a large percentage of respondents; and
- assessment of the feasibility of collecting payroll
information separately for hourly paid and salaried
workers in the CES survey.
Last Modified Date: October 16, 2001