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Fluctuations in Hours and Earnings

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 12^th of the month. For a majority of sample respondents this equates to the week including the 12^th, 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 1^st through the 15^th 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