20 Monthly Labor Review August 1999

Hours and Earnings Fluctuations Hours and Earnings Fluctuations

Noneconomic fluctuations

in hours and earnings data

BLS hours and earnings series are subject

to noneconomic calendar-related fluctuations

caused by response error in semimonthly and monthly

reports and the processing limitations of the payroll survey

Jurgen Kropf

and

Patricia Getz

Jurgen Kropf and

Patricia Getz are

economists in the

Office of Employmnent

and Unemployment

Statistics, Bureau of

Labor Statistics.

The Current Employment Statistics (CES)

survey collects payroll information from a

sample of about 390,000 business establishments across the Nation and provides monthly

estimates of nonfarm wage and salary employment, average weekly hours, and average hourly

earnings. The month-to-month movements in these

series are closely watched by policymakers, forecasters, and other analysts as timely indicators of

the overall strength and direction of the Nation’s

economy. In recent years, some CES data users

have inquired about the possibility of noneconomic,

calendar-related fluctuations in the hours and earnings series.

In 1997, researchers at the Bureau of Labor

Statistics established a correlation between overthe-month changes in the hours and earnings series

and the number of weekdays in a calendar month.

An initial review of the hours and earnings series revealed that the fluctuations were concentrated in the service-producing industries—especially in finance, insurance and real estate—and

that they could be traced to survey reporters with a

high proportion of salaried employees and semimonthly or monthly payrolls. These findings led to

an examination of how these reports are treated within the CES production system. The examination revealed that both response error

and the "normalization" process used to convert reports with other-than-weekly pay periods

to the weekly equivalent were contributing to

the noneconomic fluctuations in the hours and

earnings series.

This article describes the research methods

used and the results obtained in this study. Several methods were used to identify and measure

the noneconomic fluctuations. First, the microdata were tested for statistical differences between reported hours and earnings for months

with different numbers of workdays. Second, reporters were contacted directly in order to clarify

their reporting practices—specifically, their methods of calculating the hours and earnings data that

they provided on the survey form. Third, the CES

production process was simulated with certain

modifications, including the elimination of problematic reports and the use of different correction factors to normalize the hours and earnings

data. Finally, using the REGARIMA statistical technique, models were developed to measure and

adjust for the effect of the length of pay period on

the hours and earnings series.

To correct the noneconomic fluctuations in the

hours and earnings series, the system should be

modified to convert each report appropriately, depending on the reporting practice of the respondents. In addition, respondents should be educated

on the proper method of reporting hours in unusual cases, such as when the length of pay period is 11 or 12 days. Also, ideally, hours and earnings data should be collected separately for workers paid by the hour versus those paid by salary.

The implementation of these corrective measures

would require considerable time and resources,

however, and thus could only be accomplished as

a long-term project. In the short run, the use of
Monthly Labor Review August 1999 21

REGARIMA models continues to be the most feasible and effective method of correcting the fluctuations, although currently only the seasonally adjusted hours and earnings series

are corrected.

The Current Employment Statistics survey

In the CES survey, average weekly hours and average hourly

earnings data are not collected directly. Instead, respondents

report their gross payrolls and the corresponding total hours

paid for production workers, construction workers, and

nonsupervisory workers. (Henceforth, these three types of

workers will be referred to as production workers.) Data items

refer to persons who worked during, or received pay for, any

part of the pay period that includes the 12th of the month.

Average weekly hours are computed as

(1) AWH = WH/PW,

where

WH = total worker hours,

PW = total production workers.

Average hourly earnings are given by

(2) AHE = PR/WH,

where

PR = gross payroll (for production workers),

PW = total production workers.

Data are reported for the pay period that includes the 12th

of the month, with respondents indicating the length of the

pay period as follows:

Weekly = 5-day pay period

Biweekly = 10-day pay period

Semimonthly = 10- to 11-day pay period

Monthly = 20- to 23-day pay period.

When respondents report data for pay periods of more than 1

week in duration, the reports must be “normalized”—that is, the

payroll and hours data must be converted to 1-week equivalents.

For this purpose, conversion factors or length-of-pay-period (LP)

codes are applied to the reported figures, using the modified

formulas

AWH= ( LPD * WHR ) / PW,

and

AHE = ( LPD * PR ) / WHN,

where

LPD =

1.0 when number of days (D) in pay period (PP) = 5,

.45 when D = 11 (semimonthly),

.50 when D = 10 (semimonthly or biweekly),

.45 when D = 11 (semimonthly),

.50 when D = 10 (semimonthly or biweekly),

.22 when D = 23 (monthly),

.23 when D = 22 (monthly),

.24 when D = 21 (monthly),

.25 when D = 20 (monthly),

WHR = reported hours,

WHN = normalized hours.

Test of microdata

The normalized microdata from the survey reports were analyzed in an attempt to identify problematic reports. The underlying assumption in the CES estimation process for average

weekly hours and average hourly earnings is that respondents

vary their reported payroll and hours data according to the

number of days in their respective pay periods. This assumption is reasonable for respondents with predominantly hourly

paid employees—these respondents are most likely to have

accurate records on the number of hours for which their employees were paid.

But in cases in which the respondents have a high percentage of salaried employees who are paid a fixed amount for

each pay period, the reported payroll figure does not vary by

the number of days in a pay period, and a record of the actual

number of hours paid may not be available. The reported number of total hours worked may reflect the fixed payroll and

thus may not vary by the number of days worked either. As a

result, when respondents with semimonthly or monthly pay

periods report fixed work-hours and fixed payroll, the normalization procedure of the CES production system could introduce fluctuations for pay periods with varying numbers of workdays.

This hypothesis is translated into a test of the difference

between two population means, namely

H0: m1 - m2 = 0,

and

HA: m1 - m2 < 0,

where

m1 = population mean when D = 10, 20, and 21,

m2 = population mean when D = 11, 22, and 23.
22 Monthly Labor Review August 1999

Hours and Earnings Fluctuations

The test statistic is defined as

t = (y1 - y2) / sp Ö ( 1/n1 + 1/n2 ),

where

y1 = sample mean when D = 10, 20, and 21,

y 2 = sample mean when D = 11, 22, and 23,

n1 = number of months in which D = 10, 20, and 21,

n 2 = number of months in which D = 11, 22, and 23,

sp = estimated standard deviation s for m1 and m2,

s1,2 = sample variances.

 Note also that

sp

 = Ö [(n1-1)s1

2

 + (n2-1)s2

2

]/( n1+ n2-2)

for the rejection region, a = .025, df = n1 + n2 - 2, and we

reject H0 if t > ta.

The data tested were the calculated average weekly hours

and average hourly earnings figures for each reporter, according to formulas (1) and (2) shown above. A reporter failing this

means test (H0 is rejected) is assumed to report fixed workhours and payroll. By normalizing the reported data, the CES

production system introduces the observed fluctuations into the

data for these reporters.

Table 1 lists the distribution of reports by pay period and the

percentage of reports failing the test for average weekly hours.

The results of the means test indicate that nearly half of the

semimonthly reports display significant differences in normalized work-hours between months with varying workdays per

pay period. The table also shows that the majority of semimonthly (and hence, problematic) reporters are in the serviceproducing industries, with finance, insurance, and real estate

having the largest share.

The results of the means test for hourly earnings are not as

apparent as those for weekly hours. However, about 10 percent of semimonthly reports and 6 percent of the monthly reports display significant differences in normalized payrolls between months with varying numbers of workdays per pay period. The smaller number of reports testing significantly different for average hourly earnings can be best explained by recalling the procedure that the CES production system uses to

calculate the hourly earnings figures:

AHE = ( LPD, PP * PR ) / WHN

The product LPD, PP * PR calculates the normalized payroll, which then is divided by the normalized work-hours. The

same conversion factor (LP) is used to normalize both data

elements. Therefore, for respondents who report fixed workhours and fixed payroll, the division of the two data elements

neutralizes the conversion factors and the resulting average

hourly earnings series do not display the fluctuations introduced by the factors. Only the earnings series for those respondents who report fixed payroll figures but vary the number of reported work-hours according to the number of workdays per pay period display the fluctuations—in this case introduced by the conversion factor during the normalization of

the payroll figures.

Respondents contact

In an independent effort to confirm the results obtained from

examining the microdata, a sample of 100 monthly and semimonthly respondents was selected and each was contacted by

telephone to ask about how they report their hours and earnings data. Overall, there were 75 usable responses from the

100 sample cases. An important basic finding is that 53 of the

75—70 percent—had both salaried and hourly workers.

For their hourly paid workers, respondents stated that they

used actual hours figures more than 90 percent of the time.

For salaried workers, on the other hand, actual hours were

available only 12 percent of the time. For the rest of the time,

Table 1. Distribution of reports failing means test for average weekly hours by pay period

All pay periods Weekly pay periods Biweekly pay periods Semimonthly pay periods Monthly pay periods

Total Percent Percent of Percent Percent of Percent Percent of Percent Percent of Percent

number of failing total failing total failing total failing total failing

means test reports means test reports means test reports mean test reports reports means test

Total private .......... 223,903 8.5 52.6 3.9 32.9 4.6 9.2 46.3 5.3 16.6

Mining ................... 2,130 10.3 42.9 3.1 39.4 5.1 9.6 51.2 8.1 25.0

Construction ......... 23,320 3.1 89.2 2.7 6.6 3.8 1.1 22.1 3.1 7.8

Manufacturing ....... 48,763 5.6 74.2 4.5 20.2 4.9 3.0 32.2 2.6 12.1

Transportation and

public utilities ..... 11,660 8.7 36.2 3.2 44.1 3.2 11.9 42.1 7.7 14.1

Wholesale trade .... 17,939 10.4 47.6 3.5 35.1 4.6 10.4 52.4 6.9 24.7

Retail trade ........... 49,231 6.5 53.3 3.0 36.6 4.7 6.3 41.1 3.8 15.2

Fire, insurance,

and real estate .. 15,078 20.1 16.9 2.9 48.0 6.2 24.2 58.5 10.9 22.7

Service ................. 55,782 11.6 32.8 3.3 44.3 4.4 15.7 45.3 7.2 15.1

 Industry
Monthly Labor Review August 1999 23

the hours figures were estimated using some fixed formula or a

constant value. Respondents said that they vary the number

of hours that they report with the number of weekdays in a

month for about 80 percent of their hourly paid workers and

for only about 20 percent of their salaried workers. The results are similar for the payroll figures except that a higher

percentage of respondents stated having actual payroll data

for salaried workers—about 50 percent, compared with the 12

percent having actual hours data.

The overall conclusion from the data is that the CES conversion practices generally are appropriate for hourly paid

workers, but not for salaried workers. Because most respondents have both types of workers, collecting separate reports

for hourly and salaried workers would be better, but that would

require far-reaching changes to CES production and data collection systems. From the point of view of the respondents,

collecting separate reports may be quite feasible—77 percent of

the respondents indicated that they could provide separate payroll figures for hourly and salaried workers.

The responses from telephone contacts were compared

with the results from the means test and are shown in the

following tabulation. In about 70 percent of the cases, the

telephone survey answers supported the findings of the

means tests for average weekly hours. For example, a report failed the average weekly hours means test and the

respondent confirmed that they did in fact report a constant number of hours. For average hourly earnings, the

comparison between the means test and the telephone survey answers yielded somewhat more disparate results—

only 60 percent of the telephone respondents gave the

expected answers.

Reporting practice Failed means test Passed means test

Fixed hours .................. 43 9

Varying hours .............. 9* 2**

Fixed payroll................. 30 4

Varying payroll ............. 5* 5**

* False positive

** False negative

The lack of stronger correspondence between the means

test results and the telephone respondent answers clouds

the issue of whether the identification of the problematic

reports could be a solution to the problem of noneconomic

fluctuations in the CES hours and earnings series. Undoubtedly, at least part of the problem is due to the limitation imposed by collecting only one payroll and hours figure,

making it difficult to separately review and test salaried

and hourly worker data.

35.0

35.2

35.4

35.6

35.8

36.0

36.2

36.4

36.6

36.8

37.0

37.2

35.0

35.2

35.4

35.6

35.8

36.0

36.2

36.4

36.6

36.8

37.0

37.2

Published Reconstructed Without problem reports Failing AWH test

Chart 1. Various average weekly hours series for finance, insurance, and real estate 

Average

weekly

hours

Average

weekly

hours

1996 1997
24 Monthly Labor Review August 1999

Hours and Earnings Fluctuations

Simulation of estimates

In order to simulate the effects of three kinds of adjustments,

the CES estimation process was recreated in this study. First,

all reports with semimonthly or monthly pay periods were

removed and the hours and earnings series were reestimated

using only the remaining reports. Second, for average weekly

hours, all reports failing the means test were removed, and for

average hourly earnings, the reports passing the average

weekly hours test but failing the earnings test were removed,

and the series were reestimated using only the remaining reports. Third, the conversion factor to normalize the series was

changed to reflect the fixed work-hours and payroll reports

and the corrected factor was applied to the reports failing the

means test. The factor was changed to a fixed value of .46 for

semimonthly reports and .23 for monthly reports.

The average weekly hours series for finance, insurance, and

real estate are shown in chart 1. All three treatments successfully reduce the magnitude of the fluctuations displayed by the

published and reconstructed series during months with fewer

workdays per pay period, although some evidence of the underlying spikes remains. The treatments for average hourly earnings

produced a somewhat smoother series but because the fluctuations were not as pronounced as in the average weekly hours

series, the interpretation is more ambiguous.

An important observation here is that some of the treatments

lower the level of the series. A review of sample averages by

length of pay period confirmed that semimonthly and monthly

reports had higher paid workers as compared with weekly and

biweekly reports. It is difficult to conclude that any of the simulated series are substantially improved over the published or

reconstructed series. Moreover, because these series are not

seasonally adjusted, the interpretation is particularly difficult,

especially because the average hourly earnings series display

strong seasonal movements in some months.

REGARIMA modeling and diagnostics

The Model. For seasonal adjustment, the CES program uses the

X-12-ARIMA software developed by the Bureau of the Census.

For most of the published seasonally adjusted series, a technique known as REGARIMA modeling is used to identify the

estimated size and significance of calendar effects, adjusting for

them accordingly. Examples include the adjustments for interval

effect between survey weeks currently applied to the CES employment series and the adjustment for moving holidays in the

hours series.

The REGARIMA models evaluate the variation in levels attributable to varying calendar effects in the same month of different

years. The effects are examined by a joint chi-square test, which

provides evidence of statistical significance across all model

variables, and by t-tests on individual coefficients. Adjustment

factors are calculated and applied to the original series in connection with the seasonal factors. Because calendar effects are

known in advance, factors can be forecasted based on the observed effects in past months. The observed fluctuation in the

hours and earnings series are also related to calendar effects,

making the application of the REGARIMA modeling technique a

possible alternative in the mitigation of the fluctuations.

The multiplicative decomposition of time series is described

by the model

Y = T * S * I * P

where

T = trend component

S = seasonal component

I = irregular component

P = the prior adjustment factor with decomposition

P = PT

 * PL * PI .

In this application, the length of the period is month-specific, and is estimated as the factor PL . For seasonal adjustment, it is combined with the seasonal factor, and the seasonally adjusted values are derived from the formula

Y / ( S * PL ) = T * I * PT

 * PI .

Table 2. t-statistics for length-of pay-period variables for average weekly hours by selected industry divisions

Length-of pay- Transportation Finance,

 period and public Wholesale trade Retail trade insurance, and Services

 variable utilities real estate

January .............. 3.87 5.15 5.79 12.29 9.20

February ............. 2.19 6.30 5.06 14.28 7.53

March ................. .44 6.50 1.97 14.05 7.56

April .................... 4.49 3.87 5.94 10.11 6.70

May .................... 1.86 6.14 1.47 11.68 9.06

June ................... 3.80 5.66 4.54 14.25 6.15

July .................... 3.11 4.51 3.51 10.68 6.40

August ................ .52 4.48 2.49 12.68 6.93

September .......... 2.54 3.25 1.81 11.63 4.91

October .............. 3.26 5.78 4.02 12.10 8.23

November ........... 4.16 4.65 .98 13.13 6.63

December ........... 2.81 4.50 2.91 11.74 5.90
Monthly Labor Review August 1999 25

Smoothness tests and sliding span evaluation of the length-of-pay-period adjustment

Smoothness Tests Span I: 1988–95 Span II: 1989–96 Span III: 1990–97

Percent change

in root-meansquared

 error

Average hourly earnings:

Wholesale trade ..................... 71.0 –40.1 –53.4 11 0.00 11 0.00 12 0.00

Finance, insurance,

and real estate ................... 66.0 –52.0 –47.4 12 0.00 12 0.00 12 0.00

Services ................................ 78.0 –27.5 –31.4 11 0.00 12 0.00 11 0.00

Average weekly hours:

Transportation and public

utilities ............................... 74.0 –35.8 –46.9 7 0.00 9 0.00 10 0.00

Wholesale trade ..................... 60.0 –66.6 –89.4 12 0.00 11 0.00 11 0.00

Retail trade ............................ 68.0 –48.0 –56.8 7 0.00 8 0.00 8 0.00

Finance, insurance,

and real estate ................... 47.0 –113.0 –210.0 12 0.00 12 0.00 12 0.00

Services ................................ 45.0 –123.0 –99.2 12 0.00 12 0.00 12 0.00

As with other interventions and calendar effects, extended

ARIMA models are used to estimate the effect of the length of

pay period on the estimates by means of the formula

Log yt - å aj Mjt - å bj Xjt = y ( B, B12) at

where

yt = the observed series;

Mjt = the month variables;

Xjt = the outliers or other interventions;

aj = the noise term;

y = the seasonal ARIMA model.

On the log scale, the effect of the length of the pay period

of month j at time t is defined as

-ajMjt,

 where

Mjt =

 1.0 when t = j(mod 12), 10-day pay period,

 –0.4 when t = j(mod 12), 11-day pay period,

 0, otherwise.

The adjustment for the length of pay period is sometimes

positive and sometimes negative. Because there are more instances of 11-day pay periods, the factor -0.4 helps achieve balance in these effects. This is analogous to the property that the

mean of the seasonally adjusted series should be close to the

mean of the unadjusted series. Notice also that only two factors

are used which test only the effects of semimonthly reports on

the series. Tests showed that by including four additional factors to account for the effects of the differences in pay periods of

monthly reporters, the model does not improve and the adjustment factors estimated by the model become weaker for some

months.

Significance tests for the length-of-pay-period. Chi-square and

t-statistics were observed for testing the significance of the joint

contribution and coefficients for each of the 12 monthly lengthof-pay-period variables. As shown in table 2, of the 29 published

average weekly hours series fitted with models using the explanatory variables, all 5 service-producing divisions had t-statistics greater than 2 for at least 8 of the 12 monthly variables.

Three industry divisions—wholesale trade; finance, insurance,

and real estate; and services—had t-statistics for all 12 variables

greater than 3. The finance, insurance, and real estate division

had t-statistics greater than 10 for all 12 variables, indicating that

the length of pay period has a dominating effect on the over-themonth changes of this series. In addition to these significant tstatistics, the variables for all 5 series were positive, resulting in

regression factors greater than 1 for all months with 10-day pay

periods, therefore adjusting the series in the correct direction

and mitigating the fluctuations.

The mining and construction divisions and 22 two-digit industries in manufacturing displayed only a few significant t-statistics for the length-of-pay-period variables. Moreover, the signs

Data series and industry

division Smoothness

 ratio

Full

series

Last 3

years

Number of

months

in which

t > 0

Joint

p-value

Number of

months

in which

t > 0

Joint

p-value

Number of

monthsin which

t > 0

Joint

 p-value

Table 3.
26 Monthly Labor Review August 1999

Hours and Earnings Fluctuations

of the t-statistics were both positive and negative, therefore having coefficients, which in some months contribute to the spikes.

Based on the t-statistics and the effect of the variables, it was

concluded that the average weekly hours series for the goodsproducing industries are not significantly affected by the length

of pay period and do not require an adjustment for this effect.

Of the eight published average hourly earnings series fitted

with models using the explanatory variables, three service-producing divisions had t-statistics greater than 2 for at least 11 of

the 12 variables displaying the same sign. The other five divisions

displayed only a few t-statistics greater than 2 and the signs of

the t-statistics were not equal. Based on these results, only the

average hourly earnings series for wholesale trade; finance, insurance, and real estate; and services are adjusted for the lengthof-pay-period effect.

Smoothness tests, sliding spans, seasonal adjustment. For

validation of the REGARMIA models, four tests were conducted,

the results of which are shown in table 3. First, a smothness ratio

was calculated for each treated series by dividing the square root

of the sum of the squared first differences of the LP-adjusted

series by those of the unadjusted series. A value of less than 100

indicates that the adjusted series is smoother. Second, the

percent change in root-mean-squared error was calculated as the

percent difference between the root-mean-squared errors of the

unadjusted series and those of the LP-adjusted series. A negative

percentage indicates that the LP-adjusted series is smoother.

The percent change is calculated for the full series and for the

last 3 years.

Third, a sliding span analysis was conducted, separately testing 3 different periods: 1988–95, 1989–96, and 1990–97. A t-statistic greater than 2.0 indicates the number of significant variables or months in the model (maximum = 12) for each span. The

joint p-value of less than 0.10 indicates that the variables are

jointly significant for each span.

Finally, the sliding span analysis also included tests of the seasonal factors, the final seasonally adjusted series, and the monthto-month changes in the seasonally adjusted series for stability

over the 3 spans. Months were flagged as unstable if the difference of an analysis variable for the same month was greater

than 3 percent from one span to the next. For these tests, no

month was flagged as unstable.

The following tabulation shows statistics for finance, insurance, and real esate and for services before and after treatment.

Finance, insurance,

 and real estate Services

Statistic Before After Before After

Stable F-Statistic ........ 0.66 7.68 21.60 105.80

Moving F-Statistic ..... 1.55 1.42 .61 0.30

M7-Statistic ............... 2.83 .86 .47 .19

Q-Statistic .................. 2.30 .83 1.27 .65

Table 4. Over-the-month changes in average weekly hours, with and without length-of-pay-period (LP) adjustment,

 and difference, 1993–98

January February March April May June July August September October November December

1993:

 LP-adjusted ........... .1 0 –.2 .2 0 –.1 .1 0 .1 0 0 0

Not LP-adjusted ..... .1 0 –2 .2 .2 –.2 .1 .1 –.1 0 0 0

Difference .............. 0 0 0 0 –.2 .1 0 –.1 .2 0 0 0

1994:

 LP-adjusted ........... 0 –.2 .3 –.1 .1 0 0 –.1 0 .1 –.1 .1

Not LP-adjusted ..... .3 –.5 .3 0 .1 –.1 0 –.1 .1 .2 –.2 0

Difference .............. –.3 .3 0 –.1 0 .1 0 0 –.1 –.1 .1 0.1

1995:

 LP-adjusted ........... 0 –.2 0 0 –.2 .1 0 0 0 0 0 –.1

Not LP-adjusted ........ .3 –.4 0 .1 –.4 .2 .1 –.1 0 .1 –.1 –.1

Difference ................. –.3 .2 0 –.1 .2 –.1 –.1 .1 0 –.1 .1 0

1996:

LP-adjusted ........... –.4 .6 –.1 –.1 .1 .2 –.2 .1 .1 –.1 0 .1

Not LP-adjusted ..... –.4 .5 0 –.1 0 .4 –.4 .2 .2 –.3 .1 .2

Difference .............. 0 .1 –.1 0 .1 –.2 .2 –.1 –.1 .2 –.1 –.1

1997:

LP-adjusted ........... –.1 .1 .1 –.1 .1 –.2 0 .2 –.1 0 .1 0

Not LP-adjusted ..... –.3 .4 0 –.3 0 .1 –.2 .2 –.1 0 .3 –.2

Difference .............. .2 –.3 .1 .2 .1 –.3 .2 0 0 0 –2 .2

1998:

 LP-adjusted ........... .1 –.1 –.1 –.1 –– –– –– –– –– –– –– ––

 Not LP-adjusted .... .2 .1 –.2 –.3 –– –– –– –– –– –– –– ––

 Difference ............. –.1 –.2 .1 .2 –– –– –– –– –– –– –– ––

– = Data unavailable at time of study.

Item

Table 4.
Monthly Labor Review August 1999 27

As can be seen, the adjustment for the length of pay period

resulted in additional improvements to the data. Before the

LP-adjustment, the seasonally adjusted average weekly hours

series for these two industry divisions were not available to

the public because the data did not meet BLS publication standards. After the adjustment, both series met the publication

standards.

Effects of the treatment

The implementation of the REGARIMA-based smoothing

techniques eliminates a significant source of noneconomic

volatility in the CES hours and earning series, thereby improving the month-to-month measurement of underlying

economic trend. A recent example of this occurs for the months

of November and December 1997. As shown in table 4, the

over-the-month change for average weekly hours not adjusted for the length of pay period in November (a 10-day

pay period) is 0.3 hour. This change is reversed in December (an 11-day pay period) 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 in December is zero, indicating there is little actual change in aver-

 able 5. Over-the-month changes in average hourly earnings, with and without length-of-pay-period adjustment, and

 difference, 1993–98

January February March April May June July August September October November December

1993:

 LP-adjusted ......... 0.03 0.01 0.05 0 0.02 0.02 0.02 0.02 0.03 0.02 0.02 0.03

Not LP-adjusted .. .04 .02 .03 .01 .04 –.01 .03 .03 .01 .02 .03 .03

Difference ............ –.01 –.01 .02 –.01 –.02 .03 –.01 –.01 .02 0 –.01 0

1994:

 LP-adjusted ......... .03 .03 .01 .02 .03 .02 .02 .02 .03 .04 .02 .03

Not LP-adjusted .. .03 .04 0 .03 .03 .01 .02 .02 .03 .06 0 .03

Difference ............ 0 –.01 .01 –.01 0 .01 0 0 0 –.02 .02 0

1995:

 LP-adjusted ......... .01 .04 .02 .02 .02 .04 .04 .03 .03 .03 .02 .03

Not LP-adjusted .. .02 .04 .01 .04 0 .04 .06 0 .04 .05 .01 .02

Difference ............ –.01 0 .01 –.02 .02 0 –.02 .03 –.01 –.02 .01 .01

1996:

 LP-adjusted ......... .05 0 .03 .06 .02 .06 .03 .03 .04 .03 .05 .04

Not LP-adjusted .. .04 .02 .02 .05 .03 .07 0 .05 .05 0 .07 .05

Difference ............ .01 –.02 .01 .01 –.01 –.01 .03 –.02 –.01 .03 –.02 –.01

1997:

 LP-adjusted ......... .04 .03 .04 .03 .04 .03 .03 .07 .03 .06 .04 .03

Not LP-adjusted .. .02 .05 .04 0 .05 .04 .01 .07 .04 .05 .08 0

Difference ............ .02 –.02 0 .03 –.01 –.01 .02 0 –.01 .01 –.04 .03

1998: ........................

 LP-adjusted ............ .04 .05 .04 .07 –– –– –– –– –– –– –– ––

 Not LP-adjusted ..... .04 .07 .04 .04 –– –– –– –– –– –– –– ––

 Difference .............. 0 –.02 0 .03 –– –– –– –– –– –– –– ––

– = Data unavailable at time of study.

Table 5.

age weekly hours over those months. Similarly for average

hourly earnings, as shown in table 5, the series not adjusted

for the length of pay period increases in November by 8 cents

and is flat for the December over-the-month change. The adjustment corrects the series to increase in November by 4

cents and by 3 cents in December, figures more reflective of

the actual underlying earnings trend.

THE CES HOURS AND EARNINGS SERIES are subject to noneconomic, calendar-related fluctuations caused by response error in semimonthly and monthly reports and the processing

limitations in the CES production systems. Modeling with the

REGARIMA technique results in the successful treatment of

these fluctuations and smooths the problematic series. The

treatment succeeds both in correcting historical data and incorporating the treatment in forecasted seasonal factors. A

drawback of the treatment process is that currently only the

seasonally adjusted series are corrected. Correcting the unadjusted series would require a change in the CES data collection prodedures to solicit average weekly hours and average

hourly earnings data separately for hourly and salaried employees. It also would require a change in the way in which

hours and earnings data are handled in the CES data collection systems. BLS currently is evaluating both measures to

determine the feasibility of further action.

Item