Causes and Treatments of Non-Economic Fluctuations in

Average Weekly Hours and Average Hourly Earnings Series

Patricia Getz, Jurgen Kropf and Michael Roosma, U.S. Bureau of Labor Statistics

Jurgen Kropf , 2 Massachusetts Avenue N.E., Room 4860, Washington, DC 20212

Key Words: Time series models, X-12-ARIMA,

seasonal adjustment, calendar effects

1. Introduction

 The Current Employment Statistics (CES)

program is a survey of nearly 380,000 business

establishments nationwide, which provides monthly

estimates of nonfarm payroll jobs, average weekly

hours (AWH) and average hourly earnings (AHE) of

workers. The month-to-month movements in these

series are closely followed by policy makers and

forecasters as timely indicators of the overall strength

and direction of the nation's economy. In recent years

a number of CES data users inquired about fluctuation

in AWH and AHE series which seemed to be calendar

related rather than driven by economic reasons. In

1997, researchers both within and outside the Bureau

of Labor Statistics (BLS) established a correlation

between over-the-month changes in AWH and AHE

series and the number of weekdays in a month.

 An initial review of the AWH and AHE series

revealed that the fluctuations were concentrated in the

service-producing industries, especially in the finance,

insurance and real estate division (FIRE), and could

be traced to survey reporters with a high proportion of

salaried employees and semi-monthly or monthly

payrolls. These findings led to an examination of the

treatment of these hours and earnings reports within

the CES production system. The examination

revealed that the conversion process used to

normalize these reports, that is converting reports

with other than weekly pay periods to the weekly

equivalent, was treating some reports inappropriately

and was in part causing the fluctuations.

 Several ways of identifying and measuring the

fluctuations were approached:

• The microdata were tested for statistical

differences between reported hours and earnings

for months with fewer versus larger number of

workdays.

• Reporters were contacted in order to clarify their

reporting practices, specifically their methods of

calculating the hours and earnings they listed on

the reporting form.

• REGARIMA models were developed to capture

the effect of the length-of-pay period with

variables and to treat AWH and AHE series in

order to eliminate the fluctuations.

The methods employed in this research and the results

obtained are listed in detail in this paper. Our

findings confirmed the initial discoveries and are

summarized as follows:

• The source of the calendar related fluctuations in

the AWH and AHE series are the monthly and

semi-monthly reports and their treatment in the

CES production system.

• A modification of the CES production system

would be required to convert each report

appropriately depending upon the reporting

practice of the respondent.

• Respondents have to be educated on the 'correct'

method of reporting hours if these are calculated

by a formula rather then actually recorded.

• Payroll and hours data have to be collected as

separate data items for hourly and salaried

employees in order to ensure proper conversion.

• The implementation of these corrective measures

requires considerable time and resources and

could only be accomplished as a long-term

project.

• In the short run, the use of REGARIMA models

proved to be the most feasible and effective

measure to correct for the fluctuation, however

the correction is applied to the seasonally

adjusted data series only.

2. The Current Employment Statistics Survey

In the CES survey AWH and AHE are not

collected directly, they are derived from the data types

that are collected on the survey form. The series are

based on the reports' gross payroll and the

corresponding paid worker-hours for production

workers. The payroll data item refers to the total

gross production worker payrolls paid directly by the

company to the production workers for the pay period

reported. The worker-hours data item refers to the

total number of hours worked by production workers

and paid for by the company during the pay period

reported.

 

 Any opinions expressed in this paper are those of the

authors and do not constitute policy of the Bureau of

Labor Statistics.
AWH information relates to the average number

of hours per workweek for which pay was received

and is computed as:

AWH = WH / PW

where WH = total worker hours and PW = total of

production workers.

AHE information relates to the gross average

hourly earnings as actual return to a worker for a

stated period of time and is computed as:

AHE = PR / WH

where PR = payroll.

The pay period for which data are reported

includes the 12th of the month. The respondent

indicates the pay period as:

• weekly = assumes 5 days worked/paid

• biweekly = assumes 10 days worked/paid

• semimonthly = from 10 to 12 days worked/paid

• monthly = from 20 to 23 days worked/paid

When a respondent reports data for a pay period

that is longer than one week, it is necessary to reduce

the reported hours and payroll data to 1-week

equivalents (normalization). For this purpose a

conversion factor or length-of-pay period code is

applied to the reported figure which depends on the

number of workdays (D) in the pay period (PP).

Worker hours and payrolls are normalized and AWH

and AHE are calculated as:

AWH = ( LPD, PP * WHR ) / PW

AHE = ( LPD, PP * PR ) / WHN

.45 if D = 11 days and

PP = semimonthly

.50 if D = 10 days and

PP = semimonthly

.22 if D = 23 days and

PP = monthly

where LPD, PP = .23 if D = 22 days and

PP = monthly

.24 if D = 21 days and

PP = monthly

.25 if D = 20 days and

PP = monthly

.50 if PP = biweekly

1.0 otherwise

and WHR = reported worker hours

WHN = normalized worker hours.

3. Test of Microdata

 The microdata, that is the reported, normalized

data, was tested in an attempt to identify problematic

reports. The underlying assumption in the CES

estimation process for AWH and AHE is that

respondents vary their worker hours and payroll by

the number of days per pay period. This assumption

is certainly justify for respondents with weekly or

biweekly payrolls, with a majority of their employees

being paid hourly and with accurate record keeping of

the hours worked. In cases where the respondent has

a high percentage of salaried employees who are paid

a fixed amount for each pay period, the reported

payroll number does not vary by the number of days

in a pay period and an accurate record of the hours

worked might not be available. Here the number of

worker hours reported could reflect a fixed payroll

and might not vary by the number of days worked

either. Therefore, if a respondent with semimonthly

or monthly pay periods reports fixed worker hours

and fixed payroll, the normalization procedure of the

CES production system could introduce fluctuations

for pay periods with varying number of workdays.

This hypothesis is translated into a test of the

difference between two population (pop) means:

H0: μ1 - μ2 = 0

HA: μ1 - μ2 < 0

Test Statistic: t = (y1 - y2) / sp √ ( 1/n1 + 1/n2 )

 where sp = √ [(n1-1)s1

2

 + (n2-1)s2

2

]/( n1+ n2-2)

Rejection Region: α = .025 df = n1 + n2 - 2

Reject H0 if t > tα

Where

μ1 = pop mean for pay periods with 10 workdays

(semimonthly) or 20 and 21 workdays (monthly)

μ2 = pop mean for pay periods with 11 workdays

(semimonthly) or 22 and 23 workdays (monthly)

y1 = sample mean for pay periods with 10 workdays

(semimonthly) or 20 and 21 workdays (monthly)

y2 = sample mean for pay periods with 11 workdays

(semimonthly) or 22 and 23 workdays (monthly)

n1 = number of reported months with 10 workdays

(semimonthly) or 20 and 21 workdays (monthly)

n2 = number of reported months with 11 workdays

(semimonthly) or 22 and 23 workdays (monthly)
sp = estimate of the standard deviation σ for the two

populations, formed by pooling information from the

samples

s1,2 = sample variances

The data tested was the calculated AWH = WHn / PW

and AHE = PRn / WHn for each reporter.

Table 1. Distribution of Reports by Pay Period Failing Means Test for AWH

Industry Total Weekly Biweekly Semimonthly Monthly

Reports Failing Reports Failing Reports Failing Reports Failing Reports Failing

Total Private 223903 8.5% 52.6% 3.9% 32.9% 4.6% 9.2% 46.3% 5.3% 16.6%

Mining 2130 10.3% 42.9% 3.1% 39.4% 5.1% 9.6% 51.2% 8.1% 25.0%

Construction 23320 3.1% 89.2% 2.7% 6.6% 3.8% 1.1% 22.1% 3.1% 7.8%

Manufacturing 48763 5.6% 74.2% 4.5% 20.2% 4.9% 3.0% 32.2% 2.6% 12.1%

TPU 11660 8.7% 36.2% 3.2% 44.1% 3.2% 11.9% 42.1% 7.7% 14.1%

Wholesale 17939 10.4% 47.6% 3.5% 35.1% 4.6% 10.4% 52.4% 6.9% 24.7%

Retail 49231 6.5% 53.3% 3.0% 36.6% 4.7% 6.3% 41.1% 3.8% 15.2%

FIRE 15078 20.1% 16.9% 2.9% 48.0% 6.2% 24.2% 58.5% 10.9% 22.7%

Service 55782 11.6% 32.8% 3.3% 44.3% 4.4% 15.7% 45.3% 7.2% 15.1%

A reporter failing this means test, that is H0 is

rejected, is assumed to report fixed worker hours 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 AWH.

The results of the means test for AWH indicate

that nearly half of the semimonthly reports display

significant differences in normalized worker hours

between months with varying workdays per pay

period. The table also indicates that the majority of

semimonthly reporters are in the service-producing

industries with FIRE having the largest share.

The results of the means test for AHE are not as

apparent as for the AWH series. However, about 10

percent of semimonthly and 6 percent of the monthly

reports display significant differences in normalized

payrolls between months with varying workdays per

pay periods. The smaller number of reports testing

significantly different for AHE can be best explained

by recalling the procedure the CES production

system uses to calculate AHE:

AHE = ( LPD, PP * PR ) / WHN

The product LPD, PP * PR calculates the

normalized payroll which is divided by the

normalized worker hours. The same conversion

factor (LP) is used to normalize both data elements.

Therefore, for respondents who report fixed worker

hours and fixed payroll, the division of the two data

elements neutralizes the conversion factors and the

resulting AHE series do not display the fluctuations

introduced by the factors. Only the AHE series for

those respondents who report fixed payroll figures

but vary the number of reported worker 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.

4. Respondents Contact

 As an independent effort to confirm what we

concluded from examining the microdata, we

selected a sample of 100 monthly and semimonthly

respondents and made telephone calls to ask about

their hours and earnings reporting practices. An

important basic finding is that 70 percent of the

respondents had both salaried and hourly workers.

For their hourly paid workers respondents stated

using actual hours figures over 90 percent of the

time; for salaried workers actual hours were

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

time the hours figures were estimated usually

according to some fixed formula or using a constant

value. When asked if the number of hours they

reported would vary with the number of weekdays in

a month, about 80 percent of the respondents said

yes for the hourly paid workers but only 20 percent

varied the hours for the salaried workers. For the

payroll, the results are similar except a higher

percentage of respondents, about 50 percent, had

actual payroll data for salaried workers.

The overall conclusion from the set of data is

that the CES conversion practices are appropriate for

hourly paid workers, but not salaried worker reports.

Since most of the respondents had both types of

workers it argues for CES to collect hourly and

salaried worker reports as two separate figures and

normalize these reports independently. This would
require far reaching changes with regard to the CES

production system and electronic data collection

system. However, separate reports might be feasible

from the respondents' point of view since 77 percent

of the respondents said they could provide separate

payroll figures for hourly and salaried workers.

 The interviews with the respondents and the

test of the microdata were essential in identifying the

source of the problem, however these research

elements did not provide an immediate and feasible

solution which was found by REGARIMA modeling.

5. REGARIMA Modeling and Diagnostics

5.1. The Model

Data series in the CES program are seasonally

adjusted with X-12-ARIMA software developed by

the Bureau of the Census. A technique known in X12-ARIMA software as REGARIMA modeling is

used to identify the estimated size and significance

of calendar effects in CES series. Example of these

calendar effects are the adjustments for interval

effects between survey weeks currently applied to the

employment series of the program and the

adjustment for moving holidays in AWH 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. Since

calendar effects are known in advance, factors can be

forecasted based on the observed effects in past

months. The observed fluctuation in the AWH and

AHE series are also related to calendar effects which

makes the application of the REGARIMA modeling

technique a feasible alternative in the mitigation of

the fluctuations.

The multiplicative decomposition of time series

is described by the model Y = T * S * I * P , where

P denotes a prior adjustment factor, and has the

decomposition P = PT * PL * PI . In this

application, the length of the period is monthspecific, and is estimated as the factor PL . For

seasonal adjustment, PL is combined with the

seasonal factor, and the seasonally adjusted values

become

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

As with other interventions and calendar effects,

extended ARIMA models are used to estimate the

length-of-pay period effect, written as

Log yt - ∑ αj Mjt - ∑ βj Xjt = ψ ( B, B12) at

Where yt is the observed series, the Mj's represent the

month variables, the Xj's represent the outliers or

other interventions, at represents the noise term and

ψ denotes a seasonal ARIMA model. On the log

scale, the effect of the length of the pay period in

month j at time t is

 1, t = j (mod 12),

10 day pay period

 -αjMjt , Mjt = -.4, t = j (mod 12 ),

11 day pay period

0, otherwise

The adjustment for the length-of-pay period is

sometimes positive and sometimes negative. Since

there are more instances of 11 days 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 monthly pay

periods, the model does not improve and the

estimated adjustment factors become weaker for

some months.

5.2 Tests for Significance of the Length-of-pay

period Variables

Chi-square and t-statistics are observed to test

the significance of the joint contribution and

coefficients for the 12 monthly length-of-pay period

variables. Of the 29 published AWH series fitted

with models using the explanatory variables, all 5

service-producing divisions display t-statistics

greater than 2 for at least 8 months (see table 2.) and

Chi-square values smaller than 0.005. The FIRE

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-the-month

changes of this AWH series. For the goodsproducing industries the variables tested

insignificant. These industries do not display the

spikes and do not require an adjustment for this

calendar effect.

Of the 8 published AHE 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 5 divisions displayed only

a few t-statistics greater than 2 and the signs of the tstatistics were not equal. Based on these results, the
AHE series for the divisions wholesale, FIRE and

services are adjusted for the length-of-pay period

effect.

Table 2. T-Statistics of Length-of Pay-Period

Variable for AWH in Selected Divisions

Month TPU WholesaleRetail FIRE Services

Jan 3.87 5.15 5.79 12.29 9.20

Feb 2.19 6.30 5.06 14.28 7.53

Mar 0.44 6.50 1.97 14.05 7.56

Apr 4.49 3.87 5.94 10.11 6.70

May 1.86 6.14 1.47 11.68 9.06

Jun 3.80 5.66 4.54 14.25 6.15

Jul 3.11 4.51 3.51 10.68 6.40

Aug 0.52 4.48 2.49 12.68 6.93

Sep 2.54 3.25 1.81 11.63 4.91

Oct 3.26 5.78 4.02 12.10 8.23

Nov 4.16 4.65 0.98 13.13 6.63

Dec 2.81 4.50 2.91 11.74 5.90

5.3 Tests of Smoothness, Sliding Spans and

Seasonal Adjustment Statistics

For validation of the REGARIMA models the

following tests were conducted, the results of which

are listed in table 3:

• A smoothness ratio was calculated for each

treated series by dividing the square root of the

sum of the squared first differences of the LPadjusted series and the unadjusted series. A

value smaller than 100 indicates that the

adjusted series is smoother.

• The percent change in root-mean-squared error

is calculated as percent difference of RMSE of

the unadjusted series and the LP-adjusted series,

displayed for the full series and for the last three

years. A negative percentage indicates that the

LP-adjusted series is smoother.

• For the sliding span analysis three spans (1988-

1995, 1989-1996 and 1990-1997) were tested

separately. A t-statistic greater than 2 indicates

the number of significant variables or months in

the model (max. 12) for each span. The joint pvalue smaller than 0.10 indicates that the

variables are jointly significant for each span.

The adjustment for the length-of-pay period resulted

in additional improvements of the seasonal

adjustment procedure of the CES program. Before

the LP-adjustment, two AWH data series, for

finance, insurance and real estate and for service,

were not available to the public because their

seasonal adjustment statistics did not pass the BLS

publication standards for quality. After the

treatment of these two series for the length-of-pay

period effect, both series pass the BLS standards.

6. Effects of the Treatment on the Series

The Implementation of the REGARIMA-based

smoothing techniques eliminates a significant source

of non-economic volatility in the CES hours and

earning series, thereby improving the month-tomonth measurement of underlying economic trends

(see Tables 4 and 5). A recent example for AWH

occurs for the months of November and December

1997. As shown in table 4, the over-the-month

change for AWH 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 (a 11

day pay period) with an over-the-month change of -

0.2 hour. When the series is adjusted for the lengthof-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 AWH

for those months. Similarly for AHE, as shown in

table 5, the series not adjusted for the length-of-pay

period increases in November by +0.08 cents and is

flat for the December over-the-month change. The

adjustment corrects the series to increase in

November by +0.04 cents and by +0.03 cents in

December, figures more reflective of the actual

underlying earnings trend.

7. Conclusion and Limitations

The CES hours and earnings series are effected by

calendar related fluctuation which are caused by

semi-monthly and monthly reports and their

treatment in the CES production system. The

modeling with the REGARIMA technique results in

the successful treatment of these fluctuations and

smoothens the affected series. This treatment also

succeeds in correcting historical data and

incorporating the treatment in forecasted seasonal

factors. Its methodology is analogous to the

treatment of employment series for the interval effect

between survey periods. A drawback of this practice

is the restriction of the application to the seasonal

adjusted series, therefore the length-of-pay period

effect is not removed from the unadjusted series.

The removal of of the calendar effect from these

series requires a change in the CES data collection

procedure to solicit AWH and AHE data separated

by hourly paid and salaried employees and a change

of the CES production system with regard to the

treatment of these reports. Both measures are

currently being tested but require the investment of

resources and time and are planned for the long run.

References
Dagum, Estale Bee (1980), The X-11-ARIMA

Seasonal Adjustment Method, Catalogue12-

546E, Statistics Canada

Findley, D. F., B. C. Monsell, W. R. Bell, M. C.

Otto, and B.-C. Chen (1996), New Capabilities and

Methods of the X-12-ARIMA Seasonal Adjustment

Program, JBES, April 1998, Vol. 16, No. 2 pp.

127–152

X-12-ARIMA Reference Manual, Beta Version 1.0

(1996) Bureau of the Census

Cano, Stephanie, Getz, Patricia, Kropf, Jurgen,

Scott, Stuart, and Stamas, George. (1996) Adjusting

for A Calendar Effect in Employment Time Series,

ASA, Proceedings of the Section on Survey Research

 

 Any opinions expressed in this paper are those of

the authors and do not constitute policy of the

Bureau of Labor Statistics.
 Table 3. Smoothness Tests and Sliding Span Evaluation of the LP-Adjustment

Data Series Smoothness Tests Span 1: 1988-1995 Span 2: 1989-1996 Span 3: 1990-1997

Division

AHE

Smooth-ness

Ratio

RMSE

%-Change

Months w/

t > 2.0

Joint

p-value

Months w/

t > 2.0

Joint

p-value

Months w/

t > 2.0

Joint

p-value

Wholesale 71.0 -40.1/-53.4 11 0.00 11 0.00 12 0.00

FIRE 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

AWH

TPU 74.0 -35.8/-46.9 7 0.00 9 0.00 10 0.00

Wholesale 60.0 -66.6/-89.4 12 0.00 11 0.00 11 0.00

Retail 68.0 -48.0/-56.8 7 0.00 8 0.00 8 0.00

FIRE 47.0 -113 / -210 12 0.00 12 0.00 12 0.00

Service 45.0 -123 /-99.2 12 0.00 12 0.00 12 0.00

Table 4. CES Total Private Average Weekly Hours, Seasonally Adjusted Over-the-Month Changes,

 Length-of-Pay Period Adjustment vs. No LP-Adjustment

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

1993 LP-Treatment 0.1 0 -0.2 0.2 0 -0.1 0.1 0 0.1 0 0 0

No LP-Treatment 0.1 0 -0.2 0.2 0.2 -0.2 0.1 0.1 -0.1 0 0 0

Difference 0.0 0.0 -0.0 0.0 -0.2 0.1 0.0 -0.1 0.2 0.0 0.0 0.0

1994 LP-Treatment 0 -0.2 0.3 -0.1 0.1 0 0 -0.1 0 0.1 -0.1 0.1

No LP-Treatment 0.3 -0.5 0.3 0 0.1 -0.1 0 -0.1 0.1 0.2 -0.2 0

Difference -0.3 0.3 0.0 -0.1 0.0 0.1 0.0 0.0 -0.1 -0.1 0.1 0.1

1995 LP-Treatment 0 -0.2 0 0 -0.2 0.1 0 0 0 0 0 -0.1

No LP-Treatment 0.3 -0.4 0 0.1 -0.4 0.2 0.1 -0.1 0 0.1 -0.1 -0.1

Difference -0.3 0.2 0.0 -0.1 0.2 -0.1 -0.1 0.1 0.0 -0.1 0.1 0.0

1996 LP-Treatment -0.4 0.6 -0.1 -0.1 0.1 0.2 -0.2 0.1 0.1 -0.1 0 0.1

No LP-Treatment -0.4 0.5 0 -0.1 0 0.4 -0.4 0.2 0.2 -0.3 0.1 0.2

Difference 0.0 0.1 -0.1 0.0 0.1 -0.2 0.2 -0.1 -0.1 0.2 -0.1 -0.1

1997 LP-Treatment -0.1 0.1 0.1 -0.1 0.1 -0.2 0 0.2 -0.1 0 0.1 0

No LP-Treatment -0.3 0.4 0 -0.3 0 0.1 -0.2 0.2 -0.1 0 0.3 -0.2

Difference 0.2 -0.3 0.1 0.2 0.1 -0.3 0.2 0.0 0.0 0.0 -0.2 0.2

1998 LP-Treatment 0.1 -0.1 -0.1 -0.1

No LP-Treatment 0.2 0.1 -0.2 -0.3

Difference -0.1 -0.2 0.1 0.2

Table 5. CES Total Private Average Hourly Earnings, Seasonally Adjusted Over-the-Month Changes,

 Length-of-Pay Period Adjustment vs. No LP-Adjustment

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

1993 LP-Treatment 0.03 0.01 0.05 0.00 0.02 0.02 0.02 0.02 0.03 0.02 0.02 0.03

No LP-Treatment 0.04 0.02 0.03 0.01 0.04 -0.01 0.03 0.03 0.01 0.02 0.03 0.03

Difference -0.01 -0.01 0.02 -0.01 -0.02 0.03 -0.01 -0.01 0.02 -0.00 -0.01 0.00

1994 LP-Treatment 0.03 0.03 0.01 0.02 0.03 0.02 0.02 0.02 0.03 0.04 0.02 0.03

No LP-Treatment 0.03 0.04 0.00 0.03 0.03 0.01 0.02 0.02 0.03 0.06 0.00 0.03

Difference -0.00 -0.01 0.01 -0.01 0.00 0.01 0.00 0.00 0.00 -0.02 0.02 0.00

1995 LP-Treatment 0.01 0.04 0.02 0.02 0.02 0.04 0.04 0.03 0.03 0.03 0.02 0.03

No LP-Treatment 0.02 0.04 0.01 0.04 0.00 0.04 0.06 0.00 0.04 0.05 0.01 0.02

Difference -0.01 0.00 0.01 -0.02 0.02 0.00 -0.02 0.03 -0.01 -0.02 0.01 0.01

1996 LP-Treatment 0.05 0.00 0.03 0.06 0.02 0.06 0.03 0.03 0.04 0.03 0.05 0.04

No LP-Treatment 0.04 0.02 0.02 0.05 0.03 0.07 0.00 0.05 0.05 0.00 0.07 0.05

Difference 0.01 -0.02 0.01 0.01 -0.01 -0.01 0.03 -0.02 -0.01 0.03 -0.02 -0.01

1997 LP-Treatment 0.04 0.03 0.04 0.03 0.04 0.03 0.03 0.07 0.03 0.06 0.04 0.03

No LP-Treatment 0.02 0.05 0.04 0.00 0.05 0.04 0.01 0.07 0.04 0.05 0.08 0.00

Difference 0.02 -0.02 0.00 0.03 -0.01 -0.01 0.02 0.00 -0.01 0.01 -0.04 0.03

1998 LP-Treatment 0.04 0.05 0.04 0.07

No LP-Treatment 0.04 0.07 0.04 0.04

Difference 0.00 -0.02 0.00 0.03

Months with borders have 10 day pay periods.