t
,..--_
BEFORE THE
POSTAL RATE COMMISSION
WASHINGTON, D.C. 20268-0001
POSTAL RATE AND FEE CHANGES, 1997
Docket No. R97-1
DIRECT TESTIMONY
OF
CHRISTOPHER S. BREHM
ON BEHALF OF
UNITED STATES POSTAL SERVICE
---
CONTENTS
AUTOBIOGRAPHICAL
SKETCH .......................................................................................
I. PURPOSE AND SCOPE.. ...................................................................................................
II. REVIEW OF FRAMEWORK
FOR WINDOW SERVICE VARIABILITY
iii
I
FACTORS.. ........... 1
A. Postage Sales.. ............................................................................................................
2
.........................................................................................
3
2. Supply Side Variability.. ..........................................................................................
4
3. Network Variability.. ................................................................................................
6
4. The Combined Effect ..............................................................................................
7
B. Activities involving Classes of Mail and Special Services.. ..........................................
.7
C. Other Window Service Activities ................................................................................
10
1. Demand Side Variability
111,WINDOW SERVICE TRANSACTION
IV. DEVELOPMENT
TIME STUDY .......................................................
10
FACTORS .....................................................
11
OF NEW VARIABILITY
A. Econometric Analysis of the Economies of Scale in Postage Sales.. .........................
11
B. Econometric Analysis of Postage Sales and Activities Involving Classes of Mail and
12
Special Services .............................................................................................................
1. Equation Specification
..........................................................................................
14
2. Initial Regression.. ................................................................................................
15
3. Refined Regression ..............................................................................................
15
4. Heteroscedasticity
Tests and Correction ..............................................................
.....................................................
16
Equations ..............................................
17
5. Limiting the Effects of Influential Observations
C. Interpreting
the Intercept in the Regression
15
ii
D. Conversion
of the Marginal Increases in Time Into Variability
1. Calculation
of Marginal Increase in Transaction
2. The Formula for Converting
Time ...........................................
Marginal Increases in Time to Variability
18
Factors.. . ..2 0
Factors ...............................................................
21
FACTORS ................................................................
22
3. Updated Supply Side Variability
V. WINDOW SERVICE VARIABILITY
Estimates .................... 17
LIST OF EXHIBITS
Exhibit USPS21A:
Economies of Scale in Postage Sales
Exhibit USPSdlB:
Transaction
Time Study Regression
Results
...
III
Direct
of
Christopher
S. Brehm
AUTOBIOGRAPHICAL
SKETCH
My name is Christopher
Consulting
S. Brehm.
I am a Principal Consultant
Services division of Price Waterhouse
Arlington, Virginia.
projects for the United States Postal Service.
analysis, with an emphasis on cost analysis.
attributable
LLP (hereafter Price Waterhouse)
I have been employed by Price Waterhouse
During my career with Price Waterhouse,
in
since 1993.
I have worked on numerous consulting
My area of specialization
My experience
is in financial
with the Postal Service includes
cost analysis in the areas of retail services, transportation,
well as transportation
in the Management
and new products, as
procurement.
From 1990 to 1991, I was employed by the Bureau of Labor Statistics, where I
worked on the Occupational
Safety and Health Survey.
My academic background
where I graduated
Summa
University of Maryland.
includes an B.A. degree from James Madison University,
Cum Laude in Economics,
and a M.S. in Economic:s from the
I have also completed all of the course work for a Ph.D. in
Economics at the University of Maryland, where I concentrated
Labor Economics.
in Industrial Organization
While at the University of Maryland, I taught courses in microeconomics
and labor economics and won several teaching awards.
and
.f’
1
I.
2
PURPOSE AND SCOPE
The purpose of my testimony is to update the variability estimates for window clerk
3
costs that were presented by witness LaMorte in Docket No. R90-3 (USPS-T-6).
4
framework for estimating window service variability factors presented in Docket No. R90-1 is
5
based on three separate components;
6
network variability.
7
to update the window service supply side variability factors.
a
dataset, I estimate variability
demand-side
variability,
supply-side
variability,
I use new data from a July, 1996 window service transaction
and
time study
In addition, with this new
factors for window activities that previously were not analyzed.
My testimony is organized into the following four sections.
9
The
First, the framework that
10
was used to estimate window service variability factors in Docket No. R90-1 is reviewed.
11
Second, the transaction
12
described.
13
variability factors.
14
variability factors.
15
II.
16
time study that is used to update the supply side variability factors is
Third, the new transaction
time study data are used to c?stimate new supply side
Finally, the new estimates are used to develop updated window service
REVIEW OF FRAMEWORK
FOR WINDOW SERVICE VARIABILITY
FACTORS
Since Docket No. R76-1, window service costs have been separated into three
17
groups to facilitate variability analysis; postage sales, activities involving classes of mail and
ia
special services, and other window service costs. A listing of the activities within each of
19
these three groups and the costs that accrued to each activity in the base year are listed in
20
Table 1.
2
1
Table 1: Window
Service Activities
and Accrued
Wrndow Activities
Costa
-
- Accrued Costs’
Postage Sales
Selling Stamps
$641.321,510
$12,928J40
$27.132,220
Selling Cards
Setting Meters
Activites Involving C/asses of Mail
and Special Services
First-Class
Priority Mail
Express Mail
Second-Class
Third-Class
Fourth-Class
Other Mail
Money Orders
Post Office Boxes
Other Special Services
$84766,080
$38.454,770
$17.454.000
$1,862,810
$10.359,110
$10,500.800
$22,786,900
$78.250,030
$40.256.450
$51,242,470
Other Endow Sen/ice Activities
Clerk Waiting Time
Overhead
Uniform Allowance and Lump Sum
All Other Costs
$257,251,8’00
$124.042,040
$12,674,397
$475.336,0:20
Total Cost
$1,906,619,7*F
Table Notes
’ Accrued casts ace taken horn the window service cost pooh developed
- W
2
3
4
A.
83, W/S 3.2.1, pp.t-2.
Postage
These casts do not include variability
in USE&T-5,
factors
Sales
The postage sales category includes four subactivities;
stamp sales, meter settings,
Each of these subactivities
has a
5
stamped card sales, and stamped envelope sales.
6
separate variability factor. This factor is measured through three separate indirect effects,
7
which, when combined, describe the relationship
between volume changes and window
3
F--
1
service cost changes.
2
supply side variability
These three indirect effects are the demand :side variability,
and the network variability,
the
and are described in more detail below.’
3
1.
4
The first indirect effect of a change in postage volume is the demand side effect,
Demand
Side Variability
which measures the degree to which a change in mail volume changes the number and type
of transactions.
This variability, which is expressed as a percentage
change in transactions
caused by a percentage change in mail volume, is less than or equal to one because
a
customers may not necessarily
9
increase in mail volume.
10
In Docket No. R90-1, the estimate for the demand side effect was based on two
12
different models of customer behavior.
13
held that consumers purchase a fixed amount of postage in each tralnsaction.
14
increase in mail volume caused an increase in transactions,
15
second model, the fixed interval model, assumed that consumers
16
regular intervals.
17
regular visits to the post oftice, and no new transactions
Therefore,
The first model, the fixed size transaction
model,
Therefore, an
or visits to the post office. The
purchase postage at
an increase in mail volume was absorbed in the c:onsumers’
occurred.
For customers that followed the fixed purchase model, an increase in volume led to a
18
--
Instead, they may increase the number of services purchased
during each trip to the post office.
11
r-
increase their visits to the post office in response to an
19
proportionate
20
one. Customers that followed the fixed interval model, on the other hand, simply increased
21
the size of their postage purchase during their regular visit to the post office in response to a
22
mail volume increase.
’
2
increase in transactions.
Therefore, their demand side variability was equal to
Therefore, this group had a demand side variiability equal to zero.’
See also Docket No. R90-I. USPS-T-6, pp. 15-16.
Docket No. R90-1, USPS-T-6, p. 16.
4
A customer survey was conducted
in November, 1983 to determine the proportion of
customers that followed the fixed purchase and fixed interval behavior models.
was based on a sample of 120 post oftices and 25,689 customers.
to till out a questionnaire
that asked how their purchasing
response to a change in mail volume.
variability
The survey
Customers were asked
behavior would change in
The resulting development
of the demand side
estimates for the four categories of postage is provided in the following table,
Table 2: Development of Demand Side Variabilities’
Fnsd Purhaw,
Customrs
Fixed hlewal
C”stome,s
Demand Side
Postage sales categories
Demand Side
VartabiWf
Percentage
PerOentage
Selling Stamps
[(.6566
*
1.00)
+
(.3412
*
Selling Cards
[(.5044
-
1.00)
+
(.4956
*
Selling Meters
[(.2605
*
1.00)
+
(.7395
-
I(.4793
*
1.00)
+
(.5207
-
Selling,Plain
canand
Variability
WI
011
Side
Variability
=
=
65.66%
O)l
=
26.05%
WI
=
47.93%
50.44%
Stamped
Envelopes
8
9
IO
These estimates formed the basis for the variability estimates in Docket No. R90-I,
and are again used to represent the demand side variabilities
in the current Docket.
11
2. Supply
12
The second indirect effect of a volume increase is the supply side effect, which
13
‘14
Side Variability
measures the effect that an increase in transactions,
or a changed transaction
clerk processing time. As with demand side effects, the supply side variability
15
each of the four categories of postage.
16
Docket No. R90-1 to develop supply side variabilities
17
are refined in the current Docket are highlighted.
3
The methodology
Docket No. R90-1, USPS-T-6 pp. 16-l 9.
profile, has on
is different for
followed by witness LaMorte in
will be discussed, and the alreas that
,-
5
/-
In Docket No. R90-1, the supply side variability was estimated by separately
1
2
examining
3
mail volume increases by increasing the size of their postage purchase during their regular
4
trips to the post office. The supply side variability associated with an increase in the size of
5
a postage sale was found to be zero, due to the significant economies
6
sales. That is, the same amount of time was required to process a transaction
7
book of stamps was purchased as when two books of stamps were purchased.’
8
the most recent transaction
9
;-
fixed interval and fixed purchase consumers.
Fixed interval customers respond to
of scale in postage
in which one
Analysis of
time study confirms this finding.
Fixed purchase customers,
however, increase their visits to the post ofice, which will
10
increase clerk processing time. In Docket No. R90-1, it was estimated that these new
11
purchases would result in a supply side variability of 100 percent, because the increase in
12
clerk processing time is proportionate
13
examine this finding in more detail in section IV using the results of the recent transaction
14
time study, and find the variability to be less than 100 percent.
15
to the increase in the number lof transactions.5
I
The combined demand and supply side variability factors for ,the four postage
16
categories from Docket No. R90-1 were calculated in the following mlanner. Fclr stamp
17
sales, 65.68 percent of all consumerS follow the fixed purchase model.
18
customers, an increase in volume generated a proportionate
19
The supply side variability, therefore, was estimated to be 100 percent.
20
percent of all consumers followed the fixed interval model, and responded to volume
21
increases by making larger purchases.
22
purchases enabled window clerks to process the larger stamp purchases without incurring
4
5
Docket No. R90-1, USPS-T&, p. 21.
Docket No. R90-1, USPS-T-6, p. 20.
For these
increase in new transactions.
The significant economies
The remaining 34.12
of scale in stamp
6
additional processing time. Therefore, the supply side variability
was zero for this group.
-\
The combined demand and supply side variability for stamp purchases was then calculated
as a weighted average.6
4
3. Network
Variability
5
The third indirect effect captures the degree to which clerk staffing costs increase as
~6
clerk processing time increases.
7
the percentage change in total window costs resulting from a percentage
a
processing time. This variability
9
than 100 percent.
A variability
This effect is called the network variability
and measures
change in
can take a value of either less than, equal to, or greater
of less than 100 percent implies that post offices absortl
10
increases in processing time with relatively small increases in staffing time. ,A variability of
11
more than 100 percent means that an increase in processing time causes a
12
disproportionately
large increase in staffing.
In Docket No. R90-1, witness LaMorte compared the time that clerks spend
13
14
processing transactions
15
a transaction
16
Econometric analysis of this data found a linear relationship,
17
origin, between processing time and staffing time. This, in turn, led witness LaMorte to
18
conclude that increases in staffing time cause proportionate
19
Therefore, the network variability
20
earlier, this result is not updated in the current Docket.
6
7
to total clerk staffing time. This information
profile study that collected information
is 100 percent.’
Docket No. R90-1, USPS-T-6 pp. 21-22.
Docket No. R90-1. USPS-T-6 pp. 28-33.
on processing
was gathered as part of
and staffing time.
which emanated from the
increases in staffing time.
Like the demand side effects discussed
-..
7
/-‘
1
4.
2
The method of combining the three indirect variabilities
3
4
6s v
--=-6V s
5
where, S = Window Clerk Staffing Costs
6TV
6VT
.6CT
-6TC
into a single relationship
.bSC
-SC’S
6
V = Mail Volume
7
T = Window Transaction
8
C = Transaction
Volume
Processing Time
This equation states that window service variability is calculated
IO
three separate, indirect effects; the demand side variability
11
variability
12
6.
Es,
Activities
and the network variability
Involving
Classes
g:,
as the product of
the supply side
g:
of Mail and Special
Services
Variability estimates for activities involving classes of mail and special services were
13
.-.
Effect
between mail volume changes and window costs is shown in the folllowing equation:’
9
/-
The Combined
14
developed in a different manner than variability estimates for postage sales in Docket No.
15
R90-1. Witness LaMorte argued that demand side effects, which are measured through
16
customer isurveys, would be difficult to capture for classes of mail and special services.
17
asserted that customers would have difficulty responding
18
questionnaire
19
variability estimates for activities involving classes of mail and special services are
20
determined
8
9
regarding their purchasing
She
in a meaningful way to a
behavior for non-postage
services.
Therefore,
on the basis of how the In-Office Cost System (IOCS) assigns window costs.9
Docket No. R90-1, USPS-T-6, p. 6.
Docket No. R90-1. USPS-T-6, p. 23.
8
1
Before discussing
the specifics of how IOCS allocates costs to activities, it is useful to
2
outline the structure of a window service transaction.
There are two essential components
3
all window transactions.
4
to process the services requested by the customer.
5
service time includes the time required to place the item on the scale, determine the weight
6
and price, communicate
7
print and apply the postage strip. The second component
a
associated with all transactions,
9
includes the time it takes the clerk to wait for the customer to arrive at the window, exchange
The first is the service component, which includes the time required
For a weigh and rate activity, the
the price, or prices, to the customer, decide on a class of mail, and
is the “common time” that is
regardless of the services provided. This common time
10
greetings, accept payment, make change, and end the transaction.”
11
of a retail transaction
12
transaction,
13
re-incur the common time. It is this feature that leads to economies
14
transactions.
15
of
The essentiial feature
is that once the common time is incurred to process a one element
additional services can be processed in the same transaction
without having to
of scale in retail
IOCS assigns window costs based on the activity that is observed at a particular
16
point in time. For example, if the data collector observes the window clerk perforrning the
17
service component
10
to accrue to the weigh and rate (activities related to specific classes of mail) cost pool.”
19
addition, IOCS also attributes the common time to the product or products that are sold in
20
the transaction.
of a weigh and rate transaction,
If the weigh and rate transaction
the IOCS observation
would cause costs
In
is a one element tran:saction. the IOCS
lo It is called “common time” because it is common to all transactions.
” If the data collector observes the &ice
portion of the weigh and rate transaction, the data
collector would record the IOCS reading as a weigh and rate, regardless of whether the transaction is a
single element or multiple element transaction.
-
9
.-
1
observation
2
takes place in the transaction.
3
element transactions
5
results in a proportional
6
by both the common time and the service time as a result of the new weigh and rate request.
would be 100 percent.
That is, an increase in one new weigh and rate
increase in clerk processing time-clerk
processing time increases
Assigning the common time for a multiple element transaction
a
not as straightforward
9
transactions,
10
,/-
Witness LaMorte explained that the variability associated with an increase in single
4
7
./--
will be recorded as a weigh and rate activity, regardless of when the reading
as for a single element transaction.
to a window activity is
Therefore, for multiple element
IOCS data collectors are instructed in the following manner when sampling the
common time of a transaction:
11
12
13
14
If, at the time of the (IOCS) reading, the customer being served is either saying hello
or good-bye, or is paying for several items, then choose the item (or service)
provided by the clerk immediately after the greeting or the last service provided
before the payment and good-bye.‘2
15
These data collection rules imply that some portion of the common time is included in
Using the results of
16
the cost pools of each of the elements in a multiple element transaction.
17
a 1988 transaction
18
occurs as part of a multiple element transaction
19
figure was not known.
20
not known, combining the variabilities
21
not possible.
22
and rate activity was 100 percent.13 The variability factors for the other activities related to
23
classes of mail or special services were calculated in a similar manner.
time study, witness LaMorte found that a weigh and rate sewice that
is over 60 percent variable, but the exact
Because the exact variability for multiple element transactions
from the single and multiple element transactions
was
was
Therefore, witness LaMorte concluded that the total variability for the weigh
I2 Docket No. MC96-3, USPS LR-SSR-12, p. 75 (Handbook F-45)
” See Docket No. R90-1, USPS-T-6 p. 26.
10
C. Other
Window
Service
Activities
Window service activities other than postage sales and activities involving classes of
mail and special services were considered to be institutional
and assigned a zero percent
variability factor in Docket R90-1. The exception was clerk waiting time. The results of the
network variability
analysis, described above, showed that total processing time increases
proportionately
with total staffing time. This implied that waiting time also increases
proportionately
with processing time, and, therefore, was considered tat be 100 percent
variable.”
9
IO
III. WINDOW
SERVICE
TRANSACTION
TIME STUDY
The data used to estimate updated variability factors was collected in a re’oent study
11
of retail transactions.
12
that measured the duration of window service transactions,
13
transactions,
14
collected at 20 randomly selected post offices in July, 1996.
15
The transaction
time study (TTS) was a two-week data collection effort
the services provided during the
the method of payment, and the total transaction
For the purposes of the transaction
value.
1TS data were
time study, the beginning of a transaction
was
16
defined to be the point at which the clerk greeted the customer and indicated that they were
17
ready to help the customer.
18
were completed and the clerk was available to help another customer.
19
observed the retail transactions
20
the transaction
21
to the next open window.
22
editing and review, 7,175 transactions
23
presented in USPS LR-H-167.
The transaction
ended when all components
of the transaction
Data collectors
by standing behind the counter, where they could observe
as well as the retail terminal.
Approximately
every thirty minutes they moved
Information was collected on 7,806 transactions.
Docket No. R90-1, USPS-T6, p. 33.
remained.
After data
More detailed documentation
of the TTS is
11
/-
1
IV. DEVELOPMENT
OF NEW VARIABILITY
The new transaction
2
FACTORS
time study provides a data source to examine and update two
3
sections of the window service variability analysis from Docket No. R!30-1. The first is the
4
degree to which economies of scale exist in postage sales.
5
finding that complete economies of scale exist in postage sales. The second section is an
6
update of the supply side variability factors for postage sales and activities involving classes
7
of mail and special services.
8
transactions,
9
A.
I confirm witness LaMorte’s
In addition, variability factors are estimalted for Express Mail
which were not examined in previous studies.
Econometric
Analysis
of the Economies
of Scale
in Postage
Sales
10
An important finding in Docket No. R90-1 was the strong economies
of scale in
11
postage sales.‘5 This finding enabled witness LaMorte to conclude that consumers
12
increase the size of their postage purchases, without increasing their number of visits to the
13
post office, will not cause an increase in window clerk processing time. In the current
14
Docket, I reexamine and confirm this result with the new TTS data.
The existence of economies of scale for postage sales was investigated
15
16
regression analysis on data from single component transactions.
17
only stamp sales and meter settings are analyzed.
18
transactions,
19
transaction
After isolating the single component
between
for stamps and meters are listed below.”
20
Stamps:
transaction
time{ = p0 + p, l SNalue,
21
Meters:
transaction
time, = p0 + 6, l MEValue, + y, l check, + si
I5
using
Because of limited data,
the two equations that are used to estimate the relationship
time and the size of the transaction
that
+ y, l credit card; + y2l clreck, + E,
Selling one book of stamps, for example, takes approximately
the same amount of time as selling
two books of stamps.
l6 A variable for credit card purchases is not included in the regression for economies of scale in
meter transactions because credit cards are not an accepted method of payment for meter settings
.-
12
where, transaction
1
time, = the duration of transaction
i, in seconds
2
SNalue,
3
MEValue, = is the value of the meter setting in transaction
4
credit cad; = 1 if the customer paid with a credit card in transaction
5
check, = 1 if the customer paid with a check in transaction
= is the value of the stamp sale in transaction
i, in dollars,
i, in dollars,
i.
The results from these two equations are listed in Exhibit USPS-21A.”
6
i, and
For stamp
7
sales, the regression results show that increasing the value of the stamp sale by one dollar
a
increases the transaction
9
that results from increasing the size of a stamp purchase, the economies
10
time by 0.111 seconds.
Because of the very small increase in time
of scale in stamp
purchases are very strong.
For meter sales, the regression results show that transaction
11
tirne increases by 0.012
12
seconds for each dollar that is added to a meter.
However, the t-statistic, which ifs only
13
0.959, shows that this estimate is not statistically
different from zero.
14
statistically
15
the total transaction
16
settings appear to be strong.
17
B. Econometric’Analysis
and Special Services
18
19
Even if it were a
reliable estimate, increasing the size of a meter setting by 9400 would increase
time by only 1.2 seconds.
of Postage
In Docket No. R90-1, transaction
Therefore, the economi’es of scale in meter
Sales
and Activities
Involving
Classes
of Mail
time study data from 1988 were used to make
20
inferences about the variabilities
for a number of different window servitce activities.
21
recent TTS data, we update two components
With the
from Docket No. R90-1.
22
The first component that is updated is the supply side variability for postage sales. In
23
Docket No. R90-1, the supply side variability for postage sales for consumers that follow the
”
See USPS LR-H-167 for a explanation of the methodology and a complete listing of the results.
-
-
.-
13
1
fixed purchase model was estimated to be 100 percent.
2
purchase model respond to a volume increase by visiting the post office more often, and,
3
therefore the Postal Service incurs both the common time and service time as a result of the
4
new postage purchase.
5
and the processing time, the variability was 100 percent.
6
that all new postage sales arrive at the post office as single item transactions.
7
that customers add the new postage purchase to an existing transaction,
a
and rate, the supply side variability of new postage sales may be less than 100 percent.
9
looking at. individual transactions
r-
10
-
increase in both the transaction
This argulment, howNever, assumes
To the extent
such as a weigh
By
in the lTS data, we can estimate the actual percentage
The second component that is updated is the variability
In Docket No. R90-1, transaction
of activities involving classes
time information
was used to
12
of mail and special services.
I3
place the variability
14
percent.
However, because the exact figure was not known, it was assumed to be 100
15
percent.
With the most recent lTS, we estimate the percentage change in time caused by
16
additional window activities.
17
window service activities; selling stamps, setting meters, weighing and rating mail,
18
processing Express Mail, and selling Money Orders.
I9
-.
Because this implies a proportional
that follow the fixed
increase in time caused by an additional postage transaction.
11
,--
Consumers
of weigh and rate transactions
somewhere
between 60 percent and 100
These results are used to estimate variability factors for five
The new variability factors are estimated in two steps. First, the marginal increase in
20
processing time caused by window activities such as selling stamps, setting meters, and
21
weighing and rating mail is calculated.
22
into a variability factor. This remainder of this section describes the steps that were taken to
Second, the marginal increases in time are converted
14
1
estimate the marginal increase in clerk processing time that results from providing additional
2
services, such as selling stamps or weighing and rating parcels.‘8
1.
Equation
Specification
The equation that is used to estimate the marginal increase in ,time is specified as a
linear equation, where transaction
transaction.
7
time is a function of the activities th;at occur in a
The form of the equation is listed below:
transaction
time, = W + P,
l
ST, + f$ * WR, + b*
pj* elementj,+
MO, + !3,’ UC, -I- 5
j=l
8
+ y,
9
where, transaction
l
credit card, + y2 l check; + q
timei = the duration of transaction
i,
10
ST, = is equal to 1 if transaction
11
WRi = is the number of parcels that are weighed and rated in transaction
12
MO; = is the number of money orders that that are processed in transaction
13
UC, = is the number of Express Mail pieces that are processed in transaction
14
elementi,
15
credit card, = 1 if the customer paid with a credit card in transaction
16
check, = 1 if the customer
i,
i,
= the remaining n elements that are included iln the regression,
paid with a check in transaction
i, and
i
A complete listing of the services that are included in the initial regression is provided
17
10
i involved a stamp sale,
in Exhibit USPS-21 6.
A logarithmic
19
specification
20
because of practical considerations
21
discussion
”
was considered for this analysis, but was rejected
regarding the nature of the datasel:.
For a more detailed
of this topic, see USPS LR-H-167.
See USPS LR-H-167 for the complete documentation of the econometric analysis.
i
15
/-
,r-
‘.
1
2.
2
The initial regression
Initial
Regression
used the linear specification
described above an#d included all
3
activities that were captured in the transaction
time study. The met:hod of estimation was
4
Ordinary Least Squares (OLS). The results are displayed in the Model 1 column of Exhibit
5
USPS-21 B. The parameter estimates are expressed in seconds, and can be interpreted in
6
the following manner.
7
processing time by an additional 11.2 seconds.
0
parcel increases the total transaction
9
with a retail transaction
Adding a stamp sale to a transaction,
for example, increases the clerk
Also, weighing and rating one additional
time by 14.7 seconds.
The common time associated
is captured in the intercept term, which is 3t3.0 seconds.
10
3.
11
The initial regression results show that a number of services and activities have
Refined
Regression
12
statistically
13
frequently observed services, which makes estimating statistically
14
difficult.
15
new regression is run. The results of this regression,
16
displayed in the Model 2 column of Exhibit USPS-21B.
insignific$nt
Therefore,
marginal time estimates. These variables tend to be the less
in the next step, these variables are dropped from the analysis, and a
17
4.
10
One of the important assumptions
Heteroscedasticity
19
variance.
20
heteroscedastic.
21
consistent.
22
be affected.
23
heteroscedasticity,
significant coefficients
Tests
again estimatled using OLS, are
and Correction
of OLS is that the error terms, Q, have uniform
When the error terms have unequal variances the results are said to be
Even with heteroscedasticity,
the OLS coefficients will be unbiased and
However, the standard errors used to determine the reliability of the results will
To be more specific, the estimated coefficients are not affected by
but the standard errors of the estimates will be understated.
As a result,
-
16
1
the t-statistics may be overstated, which may cause the reliability of th’e estimates to be
2
overstated
3
I tested for,, and found, heteroscedasticity
in the TTS regression using a White test,”
4
then corrected the problem using a technique
5
White-corrected
6
column of Exhibit USPS91B.
7
standard errors are larger than the original standard errors from Model 2. The resulting t-
0
statistics are lower, but the tests for statistical significance
9
variables in the analysis.”
10
know as the White correction.”
standard errors and t-statistics
.-
I generate the
and present the results in the Model 3
The results show that the heteroscedastiicity-corrected
A more complete discussion
are not overturned
for the key
of the heteroscedasticity
test and
correction are presented in USPS LR-H-167.
11
5.
Limiting
the Effects
of Influential
12
It is reasonable to expect the transaction
Observations
time study data to contain some degree of
..-
13
variance that cannot be accounted for in the regression equations.
14
where the customer requested a specific type stamp that the window clerk had difficulty
15
finding, or other transactions
16
window clerk’s time. Because of these possibilities,
17
effects of “influential”
10
19
This could include cases
where the customer consumed an extraordinary
observations.
amount of the
I conducted a test to find and limit the
The method that was used was the DFFIT procedure.”
The DFFIT procedure examines the change in the \a predicted value of the dependent
variable, transaction
time,, when the ih observation
is omitted from the dataset and the OLS
” mite, Halbert, “A Heteroscedasticity-Consistent
Covariance Matrix Estimator and a Direct Test for
Heteroscedasticity,”
Econometrica, 48, 1980, pp.817-838. Also see pp. 419420 of Greene, William H.,
Econometric Analysis, New York, NY: MacMillan, 1990 for an explanation of this test.
z0 white (1980). Also see pp. 403405 of Greene (1990) for an explanation of this technique.
2’ The key variables are stamp sales, meter settings, weigh and rates, Express Mail, Money Orders,
and credit card and check payment variables.
22 See Be&y, D.. E. Kuh, and R. Welsch, Regression Diagnostics, identifying lnfhential Data and
Sources of Co//inc?arity. New York: Wiley. 1980.
__-~
--
-~
.-.-
17
/---
1
estimates are recalculated.
2
Large values of this statistic indicate that the observation
3
details of this procedure are provided in USPS LR-H-167.
4
equation after eliminating
5
4 of Exhibit USPSZIB.
6
the regression -the
7
time to be attributed to the common component of the transaction,
8
attributed to the services that are provided.
9
final variability estimates.
IO
C. Interpreting
11
This statistic is generated for each observation
these influential observations
may be overly “influential”.
from the dataset are found in Model
They show that this procedure increases the explanatory
R2 increases from 0.37 to 0.42. In general, this procedure caused less
the Intercept
,and more time to be
It is these results that are used to generate the
in the Regression
Equations
the intercept term is needed.
13
time associated with a transaction.
14
regardless of what services or activities are performed in the transaction.
15
distinguishes
16
for the common time to be incurred.
18
power of
In order to calculate the supply side variability factor, an acc,urate understanding
The intercept in these regressions
of the Marginal
of
is Imeasuring the common
It is the time that is common to all transactions,
this time from a “fixed time” interpretation
D. Conversion
The
The results of the regression
12
17
in the dataset.
Increases
in Time
What
is that a service must be processed
Into Variability
Estimates
The regression results presented in Model 4 of Exhibit USPS-21 B provide the
19
marginal increase in transaction
20
additional service.
21
into a percentage change.
22
transaction
23
sections.
time, expressed in seconds, as a result of processing an
In order to get a variability, this marginal change needs to be converted
The methodology
time and converting
for calculating the marginal increase in
it into a variability factor is described in the following three
18
1
1.
2
It is important to realize that each coefficient estimated in Model 4 of Exhibit USPS-
Calculation
of Marginal
Increase
in Transaction
Time
3
218 measures the increase in transaction
4
is added to an existinq transaction.
5
services that arrive at the window through new transactions.
To get an accurate estimate of
6
the increase in clerk processing time when a new transaction
arrives at the retail window, it
7
is necessary to add the marginal service time, represented
8
common time, which is represented
9
arrive as part of an existing transaction
when the service
That is, the coefficients do not account for an increase in
by the coefficient, and the
by the intercept.23 Because an additional service could
10
weighted average increase in transaction
11
the additional transaction
12
transaction,
13
time from processing a servitz,
or it could generate a new transaction,
we estimate a
time. This weighted average represents a blend of
time for the service that is processed as part of an existing
and the transaction
time when those services generate new transactions.
As an example of how the marginal increase in time is calculatecl, consider an
14
increase in transaction
15
transaction
16
the marginal increase in time when the customer adds the new, additional stamp sale to an
17
existing transaction.
,-‘8
time caused by an additional stamp sale. The avlerage increase in
time caused by the sale is a blend of two different transaction
times. The first is
From the regression results in Model 4 of Exhibit USPS91B,
increase in time is 13.3 seconds.
the
The second time is the increase in time when the
19
customer makes a new trip to the post ofice just to purchase stamps.
20
processing time generated as a result of the stamp purchase is 47.5 seconds, for a cash
21
purchase.”
Flere, the additional
23 See section IV.C for an interpretation of the intercept term.
24 The transaction time for a single element stamp sale is equal to the common time plus the service
time (24.2 seconds + 13.3 seconds = 47.5 seconds).
19
r-
.C.
An additional adjustment needs to be made, however, to the average increase in time
1
The analysis of the TTS data showed that accepting a
2
for a single element transaction.
3
credit card or check payment adds additional time to a window transaction.
4
characterize
5
transaction,
6
stamp sales, the average time for a single element stamp sale is inc:reased by (a) the
7
proportion of single element stamp sales that involve credit card sales multiplied by the
8
incremental time to process the credit card payment, and (b) the proportion of single element
9
stamp sales that are check sales multiplied by the incremental
the average increase in time caused by a new element that generates a new
the time required to process these payment methods must be added.
10
The calculations
11
the method of payment - are in Table 3.
12
13
14
15
of the average transaction
Table 3: Calculation
Transaction
L
To accurately
Increase
- accounting for
in Single Item
Time with Credit Card and Check Payment
lnaementa
Wl”dwl selvice
ktivitier
Common
nanracbon
Time’
Selling Stamps
Setting Meters
Weigh and Rate
Express Mail
hkmey Orders
34.224
34224
34.224
34.224
34.224
13.313
217.313
21.534
76.011
32.986
+
+
+
+
+
time to process the check.
time for single item transactions
of Average
For
PercentOf
Tran*acmnS
withC,Mll
card Pm
l”CMll~“td
crem card
lirm’
SSViC5
Tune’
+
+
+
+
+
102.662
102.662
102.662
102.862
102.862
*
*
*
0.66%
0.00%
0.66%
5.70%
0.00%
+
+
+
+
+
Incrementa
Check
TKne’
34395
34.395
34.395
34.395
34.395
PercentOf
l’ransactions
tim Check
Paymcntt’
Average
singe Itern
Tmnractlon
Time
14.30%
62.38%
5.31%
12.66%
0.00%
53.343
269.554
56.268
122.449
67.210
*
*
*
*
=
=
=
=
=
Table Notes
1 see Exhihti USPS21 9 for regression results
2 USPS LR-H-787
To calculate a weighted average of the single element and multiple element
16
scenarios, I use the proportion of stamp sales that are single element transactions
and those
17
that are multiple element stamp sales as the weighting factors.25 This weighted average
” This calculation assumes that the profile of the marginal transaction is like the profile of the
average transaction.
20
represents the marginal increase in time, on average, of an additional stamp sale. This time
estimate is calculated
in Table 4 for stamp sales, as well as four other window activities.
Table 4: Calculation
of Average
Increase
in Tansaction
Time
4
5
6
2.
7
The supply side variability factor is an elasticity that measures the percentage
The Formula
Factors
for Converting
Marginal
Increases
6
change in clerk processing time with respect to a percentage
9
increase in clerk processing time that was calculated
expressed in percentage terms, however, but in seconds.
11
change in transaction
12
use the following formula:
14
15
Variabilityi
Variability
=
change in transactions.‘6
The
in the previous section was not
10
13
in Time to Variability
Therefore,
t’o convert a marginal
time into an elasticity that represents the supply ,side variability,
we
6transaction time
( Gtnmsaction elementi 1
predicted timejor a single element transaction i
is the variability
factor for activity i, and element, is the independent
variable from the regression equation that causes costs to accrue to window service cost
>e. See Section ll.A.2
21
,r”-
1
pool i.272B For example, the formula for the supply side variability
2
as:
6 transaction time
Gtransaction element s7 !
3
VariabilityST =
4
The first term on the right hand side is the increase in processing time caused by an
predicted time for a single element ST transactio;n
5
additional stamp sale, which is explained above in section IV.B.3.b.
6
single element stamp transaction
The predicted time for a
is calculated as:
7
Predicted TinzeST= jo + j, *ST + &
6
Predicted Time,
9
Predicted Timen = 53.343
10
,y-.
of stamp sales is written
l
Credit + &
l
Check
= 34.224 + 13.313 * (1) + 102.662 * (0.009) + 3’4.394 * (0.143)
In the equation for predicted time, ST is equal to one for a single element stamp
11
transaction,
and Credit and Check are equal to the proportion of single element stamp
12
transactions
that have credit card or check payments, respectively.‘!’
13
3.
14
In this final step of calculating
Updated
Supply
Side Variability
Factors
supply side variability factors, i take the rnarginal
15
average transaction
16
the variability from section b above. This calculation
and
times from Tables 3 and 4, and implement the formula for calculating
is performed in Table 5.
”
Examples of window service cost pools are selling stamps, setting meters, or activities related to
classes of mail.
zB An elasticity can be defined as a marginal change divided by the average change. This formula is
the marginal increase in transaction time for element i divided by the average, or predicted, transaction
time for element i.
29 The predicted time is equivalent to the average time for a single element transaction, which is
calculated in Table 5.
22
1
Table 5: Updated Supply
WeightedAverage
Increasein
Transaction Time’
Window Sewiee
Activities
37.347
250.061
32.645
101.612
43.932
Selling Stamps
Setting Meters
Weigh and Rate
Express Mail
Money Orders
Factore
Predicted (Avg)
Transaction
Time2
/
/
I
I
I
53.343
269.554
58.260
122.449
67.210
=
=
=
=
=
70.01%
92.77%
56.37%
63.15%
65.37%
Table Notes
’ See Table 6
’ See Table 5
2
3
Side Variability
V. WINI
OW SERVICE
VARIABILITY
FACTORS
The final step in calculating the overall variability factors for window service activities
4
5
is to insert the updated supply side variability
into the three-part
chain that was outlined in
6
section ll.A.4.
7
settings - require a demand side variability to trace the window cost change back to the mail
a
volume change.=
9
to observe the number of pieces that will be generated from a postage sale. The method of
It is important to note that postage sales categories -stamp
This is needed because at the time a transaction
sales arld meter
occurs, it is not possible
10
estimating supply side variability factors in the current Docket for weigh and rate activities,
11
Express Mail, and Money Orders, however, implicitly accounts for the demand side effects.
12
This is because the TTS data collectors were able to observe the actual volume that was
13
generated in each transaction
14
Therefore, the regression analysis draws a direct link between volume changes and changes
15
in clerk processing time for these activities.
16
needed.
that involved a specific class of mail or a special
service.
A separate demand side variability factor is not
Jo Weigh and rates, Express Mail, and Money Orders do not have demand sidevariability
estimates.
In Docket No. R90-1, witness LaMorte concluded that it would be dificult to ask consumers about their
purchasing behavior related to classes of mail and special services.
,r--‘
1
2
3
The revised window service variability factors for Docket No. R97-1 are calculated
Table 6.”
in
The variability factors from Docket No. R90-1 are also displayed.
Table 6: Docket No. R97-1 Proposed
wn&w Service
Activities
Selling Stamps
Setting Meters
Weigh and Rate
Express Mail
Money Orders
DemandSide
van.b,w$
65.68%
26.06%
Window
supplyside
Variability’
-
70.01%
92.77%
56.37%
63.15%
65.37%
Service Variability
&hrOrs
Valiability’
*
*
*
100.00%
100.00%
100.00%
100.00%
100.00%
Factors
DC&etNO.R97.1
“anabilityFacm
=
=
=
=
=
46.12%
24.17%
56.37%
EI3.15%
65.37%
oocm HO.R90.1
“aliabiri Fanor’
65.88%
26.05%
100.00%
100.00%
100.00%
Table Note6
1 See Table 7.
2 ace Table 7
‘See pp. 5-5
4
‘ DLxXefNO RBO-1,
Exhibit“SPS-SB
A variability of 78.53 percent was originally calculated for Express Mail, and is included in the Base
Year calculation. Using a variability factor of 63.15% raises the volume variable costs for Express Mail
by approximately $902,000. In addition, a variability of 24.07 percent was calculated for metered mail,
Using a variability of 24.17 percent raises the volume variable costs by approximately $42,000, which
would be disttibuted to metered mail.
_-
Exhibit USPS-21A
Page 1 of 1
Economies
DePendem variable:
length of transaction
of Scale
in Postage
Sales
in seconds
Model 1
Model 2
Parameter
COmpOWnt
,nteroept
Stamp Value
Metervalue
Payment by Check
Payment by Credit Card
Adjusted R-Squared
SAS Name
INTERCPT
SNAL
MEVAL
CHECK
CREDIT
0.959
1.276
(
0.2626
)
0.0077
Exhibit IJSPS-21B
Page 1 of 2
.Transaction
Dependent
variable:
Time
length of transaction
Study
Regression
Resuks
in seconds
Model 2
Model 1
Component
Intercept
Purchase of Stamps
Weigh/Rate Quantity
Acceptance
Express Quantity
Money Order Quantii
COD Accepted Quantity
Meter set ouantt
Postage Due
Caller Service
Retail Mailing Supplies
Change of Address/Forward
Mailing Payments
Phone Card Quantity
Box Rental Quantity
Pre-Stamped
Inquiry Puanttt
Other
Passpoll cluantity
Return Receipt Quantity
Registered Quanbty
Special Services Int’l Registered
Resbicted Quantity
Certhied Quantity
Insurance Duantity
Special Services Cert Mailing
GH General
GH Parcel Quantity
Wrong Address
Returned Mail
Payment by Check
Pa,yment by Credil Card
Adjusted R-Squared
_-.
Parameter
Estimate
t-stat
37.956
11.153
24.556
5.775
WRQUAN
AC
WQUAN
MOQUAN
CAQUAN
MEQUAN
PD
cs
MS
14.655
6.926
84752
33.611
81.773
204.613
60.015
1.218
43.940
22.306
2.509
20.491
21.596
3.615
28.179
4.533
0.054
9.739
CF
MP
PCQUAN
SRQUAN
EC
IQQUAN
OT
PPQJAN
RRDUAN
RGQUAN
SIRQUAN
RDQUAN
CEQUAN
INSQUAN
SCMDUAN
30.679
60.489
77.085
127.024
10.852
42.086
93.623
161.852
10.387
94.760
66.458
142.044
20.343
71.248
20.223
3.798
5.248
1.066
15.098
1.453
16.363
17.364
12.766
2.965
16.641
2.957
2.001
7.372
14.689
0.493
GVP
GPDQUAN
WA
RM
CHECK
CREDIT
64.053
2.998
-0.587
8.702
52.957
112.257
13.532
1.888
-0.064
0.752
15.934
13.213
SAS Name
tNTERCPT
ST
0.336
F’aameter
Estimate
36.735
10.572
14.546
6.726
64260
33.420
61.717
204396
60.101
t-stat
25.121
5.544
22.233
2.447
20.435
21.532
3.812
28.142
4.540
43,477
30.120
79.954
9.653
3.732
5.214
126.527
10.388
41.568
93.311
151.233
10.333
94.949
66.028
141.452
20.265
71.078
15.047
1.392
16.275
17.313
12.720
2.951
16.983
2.938
1.993
7.347
14.680
63.477
13.443
53.073
112.334
16.000
13.225
0.366
Exhibit USPS-21 B
Page 2 of 2
Transaction
Dependent variable: leqth oftransaction
Time
Study
Regression
Results
in aemndh
Model3
component
htNC?Pt
Purchase of Stamps
WeigwRate Duantii
Acceptance
Express Cuamity
Money Order Quantity
COD Accepted Duatity
mter set au.mty
Postage Due
catlcr service
Retail Mailing Supplies
change ofAddre$slFomard
Mailing Payments
phone cati audity
BOXRental audt-j
Pre-Stamped
Inquiry Quandly
oiher
Pauporl QuaMy
Return Receipt Q”aMty
Regti-d
Duantky
Special Services InPl Registered
Res,dtrid& Duanbty
CMtted ct”antity
h-eurame Quantity
special services cert Mailing
GH General
GH Parcel aumity
Wrong Address
Retumed Mail
Payment by Cher%
Paymen, by Credit Card
Adjusted R-Squared
8AS Name
INTERCPT
ST
WRQUAN
AC
WDUAN
MOa”AN
CAOUAN
MEDUAN
PD
cs
MS
CF
MP
PCCXJAN
SRDUAN
EC
IDQUAN
OT
PPQUAN
RRQUAN
RGOUAN
SIRQUAN
RWUAN
CEQUAN
INSDUAN
SCMWAN
GVP
GPWUAN
WA
Rt4
CHECK
CREDIT
Model4
Parameter
t3timate
38.735
IO.572
14.548
6.726
64.280
33.420
61.717
204.396
80.10,
wlae
Corrected
“alia”e
7.22,
5.653
12.735
6.927
29.016
3.925
441.050
870.826
366.719
wlteGvreded
t*t.a,
14.414
4.260
4.078
2.556
15.638
16.870
3.89,
6.926
3.138
Parmeter
Estimate
34.274
13.313
21.534
1.341
78.01,
32.986
88.089
217.313
53442
MileCorreded
Mriance
1.298
1.575
I.160
2.770
8.236
1.22,
97.307
109.744
3, .2%
mieCorrected
,-stat
30.037
10.607
19823
0.806
27.183
29.847
8.930
20.744
9.559
43.477
30.,20
79.954
23.800
82.918
854082
8.912
3.308
2.738
28.141
10.628
76 :295
6.363
18.911
44.031
9.731
2.42,
11.498
128.527
10.388
41.666
93.311
151.233
10.333
94949
66028
141.452
20.285
71.078
352.589
31.25,
11.907
138.302
730.318
63.275
177.233
350.944
25.292
25.464
46.048
6.738
1.856
12.046
7.934
5.595
1.299
7.132
3.626
26.127
4.016
10.474
117.775
7.258
32.693
53.078
158.676
,8.;!49
70.110
SK!42
72.906
10.775
4.409
25.774
427.392
12.568
68.743
1.020
13.793
2.211
15.570
10.455
7.675
5.143
8456
60.65,
26.175
70.143
6.92,
17.426
8.998
16.804
63.477
32.399
11.152
52.210
14.762
13.593
53.073
112.334
27.608
267.688
10.101
8.823
34.395
102.882
6.311
33.826
13.69,
17.666
0.366
0.424