Cohenetal_Cost_Function.txt

Towards a General Postal Service Cost Function*
Robert Cohen
Postal Rate Commission
Carla Pace
Poste Italiane
Antónia Rato
CTT - Correios de Portugal
Matthew Robinson
Postal Rate Commission
Ricardo Santos
CTT - Correios de Portugal
Gennaro Scarfiglieri
Poste Italiane
Vincenzo Visco Comandini
Poste Italiane
John Waller
Postal Rate Commission
Spyros Xenakis
Postal Rate Commission
*The views expressed in this paper are those of the authors and
do not necessarilyrepresent the opinions of CTT - Correios de
Portugal, Poste Italiane or the Postal RateCommission.

1. INTRODUCTION
Mailhandling activities in the posts of industrial countries are
remarkably alike. Each of the major functions (delivery, mail
processing, transportation, and window service) is conducted using
similar methods and technologies. Therefore, it may be possible for
a fairly simple model to explain total and unit cost differences
between posts. Ideally, developing a cost model for the 20 plus
industrial posts would involve collecting data on many individual
cost elements from each and using regression analysis to estimate
the coefficients of a cost function. In today's environment this is
impossible because virtually all posts in industrial countries
consider much of their operational cost data to be commercially
sensitive and will not share them.
In our previous paper, Cohen, et al. (2002), we developed a
model that related unit costs to volume per capita. The model is
based on U.S. costs. More specifically, it is based on the accrued
cost of the major functions and their cost elasticities with
respect to volume. A plot of that cost function reveals the classic
hyperbolic shape with unit costs increasing more rapidly as volume
per capita declines because of the loss of economies of scale. See
Figure 1.
In our previous paper, we made adjustments to the model to allow
for comparison with Poste Italiane. In particular, adjustments were
made for differences in labor cost, amount of worksharing, and mix
of mail by shape.1 In this paper, we add an adjustment for counter
costs.2 The resulting model estimate of Poste Italiane's unit cost
is 74 cents versus the actual value of 79 cents. It must be pointed
out that the cost model is used to estimate costs over an extreme
range of volume. U.S. volume per capita in 1999 was 739 pieces
while Italy's was 115 pieces per capita. Given this range, the
authors are encouraged by the relatively small deviation of the
estimate from actual.
1
See the Appendix to Cohen, et al. (2002).
2
The USPS has only 14 counters per 100,000 population, while
Poste Italiane has 24 counters per 100,000 population.
Figure 1: Model Estimates of Unit Cost
Benchmarked by U.S. Costs and Volumes
2.50
2.00
Cost per Piece ($US)
1.50
1.00
0.50
0.00 0 100 200 300 400 500 600 700 800

Pieces per Capita
In this paper we examine the hypothesis that the cost model
provides reasonable estimates of the unit costs of other posts of
industrialized countries.3 The hypothesis cannot, however, be
directly confirmed because we do not have sufficient cost data on
other countries to compare with the model results.
We provide indirect confirming evidence of the hypothesis, using
the fact that the model implies that mail processing and delivery
costs will comprise specific percentages of total costs at specific
per capita volume levels. We have obtained the actual percentages
of mail processing costs and delivery costs relative to total costs
for seven posts with which we compare the predicted percentages.
Although the evidence is not conclusive, it confirms the
hypothesis.
We first present our model for total costs and unit costs. We
next present the test of our hypothesis by comparing the predicted
percentages for each of the seven posts with the actual
percentages. We then produce a trend line through the data points
and compare it with the model results. Finally, we compare actual
unit revenues, and some derived unit costs, for the seven posts
with the model's prediction of unit costs.
The editors of the book in which our previous paper [Cohen, et
al. (2002)] appears suggested that we examine the hypothesis that
the cost model accurately describes the costs of other posts.


2. THE COST MODEL
The model is the same as that used by Cohen, et al. (2001)
except that we now present it as a generalized cost function. The
model assumes that there are two primary determinants of cost for a
postal system: volume and size of the network. For each activity a
post performs, there are volume-driven attributable costs and
networkdriven institutional costs.
To create a total cost function, we use FY 1999 U.S. Postal
Service data to define the relationship between costs and cost
drivers. Costs for each postal activity (mail processing, delivery,
etc) that can be attributed to mail volumes, are divided by total
volume to obtain an estimate of the marginal cost.4 The remaining
costs are institutional costs that are primarily driven by the size
of the network. Population is a reasonable proxy for the size of
the network and therefore institutional costs are divided by the
U.S. population to obtain the additional cost per person. This
produces annual cost functions for each of the major postal
activities and a total cost function.
Since all costs are variable in the long run, it is reasonable
that non-delivery institutional costs would decline over the large
volume range we explore with this model. For purposes of this
analysis we assume that 25 percent of non-delivery institutional
costs would be volume variable.5
No portion of delivery institutional costs is considered to be
volume variable, however, because route structure generally does
not change as volume drops. As long as coverage is relatively high,
carriers will have to cover their entire route. Thus, fixed
delivery costs would not be expected to drop until volume per
capita were so low that the resulting very low coverage allowed
carriers to skip parts of their routes.
4
Attributable costs using the PRC cost treatment are greater than
volume variable costs. Consequently, the estimate is slightly
higher than the true marginal cost.
5
The results are not very sensitive to this assumption as can be
seen in Cohen, et al. (2001).
The cost function in U.S. dollars is:


Variable Institutional
Mail Processing = 0.1032V + 2.10P Delivery = 0.0525V + 42.24P
Transportation = 0.0200V + 0.92P Window Service = 0.0092V + 4.64P
All Other costs = 0.0241V + 24.41P Total costs = 0.2089V + 74.31P
where V = Volume and P = Population.
It can be seen that the total cost of providing postal service
in the U.S. for FY 1999 was 20.89 cents per piece plus $74.31 per
person. The total cost for other countries can be estimated by
substituting volume and population into the above formula.
The total cost function can be used to estimate average unit
cost by dividing the terms by V:
Average Unit Cost = 0.2089 + (74.31 P / V). This can be restated
in terms of V / P, or pieces per capita (ppc), as:
Average Unit Cost = 0.2089 + (74.31 / ppc).
The percent of total cost for each function included in the
model and cost elasticity (with respect to volume) are shown in
Table 1.
The model assumes constant unit variable costs. Thus, when
volume is reduced total variable cost is reduced by the same
percentage. At lower per capita volumes, the ratio of fixed to
variable cost increases and the cost elasticities decrease (because
a greater proportion of total costs is fixed). Similarly, the model
assumes a constant coefficient for population.
Table 1: FY 1999 USPS Percent of Total Cost and Elasticity (with
respect to Volume) of the Major

a
Source: Postal Rate Commission Docket R2000-1
b
Includes both in and out of office activities.
c
Does not include intra city transportation costs.
The U.S. cost elasticities in Table 1, when applied to the
accrued costs of each function, determine the coefficients in the
cost function, which in turn generate the unique shape of the unit
cost function (Figure 1). Further, these coefficients determine the
percent of total cost that comes from mail processing and delivery
at a specific volume per capita.
The total cost for an individual country can be expressed as a
function of pieces per capita by rewriting the above basic total
cost equation as:
Total Cost for country "i" = (0.2089 Pi)(V/Pi) + 74.31 Pi,
where Pi = population for country "i",
0.2089Pi = slope
74.31Pi = intercept. The values of the slope (rate of increase
in total costs) and intercept (institutional costs) are directly
related to the population of the country. If country A has twice as
many inhabitants as country B, then the slope and intercept of A's
cost function will be twice as large as the slope and intercept of
B's cost function.
Figure 2 displays the total cost curves as functions of pieces
per capita for each of the countries in the sample. The differences
in slopes and intercepts reflect population differences. If total
volume, instead of pieces per capita, were displayed on the
vertical axis, then the Y-intercepts would remain unchanged but the
cost curves would be parallel. Although Figure 2 shows a family of
total costs curves, Figure 1 displays a single unit cost curve
because the unit cost curve depends on only one variable, pieces
per capita.
Figure 2. Total Cost Functions for Sampled Posts
Not Adjusted for Structural Differences

0 100 200 300 400 500 600
Pieces per Capita


3. ADJUSTMENTS
To estimate the cost of a post using the model, it is necessary
to take into account labor cost differences between the U.S. Postal
Service and the given post. The test of our hypothesis, however,
does not involve predicting unit costs of other posts. It involves
predicting the percentage of total cost devoted to mail processing
and delivery. Thus, labor costs do not need to be adjusted.
The total percentage of mail processing costs would have to be
adjusted if worksharing, automation, or mail mix had significantly
different impacts on mail processing costs. We have adjusted mail
processing costs for La Poste and Posti Finland. Both France and
Finland include the costs of cancellation and mail preparation in
counter costs. Because the U.S. Postal Service classifies these
costs as part of mail processing, we adjust the percentages of mail
processing costs upward for France and Finland to reflect a similar
treatment. This has no effect on total costs, and therefore only
affects the mail processing percentage.
The number of deliveries per week varies among the posts in the
sample (Canada, Finland, and Portugal deliver five times per week,
Great Britain delivers 12 times weekly in urban areas and six in
rural areas). Consequently it is necessary to adjust the percentage
of delivery costs for these posts to the level it would be with six
deliveries per week (as in the U.S.) When the percentage of
delivery cost is increased or decreased for a given post, the
percentage of mail processing cost is decreased or increased
accordingly.6


4.
CONFIRMING THE HYPOTHESIS


4.1
Data


Canada Post, Consignia (Royal Mail), Posti Finland and La Poste
supplied the percentages of delivery and mail processing costs to
us. The authors supplied the data for CTT Correios de Portugal and
Poste Italiane. Only La Poste delivers unaddressed mail separately
from normal mail. Consequently, the volumes and percentages of
total cost for La Poste do not include unaddressed mail.
Unaddressed mail is included in the calculations for other
posts.
The cost percentages reflect labor and non labor costs, except
for Germany. The Deutsche Post percentages are derived from
workforce full time equivalents contained in its annual report for
FY 2001 and an internal Post Italiane study on German delivery
operations developed in part from meetings with Deutsche Post
management. The Deutsche Post annual report provides the total
number of full time equivalents involved in postal operations and
the Poste Italiane document provides the number involved in
delivery operations. While this is a proxy for labor and non labor
costs, it is considered realistic since in the U.S., the use of
workforce full time equivalents provide estimates within a few
percentage points of those calculated with labor and non labor
costs.
6
The population density (or more specifically the postal density
-- the average time it takes to travel between addresses) of a
country has an impact on street delivery costs. Ideally we could
adjust for this if data were available. (See Bernard, et al.
2002).
4.2 Empirical Findings
Empirical findings from the investigation are presented in
Figure 3. The top line represents delivery cost percentage (of
total cost) as a function of pieces per capita as predicted by our
cost model. The bottom line represents the same for mail processing
costs.
Figure 3: Functional Percentage of Total Costs
Benchmarked by U.S. Costs and Volumes
Percentage of Total Costs
70
60
50
40
30
20
10
0 0 100 200 300 400 500 600 700 800

Pieces per Capita
With the exception of the lowest volume post (Poste Italiane)
the model's predicted percentages are close to the actual
percentages for delivery. We think Poste Italiane, a very low
volume post, may have a somewhat lower percentage of delivery costs
than predicted owing to low coverage on very low volume routes
especially in rural areas. When carriers deliver to only a small
number of stops on a route they tend to cover the route in a way
more similar to a "traveling salesman" than following a fixed route
past every stop. Thus, there may be less fixed costs on these
routes than indicated by the elasticities embedded in the cost
model based on U.S. costs, which reflect very high coverage levels.
If this conjecture is correct, then Italy's delivery percentages
could be adjusted upwards (by an unknown amount) towards the
predicted value and their mail processing costs would then have to
be adjusted downwards. A downward adjustment would also improve
Italy's relation to the mail processing prediction but move
Portugal further away. Some of the deviation for Italy and Portugal
may be due to the fact that they have proportionally much larger
retail operations involving collection and acceptance than the U.S.
and other posts. For example, Portugal's retail post office
operations account for 21 percent of total costs, while in the
U.S. they account for approximately six percent. Poste Italiane
also has a relatively large percentage of costs in collection and
acceptance, 15 percent. Nevertheless, the authors cannot explain
why Portugal's percentage of mail processing cost is so low in
comparison to the other posts in the sample.
A significant virtue of these curves is that they are
independent of the price of labor. Thus, by using this evaluation
technique, we are able to avoid the need for obtaining productive
hourly costs translated into dollars using purchasing power
parities.
It appears that other factors, for which adjustments are not
made, do not cause significant differences. This could be because
these factors do not vary significantly from the U.S., do not drive
costs significantly, or tend to cancel each other out.
4.3 Trend Analysis
The bold lines in Figure 4 display trend curves for the actual
processing and delivery cost percentages from the test countries.7
These curves were generated using Excel. They have virtually the
same shape as the curves predicted by the model and further confirm
the fit between the model and the data. The low delivery cost
percentage of the low volume per capita country, Italy, pulls the
delivery trend line down away from the predicted line. The fact
that the actual mail processing percentages for Italy and Portugal
are about equidistant below and above the predicted values causes
the mail processing trend line to match the model line at low
volumes despite relatively large errors. These disparities at low
volumes between the trend and model lines reinforce our belief that
the model is less useful in predicting costs for low per capita
volume posts than it is for medium to high volume per capita posts.
It is to be expected that the accuracy of predictions will diminish
as the range over which the predictions are made increases.
These trend lines were selected because they best fit the data.
For delivery percentages, the trend line is y=46.943e-0.0004x with
an R2 of 0.78. For mail processing percentages the trend line is
y=10.869Ln(x) - 38.407 with an R2 of 0.69.
Figure 4: Functional Percentage of Total Costs with Regression
Curves
70
60
Percentage of Total Costs
50
40
30
20
10
0 0 100 200 300 400 500 600 700 800

Pieces per Capita
5. ESTIMATED UNIT COSTS
In order to compare unit costs, it is desirable to make the
adjustments we have discussed above plus an adjustment for
productive hourly wage in purchasing power parities (PPP). Data for
these adjustments were not available, except for Italy. The
U.S. values used in making adjustments for Poste Italiane data
are listed in the appendix. In the absence of actual cost data, we
compare model cost results to actual revenues.
For the posts in our sample we have used the model to estimate
unit costs and adjusted only for deliveries per week (Canada,
Finland, U.K., and Portugal.) In Table 2, we compare these
estimates with average revenue per piece converted to U.S. cents
using OECD's PPP for 1999.
Table 2: Comparison of Model Estimated Coststo Actual Revenue
per Piece for 1999
(U.S. cents)
Model Cost Revenue Estimates per Piecea
Canada 43 41 Finland 34 39 France 38b 40b Germany 50 57 Italy 90
79c Portugal 62 54
U.K. 46 50
U.S. 31c
a
From annual reports and Posts of authors, 2000 for
Portugal b Includes unaddressed mail
c
Actual cost per piece
The largest discrepancy appears to be Italy. We know, however,
that the Post Italiane productive hourly wage is three quarters of
that of the U.S. Postal Service. As stated in the introduction,
when we adjust for Italian labor costs, worksharing, mail mix, and
number of counters, we get a modeled unit cost of 74 cents.
6. CONCLUSIONS
The principal conclusion is that empirical evidence corroborates
the validity of this model because the predicted functional
percentages of costs are reasonably close to actual values. See
Figure 3. In particular, the general shape of the unit cost curve
(with respect to per capita volume) appears to be valid for the
posts of industrialized countries sampled. See Figure 1. The model,
however, is a more accurate predictor of the cost behavior of
medium to large per capita volume posts than for small per capita
volume posts. The model also demonstrates that both volume and
population are important explanatory factors of postal costs.
Clearly, additional research is warranted. Regulators and
operators in any industrialized country are encouraged to use the
data in the appendix on U.S. cost characteristics to make
adjustments to the model and determine if the model forecasts costs
with reasonable accuracy. Of course, we would not expect exact
correspondence even after adjustments are made owing to differences
in efficiency and service quality.
Appendix: FY 1999 USPS Operational Statistics


•
Productive hourly wage: $23.87644


•
Mail mix by shape: 72 percent letters and cards, 26
percent flats, 1 percent parcels


•
Percentage of mail with some worksharing: 72


•
Percentage of letters barcoded by mailers: 56


•
Percentage of letters barcoded by USPS: 32


•
Percentage of flats barcoded by mailers: 38


•
Percentage of mail not delivered (i.e. Post Office Box
mail): 21.4


•
Average postal density (addresses per fixed street hour):
100.5


•
Counter Costs: 5.6 percent


REFERENCES
Bernard, Stephane, Robert Cohen, Matthew Robinson, Bernard Roy,
Jöelle Toledano, John Waller, and Spyros Xenakis. 2002. "Delivery
Cost Heterogeneity and Vulnerability." Paper presented at the 10th
Conference on Postal and Delivery Economics, Potsdam, Germany.
Cohen, Robert, William Ferguson, John Waller and Spyros Xenakis.
2001 "The Impact of Using Worksharing to Liberalize a Postal
Market." Paper presented at Wissenschaftliches Institut für
Kommunikationsdienste GmbH, 6th Köenigswinter Seminar on Postal
Economics, Liberalization of Postal Markets.
Cohen, Robert, Carla Pace, Matthew Robinson, Gennaro
Scarfiglieri, Vincenzo Visco Comandini, John Waller and Spyros
Xenakis. 2002. "A Comparison of the Burden of Universal Service in
Italy and the United States." In Postal and Delivery Services:
Pricing, Productivity, Regulation and Strategy, edited by M.A. Crew
and P.R. Kleindorfer. Boston, MA: Kluwer Academic Publishers.
PRC Docket No. R2000-1 USPS LR-I-481, FY 1999 and TY Mail
Processing Unit Costs by Shape with Piggyback Factors (Update to
LR-I-81 & 464 Provided in Response to POR No. 116) Using FY 99
Base Year and Alternative IOCS Methodology