assessing the marginal infrastructure wear and tear...

ASSESSING THE MARGINAL INFRASTRUCTURE WEAR AND TEAR COSTS FOR GREAT BRITAIN’S RAILWAY NETWORK

Phill Wheat Institute for Transport Studies, University of Leeds

Andrew S.J. Smith Institute for Transport Studies, University of Leeds

1. INTRODUCTION Amongst other directives in the European Commission’s First Railway Package was 2001/14/EC which sets rules on charges to be levied on operators for the use of member states networks. Charges should be based on the direct cost of running the service, that is, the price of access should reflect the costs to the infrastructure manager and society as a whole from running the additional service. Railways in Great Britain have undergone major reform. Prior to 1993, the railway in Great Britain was vertically integrated and public owned. In 1993 a set of measures were implemented which resulted in the formation of Railtrack plc now Network Rail, a private company responsible for the management of the infrastructure. Subsequently passenger services have been franchised to private operators and freight services privatised with the freight market subject to full open access. This was in order to separate the natural monopoly element, believed to be the infrastructure, from areas that were susceptible to competition either in- or for- the market. Given the vertical separation in the UK system, it is important to establish appropriate charging systems to optimise the allocation of capacity to operators and give incentives to operators to use appropriate rolling stock. Infrastructure access charges in the UK consist of a two part tariff for franchised passenger operators. This consists of a fixed charge, that does not vary with usage and a variable charge. Freight and passenger open access operators only pay the variable access charge and the variable charge is based on the principle of marginal cost. A key research need, both to support policy in Great Britain and more widely in the European Union, is the need to value the marginal social cost of network usage. A substantial component of this is the marginal cost to the infrastructure manager; the additional maintenance and renewal cost resulting from running an extra service. However, traditionally, both industry and academic work on railway costs has focused on the characteristics of the vertically integrated railway; but as a result of the restructuring there been a strong need to examine the interaction between operations and infrastructure for pricing purposes. In academia, innovative econometric work has emerged following the seminal paper by Johansson and Nilsson (2002, reprinted in 2004).

©Association for European Transport and contributors 2006

In Great Britain marginal wear and tear costs are currently estimated using a hybrid approach between cost allocation and engineering approaches (see for example ORR, 2000 and Booz Allen & Hamilton, 1999 and 2005). These rely heavily on engineering judgement. This paper contributes to the literature by utilising the econometric approach using a cross section data set of 53 “Maintenance Delivery Units” for the Great British network in 2005/06. The approach is based on the examination of past data and should provide a useful objective benchmark for the results from other approaches. This data has now become available following the move to take maintenance in-house by the infrastructure manager. We estimate a double-log (Cobb Douglas) cost function for Permanent Way maintenance cost and compute marginal cost for different characteristics of MDUs. The structure of the paper is as follows. Following this introduction, Section 2 briefly introduces the alternative approaches taken to estimate marginal costs of infrastructure use. Section 3 outlines the data set available for the study and also the particular methods used to estimate the cost function. Section 4 discusses the results in terms of the final models and implied elasticity and marginal cost estimates and benchmarks these against results from other studies. Section 5 concludes. 2. LITERATURE REVIEW Estimation of marginal infrastructure costs can be characterised into two groups: bottom-up approaches and top-down approaches (Link and Nilsson, 2005). Bottom-up approaches rely on engineering models and judgement to determine the likely wear and tear impact of running an extra vehicle on different components of the infrastructure network. Top down approaches use data on costs of maintaining and/or renewing the infrastructure and estimate what proportion of these costs are variable with traffic. The top down approach may be implemented through two methods: estimation of an infrastructure cost function using econometric techniques; and cost allocation methods which allocate constituent parts of total cost to common cost drivers and then use engineering judgement to determine the variabilities of these categories with the cost driver. In this paper we follow the econometric approach. For the purpose of this shortened conference paper, we do not review the literature in this area; see Link and Nilsson (2005) for such a review. 3. METHODOLOGY AND DATA We now outline the methodology and data adopted for our study.

3.1. Cost function estimation

The aim of the exercise is to estimate the marginal cost of running more or less traffic on a fixed network; that is we wish to calculate short run marginal cost. The variable cost function relates total variable costs to output


variables, prices of variable inputs (labour, energy etc) and levels of fixed inputs (route miles, number of switches and crossings etc.); see, for example, NERA (2000). In keeping with the majority of the literature we adopt a double log (Cobb Douglas) functional form:

)Pln()Pln()Vln()Vln()Qln()Qln()Cln( pipiviviqiqii δ+δ+γ++γ+β++β+α= 111111 ΛΛNi ,,2,1 Κ=

where

• is the cost per annum for firm or unit i (in our case, the units are based on 53 regional, maintenance delivery units or MDUs);

iC

• is a vector of outputs for MDU i – here we consider output to be train related measures of output, primarily because this is the stage of production for which we wish to derive marginal costs;

iQ

• is a vector of fixed input levels for MDU i – In the short run several factors of production are fixed. These are assumed to be the infrastructure. Therefore, measures that naturally fit in here are track length, track quality, track capability and track age in a MDU;

iV

• is a vector of input prices; and iP• N is the number of MDUs

The specification allows for non-constant marginal effects and it is using this specification that we tested the alternative possibilities for the composition of each category of variables. However this form is restrictive since it assumes constant cost elasticities. The Translog cost function incorporates additional second order interaction terms which yields a less restrictive specification. Unfortunately it became apparent that the data, both in terms of variability and degrees of freedom, did not support the estimation of such a complex functional form. We do, however, test the inclusion of second order terms for key variables. In particular, we consider the evidence that the elasticity of cost with respect to traffic density is not constant.

3.2. Cost Data In this study we have a cross section of data provided by Network Rail for 53 Maintenance Delivery Units (MDUs) for 2005/06. However not all cost data is available at this level of disaggregation, and some data is only available at the area level (the 53 MDUs aggregate up into 18 maintenance areas). Table 1 shows the categories by which maintenance cost data was available. 60% of total maintenance expenditure is available at the MDU level. The remaining expenditure (40% of the total maintenance budget) includes maintenance of electrification and plant equipment and other expenditure and can not be allocated to individual MDUs. Instead it is allocated to one of 18


Maintenance Areas or more aggregate levels. Given the small sample size we do not analyse the maintenance area data in any great detail. Discussions with the industry suggested that the Permanent Way expenditure was the cost category that would be subject to substantial usage related variability. However concerns were raised as to the consistency of cost allocation between Permanent Way and General maintenance activity and so it was decided to analyse the combined Permanent Way and General expenditure categories together. Table 1 Cost categories available for analysis Cost Category Proportion

of Total Maintenance Expenditure

Level at Which Data is Available

Coverage

Signalling and telecoms

15 Maintenance Delivery Unit

Includes the maintenance of signalling (signals, cables, signal boxes) and telecoms (signal post telephones)

Permanent Way 34 Maintenance Delivery Unit

Includes maintenance of track, ballast and sleepers

MDU General 11 Maintenance Delivery Unit

The remaining expenditure which is incurred at the MDU level including general depot costs such as management and production, expenses, vehicle hire and property costs.

Electrification and Plant

7 Maintenance Area

Includes both maintenance of (i) contact systems (both overhead lines and 3rd Rail Conductor) (ii) plant (pumping stations, signal power supplies, points machines) and (iii)

Area other 26 Maintenance Area

Includes area services, area track engineer and area overheads

Territory and HQ 7 Territory and HQ

Not available for analysis

Source: Network Rail

3.3. Output data Our data set includes data about both the number of train miles and number of tonne miles per MDU. From the raw data, there are many potentially useful transformations of this data which can be used and Table 2 highlights the transformations that are used in subsequent analysis. Following the findings of Gaudry and Quinet (2003), who found a difference between the impact of additional gross tones resulting from heavier trains, as opposed as a result of more trains of the same weight, we adopt both a measure of the density of train miles per track-mile and the average weight of those trains1. We aim to test for statistically different impacts from each factor. Where we can not distinguish between there two separate effects we adopt the gross tonne miles per track mile measure. Data is available at three levels of disaggregation; from total traffic at the highest level to intercity passenger traffic, other passenger and freight traffic at the most granular level. Efforts have been made to investigate whether,


after accounting for the average weight of trains, there exists detectable differences in the wear and tear impacts of different types of trains. Table 2 Output data available for analysis Variable Units Name Mean St. Dev. Minimum MaximumTotal trains Average trains

per track mile per MDU

TOT_TRAIN 16324 6536 5694 31625

Average weight of trains

Tonnes per train

TOT_AWT 293.0 84.5 122.1 502.0

Total trains Tonne miles per track mile

TOT_TON_T 4809570 2304830 1172371 9027768

Total passenger trains

Tonne miles per track mile

TOTPA_TON 3345735 2110686 355828 8032005

Total freight trains

Tonnes miles per track mile

TOTFR_TON 1463835 975525 26286 3652366

3.4. Infrastructure Capability/Quality Data In order to control for the impact on cost from the levels of the fixed factors in estimation of short run marginal cost, it is necessary to select variables which reflect the quantity, capability and quality of the fixed infrastructure. Our data set includes a wide variety of measures per MDU including variables in the following categories:

• Track Length including length by track type • Route Length • Maximum Line speed capability of track • Maximum Axle load capability of track • Numbers of each signal type and Signalling equivalent units • Electrified track length (and by type of electrification) • Rail Age

Firstly, we drew on engineering expertise from within Network Rail and our own understanding and research to determine which categories of variables are relevant for the analysis of the Permanent Way cost category. Clearly the length of track will have an impact on the maintenance requirements and there are strong arguments as to why Continuously Welded Rail (CWR), jointed track and switches and crossings (S&C) should be distinguished between. S&C are relatively complex pieces of track and so the cost of maintaining them should be relatively high. Jointed track, while cheaper to install than CWR, is more susceptible to usage related damage and so should also be distinguished in the analysis. Route length relative to track length is a useful proxy for network concentration and so models would benefit from its inclusion, however its expected sign is ambiguous. On one hand a higher network concentration may mean possessions are easier to obtain as, say a four track line can be partially closed rather than a singled line that has to be completely closed and a concentrated network may mean reduced costs in getting to/from site.


However there is also an argument that the extra safety and operational measures required to work on a partially open line may outweigh these gains. Both maximum line speed and maximum axle load measures are measures of the capability of the track to allow the carriage of more demanding traffic. These variables may act as proxies for two key cost drivers. The first is that a higher line speed or axle load capability will reflect a greater quality of construction of the track which is expected to require less maintenance. On the other hand higher line speed and axle load capabilities will usually be associated with usage by higher speed and axle load traffic. It is expected that this traffic damages the track to a greater extent than other traffic. As such the overall effect on cost of these variables is ambiguous. We do note that some variables, notably CWR track vis-à-vis jointed track, should also pick up the relative quality differences of track and thus their inclusion in any specification may result in a more positive effect on costs of the capability variables2. Apart from some minor issues, we do not expect signalling and electrification variables to reasonably reflect underlying drivers of cost. Thus we do not consider them as part of the specification. Older rail age is expected to increase maintenance costs. The older the track the more maintenance it requires to keep it to a given standard. However, the selection of categories of variables is not the end of this variable selection process; there exists many possible variables that are potential measures for each cost category. The measures chosen are shown in Table 3, where the choice was made on statistical grounds (further details on the process by which the particular measures were chosen are available from the authors). The infrastructure variables that were found to be statistically superior are shown in Table 3.

3.5. Input Prices We have data on the price of labour in each MDU and this is summarised in Table 3. This data is not railway specific; instead it refers to the general level of wages in the geographical areas of each MDU. This was derived through National Statistics data. We do not have data on the price of materials and machinery, however we assume that this is constant between MDUs and thus its effect is absorbed within the constant term.


Table 3 Non-output variables chosen for possible inclusion in the Permanent Way cost function Name Description Mean3 St. Dev. Minimum MaximumInfrastructure variables TRA_LEN Length of Track (in logs) 367 153 132 873 MAL_G25_P Proportion of track length

with maximum axle load greater than 25 Tonnes

0.55799 0.21334 0 0.93397

MLS_G100_ Proportion of track length with maximum line speed greater than 100 mph

0.1743 0.19006 0 0.68408

TRACWR_PR Proportion of track length which is CWR

0.75918 0.11362 0.42322 0.91572

AGE_G30_P Proportion of track length with rail age greater than 30 years

0.45211 0.12995 0.21732 0.73305

Price variables WAGE Labour price index by

MDU (in logs) 13 2.02219 10 17

3.6. Summary of specifications The discussion above about the functional form and explanatory data leads to a number of possible model formulations that need to be and are tested as part of the analysis. Table 4 summarises these. Table 4 Summary of specifications Model Output Infrastructure data Input

Prices Model I Train miles per track mile and

AWT Full set Wage

Model II Train miles per track mile and AWT

Full set minus AGE_G30_P (see section 4.1 for explanation)

Wage

Model III Tonnage miles per track mile Full set minus AGE_G30_ Wage Model IV Passenger tonnage miles per

track mile and Freight tonnage miles per track mile

Full set minus AGE_G30_ Wage

Model V Tonnage miles per track mile and the square of Tonnage miles


Model VI As in IV but with second order interaction terms between passenger and freight variables


4. RESULTS The preferred models are shown in Table 5. We first describe each model and benchmark our findings against those in the literature and then we proceed to calculate estimates of marginal cost.


4.1. Models Estimated Model I shows the analysis of total traffic measured by train density (number of trains per track mile) and average weight of trains. First note that we find three outlying observations for this set of models for which we include dummy variables. The overall fit, 2R , is 0.78, which is in line with other models taking a double log functional form estimated by other researchers in the field. The elasticity of cost with respect to train density ( Trainε ) is 0.202 and with respect to average weight of trains (AWT) is 0.34. Both are significantly different from zero at the 5% level however a Wald test of the null hypothesis that both elasticities are equal can not be rejected at any reasonable significance level. This indicates that we can not reject the hypothesis that a proportionate increase in AWT holding the number of trains constant has the same effect on costs as the same proportionate rise in the number of trains holding AWT constant. The elasticity of cost with respect to track length ( Trackε ) is 0.5110 which is significantly different from zero even at the 0.1% level. Importantly it is also significantly different from one even at the 0.1% level. We note that this implies an estimate of economies of scale (EoS) of 1.96 which is slightly greater than from other studies (see Table 7), where we define EoS (in line with Oum and Waters 1997) as

( )Track1EoS ε= However, like in all other studies, there are increasing EoS. The Wage variable has a coefficient with the expected sign and is significantly different from zero at the 5% level. The coefficient indicates that a 1% rise in wages results in a 0.5% rise in cost. Of the three variables that proxy for track quality, not all are significantly different from zero even at the 10% level. However we included them within the specification, since removing them resulted in a relatively large change in the coefficient on TOT_TRAIN with little reduction in standard error. As such we kept these variables in the specification to guard against omitted variable bias. However, we are concerned about the sign of the coefficient on the age variable. It seems counter intuitive that older track is less costly to maintain once track quality and usage have been controlled for. We note that this result is robust across a range of models. A genuine reason for this maybe that for assets that are very close to the end of their lives, maintenance effort maybe reduced since these assets are marked for renewal. However, another reason might be the limitations of the age measure that we have adopted. In particular we recognise that age itself is not the driving factor behind maintenance requirement but instead the proportion of life expired is a more appropriate measure. This however is a function of usage and track capability/quality which are included in the specification. In addition, the age variable maybe picking up other usage characteristics, such as the speed of trains (lower speed trains tend to be on assets which are older). Thus for


these reasons and because of the counter-intuitive sign on its coefficient, it is considered that the age measure is misleading and should be removed. Model II is a re-estimation of model I excluding the age variable. We accept that the fit of the model has fallen slightly to , however the overall model is thought more robust than model I for the reasons outlined above. Both the elasticity of cost with respect to train density and AWT have increased to 0.302 and 0.399 respectively due to the removal of AGE_G30_P that is negatively correlated with both TOT_TRAIN and TOT_AWT (-0.542 and -0.304 respectively). All coefficients are statistically significant from zero at the 5 % level except some of the outlier dummies.

742.0R 2 =

However, the Wald test for the null hypothesis of equivalence between the coefficients on TOT_TRAIN and TOT_AWT could not be rejected at any reasonable significance level. This seems to be a robust result, thus we re-estimate the model with just tonne density (TOT_TON_T) rather than the two output measures. Model III shows the results. The fit of the model has fallen very slightly, , as expected and the estimates of the elasticity of cost with respect to tonnage density is significant at the 0.1% level and is 0.331, which is to be expected as this is between the two estimates using TOT_TRAIN and TOT_AWT in model II. Otherwise all other coefficients are in line with those for model II.

740.0R 2 =

In model IV we investigate the usefulness of distinguishing between passenger and freight traffic using the gross tonne measure of output4. We first note the fall in the fit of the regression, with . We also note that the freight coefficient is not significantly different from zero at the 10% level

691.0R 2 =5.

Given that passenger traffic accounts for a substantial proportion of total traffic, it should be no surprise that the elasticity of cost with respect to passenger traffic is greater than the corresponding elasticity for freight. This is not the same as saying that the marginal cost of passenger tonne-kms is greater than the marginal cost of freight tonne-kms. Whether this implies a difference in marginal cost per tonne-km will be discussed in subsequent sections. We do note that the elasticity of cost with respect to total tonnage density is 0.249 which is smaller than in model III. Given the restrictive nature of the Cobb Douglas functional form, Model V introduces a second order term in total tonnage density, TOT_TONSQ (equal to TOT_TON_T2)6. The fit of this model is superior to that in model III with

. Except for the coefficient on WAGE and MLS_G100_ all coefficients are significantly different from zero at the 5% level. The elasticity of cost with respect to tonnage density is no longer constant and given by:

756.0R 2 =

T_TON_TOT2T_TON_TOT

Costln21Tonnage β+β=

∂∂

=ε where 1β and are the

coefficients on TOT_TON_T and TOT_TONSQ respectively.

2β

Figure 1 plots the elasticity of cost with respect to tonnage density and the associated 95% confidence interval. Evaluated at the mean tonnage density,


the elasticity is 0.239. The elasticity is falling with gross tonnage density and this finding seems to be robust to inclusion/exclusion of other explanatory variables. The implication is that at higher tonnages marginal cost is a smaller proportion of average cost, other things equal. This observation is in line with findings from Johansson and Nilsson (2004) and Andersson (2005) using Swedish data, however Gaudry and Quinet (2003) find an increasing relationship using French data. Finally, Model VI generalises model V to examine the effects and interactions between passenger and freight traffic. The overall fit of the model has improved over that in model V, R , however at the loss of three degrees of freedom, which thus results in a fall in

764.02 =2R . An F-test of the null

hypothesis that all of the coefficients on the second order terms are zero is rejected at any reasonable significance level. Thus we conclude that the second order model provides some additional explanatory power over the simple Cobb Douglas model. MLS_G100_ is not in the final specification as when included its coefficient had a very low t statistic and the precision of estimation of the other coefficients improved considerably following its removal. All of the coefficients on the output variables are significantly different from zero at the 5% level except the coefficient on TOTP_TONS, i.e. the square of TOTPA_TON and TOTF_TONS i.e. the square of TOTFR_TON. The cost elasticity for passenger traffic is given by:

TON_TOTFR19569.0TON_TOTPA07105.09097.3

TON_TOTFRTON_TOTPA2TON_TOTPA

Costln321Passenger,Tonnage

−−=

β+β+β=∂

∂=ε

And for freight traffic:

TON_TOTPA19569.0TON_TOTFR05627.02374.2

TON_TOTPATON_TOTFR2TON_TOTFR

Costln354Freight,Tonnage

−+=

β+β+β=∂

∂=ε


Figure 1 Elasticity of cost with respect to tonnage – Model V

Elastciity of cost with respect to tonne density

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1000000 2000000 3000000 4000000 5000000 6000000 7000000 8000000 9000000 10000000

Tonnage per track-km

Elas

tciit

y

Elasticity Lower CI Upper CI

Figure 2 plots the elasticity of cost for passenger and freight tonnage density. First note that some observations have a negative elasticity. This is counterintuitive given it implies negative marginal cost. However for all of the observations with elasticities less than zero, the 95% confidence interval spans zero, thus we can not reject the null hypothesis that each observation has a positive elasticity. Holding freight tonnage constant, increasing passenger tonnage decreases the passenger elasticity, which is in line with the observation for total tonnage. However holding passenger tonnage constant, increasing freight tonnage increases the freight elasticity. We also note the highly significant negative coefficient on the interaction variable between passenger and freight tonnage. This implies that there are economies of scope in infrastructure maintenance costs in running both passenger and freight on the same network as opposed to on two different networks. We do, however, have concerns about the robustness of this model. First, as noted above, some of the coefficients on key output variables are not significantly different from zero at a reasonable level of statistical significance. Second, when evaluated at the mean passenger and freight tonnage, the passenger and freight cost elasticities are 0.064 and 0.096. It is surprising that the freight elasticity is greater than the passenger elasticity and also that the total tonnage cost elasticity is only 0.160, which is substantially smaller than in all other models.


Figure 2 Elasticity of cost with respect to tonnage – Model VI

Elasticity of cost with respect to tonnage density

-0.2

0

0.2

0.4

0.6

0.8

1

0 1000000 2000000 3000000 4000000 5000000 6000000 7000000 8000000 9000000

Tonnage per track-km

Elas

tcity

Passenger Freight Log. (Freight) Log. (Passenger)

Finally, we note a general difficulty associated with the analysis of data at the MDU level. An MDU is defined as the collection of tracks for which a specific maintenance depot is responsible. As such the tracks included within an MDU will not have uniform traffic, quality and capability characteristics. This, coupled with the limited number of data points and thus degrees of freedom, means that it is very difficult to adequately capture the effects of traffic, quality and capability in the econometric specification. Once better data is available, either via formation of a panel dataset through collection of more years of data or by disaggregating costs down to individual track sections, a more robust cost function can be specified and estimated. These issues may also explain some of the counter intuitive signs on the CWR variable for example.


Table 5 Preferred models Model I II III IV V VIRegressor t-stat in brackets

Constant 8.0583 6.3244 6.3872 7.8743 -34.4368 -34.0127(6.2638) (5.2147) (5.3203) (6.4783) (-1.8408) (-2.2114)

Output

TOT_TRAIN 0.20209 0.30189(2.3174) (3.5247)

TOT_AWT 0.34117 0.39877(2.8139) (3.0982)

TOT_TON_T 0.33077 5.8336(4.5723) (2.3356)

TOTPA_TON 0.17365 3.9097(3.1368) (2.5391)

TOTFR_TON 0.074929 2.2374(1.5471) (2.7283)

TOT_TONSQ -0.1818(-2.1979)

TOTP_TONS -0.035524(-.88760)

TOTF_TONS 0.028137(1.5695)

TOTPF_TON -0.19569(-4.2511)

Infrastructure

TRA_LEN 0.511 0.51671 0.53384 0.49938 0.48225 0.45786(6.8354) (6.4178) (7.0774) (5.9343) (6.5289) (5.9042)

MAL_G25_P -0.41785 -0.38337 -0.33452 -0.31764 -0.48602 -0.63729(-2.4785) (-2.1163) (-2.0498) (-1.3155) (-3.0237) (-2.8797_

MLS_G100_ -0.30947 -0.4295 -0.38442 -0.41203 -0.28955(-1.6540) (-2.1895) (-2.1139) (-1.9428) (-1.6979)

TRACWR_PR 0.49681 0.81157 0.76944 0.89079 0.84015 0.85925(1.5206) (2.14574) (2.3939) (2.4652) (2.6658) (2.5697)

AGE_G30_P -0.74702(-2.7841)

Prices

WAGE 0.48714 0.42502 0.40127 0.42352 0.23258 0.23591(2.5206) (2.0549) (1.9857) (1.8770) (1.2099) (1.1892)

Dummies

DUM35 0.33246 0.36044 0.35146 0.43436(1.7644) (1.7780) (1.7499) (1.9776)

DUM42 0.54256 0.47765 0.49019 0.47224 0.48788 0.57161(2.8780) (2.3699) (2.4606) (2.1210) (2.5300) (2.9504)

DUM44 -0.41782 -0.47956(-2.2520) (-2.5461)

DUM51 0.37498 0.29778 0.28928 0.27001(2.0393) (1.5205) (1.4908) (1.2545)

R-Squared 0.78305 0.74203 0.73951 0.69136 0.7551 0.76407R-Bar-Squared 0.72484 0.68061 0.68598 0.61787 0.70434 0.70077Equation Log-Likelihood 25.0729 20.4841 20.2262 15.7317 21.9068 22.8506DW-Statistic 2.4826 2.0387 2.055 1.9529 2.1188 2.2457

Wald test for H0: 0.97117 0.41069 6.8946coefficient TOT_TRAIN= [.324] [.522] coefficient all second [.001]TOT_AWT order = 0 F(3,41)

F-Test for H0:


4.2. Marginal cost calculation We now proceed to calculate the marginal usage costs. We first note the relationship between the marginal usage cost for MDU i ( ) and the usage elasticity for that zone:

iMC

iii ACMC ⋅ε= since i

ii AC

MC=ε and

i

ii miles_Tonne

CAC = is the average cost

of usage. The estimate of MC , , is given by i iCM

i

iiiii miles_Tonne

CˆCAˆCM ⋅ε=⋅ε=

Following Munduch et al (2002), we note that from our double log formulation and assuming that the residuals are distributed normal:

( )( )2iii ,uClnN~)Cln( σ− where ( )iCln is the fitted value of from the

regression which is equivalent to the expectation of ( iCln )

( )iCu

ln conditional on the vectors Q , is the variance of the error term and is the error term. iii P,V, 2σ i It then follows that C is distributed log-normal. As such the estimate of is given by:

iˆ

iC

( )( )2

iii ˆ5.0uClnexpC σ+−= Figures 3 and 4 show plots of the marginal cost estimates for Models I and II and Models III-VI respectively. Apart from the freight marginal costs in model IV, for all models marginal cost is falling with traffic density, but at a decreasing rate. Thus there seems to be a levelling off of marginal cost at higher tonnage density levels. In addition, mean marginal costs are calculated as a weighted sum of each zones marginal costs, weighted by tonnage-miles (or train miles in the case of models I and II):

( )∑∑ =

=

⋅⋅=53

1ii53

1i

miles_TonneCMmiles_Tonne

1CM

Table 6 shows the mean marginal cost for each of the six models estimated. We present for each model the mean marginal costs per gross tonne and per train. We compute the gross tonnage estimate (trains estimate) for models I


and II (models III-VI) by multiplying (dividing) the trains estimate (tonnage estimate) by AWT. Figure 3 Marginal costs for Models I and II

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5000 10000 15000 20000 25000 30000 35000

Train miles per track mile

Mar

gina

l cos

t per

trai

n m

ile £

Model II Model I Log. (Model I) Log. (Model II) Figure 4 Marginal costs for Models III-VI

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0 1000000 2000000 3000000 4000000 5000000 6000000 7000000 8000000 9000000 10000000

Gross tonnage miles per track mile

Mar

gina

l cos

t per

tonn

e m

ile £

Model VI - Freight Model VI - Passenger Model V Model IV - Freight Model IV - Passenger Model III


Table 6 Mean marginal cost estimates

Model I II III IV (Passenger)

IV (Freight) V

VI (Passenger)

VI (Freight)

£ Per Thousand Gross Tonne Miles

1.046 1.563 1.712 1.343 1.176 1.370 1.065 1.747

£ Per Train Mile 0.3095 0.4627 0.5051 0.3016 0.9834 0.4055 0.2392 1.4603

4.3. Comparisons against other studies Table 7 shows the results from other studies. It can be seen that the estimates of the (average) elasticity of cost with respect to traffic density range from 0.13 to 0.37. All the estimates from our models fit into this range. Given that we adopt a narrow cost base i.e. focusing on Permanent Way, which we would expect to contain the components of maintenance activity that are most associated with traffic, we would expect our elasticity estimates to be in the high part of the range observed in other studies. For models II and III this is the case since the elasticity estimate is in excess of 0.3. For model I, the elasticity estimate is only 0.2, however we feel that this is not a robust model for reasons outlined above. The total elasticity in model IV may seem slightly low given the expectations outlined above however we note that only one study (Gaudry and Quinet, 2003) has found an average elasticity greater than 0.27 and so 0.249 is at the high end of all the other studies’ estimates. The elasticity for passenger is greater than freight as is expected as passenger tonnage is substantially greater than freight tonnage. The Booz Allen & Hamilton (2005) study utilised a cost allocation approach to determining the variability of cost with respect to usage for Great Britain. Overall for maintenance they found that 18% of cost was variable with usage, however like with all of the cost studies it is necessary to consider the cost base that was considered. This includes more items than our cost base. For track maintenance specifically, the study estimated variability of 24% which is more inline with our findings. Models V and VI incorporate 2nd order traffic terms. Model V seems to give a reasonably acceptable average elasticity of 0.239. We are surprised about the result that the elasticity of cost with respect to traffic density is falling with traffic density as this indicates that marginal cost is decreasing at a faster rate than average cost. However, we do note that this is consistent with the findings of Johansson and Nilsson (2004) and Andersson (2005) for Sweden, but that Gaudry and Quinet (2003) found the opposite result. Model VI gives us cause for concern both in terms of the average total elasticity and that the passenger elasticity is smaller than the freight elasticity. Since passenger tonnage-miles substantially exceed freight tonnage-miles on the network (see Table 2), it seems difficult to believe this result.


Table 7 Results from other studies compared against the estimated models Study (maintenance costs only) / Model estimated

Country Returns to track length

Elasticity of cost with respect to tonne-km

Marginal Cost Estimates (Average) Euro per Thousand Gross Tonne-km

Johansson and Nilsson (2004) Sweden

1.256 0.169 (average)

0.127

Johansson and Nilsson (2004) Finland

1.575 0.167 (average)

0.239

Tervonen and Idstrom (2004) Finland

1.325 0.133-0.175

0.18

Munduch et al (2002) Austria 1.621, 1.449 0.27 0.55 Gaudry and Quinet (2003) France

0.37 (average)

Not reported

Andersson (2005) Sweden 0.1944 (average pooled OLS model) 0.1837 (average Random effects model)

0.293 (pooled OLS model) 0.272 (random effects model)

Booz Allen & Hamilton (2005)

UK N/A Proportion of maintenance cost variable with traffic: 0.18; 0.24 for track maintenance 1.196

Model I UK 1.957 0.202 (wrt trains) 0.944

Model II UK 1.935 0.302 (wrt trains) 1.411

Model III UK 1.873 0.331 1.545 Model IV UK 2.002 0.174

Passenger 0.075 Freight 0.249 Total

1.939 passenger 1.698 freight

Model V UK 2.002 0.239 (average) 1.978

Model VI UK 2.184 0.064 Passenger 0.096 Freight 0.16 Total

1.538 passenger 2.522 freight

Only mean marginal costs are reported, however within studies there are large variations in marginal costs for specific observations and even groups of observations with specific characteristics. For example Munduch et al (2002) found that the average marginal cost for secondary lines in Austria was 3.09 Euro per thousand gross tonne-km which is more than 5 times greater than the average marginal cost! Thus it maybe of no great concern that the average estimate is so large relative to those from other countries. However further work is needed to benchmark these results and to understand the reasons for differences in marginal costs observed.


5. CONCLUSIONS In this paper we have outlined the estimation a cost function for Permanent Way maintenance costs. This was motivated by the need to provide objective benchmarks to existing cost allocation analyses for the UK and to utilise an emerging rich data set following the taking of maintenance in-house by the infrastructure manager, Network Rail. We have tried to test hypotheses suggested in the literature. In particular we can not find evidence to reject the use of tonne-kms as an output measure in favour of using both train-kms and average weight of train s output measures. We have found elasticity estimates that are broadly in line with other econometric studies undertaken in Europe and also consistent with existing cost allocation undertaken for the UK. Model V incorporated a variable elasticity of cost with respect to tonnage density and the elasticity is found to be a decreasing function of tonnage density. This seems counter intuitive as it implies that marginal cost falls faster than average as tonnage density increases. We do note that this finding is consistent with some but not all of the literature e.g. Johansson and Nilsson (2002) and Andersson (2005). Mean marginal cost estimates are between just 0.944 to 1.978 Euros per Thousand Gross Tonne-km7, however these vary considerably between observations. In general marginal costs are found to be falling with traffic density with very low marginal costs associated with high tonnage density. We conclude that the approach taken has produced results that are consistent with econometric studies across Europe and cost allocation work undertaken for the UK network. As such this method seems to be a promising line of research. There exist a number of ways to take the analysis forward, including the use of a more disaggregate data set should this develop and the use of panel data techniques should more years of data become available. In addition the analysis could be expanded by adopting a stochastic frontier, and by applying more advanced approaches to deal with potentially endogenous quality variables in the cost function.


REFERENCES Andersson, M. (2005) Econometric Models of Railway Infrastructure Costs in Sweden 1999-2002, Proceedings of the third Conference on Railroad Industry Structure, Competition and Investment. Stockholm School of Economics, Sweden. Booz, Allen & Hamilton (1999). Railway infrastructure cost causation, Report to the Office of the Rail Regulator, London. Booz, Allen & Hamilton with TTCI UK (2005) Review of Variable Usage and Electrification Asset Usage Charges: Final Report, Report to the Office of Rail Regulation, London. Gaudry, M., and Quinet, E (2003) Rail track wear-and-tear costs by traffic class in France, Universite de Montreal, Publication AJD-66. Johansson, P. and Nilsson, J. (2004) An economic analysis of track maintenance costs, Transport Policy 11(3), pp. 277-286. Link, H. and Nilsson, J. (2005) Infrastrucutre. In Nash, C. and Matthews, B. Editors (2005) Measuring the Marginal Social Cost of Transport, Research in Transportation Economics Volume 14. Elsevier, Amsterdam. Munduch, G., Pfister, A., Sogner, L. and Stiassny, A. (2002) Estimating Marginal Costs for the Austrian Railway System Working paper 78. Department of Economics Working Paper Series. Vienna University of Economics & B.A., Vienna. NERA (2000) Review of Overseas Railway Efficiency Draft final report to the Office of the Rail regulator. London Office of the Rail Regulator (ORR) (2000) Periodic review of Railtrack's access charges: Final conclusions Volume I, London Available at www.rail-reg.gov.uk Tervonen, J., Idström, T. (2004) Marginal Rail Infrastructure Costs in Finland 1997-2002, Report from the Finnish Rail Administration. Available at www.rhk.fi accessed 20/07/2005.


http://www.rail-reg.gov.uk/

http://www.rail-reg.gov.uk/

http://www.rhk.fi/

NOTES 1 We note that because we adopt a double log functional form (see below) the model using these two measures is the same, all other things equal, as a model with say trains per track-km and tonnage per track-km i.e. the coefficients from one model can be combined to give the coefficients in the other model. The choice of this formulation is that the coefficients estimated are directly of interest, in particular the coefficient on trains per track-km can be interpreted as the elasticity of cost with respect to traffic density holding average weight of trains constant. 2 It should be noted that although we have a variable AWT, this is a measure of the weight of trains rather than an axle load weight measure. Thus we can not separately control for the actual weight axle loads run on the network. 3 Mean, St Dev, minimum and maximum are for the variable before it has been subject to the ln transformation, where applicable 4 Very little success was found using the number of trains and AWT 5 In addition there maybe a case for exclusion of the MAL_G25_P variable on the grounds of an insignificant t-statistic, although doing this results in large changes in the values of other coefficients and substantial reductions in the precision of estimation of other coefficients. As such it is retained. 6 Note, we had little success in incorporating a second order term in track length and an interaction term between track length and tonnage density and do not report these models here. 7 Excluding model VI.


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