Infrastructure cost allocation methodology and practices

Heike Link

CATRIN SeminarSopot, 21 January 2009

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Background for the CATRIN work

1. Cost allocation approaches for full-cost studies:• Long tradition• Highly sensitive on assumptions!

2. Marginal cost estimation:• Releatively new field• Too few studies for generalisation of results• Diverging results, wide range of estimates• Differentiation by vehicle types so far lacking

Focus of CATRIN: new evidence on MC!

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MC estimation for road - Methodologies

1. Duration approaches …

• analyse impacts of traffic load and climate on lifetime of road surface

• are based on measurements of road condition

• assume a condition-responsive maintenance strategy

• MC estimates based on „ideal“ conditions, might be overestimated

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MC estimation for road - Methodologies

Examples:

• AASHO road test (4th power rule)

• Newbery‘s fundamental theorem (1988)

• Small and Winston 1988, Small 1989

• Lindberg 2002 (empirical test of the fundamental theorem), Haraldsson 2006

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MC estimation for road - Methodologies

2. Econometric cost function approaches …

• analyse the functional relationship between expenditures, traffic load,climate etc.

• use neoclassical production and cost function analysis

• are based on observed spending for road maintenance/renewal

• MC estimates based on real expenditures, might be underestimated

• Problems to include more than one traffic variable

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MC estimation for road - MethodologiesExamples:

1. Log-linear single equation models• Sedlacek et al. 2002: Austrian roads• Schreyer et al. 2002: Swiss roads• Bak et al. 2006: Polish roads

2. Translog single equation models• Link 2002: German motorways• Haraldsson 2006: Swedish roads (reduced TL)

3. Translog multi-equation models• Link 2006: German motorways

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country AT PL CH SE - 2006 SE - 2007 D - 2002 D - 2006

type of measure maint. +renewal

op. maint.

constr.maint.

op. maint. op. maint. renewal

traffic volume total vkm total vkm total vkm

ESAL total vkm

ESAL ratio trucks/pass.cars

vkm trucks

model

a) single-eq., log-linear

√ √ √ √ √ √ √

b) single-eq., TL √c) single-eq., reduced TL

√ √

d) multi-eq. TL √cost elasticity

a) fixed √ √ √ √ √ √ √b) variable √ √ √ √

Overview cost function studies - road

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MC functions – cost function approach

Marginal Costs - Roads

00.010.020.030.040.050.06

ratio AADT trucks and AADT passenger cars

Euro

D – renewals (Link 2006)D – renewals (Link 2002)

CH – constr. maint. AT –maint.+renewal

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MC functions – cost function approachSE – operation (Haraldsson 2006) SE – maint. (Haraldsson 2006)

PL – renewals (Bak et al. 06) PL – renewals + maint. (Bak et al. 06)

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Duration approach - MC studies

Lindberg 2002

Haraldsson 2006

Model considers … x x

… age distribution of roads - x

… climate effect - x

Data refer to …

… optimal renewal cycles x -

… observed renewal cycles - x

Findings on …

…MC curve increasing decreasing

…cost elasticity (mean) 0.8 0.039

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Duration approach - MC studies

a)... with condition-responsive renewal strategy (Lindberg 2002)

findings:• increasing MC curve• cost elasticity 0.8

b)... with observed renewal

intervals (Haraldsson 2006)

findings:• decreasing MC curve• very low cost elasticity (- 0.039)

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Findings from MC studies – before CATRIN

1. All MC studies derive non-linear curves

2. Rather weak non-linearities might allow MC=VC

3. Mean of cost elasticity ε = MC/AC generally below 1

4. εrenewals > εmaint > εoperation

5. Road operation seems to be a fixed cost activity

6. Diverging results for shape of MC curves• Most studies: decreasing MC curves• increasing curves for D, AT, S

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Country AUS US CH DK SF D a D b NL UK SE

Official study √ √ √ √ √ √ Scientific and empirical background studies

√ √ √ √ √ √ √ √

Repeated studies √ √ √ √ √ Overall methodology

- top-down √ √ √ √ √ √ √ √ √ √- club approach for

joint costs√

- incremental costs √ Cost / expenditure categories

7 5 6 5 6 21 3 17 8

No. of vehicle categories 33 6 30 6 6 6 27 37 10

No. road types 2 2 3 2 2 2 2 4 3

FAC studies road - Characteristics

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Road – Cost variability in FAC studies

Country Relates to ...

% variable costs

SF 21% Total maintenance expenditures

D 15% Total costs (capital + running)

SE 28% Total maintenance expenditures

NL (’92) 58% Maintenance, operation expenditures, overheads

% weight-dependant costs

Australia 46% Total expenditures

UK 33% Total expenditures

CH 7% Investment costs

CH 45% Constructional maintenance

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US AUS CH DK SF D a D b NL UK SE

VKM √ √ √ √ √ √ √ √ √ √Axle-loads – 4th power √ √ √ √ √ √ √ √ √ √Axle-loads – 2nd power √ AGM √ √ Coefficient agressivite √ Max. gross weight √ PCU √ √ √ √ √ √ PCU at 60 km/h √ PCU at 100 km/h √ Vehicle Length √ √

Allocation factors FAC studies - road

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Cost considered Data Type Functional Form No./ weight of trains

Input prices

SE a maint. Pooled OLS TL

SE b maint., op. Pooled OLS, random effects

TL maint., op., renewals

SF a maint. Pooled OLS TL

maint., renewals

SF b maint. Pooled OLS 1st order double log

maint., renewals

AT maint. Pooled OLS double log, interaction terms

FR maint., op. Cross section Unrestricted GBC

CH maint., renewals Pooled OLS 1st order double log

UK maint. Cross section double log, squared and cubic terms

MC estimation for rail - Methodologies

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Cost elasticities Rail Infrastructure - Maintenance only

0 0.2 0.4 0.6 0.8 1

Gaudry and Quinet, FR

Munduch et al., AT

Tervonen and Idstrom, SF

Marti / Neuenschwander, Model II, CH

Marti / Neuenschwander, Model I, CH

Andersson, SE

Booz Allen Hamilton, UK

Weath and Smith, Model IV, UK

Weath and Smith, Model VI, UK

Proportion of Maint. Cost considered in the study

Reported Total Usage Elasticity (Average)

Scaled Elasticity

...

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0 0.2 0.4 0.6 0.8 1

Tervonen and Idstrom, SF

Marti / Neuenschwander, CH

Andersson, SE

Proportion of Maint. Cost considered in the study

Reported Total Usage Elasticity (Average)

Scaled Elasticity

...

Cost elasticities Rail Infrastructure - Maintenance + Renewals

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MC estimates rail - Maintenance onlyFalling

Falling

Falling, than increasing

Not tested

Not tested

Falling

Falling

Not tested

Not tested

Increasing

Not tested

Curve

0 0.5 1 1.5 2

Booz Allen Hamilton, UK

Gaudry and Quinet, FR

Munduch et al., AT

Tervonen and Idstrom, SF

Johannson and Nilsson, SF

Johannson and Nilsson, SE

Marti / Neuenschwander, Model II, CH

Marti / Neuenschwander, Model I, CH

Weath and Smith, Model VI, UK

Weath and Smith, Model IV, UK

Andersson, SE

Usage Elasticity Average MC

...

EUR / 1000 gross tonne-km

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MC estimates rail - Maintenance and renewals

Falling

Not tested

Not tested

Not tested

Curve

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Andersson, SE

Marti / Neuenschwander, CH

Tervonen and Idstrom, SF

Booz Allen Hamilton, UK

Usage Elasticity Average MC

...

EUR / 1000 gross tonne-km

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Rail Cost variability estimates for the UK (in use 2005)Cost category % variable

with traffic

Track Maintenance 30

Renewals Rail 95

Sleepers 25

Ballast 30

Switches with crossing 25

Structures 10

Signals Maintenance 5

Renewals 0

Electrification Maintenance

AC 10

DC 10

Renewals

AC 35

DC 41

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Rail Cost variability estimates for the UK (in use 2005)

Cost Category % variability with traffic

Maintenance

Track 28%

Structures 0%

Signalling 3%

Electrification 9%

Renewals

Track Plain line 44%

Switches and crossings 47%

Structures 3%

Signalling 4%

Electrification AC 11%

DC 6%

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MC estimation for aviation - Methodologies

• Mostly econometric cost function studies

• Motivated by deregulation issues rather than MC estimation

• Functional forms: Cobb Douglas, translog, multivariate time series approach

• MC estimates hardly comparable due to:

a) different output measures (WLU, ATM, PAX)b) different cost categories considered

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Cost shares in the FAC study for US airports

0 20 40 60 80

All lines of business

Total Air traffic Services

En-route facilities

Terminals and radar towers

Domestic en route services

incremental fixed common

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Fixed/variable costs inland waterways NL

0 2 4 6 8 10

> 3000

2000 - 3000

1500 - 2000

1000 - 1500

650 - 1000

400 - 650

250 - 400

< 250

user dependent fixed

(CE 2004)

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Starting point at the beginning of CATRIN

• Evidence on cost variability and cost elasticity

• No convergence on shape of MC curve

• MC estimates need to be disaggregated by vehicle types

• Comparability problems due to different cost categories, output measures, methodologies

• Huge efforts of researchers to collect and compile data!