Presentation by Dr Phill Wheat, Senior Research Fellow, to Paris School of Economics, 24 June 2014. www.its.leeds.ac.uk/people/p.wheat

1. Institute for Transport Studies
FACULTY OF ENVIRONMENT
Returns to scale and density in passenger
train operations in the presence of
heterogeneity in outputs
Phill Wheat, Senior Research Fellow
Presentation to Paris School of Economics
24th June 2014

2. Policy Context
• Railways in Europe have separated infrastructure (tracks
etc) from operations (running trains) in some form
• To some extent treated as separate entities for regulatory
purposes
• Infrastructure has clear increasing returns to density, less
clear on returns to scale (MC(wrt traffic)<AC) – RPI-X
regulation
• Results for train operations less well researched
– Important due to the desire for competition for the market – tendering
• Fourth Railway Package
• Push for larger, more heterogeneous franchises in Britain

3. Tendering in Britain
• Vertically integrated railway privatised between 1993 and
1997
• Single infrastructure manager: Railtrack (later Network Rail)
– RPI-X regulation
• Freight open access
• Passenger operations put out to tender
– Rolling stock leased to reduce barriers to entry
– Initially by both region and service type
– Led to some tenders overlapping (each offering differed service type)
– Now move to bigger and non-overlapping tenders
– Cost reduction (while accommodating passenger growth) is the
primary aim

4. Returns to Scale and Density
• We make the following definitions
• Returns to Scale (RtS) measures how costs change when a
TOC grows in terms of geographical size holding utilisation
constant.
– Policy implications: Size of tenders
• Returns to Density (RtD) measures how costs change when a
TOC grows by running more services (measured by train-hours)
on a fixed network.
– Policy implications: Extent of tender overlap and expected unit cost
changes from growth
• Why? Expect there to be a difference between how costs change
as the geographical scope of the service increases versus utilising
the existing network further
– In Britain both the scale and density of tenders are being increased

5. Heterogeneity in service provision
• One train hour is rarely the same as another train hour
• Therefore need to control for characteristics of the operation
Average length of train, Average speed of service,
passenger load factor
• But often changing the scale (or density) of a tender involves
making the tender more heterogeneous
– Does such heterogeneity prevent density or scale benefits being
realised in practice?
– Policy issue in Britain as the trend is to larger tenders with less
overlap (more heterogeneous and greater density)

6. Research Questions
• Are there increasing returns to density and scale in train
operations
• If so, can they be realised when in practice larger or more
dense tenders have more service heterogeneity
– Ultimately is merging tender areas into ‘super tenders’ likely to
reduce costs?

7. The data
• 243 observations
– 11 years of data – 2000/01 to 2009/10
– Unbalanced panel of 28 train operating companies (TOCs)
• Three ‘Primary Outputs’
– Train Hours
– Stations Managed
– Route-km operated (do not want to constrain RtS variation relative to
RtD variation)
• Two prices (fairly aggregate measures)
– Average salary (payroll staff)
– Average rolling stock charge (per unit)

8. The data
• Characteristic variables associated with the train hours
output
– Average train speed
– Average train length
– Average passenger load per train
– Tender service type variables (intercity, commuting, regional)
– Mixed tender indicators
– Number of ‘generic’ rolling stock types operated
• Clearly many variables available, the econometric challenge
is how to input these into a model

9. The model – Hedonic Cost Function
• Hedonic cost function proposed by Spady and Friedlaender
(1978)
• Standard Translog Cost Function with Cost Share Equations
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10. The model – Hedonic Cost Function
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2 2 12 22 32 y q q q    
12 22 32

11. The model: Output heterogeneity
• The use of a hedonic cost function is motivated primarily by
the need to a priori impose more parsimony on the model
• Alternative is a full Translog with circa 140 parameters
• ‘Quality separable’ restriction implies:
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to the cost elasticity of the primary output

12. Returns to Density
• All existing TOCs operating with increasing returns to
density
• Increasing returns to density can arise for a number of
reasons e.g. better rolling stock and staffing diagraming
• Growth in train hours will lower average costs
• This result would imply removing tender overlap would
decrease costs (as density will increase)

13. Returns to Density

14. Returns to Scale
• In contrast, over 70% of tenders are estimated to suffer from
decreasing returns to scale – be it only a small decrease for
many tenders
• Making tender areas larger will increase overall costs
• It is intuitive that RtS are less than RtD (e.g. less scope for
diagramming improvements), but decreasing RtS seems
difficult to justify
• However the finding is consistent across service types

15. Returns to Scale

16. Output Heterogeneity
• Can look at partial effects within the hedonic function
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0.701 Average Train Length
0.856 Average Speed
0.059 Passenger Load Factor*
• Intuitive that these are less than unity e.g. lengthening an
existing train increases cost by 70% of that of running more
train hours (e.g. because still only one driver)
• A similar exercise can be conducted for the tender service
type and rolling stock variables
*not stat sig

17. Evaluating Tender Remappings
• Mergers are discrete
• Partial analysis is useful but really need to evaluate the
model before and after
• Still try to provide a decomposition.
• Consider remapping A to B
2’
1 1’
2
3
overlap

18. Evaluating Tender Remappings
• Expected impacts from consolidating tenders:
• Increase in scale (per tender) – expected to increase costs
• Increase in density (per tender) – removing franchise
overlap
• More service heterogeneity – does this prevent exploitation
of increasing density?

19. Evaluating Tender Remappings
• Define % change in density
as
• Define % change in
‘heterogeneity adjusted
density’ as
1
a ,b   
y
y
y
y
y
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a
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b
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a ,b y y
1
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1
the exploitation of returns to density
1
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a
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a
2a
b
1b
b
2b
1
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20. The results for Britain
Percentage change in Characteristics (+ indicates increase) Cost Change
Name
Route-km
Train-hours
Hetrogeniety
Adjusted
Density £'000 Percent
Year of
remapping
Train Hours
Density
2006/07 Greater Western -36% 0% 57%
12% 45.6 9%
2004/05 ONE/Great Northern -3% 0% 3%
-4% -17.9 -6%
2010/11 -
hypothetical New Northern -24% 0% 32%
34% 52.6 10%
• Not what was expected (at the outset)!
• Tenders getting bigger  Decreasing returns to scale
(particularly GW and NN
• Density does increase (substantial removal of overlap)
• However for 2 out of 3 this can not be exploited in practice
due to service heterogeneity

21. Conclusion
• Service heterogeneity is important
• To understand RtS and RtD need to control for service
heterogeneity
• Passenger Train Operations are subject to increasing
returns to density
– Average costs should fall as passenger demand grows (subject to
capacity)
• But tenders should not simply be made larger:
– Decreasing Returns to Scale
– Increasing service heterogeneity prevents exploitation of RtD