Institute for Transport StudiesFACULTY 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

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

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

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

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)

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?

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)

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

• Hedonic cost function proposed by Spady and Friedlaender

(1978)

• Standard Translog Cost Function with Cost Share Equations

The model – Hedonic Cost Function

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• Standard Translog Cost Function with Cost Share Equations

• But outputs are defined as an aggregator function

• 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:

• i.e. elasticity of cost wrt a quality characteristic is proportional

to the cost elasticity of the primary output

The model: Output heterogeneity

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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)

Returns to Density

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

Returns to Scale

Output Heterogeneity

• Can look at partial effects within the hedonic function

• 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

it

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0.701 Average Train Length

0.856 Average Speed

0.059 Passenger Load Factor*

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

23

overlap

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?

Evaluating Tender Remappings

• Define % change in density

as

• Define % change in

‘heterogeneity adjusted

density’ as

1

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y

y

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a

a1

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• If then service heterogeneity is dampening

the exploitation of returns to density

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The results for Britain

Name

Route-

km

Train-

hours

Hetrogeniety

Adjusted

Density £'000 Percent

2006/07 Greater Western -36% 0% 12% 45.6 9%

2004/05 ONE/Great Northern -3% 0% -4% -17.9 -6%

2010/11 -

hypothetical New Northern -24% 0% 34% 52.6 10%

Year of

remapping

Train Hours

Density

Cost ChangePercentage change in Characteristics (+ indicates increase)

57%

3%

32%

• 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

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