Review and meta-analysis of U.K. time elasticitiesof travel demand

Mark Wardman

Published online: 30 August 2011� Springer Science+Business Media, LLC. 2011

Abstract In contrast with reviews of values of time and price elasticities, the

literature contains little by way of detailed reviews of travel time based choice and

demand elasticities. This paper reports the most extensive meta-analysis of time-based

demand elasticities yet undertaken, supplemented with a review of literature not

previously in the public domain. The meta-analysis is based upon 427 direct elasticities

covering travel time, generalised journey time (GJT) and service headway and drawn

from 69 UK studies. The elasticities are found to vary, as expected, across attributes,

and quite strong effects have been detected according to distance. We provide inter-

esting insights into the relationship between long and short run elasticities and elas-

ticities obtained from static models and choice models based on actual and hypothetical

preferences. Significantly, the results seem to indicate that the duration for the long

run demand impact to work through depends upon the periodicity of the model esti-

mated. There is little variation apparent by journey purpose, source of the evidence,

nor over time or by region/flow type, whilst travel time elasticities for high speed rail

are not materially different from conventional contexts. The findings support some

official elasticity recommendations and conventions but challenge others, and can be

used to provide time-based elasticities where none exist or to assess new empirical

evidence.

Keywords Direct elasticities � Travel time � Headway �Generalised journey time (GJT) � Meta-analysis � Review

Electronic supplementary material The online version of this article (doi:10.1007/s11116-011-9369-2)contains supplementary material, which is available to authorized users.

M. Wardman (&)Institute for Transport Studies, University of Leeds, Leeds LS2 9JT, UKe-mail: m.r.wardman@its.leeds.ac.uk

123

Transportation (2012) 39:465–490DOI 10.1007/s11116-011-9369-2

Introduction

Background

Two of the most influential attributes under the control of operators and decision makers in

the transport market are the monetary cost and the journey time. As a result, elasticities

with respect to price and time, along with monetary values of time, are of critical

importance in transport planning and management and in the appraisal of transport policies

and investment. Evidence on the behavioural response to changes in service frequency is

also important to operators and regulators since this is a measure used to exploit com-

mercial opportunities and manage demand changes.

This importance is evidenced in a very considerable amount of literature covering

values of time and price elasticities in the transport market, so much so that it has stim-

ulated a number of extensive classic literature reviews of values of time (Waters 1995;

Booz Allen and Hamilton 2000; Litman 2009) and of price elasticities (Transport and Road

Research Laboratory 1980; Goodwin 1992; Oum et al. 1992; Graham and Glaister 2004;

Transportation Research Board 2004a; Transport Research Laboratory et al. 2004; Wallis

2004; Litman 2011). Indeed, there is sufficient evidence to have supported meta-analysis of

values of time (Wardman 1998, 2001, 2004; Zamparini and Reggiani 2007; Shires and de

Jong 2009; Abrantes and Wardman 2011) and of price elasticities (Nijkamp and Pepping

1998; Kremers et al. 2002; Wardman and Shires 2003; Jevons et al. 2005; Holmgren 2007;

Hensher 2008; Wardman and Grant-Muller 2011).

In stark contrast, there are few comprehensive reviews of time based elasticities. Indeed

we would contend that, despite their lesser importance, reviews of rolling stock valuations

(Wardman and Whelan 2001), crowding multipliers (Wardman and Whelan 2011), con-

gestion time multipliers (Wardman and Ibanez 2011) and public transport service quality

features (MVA and ITS Leeds 1989; Faber Maunsell 2003) compare favourably with the

current status of reviews of time based elasticities.

The extensive demand elasticity reviews of Litman (2011), Transport Research

Laboratory et al. (2004) and Wallis (2004) have relatively little to say about travel time

elasticities, particularly in comparison to their coverage of price elasticities, whilst the US

Transportation Research Board’s Travel Response to Transport System Change Handbook

Series covers price elasticities in considerable detail (Transport Research Board 2004a)

and does address headway elasticities (Transportation Research Board 2004b) but sheds

little light on journey time elasticities. Association of Train Operating Companies (2009)

contains a large amount of British evidence on time based elasticities although it is

essentially a description of studies without an explicit synthesis of the diverse range of

evidence.

De Jong and Gunn (2001) reviewed 50 European studies covering time and cost elas-

ticities for car travel, and supplemented this with the outputs from three national/regional

transport models. Although this would seem be the most extensive review of time elas-

ticities, despite being restricted to car travel, it makes no systematic attempt to explain

variations in elasticities across studies. Indeed, the cross-cultural issues can be seen as a

handicap and it is noticeable that there are some very large unaccounted for variations in

elasticities across countries.

Although the meta-analyses of Hensher (2008) and Holmgren (2007) include travel time

related elasticities in their coverage of a broader range of factors, the evidence base is

somewhat smaller than herein, including 57 in-vehicle time and 21 headway elasticities in

the former study, distributed over several countries, and in the latter study 58 observations,

466 Transportation (2012) 39:465–490

123

also across a number of countries, of the elasticity of public transport demand to vehicle

kilometres supplied.

The conclusions of two of the most extensive reviews of transport demand elasticities

were that:

With respect to in-vehicle time, evidence on elasticities is limited (Transport

Research Laboratory et al. 2004).

Both more recent and earlier international evidence in relation to (public transport)

in-vehicle time elasticities is very limited … and… Few studies available have

examined the impact of changes in in-vehicle time on car travel demand (Wallis

2004).

Indeed, Transport Research Laboratory et al. (2004) make much use of deducing public

transport time and headway elasticities from price elasticities given the relationships of

economic theory and evidence on the monetary valuations of time and headway. Inferring

time elasticities from price elasticities is also commonplace in the car market.

Whilst the somewhat lesser evidence base for time than price elasticities is here

recognised, nonetheless we show that there is actually sufficient evidence to be assembled,

even in the British context, to conduct informative analysis into travel time based elas-

ticities and the key factors that influence them.

Objectives

This paper is novel in terms of providing, to the best of our knowledge, by far the most

extensive review and meta-analysis of direct time elasticities covering journey time, the

closely related concept of generalised journey time (GJT), and service headway.

GJT is a parameter widely used in the railway industry in Great Britain (Association of

Train Operating Companies 2009), and is composed of station-to-station journey time,

headway and interchange, with the latter two converted into equivalent units of time using

headway and interchange penalties. The journey time elasticity implied by a GJT elasticity

depends upon the proportion that journey time forms of GJT and hence varies across

different contexts.

We here cover 69 studies that yield 427 time based direct elasticities reporting between

1977 and 2010. They are sourced solely from UK studies which thereby avoids the dif-

ficulties of cross-cultural comparisons. We have 168 (39.3%) travel time elasticities,1 209

(48.9%) GJT elasticities and 50 (11.7%) headway elasticities. This compares favourably

with the 444 observations from the first ever value of time meta-analysis (Wardman 1998)

and the 319 observations from 39 studies of the Hensher (2008) meta-analysis which also

includes price elasticities. The vast majority of the elasticity evidence relates to trips but

there are also vehicle kilometre elasticities for car travel in our data set.

This paper is structured as follows. The ‘‘Summary of key characteristics and direct

elasticity values’’ section summaries the key features of the assembled data, including a

high level examination of how the various time based direct elasticities vary with key

explanatory variables. Prior to the quantitative analysis of the assembled elasticities, which

treats all evidence anonymously, ‘‘More detailed elasticity variation evidence’’ section

draws out interesting findings from specific studies, with an emphasis on unpublished

1 For reasons explained in ‘‘Insights not covered in meta-analysis’’ section, the meta data set does notinclude time elasticities for high speed rail. However, some key findings are reported in that section.

Transportation (2012) 39:465–490 467

123

literature, and reports elasticity variation apparent within as opposed to across studies. The

main meta-analysis of 427 elasticities is reported in ‘‘Meta-analysis of time based elas-

ticities’’ section whilst ‘‘Illustrative outputs’’ section sets out some illustrative elasticities

implied by the meta-model. Concluding remarks are provided in ‘‘Conclusions’’ section.

Summary of key characteristics and direct elasticity values2

The number of studies and elasticities according to time period, which for time series data

is taken as the midpoint of the series, and by year of publication is given in Table 1. Few

elasticities cover the time period up to 1980 whilst the large number of 1990s elasticities

per study reflects the interest in distinguishing short run and long run effects, thereby

increasing the amount of evidence available, as well as greater use of stated preference

(SP) methods which provide relatively large numbers of elasticities per study. The latter

reasons are behind the large number of elasticities per study published between 2001 and

2010. Nonetheless, we have observations covering a broad time period which supports the

examination of inter-temporal elasticity variations.

Table 2 indicates the sources of the studies and elasticities. The critical importance of

exploiting the grey literature3 in achieving a large sample size is readily apparent. There is

a tradition in the UK of research studies being conducted by commercial organisations that

do not have the same imperative to publish the results in academic journals whilst some

evidence cannot be published for confidentiality reasons. Nonetheless, this tends to be high

quality research that makes a valuable contribution to the evidence base.

Table 3 lists the influential variables about which we have collected information,

provides summary statistics of the various elasticities across key dimensions, and indicates

the amount of evidence available for each elasticity type. Whilst we have to be careful in

interpreting the results of such one-dimensional segmentations, due to possible con-

founding effects, a number of interesting findings are apparent.

Starting first with the sample sizes, we note that all the GJT elasticities relate to rail and

to secondary, ticket sales data,4 whereupon the only separately identified journey purpose

is commuting for season tickets. The elasticities are mainly drawn from pooled time-series

Table 1 Studies and elasticities by time period

Elasticity time period Publication date

Years Studies Elasticities Years Studies Elasticities

1969–1980 9 (12.3%) 40 (9.4%)

1981–1990 21 (28.8%) 76 (17.8%) 1977–1990 15 (21.7%) 68 (15.9%)

1991–2000 30 (41.1%) 223 (52.2%) 1991–2000 30 (43.5%) 167 (39.1%)

2001–2010 13 (17.8%) 88 (20.6%) 2001–2010 24 (34.8%) 192 (45.0%)

Note Some studies report results for more than one time period

2 More details of each of the 69 studies are provided in electronic supplementary material.3 Grey literature is unpublished work that generally cannot be easily found through conventional channelsand has not been through formal peer review processes.4 Ticket sales data is a record of tickets sold for travel between origin and destination stations. In GreatBritain, it is regarded to be an accurate guide of station-to-station travel and has supported a considerableamount of econometric analysis over the past 30 years.

468 Transportation (2012) 39:465–490

123

and cross-sectional data with an emphasis on inter-urban journeys and data centring on the

1990s.

The journey time elasticities have a broader spread across purposes, as a result of the

use of primary data, but again there is more evidence for rail due to the pioneering use of

SP methods in the rail industry and the availability of large amounts of ticket sales data.

Again there has been a focus on inter-urban travel but there is a reasonable spread of

observations across time periods. Given the prevalence here of SP and revealed preference

(RP)5 choice data, it is not surprising that mode choice elasticities form such a large

proportion of the total.

The headway sample is small but with an even spread across purposes whilst SP

provides a large proportion of observations. The reason for the low proportion of RP

elasticities for headway is because some studies, and particularly early ones, instead

specified wait time. Headway elasticities for bus are well represented, and this is likely to

have been driven by policy issues concerned with inducing mode switch to bus through

more frequent services, and this will have contributed to the relatively large number of

elasticities for urban travel.

Turning to the elasticities themselves, there is surprisingly little variation in elasticities

by journey purpose. The GJT elasticities for commuting and non-commuting are consistent

with those for a mix across purposes whilst the time and headway elasticities vary little

except for the categories with few observations. We might have expected business trav-

ellers and commuters to be more sensitive to the time and headway variables that compose

GJT.

The time elasticity is noticeably lower for car and the time and headway elasticities are

similar for the two public transport modes. The GJT and time elasticities seem to be higher

for longer distance journeys, with a mix of the two consistent with this relationship, but

these figures mask the headway elasticity increasing with distance for bus but falling with

distance for rail. There is a suggestion that the elasticities might be falling over time.

In addition to separating full (demand) and mode choice elasticities, we distinguish

between pure mode choice elasticities and those cases, denoted mode choice ‘plus’, where

an allowance for trip generation has been included in the reported elasticity. The pattern of

elasticities is not what would be expected.

Finally, as far as data type is concerned, most of the GJT elasticities are drawn from

pooled time-series and cross-sectional data and hence we ought not to place too much

Table 2 Sources of elasticityevidence

Source Elasticities Studies

Journal/book 34 (8.0%) 7 (10.1%)

Conference paper 6 (1.4%) 1 (1.5%)

Published report 107 (25.0%) 11 (15.9%)

Unpublished operatorcommissioned report

134 (31.4%) 24 (34.8%)

Unpublished Governmentcommissioned report

66 (15.5%) 8 (11.6%)

Unpublished academic report 52 (12.2%) 10 (14.5%)

Unpublished in house report 28 (6.5%) 8 (11.6%)

Total 427 69

5 Whilst the time-series, cross-sectional and pooled aggregate ticket sales data are Revealed Preference,we reserve the use of the latter term for disaggregate data relating to individuals’ actual choices.

Transportation (2012) 39:465–490 469

123

Tab

le3

Key

sum

mar

ym

easu

res

Pu

rpo

seA

llG

JTT

ime

Hea

dw

ay

Sam

ple

Ela

stic

ity

Sam

ple

Ela

stic

ity

Sam

ple

Ela

stic

ity

Sam

ple

Bu

sines

s3

6(8

.4%

)–

–-

0.5

6(0

.06

)3

0(1

7.9

%)

-0

.22

(0.0

5)

6(1

2.0

%)

Co

mm

ute

56

(13

.1%

)-

0.6

3(0

.05

)2

3(1

1.0

%)

-0

.47

(0.0

6)

23

(13

.7%

)-

0.2

4(0

.04

)1

0(2

0.0

%)

Lei

sure

48

(11

.2%

)–

–-

0.4

9(0

.06

)3

7(2

2.0

%)

-0

.25

(0.0

3)

11

(22

.0%

)

No

nco

mm

uti

ng

21

6(5

0.6

%)

-0

.85

(0.0

4)

14

5(6

9.4

%)

-0

.75

(0.0

4)

57

(33

.9%

)-

0.2

4(0

.06

)1

4(2

8.0

%)

No

nb

usi

nes

s1

0(2

.3%

)–

–-

1.2

6(0

.33

)6

(3.6

%)

-0

.52

(0.0

8)

4(8

.0%

)

Mix

61

(14

.3%

)-

0.7

5(0

.07

)4

1(1

9.6

%)

-0

.32

(0.0

7)

15

(8.9

%)

-0

.28

(0.0

6)

5(1

0.0

%)

Car

36

(8.4

%)

––

-0

.30

(0.0

6)

36

(21

.4%

)n

an

a

Bu

s3

2(7

.5%

)–

–-

0.6

3(0

.16

)1

6(9

.5%

)-

0.2

9(0

.05

)1

6(3

2.0

%)

Tra

in3

59

(84

.1%

)-

0.8

1(0

.03

)2

09

(10

0%

)-

0.6

9(0

.03

)1

16

(69

.0%

)-

0.2

6(0

.03

)3

4(6

8.0

%)

Cro

ssse

ctio

nal

16

(3.7

%)

-1

.11

(0.2

1)

5(2

.4%

)-

1.1

8(0

.12

)6

(3.6

%)

-0

.25

(0.0

8)

5(1

0.0

%)

Tim

ese

ries

41

(9.6

%)

-0

.96

(0.1

9)

9(4

.3%

)-

0.6

5(0

.05

)3

2(1

9.0

%)

––

Po

ole

d2

25

(52

.7%

)-

0.7

9(0

.03

)1

95

(93

.3%

)-

0.6

4(0

.07

)1

9(1

1.3

%)

-0

.20

(0.0

3)

11

(22

.0%

)

Sta

ted

pre

fere

nce

82

(19.2

%)

––

-0

.63

(0.0

5)

58

(34

.5%

)-

0.2

8(0

.04

)2

4(4

8.0

%)

Rev

eale

dpre

fere

nce

(choic

e)59

(13.8

%)

––

-0

.45

(0.0

6)

53

(31

.5%

)-

0.3

7(0

.08

)6

(12

.0%

)

Tra

nsf

erp

rice

a4

(0.9

%)

––

––

-0

.25

(0.0

4)

4(8

.0%

)

Urb

an8

8(2

0.6

%)

-0

.65

(0.0

5)

45

(21

.5%

)-

0.4

1(0

.06

)2

8(1

6.7

%)

-0

.26

(0.0

3)

15

(30

.0%

)

Inte

r-u

rban

30

1(7

0.5

%)

-0

.87

(0.0

4)

14

6(6

9.9

%)

-0

.65

(0.0

4)

12

8(7

6.2

%)

-0

.27

(0.0

4)

27

(54

.0%

)

Bo

th3

8(8

.9%

)-

0.7

0(0

.08

)1

8(8

.6%

)-

0.4

5(0

.09

)1

2(7

.1%

)-

0.2

7(0

.03

)8

(16

.0%

)

19

69

–1

98

04

0(9

.4%

)-

1.0

5(0

.25

)2

(1.0

%)

-0

.70

(0.0

5)

36

(21

.4%

)-

0.4

0(0

.17

)2

(4.0

%)

19

81

–1

99

07

6(1

7.8

%)

-0

.90

(0.0

7)

39

(18

.7%

)-

0.5

6(0

.06

)3

0(1

7.9

%)

-0

.23

(0.0

4)

7(1

4.0

%)

19

91

–2

00

02

23

(52

.2%

)-

0.7

8(0

.04

)1

34

(64

.1%

)-

0.6

8(0

.06

)5

5(3

2.7

%)

-0

.28

(0.0

3)

34

(68

.0%

)

20

01

–2

01

08

8(2

0.6

%)

-0

.79

(0.0

7)

34

(16

.3%

)-

0.4

5(0

.06

)4

7(2

8.0

%)

-0

.20

(0.0

3)

7(1

4.0

%)

470 Transportation (2012) 39:465–490

123

Tab

le3

con

tin

ued

Pu

rpo

seA

llG

JTT

ime

Hea

dw

ay

Sam

ple

Ela

stic

ity

Sam

ple

Ela

stic

ity

Sam

ple

Ela

stic

ity

Sam

ple

Fu

ll(d

eman

d)

elas

tici

ty2

86

(67

.0%

)-

0.8

1(0

.03

)2

09

(10

0.0

%)

-0

.70

(0.0

4)

57

(33

.9%

)-

0.2

2(0

.03

)2

0(4

0.0

%)

Mo

de

cho

ice

‘plu

s’4

9(1

1.5

%)

––

-0

.53

(0.0

5)

39

(23

.2%

)-

0.1

6(0

.01

)1

0(2

0.0

%)

Mo

de

cho

ice

elas

tici

ty9

2(2

1.5

%)

–0

(0.0

%)

-0

.55

(0.0

5)

72

(42

.9%

)-

0.3

7(0

.04

)2

0(4

0.0

%)

To

tal

42

7(1

00

%)

-0

.81

(0.0

3)

20

9(1

00

%)

-0

.60

(0.0

3)

16

8(1

00

%)

-0

.27

(0.0

2)

50

(10

0%

)

Not

eE

last

icit

yfi

gure

sar

eth

em

ean

and

,in

bra

cket

s,th

est

andar

der

ror

of

the

mea

n.

Th

esa

mp

lefi

gu

res

den

ote

the

nu

mb

ero

fo

bse

rvat

ion

san

dw

ith

inco

lum

np

erce

nta

ges

aT

ran

sfer

Pri

ce(T

P)

sho

uld

no

tb

eco

nfu

sed

wit

hth

eC

on

tin

gen

tV

alu

atio

nM

etho

d(C

VM

).T

he

latt

eras

ks

for

aw

illi

ng

nes

sto

pay

for

anim

pro

vem

ent

or

toav

oid

ad

eter

iora

tio

nin

som

eat

trib

ute

.In

con

tras

tT

Pas

ks

for

that

pri

cein

crea

seat

wh

ich

ab

ehav

iou

ral

chan

ge

wo

uld

occ

ur,

ther

eby

read

ily

sup

po

rtin

gth

eca

lcula

tion

of

elas

tici

ties

.O

fco

urs

e,T

Pis

her

ein

tim

en

ot

mo

ney

un

its,

that

is,

the

tim

ein

crea

sesu

ffici

ent

toca

use

ach

ang

ein

curr

ent

beh

avio

ur

Transportation (2012) 39:465–490 471

123

emphasis on the high elasticities from cross-sectional data. However, the time elasticity is

noticeably higher when obtained from such data but fairly similar for the other sources.

In general, there would not seem to be a clear pattern across sources, although there are

confounding effects here with mode and whether the elasticity is long run, static or short

run. The aim of the meta-analysis is to disentangle such effects.

The elasticities estimated using pure time-series or pooled data can, subject to appro-

priate modelling, provide evidence on the dynamic nature of behavioural response and

distinguish between short run and long run adjustments. The short run response is likely to

be less than the long run due to greater constraints on individuals being able to amend

behaviour in the short run and lesser awareness of changes. We are also in a position to

compare these with the not uncommon results from static models where no such distinction

is made. This is useful in interpreting the status of static elasticities.

Table 4 distinguishes between elasticities for short run, long run and static models

and also by the periodicity of the data and the lag structure. The short run is that period

upon which the model is estimated, and can be either four weekly or annual. The long run

is defined as the time period over which 95% of the full effect is forecast to work through.

Where four weekly data is used, we observe models with simple one period lags and

models with both a one period and 1 year lag. There are no cases of just a 1 year lag. With

annual data, the lag is always one annual period. We report results only for GJT since 42 of

the 51 time elasticities and all of the headway elasticities are static. Of the 72 short and

long run GJT elasticities, 26 (36%) are from partial adjustment models, 6 (8%) from error

correction models, 32 (45%) from autoregressive distributed lag models and 8 (11%) from

models with geometrically lagged independent variables.

The average long run elasticity is around twice as high as the average short run elas-

ticity, although when we calculate the mean of the individual ratios we find it to be nearer 3

with 10th and 90th percentiles of 1.12 and 5.02. The mean static elasticity is around

midway between the mean for short and long run. This is useful to know if all we have is

information from static models but there is a desire to distinguish between short and long

run effects.

The periodicity might be expected to influence the short and long run results.

As expected, the short run elasticity is larger for annual than four weekly data given it is

defined as the time period upon which the model is estimated. A similar relationship is

apparent for the long run elasticities. However, there is no clear trend in the static elasticity

across four weekly, quarterly and annual data.

When we examine the ratio of long run and short run elasticities, which is a more

controlled comparison, it falls as the periodicity increases, presumably because the short

run elasticities are low for short time periods.

Table 4 also indicates how long the long run is. Whilst the long run elasticity does not

vary greatly across the data and lag types, how long that long run is clearly does! With four

weekly data it takes less than 3 years to reach the long run but it is almost 5 years for

annual data. It would have been informative to develop models to explain the ratio of long

run and short run elasticities and the length of the long run as a function of causal factors;

unfortunately there is insufficient data to conduct a robust investigation.

More detailed elasticity variation evidence

The emphasis of meta-analysis is on explaining variations across studies. This inevitably

misses some of the detailed, important insights that specific studies provide and which tend

472 Transportation (2012) 39:465–490

123

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Transportation (2012) 39:465–490 473

123

to be captured in classic literature reviews. We here address some more detailed issues

which would otherwise be overlooked, exploiting the grey literature not in the public

domain and the elasticity variation that is apparent within rather than across studies.

Insights not covered in meta analysis

Continuing to restrict ourselves to UK experience, since this is the context in which our

meta-analysis is set, there have been a number of studies addressing the potential for new

high speed rail lines. We did not include these in the main data set since the models

sometimes focus only on the rail and air sub-market, assumptions are sometimes used in

arriving at overall elasticities from mode choice elasticities, some markets are atypical

even of inter-urban travel given the relatively long distances involved, and it is not

unknown that the elasticities are not simply the output of empirical study but are subject to

amendment through calibration processes. We must also recognise that the conventional,

linear-additive, form of utility function within discrete choice models forces the elasticity

to increase with journey duration and very little research has been conducted on whether

this is empirically justified across the large range of distances typically involved in such

studies. Nonetheless, we might expect the time elasticities to be larger on the grounds of

the larger time savings on offer, with the figure of -1.6 achieved by the first stage of Paris

to Lyon high speed line often cited in this context.

Wardman (1993a) reports an SP study that examined the mode choices of business

travellers between Edinburgh and London in response to high speed rail options. The

model validated well against existing mode choices and, for a 70 minute saving on a 4� h

journey, the journey time elasticity was -1.06.

A study of the potential demand for a high speed link between Heathrow Airport and

Paris (Halcrow Fox 1998), covering business and leisure travel, obtained a journey time

elasticity of around -1.0 even without a generation effect.

Research for Eurostar addressing significant time savings due to the planned Channel

Tunnel high speed rail link, and based on SP parameters scaled to corresponding RP

choices, produced time elasticities of around -0.7 for both business and leisure travel,

including adjustment for newly generated traffic on the basis of past experience (Wardman

and Murphy 1999).

In work for the UK Strategic Rail Authority on high speed rail options, Atkins (2002)

used SP and RP evidence to derive time elasticities for business and leisure of -0.92 and

-0.78 respectively for the East Coast corridor between London and Edinburgh and -1.31

and -0.88 respectively for the West Coast corridor between London and Glasgow.

A recent study of a new high speed line from London to the North via Birmingham

(Steer Davies Gleave 2009) estimated the journey time elasticities to be -0.4 for Bir-

mingham to London, -0.8 for Manchester to London and -1.5 for Edinburgh to London.

The high elasticity for the latter flow was due to capturing traffic from an existing large air

market.

The high speed rail elasticities from UK evidence do vary somewhat across studies and

it is not altogether clear why. What is clear though is that the time elasticities recovered

somewhat exceed the average value for train of -0.69 reported in Table 3. However, given

the results of our meta-analysis reported in the ‘‘Illustrative outputs’’ section, which

indicate a long run time elasticity exceeding -1.3 for journeys over 200 miles, and

implicitly higher for yet longer journeys, and that SP can be taken to represent more than

just a short run effect, we could conclude that the time elasticities of high speed rail studies

are not materially different from those obtained from more conventional contexts.

474 Transportation (2012) 39:465–490

123

One factor that could contribute to the differential time elasticities across high speed rail

studies is the competitive situation, and indeed this was claimed as a causal factor in the

Steer Davies Gleave (2009) study. Economic theory would suggest rail elasticities to be

lower when it is in a stronger competitive position. As far as we are aware, Wardman

(1993b) reports the only study to freely estimate how the strength of competition impacts

on rail elasticities, in contrast to modelling approaches that force such a relationship. The

rail GJT elasticity (gGJT) was estimated as:

gGJT ¼ �0:23ðp2:7B þ p1:8

C Þ ð1Þ

where pB and pC denote the ratio of rail generalised cost to bus and car generalised cost

respectively and measures the competitive situation. This was a recommendation of the

Passenger Demand Forecasting Handbook (PDFH) and implied GJT elasticities for inter-

urban journeys ranging from around -0.5 to -1.4. The view here is that there has been too

little of this functional form research and too much reliance on forced relationships.

Finally, an interesting insight is provided in unpublished research by Steer Davies

Gleave (2004). They explored the impact of car congestion on the demand for rail travel,

set against a background that a contributor to the strong rail demand growth witnessed in

the mid and late 1990s had been increasing road congestion.

The study distinguished car travel time according to six different forms of road traffic

condition: free flow; busy, where travel is at the speed limit but with some forced lane

changes; light congestion, where there is slowing down every so often for no apparent

reason; heavy congestion, where speed is noticeably restricted with frequent gear changes;

stop-start; and gridlock, where the motorist is only able to move at a crawl at best.

The mode choice model, based on inter-urban car users for business or leisure, is

reported in Table 5. Not only are the findings remarkable in terms of the monotonic

relationship between the disutility of travel time and the conditions in which it is spent,

and the variation in time disutility seems reasonable, such a model can usefully provide

not only an indication of motorists’ behavioural responses to changes in travel time but

also their responses to changes in the conditions in which that time is spent. Just as

value of time studies are not always unambiguous as to what type of travel time has

been valued, so demand elasticity studies tend not to distinguish between time spent in

different types of condition, such as crowded trains, congested roads or uncomfortable

buses, and this study sets an important standard in an increasingly congested transport

world.

Table 5 Steer Davies Gleave enhanced time mode choice model

Variable Coeff (t) Variable Coeff (t)

Constant (rail) -0.980 (4.2) Free flow time -0.010 (2.5)

Rail time -0.015 (7.3) Busy time -0.012 (4.1)

Trains per hour 0.228 (2.6) Light congestion time -0.014 (4.8)

Delays 0.006 (1.7) Heavy congestion time -0.015 (4.2)

Cost -0.069 (4.7) Stop–start time -0.017 (5.3)

Gridlock time -0.020 (6.2)

Note Cost is in return units and pounds but other variables are in one-way units. Time is in hours

Transportation (2012) 39:465–490 475

123

Within-study elasticity variation

We can examine variations in elasticities that occur within studies when just one variable

differs between model segmentations. This makes for a very controlled comparison that

avoids confounding effects, albeit at the expense of a much smaller evidence base than

comparing across all the evidence. We have already done this in Table 4 with regard to the

ratio of long run and short run elasticities. Table 6 reports ‘within-study’ variations

according to mode, purpose and data type, largely relating to journey time.

With regard to mode effects, we see that both bus and train have somewhat larger time

elasticities although, presumably due to the small sample sizes, these are not significantly

different.

As for journey purpose, the results tend to confirm the simple tabulations in Table 3 of

no clear pattern of variation. With the exception of the comparison of GJT elasticities for

commuting and all trips, where the commuting elasticity is somewhat lower although not

significantly so, the elasticities are very similar.

Finally, there are five cases where the only difference is whether the time elasticity

relates to RP or SP data. The SP time elasticities are somewhat larger than the RP, adding

to the evidence base of the relationship between RP and SP parameters whilst acknowl-

edging that RP models are not themselves perfect. The difference may be because there is

inherently a greater awareness of changes within the SP method, since they are presented

to respondents thereby reducing habit effects, whilst there is the possibility that the con-

straints on real-world behaviour do not always work through to influencing SP responses.

We note however that these findings contrast with those of our value of time meta-analysis

(Abrantes and Wardman 2011) where RP valuations were 22% higher than SP valuations.

Nonetheless, the evidence base is here small and the difference is not quite significant at

the 10% level.

The final within-study variation we examine relates to journey duration. The most

common segmentation in the modelling process along with purpose and mode is journey

duration. However, we cannot simply compare two discrete categories since distance is a

continuous variable. Having identified all the within-study elasticities that differ only in

terms of distance, we estimated the implied distance elasticity (b) from a regression model

of the form:

lngR

gB

¼ aþ b lnDR

DB

ð2Þ

Table 6 Within-study elasticity variations

Attribute Variable 1 Variable 2 Mean 1 Mean 2 Difference Sample

Time Bus Car -0.89 (0.28) -0.55 (0.21) -0.34 (0.28) 8

Time Train Car -0.82 (0.04) -0.57 (0.28) -0.25 (0.28) 4

Time Business Commuting -0.38 (0.09) -0.36 (0.08) -0.02 (0.04) 7

Time Business Leisure -0.51 (0.05) -0.50 (0.06) 0.01 (0.06) 31

Time Commuting Leisure -0.47 (0.09) -0.43 (0.09) -0.04 (0.11) 15

Headway Commuting Leisure -0.25 (0.07) -0.23 (0.04) -0.02 (0.04) 5

GJT Commuting All -0.69 (0.07) -0.83 (0.20) -0.14 (0.22) 7

Time SP RP -1.17 (0.32) -0.77 (0.33) -0.40 (0.26) 5

Note The mean levels are reported with the standard error of the mean in brackets

476 Transportation (2012) 39:465–490

123

R denotes a ‘reference’ elasticity (g) and B is some ‘base’ level, here taken to be for the

lowest distance (D) for which a study provides a separate elasticity. Data is pooled across

all the studies that provide elasticities that differ only according to distance. Our meta-data

set yields 222 such observations since we take all within-study combinations.6

The results are reported in Table 7. Given the form of the model, it is to be expected

that the constant term is insignificant. However, the goodness of fit is disappointing given

that we are dealing with distance induced elasticity variations that occur within studies.

The base distance elasticity (Miles) is highly significant and noticeably strong. To this is

added the incremental effects, which are all interactions of Miles, that were found to be

significant. The distance elasticity for rail time (0.195) is somewhat lower than for the base

(0.374). The base essentially relates to GJT and to bus given that there are only three

observations for car.

Headway is not only less important for longer distance rail journeys but the demand

sensitivity continues to fall with distance given an elasticity of -0.618. Whilst the sign of this

effect is not surprising, since rail travellers might expect frequencies to be lower for longer

distance journeys and be more prepared to plan accordingly, the magnitude of the effect is.

Whilst it could be claimed that the same argument applies for bus, the evidence of a

distance elasticity of 0.757 does not confirm this. We might contend that the urban and

inter-urban bus markets are completely different in character; for example, the former

contains a larger proportion of ‘captive’ travellers whilst frequencies tend to be relatively

low on inter-urban bus journeys and hence we might expect higher sensitivities to

improvement. However, we should note that we do not have many observations for inter-

urban bus travel.

Finally, the distance elasticity for business travel is 1.03. Although we have relatively

few observations for urban business travel, it would seem that the ‘briefcase’ nature of

inter-urban compared to local business travel is such that elasticities in the former market

segment are somewhat larger.

Meta analysis of time based elasticities

Holmgren (2007) states that, ‘‘meta-analysis can be defined as the study of studies’’.

It essentially involves assembling a large amount of empirical evidence on, say, demand

elasticities, and then conducting quantitative analysis to explain variation across studies.

Table 7 Modelling of withinstudy elasticity variation bydistance

Variable Coeff (t)

Constant 0.016 (0.2)

Miles 0.374 (4.0)

?RailTime -0.179 (2.0)

?RailHeadway -0.992 (3.2)

?BusHeadway 0.383 (1.9)

?Business 0.654 (4.3)

Adjusted R2 0.18

Observations 222

6 So if we have four elasticities in a study, it contributes six observations (ratios) to the model. This willexaggerate the t ratios but it avoids the results depending upon which elasticity we take as the reference.

Transportation (2012) 39:465–490 477

123

Meta-analysis should be seen as a complement rather than challenge to or replacement

of specific studies and it has a number of attractions. In summary, meta-analysis can

provide powerful insights as a result of drawing together a wealth of elasticity evidence

across numerous studies and attempting to explain the variations in it. In particular, it is

generally preferable to base recommended values on, or challenge established conventions

with, the results of numerous studies rather than a few whilst it is possible to draw

conclusions, including those of a methodological nature, relating to spatial and temporal

variations in elasticities that are beyond the scope of a single study. The estimated models

can provide elasticity estimates in contexts where none otherwise exist whilst results not in

the public domain can be exploited on the grounds of anonymity. Finally, traditional

literature reviews focus on mean values rather than the variation and there is always a risk

that a comparison of means, rather than some more systematic quantification of all effects,

is distorted by confounding factors.

Of course, meta-analysis cannot examine elasticities in the level of detail that specific

behavioural studies can, such as whether elasticities vary according to the size or sign of

the time change and the competitive situation in which these occur. Nor is it immune from

confounding effects, such as those with higher incomes travelling farther or larger time

variations being offered on longer journeys. These factors should be borne in mind when

interpreting the results.

The variables that we have collected information on in order to explain the variations in

the time based elasticities were largely but not wholly presented in the ‘‘Summary of key

characteristics and direct elasticity values’’ section. These are: journey purpose; mode; data

type, including periodicity of data and distinguishing between long run and short run and

the type of estimated model; level of aggregation, including distinctions by area and flow

type; journey distance, and whether the elasticity relates to urban, inter-urban or all trips;

rail ticket type; sample size; year; source of the evidence; and whether the elasticity

denotes a full behavioural response or a mode choice effect, is an arc or point elasticity,

is derived from a constant or variable elasticity model, or is a trips or vehicle kilometres

elasticity. The meta-model takes the form:

g ¼ sYn

i¼1

Xai

i e

Pp

j¼1

Pq�1

k¼1

bjkZjk

ð3Þ

There are n continuous variables (Xi) and the ai denote elasticities of the time elasticity

with respect these variables. The Zjk are dummy variables representing the p categorical

variables. There are q - 1 dummy variables for a categorical variable of q levels and

their coefficient estimates (bjk) are interpreted relative to the arbitrarily omitted level.

The exponential of bjk denotes the proportionate effect on an elasticity of level k of the jth

categorical variable relative to its omitted category. Dummy variables are also used to

discern study specific effects.

A logarithmic transformation of the multiplicative model allows the estimation of its

parameters by ordinary least squares.7 This takes the form:

ln g ¼ ln sþXn

i¼1

ai ln Xi þXp

j¼1

Xq�1

k¼1

bjkZjk ð4Þ

7 The elasticities (g) are therefore specified in absolute form prior to taking logarithms.

478 Transportation (2012) 39:465–490

123

Table 8 Meta-models

Variable Model I Model II

Coeff (t) Effect Coeff (t) Effect

Constant -1.429 (11.9) -1.336 (13.3)

Attribute and mode specific (base = GJT)

Time-rail -0.662 (2.2) -48.4% -0.480 (1.8) -38.1%

Time-car -1.212 (6.4) -70.3% -1.361 (7.7) -74.4%

Time-bus ns – ns –

Head-rail -0.211 (1.5) -19.0% -0.306 (1.9) -26.4%

Head-bus -0.722 (3.3) -51.4% -0.877 (4.7) -58.3%

Model type (base = static-4 week)

Static-Quarterly ns – ns –

Static-Annual 0.382 (5.2) ?46.5% 0.340 (5.5) ?40.5%

Short-4Week -0.598 (4.5) -45.0% -0.617 (5.4) -46.0%

Short-Annual ns – ns –

Long-Lag4Week 0.867 (3.4) ?138.0% 0.811 (3.9) ?125.0%

Long-LagAnnual 0.628 (5.6) ?87.4% 0.648 (6.9) ?91.2%

Long-Lag4WeekandAnnual 0.267 (1.7) ?30.6% 0.234 (1.8) ?26.4%

Cross 1.374 (5.2) ?295.1% 1.360 (6.2) ?289.6%

SP-time 0.239 (2.4) ?30.0% 0.213 (2.5) ?23.7%

SP-headway 0.526 (3.1) ?69.2% 0.551 (3.9) ?73.5%

RP (choice) ns – ns –

TP 0.636 (2.0) ?88.9% 0.699 (2.6) ?101.2%

Context (base = inter-GJT)

Inter-TimeCar 0.516 (2.4) ?67.5% 0.577 (2.9) ?78.1%

Inter-TimeHeadBus 0.545 (2.3) ?72.5% 0.836 (3.7) ?130.7%

Inter-TimeRail ns – ns –

Inter-HeadRail -0.590 (3.1) -44.6% -0.650 (4.1) -47.8%

Distance

GJT 0.218 (7.8) 0.218 0.202 (8.6) 0.202

Time-car ns – ns –

Time-bus ns – ns –

Time-rail 0.295 (4.7) 0.295 0.247 (4.6) 0.247

Head-bus ns – ns –

Head-rail ns – ns –

Purpose (base = leisure)

Commuting 0.133 (1.3) 14.2% 0.131 (1.5) ?14.0%

Business ns – ns –

Non commuting ns – ns –

Non business ns – ns –

Mix ns – ns –

Type (base = trips)

VehKm 1.001 (4.1) ?172.1% 1.006 (4.9) ?173.5%

Study specific fixed effects

A 0.949 (5.0) ?158.3% 0.553 (3.0) ?73.8%

Transportation (2012) 39:465–490 479

123

The estimated models are reported in Table 8, containing those coefficient estimates

that were significant at the 90% level or which had some other reason for retention. This

multiplicative form performed better than the corresponding additive version and is hence

reported.

Given 69 studies, we created 68 dummy variables to discern the ‘fixed effects’ asso-

ciated with specific studies that are not accounted for by the explanatory variables and also

to allow for the variably multiple observations per study. Only 15 of the fixed effect

coefficients were statistically significant, although this is hardly surprising given that many

studies contribute only a few observations.

Model II removes ‘outlier’ observations defined as those 5% of observations having a

standardised residual outside of the range of ±2. This improves the adjusted R2 goodness

of fit somewhat, although in any event it compares favourably with that achieved in other

elasticity and value of time meta-analyses and is very respectable given the diverse nature

of the studies. The results are not greatly different for Model II and this is the one we focus

on in the discussion below.

We tested whether the error variance varied with the sample size upon which the

elasticity was estimated, in the absence of standard errors for all elasticity estimates in our

sample. The weight was the inverse of the sample size raised to a power. The power that

gave the best fit to the data was 0.1, indicating that sample size has very little effect on the

reliability of the elasticity data.

With regard to correlations of coefficient estimates, these were generally very low. One

notable exception is a correlation of -0.9 between the estimated coefficients relating to

whether the elasticity was for rail journey time and to the logarithm of distance for rail

Table 8 continued

Variable Model I Model II

Coeff (t) Effect Coeff (t) Effect

B 0.600 (1.7) ?82.2% 0.561 (1.9) ?75.2%

C 1.144 (3.9) ?213.9% 1.773 (5.9) ?488.8%

D 1.124 (6.0) ?207.7% 0.954 (5.2) ?159.6%

E -0.607 (1.8) -45.5% -0.605 (2.2) -45.4%

F 1.099 (3.8) ?200.1% 1.103 (4.6) ?201.3%

G -0.467 (2.5) -37.3% -0.465 (3.1) -37.2%

H -0.583 (3.9) -44.2% -0.662 (5.0) -48.4%

I 0.440 (2.3) ?55.3% 0.421 (2.7) ?52.4%

J 0.554 (1.6) ?74.0% 0.568 (1.9) ?76.5%

K -0.851 (2.9) -57.3% -0.851 (3.5) -57.3%

L -0.398 (2.8) -32.8% -0.423 (3.7) -34.5%

M -0.394 (3.2) -32.6% -0.291 (2.8) -25.2%

N 0.547 (1.5) ?72.8% 0.467 (1.6) ?59.5%

O 0.201 (1.9) ?22.3% 0.204 (2.2) ?22.6%

Adj R2 0.642 0.729

Observations 427 409

Note Effect is the proportionate change in elasticity attributable to a level of a variable relative to its basecategory. It is the exponential of the coefficient estimate expressed as a percentage change

480 Transportation (2012) 39:465–490

123

journey time. However, we are not unduly concerned by this given what turns out to be a

sensible distance effect for rail time compared to that for GJT where no such correlation

problems were present. Beyond that, the only correlations in excess of 0.6 were between

the coefficients for the dummy variables relating to a headway elasticity for rail and

whether it was for an inter-urban trip (-0.63) and between the coefficients for dummy

variables relating to a time elasticity for car and whether it too was for an inter-urban

journey (-0.61).

Attribute and mode specific

Since elasticities are expected to vary by mode as well as attribute, we distinguish between

GJT, which relates solely to rail, time elasticities, that are available for all three modes, and

headway elasticities relevant to the two public transport modes. The coefficient for bus

time elasticities was not significantly different from the base of GJT elasticities. Whilst

other factors will have a bearing, the results indicate that GJT elasticities in particular and

other public transport time elasticities will be relatively high with headway and car time

elasticities relatively low. This is not unexpected. It is also reassuring that the rail time

elasticity is less than the rail GJT elasticity, all else equal.

Model type

Elasticities have been drawn from a number of different model types and this is a key

factor in influencing elasticities. We distinguish between models which have a temporal

dimension, which is either pure time-series or pooled time-series and cross-sectional, pure

cross-sectional models based on aggregate, secondary data (Cross), SP models, RP discrete

choice models (RP choice), and transfer price (TP). In addition, the pooled and time series

models distinguish between static, short run and long elasticities. Since the time period and

lag structure may well influence the elasticities, a further disaggregation is made by these

factors.

The base here relates to static models estimated to four weekly data (Static-4Week).

Static models estimated to quarterly data (Static-Quarterly) yield elasticities that were far

from significantly different to those obtained from four weekly data. However, such

models estimated to annual data (Static-Annual) provide, as expected since the time period

is longer, somewhat larger elasticities. The short run elasticities estimated on annual data

(Short-Annual) are lower than the static annual elasticities but not significantly different to

the static elasticities obtained from the shorter time periods. The short run elasticity based

on four weekly data (Short-4Week) is the smallest of the dynamic elasticities, being 46%

lower than the short run annual elasticity, presumably as a result of shorter time period in

which behaviour can respond.

We distinguish three long run effects, all of which are larger than the short run effects.

The long run effect obtained from models estimated to four weekly data which contain

both four weekly and annual lags (Long-Lag4WeekandAnnual) is not significant at the 95%

level and is less than the static annual elasticity. The other two long run effects, based on

four weekly data with a 4 week lag (Long-Lag4Week) and annual data with an annual lag

(Long-LagAnnual) are more plausible, implying elasticities between 90 and 125% larger

than the base. However, whilst the ratio of short run and long run is 1.9 for annual data, it is

4.2 for the four weekly data largely driven by the low short run elasticity for four weekly

data.

Transportation (2012) 39:465–490 481

123

There is a view that pure cross-sectional econometric models that are based on

comparing demand levels across routes provide elasticities closer to the long run equi-

librium than the short run. There is also a view that they provide inflated elasticities since

they confuse cause and effect; in particular, operators provide a good service frequency

where demand levels are buoyant and poorer frequencies where demand is weak. We

allowed the incremental cross-sectional effect to vary across GJT, journey time and

headway but found them to be very similar (1.22, 1.49 and 1.22 respectively) and so

combined them. The results indicate that elasticities from cross-sectional models are 290%

larger than static models based on four weekly time series data and indeed very much

larger than the explicitly long run elasticities. These findings would cast doubt on the

reliability of elasticities obtained from cross-sectional models.

The evidence based on primary data, covering SP, RP and TP, yields time and headway

elasticities but GJT is specific to secondary data. There are a number of factors relevant to

the interpretation of the SP elasticities which are the most common of these three

categories.

Sixty five SP elasticities from 11 studies have been obtained from discrete choice

analysis and subsequent calculation of the demand response to a small percentage change

in time or headway. In all cases these were standard multinomial or hierarchical logit

models. The remaining 17 SP elasticities, drawn from 4 studies, were directly obtained

from constant elasticity demand functions estimated to SP data aggregated to indicate

changes in demand relative to a base scenario. There was no significant difference between

the elasticities obtained by the two means.

The hypothetical nature of SP data is a potential limitation, particularly if the purpose of

the exercise is transparent which could invite exaggerated responses in order to influence

policy, whilst even random error not linked to real-world behaviour will impact on the

scale of the model’s coefficients and hence its forecasts and elasticities. Should there be too

much random error in SP data, this will reduce the elasticities of minor modes. In addition,

it is not clear to what extent SP data represents a long run effect. Whilst the presentation of

the attribute levels overcomes the real-world problems of information acquisition in the

short run, we cannot be sure that SP responses are free of all of the short run behavioural

constraints so as to represent a genuine longer run effect. Finally, SP responses in some

contexts, such as leisure travel, only reflect mode choice and not the full behavioural

response.

The journey time and headway elasticities derived from SP data were found to be

significantly different. The larger incremental effect for headway may be because this is

more readily varied by operators and planners and hence attracts more policy response

bias. We specified a term to signify cases where the elasticities of an SP model, and indeed

of an RP model, would cover only mode choice responses but, surprisingly, the incre-

mental effect was far from significant.

It would seem unwise to claim that SP data provides us with a long run effect, and

essentially there is a degree of ambiguity as to what SP elasticities represent. We note,

however, that as with the within study variation in the ‘‘Within-study elasticity variation’’

section, they are larger than the RP elasticities which themselves lie between short run and

long run effects. These results are therefore consistent with choice models based on actual

data not reflecting the full long run effect and an additional increment for SP elasticities as

a result of their hypothetical nature and overcoming of habit effects.

A TP question asks an individual at what increased journey time they would switch

from their current behaviour. Since, in contrast to SP exercises, there is nothing offered in

return for the time increase, such as an improved headway, and the purpose of the question

482 Transportation (2012) 39:465–490

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is quite transparent, it is widely regarded that the incentive to bias is larger than for SP and

that TP would yield larger elasticities. This would in fact seem to be the case, with TP

elasticities being 63% and 16% larger than the SP based elasticities for journey time and

headway. Whilst the TP elasticities turn out to be remarkably close to long run values

derived from analysis of changes in actual behaviour over time, we would feel extremely

uncomfortable in recommending the TP method as an appropriate means of estimating

long run behavioural response.

Context and distance

Dummy variables were specified to denote whether the trip was inter-urban (Inter), defined

as being over 20 miles, alongside distance terms in constant elasticity form. It turned out

that it was not possible to recover significant and right sign effects for both terms. Where

both were significant, we found a positive distance elasticity combined with a negative

inter-urban coefficient, and this is the result of large correlations between the two. For rail

time and GJT, the formulation based solely on a distance elasticity was statistically

superior, with the inter-urban term performing better in the remaining cases. The lack of

large numbers of observations covering a wide variety of distances will have hampered our

ability to discern distance elasticities as opposed to the simpler inter-urban increment. For

example, 50% of the car time elasticities cover journeys between 80 and 150 miles whilst

78% of bus elasticities are for journeys of 10 miles or less.

The distance elasticities for GJT and time are positive, highly significant, plausible and

similar. Given that the headway elasticity for rail turned out to be lower for inter-urban

journeys, we might expect the distance elasticity for time to be stronger than for GJT. Rail

headway is 48% less important for longer distance and less regularly made trips and this

seems reasonable.

We also observe the car time and a combined time and headway term for bus to indicate

higher elasticities for inter-urban travel. In the case of bus, we contend that this market and the

trips being made are completely different to the urban bus market, whilst relatively poor

headways and journey times, particularly in relation to other modes, could be further con-

tributory factors. The inter-urban time and headway elasticities for bus are 130% larger,

although the limited sample size here of seven observations should be borne in mind. It might

also be argued that the blend of trips for inter-urban car travel is likely to be more responsive to

journey time changes, and here the time elasticity is 78% larger than for local trips.

Purpose

One of the most influential factors on the value of time and on price elasticities is journey

purpose. However, we have already observed relatively little within-study variation in time

elasticities by purpose and this is also apparent in the meta-analysis. The only effect

retained of the numerous tried, including splitting purpose effects by mode and by variable,

indicates a slightly larger (14%) elasticity for commuting. Whilst not significant at the 90%

level, we would expect commuters to be more sensitive to time.

Vehicle kilometres

Of the 36 car time elasticities, 8 (22%) relate to vehicle kilometres rather than trips. We

found that this has a significant effect, with the car time elasticity 2.7 times larger when

Transportation (2012) 39:465–490 483

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relating to vehicle kilometres rather than trips. This indicates that the primary response of

motorists to changes in journey time is to change journey length rather than the frequency

of making a particular trip.

Insignificant effects

We have already reported a number of factors having an insignificant effect amongst a

broader consideration of specific variables, such as the type of SP model estimated, various

journey purposes, some data types, and whether the elasticity was a demand elasticity, purely

a mode choice elasticity or a mode choice elasticity adjusted to account for generation effects,

although the pure mode choice effect is confounded with SP and RP data types.

There were a number of other variables that had no significant effects whatsoever.

These included temporal variations, the source of the elasticity evidence, sample size,

whether the elasticity was an arc or point elasticity or derived from a constant or variable

elasticity model, the level of spatial aggregation of the data, rail ticket type, and area and

flow type. We examined whether the number of elasticities provided per study had any

effect and it was far from significant.

Quality of studies

A comment that is frequently made about meta-analysis is that it does not control for

differences in quality across studies. More than that, there may be a tendency for studies to

report models that have key parameters that accord with the ‘conventional wisdom’.8

Whilst systematic misreporting to fit with the conventional wisdom will have a distorting

effect, detecting it is at best controversial and more than likely impossible, although fixed

effects might account for it. Of greater practical significance is the inevitability that there

will be variations in the quality of data and of its analysis across studies. However, there

are a number of reasons why this need not unduly concern us here.

Firstly, the precision of elasticity estimates can be taken to be, in some measure, a function

of the quality of the data and analysis. Whilst variances of the estimated elasticities are not

reported in all studies, sample size can nonetheless be taken as a reasonable proxy for

precision and we used it in weighted estimation. The search for the best fit returned a model

that placed almost no weight on the sample size with, as might then be expected, very little

effect on the coefficient estimates and associated t ratios. We have also pointed out the

elasticities are not influenced by the number of observations provided by each study.

Secondly, we have removed those observations where the standardised residual lies

outside the range ±2. These could be taken to represent the 5% of observations of poorest

quality. This is more objective than the contentious process of removing those elasticity

observations that on inspection seem not to fit with the rest of the data. We have seen that

this process does not make a great deal of difference to the results.

Thirdly, fixed effects unique to studies have been specified. These dummy variable terms

will, amongst other things, discern systematic effects on elasticities due to quality factors.

Fourthly, it can be argued that the quality of a study tends to have a random effect on

elasticities. Why should poor studies always produce lower or higher elasticities? If it is a

random effect, it will be contained within the error term and not bias the coefficient

estimates.

8 Akin to the suspicions that in the early literature there was under-reporting of non-work values of time thatdid not fit with the convention of being around 25% of the wage rate.

484 Transportation (2012) 39:465–490

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Finally, we have pointed out that the elasticities do not vary with their source, which

might be another proxy for quality. Indeed, this was also the case in our meta-analysis of

values of time (Abrantes and Wardman 2011) whilst in our meta-analysis of price elas-

ticities (Wardman and Grant-Muller 2011) unpublished studies were found to yield elas-

ticities only 10% larger.

Transferability of results

The meta-model is based solely upon UK evidence. Nonetheless, the results reported here

have broader relevance for a number of reasons. Firstly, even if the absolute elasticity

values are not strictly transferable, they will still be of interest in similar developed country

contexts where there is limited evidence, thereby providing a benchmark, or indeed where

there is no other evidence. Secondly, the relativities are inherently more transferable, so

that, for example, where there is no headway elasticity evidence it can be deduced from

local time elasticities along with the results reported here whilst the distance effects could

be expected to transfer. Finally, the methodological issues relating to model type and data

are inherently of broader interest.

Illustrative outputs

One of the purposes of the meta-analysis is to provide ‘forecasts’ of elasticities in situa-

tions where few or none exist or to provide an assessment of new evidence or indeed

conventional wisdom against a wealth of other evidence. Table 9 provides such elasticities

Table 9 Illustrative elasticities

Period Miles Rail GJT Rail time Rail headway Bus time Bus headway Car time

Short run (4 week) 2 -0.19 -0.12 -0.12 -0.16 -0.07 -0.04

10 -0.26 -0.18 -0.12 -0.16 -0.07 -0.04

25 -0.31 -0.22 -0.06 -0.37 -0.16 -0.07

50 -0.36 -0.26 -0.06 -0.37 -0.16 -0.07

100 -0.41 -0.31 -0.06 -0.37 -0.16 -0.07

200 -0.47 -0.37 -0.06 -0.37 -0.16 -0.07

Static (annual) 2 -0.48 -0.31 -0.31 -0.42 -0.18 -0.11

10 -0.67 -0.46 -0.31 -0.42 -0.18 -0.11

25 -0.81 -0.58 -0.16 -0.97 -0.40 -0.19

50 -0.93 -0.68 -0.16 -0.97 -0.40 -0.19

100 -1.07 -0.81 -0.16 -0.97 -0.40 -0.19

200 -1.23 -0.96 -0.16 -0.97 -0.40 -0.19

Long run (annual) 2 -0.66 -0.42 -0.42 -0.57 -0.24 -0.15

10 -0.91 -0.63 -0.42 -0.57 -0.24 -0.15

25 -1.10 -0.78 -0.22 -1.32 -0.55 -0.26

50 -1.26 -0.93 -0.22 -1.32 -0.55 -0.26

100 -1.45 -1.11 -0.22 -1.32 -0.55 -0.26

200 -1.67 -1.31 -0.22 -1.32 -0.55 -0.26

Transportation (2012) 39:465–490 485

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across the key dimensions of variable, mode and distance implied by Model II of Table 8,

with a sample enumeration approach adopted to account for the study specific fixed effects.

Given the shortest period used in model estimation is four weekly, this is used to denote

the short run (instantaneous) elasticity. We have based the long run elasticity around the

annual figure because this is the most precisely estimated and since the four weekly data

produces two very different long run effects. The implied elasticities are for non-com-

muting trips; commuting elasticities would be slightly larger. The long run elasticities are

around 3� times larger than the short run.

The distance effect in the rail GJT elasticities is apparent. The railway industry’s PDFH

recommends GJT elasticities ranging from -0.7 to -1.1 across a wide range of different

flow types (Association of Train Operating Companies 2009). The recommendations are

not explicitly of any time dimension but would seem to relate to static models. There

would seem to be some evidence here to support explicitly long run elasticities that are

larger than current recommendations and to include a modest but sensible distance effect.

Since the railway industry in Great Britain uses GJT, PDFH does not provide any

journey time elasticity recommendations. The time elasticities in Table 9 are of the order

of 60–75% of the GJT elasticities, and encouragingly this is very much in line with the

proportion that journey time typically forms of GJT.

Nor are there any official recommendations relating to the rail headway elasticity, given

the reliance on GJT. However, we note that the sum of the time and headway elasticities

are, particularly for inter-urban trips, broadly in line with the GJT elasticities. PDFH would

imply headway elasticities with a tendency to fall with journey distance as time (headway)

forms a higher (lower) proportion of GJT and the rail headway elasticity is here smaller for

inter-urban trips.

The best we can do for official recommendations for the journey time elasticity for

urban bus journeys is the Transport Research Laboratory et al. (2004) review. It states,

based on limited evidence and some deducing of the time elasticity from price elasticities,

that ‘‘Our best estimate is that a representative in-vehicle time elasticity for local bus might

be in the range -0.4 to -0.6 (whilst for rail it might be -0.6 to -0.8)’’. They are not clear

on the time dimension. The long run time elasticity for local bus here places it at the top of

the range cited. Similarly, our figure for suburban rail also fits the cited range. The study

does not recommend headway elasticities, preferring instead elasticities to the vehicle

kilometres supplied.

As for car time elasticities, the official recommendations (Department for Transport

2009) cover a range. For commuting, the recommended long term time elasticities for car

trips are -0.22 and -0.14, depending upon whether there is high or low modal compe-

tition. Our long run figures for commuting would be -0.17 for urban trips, very much

confirming the official values. Matters are, however, somewhat different for other contexts.

The official figures for business trips are -0.60 and -0.35 according the strength of

competition, -0.47 and -0.26 for essential other and -0.35 and -0.20 for discretionary

other. Our implied car time elasticities of -0.15 for urban journeys and -0.26 for inter-

urban trips are generally smaller than the six recommended elasticities, and we should

recall that urban car trips dominate. Whilst we could not confidently use our results to

assess the official recommendations at the level of journey purpose, taken as a whole the

meta-analysis would suggest that the official car time elasticities for other than commuting

trips are somewhat on the high side.

We can also compare the elasticities against a background of evidence suggesting

constant travel time budgets (Brog 1993; Transport Research Laboratory et al. 2004; Metz

2008). In its extreme form, this would imply time savings are just converted into longer

486 Transportation (2012) 39:465–490

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journeys, and hence a distance elasticity of unity in the absence of modal change and trip

elasticities of zero. The only distance based elasticity we have is for car. This is 2.73 times

larger than the trip elasticity. Converting the long run car trip time elasticities in Table 9

into vehicle kilometre elasticities implies -0.41 for urban trips and -0.71 for far less

commonly made inter-urban trips, somewhat short of the figure implied by constant travel

time budgets. Nor does our evidence support long run rail and bus trip based time elas-

ticities remotely near zero.

Conclusions

This paper has reported the most extensive review of travel time-based direct elasticities,

although focussing only on UK evidence. In its quantitative analysis of results pooled

across studies, termed meta-analysis, it has covered 427 time based elasticities from 69

studies, reporting between 1977 and 2010, and of these elasticities 168 (39%) relate to

travel time, 209 (49%) to GJT and 50 (12%) to service headway. Supplementing this is

more controlled analysis based on elasticity variation that occurs within studies along a

single standard dimension, such as mode, distance, purpose and data type, although with a

significantly reduced evidence base. We have also reviewed evidence, largely not in the

public domain, that provides important insights into elasticity variation of a detailed nature

but which are not sufficiently common to include in our meta-data. Across these various

analytical dimensions, a number of interesting and significant findings have emerged.

The meta-analysis has provided important insights into the relationship between elas-

ticities that are explicitly short run and long run, and indeed also cross-sectional and static

econometric analysis of secondary data. Although influenced by the length of the time

period, the static elasticities cannot be interpreted as either short run or long run effects but

instead lie somewhere between the two. Taking four weekly data to represent a short run

effect, and basing the long run effect on annual data, the ratio of long run to short run

elasticities is around 3�. We have serious reservations about the very high elasticities

obtained from cross-sectional analysis of secondary data.

There is an element of indeterminacy about the nature of elasticities obtained from RP

and SP choice data. Our findings indicate that they cannot be interpreted as long run

effects. Of note, though, is that the SP based elasticities are somewhat larger than corre-

sponding RP elasticities.

The elasticities vary little by purpose but do vary by mode and distance. The rail GJT

elasticity, as would be expected, exceeds the rail time elasticity and both increase in a

reasonable fashion with distance, exhibiting an elasticity of around 0.2. The rail headway

elasticity is lower for inter-urban journeys and along with the time elasticity is broadly

consistent with the GJT elasticity. Both the time and headway elasticities for bus are larger

for inter-urban trips, as is the case for the car time elasticity but which is somewhat lower

than for the other two modes. However, the car kilometres time elasticity is around 2.7

times larger than the trip elasticity, indicating that the main response to time variations is

the distance travelled.

The within-study analysis with respect to purpose, distance, mode and whether the

elasticity is obtained from RP or SP data largely supports the across-study meta-analysis. A

significant feature to emerge from this within study analysis is that the length of the long

run is strongly dependent upon the periodicity of the data. More appropriate modelling of

time series data to overcome this undesirable feature is called for.

Transportation (2012) 39:465–490 487

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We have separately reviewed time elasticities relating to high speed rail options. Our

conclusions are that the time elasticities obtained from such studies are not materially

different from those obtained from conventional studies, although with allowance needed

for particular competitive situations such as strong existing air markets. Finally, attention is

drawn to the fact that, as with value of time studies, time is not time, and in a period of

increasingly congested networks and modes, models should be able to discern and forecast

the impact of changes in travel conditions as well as changes in travel time itself.

The meta-analysis findings can be used to provide elasticity estimates where none

otherwise exist or, importantly, to assess official recommendations and conventional

wisdom in the light of an appreciable amount of ‘explained’ empirical evidence. The

analysis was based on a considerable amount of rail evidence and would support explicitly

long run elasticities that are larger than current UK recommendations and include a modest

and sensible distance effect. The rail time and headway elasticities obtained are broadly

consistent with what would be implied by the GJT approach after adjustment to the long

run context.

Our evidence broadly supports what might be regarded to be the conventional wisdom

for time elasticities in the urban UK bus market and provides headway elasticities where no

recommendations and little previous evidence exist. There is support, again in a context

where elasticity evidence is sparse, for larger bus elasticities in the inter-urban than local

market. Although our car (trip) time elasticities strongly support official UK recommen-

dations for the commuting market, they do challenge what seem to be too high official

elasticities for other car markets.

The evidence does not support the constant travel time budget implication that trips will

not vary in response to time variations or that time variations are simply converted into

corresponding differences in distance travelled. Whilst the evidence is UK based, the

absolute elasticities ought to be of interest in other developed countries, not least for

benchmarking purposes, whilst the elasticity relativities and methodological insights are

clearly transferable across different countries.

Acknowledgment The author is grateful to the Department for Transport for supporting this work,although all opinions expressed are those of the author, and to Pedro Abrantes for contributing to the dataassembly. The extensive comments of four referees are also appreciated.

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Author Biography

Mark Wardman is Professor of Transport Demand Analysis at the Institute for Transport Studies,University of Leeds. He has 25 years experience of behavioural research in the travel market, with anemphasis on rail travel and a particular interest in demand elasticities and the valuation of transportattributes. This experience has enabled him to pursue some of the most extensive meta-analyses in thetransport market.

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