BUS FARE ELASTICITIES2011121134420 by dfsiopmhy6

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									BUS FARE ELASTICITIES
          Report to the
  Department of the Environment,
    Transport and the Regions




  Joyce M Dargay and Mark Hanly

ESRC TRANSPORT STUDIES UNIT
 UNIVERSITY COLLEGE LONDON
                   December 1999

                ESRC Transport Studies Unit
University College London, Gower Street, London WC1E 6BT
                 Phone/Fax: 020 7679 1586
     http://www.ucl.ac.uk/transport-studies/tsuhome.htm
    BUS FARE ELASTICITIES

                 Report to the
Department of the Environment, Transport and the
                    Regions




                Joyce M Dargay
                      and
                  Mark Hanly



       ESRC TRANSPORT STUDIES UNIT
        UNIVERSITY COLLEGE LONDON
                    Gower Street
                 London WC1E 6BT
                Tel: +44 171 391 1586
                Fax: +44 171 391 1586




                          i
              This project was carried out for the DETR by the
              ESRC Transport Studies Unit, University College
              London (statistical analysis, reporting and project
              management) and the TAS Partnership Ltd. (data
              collection and liaison with operators).

              Members of the project team are:

              Joyce Dargay, Mark Hanly, Phil Goodwin (TSU)
              Peter Huntley, David Hall, James Rice (TAS)

              DETR project co-ordinator: Steve Grayson




Acknowledgements: We would like to thank the bus companies who gave permission to
use the data they provided to STATS100, the Passenger Transport Executives of Greater
Manchester (GMPTE), Merseyside (Merseytravel), South Yorkshire, Tyne and Wear
(Nexus), West Yorkshire (Metro) and West Midlands (Centro) for the kind provision of
data and all those who replied to our questionnaire for their helpful information and
comments.

The contents of this report are the sole responsibility of the authors and in no way
reflect the views of the DETR or data contributors.




                                         ii
                                             TABLE OF CONTENTS

EXECUTIVE SUMMARY .............................................................................................. ii
1. Introduction .............................................................................................................. 1
  1.1 Background........................................................................................................... 1
  1.2 The main objectives of the study.......................................................................... 1
  1.3 Specific issues to be addressed............................................................................. 1
  1.4 Approach to elasticity modelling.......................................................................... 2
  1.5 Definition of the fare elasticity in the short and long run..................................... 2
  1.6 Data....................................................................................................................... 4
  1.7 The experience of practitioners ............................................................................ 5
  1.8 Outline of the report ............................................................................................. 5
2. Literature Review ..................................................................................................... 7
  2.1 Introduction .......................................................................................................... 7
  2.2 Evidence from literature reviews.......................................................................... 7
  2.3 Evidence from the UK.......................................................................................... 9
  2.4 Evidence from Europe and Australia.................................................................. 13
  2.5 Conclusions ........................................................................................................ 18
3. The Aggregate Data................................................................................................ 20
  3.1 Introduction ........................................................................................................ 20
  3.2 National GB data ................................................................................................ 22
  3.3 Regional data ...................................................................................................... 29
  3.4 Individual English Metropolitan areas ............................................................... 34
4. Aggregate Elasticities ............................................................................................. 38
  4.1 Introduction ........................................................................................................ 38
  4.2 Results at the national level - Great Britain as a whole...................................... 38
  4.3 Estimation results for GB regional data ............................................................. 42
  4.4 Estimation results for individual English Metropolitan areas ............................ 46
  4.5 Conclusions ........................................................................................................ 48
5. County Level Data - STATS100A .......................................................................... 51
  5.1 Introduction ........................................................................................................ 51
  5.2 County level data in England.............................................................................. 51
6. County Level Elasticities........................................................................................ 62
  6.1 Introduction ........................................................................................................ 62
  6.2 Results at the English county level..................................................................... 62
  6.3 County-specific fare elasticities.......................................................................... 64
  6.4 Conclusions ........................................................................................................ 68
7. The PTE Data ......................................................................................................... 70
  7.1 Introduction ........................................................................................................ 70
  7.2 Comparison of the data from the three data sources .......................................... 71
  7.3 The data used for the analysis ............................................................................ 73
  7.4 Estimation results ............................................................................................... 78
  7.5 Conclusions ........................................................................................................ 79
8. Bus Fare Elasticity Questionnaire .......................................................................... 82
Appendix A: Technical Appendix                                                                                              A-1
Appendix B: Statistical Appendix                                                                                            B-1




                                                                 i
                            EXECUTIVE SUMMARY




INTRODUCTION

This report presents the results of a study to determine the bus fare elasticity, carried out
by the ESRC Transport Studies Unit, University College London, and TAS Partnership
Ltd. for the Department of the Environment, Transport and the Regions. The main
objective of this study is twofold. Firstly, to obtain fares elasticities which could be used
in policy calculations to project the change in bus patronage nationally as a result of a
given ‘average’ fare change. The second is to investigate possible variation in the
elasticities due to differences in passenger characteristics, local circumstances, service
quality, fare level, and magnitude and direction of fare change.

Two clarifications regarding the elasticities to be estimated need to be made. Firstly, the
intention is to estimate market elasticities, which measure the effect on bus patronage of
average fare changes of all services in a given area. These will, of course, differ from
operator elasticities, which measure the effect on an individual operator’s patronage
resulting from a change in their own fares in relation to those fares of other companies
in competitive markets. Secondly, the study is concerned only with the non-
concessionary bus market. It is not the intention to investigate the effects of
concessionary fares or fare changes, or to contribute to policy discussions relating to
these.

A number of specific points and questions relating to the bus fare elasticity are
contained in the Project Brief, and thus addressed in this report. Most importantly, it is
requirement that both short- and long-term elasticities are estimated, i.e. that the effect
of fare changes on patronage in different time perspectives is considered. Differences in
elasticities relating to local characteristics, to the fare level and to the magnitude and
direction of the fare change are also explored. In addition, the effect of service quality
on patronage is investigated so that the over-all impact of fare increases combined with
quality improvements can be determined. Finally, the impact of changes in bus fares on
car use is examined.


DATA AND METHODOLOGY

The ability to investigate these issues empirically is highly dependent on the quantity
and quality of data available. Basically, two sorts of data can be used: data on actual bus
patronage (Revealed Preference, or RP data) and stated preference (SP) surveys.


                                             ii
Although the use of SP data may be warranted when real data are impossible or difficult
to obtain, SP surveys are costly and time-consuming to carry out and the results based
on them are often difficult to interpret. Because of this, the analysis is based entirely on
existing data on actual patronage. Three sources are used: Bus and Coach Statistics
Great Britain, the Stats100A database and information from the Passenger Transport
Executives (PTEs). The first two sources provide an empirical basis for estimating
demand relationships at the national, regional and county level. The breadth of the
sample assures that different types of fare changes and area characteristics are
represented, so that the specific issues relating to variation in elasticities can be
addressed. However, these two data sources do not distinguish between different types
of patronage, so the elasticities obtained relate to the total market, i.e. concessions as
well as full-fare-paying patrons. The extent to which the total market elasticities
correspond to those for the non-concessionary market is explored with the PTE data,
which differentiate between the two market segments.

The fare elasticities are estimated on the basis of dynamic econometric models relating
per capita bus patronage (all journeys) to real per capita income, real bus fares (average
revenue per journey) and service level (bus vehicle kilometres). The dynamic
methodology employed distinguishes between the short- and long-term impacts of fare
changes on bus patronage, as well as providing an indication of the time required for the
total response to be complete.

The fare elasticity is defined as the percentage change in patronage resulting from a 1-
percent change in fare, given that all other variables in the model – income and service
level - remain constant. The short-run elasticity is defined as the effect on patronage
occurring within one year of a fare change. The time-period characterising the short-run
is determined by the time interval of the data on which the estimate is based – in this
case annual data. It should be noted that the immediate response to a fare change - that
which occurs within a few weeks or months - is only included in the short-term
elasticity if the effect persists a year after the fare change. The long-run elasticity
measures the total response to a fare change over time, when all adjustment to the new
fare is complete.

In order to publicise the results of this study and to obtain the views of practitioners, a
brief summary of the findings and a questionnaire were produced and sent out to bus
operating companies and local authorities. Many useful comments and views were
expressed. These are discussed in Chapter 8.


REVIEW OF THE LITERATURE

As a background to the study, the report includes a review of the most recent evidence
regarding bus fare elasticities, both for the UK and for other countries. A most striking
feature is the variation in the elasticities obtained in the individual studies, which is not
surprising given the differences in data and methodology used and circumstances
considered. Concerning the aggregate market, a short-run (one year) fare elasticity of
around –0.3 seems to be the consensus. There is also a good deal of empirical evidence
that the elasticity increases over time, with the long-run elasticities generally from 1 ½


                                             iii
to over 3 times higher than the short-run elasticities. Although there is far less
agreement as to the long-run elasticity, the majority of estimates range from -0.5 to -1.0.

The studies indicate that the fare elasticity varies by trip purpose, time of day and type
of patron. The elasticity for leisure and other off-peak trips is about twice that for
commuting, peak-time trips. Higher income groups seem to be more sensitive to
changes in bus fares, and non-concessionary patrons more responsive than
concessionary patrons.

Regarding the influence of other factors on bus use, the consensus is that service
quality, generally measured in terms of bus-kilometres, has a positive impact on
ridership, while the income elasticity is negative. Few studies consider the modal
substitution, but in those that do, bus fares appear to have negligible effects on car
travel, while the effects of motoring costs on bus patronage are slightly greater.


ESTIMATES OF THE BUS FARE ELASTICITY

The values for the fare, income and service elasticity values obtained from the dynamic
models in this study are broadly in line with those cited in the literature. There is
substantial variation in the estimated elasticities, dependent on the data and fare
measures used, the model specification and the level of aggregation. This is to be
expected in any empirical study, and all statistical results are surrounded by a degree of
uncertainty. It is our general assessment, however, that the levels of the fare elasticities
obtained for more aggregate regions and the relationship between short- and long-term
effects are quite robust results, adequately supported by the quality of the data available
and the statistical tests. The results for the individual counties are less well supported,
and at least part of the differences noted is likely to be due to random effects and
inadequate data, rather than reflecting genuine differences. Most of the elasticities
reported below relate to the entire local bus market, i.e. both concessions and full-fare-
paying patrons.

Aggregate national bus fare elasticities

The most-likely values for the fare elasticity for Great Britain as a whole are about –0.4
(±0.1) in the short run and –0.9 (±0.1) in the long run. The evidence suggests that the
long-run values are at least twice the short-run elasticities and probably nearly three
times those, and that the total response takes about 7 years.

The interpretation of the elasticities is that if the average fare of all operators in a local
market increases by 10%, total patronage will decline by 4% within one year. The
complete response takes around 7 years, by which time patronage will have declined,
due to the fares change, by a further 5%, giving 9% in total, not taking account of
changes due to other factors such as income, car ownership, or inflation. The dynamic
elasticity is illustrated in the following figure. The fare elasticity increases over time,
but at a declining rate, finally to reach its long-run value.




                                             iv
                                                                   The dynamic elasticity
                                          0

                                        -0.1
                                                   Short run (1-year)
                                        -0.2
                                                     -0.4
                                        -0.3

                                        -0.4
                           Elasticity




                                                            -0.6
                                        -0.5                                                                       Long run
                                        -0.6                       -0.75
                                                                                                                     -0.9
                                        -0.7                                   -0.81
                                                                                           -0.84
                                        -0.8                                                       -0.86   -0.87   -0.88       -0.88

                                        -0.9

                                         -1
                                               0     1      2         3          4          5      6        7        8            9        10

                                                                      Years following fare change


The implications of the dynamic elasticity are illustrated in the following figure, which
shows bus patronage over time following an initial increase in fares by 20% which then
remains at an unchanged (real) level. Patronage declines by 8% in the first year
following the fare increase and by about 15% after 3 years. After about 7 years,
patronage has declined by nearly 18%, and further effects are negligible.

                                                   Bus Patronage over time resulting from a
                                                          20% increase in Bus Fares
                 110


                 100
                                                                                                  Long-run effect:
                                                                                                   (after 7 years)
                  90
 Bus patronage




                                                                                           reduction in patronage by 18%

                  80

                                 Short-run effect:
                  70               (after 1 year)
                           reduction in patronage by 8%
                  60


                  50
                       0                 1          2        3             4           5           6         7             8           9        10

                                                             Years following fare increase



The most likely fare elasticities for England are –0.30 to -0.40 in the short-run and –
0.70 to –0.90 in the long run. The elasticities for England are slightly lower than those



                                                                                       v
for GB, which suggests that the elasticities for Scotland and Wales are higher than the
average for England.

Regional variation in fare elasticities

That there is variation in the elasticities in different regions and areas is quite apparent.
The estimated elasticities for the individual counties of England range from 0 to over -3
in the long run. However, as mentioned earlier, these results most likely reflect
inadequacies in the data rather than genuine differences, and thus should be interpreted
with caution. There is a significant positive relationship between the magnitude of the
fare elasticity and the fare level, but no evidence of any relationship between the
elasticity and income or the variability of fares. The evidence suggests that demand is
50% to 100% more fare-sensitive in the less-urban areas (the English Shire counties)
than in the more urban areas (the Metropolitan areas). The most-likely values for the
Shire counties are –0.5 in the short run and –0.7 in the long run, while the comparable
values for the Metropolitan areas are –0.2 and –0.4. Regarding the other regions, the
results are less-clear cut. For London the results are generally not well established from
a statistical point of view (but these appear lower than elsewhere) and there are
inconsistencies for the other regions (Scotland and Wales), which limits firm
conclusions about regional differences.

Concerning the individual Metropolitan areas, we find a wide range of elasticities. In
the long run, these range from between zero in Merseyside to over –1 in the West
Midlands. The results for the other Metropolitan areas are more consistent, with a short-
run value of about –0.3 and between –0.5 and –0.6 in the long run.

Variation among user groups

There is some indication that full-fare-paying patrons are slightly less fare-sensitive
(-0.15 and –0.38 in the short and long run) than the ‘average’ bus user (-0.24 and –0.52
in the short and long run), and thus appreciably less fare-sensitive than concessionary
patrons, at least in the PTE areas. Since the statistical evidence for this difference is
rather weak, it would be justified to conclude that the elasticities based on total
patronage might overestimate the price sensitivity for the full-fare-paying market, but
that the overestimation is marginal.

Other factors affecting the magnitude of the elasticity

There is statistical evidence that demand is more price-sensitive at higher fare levels.
This conclusion is drawn on the basis of a model in which the fare elasticity is related to
the fare level. The variation in the elasticity ranges from –0.13 in the short run and –
0.27 in the long run for the lowest fares (17 pence in 1995 prices) to –0.77 in the short
run and -1.6 in the long run for the highest fares (£1 in 1995 prices).

There is no evidence that the fare elasticity increases or decreases for larger fare
changes.




                                             vi
There is some indication that demand is slightly more sensitive to rising fares (-0.4 in
the short run and –0.7 in the long run) than to falling fares (-0.3 is the short run and –0.6
in the long run). However, the difference is marginal and not statistically significant. A
reason for the inconclusiveness of the results is that fares have primarily been rising
over time, with relatively few instances of fare reductions to provide a sufficient
empirical basis on which to test asymmetry.

Service Elasticities

The measure of service quality used in this study is per capita bus kilometres for the
market considered. Clearly, this is very crude approximation for the many factors that
make up the quality of a bus service. It is, however, the only feasible measure on the
aggregate level, and the one most commonly used in such studies. In general, the
estimated service elasticities are the same order of magnitude as the fare elasticities,
although opposite in sign. At the national level, for example, the elasticities indicate that
a 10% increase in service, as measured by bus vehicle kilometres for the local market as
a whole, results in a patronage increase of 4% within one year, and 9% within 7 years.
Since both the fare and service elasticity are of similar order of magnitude, but of
opposite sign, this suggests that an increase in fares combined with an increase in
service would leave demand unchanged. For example, if fares were increased by 10%
and the number of vehicle kilometres also increased by 10%, patronage would remain
approximately the same as previously.

Income elasticities

All of the evidence is in agreement regarding the sign of the income elasticity – it is
undoubtedly negative in the long run, suggesting bus travel to be an inferior good. This
is in agreement with most other studies. There is a considerable degree of uncertainty in
the magnitude of the elasticity, and ranges of between –0.3 and –0.4 in the short run and
-0.5 and –1.0 in the long run seem most likely. The negative long-run elasticity reflects
the effect of income through its positive effect on car ownership and use, and the
negative effect of the latter on bus patronage. It should be stressed, however, that the
negative income elasticity pertains to a period of rising car ownership and use. As
private motoring approaches saturation, which it must do eventually, or is limited by
political means, it is likely that income’s negative effect on bus patronage will become
smaller, and possibly become positive.

Substitution between bus use and car travel

As would be expected, there is a strong negative relationship between car ownership
and bus patronage in the long run. In the short run, the effect is negligible.

The cross-elasticity between bus patronage and motoring costs appears to be negligible
in the short run, and about 0.3 to 0.4 in the long run. Clearly, there is a price-
substitution between bus and car use, although comparatively small. Again we must
keep in mind that these elasticities were estimated over a period in which bus fares rose
substantially in comparison to motoring costs (i.e. a reduction in relative car costs took
patronage away from buses), and the opposite change may not necessarily produce an


                                             vii
equivalent impact.

The rising bus fares over the period appear to have had a small but significant impact on
both car ownership and use. The short-run elasticity of car ownership and car use with
respect to the bus fare is around 0.2, while the long-run elasticity is 0.4 for car
ownership and 0.3 for car use.


RECOMMENDATIONS

From the estimates obtained from the different data sources, model formulations, and
area and patronage groupings, it is impossible to arrive at a single value for the bus fare
elasticity. As stated above, all empirical estimates are surrounded by some degree of
uncertainty and it is not unusual that the evidence is conflicting. A decision on the most
appropriate elasticity to use in any specific application needs to judiciously consider the
various evidence. By doing so, we can at least arrive at most probable ranges for the
elasticity. For full-fare-paying patrons we suggest the elasticity ranges shown below.


                     Bus fare elasticities: full-fare-paying patrons

                                         Short run          Long Run
                  Great Britain         -0.2 to -0.3       -0.7 to -0.9
                  England               -0.2 to -0.3       -0.6 to -0.8
                  Non-Urban             -0.2 to -0.3       -0.8 to -1.0
                  Urban                 -0.2 to -0.3       -0.4 to -0.6



A short-run elasticity of between –0.2 and –0.3 appears to be a valid approximation
generally. This measures the effect on full-fare-paying patronage of change in the
relevant fare that would occur within one year of the fare change. The long-run
elasticity – which measures the effect that would occur after 6 to 7 years – would differ
in the different areas. It would be greater for Great Britain than for England, since the
evidence suggests a slightly more elastic demand in Scotland and Wales than in
England. Demand in non-urban areas is also more fare-sensitive that in urban areas.

Since the empirical evidence strongly indicates that demand is more fare-sensitive at
higher fare levels, it would be appropriate, for individual urban or non-urban areas, to
use the higher elasticities for those with higher than average fares, and to use the lower
elasticities for those with lower fares.

Although the evidence for asymmetry was non-conclusive, we would suggest that for
fare rises, the higher of the range is perhaps more suitable, while for fare decreases the
lower elasticities are recommended.




                                            viii
1. INTRODUCTION
1.1    Background

This report presents the results of a study to investigate the effect of fare changes on
local bus patronage in the UK. It has been carried out by the ESRC Transport Studies
Unit at University College London and TAS Partnership Ltd. for the Department of the
Environment, Transport and the Regions. The study is concerned with the non-
concessionary bus market only. It is not the intention to investigate the effects of
concessionary fares or fare changes, or to contribute to the policy discussions relating to
these.


1.2    The main objectives of the study

The main objectives of this study, as set out by the DETR, are to obtain a “broad own
price fares elasticity which can be used as a policy tool and sufficient disaggregated
elasticities to permit more detailed analysis”. The own fare elasticity is interpreted to
mean an elasticity that could be used both at the national level to project the change in
bus patronage nationally as a result of a given ‘average’ fare change and also as an
approximation for particular areas, given that more specific estimates are unavailable.
However, given that the elasticity may vary in different areas and over time, due to
differences in passenger characteristics, local circumstances, service quality etc., more
detailed analysis of specific areas is necessary to provide a basis for determining the
degree of this variation and the factors that influence it. The study is concerned
primarily with local bus services outside London, although elasticity estimates for
London are also obtained for comparison.

1.3    Specific issues to be addressed

The Brief contains a number of specific issues to be addressed in the project. These are
listed below.
♦     Short- and long-term elasticities
♦     Relationship between bus fares and car travel
♦     Variation in elasticities across areas
♦     Fare increases combined with quality improvements
♦     Asymmetric price response
♦     Differences in elasticities for small and large price changes
♦     Relationship between the elasticity and the fare level

The ability to investigate these issues empirically is highly dependent on the quantity
and quality of data available. Because of this, an important part of the work has been to
assess the feasibility of examining these questions on the basis of the readily obtainable



                                               1
data. Although attempts have been made to address all the above issues, data limitations
have often made it necessary to resort to rather simplistic methods. We have been more
successful in some instances than in others.

1.4    Approach to elasticity modelling

Basically, two approaches can be used to estimate the fare elasticity, dependent on the
type of data utilised. The first relies on actual data on bus patronage; the second on
stated preference surveys. Recently, there have been many studies using stated
preference methods which, when real data are impossible or difficult to obtain, can
prove indispensable. However, such methods have their limitations and the results are
often difficult to interpret. They also require extended - and costly - data collection.
Because of this, it is sensible to exploit the existing data on actual patronage before
carrying out any new SP work. The present analysis is thus entirely based on actual
patronage data.

In judging the impact of a given change in bus fares, it is essential to define the time
perspective concerned. The brief states that it “is necessary to consider both short- and
long-run elasticities”. In recent years two quite different methods have been used to
make such a distinction. The first is to define, a priori, certain classes of behavioural
response as ‘short term’ and others as ‘long term’. In principle this enables cross section
models to be interpreted as indicating something about the time scale of response, by
consideration of which responses are included. The conditions for this to be valid are
stringent and rarely fulfilled, and even where they are, no statements are possible about
how many months or years it takes for the long-term effect to be completed. We do not
favour this method. The second approach is to use time series data with a model
specification in which a more or less gradual response over time is explicit, the time
scale being determined empirically as one of the key results of the analysis.
Methodologically, we consider this method superior. It also has another advantage: for
policy purposes it is necessary to know not only the level of the response in the “long
run”, but also how long the adjustment takes. This can only be achieved on the basis of
dynamic models which explicitly take into account the effects of fares and other
relevant factors in different time perspectives. Such an analysis requires observations of
changes in bus patronage, fares etc. over time. The approach taken in this study is to
employ a dynamic methodology to investigate the response to fare changes over time.
This allows us to fulfil the requirement in the Brief to distinguish between short- and
long-run elasticities, as well as adding extra information on what happens in between.

1.5    Definition of the fare elasticity in the short and long run

The fare elasticity is defined as the percentage change in patronage resulting from a one
percent change in fare, given that all other variables included in the model remain
constant. As most of the models in this study include income, population and service
measures, the elasticity measures the change in patronage, which would occur following
a change in fares, if income, population and service were to remain at their initial levels.
In reality all of these factors do change, so that the change in patronage predicted by the
elasticity would rarely be observed in practice. As an example, assume the fare
elasticity is –0.5. This would imply that a 20% increase in fares would reduce patronage


                                             2
by 10%. But assume that income rises at the same time. As rising income is generally
thought to have a negative influence on bus patronage, the effect of the income change
would be to reduce bus patronage. Consequently, the fall in bus patronage observed
would be greater than the 10% implied by the fare elasticity, but some of this would be
the effect of the rising income. Conversely, if the bus fare were to be reduced by 20%,
the fare elasticity would imply a 10% increase in patronage. But if income were to rise
at the same time, this could have a downward impact on bus use, so that patronage
would not rise as much as predicted by the fare elasticity. However, had fares not be
cut, patronage would have fallen even more as a result of the rising income. Clearly, in
the interpretation of the fare elasticity it is essential to keep in mind which factors are
assumed to be held constant. This is particularly important when considering long-run
elasticities and impacts, since in reality all other factors do change over sufficiently long
periods of time.

The short-run elasticity in this study is defined as the effect on patronage occurring
within one year of a fare change. The time-period characterising the short-run is
determined by the time interval of the data on which the estimate is based – in this case
annual data. It should be noted that the immediate response to a fare change - that which
occurs within a few weeks or months - is only included in the short-term elasticity if the
effect persists a year after the fare change. In many cases, the immediate response to a
fare change might be higher than the effect that remains after a year. This type of over-
shooting occurs when consumers over-react to a price change. The initial response to a
fare change might be relatively strong, but as time goes on, some individuals may re-
assess their behaviour For example, assume the short-run (one-year) fare elasticity is –
0.2. A fare increase of 20% would thus reduce patronage by 4% within one year.
Immediately following the fare increase, patronage might fall by more than this as many
existing bus users opt for other modes – for example, the car, if available, and some
would-be bus users are dissuaded from using the bus. Over time – say a month or so -
some of these may find the car less-convenient, because of congestion or parking
problems, or more costly than they had thought, and go back to or begin using the bus.
However, as the same time goes on, more bus users may find other options – arranging
rides with car users or some initially without cars may purchase them. Such processes
can take well over a year.

The long-run elasticity measures the total response to a fare change over time, when all
adjustment to the new fare is complete. It is generally accepted that the long-term
effects are greater than those which occur within a year. The behavioural processes at
work have largely to do with longer-term decisions – like moving house or changing job
– or changes in the life cycle – getting married, having children, having grown-up
children leave home, retirement - at which time people reassess their travel options.
Some of these might have opted for the bus, had fares hadn’t risen, or opted for the car
if fares hadn’t fallen. In addition, the market is continually changing, with potential
users coming in and out of the market, who base their travel decisions on the existing
fares, which are an summation of all previous fare changes. Although the additional
effects on demand of a given fare change dwindles over time, the cumulative effect
becomes larger.




                                             3
It must be stressed that even the long-run elasticity assumes that certain determinants of
bus use remain constant, which are hardly likely to do so when the time period
concerned is measured in years. As these factors change, bus patronage will also be
affected, so that the actual patronage, say 5 years after a fare change, will not be that
predicted by the fare elasticity alone. For example, we would expect average income to
rise over a 5 year’s time perspective and the (presumably) negative influence of this on
bus patronage might over shadow any patronage gains (losses) resulting from fare
reductions (increases). However, the main point is that patronage would have been
lower (higher) had fares not fallen (risen).

1.6    Data

The estimation of bus fare elasticities is based on actual data on bus patronage, fares and
other relevant factors influencing bus use. Given the dual objective of producing
elasticity estimates that can be used on a national level and providing a more in-depth
understanding of possible differences in elasticities in specific areas and circumstances,
it is not possible to rely solely on one data source. Some types of data are more suited to
the investigation of specific issues than others. It is thus necessary to exploit a range of
different sources of information and to combine various types of evidence to construct a
comprehensive view of the factors underlying the fare elasticity. As stated earlier, an
important part of the project has been to assess the suitability of various data sources.
Initially, three types of data were investigated:

1. Aggregate time series data on local bus services, patronage and fares obtained from
   Bus and Coach Statistics Great Britain, complemented with economic data,
   motoring costs, car ownership and car use.

2. The Stats100A database. These data relate to specific operators and provide
   information on passenger journeys, receipts, concessionary fare reimbursement and
   bus vehicle kilometres on an annual basis.

3. Cohort time-series data constructed from Family Expenditure Surveys, comprising
   information on household expenditures on bus transport and other travel modes, car
   ownership, income and related variables.

The results presented in this report are based primarily on data from Bus and Coach
Statistics Great Britain and the Stats100A database. These data provide an empirical
basis for estimating demand relationships at the national, regional and county level. The
breadth of the sample assures that different types of fare changes and area
characteristics are represented, so that the specific issues relating to variation in
elasticities can be addressed.

There has been less success with exploiting the Family Expenditure Surveys. It was
hoped that this individual household data could provide an empirical basis for exploring
issues concerning variation in elasticities due to differences in market characteristics –
income, age-structure, car ownership level, employment status and geographic area.
However, this has not been the case, due to difficulties in converting expenditures on
bus transport to a meaningful measure of bus use at a detailed household level. The


                                             4
aggregate results, however, are roughly in agreement with those obtained from the other
data sources, and as we feel that the latter are more reliable, the results using the FES
data are not presented here.

One of the limitations of all the aforementioned data is that they do not distinguish
between full-fare paying and concessionary bus patronage. For this reason, the elasticity
estimates obtained on the basis of these data relate to total bus patronage – i.e., they
indicate the change in both full-fare paying and concessionary patronage given a change
in a weighted average of non-concessionary and concessionary fares. The elasticity
obtained is thus a composite of the elasticities for the individual sub-markets. Since the
primary focus of this study is the non-concessionary market, it is essential to determine
the extent to which the demand relationships in these two market segments differ. This
requires data on full-fare paying trips and fares. For this reason, the possibility of using
another source of data has been investigated:

4. Data on concessionary and non-concessionary patronage and fares from Local
   Authorities (PTEs).


1.7    The experience of practitioners

It was suggested by the DETR that the results of this study be circulated to practitioners
and academics concerned with the bus industry for their response and comment. A brief
summary of the main results was prepared for this purpose, along with a questionnaire.
The objective of the questionnaire was to determine the extent to which the results
obtained conform with current opinion regarding the impact of fares on bus patronage
as well as to gain an insight into operators’ and public authorities’ views and
experience. This has been distributed to over 300 transport practitioners - bus operators
and public transport organisations.

1.8    Outline of the report

The summary and questionnaire mentioned above follow this introduction. Chapter 2
presents a review of the most recent literature on bus fare elasticities. The survey
summarises the results presented in earlier literature reviews and complements this with
more recent evidence. As studies carried out for the UK over the past few years are
rather limited (and largely composed of re-compilation of earlier studies with stated
preference results added), studies for other countries are also included. The review
concludes with a 'most-likely' range for the short- and long-run elasticity and evidence
concerning variation in elasticities.

Chapter 3 describes the aggregate time-series data, and Chapter 4, the elasticities
estimated on the basis of these data. Both chapters begin with the National GB data.
This is then split into 5 regions: Greater London, English Metropolitan areas, English
Shire counties, Scotland and Wales. Finally, the 6 Metropolitan areas are considered
individually. Chapter 4 concludes with a summary of the empirical results concerning
the aggregate national elasticity and the variation in elasticities amongst regions. In
addition to fare elasticities, estimates of income and service elasticities are presented.


                                             5
Evidence concerning the relationship between the elasticity and fare level, asymmetric
response, and the relationship between motoring and bus use is presented.

Chapters 5 and 6 concern the STATS100A bus operators' data aggregated by county.
Only English counties are considered, as the data for Wales and Scotland are less
comprehensive. Chapter 5 describes the data and Chapter 6 presents the econometric
results. Overall elasticities for England are obtained as well as elasticities for individual
counties. Questions concerning the relationship between the fare elasticity and the fare
level and the magnitude of the change in fares are discussed, as well as the issue of
asymmetric response.

Chapter 7 concerns the analysis of the data obtained from the PTEs. The main objective
is to determine the extent to which the elasticities obtained on the basis of total
patronage reflect the non-concessionary market. Finally, Chapter 8 concerns the views
of practitioners concerning the bus fare elasticity and their comments to the summary of
this study which they received along with the questionnaire.

The methodology and specific models used in the analysis are discussed in the
Technical Appendix (A). The Statistical Appendix (B), contains the full econometric
results.




                                             6
2. LITERATURE REVIEW
2.1      Introduction

The aim of this section is to review the most recent literature on bus fare elasticities.
Most studies prior to 1990 are summarised in Goodwin (1992) and Oum et al (1992)
and this section will present the main results of these summaries complemented with
more recent evidence. When setting out the scope of this literature review, it was
decided to focus on those studies which answer questions under investigation in this
project (in so far as is practicable). Specifically, we seek to address the following
questions:

a.    short- and long-term elasticities
b.    relationship between bus fares and car travel
c.    variation in elasticities across areas
d.    fare increases combined with quality improvements
e.    asymmetric price response
f.    differences in elasticities for small and large price changes
g.    relationship between the elasticity and the fare level
h.    aspects to be considered in elasticity estimation

In the literature review, we have found studies that investigated some but not all of these
questions. For example, there has been increasing interest in the dynamics of response
to fare and other price changes in public transport demand literature since the mid- to
late 1980’s. There has also been considerable interest in the effects of public transport
and car prices both on use of the former, and on ownership and use of the latter.
Similarly, a number of studies have considered the effects of different tariff structures
and the impact of service quality on patronage. Less work has been done to explicitly
assess the impacts of large and small fare changes, and this has generally been done
using before-and-after survey analysis. However, while recent work by Dargay (1999)
and Dargay and Gately (1999) has looked at the asymmetric price response for car
ownership and transport fuel use, as far as we are aware, no analysis of this sort has
been done in the field of public transport demand. The literature survey presented here
has focused mainly on work that has been similar in nature to that of the project in hand
i.e. where possible using revealed preference time series data and econometric analysis.
For comparison, results of some studies using other kinds of data and/or analytical
techniques are presented when it is felt that they are relevant and add to the discussion.


2.2      Evidence from literature reviews

The influential review of public transport elasticities edited by Webster and Bly (1980)
concluded that a reasonable rule of thumb for public transport fare elasticity was -0.3.
This figure was widely acknowledged to be correct for much of the 1980’s. However,
towards the beginning of the 1990’s, it was starting to look as if there was a drift
upwards in the fare elasticity to somewhere in the range -0.3 to -0.4 or more. Two wide
ranging reviews of public transport demand studies, the first by Goodwin (1992) and the


                                               7
second by Oum et al (1992) between them summarised most of the elasticity studies
prior to 1990 and in the process updated the work of Webster and Bly (1980). Goodwin
(1992) reviewed 50 demand elasticities for bus use, based on studies for the UK and
elsewhere, and calculated a non-weighted average of -0.41. His summary table of
elasticity values classified by type of study and time period covered by the studies
(either explicitly or implicitly) is reproduced here.

Table 2.1: Bus fare elasticities related to time period. Goodwin (1992).
Type of study                  Time period              Average                 Standard             No. in Sample
                                                       Elasticity               Deviation
Before and after            around 6 months               -0.21                    0.12                     3
Explicit short              0-6 months                    -0.28                    0.13                     8
Unlagged time series        0-12 months                   -0.37                    0.18                    24
Explicit “long” run         4+ years                      -0.55                    0.20                     8
Equilibrium models          5-30                          -0.65                    0.18                     7
Note: The standard deviation does not pertain to the statistical estimates, but rather to the variation of the
elasticity estimates making up the average.

Goodwin concludes that it would make sense to consider the static elasticity figure of
-0.3 from the Webster and Bly (1980) review as a reasonable figure for the effects
within the first year; that the effect after four years or so (the “medium term”) would be
-0.55; rising to -0.65 over a period of about a decade. Overall there is a clear pattern for
long-term elasticities to be between 50 per cent and three times higher than the short
term.

Concerning the relationship between car ownership and public transport, Goodwin
concludes that the results in Bates and Roberts (1979, 1981) and Copley and Lowe
(1981) give broad support to an elasticity of car ownership with respect to public
transport service level of about -0.1. He concludes that the elasticity of car ownership
with respect to public transport generalised costs “is not likely to be less than +0.1, or
more than about +0.3, implying a rather small figure of less than +0.1 for fares alone.”

The corresponding table from Oum et al (1992) is reproduced in Table 2.2 below. Most
of the studies cited relate to North and South America and to Asia, and no distinction is
made between short- and long-run elasticities. Again a wide range of elasticity
estimates can be seen. The elasticities given relate to peak and off-peak traffic
separately, and to total patronage. The first column of the table shows the own-price
elasticity of the demand for transport, i.e. transport by all modes. The mode-choice
elasticities give the fare-elasticity of bus travel, holding total transport demand constant.
These differ from the ordinary demand elasticities considered thus far in that they only
take into account the effect of fare changes on substitution between modes, but not on
total travel. They can therefore be considered as a lower bound for ordinary elasticities.
The final column presents a ‘most-likely’ range of total fare elasticity estimates based
on the authors’ own subjective consideration of the studies reviewed. In general, the
ranges are quite broad, reflecting the diversity of the countries and models used.
However, it does seem that some tentative conclusions could be drawn. Particularly,
off-peak traffic is more price sensitive than peak traffic. This is as would be expected,
since peak traffic is essentially work and school trips, which are not as easy to forgo as
off-peak leisure or shopping trips. In addition, such trips may be less amenable to


                                                    8
transfer to car because of the higher costs in terms of time, resulting from congestion, or
because parking is unavailable or prohibitively expensive.

Table 2.2: Bus fare elasticities from discrete choice models. Oum et al (1992).
                  Total transport       Mode choice              Total fare       No. of studies
                   demand cost          fare elasticity           elasticity
                     elasticity                               Most likely range
      Peak             0.00             -0.03 to -0.58         -0.10 to -0.70           6
      Off-peak    -1.08 to -1.54        -0.01 to -0.69         -0.10 to -1.10           3
      All day     -0.10 to -1.62        -0.03 to -0.70         -0.10 to -1.30          11



Fowkes et al (1992) review the existing literature for evidence on possible differences
in price-sensitivity for different trip purposes. They consider previous reviews by Oum
et al (1990), Kemp (1973) and Goodwin (1988). Their suggested average own-price
elasticities are shown in Table 2.3. The results confirm those above – the fare elasticity
for leisure trips (generally off-peak) is twice that for commuting and business trips
(generally peak). Again, no distinction is made between the short and long run.

Table 2.3: Fare elasticities by trip purpose. Fowkes et al (1992).
                          Trip purpose           Own-price elasticity
                          Commuting                      -0.3
                          Business                       -0.3
                          Leisure                        -0.6




2.3      Evidence from the UK

Work by Gilbert and Jalilian (1991) on bus-travel demand in London yield elasticities
that are considerably higher in absolute value than those in the majority of previous
studies reviewed in Goodwin (1992) and Fowkes et al (1992). This is particularly true
for the short-run elasticity. However, the relationship between short- and long-term
values is consistent with the other studies: the long-run elasticity is 50% higher than the
short-run elasticity. Their results are reproduced in Table 2.4.

Table 2.4: Bus fare elasticities for London. Gilbert and Jalilian (1991).
                                                      Elasticity
                                    Short term        -0.8
                                    Long term         -1.2 to -1.3



Bus fare elasticities for London were also estimated by London Transport in 1987 and
1992. The results are summarised in Table 2.5. The own-price fare elasticities give the
change in demand if only bus fares change, while the conditional elasticities give the
effect on bus demand if bus, underground and BR fares all change by the same
proportion. Here the medium term refers to around one year and the short term implies


                                                  9
the ‘immediate effect’. The two studies produce rather similar results, although the own-
price elasticity is somewhat greater in the more recent study. As expected, the
conditional elasticities are smaller in absolute value than the own-price elasticities,
reflecting the substitution between modes. The cross-price elasticities are positive, but
small. It should be stressed, however, that these are ‘immediate effects’, and that we
could expect the medium- and long-term elasticities to be far greater. The 1987 study
also estimates a service elasticity, which is of a magnitude comparable to other studies.

Table 2.5: Bus fare elasticities for London. London Transport (1987 and 1992).
    Elasticity                                  1987                           1992
                                           Medium term            Short term    Medium term
    Own-price                                  -0.40                 -0.46          -0.62
    Conditional own-price                      -0.27                 -0.20          -0.35
    Cross-price:
     Underground fares                            +0.10              +0.14
     BR Fares                                                        +0.13
    Service elasticity                            +0.38



In their report for the London Congestion Charging project for the Department of
Transport, Halcrow Fox (1993) undertook a stated preference study of travel demand
elasticities. The values obtained for buses for different trip purposes and income groups
are shown in Table 2.6. Both normal price elasticities – relating to fare only – and
generalised cost elasticities – including travel time costs etc. – are presented. Clearly,
the generalised cost elasticities are greater than those relating to fare only. Two major
conclusions are apparent from the figures given. Firstly, the higher income groups are
more sensitive to bus fares and to generalised costs. This could be explained by the fact
that a larger proportion of this group has access to a car as a substitute mode, and that
they have a higher value of time. Secondly, non-work related trips are far more price-
sensitive than are work-related trips – either for commuting or employers’ business.
This is explained by the necessary nature of the latter trips.


Table 2.6: Recommended public transport own-price elasticities for London.
Stated Preference results. Halcrow Fox (1993).
                                Price Elasticities                         Generalised Cost Elasticities
                     Low            Medium             High             Low          Medium           High
                   Income           Income           Income           Income         Income         Income
Home-Work        -0.2 to -0.4     -0.3 to -0.4     -0.4 to -0.5     -0.4 to -0.5   -0.5 to -0.7  -0.6 to -0.8
Home-Other       -0.4 to -0.6     -0.5 to -0.7     -0.6 to -0.8     -1.3 to -1.5   -1.4 to -1.6  -1.5 to -1.7
Employers’
business                           -0.3 to -0.4                                    -0.6 to -0.8



Preston (1998) in a study of bus fare elasticities in three different metropolitan areas in
England concludes that the use of a global aggregate price elasticity “masks the
complexity of the urban public transport market” and recommends the use of a more
disaggregate approach to modelling urban public transport elasticities. He investigated



                                                  10
different types of variation: (a) by time of day/day of week; and (b) by user and ticket
type, using a log-linear least squares model in both cases. The main results are reported
below.

Variation by time of day/day of week

The study broke the data into the following time periods: early morning, peak morning,
peak evening, inter-peak, late evening, Saturday and Sunday. The resulting fare and
service elasticities are shown in Table 2.7. It can be seen that bus fare elasticities are
lowest in absolute terms for early morning, peak morning, peak evening and Saturday
travel, with a long-run elasticity of -0.3, and highest for evening and Sunday travel, with
a corresponding elasticity slightly in excess of –1.0. On average, the long-run elasticity
is about 50% higher than the short-run elasticity, but this varies for the different periods
– from 35% higher for Saturday traffic to over 400% higher for evening traffic. It would
appear that adjustment to fare changes occurs most rapidly for Saturday travel and most
slowly for evening travel, while the most substantial short-run effects relate to Sunday
traffic. Generally, the results are as expected – necessary travel to work and school at
peak hours is much less price-sensitive than leisure and shopping trips which are
generally off-peak and on weekends. The low elasticities on Saturdays may reflect the
more-necessary shopping trips made to the city centre on this day. For all periods, the
study yielded a fare elasticity of -0.78.

Table 2.7: Bus fare and service elasticities by time of day/week for English
Metropolitan areas. Preston (1998).
                                      Fare elasticity                    Service elasticity

                               Short run             Long run       Short run          Long run
Early morning and peak       -0.16 to -0.20        -0.24 to -0.31     0.38               0.58
Inter-peak                       -0.31                 -0.55          0.17               0.30
Evening                          -0.19                 -1.06          0.35               1.95
Saturday                         -0.20                 -0.27          0.52               0.67
Sunday                           -0.69                 -1.06          1.05               1.61
All periods                                            -0.78                             0.13



The service elasticities are lowest in the inter-peak period, higher in the peak periods,
yet higher on Saturdays and higher still on Sundays and evenings. Notably, the highest
service elasticities (1.95 in the long run) are found for the time periods with the highest
fare elasticities. It should be noted, however, that all of the elasticity figures quoted
have quite wide confidence intervals, so that some of the differences between time-
periods may not be statistically significant at normal confidence levels.

In addition to the above-mentioned elasticities, the study attempts to estimate the effect
of car ownership on bus travel. Car ownership was found to have a statistically
significant effect on demand only on weekdays before 9 am and on Saturdays.

Variation by user and ticket type




                                              11
As in previous work in this area, Preston focused on the differences between children,
adults, and the elderly and disabled. The resulting elasticities, along with their 95%
confidence intervals, are shown in Table 2.8. The elderly and disabled cash fare
elasticity is -0.29 and that of adults is -0.28. Both are consistent with the adult value of -
0.3 in the study by Goodwin, Hopkin and McKenzie (1988). The child cash fare
elasticity is higher at -0.40. For adult pre-paid tickets, the fare elasticity is higher yet at -
0.74. The latter two results, however, have extremely wide confidence intervals.

For part of the period investigated, the elderly and disabled had zero fares in off-peak
periods. One problem with the log-linear model is that it forecasts infinite demand at
zero price. To overcome this Preston estimated an alternative model using non-linear
least squares. For peak travel, this yielded a short-run elasticity of -0.11 rising to -0.30
in the long run. The comparable elasticities for inter-peak travel were -0.23 and -1.47.

Table 2.8: Bus fare elasticities by user, ticket type and peak/off-peak travel for
English Metropolitan areas. Preston (1998).
                   Cash fare        Pre-paid ticket    Peak                     Off-peak
                   Medium term      Medium term        Short run    Long run    Short run    Long run
Adults             -0.28 (±0.12)    -0.74 (±0.39)
Children           -0.40 (±0.39)
Elderly/disabled   -0.29 (±0.07)
All                                                    -0.11        -0.30       -0.23        -1.47



Preston also quotes results from the ISOTOPE (1997) study of variation of elasticity by
city size in which data from 89 European cities were analysed. The results from the
study suggest that bus fare elasticities are greater in small cities (those with a population
of less than 0.5 million) than in large ones (-0.50 in comparison to -0.34). This contrasts
with the conclusion of Webster and Bly (1980) for North American cities which found
the opposite to be true. Preston puts forward the argument that the lower fare elasticity
in large European cities may reflect a combination of passengers’ greater captivity to
public transport because they travel longer distances in general than those in smaller
cities (and hence alternatives such as walking and cycling are less attractive), and the
greater congestion and parking problems in large cities which makes travel by car less
attractive.

The same study also indicates that service elasticities are greater in large cities than in
small cities (0.49 and 0.33 respectively). A possible explanation for this may be that
there is greater modal competition in larger cities. Normally fares for all modes change
proportionally, whereas service changes in public transport modes are not proportional,
in general. The greater service elasticity in larger cities would therefore reflect the
greater service competition between public transport modes.




                                               12
2.4    Evidence from Europe and Australia

A study of bus trip demand in 11 Spanish cities by de Rus (1991) estimated both
dynamic and static demand models. In the dynamic model, the short-term own-price
elasticity for bus fares (all ticket types together) ranges from -0.06 to -0.39 with an
unweighted average of -0.28 and the corresponding range of long-term elasticities is -
0.09 to -0.48. The long-run elasticities are of the order of 1.2 to 2 times the magnitude
of the short-run values. In the same paper, he also estimated both dynamic and static
models in which cash-fare tickets and multi-ride tickets are disaggregated, but reported
only the results for the static model. The direct elasticities for cash fares lie in the range
-0.7 to -1.2, while the range for multi-ride tickets is considerably wider. As expected,
the individual ticket types are more price-sensitive than is the aggregate, which reflects
the substitution between the two types of ticket. The effects of increasing both fare
types equiproportionally are shown in the final column. In general, it appears that this
would be to the relative advantage of the multi-ride ticket, and may even result in an
absolute increase of the use of such tickets.

The paper also presents service elasticities. These are positive, confirming that service
quality has a positive impact on bus patronage. However, the effect is quite variable –
with a range from 0.39 to 1.88 in the long run for the different cities.

Table 2.9: Bus fare and service elasticities. Spanish cities. de Rus (1991).
        Elasticity              Short-term           Long-term       Equiproportional
                                                                     Price changes
        Own-price             -0.06 to –0.39        -0.09 to –0.48
        Cash fare             -0.73 to –1.16                           -0.39 to –0.53
        Multi-ride ticket     -0.27 to –2.25                           -0.21 to +0.44
        Service                0.26 to 1.54          0.39 to 1.88

In their study of public transport demand in Finland, Dargay and Pekkarinen (1998)
estimated the short- and long-term own-price elasticities for three types of bus ticket
using monthly data for the period April 1993 to October 1996 for individual Finnish
districts. The ticket types are: (a) regional bus cards (RBC) - a popular form of bus
subsidy in Finland - which are valid on all buses operating in a particular region and for
all bus trips in the region; (b) a “40-trip ticket” - this is a subsidised ticket valid for 40
trips of a given distance on one route; and (c) single trip tickets. The results are
reproduced in Table 2.10. Regarding fare elasticities, the results suggest that the
demand for regional bus cards is more price sensitive than are trips made by bus cards.
An increase/decrease in card price increases/decreases the number of trips made per
card, suggesting that a price increase/decrease encourages less-frequent users to
abandon/start purchasing bus cards. The closest substitute fare, the 40-trip ticket, has a
positive influence on the number of RBCs sold, but a negative impact on the number of
trips made per RBC – as the price of the 40-trip ticket increases relative to that of the
RBC, more RBCs are purchased, but these are used less, since the RBC becomes
economically attractive to even less frequent users. The two effects more-or-less cancel
out, however, so the impact on total trips by RBC is negligible. Finally, if the prices of


                                               13
both ticket types increase equiproportionally, the demand for RBCs and trips by RBC
decline substantially, but the number of trips made per card declines only marginally.

Table 2.10: Elasticities of the demand for regional bus cards and trips in Finland.
Dargay and Pekkarinen (1998).
                           Regional Bus Cards        Trips per Card             Trips by Regional Bus
                                                                                Card
                           Short run     Long run    Short run     Long run     Short run   Long run
Own price                   -0.9          -1.3         0.3           0.4         -0.5        -0.9
Price of 40 trip ticket      0.3           0.4        -0.3          -0.5           -          -
Equal % change in prices    -0.6          -0.9         0.0          -0.1         -0.5        -0.9
Service                      0.1           0.2         -             -             -          -
Petrol price                 -             -           0.5           0.7          0.6         1.1

The service elasticity is found to be positive, but rather small, and affects mainly card
puchases, rather than trips per card. The petrol price, on the other hand, has a more
substantial impact on the number of trips made per card than on the number of cards
purchased.

The same study also estimates own- and cross-price elasticities for trips by different fare
types in the Finnish cities of Oulu and Kuopio. The results, given in Table 2.11, indicate
that trips by 40-trips tickets are less-price sensitive than those made by other ticket
types. Significant cross-fare elasticities, however, were only found in a few cases.
Again, there is a substantial difference between short- and long-run elasticities, with the
long-run values being 2 to 3 times those in the short run.

Table 2.11: Summary of elasticities for different ticket types in two Finnish cities
(Oulu and Kuopio). Dargay and Pekkarinen (1998).
                          Trips by                         Trips by                    Trips by
                        Single Ticket                    40-trip ticket          Regional Bus Card
Fare type:       Short run        Long run          Short run        Long run   Short run    Long run
Single ticket      -0.3              -0.9             0.9                1.4
40-trip ticket                                        -0.3              -0.5
RBC                                                                               -0.4        -0.8
City ticket         0.1                0.5



It is important to note is that since the models are estimated on a combination of cross-
section and time-series data, and since most of the variation in the sample is due to
differences between the communities, the short-run elasticities do not represent the
response within the first month to changes in the explanatory variables, but instead
some intermediate term effect. Similarly, the long-run elasticities may not capture the
true equilibrium response, since the estimates are based on monthly data for a relatively
short time period and on a lag of a single month.

Hensher and King (1998b) estimate elasticities for concession and non-concession
markets segmented by trip length in the Australian city of Newcastle. They focus on
buses and cars only and use a random effects heteroskedastic extreme value model



                                             14
(HEVL) to jointly estimate stated preference and revealed preference data. The existing
ticketing system consists of three ticket types: (a) single journey tickets; (b) a 10-trip
TravelTen ticket allowing users 10 one-way trips over an agreed number of sections;
and (c) a weekly TravelPass allowing passengers an unlimited number of trips over a
seven day period within specified sections. The authors consider two possible future
scenarios: (a) scenario I - replacement of the existing system with a system of 4 timed
tickets (one-hour, four-hour, one-day and weekly); and (b) scenario II - introduction of
the four timed tickets and retention of the single trip ticket from the current system.
Short and long trips are considered and the authors distinguish between non-concession
holders and concession holders/non-pensioners.

The results for Scenario I are summarised in Table 2.12. The models are estimated on
the basis of cross-section data, and no mention is made of time horizon.

Table 2.12: Bus fare elasticities by ticket type for Newcastle, Australia. Scenario I.
Hensher and King (1998a).
                              1-hour ticket   4-hour ticket   Day ticket     Weekly ticket
Own-price elasticity
 Short trips
   Concession                     -1.15            -1.17         -1.83           -1.30
   Non-Concession                 -1.52            -1.01         -1.24           -1.45
 Long trips
   Concession                     -0.30            -0.46         -0.55           -1.02
   Non-Concession                 -1.20            -1.29         -1.77           -1.62
Cross-fare elasticities
 Short trips
   Concession                  0.27 to 0.30    0.28 to 0.30   0.37 to 0.60   0.29 to 0.33
   Non-Concession              0.39 to 0.43    0.21 to 0.42   0.32 to 0.40   0.30 to 0.48
 Long trips
   Concession                  0.07 to 0.09    0.10 to 0.17   0.04 to 0.33   0.20 to 0.28
   Non-Concession              0.25 to 0.38    0.31 to 0.37   0.42 to 0.54   0.40 to 0.45
Cross-price: motoring costs
 Short trips
   Concession                      0.30            0.30          0.42             0.37
   Non-Concession                  0.28            0.09          0.20             0.27
 Long trips
   Concession                      0.06            0.09          0.08             0.30
   Non-Concession                  0.23            0.26          0.35             0.35

The wide variation in elasticities for different ticket types, trip lengths and patrons is
apparent. The own-price elasticity ranges from -0.3 to nearly -1.8, and the cross-fare
elasticities from 0.04 to 1.4. Although, not totally consistent, a few general trends can
be noted: the day ticket seems to be most price-sensitive in the majority of cases, while
the 1-hour ticket is least price-responsive; non-concessionary fares appear more price-
sensitive than concessionary fares; short trips are more price sensitive for concessionary
patrons than are long trips, while the opposite seems to be the case for non-
concessionary patrons. Finally, the elasticities with respect to motoring costs are
generally quite low, falling between 0.06 and 0.42. For long trips, these are higher for
non-concessionary patrons than for concessions, but the opposite appears the case for
short trips. Comparing the motoring cost elasticities for short and long trips, no trends
are discernible.


                                              15
The study also investigates the effects of bus fares on car travel. In general, the
elasticities are very small, averaging around 0.04 for the individual ticket types.

In another recent paper Hensher (1998a) estimates direct- and cross-share elasticities for
the Sydney Metropolitan area, again using SP and RP data and HEVL and MNL
methodologies and distinguishing between mode (train, bus and car) and ticket type
(single cash fare, weekly train or bus card, and bus and train travel passes). The results
of direct interest to the current project are reported in Table 2.13. As in the previous
study, no mention is given to time horizon. Here we find that the elasticities are much
lower than those in the previous table, and also rather lower than those found in other
studies. The single ticket appears to be more price sensitive than the other ticket types,
and motoring costs have little effect on bus demand. The two estimation methods
produce rather different elasticities, which are generally lower using the MNL method.

Table 2.13: Fare elasticities for trips by different ticket types in Sydney, Austrailia.
                                    Hensher (1998a).
                                            Single ticket   Travel ten ticket   Travel pass
   own-price elasticity
    HEVL method                                  -0.36            -0.16              -0.10
    MNL method                                   -0.14            -0.02              -0.01
   Motoring costs cross-price elasticity
    HEVL model                                   0.07              0.02              0.00
    MNL model                                    0.05              0.01              0.02



Tegner, Loncar-Lucassi and Nilsson (1998) estimate a two-stage aggregate non-linear
time series demand share model for public transport trips in Stockholm to investigate
the elasticities for different types of ticket (single ride ticket, multi-ride ticket, etc.) over
the period 1973 to 1996. The three main types of ticket sold by the Stockholm Greater
Transit Company are monthly cards, pre-paid coupons (strips) and cash-paid coupons.
A “share” model is used and the results are presented in terms of share price elasticities,
i.e. the percentage change in the share of a given ticket type resulting from a percentage
change in its price. These are summarised in Table 2.14, and relate to the medium term.
The share elasticities are not the same as normal price elasticities, and further
information is required to convert them to elasticities comparable to those of other
studies. This is only done for the case of monthly cards, for which a fare elasticity of –
0.35 is obtained. The share elasticities for the different ticket types, however, can be
compared directly to determine relative fare sensitivity. From the results shown, cash
coupons are the most price-sensitive fare type, while monthly cards are least sensitive.

The same study also estimates service elasticities and the cross-elasticity with respect to
petrol prices for total public transport demand. The service elasticity is found to be 0.29
and the cross-elasticity with respect to the petrol price, 0.15.

 Table 2.14: Elasticities by ticket type in Stockholm. Tegner, Loncar-Lucassi and
                                    Nilsson (1998).



                                               16
                       Ticket Type          Average share elasticity
                       Monthly cards                 -0.2
                       Cash coupons                  -1.8
                       Pre-paid coupons              -0.8



Alexandersson et al (1998) estimate the effects of deregulation of the bus industry on
bus travel in Sweden. Data on annual bus passengers on a county level over the period
1987 to 1993 are used to estimate a static logarithmic model for aggregate bus demand.
The own-price elasticity obtained, -0.23, is low in comparison to results from other
countries. The authors believe that this may be due to a number of factors including the
high (50%) fare subsidy provided by the Swedish government and the fact that many
counties in Sweden do not have a separate system of school buses.

In their recent review of transport elasticities for public transport demand, Nijkamp and
Pepping (1998) compare 12 studies from four European countries (Finland, the
Netherlands, Norway and the United Kingdom) in order to assess the factors that
influence the sensitivity of travellers to public transport travel costs in Europe. They use
meta-analysis, a statistical procedure for combining and comparing research findings
from different studies focusing on similar phenomena. It is particularly useful in cases
where there are no controlled conditions, such as in comparing elasticity estimation
studies which have been carried out independently and for different areas and
conditions. A summary table of their information survey containing (the eight) site- and
study-specific characteristics of the various studies used in their analysis is reproduced
here in Table 2.15.

It is clear from this table that the range of elasticity values is quite wide, from a low of
-0.15 in the UK study to a high of -0.8 in one of the studies for the Netherlands (Fase,
1986). The time scale to which the elasticities pertain is not explicitly stated, but it can
generally be assumed that those based on cross-section data and the higher of the two
given for time-series data represent a longer-term response. There is also considerable
diversity in modes included, type of data (e.g. aggregated time series data, aggregated
cross-section data, before-and-after survey data, stated preference data, model-based
elasticities), methods of estimation (e.g. random utility model, logit model, nested logit,
linear demand OLS, discrete choice), amount of data used in estimation, and
geographical location and specificity. This is, of course equally true of the results from
the other studies cited in this literature review. Nijkamp and Pepping’s analysis broadly
supports the main findings from existing reviews - i.e. the importance of the difference
between aggregated, empirical-based research methods and disaggregated choice
models as well as of the model assumptions and the number of competitive modes. In
addition, they find that country-specific factors have a strong influence on elasticity
size. For example the natural circumstances and travel distances in a country may
influence the mode of travel that is chosen (they cite the bicycle in Holland). They
advise that care should thus be taken when comparing elasticities for different European
countries even when the estimation methods are the same.

 Table 2.15: Survey of elasticities for public transport in four European countries.
                           Nijkamp and Pepping (1998).


                                            17
Source         Country       Data      Modes          Indicator   Geo-         Number     Data       Model        Elasticity
                             period                   of          graphical    of com-    Type       type         value
                                                      demand      coverage     petitive
                                                                               modes
EXTRA*         Finland       1988      Bus, tram,     Trips       Urban        2          Cross-     Nested       -0.48
                                       metro, train                                       Section    logit
EXTRA          Finland       1995      Bus, tram,     Trips       Urban        3          Cross-     Logit        -0.56
                                       metro, train                                       Section
Sullström      Finland       1966-90   Bus, tram,     Person-km   Urban,       1          Repeated   Linear       -0.75
                                       metro, train               interurban              Cross-     demand
                                                                                          section    OLS
EXTRA          Netherlands   1984-85   Bus, tram,     Trips       Urban,       2          Panel      Linear       -0.35/
                                       metro                      semi-urban                         demand       -0.40
                                                                                                     OLS
BGC, 1988      Netherlands   1980-86   Bus, tram,     Trips       Urban,       2          Time       Linear       -0.35/
                                       metro                      semi-urban              Series     demand       -0.40
                                                                                                     OLS
Roodenburg     Netherlands   1950-80   Bus, tram,     Person-km   Urban,       1          Time       Linear       -0.51
, 1983                                 metro                      semi-urban              Series     demand
                                                                                                     OLS
Fase, 1986     Netherlands   1965-81   Bus, tram,     Person-km   Urban        1          Time       Linear       -0.53/
                                       metro                                              Series     demand       -0.80
                                                                                                     OLS
Gunn, 1987     Netherlands   1986      Train          Person-km   Semi-urban   2          Cross-     Discrete     -0.77
                                                                                          Section    choice
Oum, 1992      Netherlands   1977-91   Bus, tram,     Person-km   Urban,       2          Time       Translog     -0.74
                                       metro                      semi-urban              Series     utility
                                                                                                     function
EXTRA          Norway        1990-91   Bus, tram,     Trips       Urban        3          Cross-     Multinomia   -0.40
                                       metro, train                                       Section    l
                                                                                                     logit
EXTRA          Norway        1991-92   Bus            Trips       Interurban   5          Cross-     Multinomia   -0.63
                                                                                          Section    l
                                                                                                     logit
EXTRA          UK            1991      Bus, tram,     Trips       Urban,       4          Cross-     Nested       -0.15
                                       metro, train               interurban              section    logit

* These results are from the EXTRA project for the European Commission.




2.5         Conclusions

Despite the diversity of the elasticities obtained from the individual studies, a few
general conclusions can be drawn.

♦        Short- and long-run elasticities

There is a substantial difference in the response to fare changes in different time
perspectives. The evidence suggests that long-run elasticities are from 1.5 to over 3
times higher than the short-run elasticities. From the empirical evidence, it appears that
a ‘likely’ value for the short-run (one year) average fare elasticity is around –0.3. There
is far more uncertainty concerning the long-run elasticity, however, with a probable
range from -0.5 to -1.0.


♦        Differences in elasticities by trip purpose and time of day




                                                      18
Commuting trips are less responsive to fare changes than other trips. Similarly, peak
travel is less price-sensitive than off-peak travel. The elasticity for leisure and other off-
peak trips is about twice that for commuting, peak-time trips.

♦     Difference in elasticity between different groups

Higher income groups seem to be more sensitive to changes in bus fares, and non-
concessionary patrons more responsive than concessionary patrons. Again, however, the
empirical evidence is limited.

♦     Difference in elasticities for different fare types

Trips by individual fare types are more price-sensitive than total trips, reflecting the
substitution between fare options. There is a wide variation in elasticities for different
ticket types, but these differ from place to place and no general conclusions can be
drawn.

♦     Service elasticities

Service quality, generally measured in terms of bus-kilometres, is found to have a
positive impact on ridership, although the elasticities differ substantially from study to
study. Off-peak travel appears to be more responsive to service changes than peak
travel.

♦     Relationship between car and bus travel

Although the empirical evidence is limited, bus fares appear to have negligible effects
on car travel. The effects of motoring costs on bus travel, however, are slightly greater.

In light of the discussion in Nijkamp and Pepping (1998) and Oum et al (op. cit.),
estimated elasticities from different studies are not directly comparable. Even allowing
for the distinction between mode choice elasticities and market demand elasticities,
different mode choice elasticities may not be comparable due to the inclusion of
different alternative modes or of specific geographical characteristics or properties of
the data used in a particular study. Following this line of argument, it is inappropriate
both to generalise the value of an estimated elasticity to different circumstances and to
calculate the mean of elasticities from different studies. However, when a number of
studies with different data and models yield similar elasticity values, the result may be
regarded as robust.




                                             19
3. THE AGGREGATE DATA


3.1    Introduction

The remit of the current project is to analyse the factors that influence bus patronage in
Great Britain, and in particular, to assess the impact of bus fare levels on bus ridership.
Analysis is to be at both the aggregate level and at more local levels. Both short- and
long-run elasticities are to be estimated. The objective is to establish not only a national
bus fare elasticity for the country as a whole, but to investigate also in greater detail
what is going on at a regional level, and if the regions differ both from each other and
from the national aggregate. It is suspected that regional specificity will play a big part
in determining local conditions (the evidence in the literature review would seem to
indicate that this is a valid hypothesis for investigation) and that a single national figure
would mask these regional effects by aggregating them all together.

It was decided to undertake the initial aggregate national and regional analyses based on
those regions for which sufficient detailed time-series data is available in Busdata 1998.
These regions are as follows: Great Britain as a whole, London, English Metropolitan
areas (together), English Shire counties (together), Scotland and Wales. A further
breakdown of the data into separate English Metropolitan areas (i.e. West Midlands
metropolitan county, Greater Manchester, Merseyside, South Yorkshire, West
Yorkshire, Tyne & Wear, and Greater London) was also possible using data provided
directly by the DETR and from the publications Transport Statistics for London: 1997
edition and Transport Statistics for Metropolitan Areas 1995.

The primary data sources are listed below:
• Economic Trends
• The Blue Book - Office of National Statistics
• Annual Abstract of Statistics
• Transport Statistics Great Britain
• Busdata 1998
• Regional Statistics
• Transport Statistics for London
• Transport Statistics for Metropolitan Areas
• DETR
• OPCS

In general, the demand for bus services is determined by the attributes of the population
and the characteristics of the competing modes. The attributes of the population include
economic factors such as disposable income and the demographic characteristics of
areas e.g. the population density, the level of urbanisation, the age structure of the
population, employment levels and car ownership. The characteristics of the modes can
be described by the generalised costs of the various alternatives: by the time and
(in)convenience costs as well as the monetary costs. For bus services, the generalised
costs can be specified in terms of fares, and service levels and quality - for instance bus


                                             20
vehicle kilometres, frequency of services, bus headways at given times of the day or
year, average headway over the year, the number of routes or distance covered and the
number of or distance between stops. If other public transport modes are available
(underground, trams, local trains, etc.) the generalised costs of these modes should also
be included. Finally, as cars provide a major alternative to bus travel for a segment of
bus users, the cost of car travel should also be taken into account.

Many of these measures are, however, meaningful only on an individual trip level. For
example, the concept of generalised costs requires information on time and
inconvenience costs as well as on monetary costs for both bus use and competing
modes, and at an aggregate national, regional or even local level such costs are
impossible to measure. Because of this we are forced to rely on monetary costs alone –
i.e., bus fares, alternative fares and the monetary costs of car ownership and use. A
similar problem concerns service level and quality. Service level is often approximated
by bus vehicle kilometres. This measure, however, does not take into account bus
capacity. If capacity has changed, for example with the introduction of minibuses,
vehicle kilometres will overestimate actual service improvements. In general, such
measures become less meaningful the higher the level of aggregation. Service quality is
even more problematic, as it is difficult to measure even for a particular operator on a
given route, and certainly impossible to measure on an aggregate level.

The variables used for the aggregate analysis are:

Dependent variables:

   Passenger kilometres travelled by bus
   Bus journeys

Independent variables:

   Bus fares
   Disposable income
   Population
   Bus vehicle kilometres
   Car ownership
   Motoring costs
   Rail fares


These are described in the following sections.




                                           21
3.2     National GB data

Data for many, but not all, of the variables of interest exist at the national level for a
considerable length of time. The time series used in the current project goes back as far
as 1970. It was decided not to investigate data before this date in order to ensure
compatibility and consistency of variable definitions. At the national level, both
passenger journeys per capita and passenger kilometres per capita are available as
independent variables. The available independent variables of interest are personal
disposable income per capita, bus fare indices, rail fare indices, car purchase cost
indices, car running cost indices, and bus vehicle kilometres per capita (this latter as a
proxy for service levels). The percentage changes in the key variables over the period
1974 to 1996 are summarised in Table 3.1.

 Table 3.1: Percentage changes in key data variables, Great Britain 1974 to 1996.
                                           % change 1974 to 1996

              Bus passenger trips per                  -47.0
              capita
              bus passenger km per                     -31.0
              capita
              bus vehicle km per capita                +6.3

              personal disposable                     +61.4
              income per capita

              bus passenger receipts                   -12.2
              (1995 prices)
              average revenue per trip                +55.5
              CFR as proportion of                    +75.0*
              receipts
              DETR bus fare index                     +69.9
              DETR rail fare index                    +74.8

              car purchase index                      -21.1
              car running index                       +12.4
              car all cost index                       -1.6
              petrol price                            -12.0

              car ownership per capita                +69.2
              car passenger km per                    +77.3
              capita

                                * % change from 1977 to 1996.


3.2.1   Bus patronage

As can be clearly seen from Figure 3.1 below, bus passenger journeys per capita fell
nationally by almost 50% over the period 1970 to 1996 from 160 journeys per capita to
almost 80 journeys per capita. Bus passenger kilometres per capita also declined



                                             22
continuously over the same period, but the decline at 31% was not as steep as that for
bus passenger journeys per capita.

 Figure 3.1: Bus passenger journeys and bus passenger kilometres per capita, GB.

                            180                                                                      1200

                            160                                           Passenger
                                                                          kilometres per capita      1000




                                                                                                            passenger kms per capita
                            140
      journeys per capita




                            120                                                                      800

                            100
                                                                                                     600
                             80
                                                           Journeys per
                             60                            capita                                    400

                             40
                                                                                                     200
                             20
                                 0                                                                   0
                                 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996



Interestingly the ratio of bus passenger kilometres to bus passenger journeys (Figure
3.2) increased steadily from 7 km/passenger journey in 1970 to just over 10
km/passenger journey in 1996. This seems to indicate that although overall bus
patronage has declined, each passenger trip is on average getting longer. However, a
word of caution is in order here. The measure of bus passenger journeys includes only
local bus services, while that of bus passenger kilometres includes both local and long-
distance bus services. Since there is no data on local bus passenger kilometres (or total
passenger journeys by bus), no conclusions concerning average trip length can be made.
In addition, since the available data on bus passenger kilometres also includes non-local
bus services, it is not an appropriate measure of bus demand for the current study.

                                 Figure 3.2: Bus passenger kilometres per bus passenger journey, GB.

                            12

                            10
 pkms per journey




                             8

                             6

                             4

                             2

                             0
                             1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996




                                                                   23
3.2.2                  Bus fares

On the aggregate level, there are two available options for defining the fare variable -
the bus fare index provided by the DETR and an average journey cost calculated using
data on bus revenues and journeys. Both of these are described below.

The revenue data used to construct the average journey cost is shown in Figure 3.3.
There are two alternatives: receipts including concessionary fare reimbursement and
receipts excluding CFR. Bus passenger receipts including CFR declined slightly (by
12%) in real terms over the period. Receipts excluding CFR (available only from 1977)
show a similar trend.

                                Figure 3.3: Bus passenger receipts, GB. 1995 prices1.

                      3500
                                                             In c lu d in g
                      3000

                      2500
                                            E xc lu d in g
     million 1995 £




                      2000

                      1500

                      1000

                       500

                         0
                         1970   1972 1974    1976 1978             1980 1982   1984 1986   1988 1990   1992 1994   1996




Figure 3.4 shows how concessionary fare reimbursement as a proportion of bus
passenger receipts (inclusive of the reimbursement) has changed over the past twenty
years. It increased from 11% in 1977 to nearly 20% in 1990 and fell to 18% in 1996.
Although it has increased substantially over the period, the greatest increase occurred
prior to deregulation. This suggests either that the proportion of concessions in total
ridership has increased and/or that concessionary subsidies have become more
generous. There is a problem, however, in comparing the pre- and post-1986 data. The
1985 Transport Act formalised the basis for calculating concessionary support. Prior to
this, concessionary reimbursement was one part of a general subsidy given to operators
and it is quite possible that some of the payments labelled as ‘general support to bus
services’ were, in practice, concessionary support – or vice versa.




1   data on CFR available as of 1977


                                                                        24
Figure 3.4: Concessionary fare reimbursement as proportion of passenger receipts,
             GB. Ratio of CFR to passenger receipts including CFR.

                  0.25


                    0.2


                  0.15
          Ratio




                    0.1


                  0.05


                     0
                     1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996



Using these data on receipts combined with the data in the previous section on bus
journeys, the average revenue per bus trip can be calculated. The resulting 'fares', in
1995 £s per journey, are shown in Figure 3.5, both including and excluding
concessionary fare reimbursement. The fare calculated by excluding CFR is clearly
lower than that including CFR, but the trends are similar.

        Figure 3.5: Bus fares, GB. Pounds per passenger journey, 1995 prices.

              0.6
                            including CFR
              0.5

              0.4
     1995 £




              0.3                                                excluding CFR

              0.2

              0.1

                  0
                  1965      1970        1975    1980      1985         1990      1995   2000



By including CFR we get an approximate measure of the average non-concessionary
fare, i.e., of the fare that would be required were there no concessions. Excluding the
CFR gives a more accurate measure of the average fare actually paid by patrons per
journey. It allows for the changing mix of ticket and passenger types (for example
between travelcard and cash fares, and between full-fare-paying and concessionary
travellers). For this reason, it is a more appropriate fare measure for the current study,
since the only patronage variable available includes trips by all fare types - both
concessions and non-concessions.




                                                   25
Figure 3.6 shows the relationship between these two constructed fare variables and the
DETR index of bus fares in Great Britain (in 1995 prices). All three are shown in index
form with 1977 set equal to 1. Although the three 'fares' show a broadly similar
development, there is a considerable difference in the rates of growth over time. The
DETR bus fare index increased by 48% over the period, while both constructed fares
increased by somewhat less - the fare excluding CFR by 22% and the fare including
CFR by 32%. Since deregulation, the development of the three fare measures has been
roughly similar, with all of them increasing by 18% to 19% since 1986. The difference
between the rate of increase of the three price series is most evident prior to
deregulation. The fare including CFR rose by 11%, excluding CFR by 3% and the bus
fare index by 24%. The difference in the rate of growth of the two indices constructed
from receipts results from the increase in the proportion of CFR prior to deregulation
noted above in Figure 3.4. As the proportion of CFR increases, the average fare paid by
bus users (i.e. the fare excluding CFR) increases less rapidly than the non-concessionary
fare (i.e. the fare including CFR).

                                   Figure 3.6: Bus fares, GB. 1995 prices. Index 1986 = 1.0.

                    1.2


                   1.15


                    1.1


                   1.05
                               Fare excluding CFR
                     1
  Index 1986=1.0




                   0.95
                                Fare
                    0.9       including
                                CFR                 Bus fare index

                   0.85


                    0.8


                   0.75


                    0.7
                          1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996




The DETR bus fare index is constructed from information on fare changes from a panel
of operators who account for 85% of passenger receipts on local services. In theory, the
index is intended to measure the average charge to the fare-paying passenger. As such,
it should be closer to the constructed fare excluding CFR. This is actually the case for
the larger part of the post-deregulation period. The reason for the divergence between
the fare index and the constructed fare excluding CFR prior to deregulation is unclear. It
may partially be explained by the fact, noted in Transport Statistics Great Britain, that
'changes in the generosity of concessionary fare schemes may not always be included in
the fare changes supplied by operators'. As it appears that such changes were most
evident prior to deregulation (see Figure 3.4 above), this would account for the greater
increase in the bus fare index during that period. However, the bus fare index also




                                                                            26
increases more rapidly than the average full fare (including CFR), which cannot be
explained by this omission.


3.2.3           Service

As mentioned earlier, the only available measure of bus service is bus vehicle
kilometres. This is shown in Figure 3.7 in per capita terms. Two distinct periods are
evident - pre- and post-deregulation of the bus industry outside London. Prior to
deregulation, between 1970 and 1985, per capita bus vehicle kilometres declined
steadily, by 22% over the period. This trend was reversed after deregulation, so that bus
vehicle km per capita increased by nearly 25% between 1985 and 1996. For the period
as a whole, the result has been a slight decline of a little over 3%.

                             Figure 3.7: Bus vehicle kilometres per capita, GB.

                     55
                     50
                     45
                     40
                     35
        kms/capita




                     30
                     25
                     20
                     15
                     10
                      5
                      0
                      1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996



As a bus-kilometre is defined as a bus running 1 kilometre in passenger service and
makes no allowance for size of the vehicle, it is therefore a rather poor measure of
capacity. After deregulation there was a rapid increase in mini- and midi-bus operations,
particularly in the period 1986-1988, so that it is likely that total capacity has risen
much less than bus kilometres, and in some places not at all.

3.2.4           Other variables

The demand for bus services is also influenced by income and the availability costs of
other transport alternatives, particularly the private car. Since 1970 personal disposable
income per capita has increased by over 85% in real terms and car ownership per capita
has doubled (Figure 3.8).




                                                     27
Figure 3.8: Personal disposable income per capita, 1995 prices, and car ownership
                           per capita in Great Britain.

                                    10000                                                                  0.4
                                     9000                                                                  0.35
        income per capita, 1995 £



                                     8000                      Cars per capita                             0.3
                                     7000




                                                                                                                  cars per capita
                                     6000                                         Income per capita        0.25

                                     5000                                                                  0.2
                                     4000                                                                  0.15
                                     3000
                                                                                                           0.1
                                     2000
                                     1000                                                                  0.05

                                        0                                                                   0
                                        1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996




These changes have been accompanied by a modal shift from bus to car. As illustrated
in Figure 3.9, car passenger kilometres per capita doubled over the same period, while
bus passenger kilometres declined by 30%.

   Figure 3.9: Passenger kilometres per capita by bus and car in Great Britain.

                                    12000

                                    10000
                                                                 car
      pkms per capita




                                     8000

                                     6000

                                     4000
                                                                                       bus

                                     2000

                                        0
                                        1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996



Relative prices by different modes have also changed substantially over the period.
Figure 3.10 shows rail fare indices and motoring cost indices, along with the DETR bus
fare index. Both bus and rail fares show a similar development and have increased
substantially in real terms (by 70% and 80% respectively) from 1974 to 1996. In
contrast, car purchase costs have declined by 21% and car running costs have increased
by 12%, so that overall motoring costs have remained relatively stable. There has thus
been a substantial reduction in the cost of motoring (whether defined as purchase,
running or total motoring costs) relative to public transport fares.




                                                                         28
                 Figure 3.10: Bus fare, rail fare and motoring indices, GB. 1995=100.
         160.0


         140.0
                                                          Car purchase costs

         120.0
                            All motoring costs

         100.0
                             Car running costs
 Index




          80.0       Bus fares


          60.0
                      Rail fares

          40.0


          20.0


           0.0
              1974       1976      1978     1980   1982       1984     1986    1988   1990   1992   1994   1996




3.3          Regional data

In the annual publication Bus and Coach Statistics Bulletin, the DETR aggregates the
data received from operators according to different regions in Great Britain (data for
individual operators are regarded as confidential). The regions are as follows:

Greater London        the area covered by the former Greater London Council, and
                      the responsibility of London Transport under the 1984 London
                      Regional Transport Act;
English Metropolitans the six former metropolitan counties in England, covered by
                      the PTA’s/PTE’s (Passenger Transport Authorities/Passenger
                      Transport Executives);
English Shires        the rest of England, including large rural areas. However, most
                      bus use within them is concentrated in urban areas including
                      cities up to the size of Bristol (about 400, 000 population).
Scotland              all urban and rural areas in Scotland;
Wales                 all urban and rural areas in Wales.

It was decided to retain this classification in the initial analyses for simplicity of data
collection and ease of comparison with other published work.

The available time series for regional data is considerably shorter than that for national
data for most variables of interest. This is particularly true for data relating to fare


                                                            29
indices and operating costs, which are available only from 1985 for most regions (and
only from the early 1990’s onwards for Wales). Greater London is a special case in that
data has been collected over a longer period than for other regions. The dependent
variable in all of the analyses at regional and individual metropolitan area levels is bus
passenger journeys per capita. Data on bus passenger kilometres per capita are not
published at the regional level.

Table 3.2 summarises the percentage changes in bus ridership (defined as annual bus
passenger journeys per capita), bus vehicle kilometres per capita, household disposable
income per capita, the DETR bus fare index and a calculated revenue per journey in real
prices over the period 1985 to 1996 in the regions defined above. The development of
these variables over time is illustrated in the figures that follow.

    Table 3.2: GB regions. Percentage changes in relevant variables 1985 to 1996.
Area                      Bus            DETR            Average fare     Household       Bus vehicle
                       passenger       fare index         per journey     disposable      kilometres
                    trips per capita                      exc. CFR2       income per       per capita
                                                         (1995 prices)       capita
                                                                         (1995 prices)

Metropolitans            -39.4           +57.8              +52.4           +36.9            +21.4
English Shires           -24.3           +14.0              +13.5           +37.7            +30.4
Scotland                 -30.7           +11.1              +13.8           +42.9            +28.6
Wales                    -23.4            n/a3               -1.9           +39.2            +21.4
Greater London           +3.7            +37.9              +20.3           +42.8            +20.5

Great Britain            -25.6           +26.2              +21.8           +38.4            +24.9


3.3.1   Bus patronage

The trend in passenger journeys per capita in Figure 3.11 shows that for all regions
except London there has been a substantial and continuous decline ranging from 24% in
the case of the Shire counties of England, up to 39% for the English Metropolitan areas.
Passenger journeys per capita in London have exhibited more fluctuation than in any
other region, but overall there has been a 4% increase over the 11 years.




2 Data on revenues for regions outside London exist only as of 1985/86.
3 Data on bus fare indices for Wales has been routinely made available only since the early 1990’s. This
is insufficient to yield any useful information for the present analysis and is thus omitted.


                                                    30
                                              Figure 3.11: Bus passenger journeys per capita by region.
                                   200
                                   180                                                               London
   passenger journeys per capita




                                   160
                                   140                                                                   English Metropolitan areas
                                   120
                                                                  Scotland
                                   100
                                    80
                                    60
                                                                                                   Wales
                                    40
                                    20                     English Shire counties

                                     0
                                           1985     1986   1987    1988    1989     1990   1991   1992   1993   1994   1995   1996



3.3.2                                    Bus fare

The following figures show the changes in real fares in two forms: (a) the DETR’s price
index, based on returns from a sample of operators; and (b) the average fare per trip
(excluding CFR). In Figure 3.12, fares have risen in all areas, but more so in London
and the English metropolitan areas than in Scotland and the English Shire counties.

                                    Figure 3.12: Bus fare indices by region. DETR bus fare index. 1995=100.
                                   110

                                   100                                   English Shire counties
                                              Scotland

                                    90
                                           English Metropolitan areas
 fare index




                                    80
                                                                      London
                                    70

                                    60

                                    50
                                           1985     1986   1987   1988     1989   1990     1991   1992   1993   1994   1995   1996


From Figure 3.13 average real bus fares excluding CFR are twice as high in the English
Shire counties and Wales than in London and the English Metropolitan areas. Over the
period, fares have increased everywhere except Wales. The greatest increase occurred in
the English Metropolitan areas (52%), followed by London (20%), while Scotland and
the English Shire counties experienced a relatively smaller increase (13%).


                                                                                     31
                                                     Figure 3.13: Passenger fares by region excluding CFR (1995 prices).

                                                0.7

                                                0.6                                              English Shire counties
                  pounds per journey, 1995 £




                                                0.5
                                                                                             Wales
                                                0.4                                                                     English Metropolitan areas
                                                                 Scotland

                                                0.3
                                                                                                                                     London
                                                0.2

                                                0.1

                                                     0
                                                          1985   1986   1987    1988     1989    1990     1991   1992    1993      1994    1995     1996



The differences in fare levels are explained partially by differences in concessions. This
is illustrated in Figure 3.14, which shows concessionary fare reimbursement as a
proportion of passenger receipts including CFR. The regions with the highest fares have
the lowest proportion of CFR. In most areas the changes over the period have been very
small. The exception is London, which shows a reduction from 28% to 22%.

                              Figure 3.14: Concessionary fare reimbursement as proportion of passenger
                                                 receipts including CFR, GB regions.
                                               0.3



                                  0.25
                                                                                                                     English Metropolitan areas
  Ratio of CFR to receipts




                                                                                                 London
                                               0.2

                                                                                                                        Scotland
                                  0.15
                                                                        English Shire counties

                                               0.1

                                                                                                             Wales
                                  0.05



                                                0
                                                         1985    1986   1987    1988     1989    1990     1991   1992      1993     1994     1995    1996




3.3.3                                            Service




                                                                                                 32
As for GB as a whole, the only available measure of bus service is a rather crude proxy
- bus vehicle kilometres per capita. This is shown for each region in Figure 3.15.
Clearly, there is a considerable variation across regions. The English Shire counties
show the lowest per capita bus service, followed by Wales. These two regions also have
the lowest bus patronage per capita (see Figure 3.11), so this is not surprising.
Interestingly, Scotland shows the highest service level, followed by the English
Metropolitan areas and then by London. This is just the opposite of patronage: as shown
in Figure 3.11, per capita patronage is highest in London, followed by the Metropolitan
areas and then Scotland.

All regions except Wales show a small overall increase over the period with the largest
increases in Scotland, the English Metropolitan areas and London.

                               Figure 3.15: Bus vehicle kilometres per capita by region.
                    80

                    70                                   Scotland

                    60
bus km per capita




                    50                                                            London
                            English Metropolitan areas
                    40
                                                                     Wales
                    30

                    20                                              English Shire counties

                    10

                     0
                         1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996




3.3.4                    Income

There is significant regional variation in real household income per capita (Figure
3.16).. Income is lowest in the English Metropolitan areas and Wales, and highest in
London. The Shire counties and Scotland have similar income levels, and lie in
between. Real income has increased by between 35% and 45% in all regions, the largest
increase being in Greater London and the lowest in English Metropolitan areas, 43%
and 37% respectively.



                         Figure 3.16: Real household disposable income per capita by region.




                                                               33
  11000

  10000
                                                             London
                                                                           English Shire counties
     9000
                                                                                            Scotland
     8000                                                                           Wales
 1995 £




     7000                                                                English Metropolitan areas

     6000

     5000

     4000
             1985   1986    1987     1988   1989   1990    1991   1992   1993   1994    1995    1996



3.4         Individual English Metropolitan areas

The DETR collects data on 6 Metropolitan areas in England outside of London. They
are:
    ∗ Greater Manchester
    ∗ Merseyside
    ∗ West Midlands Metropolitan County
    ∗ South Yorkshire
    ∗ West Yorkshire
    ∗ Tyne and Wear

The overall changes for the period are summarised in Table 3.3 and the data are
illustrated in the figures that follow.

    Table 3.3: Metropolitan areas. Percentage change in relevant variables 1987 to
                                        1996.
Area                           Bus            DETR          Average      Household           Bus vehicle
                           passenger        fare index      fare per     disposable         kilometres per
                            trips per                       journey      income per             capita
                              capita                       excl. CFR        capita

Tyne and Wear                -31.5             n/a          +59.1           +24.1               +5.2
Merseyside                   -23.7             n/a          +3.6            +24.0               +24.8
Manchester                   -31.5             n/a          +12.7           +32.0               +4.6
South Yorkshire              -37.2             n/a          +86.4           +19.4               +29.2
West Yorkshire               -32.1             n/a          +25.0           +24.6               +3.6
West Midlands                -17.8             n/a           -0.6           +29.4               +16.4

Greater London                -1.0            +33.1         +25.4           +35.5               +19.2

Great Britain                -20.5            +16.6         +17.5           +21.7               +11.4

3.4.1       Bus patronage



                                                      34
Figure 3.17 shows bus passenger journeys per capita for each of the 7 Metropolitan
areas. The variation among them is apparent. For example, in 1996, there are nearly 200
journeys in London compared to half this number in Greater Manchester. It is clear that
there has been a significant drop in bus journeys per capita in most areas in the 9-year
period. It has been most dramatic in South Yorkshire at 37% with West Yorkshire, Tyne
& Wear and Greater Manchester also having a substantial decline at about 32% each.
Merseyside and the West Midlands Metropolitan County exhibit a somewhat smaller
decline (24% and 18% respectively). In contrast, London displays only a marginal
decline of 1%. It is clear from these figures that aggregation, even of similar areas, can
mask wide variation between individual areas.


 Figure 3.17: Bus journeys per capita, individual Metropolitan areas in England.

                            300                                             West Midlands
                                                                            Greater Manchester
                                                                            Merseyside
                            250                                             South Yorkshire
  bus journeys per capita




                                                                            West Yorkshire
                                                                            Tyne & Wear
                            200                                             London


                            150


                            100


                             50
                                  1987   1988   1989   1990   1991   1992    1993      1994      1995   1996



3.4.2                         Bus fare

As the DETR does not calculate a bus fare index for each of the Metropolitan areas, the
fare variable must be constructed from revenue data. As argued previously, the most
appropriate fare measure is average revenue (excluding CFR) per journey. Since the
published data do not contain information on concessionary fare reimbursement for the
individual metropolitan areas, these have been obtained from the STATS100 data.

The constructed fares are shown in Figure 3.18 for each of the individual Metropolitan
areas. Clearly, Greater Manchester stands out as having the highest fares over the entire
period on this basis. The lowest change over time is in Greater London (20% increase).
The biggest increases occurred in South Yorkshire and Merseyside (202% and 119%
respectively), and reflect the particular operating conditions of these areas. In South
Yorkshire fares were held at their nominal level for a 10-year period from 1976 to 1985
by increasing the level of subsidy (leading to a real fare reduction of 59% by autumn
1984). In connection with local government reorganisation and national government
public expenditure policy, 1985/86 saw the first and largest of several fares increases
implemented (225%). Merseyside experienced something similar.




                                                               35
  Figure 3.18: Bus passenger fares in English Metropolitan areas excluding CFR.

                                  0.7


                                  0.6


                                  0.5
     pounds per journey, 1995 £




                                  0.4

                                                                                                           West Midlands
                                  0.3                                                                      Greater Manchester
                                                                                                           Merseyside
                                                                                                           South Yorkshire
                                  0.2
                                                                                                           West Yorkshire
                                                                                                           Tyne & Wear
                                  0.1                                                                      London


                                   0
                                          1987    1988      1989     1990       1991     1992    1993     1994     1995         1996




3.4.3                                   Service

Figure 3.19 illustrates bus vehicle kilometres per capita. Service intensity is clearly
lowest in London. The largest increases are in South Yorkshire, Merseyside and Greater
London (29%, 25% and 21% respectively) followed by the West Midlands at 16%. The
increases in the other areas are much smaller - of the order of 2% to 3%.

           Figure 3.19: Bus vehicle kilometres per capita for English Metropolitan areas.

                                  100

                                                                                                        Tyne & Wear
                                   90
 bus vehicle kms per capita




                                   80
                                                                            South Yorkshire

                                   70
                                                                                          Merseyside
                                                    West Yorkshire
                                   60

                                   50                     Gtr Manchester

                                          West Midlands                                                               London
                                   40
                                          1987    1988     1989     1990       1991    1992     1993    1994     1995     1996



3.4.4                                   Income




                                                                                  36
The changes in real disposable household income per capita for the different
Metropolitan areas can be seen in Figure 3.20. Greater London enjoys consistently
higher disposable income than any other area. Disposable income levels in all other
metropolitan areas in England are relatively close together. The differential between
Greater London and the other areas has grown by about 3% over the period 1985/86 to
1996/97 going from 26% to 29%. Growth in household disposable income per capita is
not similar in all areas. Tyne and Wear and South Yorkshire experienced the lowest rate
of growth over the ten years (at 23% and 30% respectively), while in all other
metropolitan areas, growth was of the order of 38% to 44%. London and the West
Midlands Metropolitan County exhibited the largest growth at about 43% each.

Figure 3.20: Real disposable household income per capita in English Metropolitan
                                     areas.

          12000

          10000

           8000
 1995 £




                                                                   West Midlands
           6000
                                                                   Greater Manchester
                                                                   Merseyside
           4000                                                    South Yorkshire
                                                                   West Yorkshire
           2000                                                    Tyne & Wear
                                                                   London
              0
                  1987   1988   1989   1990   1991   1992   1993   1994     1995        1996




                                               37
4. AGGREGATE ELASTICITIES


4.1    Introduction

This section summarises the results obtained on the basis of the aggregate data
described in the Chapter 3 – the national GB data, the regional data and the individual
Metropolitan areas. For ease of readability, only the bus fare and other relevant
elasticities are presented here. The full estimation results, goodness-of-fit measures,
statistical tests, etc. are given in the Statistical Appendix (B), and are only referred to in
the text. Similarly, the models employed are described only cursively. The full
specification of the econometric models and the derivation of the elasticities are
presented in the Technical Appendix (A), and the relevant sections are referred to in the
text.

Passenger journeys per capita is the dependent variable for most of the estimations. In
addition, for estimation at the national level, passenger kilometres per capita are used as
an alternative dependent variable in separate estimations. A number of different ‘fare’
measures are used in the separate estimations, depending on availability. The bus fare
index supplied by the DETR, the calculated average fare per journey (or passenger
kilometre) based on receipts excluding concessionary fare reimbursement (CFR), and
the calculated fare per journey (or passenger kilometre) including CFR. As argued
previously, the fare calculated excluding CFR is the most appropriate, and that
including CFR is only used for the sake of comparison. The income variables used are
household disposable income per capita in the case of regional level analysis and
personal disposable income per capita at the national level. All price and income
variables are converted into real terms using the Retail Price Index.


4.2    Results at the national level - Great Britain as a whole

Both bus passenger journeys per capita and bus passenger kilometres per capita are
available for Great Britain as far back as 1970 and are used as the dependent demand
variable in separate regressions. The bus fare index goes back to 1974, the calculated
price per journey including concessionary fare reimbursement (CFR) back to 1970, and
the calculated price per journey excluding CFR back to 1977. Each is used separately as
the independent price variable. The income variable used is personal disposable income
per capita, which is available back to 1970. The basic model estimated is:

                            Bus demand = f(bus fare, income)

No measure of bus service is used for the national models. Although we have a measure
of bus vehicle kilometres, this is not a meaningful measure of service level or quality at
such an aggregate level.

The data used for the aggregate GB analysis are shown in Section 3.2. It is clear that
there is little annual variation in the data, and that the majority of the variables either


                                             38
  rise (bus fares, income and car ownership) or fall (bus passenger kilometres, bus
  journeys) more-or-less continuously over the observation period. The evidence of non-
  sationarity of the variables (see Table B.1.1) suggests that cointegration techniques are
  appropriate. The dynamic representation is based on an error-correction model and an
  Engle-Granger 2-step procedure is used for the estimation. These are described in
  Section A.3 of the Technical Appendix. The estimated models and statistical tests are
  presented in Tables B.1.2 to B.1.7 in the Statistical Appendix. The short- and long-run
  elasticities are reproduced in Table 4.1 below.

    Table 4.1: National GB bus fare elasticities. Error-Correction constant elasticity
                                        models.
                                Journeys per capita                    Passenger kilometres per capita
                              Fare             Income                      Fare             Income
                        Short    Long     Short     Long             Short    Long     Short     Long
                        run      run      run       run              run      run      run       run

Fare index              -0.34      -0.88       0.28**      -0.45     -0.19    -0.71    0.05**    -0.15
Fare per journey -0.33*            -0.62       0.41*       -0.80     -0.18    -0.43    0.16*     -0.63
excluding CFR
Fare per journey -0.40             -0.95       0.18**      -0.57     -0.19    -0.92    0.04**    -0.54
including CFR
  Note: * not significant at the 5% level, but significant at the 10% level
       ** not significant at the 10% level.



  As discussed earlier, the three variables used for the bus fare are rather different. They
  all yield rather similar short-run fare elasticities (-0.3 to –0.4 for journeys and –0.2 for
  passenger kilometres), but show a greater variation in long-run elasticities (-0.6 to –1.0
  for journeys and –0.4 and –0.9 for passenger kilometres). The fare elasticities are
  smallest using the fare per journey excluding CFR and greatest using the fare per
  journey including CFR, while those based on the bus fare index lie in between. One
  reason for this may have to do with the differences in observation period; fare excluding
  CFR is available for a shorter period (1977-) than either the fare index (1974-) or the
  fare including CFR (1970-). However, this was found not to be the case. Estimation
  using the latter price variables for the shorter time period (1977-96) shows the results to
  be quite stable. The explanation must therefore be found in the definitions of the price
  variables. As argued earlier, the fare per journey including CFR is the least appropriate
  measure, so the results based on it are the most questionable.

  There is a similar variation in the long-run income elasticities obtained using the
  different fare measures, but these are in all cases negative, suggesting that bus travel is
  an inferior good, a result supported by the majority of bus travel demand studies. The
  short-run income elasticity, however, is found to be positive in all models, although it is
  not statistically significant from zero at the 5% level in any instance. It is, however,
  significant at the 10% level in the models using the fare calculated using receipts
  excluding CFR. An income elasticity which is positive (or zero) in the short run and
  negative in the long run is not unreasonable for bus demand. Although income rises
  may lead to an increase in (or have no effect on) demand in the short run, in the longer



                                                       39
term, rising income leads to increased car ownership (and car use) thus having a
negative impact on bus patronage.

There is also a difference between the elasticities estimated with the two measures of
bus demand. In general, both the fare and income elasticities are smaller (in absolute
value) for passenger kilometres than for journeys. This is explained by the different
development of the two variables over the observation period. As shown in Figure 3.2,
these two series indicate an implicit increase in average journey length from 7 to 10
kilometres. The interpretation of the differences in elasticities can be shown from the
results using the fare index. Since passenger kilometres is equal to journeys times
average journey length, the fare elasticity of passenger kilometres, ε F , is equal to the
                                                                       K


fare elasticity of journeys, ε F , plus the fare elasticity of journey length. Since
                                J


ε F > ε F , ε F > 0, so that increasing fares lead to increasing journey lengths. A similar
  J     K     L


relation holds for the income elasticities, increasing income leads to a reduction in
journeys and total passenger kilometres, but to an increase in average journey length.
Whether or not these results are meaningful will depend on the validity of the measure
of passenger kilometres.

Cross-price elasticities

Of other variables which can be thought to influence bus use, only motoring costs are
strictly meaningful at the national level. The availability of alternative public transport
modes is too location specific to be meaningful at such an aggregate level. In order to
investigate the effects of motoring costs on bus patronage and the effects of bus fares on
car use, a structural model of bus and car transport was estimated. This involves
estimating four equations simultaneously:

       Bus passenger kilometres = f (fares, income, car ownership, motoring costs)
       Bus journeys = g (fares, income, car ownership, motoring costs)
       Car ownership = h (fares, income, motoring costs)
       Car passenger kilometres = k (fares, income, car ownership, motoring costs)

The structural approach permits the investigation of the process through which the
independent variables influence bus patronage and car use and the estimation procedure
allows us to take into account the interactions between the two, and between each of
them separately with car ownership. The full structural model and the derivation of the
elasticities are presented in Section A.4. of the Technical Appendix.

The bus fare index is used for the price variable. The dynamics are represented by an
error-correction model, and weighted 3-stage least squares techniques used for
estimation. The estimation results are reported in Section B.2 in the Statistical Appendix
and the resulting elasticities are presented in Table 4.2 below. All reported elasticities
are significant at at least the 5% level.

Firstly, car ownership has a substantial impact on bus patronage (but only in the long
run), and on car use (the effect here appears to be instantaneous). Regarding bus fares,
we find that these have a substantial negative impact on bus patronage and a smaller,


                                            40
but significant, positive impact on car ownership and use in the short run. As expected,
the effects are much greater in the long run. The estimated long-run own-price
elasticities for bus passenger kilometres and journeys (-0.9 and –1.1, respectively) are
comprised of a direct effect (-0.6 and -0.8) and an indirect effect through car ownership
and use (-0.3 in both cases). The impact of bus fares is greater on journeys than it is on
passenger kilometres, confirming our earlier results indicating that as fares increase,
journey length increases. The long-run cross-price elasticities for car ownership and use
are, as expected, smaller, but do suggest that bus fares have a significant influence on
car travel.

The short- and long-run income elasticities are shown in the next two rows. For both
bus passenger kilometres and journeys, the short-run elasticity is positive, confirming
our earlier results. The long-run elasticities, however, differ in sign for the two measures
of bus patronage – income has a positive, but small effect on passenger kilometres and a
negative impact on journeys. The long-run effects are comprised of a direct positive
effect and an indirect negative effect through car ownership.

The final rows show the impact of motoring costs – the cross-elasticities for bus demand
and the own-elasticities for car ownership and use. In the short-run motoring costs have
no significant effect on bus patronage, but, as expected, do have a negative impact on
car ownership and travel. In the long run, however, these costs affect both bus and car
use. The cross-elasticities for bus patronage are small, -0.33 and –0.37, for passenger
kilometres and journeys, respectively. This is solely an indirect effect through car
ownership.

 Table 4.2: Elasticities estimated on the basis of a structural model of bus and car
                                         use.
                     Bus passenger kms Bus journeys Car ownership Car passenger kms

  Car ownership
     Short run                                0                 0                    0.94
     Long run                            -0.73              -0.64                    0.81
  Bus fare
     Short run                           -0.31              -0.52   0.19             0.18
     Long run                            -0.94              -1.08   0.42             0.34
  Income
     Short run                            0.14               0.38   0.37             0.14
     Long run                             0.07              -0.26   0.56             0.70
  Motoring costs
     Short run                                0                0    -0.38           -0.44
     Long run                             0.37              0.33    -0.51           -0.96
  Note: All elasticities are significant at the 5% level.

The bus fare and income elasticities compare reasonably well with those based on the
single-equation models shown in Table 4.1 using the same fare variable, the fare index.
The fare elasticities, however, are slightly higher in the structural model.

Variation in elasticities



                                                     41
All of the results presented above are based on models which constrain the elasticities to
be constant over time and for all fare levels and changes. This assumption was tested by
the estimation of models based on different functional forms, which allow the elasticity
to be related to the fare level and/or to the level of bus patronage. In all cases, the
constant elasticity model was preferred to the alternative specifications on the basis of
statistical tests. Statistical tests were also performed to investigate the stability of the
estimated elasticities over time, and in all cases, stability could not be rejected. There is
thus no evidence that the elasticities vary either over time or with the level fare or bus
patronage.

Asymmetry of response

Models allowing for asymmetric response of bus patronage to rising and falling prices,
based on the price-decomposition techniques described in Appendix A.5 were estimated
for the single equation bus fare models. In no case was there any significant evidence of
asymmetry. This is hardly surprising, however, in view of the development of bus fares
over the period. As shown in Figure 3.5 earlier, these were generally rising over time,
with very few instances of falling fares on an annual basis. With so few observations of
instances of fare reductions it is impossible to statistically differentiate between the
impact of rising versus falling fares.


4.3    Estimation results for GB regional data

The data for the GB regions described in Section 3.3 cover a much shorter time period
than those for GB as a whole. Both demand and fare variables are available only from
1985 to 1996 – 12 annual observations. Given this limited data sample, we could not
expect to estimate fare elasticities with any degree of certainty for the individual
regions. For this reason, we have adopted another approach – instead of estimating
models for each region separately, we have pooled the regions to estimate a combined
time-series cross-section model. This method increases the number of observations
available, but necessitates some constraints on the parameters for the different regions.
As earlier, a dynamic error correction model is used. The pooled model is described in
Appendix A.6.

The dependent variable used is bus passenger journeys per capita. The independent
variables are bus fares, household disposable income per capita, bus vehicle kilometres
per capita and regional dummy variables. Two different price variables were used in
separate specifications - the calculated fare per passenger journey excluding CFR, and
the bus fare index from published statistics where available. The fare per journey
including CFR is not used since it is a poor measure of fares actually paid. Bus vehicle
kilometres is used as a measure of service supply. Although this is not ideal, it makes
more sense as a service measure on the regional than on the national level and the
variation among regions in service is clearly an important factor in variation in
patronage.

              Bus demand = f(bus fare, service, income, regional dummy)



                                             42
Two different functional specifications were estimated: (a) a “constant elasticity” model
in which all variables were specified in natural logarithms, and whose coefficients yield
the elasticities of interest directly; and (b) a model in which all variables were in natural
logarithms except the price (fare) variable which was specified in level terms. In the
latter, the elasticity is not constant but increases with the price level (bus fare).

Two variants of the constant elasticity model were estimated. One in which the fare,
income and service elasticities are constrained to be the same for all regions, and one in
which the fare elasticities are allowed to vary regionally. Because of the limited number
of observations for each region, income and service elasticities are constrained to be the
same for all regions. The estimated models are reported in Section B.3 in the Statistical
Appendix and the resulting elasticities are shown below in Table 4.3.

The elasticities in bold are for the specifications in which the elasticities are constrained
to be equal for all regions. We would expect these to be roughly similar to those
estimated on the basis of the aggregate national data presented in Table 4.1 above.
Using the fare index (fare per journey), the fare elasticities are –0.5 and –0.9 (-0.2 and –
0.8) for the regional model, compared to –0.4 and –0.9 (-0.3 and –0.6) for the aggregate
model. In both cases the fare index indicates a slightly greater estimated price
sensitivity. Again, the long-run fare elasticities are 2 to 3 times the short-run elasticities.
The regional and aggregate models are less in agreement concerning the income
elasticities. Both indicate a substantial negative income elasticity in the long run,
although the magnitude is greater in the regional models. The regional model, on the
other hand, supports a negative (but small) short-run income elasticity as well, in
contrast to the positive values suggested in the aggregate model. However, the majority
of the short-run income elasticities are not statistically significant.

    Table 4.3: Estimated elasticities based on pooled regional data and constant
                        elasticity Error-Correction Model.
                              Fare elasticity             Income elasticity            Service elasticity
                          Short run   Long run         Short run   Long run          Short run Long run
Fare Index
  All regions                  -0.49           -0.88       -0.07**         -0.64        0.26           0.36
  London                       -0.20**          0.18**     -0.03**         -0.46        0.33          0.25
  Metros                       -0.60           -0.98         “ “            “ “         “ “            “ “
  Shires                       -0.76           -1.67         “ “            “ “         “ “            “ “
  Scotland                     -1.22**        -0.92**        “ “            “ “         “ “            “ “
  Wales                         2.00**          0.43**       “ “            “ “         “ “            “ “
Fare per journey
excluding CFR
  All regions                  -0.22           -0.81        -0.27          -1.13        0.43           0.81
  London                       -0.13**          0.41**      -0.29          -1.01        0.46          0.69
  Metros                       -0.57           -0.76         “ “            “ “         “ “            “ “
  Shires                       -0.12           -1.08         “ “            “ “         “ “            “ “
  Scotland                     -0.31**         -0.57         “ “            “ “         “ “            “ “
  Wales                        -0.26**          0.35**       “ “            “ “         “ “            “ “
Note: All elasticities are significant at the 5% level except those indicated by ** which are not significant
at the 10% level.




                                                    43
The regional fare elasticities estimated using the two fare measures are also shown in
the table. Clearly the results are much poorer. In the case of London and Wales the
values are positive, but not statistically significant. For the other regions, the results are
more reasonable, and generally statistically significant. It appears that bus patronage is
most price-sensitive in the Shire counties and least price-sensitive in Scotland, with the
Metropolitan areas falling in between.

Regarding the service elasticities, we find that these are positive in all cases, as
expected. These are highly sensitive, however, to the definition of the fare variable.
Using the fare per journey, the service elasticity is twice that using the fare index. The
reason for this may be the simultaneity between vehicle kilometres and the fares.
Theoretically, vehicle kilometres are a measure of supply, and in a competitive market,
supply is not exogenous, but is a function of prices (fares). Ideally, this simultaneity
should be taken into account in the model specification. This, however, would require
more information than is available.


Relationship between fare elasticity and fare level

As with the aggregate data, other functional specifications were estimated to investigate
the relationship between the fare elasticity and the fare level. In the case of the regional
data, there does seem to be a significant relationship. The specific functional form and
the derivation of the elasticities are given in Appendix A.7. The econometric results are
shown in Section B.4 in the Statistical Appendix. Here, we find that the semi-log model
is preferred statistically to the double-log (constant elasticity). In the semi-log model,
the fare elasticity is directly proportional to the fare level. Since fares differ across
regions as well as over time this model results in different elasticities for different
regions. The elasticities calculated at the minimum and maximum average fares for all
regions are reported in Table 4.4. These are – as would be expected – quite similar to
those for all regions using the constant elasticity model and fare per journey variable
reported in Table 4.3. Since average fares do not change very much over time, the range
of elasticities is rather small.

  Table 4.4: Average elasticities based on pooled regional data and variable fare
           elasticity EC model. Fare: fare per journey excluding CFR.
           Fare elasticity               Income elasticity             Service elasticity
    Short run          Long run       Short run      Long run       Short run     Long run
 -0.12 to –0.15    -0.70 to –0.86      -0.29           -1.04          0.46           0.74



Fares do differ considerably for the different regions, however. As shown in Figure 3.13
in Section 3.3, fares measured in pence per journey are twice as high in the Shire
counties and Wales as they are in London and the Metropolitan areas, while those in
Scotland lie in between. The favoured functional specification implies that the elasticity
is related to the fare level – the higher the fare level, the more elastic is demand. Thus
the elasticities will be greater for those regions with higher fares – the Shires and Wales
– than for the lower fare regions. The calculated elasticities for the individual regions
are shown in Figure 4.1.


                                             44
  Figure 4.1: Regional fare elasticities for the period 1985-1996 based on variable
      elasticity EC model. Short run (dotted lines) and long run (solid lines).


            0.0

           -0.2
                  London     Metropolitan
           -0.4              Areas
                                                     Scotland
                                          Shires
           -0.6                                                   Wales

           -0.8

           -1.0

           -1.2


For London, the short-run elasticity is about –0.15 and the long-run elasticity increases
from about -0.6 to –0.7 over the period (as fares rise). The elasticities for the other
Metropolitan areas are of a similar order of magnitude. Bus patronage is considerably
more fare-sensitive in the Shires and Wales – with a short-run elasticity of about –0.2
and a long run elasticity of just in excess of –1.0 (in absolute value). Scotland lies
between the other four regions, with a short-run fare elasticity of slightly under –0.2,
and a long-run elasticity of between –0.8 and –0.9 over the period.

The regional elasticities shown in the figure do not agree with those estimated from the
constant elasticity model with individual regional fare elasticities shown in Table 4.3.
Many of the elasticities reported in Table 4.3, however, are not significantly different
from zero – those for London, Scotland and Wales. For the two remaining regions – the
Shires and Metropolitan Areas, both models suggest that bus patronage is significantly
more fare-sensitive in the Shire counties. This is not unreasonable. With bus services
being generally more convenient in more urban areas and car use less advantageous in
terms of time and costs, one would expect the bus fare to be less important in
determining demand.

Asymmetry of demand with respect to rising and falling fares

As on the aggregate national level, bus fares at the regional level increase more-or-less
continually over the observation period, and there are few examples of falling prices
(see Figure 3.12 and Figure 3.13 above). Because of this limited price variation,
attempts to estimate asymmetric response showed no significant asymmetry.



                                            45
4.4      Estimation results for individual English Metropolitan areas

The available data for the seven individual English Metropolitan areas are shown in
Section 3.4. The data sample is rather limited, with all variables being available only for
the 9-year period from 1987 to1996. The demand variable is journeys per capita and the
fare measure is that constructed using receipts excluding CFR per journey. As for the
regional data, the limited number of observations for the individual areas requires a
pooled approach. Two specifications are estimated – one constraining all coefficients to
be the same across areas and one in which the coefficients of the fare variable, and the
price elasticity, is area specific. In both cases, a constant elasticity specification is used.
The basic model is:

                   Bus demand = f(bus fare, service, income, area dummy)

Estimation of the model based on all seven areas resulted in rather poor results.
However, the exclusion of London produced far more acceptable estimates. This is not
surprising considering the results of the regional estimation. There, too, we noted
problems with London (recall the positive price elasticities in Table 4.3). Omitting
London, and basing the estimation on the 6 remaining Metropolitan areas produces far
more reasonable results. The estimation results for the pooled ECM formulation are
reported in Appendix B.5, and the elasticities are presented in Table 4.5 below.


Table 4.5: Estimated elasticities based on pooled data for the English metropolitan
areas (excluding London) and constant elasticity Error-Correction Model. Fare
variable: fare per journey excluding CFR.
                         Fare elasticity             Income elasticity           Service elasticity
                         Short run      Long run     Short run     Long run      Short run    Long run
  All areas                 -0.24          -0.45       -0.20**        -1.27         0.27         0.24*
  Manchester                +0.03**        -0.45        -0.37*        -1.13         0.29          0.22
  Merseyside                -0.13**        +0.24**       “ “           “ “          “ “           “ “
  South Yorkshire           -0.30          -0.57         “ “           “ “          “ “           “ “
  West Yorkshire            -0.52**        -0.84         “ “           “ “          “ “           “ “
  Tyne and Wear             -0.39          -0.52
  West Midlands             -0.86          -1.08         “ “           “ “          “ “           “ “
Note: All elasticities are significant at the 5% level except those indicated by * which are significant at
the 10% level and those indicated by ** which are not significant at the 10% level.


The elasticities in bold pertain to the constrained model in which the coefficients of all
variables are assumed to be the same for all areas. These can be compared to those
obtained for the Metropolitan areas, based on the unrestricted regional model using fare
per journey excluding CFR as the price variable, shown in Table 4.3. We find that the
fare elasticities are somewhat smaller than those obtained from the regional model.
However, they do compare rather well to the elasticities for the Metropolitan areas
based on the variable elasticity model (Figure 4.1). Since the estimates for the pooled
Metropolitan areas are based solely on the variation in demand, fares etc. in these areas,
they are likely to be more reliable than those based on the broader regional data.


                                                   46
The elasticities for the individual metropolitan areas based on the unconstrained model
are given in the remainder of the table. Apart from Merseyside, where the elasticities are
not significantly different from zero, and West Midlands, where the short-run elasticity
is unreasonably high, the short-run elasticity is of the order of –0.3 and the long-run
elasticity lies between –0.5 and –0.6.

The income and service elasticities are negative and positive, respectively, as expected,
and in agreement with our earlier results. The long-run fare elasticities are around twice
the short-run values.

Because of the short time period involved, the tests for stationarity of the variables
included in the model are highly uncertain, and thus the procedure used for estimation
may be questionable. For this reason, the Metropolitan area model was also estimated
using a partial adjustment specification (see section A.1 in the Technical Appendix).
The partial adjustment model implies that the relationship between the short- and long-
run elasticities is the same for all independent variables. The estimation results are
presented in Section B.6 and the elasticities are reproduced in Table 4.6 below.

Table 4.6: Estimated elasticities based on pooled data for the English metropolitan
areas (excluding London) and constant elasticity Partial Adjustment Model. Fare
variable: fare per journey excluding CFR.
                               Fare elasticity           Income elasticity          Service elasticity
                         Short run      Long run     Short run     Long run      Short run    Long run
  All areas                 -0.23           -0.44       -0.84         -1.59         0.35          0.67
  Manchester                -0.28           -0.47       -0.88         -1.46         0.38          0.64
  Merseyside                 0.11**          0.19**      “ “           “ “          “ “           “ “
  South Yorkshire           -0.36           -0.60        “ “           “ “          “ “           “ “
  West Yorkshire            -0.32           -0.54        “ “           “ “          “ “           “ “
  Tyne and Wear            -0.28*          -0.47*
  West Midlands             -0.95           -1.59        “ “           “ “          “ “           “ “
Note: All elasticities are significant at the 5% level except those indicated by * which are significant at
the 10% level and those indicated by ** which are not significant at the 10% level.


For the constrained model (all areas), the fare elasticities are nearly identical to those
obtained from the Error-Correction Model, but both income and service elasticities are
slightly larger. Adjustment is relatively quick, with about 50% occurring within the first
year after the change in the independent variables, so the long-run elasticities are only
twice the short-run values. This agrees well with the ECM specification. The fare
elasticities for the individual Metropolitan areas are also similar to those obtained with
the ECM – again, those for Merseyside are insignificant and those for the West
Midlands excessively high. It would appear that demand is more fare-sensitive in the
West Midlands than in other areas, but given the small number of observations on
which the elasticities are based, much weight cannot be placed on this result.

Relationship between fare elasticity and fare level




                                                   47
The results presented above are based on constant elasticity models which constrain the
elasticities to be same for all fare levels and changes. As previously, this assumption
was tested by the estimation of models based on different functional forms, which allow
the elasticity to be related to the fare level and/or to the level of bus patronage. For both
the partial adjustment and the error-correction models, the constant elasticity
specification is preferred to the alternative specifications on the basis of statistical tests.
There is thus no evidence that the elasticities vary either over time or with the level fare
or bus patronage.

Asymmetry of response

Models allowing for asymmetric response of bus patronage to rising and falling prices,
based on the price-decomposition techniques described in Section A.5 in the Technical
Appendix were estimated for both PA and ECM specifications. In no case was there any
significant evidence of asymmetry. Again, this is unsurprising given the development of
bus fares over the period. The relatively few instances of fare reductions over the period
do not allow separate estimation of the impact of rising versus falling fares.


4.5     Conclusions

The econometric results presented above show a high degree of variation in the
estimated fare elasticities. These are found to be sensitive to the demand and fare
measures used, to the model specification and to the level of aggregation of the data.
This is not an unusual result, as was noted in the studies summarised in the literature
review. Such sensitivity in estimated elasticities, however, is a common problem of
econometric modelling, so that there is often a necessity to arrive at some general
conclusions and ‘most-likely’ values on the basis of a large body of disparate results.
We will attempt to do so here.

♦      Aggregate GB bus fare elasticities

The most-likely values for GB as a whole are –0.35 in the short run and –0.85 in the
long run. There is a degree of uncertainty in these values (as with all statistical
estimates), and we would suggest a 95% confidence interval4 of –0.25 to –0.45 in the
short run and –0.8 to –1.0 in the long run. The evidence suggests that the long-run
values are at least twice the short-run elasticities and probably over three times those.

♦      Regional variation in fare elasticities

That there is variation in the elasticities in different regions and areas is quite apparent.
The evidence seems to suggest that demand is 1 ½ times to twice as fare-sensitive in the
less-urban areas (the English Shire counties) than in the more urban areas (the
Metropolitan areas). Regarding the other regions, the results are less-clear cut. For


4 These confidence intervals represent a judgement based of the various estimated values and confidence
intervals rather than strictly statistical estimates.


                                                  48
London the results are generally very poor and there are inconsistencies for the other
regions.

Concerning the individual Metropolitan areas, we find a wide range of elasticities. In
the long-run, these range from between zero in Merseyside to over –1 in the West
Midlands. The results for the other Metropolitan areas are more consistent, with a short-
run value of about –0.3 and between –0.5 and –0.6 in the long run.

♦     Relationship between fare elasticity and fare level

There does seem to be a suggestion that demand is more fare-sensitive at higher fare
levels. However, this result requires further study on the basis of more disaggregate
data, showing more fare variation.

♦     Asymmetry of demand with respect to rising and falling fares

No indication of fare asymmetry is found for any of the models. However, we would
not rule out asymmetric response on this basis. All of the fares analysed are primarily
rising over time, with few instances of fare reductions. This does not provide a
sufficient empirical basis on which to test the asymmetry hypothesis. More disaggregate
data showing more fare variation, and particularly instances of falling fares are required
to draw any meaningful conclusions on the question of asymmetry.

Here it should also be pointed out that as the fare elasticities presented thus far are
primarily estimated on periods of rising bus fares, they may not be applicable to periods
of falling bus fares. Without further analysis on the basis of periods of falling fares,
there is no basis for inferring whether fare decreases will have the same, a greater or a
smaller impact on bus patronage.

♦     Income elasticities

All of the evidence is in agreement regarding the sign of the income elasticity – it is
undoubtedly negative in the long run, suggesting bus travel to be an inferior good. This
is in agreement with most other studies. There is a considerable degree of uncertainty in
the magnitude of the elasticity, and a range of between –0.5 and –1.0 in the long run
seems most likely. The negative long-run elasticity reflects the effect of income through
its positive effect on car ownership and use, and the negative effect of the latter on bus
patronage. It should be stressed, however, that the negative income elasticity pertains to
a period of rising car ownership and use. As private motoring reaches saturation, which
it must do eventually, or is limited by political means, it is likely that income’s negative
effect on bus patronage will become smaller, and possibly become positive.




                                            49
♦     The effect of car ownership on bus patronage

As would be expected, there is a strong negative relationship between car ownership
and bus patronage in the long run. In the short run, the effect is negligible.

♦     The relationship between motoring costs and bus patronage

The cross-elasticity between bus patronage and motoring costs appears to be negligible
in the short run, and about 0.3 to 0.4 in the long run. Clearly, there is a price-
substitution between bus and car use, although comparatively small. Again we must
keep in mind that these elasticities were estimated over a period in which bus fares rose
substantially in comparison to motoring costs, and an opposite development need not
produce an equivalent impact.

♦     The relationship between bus fares and car ownership and use

The rising bus fares over the period appear to have had a small but significant impact on
both car ownership and use. The short-run elasticity of car ownership and car use with
respect to the bus fare is around 0.2, while the long-run elasticity is 0.4 for car
ownership and 0.3 for car use.

♦     Comparison with other studies

The values for the fare, income and service elasticity values obtained from the dynamic
models are broadly in line with those cited in Goodwin (1992), Fowkes et al (1992),
Nijkamp and Pepping (1998) and elsewhere in the literature (cf., the literature review).




                                           50
5. COUNTY LEVEL DATA - STATS100A


5.1     Introduction

Permission was sought from the large bus operators in Great Britain (i.e. those with a
fleet size of 50 or more) to have access to their STATS100A data returns to the DETR.
STATS100A is a database of financial year returns to the DETR from bus operators
which is completed by all operators licensed for 20 or more vehicles. It contains
information on vehicle miles, passenger receipts, passengers carried, number of vehicles
and staff, and (for operators of local services) concessionary fare contributions, public
transport support, and fuel duty rebate. In addition, operators are also asked to estimate
a breakdown, by county, of passenger journeys and receipts, revenue support,
concessionary fare contributions and vehicle miles, as well as information on operating
and administrative expenditure, depreciation and profitability. These data have been
collected in this form since the 1986 deregulation of bus services outside London.

Of the 140 operators asked, over 100 gave permission for use of their data. In
consultation with the DETR, it was decided to analyse only the data for England and not
for the rest of Great Britain. The reason for this is that the large operators have a greater
market share in England and that permission to use their data was granted by nearly all
operators. The operators used in the analysis make up 87% of bus vehicle kilometres
and 93% of passenger journeys in England. The data employed for the resulting 46
counties are described in the following sections. They are complemented with
information on household income and population at the county level obtained from
Regional Statistics.

The data described in the following sections - and used in the empirical analysis - relate
to the financial years 1987/88 to 1996/97. For simplicity, these are referred to as 1987 to
1996.

5.2     County level data in England

5.2.1   Bus patronage

As was shown in Figure 3.11, there are considerable differences in per capita bus
patronage in different areas. For obvious reasons, per capita bus use is nearly three
times as high in metropolitan areas as in non-metropolitan areas. In addition, we have
noted a considerable variation amongst the individual Metropolitan areas (Figure 3.17)),
where per capita bus patronage differs by nearly a factor of two. Clearly, there is also a
substantial variation in the non-metropolitan counties. These differences are illustrated
in Figure 5.1, which shows average bus journeys per capita for the period 1987 to 1996
on a county level. The variation is apparent, ranging from over 170 journeys in Tyne
and Wear to around 10 in Cornwall. Of the metropolitan counties, Greater Manchester
has the lowest per capita bus use - about half that of Tyne and Wear and London.
Clearly, the metropolitan areas show the most intensive bus use, followed by


                                             51
Nottinghamshire, Durham, Lancashire, Leicestershire and Avon. The majority of
counties show an average bus use of between 20 and 60 journeys per capita, while only
four lie below this. In general, the more densely populated counties have a more
intensive bus use. There are a number of exceptions, however. For example, the densely
populated counties around London - Surrey, Berkshire and Hertfordshire have relatively
low bus use, while sparsely populated Northumberland has a comparatively high per
capita patronage.

                       Figure 5.1: Bus journeys per capita in English counties. Average 1987-96.

                               180
                                             Tyne & Wear           London
                               160
                                               W Mids
                               140
                                                S Yorks
   Mean patronage per capita




                                                Mersey
                               120
                                                W Yorks

                               100
                                               Gtr Manch
                                                   Notts
                                80
                                            Durham Lancs      Leics    Avon
                                60
                                     Northumb                      Derbys                                    E Sussex
                                               Cleveland                                              Humber
                                     Hants               Devon Cheshire       Oxon Cumbria     Staffs                 Isle of Wight
                                40
                                     Beds         N Yorks    Essex Bucks Northants                              Berks
                                          Dorset                                        Suffolk Kent Wilts Shrops Herts Glos Worcs
                                                           Norfolk    Cambs        Warks
                                20   Lincs       Somerset      W Sussex     Surrey Cornwall
                                 0




As is the case for Great Britain as a whole, bus use has been declining over the past
decade in most English counties. This is illustrated in Figure 5.2, which shows the
percent change in per capita bus journeys at the county level over the period 1987 to
1996. As these changes are based only on the initial and final years of the data sample,
they give no indication of variation within the period. Of the two counties which show a
substantial rise in patronage, only Oxfordshire is characterised by a continual increase
over the entire period. In Dorset, the data show a fall in patronage for all but the last
year, when patronage increases by 85% in a single year. Clearly, this observation is
suspect, and most likely reflects an error in the data. Of the counties with small
increases in patronage, all show a decline up until the past few years, when rising
patronage compensates for the patronage lost in previous years. A similar 'falling then
rising' pattern is also noted for many of the counties in the 0% to -20% bracket. In the
majority of counties showing the greatest percentage loss in patronage, demand has
been declining continually over the entire period. On average, patronage changes by less
than ±5% per annum in the individual counties. However, there are some notable
exceptions where the data show patronage changes in excess of ±25% in a single year:
Northumberland (+25% in 92), Durham (+85% in 91), Cleveland (-41% in 88 and
+64% in 95), Humberside (-35% in 96), Cheshire (+27% in 96), Lincolnshire (-23% in
90 and +115% in 96), Warwickshire (-34% in 88), Cambridgeshire (+26% in 96),
Buckinghamshire (+25% in 88 and -33% in 91), Surrey (+35% in 92), West Sussex
(+46% in 93) and East Sussex (+36% in 94). The magnitude of these annual changes in
patronage are suspiciously excessive, suggesting that at least some of these observations


                                                                              52
may be spurious, reflecting errors in the data rather than actual changes in bus demand.
The results for these counties must therefore be treated with caution.

 Figure 5.2: Bus journeys per capita in English counties. Percent change 1987-96.

                                                  60%

                                                                                                                 Oxon
   % change in bus journeys per capita




                                                  40%
                                                                                                                                               Dorset


                                                  20%
                                                                                  Cheshire
                                                                            London                     Warks        Glos                 W Sussex
                                                  0%                  Lancs             Lincs
                                                                                               Norfolk Cleveland           Somerset                     Surrey
                                                        Northumb     Cambs  Cumbria      Worcs                                        Shrops
                                                                                                                            Avon
                                                                          Leics                                                          E Sussex
                                            -20%                                                   W Mids       Beds
                                                                 Staffs                   Northants
                                                                                      Notts                                Cornwall Hants
                                                        Durham    Kent    Mersey        Wilts       Devon     Bucks Essex
                                                               W Yorks           Gtr Manch N Yorks
                                                                                                       Suffolk              Tyne & Wear Isle of Wight
                                                                        S Yorks                                   Herts
                                            -40%                                                                          Berks
                                                                                                                                       Derbys
                                                                       Humber

                                            -60%



The data for a selection of counties is shown in Figure 5.3 and Figure 5.4. The former
figure shows patronage in a number of counties surrounding London. These illustrate
the various patterns found for the majority of counties. Berkshire and Hertfordshire -
show a generally falling bus use over the period - the predominant feature of most
counties. Kent shows a falling, then rising bus demand while in Surrey demand
fluctuates without any apparent trend. Only in Oxfordshire is patronage continually
rising Figure 5.4. illustrates the large annual changes noted above for some of the
counties.

  Figure 5.3: Bus passenger journeys per capita in a number of English counties
                         around London, 1987 to 1996.

                                                  60
                                                                                                                   Oxfordshire
                  Passenger journeys per capita




                                                  50

                                                  40
                                                                                                                         Berkshire
                                                  30                                            Kent
                                                               Hertfordshire

                                                  20
                                                                                                               Surrey
                                                  10

                                                   0
                                                        1987       1988      1989      1990      1991      1992         1993       1994         1995         1996




                                                                                                  53
 Figure 5.4: Bus passenger journeys per capita in some English counties showing
                       large annual changes, 1987 to 1996.
                                                     100
                                                             90
   Passenger journeys per capita




                                                             80
                                                             70
                                                                                                                                                   Durham
                                                             60
                                                             50
                                                             40
                                                                                                                                    Cleveland
                                                             30
                                                                                                                                                                     Dorset
                                                             20
                                                             10                                                      Lincolnshire
                                                              0
                                                                   1987         1988            1989         1990          1991        1992          1993       1994           1995              1996




5.2.2                                                        Bus fare

As earlier, the fare variable is calculated as real average revenue per passenger journey
excluding concessionary fare reimbursement. As this is the only fare variable used in
this and the following chapter, it will simply be referred to as the 'bus fare' or 'fare'.

The average fares, calculated in this manner, for each of the counties over the period are
shown in Figure 5.5. The considerable variation amongst counties is apparent - from 22
pence per journey in Merseyside to 88 pence in Cambridgeshire. Fares are, on average,
considerably lower in the more urban counties - London, the six former Metropolitan
counties of England, and Cleveland than in the more suburban and rural counties.

  Figure 5.5: Bus fares in English counties, 1995 £ per journey. Average 1987-96.

                                                              1
                       Average revenue per journey, 1995 £




                                                             0.9
                                                                                                                                    Cambs
                                                                                                           Isle of Wight                                                        Surrey
                                                             0.8
                                                                                                                                                Beds                               Kent
                                                                                                                                                    Herts
                                                             0.7                Essex           E Sussex                                Bucks                Cornwall
                                                                                                                 Norfolk       Warks                Dorset                            W Sussex
                                                                   Northumb                                                                                             Somerset
                                                                                        Wilts                                 Avon                                                    Devon
                                                             0.6                                                                            Oxon
                                                                                                       Derbys                                                Berks
                                                                                                                           Northants                                                      Glos
                                                                                   N Yorks                           Leics
                                                                     Cumbria                               Lincs                      Staffs Humber            Lancs          Hants
                                                             0.5      Durham                                    Shrops             Suffolk
                                                                                                         Notts            Worcs              Cheshire
                                                                                 Gtr Manch
                                                             0.4
                                                                                   W Yorks        S Yorks                                                      London
                                                                    Cleveland                                              W Mids
                                                             0.3                                                                       Tyne & Wear
                                                                                             Mersey
                                                             0.2




                                                                                                                            54
In general, the counties with the lowest fares have the most favourable concessionary
schemes. The proportion of concessionary fare reimbursement in total receipts including
CFR is shown in Figure 5.6. There is substantial variation in the proportion of
concessionary fare reimbursement across counties, from 40% in Merseyside to 0% in
Bedfordshire. In the majority of counties, CFR is well under 20% of total receipts. The
only exceptions are the former Metropolitan counties, and Cleveland and Suffolk.

  Figure 5.6: Concessionary fare reimbursement as % of total receipts including
                   CFR in English counties. Average 1987-96.

                                     45
                                                                                 Mersey
                                     40
    % concesssionary reimbursement




                                     35
                                                         Tyne & Wear

                                     30                        Cleveland                                        W Mids
                                                                                    Gtr Manch
                                     25                                        S Yorks
                                                  W Yorks
                                                                                                                              Suffolk
                                     20
                                                                                                Lincs              Worcs                                    London
                                                                                                                                                                          Hants
                                     15                                                                                                 Bucks
                                                  Cumbria                                                                                                 Berks                      W Sussex
                                                                Durham     Lancs                                                            Herts
                                     10                                                Cheshire                      Warks        Glos                                                Staffs
                                                                                                      Shrops                                          Wilts                              Dorset
                                                Northumb        N Yorks         Oxon       Notts                   Norfolk     Northants          Essex              Somerset
                                                               Kent                                                                                      Devon       Isle of Wight
                                      5                                                   Derbys              Humber                                Avon
                                              E Sussex                     Leics                                             Cambs
                                                                                          Cornwall                                                                           Surrey
                                      0                                                                                                    Beds


As shown in Figure 5.7, there is a strong correlation between proportion CFR and the
average fare. The counties with the lowest fares - London, the Metropolitan counties
and Cleveland - have a very high proportion of CFR, while those with the highest fares -
Cambridgeshire, Surrey, Isle of Wight, Kent and Bedfordshire - have a low proportion
of CFR. There are a few obvious exceptions: Cheshire, for example, has a relatively low
fare, but also a low proportion of CFR.

 Figure 5.7: Relationship between fares and proportion CFR in English counties.
                                Average 1987-96.

                                     45
                                                                   Mersey
                                     40

                                     35
                                                                   Tyne & Wear
                                     30                                                       Cleveland
                                                                               W Mids
                                                                                                                  Gtr Manch
    % CFR




                                     25                                            S Yorks
                                                                                                     W Yorks
                                     20
                                                                                   London
                                     15

                                     10                                                         Cheshire
                                                                                                                                                                  Isle of Wight
                                                                                                                                                          Kent
                                      5                                                                                                                                          Cambs
                                                                                                                                                             Beds          Surrey
                                      0
                                          0              0.1             0.2            0.3             0.4            0.5           0.6            0.7           0.8           0.9             1

                                                                                                                 fare 1995 £




                                                                                                                  55
In real terms, average revenue has gone up in most English counties since deregulation
in 1986. This is illustrated in Figure 5.8, which shows the percentage change in fares
from 1987 to 1996. For 87% of counties, the fare increase was less than 40% and less
than 20% for over 60% of counties. The greatest fare increases are noted for Cleveland
and South Yorkshire. In a few counties - Cumbria, Norfolk and West Midlands - fares
have remained more-or-less constant over the period, and only in one county -
Oxfordshire - have fares actually fallen.

                                                   Figure 5.8: Bus fares in English counties, 1995 £ per journey.
                                                                     Percent change 1987-96.

                      120.00
                                                           Cleveland
                      100.00

                                                                        S Yorks
                            80.00
  % change in fares




                            60.00                       Tyne & Wear                                                                        Isle of Wight
                                                                                                                             Berks
                                                                       Humber
                            40.00                     Durham                                                                Wilts
                                                                                                   Warks             Herts
                                                                W Yorks                    Leics                           London
                            20.00                                    Notts     Derbys      Staffs    Northants                     Cornwall Devon
                                                 Northumb                                                               Essex
                                                               Lincs      Gtr Manch     Shrops      Glos                                  Surrey  E Sussex
                                               Cheshire Lancs                                                      Beds   Kent    Dorset
                                                              Hants              N Yorks     Worcs Cambs Suffolk Bucks         Avon      Somerset
                                                                       Mersey                                                                     W Sussex
                                   0.00            Cumbria                           Norfolk                                 W Mids

                        -20.00


                        -40.00                                                                               Oxon




In general, real fares fluctuate by less than 10% per year, with a predominantly rising
trend. A few counties, however, show changes in fares of over 25% in a single year.
The development of fares over time in some of these are shown in Figure 5.9 and Figure
5.10.

 Figure 5.9: Bus fares in some English counties, 1995 £ per journey. 1987 to 1996.

                                              1
                                             0.9                                                                                Surrey
                                             0.8
                      Average fare, 1995 £




                                             0.7
                                                                                                                         Hertfordshire           Cumbria
                                             0.6
                                             0.5
                                             0.4
                                             0.3
                                             0.2                                                                         Cleveland
                                             0.1
                                              0
                                                    1987       1988         1989     1990       1991       1992       1993       1994       1995           1996




                                                                                                 56
Figure 5.10: Bus fares in some English counties, 1995 £ per journey. 1987 to 1996.

                                 1.2

                                    1
                                                                                                                                        Isle of Wight
    Average fare, 1995 £




                                 0.8
                                                                      Warwickshire
                                 0.6
                                                                                                                                 S Yorkshire
                                 0.4

                                 0.2                                                                       Tyne & Wear

                                    0
                                          1987       1988         1989      1990           1991          1992          1993           1994         1995         1996



The proportion of CFR also changes over the period, but not in a similar fashion in all
counties. This is illustrated in Figure 5.11, which shows the percentage change in the
proportion of CFR over the period. About 2/3 of the counties show reductions in the
proportion of CFR, many of over 50%. Although a number of counties show
considerable increases in the proportion of CFR, many of these still have very low
proportions (5% or less) - Humberside, Cornwall and Bedfordshire. In general, there is
no clear relationship between the change in the proportion of CFR and the proportion of
CFR.

  Figure 5.11: Concessionary fare reimbursement in % of total receipts including
                CFR in English counties. Percent change 1987-96.

                                 150


                                                            Humber
                                 100
    % change in proportion CFR




                                                                                                 Beds
                                                                  Mersey                                                                Cornwall
                                                                           Bucks                                       Somerset
                                  50                 N Yorks                                                                              Devon
                                                                                           W Mids               Oxon
                                                               Gtr Manch      Staffs                                                                     Kent
                                                                                                        Cambs                  Avon
                                                                                                                                                     Hants
                                   0                                                                     Suffolk        Herts
                                        E Sussex         W Yorks                       Norfolk                                               Isle of Wight
                                                                                                                             London                       W Sussex
                                                Tyne & Wear             Derbys                       Lancs
                                                                                   Lincs                           Essex          Berks         Dorset
                                            Cumbria                   Cheshire               Worcs                                               Northants
                                  -50                  S Yorks                                             Glos
                                                                                                 Warks                            Northumb
                                              Durham                      Notts   Shrops                               Wilts
                                                            Cleveland
                                                                                    Leics                                                             Surrey
                                 -100



                                 -150


There is, however, a weak relationship between the change in the proportion of CFR
and the change in fares, as illustrated in Figure 5.12. Of the counties with the largest
fare increases, only Humberside shows an increase in the proportion of CFR. The
county with the largest fare decrease - Oxfordshire - also shows a substantial increase in
the proportion of CFR. A few counties with smaller fare increases - particularly, Surrey
and Leicestershire - have had relatively large decreases in the proportion of CFR. In
these counties, however, the average proportion of CFR is very low - less than 5%.


                                                                                            57
Figure 5.12: Relationship between % change in fares and % change in proportion
                        CFR in English counties, 1987-96.
                                                                                          150


                                                                                                                                          Humberside
                                                                                          100
   % change in proportion CRF




                                                                   Oxfordshire
                                                                                              50

                                                                                                                                          Isle of Wight
                                                                                               0
                                                     -60.00     -40.00       -20.00             0.00          20.00            40.00            60.00       80.00         100.00       120.00
                                                                                                                                                    Tyne & Wear
                                                                                          -50                                          Berks
                                                                                                                                                          S Yorkshire
                                                                                                                                                                              Cleveland
                                                                                         -100                          Leics
                                                                                                         Surrey

                                                                                         -150

                                                                                                             % change in fare


The relationship between average fares and journeys per capita is illustrated in Figure
5.13. There does appear to be a positive relationship - although not a linear one -
between patronage and fare level. A number of counties, however, show a significant
deviation from the 'best-fit' line. Particularly, patronage is higher in Tyne & Wear,
London and the Isle of Wight than would be suggested by their fare levels. Similarly,
patronage is lower in Cleveland, Cheshire, Worcestershire, Lincolnshire, Suffolk and
Shropshire.

  Figure 5.13: Relationship between average fares and bus patronage in English
                                counties, 1987-96.

                                                     200

                                                     180                         Tyne & Wear
               Average journeys per capita 1988-96




                                                                                                          London
                                                     160

                                                     140                         W Midlands
                                                                                                         S Yorkshire
                                                     120

                                                     100

                                                      80

                                                      60                                                                                                                    Isle of Wight
                                                                                   Cleveland
                                                      40                                               Cheshire
                                                                                                                      Suffolk
                                                                                                   Worchestershire                                                          Cambridgeshire
                                                      20                                                                  Shropshire
                                                                                                                                 Lincolnshire
                                                        0
                                                            0      0.1           0.2           0.3          0.4            0.5           0.6           0.7          0.8        0.9           1
                                                                                                         Average fare 1988-96, 1995 £




                                                                                                                      58
5.2.3                                                Service

As before, bus vehicle kilometres per capita is used as the proxy for level of service.
The large variation among the counties is illustrated in Figure 5.14. Tyne & Wear has
the highest service intensity and West Sussex the lowest. In general, the most densely
populated counties have better bus service than more rural counties. Overall, bus vehicle
kilometres tend to be higher in the six former Metropolitan counties of England than
elsewhere in the country. Again this is not very surprising.

                       Figure 5.14: Bus kilometres per capita in English counties. Average 1987-96.

                                                 90


                                                 80               Tyne & Wear


                                                 70
                            Bus kms per capita




                                                                                     S Yorks
                                                 60

                                                                                                              Mersey
                                                                      W Yorks                                                           Durham
                                                 50                                          Gtr Manch
                                                         Northumb                                                       W Mids
                                                                                                                                                                    London
                                                                                                                                                       Avon
                                                                                                   Notts
                                                 40
                                                                            Lancs                Derbys         Leics                                                      Devon
                                                                                                                                          Oxon                                         Isle of Wight
                                                                                                           Staffs
                                                 30                                            Cheshire                                     Bucks                                  Hants       E Sussex
                                                       Cumbria                  Humber                                   Beds                             Essex
                                                                    Cleveland                           Shrops    Worcs                                              N Yorks
                                                                                                                                                  Herts                                 Kent
                                                                            Northants         Cambs                                                          Wilts
                                                 20              Cornwall                                Norfolk    Warks Suffolk                Berks                       Somerset
                                                        Glos                            Surrey                                                                                                  Dorset
                                                                                                  Lincs          W Sussex
                                                 10


In most counties, bus service has been increasing over the past 10 years. This is
illustrated in Figure 5.15. The greatest percentage increases are in Cleveland, Surrey,
Oxfordshire, Gloucestershire and Bedfordshire - well over 40% in all cases.
Buckinghamshire, Hertfordshire and Derbyshire show the greatest decline. For most
other counties, service has increased by less than 20%.

        Figure 5.15: Bus kilometres per capita in English counties. % change 1987-96.

                                      100


                                                                   Cleveland
  % Change in bus kms per capita




                                             80



                                             60
                                                                                                                                                                                   Surrey
                                                                                     Oxon                  Glos
                                                                                                                                            Beds
                                             40
                                                                                                                              Norfolk
                                                                                                           Shrops
                                                                                    S Yorks                                                                                  Dorset
                                             20                    Warks                                                    Northants                             London
                                                       Cambs                         Notts               Staffs                                    Essex                                W Sussex
                                                                     Lancs                                           W Mids                                         Cornwall
                                                                   N Yorks       Cheshire                              Suffolk     Tyne & Wear                                              E Sussex
                                                                             Mersey                                                                       Wilts                Hants
                                                             Durham                                          Leics                          Berks
                                                 0                        Humber                                           Devon                                           Cumbria Isle of Wight
                                                        Northumb                  Gtr Manch                  Lincs                   W Yorks              Somerset
                                                                    Avon                                                Worcs
                                                                                                                                                                                   Kent
                                                                                               Derbys                                         Herts
                                         -20                                                                                              Bucks




                                                                                                                         59
In general, annual changes in bus vehicle kilometres are relatively small - usually
significantly less than 10%. A few counties do, however, show more considerable
changes in some years, and some show rather large fluctuations. As seen in Figure 5.16,
the data for Durham and Cleveland indicate substantial increases in 1991 and 1995
respectively. In both Dorset and Lincolnshire, bus vehicle kilometres remained
comparatively constant until 1996 when increases of over 40% are noted. Other
counties with relatively large annual changes are shown in Figure 5.17.

 Figure 5.16: Bus vehicle kilometres per capita in some English counties, 1987-96.

                                 70

                                 60
   Bus vehicle kms per capita




                                 50                                        Durham

                                 40

                                 30
                                                                  Cleveland                                    Dorset
                                 20

                                 10
                                                                                                               Lincolnshire
                                  0
                                      1987   1988   1989   1990   1991       1992      1993       1994      1995       1996




 Figure 5.17: Bus vehicle kilometres per capita in some English counties, 1987-96.

                                 45
                                 40
   Bus vechicle kms per capita




                                 35                                            Oxfordshire

                                 30
                                                                                                         East Sussex
                                 25
                                                     Cambridgeshire
                                 20
                                 15
                                 10
                                                                                    West Sussex
                                  5
                                  0
                                      1987   1988   1989   1990   1991       1992      1993       1994      1995       1996



As expected, there is a clear correlation between bus vehicle kilometres per capita and
bus journeys per capita. This is illustrated in Figure 5.18. Tyne & Wear has the highest
journeys and vehicle kilometres, while West Sussex has the lowest. Most counties lie
very close to the linear regression line shown. There are, however, a few notable
exceptions. Both London and West Midlands have a high number of journeys in



                                                                      60
comparison to vehicle kilometres, while Avon, Durham, Devon, Northumbria and
Buckinghamshire have a relatively small number of journeys in relation to vehicle
kilometres.


  Figure 5.18: Relationship between bus vehicle kilometres and bus journeys in
                     English counties. Average 1987 to 1996.

                         200

                         180
                                                                        London
                         160
                                                                                                     Tyne & Wear
   Journeys per capita




                         140                             W Midlands

                         120

                         100

                         80
                                                                      Avon        Durham
                         60

                         40                                             Northumbria
                                                            Devon
                         20        W Sussex        Buckinghamshire
                          0
                               0     10       20   30          40            50            60   70      80         90

                                                            Bus kms per capita




                                                                 61
6. COUNTY LEVEL ELASTICITIES


6.1    Introduction

This section summarises the results obtained on the basis of the operator data for the
English counties described in the previous chapter. For ease of readability, only the bus
fare and other relevant elasticities are presented here. The full estimation results,
goodness-of-fit measures, statistical tests, etc. are given in the Statistical Appendix (B),
and are only referred to in the text. Similarly, the models employed are described only
cursively. The full specification of the econometric models and the derivation of the
elasticities are presented in the Technical Appendix (A), and the relevant sections are
referred to in the text.

Passenger journeys per capita is the dependent variable for all of the estimations. A
single ‘fare’ measure is used - the calculated fare per journey based on receipts
excluding concessionary fare reimbursement (CFR) because, in our opinion, this best
represents the fare faced by the average bus patron. (There is no standard bus fare index
available from the DETR at the county level.) Bus vehicle kilometres per capita is used
as a proxy for the service level. The income variable used is household disposable
income per capita. All price and income variables are converted to 1995 prices using the
Retail Price Index.


6.2    Results at the English county level

As for the GB regions in Section 4.3, the data sample for the counties is rather limited,
with all variables being available only for the 10-year period 1987 to 1996, and, thus, a
pooled approach is required (see section A.6 in the Technical Appendix). Two
specifications are estimated – one constraining all coefficients to be the same across
counties and one in which the coefficients of the fare variable, and the price elasticity,
are county-specific. The basic model is once again:

               Bus demand = f(bus fare, service, income, county dummy)

The dynamics are specified using a partial adjustment model (see section A.1 in the
Technical Appendix) which implies that the relationship between the short- and long-
run elasticities is the same for all independent variables. A dynamic error correction
specification was also tested, but given the limited time series available, no firm
conclusions could be drawn as to either the suitability of such a model or the veracity of
the elasticities obtained.

In addition, for each of the specifications (constrained and unconstrained) two different
functional specifications are estimated: (a) a “constant elasticity” model in which all
variables are specified in natural logarithms, and whose coefficients yield the elasticities
of interest directly; and (b) a model in which all variables are in natural logarithms


                                            62
except the price (fare) variable which is specified in level terms. In the latter, the
elasticity is not constant but increases with the price level (bus fare).

The results for the four estimated models are reported in Section B.7 and the statistical
tests for model selection are shown in Table B.7.5 in the Statistical Appendix. For the
constant elasticity models, the constrained version is rejected in favour of the
unconstrained formulation, implying that the fare elasticity is not the same for all
counties. For the variable elasticity models, on the other hand, the constrained version
cannot be rejected. This indicates that there is no significant difference in the fare
elasticity amongst counties that cannot be accounted for by allowing the fare elasticity
to be dependent on the fare level. Comparing the constrained versions of the constant
and variable elasticity models clearly rejects the constant elasticity formulation in
favour of the variable elasticity version. The fare elasticity is thus not constant, but
depend on the fare level. Conversely, comparing the unconstrained versions of the
constant and variable elasticity models does not reject the constant elasticity
formulation. Once the fare elasticity is allowed to be county specific, allowing it to vary
according to the fare level offers little additional explanatory power. In summary, the
statistical tests favour either the unconstrained constant elasticity model or the
constrained variable elasticity model and there is little statistical evidence to choose
between them. Both imply that the fare elasticity will vary among counties; the first,
independent of any particular explanatory factor, and the second, dependent on county-
specific differences in the level of fares.

The resulting elasticities for the four model specifications are shown in Table 6.1. The
first two rows report the elasticities for the constrained and unconstrained versions of
the constant elasticity model. As mentioned above, the unconstrained variant of this
model is preferred statistically. The fare elasticity shown for the unconstrained model is
the average of the elasticities estimated for the individual counties. The results for the
two models are quite similar. The average fare elasticity is slightly higher in the
unconstrained model and the service elasticity is somewhat lower.

The next set of results is for the variable elasticity model. In the constrained model, the
fare elasticity is dependent on the fare level, and the fare elasticities shown in the table
are calculated at the minimum, average and maximum fare (in 1995 £) for all counties
over the observation period. For the unconstrained model, the fare elasticity varies by
county as well as by fare level. The elasticities shown are the averages of the elasticities
for the individual counties calculated at the minimum, average and maximum fare for
each county. The 'average fare' elasticities are very similar in both specifications, as
would be expected. These are also close to the average elasticity in the unconstrained
constant elasticity model. The range between the minimum and maximum is smaller for
the unconstrained model simply because these are the averages of the elasticities
calculated at the minimum and maximum fare for each of the counties, rather than the
elasticities calculated at the minimum and maximum fare for all counties. The income
and service elasticities are also of a similar order of magnitude as those obtained with
the other specifications. In all cases, the long-run values are just over twice their short-
run equivalents.




                                            63
For comparison, the elasticities obtained from the aggregate and regional GB data using
the same fare variable in Section 4.3 are shown in the table. We would expect the
results to be roughly similar. However, we would not expect the results to be perfectly
identical since the present data set is slightly less inclusive than that used for the
aggregate models, leaving out as it does those operators with a fleet size of less than
fifty vehicles, which account for approximately fifteen percent of national passenger
receipts. Also, the aggregate GB estimates are based on a much longer observation
period. Despite this, the resulting elasticities are not very different.


Table 6.1: Estimated elasticities based on pooled data for English counties. Partial
                                 adjustment model.
                                    Fare elasticity          Income elasticity     Service elasticity
                                Short run   Long run       Short run  Long run   Short run   Long run
Constant elasticity model
 Constrained                       -0.33          -0.71      -0.31      -0.66      0.48        1.04
 Unconstrained                     -0.43*         -0.82*     -0.35      -0.68      0.41        0.79

Variable elasticity model
 Constrained                                                 -0.33      -0.70      0.45        0.95
  Minimum fare = 17p               -0.13         -0.27
  Average fare = 56p               -0.42         -0.88
  Maximum fare = £1                -0.77         -1.62
 Unconstrained                                               -0.37      -0.72      0.42        0.79
  Minimum fare                     -0.36*         -0.69*
  Average fare                     -0.41*         -0.79*
  Maximum fare                     -0.48*         -0.93*

Aggregate GB                       -0.33           -0.62      0.41      -0.80       Not estimated
Regional GB data                   -0.22           -0.81     -0.27      -1.13      0.43        0.81
* average of individual elasticities for all counties




6.3      County-specific fare elasticities

We now turn to the elasticities for the individual counties. For the constant elasticity
model, the unconstrained version results in estimates of separate fare elasticities for
each county. These are shown in Table 6.2, classed according to fare sensitivity. The
estimates are based on relatively few data points - 9 annual observations in each case -
so it is not surprising that there is a large degree of uncertainty in the estimates. In fact,
only 22 of the 46 estimated fare elasticities are statistically significant at the usual
levels. These are shown in bold. Of those shown in the 'insensitive' class, none are
statistically different from zero, and in the 'below average' class, only the elasticity for
London is significant. The elasticities in the 'mean' and higher fare sensitivity classes
are more generally significant.

Based on the literature review and the aggregate estimates, we consider the 'mean' class
to contain the most likely elasticities values (between -0.4 and -0.5 in the short run, and
between -0.6 and -1.0 in the long run). Values below and above this can be expected in


                                                      64
certain instances, so that the 'below average' class (-0.1 to -0.3 and -0.3 to -0.6 in the
short and long run, respectively) can also be considered acceptable, as can the 'above
average' class (between -0.5 and -0.7 in the short run, and between -1.0 and -1.3 in the
long run). The counties listed in the 'very sensitive' class, on the other hand, have long-
run elasticities in excess of -1.5, rather greater than would be considered reasonable. It
can be noted that many of the counties with insignificant or excessive elasticities are
among those mentioned in the previous chapter as having questionable data.

Clearly, these elasticities must be interpreted with caution. At best they give an
indication of the wide range in which the fare elasticity can fall in specific areas.

  Table 6.2: Fare elasticities for English counties. Unrestricted constant elasticity
                                        model.
                    Short run Long run                               Short run Long run

   Insensitive                                      Below average
Somerset                1.25       2.40            London                -0.15     -0.29
Merseyside              0.21       0.40            Warwickshire          -0.15     -0.28
Cleveland               0.10       0.20            Lincolnshire          -0.16     -0.31
Durham                  0.01       0.02            Shropshire            -0.19     -0.36
West Sussex            -0.05      -0.10            Dorset                -0.20     -0.39
Northumberland         -0.06      -0.11            North Yorkshire       -0.21     -0.41
Gloucestershire        -0.07      -0.14            Cheshire              -0.24     -0.46
                                                   Wiltshire             -0.24     -0.45
                                                   Lancastershire        -0.29     -0.55

       Mean                                              Mean
Oxfordshire            -0.32      -0.61            Gtr. Manchester       -0.42     -0.82
Suffolk                -0.33      -0.63            Hertfordshire         -0.46     -0.88
Essex                  -0.34      -0.66            Leicestershire        -0.47     -0.90
Buckinghamshire        -0.39      -0.75            Worcestershire        -0.47     -0.90
Cumbria                -0.40      -0.77            Berkshire             -0.48     -0.92
Northamptonshire       -0.41      -0.79            Kent                  -0.49     -0.94
Derbyshire             -0.41      -0.79            Tyne & Wear           -0.49     -0.93
                                                   West Yorkshire        -0.50     -0.96
                                                   Avon                  -0.51     -0.97

  Above average                                     Very sensitive
Nottinghamshire        -0.52      -1.00            Devon                 -0.78     -1.50
South Yorkshire        -0.52      -1.00            East Sussex           -0.79     -1.52
Bedfordshire           -0.58      -1.11            Staffordshire         -0.86     -1.66
Isle of Wight          -0.60      -1.15            Cambridgeshire        -1.08     -2.08
Hants                  -0.62      -1.19            W. Midlands           -1.19     -2.29
Cornwall               -0.66      -1.28            Surrey                -1.20     -2.32
                                                   Humberside            -1.21     -2.33
                                                   Norfolk               -1.61     -3.09



In order to investigate possible reasons behind the differences in elasticities, the
relationship between the elasticities and various factors - population density, income


                                            65
level and fare level - were examined. The only statistically significant correlation is a
positive relationship between elasticity and fare level. This supports the results
presented earlier for the variable elasticity model - the fare elasticity increases at higher
fare levels.

The variable fare elasticity model also results in different elasticities for individual
counties, but in this case the variation is purely dependent on differences in fare levels
among counties. As shown in Figure 5.5 above, the mean fare over the period for the
individual counties ranges from 25 pence per journey in Merseyside to nearly 90 pence
in Cambridgeshire. For the variable elasticity model, the average elasticities for the
individual counties will show a similar range of variation. The long-run elasticities for
the individual counties, calculated at the mean fare in each county over the 1987-96
period, are shown in Figure 6.1. The short-run elasticities are approximately 1/2 the
long-run values. The variation in fares amongst counties is reflected in the variation in
fare elasticities - from -0.4 in Merseyside to -1.4 in Cambridgeshire. For the majority of
counties, the long-run elasticity is in the region of -0.7 to -1.1. Those with the lowest
elasticities are the Metropolitan counties where fares are lowest.

                   Figure 6.1: Long run bus fare elasticities for English counties, calculated at
                                 average fare 1987-96. Variable elasticity model.

                                0


                              -0.2


                              -0.4     Mersey
   Long run fare elasticity




                                                      W Mids                                  Cleveland                              Tyne & Wear
                                                                           West Yorks                             S Yorks   London
                              -0.6
                                                        Gtr Manch                                      Cheshire
                                                                                Worcs        Notts               Shrops    Suffolk
                                                            Durham                                                                             Staffs
                              -0.8   Hants            Lincs                          Cumbria               Lancs
                                                                N Yorkshire                    Leics              Northants           Humber
                                                 Glos                                    Berks           Derbys
                                        Devon                                                        Avon                  Oxon           Wilts
                               -1                               Somerset      Dorset Warks                 Northumb
                                                     Cornwall                                   Norfolk               W Sussex        E Sussex
                                     Bucks                                                               Essex
                                                                                                                             Herts
                              -1.2                                            Kent                                                   Beds
                                                                                                                                         Surrey
                                                                                                     Isle of Wight
                              -1.4           Cambs


                              -1.6




Clearly, there is a considerably smaller range in these elasticities than in those shown in
Table 6.2. In fact, 23 of the 46 counties show elasticities in the mean-value range above
- between -0.6 and -1.0 in the long run - as opposed to only 16 previously, and none lie
in the 'insensitive' and 'very sensitive' categories of Table 6.2, which are considered
rather dubious. In general, these elasticities are more reasonable than those presented
above, and all are significantly different from zero, since they are based on a single,
highly significant fare coefficient. However, as with the county level elasticities in
Table 6.2, the elasticities are not all necessarily significantly different from each other
statistically.

In order to further investigate differences in fare elasticities between urban and less
urban areas, separate models were estimated for the Shire counties and the Metropolitan


                                                                                        66
areas. These are reported in Tables B.7.7 and B.7.8, and the resulting elasticities
presented in Table 6.3. As expected, the fare elasticity is on average higher in the Shire
counties than in the Metropolitan areas, and significantly so. This result agrees with
those found earlier, both in this chapter and in Chapter 4. Unfortunately, the explanation
for this difference cannot be determined from the data. The Metropolitan areas are more
urban than the Shire counties and have better bus service and lower fares, but the
separate effects of these individual factors on the elasticity cannot be distinguished from
the data.

It also appears that the income elasticity is more negative and the service elasticity
lower in the Metropolitan areas than in the Shire counties. Both these results are
reasonable. Rising income has a greater negative effect on bus patronage because car
ownership is lower. Service is more important in the Shires because car transport is a
more viable alternative.

 Table 6.3: Estimated elasticities based on pooled data for English Shire counties
                and Metropolitan areas. Partial adjustment model.
                                 Fare elasticity       Income elasticity       Service elasticity
                            Short run    Long run   Short run   Long run     Short run   Long run
Shire counties              -0.51        -0.70        -0.64       -0.87        0.64        0.87
Metropolitan areas          -0.21        -0.43        -1.02       -2.08        0.35        0.71



Variation in elasticities

As shown above, there is a clear and statistically significant relationship between the
elasticity and the fare level. Demand appears to be relatively insensitive to fare changes
at low fare levels, but as the fare increases, demand becomes more fare sensitive, and
the elasticity increases to values over -1.0.

Models have also been estimated to investigate whether or not the elasticity is
dependent on the magnitude of the fare change. None of the specifications used indicate
any variation in the elasticity owing to such differences. There is thus no evidence from
the data that patrons react differently to small and large annual fare changes.

Asymmetry of response

As earlier, models allowing for asymmetric response to rising and falling fares were
estimated. The county level data shows much more fare variation than the aggregate
data, and many more instances of falling fares, so that we might expect to be able to
statistically differentiate between the effects of rising and falling fares. The resulting
estimates are shown Section B.8 in the Statistical Appendix and the elasticities shown in
Table 6.4. We see that there is an indication that the response to fare increases is slightly
greater than that to fare decreases. The elasticity for rising fares -0.36 and -0.74 in the
short and long run, respectively, compared to -0.27 and -0.56 for falling fares. However,
as shown by the F-test in the table, this difference is not statistically significant, so that
the evidence of asymmetry is rather weak.



                                             67
    Table 6.4: Asymmetric fare elasticity model. Pooled data for English counties.
              Constrained constant elasticity partial adjustment model.
                                      Short run                       Long run
    Rising fares                       -0.36                            -0.74
    Falling fares                      -0.27                            -0.56
    Income                             -0.25                           -0.51
    Service                             0.49                            1.02

    Test for symmetry          F = 0.67      Prob. = 0.41      cannot reject symmetry




6.4      Conclusions

Although, again, we must be cautious about a overly-strict interpretation of the
individual results based on the county data, a few general conclusions can be drawn.
These are summarised below.

♦       Aggregate bus fare elasticities for England

The econometric results presented above are in good agreement with the results for
Great Britain as a whole in Chapter 4. The most likely values for England as a whole are
–0.30 to -0.40 in the short-run and –0.70 to –0.90 in the long run. The evidence suggests
that the long-run elasticities are about twice the short-run elasticities. The mean
elasticities obtained in the variable elasticity specification are slightly higher than those
obtained in the constant elasticity model. The variable elasticity specification is
preferred to the alternative specification on the basis of statistical tests.

♦       County variation in fare elasticities

A constant elasticity model with separate fare elasticities is statistically preferred to a
similar specification in which the fare elasticity is constrained to be equal for all
counties. The results of the unconstrained model show a considerable variation in the
fare elasticity across counties - a range from 0 to over -3 in the long run. There is a
significant positive relationship between the magnitude of the fare elasticity and the fare
level, but no evidence of any relationship between the elasticity and income, population
density, or the variability of fares. Separate estimates of the fare elasticity for the Shire
counties and the Metropolitan areas (excluding London) indicate that patronage in the
former is on average more sensitive to fare changes than in the latter, and significantly
so. This result agrees with those found earlier. The less-elastic demand in the
Metropolitan areas can be explained in terms of their urban characteristics, better bus
service provision and lower fares. The separate contributions of these various factors,
however, cannot be disentangled from the existing data.

♦       Relationship between fare elasticity and fare level

There is statistical evidence that demand is more price-sensitive at higher fare levels.
This is based on the results of the unconstrained constant elasticity model referred to



                                             68
above and the estimation of a variable elasticity specification, in which the elasticity is
related to the fare level. This latter model indicates that the long-run fare elasticity
increases from -0.27 for the lowest fares to -1.6 for the highest fares.

♦     Relationship between fare elasticity and the magnitude of the fare change

There is no evidence that the fare elasticity increases for larger fare changes.

♦     Asymmetry of demand with respect to rising and falling fares

There is an indication that demand is slightly more sensitive to rising than to falling
fares. However, the difference is marginal and not statistically significant.

♦     Income elasticity

The income elasticity is negative in both the short and long run. In the short run the
most likely value is in the range –0.3 to –0.4; in the long run the range is –0.6 to -0.7.
The long-run results are of the same order of magnitude as those obtained from the
aggregate analysis. There is also an indication that the income elasticity is more-
negative in the Metropolitan areas than in the Shire counties. An explanation for this
may be that since both incomes and car ownership are lower in the Metropolitan areas,
increasing income will have a greater (positive) impact on car ownership, and thus a
greater (negative) impact on bus use.

♦     Service elasticity

The most likely range for the service elasticity is between 0.4 and 0.5 in the short run
and between 0.8 and 1.0 in the long run. Again, these are comparable to those obtained
in the aggregate analysis. The service elasticity appears to be lower in the Metropolitan
areas than in the shire counties. Since, in general, service is poorer in the Shire counties,
improvements in service will have more of an impact on demand.




                                             69
7. THE PTE DATA
7.1    Introduction

The elasticities presented thus far measure the effect on all bus journeys given a change
in the average fare for all passengers, full-fare paying as well as concessions. As stated
in the introduction, the major aim of this project is to estimate the effect on full-fare-
paying patronage of a change in the non-subsidised fare. The available data, however,
did not permit the distinction between the two types of passengers, and for this reason it
has been necessary to base the analysis on total patronage. How well the estimated
elasticities reflect the fare-sensitivity of the full-fare-paying market will depend on
whether or not the two sub-markets respond to the same degree to fare changes. There
can be arguments in either direction. The concessionary market may more sensitive to
fare changes since there is a larger proportion of unnecessary trips which can be more
easily foregone as fares rise. Alternatively, it may be less fare-sensitive since it
represents more of a captive market, with fewer possibilities to transfer to car. If the
concessionary market is less price-sensitive than the non-concessionary, the elasticities
obtained on the basis of total patronage will underestimate the fare sensitivity of full-
fare-paying market. Conversely, if concessions are more fare-sensitive, the aggregate
elasticity will overestimate the effect of non-concessionary fare changes.

For this reason, it was decided necessary to attempt to distinguish full-fare-paying
patrons from the total market. The most readily accessible source of such data are the
Passenger Transport Executives (PTEs) in the six former Metropolitan counties of
England. In Great Britain, the level of concessionary fares is determined by the county
authorities and PTAs, who are then responsible for reimbursing operators. The majority
of CFR is allocated to the large conurbations, and in the six former Metropolitan
counties of England the PTEs have responsibility for monitoring the public transport
services provided. For this reason, the PTEs collect and compile data on both full-fare-
paying and concessionary bus patrons (i.e. the elderly, the disabled and children, of
which the elderly form the greatest proportion).

To monitor bus services, PTEs generally carry out on-board surveys of passengers on a
mix of routes in their area to determine average journey distance, average full fare,
average concession fare, and the proportions of full-paying and concessionary patrons.
These data are subsequently aggregated up over the year and over all routes in the area,
and over different classifications of patron to yield an estimated annual total.

Nearly all PTEs have ready access to data on mileage, patronage and concessionary
fares. Most found it more difficult to estimate an annual adult cash fare, or at least to
extract and provide us such data as would allow it to be calculated. Five of the six PTEs
approached were able to provide data on annual average adult cash fares. They are
Merseytravel, Greater Manchester PTE, West Yorkshire PTE, South Yorkshire PTE and
Nexus (Tyne and Wear PTE). Centro (West Midlands PTE) provided an index tracking
the change in the average adult cash fare, but were unable to provide actual cash fares
for reasons of confidentiality.




                                           70
7.2     Comparison of the data from the three data sources

Three data sources have been used in this project for the Metropolitan counties of
England: (a) national aggregate published statistics; (b) data from the STATS100A
database; and (c) data from the six English PTEs. The data from the STATS100A
database form the core of the national aggregate statistics and account for about 80% of
total bus revenues in Great Britain. Hence, only the national aggregate statistics and the
PTE data will be compared here. The data from the two sources will differ and to quote
from the DETR “These [the national aggregate statistics] will differ from returns from
the PTEs as they are for operators working in the relevant areas, whether or not they are
under contract to provide services for that PTE. Our survey cannot separate PTE
contracted/supported operators from other operators providing services in the area.”

7.2.1   Total bus passenger journeys

In all PTE areas, bus journeys are generally 2% to 12% higher from the PTE returns
than from the aggregated national statistics (Figure 7.1), though this varies from year to
year and there is no rising or falling pattern over time for any PTE area. In Merseyside
the difference between the PTE bus journey data and the national aggregate statistics is
higher than for any other PTE being in the range 3% to 20%. The areas showing the
next highest differences are Tyne and Wear, Greater Manchester and West Yorkshire. In
general, bus passenger patronage follows the same overall path in both the national
aggregated data and the data collected by the PTE. South Yorkshire is not shown since
information on total passenger journeys was not available from the PTE.


  Figure 7.1: Ratio of PTE bus passenger journey data to the national aggregate
                    data for the former Metropolitan counties
1.3


                         Merseyside
1.2


                                                              West Yorkshire
1.1                            Gtr Manchester




  1

                                                                 West Midlands

0.9       Tyne & Wear




0.8
        1987     1988   1989        1990        1991   1992      1993          1994   1995   1996




                                                  71
7.2.2   Average bus fares

In Figure 7.2, the average weighted bus fare provided by the PTE (weighted for price
and proportion of concessionary journeys and full fare-paying journeys) is compared to
the average revenue excluding CFR per bus passenger journey. In both cases, this is the
fare that the average bus user would face.

In general, the average bus fare provided by the PTEs is higher than the average revenue
per bus journey calculated for the former Metropolitan counties in the Chapter 3 (using
the STATS100 data). The PTE fares for Merseyside are 1.5 to 2 times higher than those
fares calculated for Chapter 3, while those for Tyne and Wear and West Yorkshire are
about 1.3 to over 1.5 times higher. Only the PTE fares for Greater Manchester are close
to the average revenue per journey figures. The comparison is not possible for West
Midlands since information was not available on the average adult fare.

Figure 7.2: Ratio of PTE average weighted fares to the national aggregate average
                  revenue per passenger journey excluding CFR

  2.3

  2.1
                                                                            Merseyside

  1.9

  1.7                                                    Tyne & Wear


  1.5

  1.3
                                   West Yorkshire

  1.1
                                                         South Yorkshire

  0.9
                                                    Gtr. Manchester
  0.7
         1987      1988     1989      1990      1991         1992          1993     1994   1995   1996




7.2.3   Bus vehicle kilometres

The PTEs’ estimates of bus vehicle kilometres are lower in all cases than the data from
the national statistics (Figure 7.3). There is variation both between the different PTEs
and between years, and again there is no rising or falling pattern. A general
approximation is that on average, bus vehicle kilometre estimates for the PTEs are about
10% lower than those in the national statistics5. Neither West Midlands nor South


5 This may have to do with different methods of measurement. The operators have actual data for vehicle
kms during the year, while these are only estimated by the PTEs.


                                                    72
Yorkshire are shown in this graph as PTE estimates are not available over a sufficiently
long period for either of these areas.

Figure 7.3: Ratio of PTE bus vehicle kilometre data to the national aggregate data
                       for the former Metropolitan counties

    1.1


                                                         Gtr. Manchester

      1                         Merseyside

          West Yorkshire



    0.9


                                                             Tyne & Wear
    0.8




    0.7
           1987       1988   1989      1990      1991      1992       1993      1994    1995     1996




7.3       The data used for the analysis

In cases where the PTEs were unable to provide data for a particular variable, these data
were supplied from a different data source. These variables are as follows:


Variable                                      PTE                          Data source used

Total bus passenger journeys                  South Yorkshire6     National statistics (DETR)
Bus vehicle kilometres                               South Yorkshire      National      statistics
(DETR)
                                              West Midlands
Average full-price bus fare                   West Midlands                Stats100A


Table 7.1 summarises the percentage changes in key data in the 6 English PTE areas
over the period 1988 through 1996.7

6 Note: SYPTE provided the proportions of annual bus passenger journeys made by full fare-paying and
concessionary patrons, but not the annual totals for each. The total patronage data is taken from the
national statistics and split into concessionary and full-fare-paying in line with the SYPTE proportions.
7 Note: data are available for more years for most PTEs but not always for the same years. The period
1988 through 1996 is the longest period for which data is available for all PTEs.


                                                    73
 Table 7.1. Percent changes in key PTE data (per capita basis) 1988 to 1996
                                                          West          Greater            Merseyside         South .       West      .    Tyne &
                                                          Midlands      Mancheste                             Yorkshire     Yorkshire      Wear
                                                                        r
total bus journeys per capita                             -17           -29                -21                -34           -31            -24
Full-fare bus journeys per
capita                                                    -21           -31                -29                -31           -31            -18
Concessionary bus journeys
per capita                                                -8            -25                +7                 -39           -28            -36
bus vkm per capita                                        +21           -1.0               +12                +15           -1             +6
Real average weighted bus
fare                                                      +3            +15                +33                +68           +20            +42
Real average full-price bus
fare                                                      +15           -4                 +51                +38           +22            +18
Real concessionary fare                                   Zero          +105               Zero               +325          +8             +364



 7.3.1                          Bus patronage

 Total bus passenger journeys (Figure 7.4) declined overall in all areas with the highest
 reductions in South Yorkshire, West Yorkshire and Greater Manchester where bus
 patronage declined by 30% to 35%. Non-concessionary bus journeys (Figure 7.5)
 follow a similar pattern. Concessionary journeys (Figure 7.6) also follow a similar
 pattern albeit with some interesting differences. Concessionary patronage fell in all six
 PTE areas except Merseyside where there was an increase of 7%. The largest decline in
 concessionary patronage was again in South Yorkshire (39%) but this time Tyne &
 Wear exhibited the second largest decline (36%) followed by West Yorkshire (28%).
 The decline in concessionary patronage was higher than the decline in non-
 concessionary patronage in all PTEs except in the West Midlands and in Merseyside.

                                    Figure 7.4: Bus journeys per capita in the English PTEs 1987-1998

                              230

                              210

                              190
                                                                                     Tyne & Wear
    bus journeys per capita




                              170
                                                                          West Midlands
                              150
                                      West Yorkshire
                              130                                                                  South Yorkshire

                                                                                                                              Merseyside
                              110

                               90                                  Gtr. Manchester


                               70

                               50
                                     1987    1988      1989     1990   1991    1992      1993      1994     1995     1996   1997    1998




                                                                               74
                                                Figure 7.5: Full-fare bus journeys per capita in the English PTEs 1987-1998

                                                    160
                                                                Tyne & Wear

                                                    140
 full-fare bus journeys per capita




                                                    120
                                                                                       Merseyside

                                                    100
                                                                                                              West Midlands
                                                           South Yorkshire

                                                     80
                                                                                                             West Yorkshire
                                                              Gtr. Manchester
                                                     60


                                                     40
                                                          1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998




Figure 7.6: Concessionary bus journeys per capita in the English PTEs 1987-1998

                                                    80
  concessionary bus passenger journeys per capita




                                                                                      Tyne & Wear
                                                    70

                                                                         South Yorkshire
                                                    60

                                                                   West Midlands
                                                    50

                                                            Merseyside
                                                    40
                                                                                                         Gtr. Manchester

                                                    30
                                                                             West Yorkshire


                                                    20
                                                          1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998




                                                                                                    75
Concessionary journeys as a proportion of total bus journeys (Figure 7.7) remained
relatively stable in most areas (varying by about 2% to 4%). An exception to this is
Merseyside where the proportion rose from 25% to 35% between 1988 and 1998.


 Figure 7.7: Ratio of concessionary bus passenger journeys to total bus passenger
                      journeys in the English PTEs 1987-1998

                                                          0.45
 ratio of concessionary to total bus passenger journeys




                                                                                                                                        Gtr. Manchester

                                                           0.4
                                                                                                                               South Yorkshire

                                                          0.35


                                                           0.3
                                                                   West Midlands                   Merseyside                            Tyne & Wear

                                                          0.25

                                                                   West Yorkshire
                                                           0.2


                                                          0.15
                                                                 1987    1988      1989   1990   1991   1992    1993   1994   1995   1996        1997   1998




7.3.2                                                        Bus fares

There are data on average real cash fares paid by non-concessionary patrons for each of
the PTEs except the West Midlands for which the average revenue including CFR per
bus journey from the STATS100A data is used here. Fares increased in all areas with the
greatest percentage increases in Merseyside and South Yorkshire at close to 50% and
40% respectively (Figure 7.8). The increases in Tyne and Wear and in West Yorkshire
were smaller at close to 20% each. Real non-concessionary fares in the Greater
Manchester PTE are fell by 4% between 1988 and 1996. Merseyside and Tyne and
Wear exhibited the highest non-concessionary fare levels over the entire period.

As shown in Figure 7.9, the average concessionary fare varies by PTE. In the West
Midlands and Merseyside, concessionary patrons pay nothing. In West Yorkshire the
average concessionary fare fell from 25 pence to 20 pence in the early nineties and rose
again to 25 pence in the latter half of this decade. Concessionary fares in the remaining
three PTE areas rose steeply in percentage terms, although in all cases the starting base
was relatively low.




                                                                                                        76
                                              Figure 7.8: Average full fare in the English PTEs 1987-1998

                                  0.9

                                                                                                                              Merseyside
                                  0.8
  pounds per journey, 1995 £




                                                                                                                                 Tyne & Wear
                                  0.7
                                                                                                                              West Yorkshire

                                  0.6                                                                                         South Yorkshire


                                  0.5                                                                                     Gtr. Manchester


                                                                                                              West Midlands
                                  0.4


                                  0.3
                                            1987    1988    1989      1990   1991   1992      1993     1994   1995   1996     1997     1998




                                        Figure 7.9: Real concessionary fares in the English PTEs 1987-1998

                                   0.4

                                  0.35
                                                                                    Gtr. Manchester

                                   0.3                                                                               South Yorkshire
     pounds per journey, 1995 £




                                                     West Yorkshire
                                  0.25

                                   0.2

                                  0.15
                                                                                         Tyne & Wear
                                   0.1

                                  0.05

                                        0
                                             1987    1988   1989      1990   1991    1992     1993     1994   1995    1996     1997    1998




7.3.3                                   Bus vehicle kilometres

Bus vehicle service kilometres (Figure 7.10) increased in all areas except West
Yorkshire and Greater Manchester which each exhibited little or no change. The largest




                                                                                    77
increases were in the West Midlands (21%), South Yorkshire (15%) and Greater
Manchester (12%). Tyne and Wear showed a relatively low increase of 6%.

                    Figure 7.10: Bus vehicle kilometres per capita in the English PTEs 1987-1998

                                      90.00



                                      80.00           Tyne & Wear
  bus vehicle kilometres per capita




                                                                                                                  South Yorkshire
                                      70.00



                                      60.00                          Merseyside


                                                                                                                                    Gtr. Manchester
                                      50.00
                                                                                              West Yorkshire
                                                     West Midlands
                                      40.00
                                              1987   1988   1989       1990       1991    1992      1993       1994   1995   1996    1997     1998




7.4                                     Estimation results

Separate estimations for total bus journeys and adult (non-concessionary) bus journeys
were made using a partial adjustment constant elasticity dynamic specification
(Appendix A.2). Because of the small number of annual observations a pooled approach
was adopted (Appendix A.6). In both cases the fare elasticity was constrained to be the
same for all 6 PTE areas. The results of the estimations are reported in Section B.9 in
the Statistical Appendix and the resulting elasticities are given in Table 7.2 below. All
coefficients are of the expected sign and significant at the usual levels. The elasticities
for all journeys are in close agreement to those found earlier for the Metropolitan
counties using the national aggregate data (Table 4.6) and the STATS100 data (Table
6.3). Although the fare elasticities for full-fare journeys is lower than that for total
journeys, indicating that full-fare patrons may be less price sensitive than concessionary
patrons, the elasticities are not significantly different statistically. Thus, on the basis of
the given data, it cannot be concluded with certainty that there is a difference between
the fare elasticity for full-fare bus patrons and for all bus patrons together. Given these
results, however, it would be justified to conclude that the elasticities based on total
patronage might overestimate the price sensitivity for the full-fare-paying market, but
that the overestimation is marginal.




                                                                                         78
      Table 7.2: Estimated based on pooled PTE data for the Metropolitan areas.
                              Partial adjustment model.
 Independent variable        Fare elasticity        Income elasticity       Service elasticity
                          Short run   Long run   Short run   Long run     Short run   Long run
  Total bus journeys       -0.24        -0.52     -0.72        -1.56       +0.20       +0.44

 Full-fare bus journeys    -0.15       -0.38       -0.67        -1.72       +0.20       +0.50




7.5      Conclusions

In this Chapter, an attempt was made to determine whether or not the elasticity
estimated on the basis of total patronage is a good approximation for the fare sensitivity
of full-fare-paying market. Although there is some indication that full-fare-paying
patrons are slightly less fare-sensitive than the ‘average’ bus user, and thus appreciably
less fare-sensitive than concessionary patrons, the statistical evidence is rather weak.
This is perhaps not surprising given that the data used in the analysis contains a number
of inconsistencies. Data provided by the PTEs are not always entirely comparable with
each other, and in many instances the PTE data needed to be complemented with
information from other sources. Despite this, the estimates for the aggregate market in
the Metropolitan areas are in good agreement with those obtained on the basis of the
national aggregate and STATS100 data.




                                           79
        Addendum on the calculation of the average adult fare in each PTE

West Midlands (Centro)

No actual adult cash fares were provided for legal reasons. Centro obtains actual fares
data from the bus operators and the use and disclosure of this information is governed
by confidentiality agreements which precludes disclosure to a third party. Instead an
index tracking the change in fare level was provided. This index is based on fares for
the entire network and includes prepaid fares.

Greater Manchester (GMPTE)

Bus revenue data for the period 1986 to 1997 were obtained from the GMPTE
publication “Trends and Statistics 1986-1998”. These revenues do not include the CFR
paid by central government to the bus operators. The average fare paid by the average
bus user (i.e. an amalgam of full fare-paying adults and concessionary users) was
calculated by dividing these revenues by total bus passenger journeys for the year. The
average adult fare was calculated by multiplying the number of concessionary bus
passenger journeys by the average concessionary fare, subtracting the resulting figure
from total bus revenues to get full fare-paying revenues and dividing this by total annual
full fare-paying bus passenger journeys.

Merseyside (Merseytravel)

Merseytravel use the actual cash peak and off-peak fares for each of 6 operators in the
area and these are given for different trip lengths (1 mile, 2 miles, etc.). Total annual
mileage for each operator is also provided. The proportion of trips made in each
distance category is obtained by upward aggregation from on-bus surveys. It is
assumed that the same proportions hold for peak and off-peak travel. The overall
average peak fare is calculated in a number of steps. First, the actual fare charged by a
particular operator for a given journey length (say 3 miles) is multiplied by the
proportion of total annual bus miles supplied by that operator. The result is summed
over all operators to yield the overall average 3-mile peak fare in Merseyside. This
operation is repeated for each journey length. The overall average adult peak fare is
obtained as the weighted average of these average fares for each distance (weighted by
proportion of total journeys of each distance). The average adult off-peak fare is
calculated similarly. Note that the calculated proportion of bus miles supplied by the
operator is the total bus miles supplied by that operator for the year divided by total bus
miles supplied by all operators in the year. It is thus the same for all journey distances
and peak and off-peak.

South Yorkshire

The average fare data is a reflection of average adult fare i.e. single fares, return fares
(counted as two journeys at half the fare paid) and a few multi-journey tickets on one
minor operator (e.g. a £6.25 ten-journey ticket treated as 10 journeys at 62.5p).




                                            80
They are the only fares received from the PTE’s that are similar to the bus fare (average
revenue per bus trip including CFR) calculated in other sections of the project with
operator (= government data).

West Yorkshire (Metro)

Metro interview about 1.3 million passengers every year in on-board surveys. The
surveys are continuous throughout the year and are designed to look at the travel
behaviour of different categories of fare paying patrons (e.g. adult cash fares, travel pass
holders, concessionary patrons). Based on the fares information obtained about adult
cash fares, a simple arithmetic mean adult cash fare is calculated for the sample.

Tyne and Wear (Nexus)

The average adult fare used is based on a so-called “Elderly Equivalent Adult Fare”.
This latter is the result of extensive on-bus monitoring surveys of concessionary patrons
(undertaken to monitor as closely as possible the needs and travel behaviour of these
patrons). The distances and journeys travelled are aggregated up over the entire
network using a countywide weighting scale for routes and operators. Commercial fare
schedules are applied to the journeys to find the equivalent fare which would be paid by
a non-concessionary patron making the same journey. It is assumed for the purposes of
this exercise that concessionary and non-concessionary patrons have similar travel
patterns (i.e. a similar distribution of journey lengths). The argument put forward by
Nexus for supplying this fare as a proxy for the full-paying average adult fare is that in
the first place it is to hand since Nexus calculate it anyway as part of the assessment
procedure for determining concessionary fare reimbursement to operators. Secondly,
the commercial information on fares supplied to Nexus by the bus operators is
commercially sensitive and use and dissemination of this information by Nexus is
governed by strict contracts. And thirdly, the source at Nexus is of the opinion that the
average elderly equivalent fare matches the average non-concessionary fare quite
closely, though no quantitative estimate of how closely has been provided.




                                            81
8. BUS FARE ELASTICITY QUESTIONNAIRE


In order to publicise the results of the bus fare elasticity study and to obtain the views of
practitioners, a brief summary of the findings and a questionnaire were produced. Over
350 summaries and questionnaires were sent out, in some instances to more than one
contact person in a given organisation. Representatives of 120 different bus-operating
companies, 119 local authorities (city, borough and county councils) and the 6 PTEs in
England were contacted. The remaining recipients include trade publications, public
transport interest groups, and consultants and academics in the public transport field.

Of the 64 responses received, 41 are from bus operating companies and 14 from local
authorities, 3 from PTEs and the remainder from the other groups cited above. Overall
the response rate is about 18%. The response rate for the bus operators is significantly
higher (30%) than for the local authorities (12%), which is perhaps not surprising as the
questionnaire was more aimed at the former constituency.

A summary of the replies to the individual questions is shown and discussed in the
following. The percentages are based on the total sample of respondents including
missing responses, so that the percentages do not necessarily sum to 100%.


Q.1   What is your opinion of the market fare          About      Too low    Too high      Don’t
      elasticity estimated in this study?               right                              know
                              SR
                          (1 year)                      77%          8%         6%          6%
                             –0.4

                           LR
                        (7 years)                       41%          3%        28%          16%
                          –0.9

For this question, more respondents gave their opinion of the short-run elasticity
estimate (-0.4) than of the long-run value (-0.9): 97% and 88% of all respondents
respectively. In addition, of those who responded, 16% answered "don't know" for the
long-run elasticity, while only 6% gave this reply for the short-run elasticity. Regarding
the short-run elasticity, 77% consider the estimated value of -0.4 to be "about right",
with 8% considering it "too low" and 6% "too high". The distribution of responses is
similar for both operators and government agencies. There is far more uncertainty
regarding the long-run elasticity value of -0.9, with 28% of respondents replying “don’t
know” or giving no response, compared to only 9% for the short-run elasticity. Only
41% consider the estimated long-run value "about right", 28% think it "too high", but
only 3% regard it "too low". A larger proportion of government authorities (47%) than
bus operators (34%) regard the long-run value to be "about right", while far more
operators (34%) than authorities (24%) consider it "too high". Clearly, there is far less
consensus concerning the effects of fare changes in the long run than in the short run,
and far more respondents consider the estimated values higher than they expect.



                                             82
However, from the comments given, it appears that there is some confusion concerning
the concept of the long-run elasticity itself.


Q.2   Do you think the effect of a fare change on            Yes              No         Don’t
      patronage over time is similar to that                                             know
      shown in the figure on page 2?

                         Market                              53%          12.5%          30%
                        Operator                             39%           11%           34%

Here the respondents were asked their view concerning the effects on patronage of a
fare change over time, being referred to a figure showing the dynamic bus fare elasticity
estimated in the study. They were asked how this applies to the market elasticity as well
as to the operator elasticity. The definitions given for the two elasticities are: ‘Market’
elasticity – if all operators in a local bus market change fares (service) equally, and
‘Operator’ elasticity – if only one operator changes its fares (service). Over 1/3
answered "don't know" or gave no response regarding the market elasticity, while 50%
expressed no opinion regarding the operator elasticity. Slightly over 50% agreed with
effects shown in the figure for the market elasticity, while just under 40% agreed for the
operator elasticity. Although only a few respondents qualified their responses in terms
of the market and operator elasticities, some comments were "the curve is steeper for
the operator elasticity", "the operator elasticity is greater than the market elasticity" and
"the operator elasticity is more dominated by the short run". Others agreed with the
slope of the curve, but felt that the long-run elasticity was too high, or that the initial
drop in patronage would be greater. The major disagreement concerned the large
difference between the short- and long-run elasticity estimated in the study. A few of
the respondents suggested that the effect on patronage declines over time.


      Q.3   Does your organisation have or use any                 Yes             No
            elasticity estimate? If so, what is it?
                                                                   44%             52%

                   Market SR elasticity (15 replies)         -0.30 to –0.60
                   Market LR elasticity (4 replies)           -0.35, -0.50,
                                                              -0.80, -0.90
                     Market length of LR (1 reply)               1 year

              Operator SR (1 year) elasticity (16 replies)   -0.30 to –0.60
                  Operator LR elasticity (3 replies)          -0.35, -0.80,
                                                                  -0.90
                   Operator length of LR (2 replies)           1 yr, 5 yrs


As shown in the question above, 44% of respondents (59% of operators and 18% of
local authorities and PTEs) have or use an elasticity estimate. Despite this, only 24% of
respondents (12 operators, 2 PTEs and 1 academic) volunteered a value for the short-run
market elasticity estimate. Of these, 86% said that they used a short-run market
elasticity estimate of between -0.30 and –0.40 (or 60% said that they used a value of –
0.35 to –0.40).


                                               83
Only 4 respondents (2 operators, 1 PTE and 1 academic) gave a long-run market
elasticity estimate, and each gave a different value. The four different values are -0.35, -
0.50, -0.80 and -0.90. Only a single respondent quantified the length of the market long
run and put it at 1 year.

As for the operator elasticity, 25% of respondents (14 operators and 2 PTEs) gave a
value for the short-run of which 81% give a value of between –0.30 and –0.40 (or 45%
between –0.35 and –0.40). Only three respondents gave a long-run operator elasticity
estimate and each was different (-0.35, -0.50 and –0.90). Only two respondents gave a
quantified estimate of the length of the operator long-run and each was different (1 year
and 5 years).

For those reporting both a market and an operator elasticity, the values were identical in
all cases.

The values given for the short-run elasticities are well in line with that indicated by the
study. From the responses given for the long-run elasticity, it would appear that longer-
term effects of fare changes are rarely considered in practice.


Q.4   Do you think that the fare elasticity                Yes              No           Don’t
      increases at higher fare levels?                                                   know

                                                          48%             33%            19%

From question 4 it appears that nearly half of the respondents believe that the fare
elasticity increases at higher fare levels, while 1/3 do not. There thus seems to be some
support for the results of the study, which indicate that the elasticity is not constant, but
that it increase with the fare level.


Q.5   Which do you think has a greater effect on      Same       Decrease        Increase        Don’t
      patronage: a 30% fare increase or a 30%                                                    know
      fare decrease?

                         Market                         5%         11%             67%         12.5%
                        Operator                        3%        12.5%            56%          9%

As shown by the responses to question 5 above, the majority of respondents feel that a
fare increase has a greater effect on patronage than a fare decrease, and more think this
is true for the market as a whole than for the individual operator. A few respondents
commented. One points out that it "depends on the starting point", another remarks that
"while current users will see an increase it is unlikely that all potential users will see a
decrease", others suggest that for the operator, it "depends on competition".


Q.6   Which do you think has a greater impact          Same      Decrease         Increase       Don’t
      on patronage: a 30% decrease in fares or a                  in fares       in service      know
      30% increase in service (vehicle kms)?



                                             84
                        Market                         5%         22%          44%           19%
                       Operator                        5%         19%          38%           17%

There is less agreement about the effects of fare reductions as compared to service
improvement, although twice as many respondents believe that an increase in service
has a greater effect on patronage than a decrease in fares. Bus operators are more in
agreement than are local authorities. Of responding operators nearly 50% feel that an
increase in service has a greater effect, while only 20% think a reduction in fares has a
greater effect. Local authority respondents are split evenly between fares and service,
about 30% each. From these responses it would appear that bus operators are more
optimistic about the possibility of increasing patronage by service improvements than
by fare reductions. A number of respondents point out that the relative effects of fares
and service changes would depend on the initial service level.


Q.7   In general, do you think that improving            Yes            No           Don’t
      service frequency could compensate for                                         know
      patronage lost through fare increases?
                                                         63%            25%          11%

Question 7 addresses the issue of fare versus service in a slightly different fashion. Here
63% believe that improving service could compensate for patronage lost through fare
increases. Again, the replies differ for bus operators and local authorities - 68% versus
47%. There is a clear relationship between the response to this question and the
previous one: 65% of those answering "yes" also believe that service improvements
have a greater effect on patronage than fare reductions (Q.6), while 54% answering "no"
believe the opposite.


Q.8   Do you think motoring costs have a                 Yes            No           Don’t
      significant impact on bus patronage?                                           know
                                                         52%            44%           3%



Question 8 concerns the views of the respondents about the effects of motoring costs on
bus patronage. In total the opinions are rather split: 52% consider motoring costs to
have a significant effect, 44% do not. Notably, there is a difference between operators
and local authorities. A slight majority of operators (49% versus 46%) think motoring
costs do not have a significant effect on bus patronage, while for local authorities a
somewhat larger majority (53% versus 41%) think that motoring costs do have a
significant impact. It would appear that local authorities are more optimistic about the
possibility of encouraging bus use by increasing motoring costs than bus operators are.

A few respondents provided additional comments. Some agree that there is a small
effect, but not a 'significant' one. Two especially point to parking charges as being
particularly important. Another feels that low motoring costs effect patronage, but not
high costs, which suggests an asymmetry in the cross-price elasticity.




                                            85
Q.9   Do you expect the market elasticity for        Same        Lower     Higher    Don’t
      your county to be higher or lower than the                                     know
      average for GB?
                                                      33%         27%        25       5%

 From the above question, 33% of respondents think that the market elasticity for their
 county is the same as the average for the UK, 27% think it lower and 25% higher. Those
 who thought is was different were asked to say why. In general, the majority who felt
 the elasticity for their county was lower operate in more densely populated cities or
 conurbations, while those operating in less-densely-populated areas thought their
 elasticity to be higher. The reasons given largely have to do with low car ownership or
 with constraints on car use in urban areas – congestion, limited parking or high parking
 fees. However, there are exceptions. Some counties were considered to have a higher
 elasticity, despite their urban conditions and comparatively low car ownership. Feelings
 were also mixed about the effects of income and make-up of the population. Low
 income and a large proportion of OAPs were cited as justifications for both higher
 elasticities (unnecessary trips would be foregone) and lower elasticities (a more captive
 market because of fewer alternatives). The level of fares was not cited as factor
 influencing fare-sensitivity, but good service and a positive attitude to public transport
 was mentioned as a reason for lower elasticities.

 Finally, respondents were asked to provide “any other comments”. The majority did so,
 and a few expressed longer comments in letters. Many comments concern short-
 comings of the study and suggest that other factors need to be considered: service
 reliability, alternative services and modes, traffic and parking conditions, information,
 marketing, differences in market segments, between ticket types and between time of
 day. There also seemed to be some confusion concerning the long-run elasticity, both as
 to how it’s defined as well as how it could be estimated empirically.




                                            86
                                     References

Alexandersson, G., Hulten, S. and Folster, S. (1998), “The Effects of Competition in
   Swedish Local Bus Services”, Journal of Transport Economics and Policy, 32(2),
   pp. 203-220
Bates, J.J., and Roberts, M. (1979), “The Interrelationship of Car Ownership and Public
   Transport”, Paper MI, PTRC, July
Bates, J.J., and Roberts, M. (1981), “Forecasts for the Ownership and Use of a Car”,
   Round Table 55, European Conference of Ministers of Transport, Paris
Copely, G. and Lowe, S. (1981), “The Temporal Stability of Trip Rates”, Paper N19,
   PTRC, July
Dargay, J. M. (1999), “The Effect of Income on car Ownership: Evidence of
   Asymmetry”, ESRC TSU, March
Dargay, J. M. and Gately, D. (1999), “The Demand for Transportation Fuels: Imperfect
   Price Reversibility?”, Transportation Research, A, 33A, pp. 71-82
Dargay, J. M. and Pekkarinen, S. (1998), “The Effects of Public Transport Subsidies on
   Bus Travel Demand - Regional Bus Cards and City Travel Tickets in Finland”, 8th
   World Conference on Transport Research, Antwerp, Belgium, July, 1998
De Rus, G. (1990), “Public Transport Demand Elasticities in Spain”, Journal of
   Transport Economics and Policy, 24(2), 189-201
Fowkes, A.S., Sherwood, N. and Nash, C. N. (1992), “Segmentation of the Travel
   Market in London and Estimates of Elasticities and Value of Travel Time”, ITS
   Working Paper 345, University of Leeds
Gilbert, C. L., and Jalilian, H. (1991), “The Demand for Travel and for Travelcards on
   London Regional Transport”, Journal of Transport Economics and Policy, 25(1), 3-
   29
Goodwin, P.B., Hopkin, J. and McKensie, R. (1988), “Bus Trip Generation from
   Concessionary Fare Schemes: A Study of Six Towns”, Research Report 127, TRRL,
   Crowthorne
Goodwin, P.B. (1973), "Some causes and effects of variations in the structure of
   demand for urban passenger transport", Ph. D. Thesis, University of London.
Goodwin, P.B. (1988), "Circumstances in which people reduce car ownership: a
   comparative analysis of three panel data sets", Journal of the International
   Association of Traffic and Safety Sciences, 12,2, Tokyo.
Goodwin, P.B. (1992), “A Review of New Demand Elasticities with Special Reference
   to Short and Long Run Effects of Price Charges”, Journal of Transport Economics
   and Policy, 26(2) May, pp.155-170
Goodwin, P.B., Oum, T.H., Waters II, W.G., Yong, J.S., “An Annotated Bibliography
   on Demand Elasticities”, TSU Oxford, Working Paper, July 1992, TSU Ref: 682
Halcrow Fox (1993), “London Congestion Charging: Review and Specification of
   Model Elasticities”, Leeds, England
Hensher, D.A. (1998a), “Establishing a Fare Elasticity Regime for Urban Passenger
   Transport”, Journal of Transport Economics and Policy, 32(2), pp. 221-246
Hensher, D.A. and King, J. (1998b), “Establishing Fare Elasticity Regimes for Urban
   Passenger Transport: Time-Based Fares for Concession and Non-Concession
   Markets Segmented by Trip Length”, Journal of Transportation and Statistics, 1(1),
   pp. 43-61
ISOTOPE, (1997), "Improved structure and organisation for urban transport operations


                                          87
   of passengers in Europe", Transport Research 4th Framework Programme, Urban
   Transport, DGVII, European Commission, Brussels
Kemp, M.A. (1973), "Some evidence of transit demand elasticities", Transportation, 2,
   25-52
London Transport (1987), “Traffic Trends since 1970”, Economic Research Report
   R266
London Transport (1992), “Traffic Trends 1979-90”, Research Report R273
Nijkamp, P. and Pepping, G. (1998), “Meta-Analysis for Explaining the Variance in
   Public Transport Demand Elasticities in Europe”, Journal of Transportation and
   Statistics, 1(1), pp. 1-14
Oum, T.H., Waters II, W.G., Yong, J.S. (1990), "A survey of recent estimates of price
   elasticities of demand for transport", World Bank Working Paper, WPS359,
   Washington D.C.
Oum, T.H., Waters II, W.G., Yong, J.S. (1992), “Concepts of Price Elasticities of
   Transport Demand and Recent Empirical Estimates”, Journal of Transport
   Economics and Policy, 26(2) May, pp.139-154
Preston, J.(1998), “Public Transport Elasticities: Time for a Re-think?”, UTSG 30th
   Annual Conference, TSU, University of Oxford, January
Tegner, G., Loncar-Lucassi, V. and Nilsson, C. (1998), “The Demand for Public
   Transport Trips in Stockholm County”, Workshop 8, Economics and Institutions of
   Transport, Borlange, Sweden
Watts, P. F., Turner, R.P and Whilte, P.R. (1990), "Urban minibuses in Britain:
   development, user responses, operations and finances", TRL research report 269
Webster, F.V and Bly, P. H. (eds) (1980), “The Demand for Public Transport”, Report
   of an international collaborative study, Transport and Road Research Laboratory,
   Crowthorne, Berks.
White, P. (1995), "Deregulation of local bus services in Great Britain: an introductory
   review", Transport Reviews, 15, 2, 185-209


Statistical Sources:

Census 1991, Office of Population Censuses and Surveys Report for Great Britain Part
2, HMSO, London, 1993
Blue Book, Office of National Statistics (ONS)
Economic Trends, HMSO, London
Annual Abstract of Statistics 1998, HMSO London
Transport Statistics Great Britain, HMSO London
Busdata, HMSO London
Regional Trends, HMSO London
Transport Statistics for London, HMSO London
Transport Statistics for Metropolitan Areas, HMSO London




                                          88
    APPENDIX A

TECHNICAL APPENDIX
A.1. MODELLING FRAMEWORK

In general, the long-run equilibrium demand for bus services can be expressed as


QB = f ( PB , PA , PC , S , I , D)
 *
                                                                                    (1)

where Q*B,t is the number of passenger kilometres or passenger trips travelled by bus.
This is assumed to be some function f of the bus fare, PB, the fares of competing public
transport modes (where applicable), PA, motoring costs, PC, the service level and quality
of bus travel, S, and the characteristics of the market represented by disposable income,
I, and the other socio-demographic characteristics. Since the data used concern
aggregate rather than individual trips, and no information is available regarding average
journey time by different modes, costs are expressed purely in terms of monetary costs.
D can include population, employment rates, age structure, car ownership levels and
population density.

The complexity of the model, particularly in terms of the explanatory variables
included, will depend on data availability and will be different for the three data sources
used. The aggregate data analysis will rely on averages over rather wide geographic
areas, so that socio-economic and demographic characteristics, bus fares and alternative
public transport fares will be represented by broad averages and bus service quality will
necessarily be limited to rather rough measures.

A dynamic modelling strategy is required for the estimation of both short- and long-run
elasticities on the basis of the time series data. Two types of dynamic model have been
used for the analysis – a partial adjustment model and an error correction model. These
are described below.


A.2. THE PARTIAL ADJUSTMENT MODEL

In any given time period, actual bus patronage could only be expected to be in
equilibrium with respect to prevailing fares, prices, incomes etc. if the latter have
remained constant over a considerable period of time. Such is generally not the case.
For this reason, the desired long-run patronage, given the prices and incomes at time t,
Q*B,t, is not observable, so we need to relate it to actual patronage in time t, QB,t. This
can be accomplished by assuming that an attempt is made to bring Q to its desired level,
but that only a proportion, θ, of the gap between desired patronage and actual patronage
is closed each year.
                     (
QB ,t − QB ,t −1 = θ QB ,t − QB ,t −1
                      *
                                        )                                           (2)

where 0 ≤ θ < 1 is the adjustment coefficient, which indicates the rate of adjustment to
long-run equilibrium. There are numerous reasons why complete adjustment is not




                                            A-1
achieved in a single period. These include persistence of habit, uncertainty and
imperfect information regarding alternatives and price and costs of adjustment.

By substituting desired long-run patronage from (1) into the above and solving for QB,t
we have

              (                                 )
Q B ,t = θ f PB ,t , PA ,t , PC ,t S t , I t , Dt + (1 − θ )Q B ,t −1                (3)

The presence of demand in the previous period on the right-hand side of the equation
can be interpreted in terms of habits or inertia - what individuals do in the past also
affects their future behaviour. Also, since demand in period t-1 is influenced by prices,
etc. in period t-1, and similarly for all other previous periods, demand in any period is
determined by the entire past history of prices and other relevant variables. Individuals
do not respond to changing circumstances instantaneously, but with a delay. This can
be seen by repeated substitution in (3):

QB ,t = θ f ( X t ) + (1 − θ )θ f ( X t −1 ) + (1 − θ ) θ f ( X t − 2 )+...
                                                         2
                                                                                     (4)


                  (                                 )
where X t = PB ,t , PA ,t , PC ,t , S t , I t , Dt for simplicity.

Assuming f to be a linear function, X the vector of independent variables and a constant
and all variables to be in logarithmic forms results in a constant elasticity specification.
The long-run relationship becomes:

LnQB ,t = β LnX t
   *
                                                                                     (5)

and the estimated model is

LnQB ,t = θ β LnX t + (1 − θ )LnQB ,t −1                                             (6)

The short-run elasticities are obtained directly from the coefficients of the independent
variables, while the long-run elasticities are calculated as the short-run elasticities
divided by the adjustment coefficient θ:

ε SR = θβ
                                                                                     (7)
ε LR = θβ θ = β

The lower the θ, the slower the speed of adjustment and the greater the difference
between the short- and long-run elasticities. From the coefficient θ, the number of
periods required to close a given proportion p of the gap between the long-run and
actual value of Q can be calculated. This is given by:

     Ln (1 − p )
n=               .                                                                   (8)
     Ln (1 − θ )


                                                             A-2
A.3. ERROR-CORRECTION MODEL

Another form which is often used to introduce dynamics into an economic model is an
error-correction mechanism. The dependent variable in an error-correction model is
specified in terms of differences, rather than levels. This has certain advantages for the
statistical estimation, as will be discussed below. The error-correction model can be
written as:

∆QB ,t = (ϕ − 1)QB ,t −1 + β 0 ∆X t + ( β 0 + β1 ) X t −1                             (9)

or alternatively as:

                                        (β + β1 )        
∆Q B ,t = β 0 ∆X t + (ϕ − 1) Q B ,t −1 − 0        X t −1  .                         (10)
                                         (1 − ϕ )        

The parameter β0 is the impact, or short-term, effect and (1-ϕ) is the feedback effect,
which is similar to the adjustment coefficient, θ, in the Partial Adjustment Model. The
long-run response is given by ( β o + β 1 ) (1 − ϕ ) . The term in the square brackets in
equation (10) is called an ‘error-correction mechanism’ since it reflects the deviation
from the long run, with (1-ϕ) of this deviation being closed each period.

The Error Correction Model imposes a less restrictive lag structure than the Partial
Adjustment Model by including lagged independent variables. The short-run (or first
period) response is thus not necessarily the same proportion of the long-run response for
all independent variables. Further, if the ECM is the correct specification, the estimates
obtained from the Partial Adjustment Model will suffer from biases, since it omits X t-1
which is often highly correlated with Xt. Another problem with the Partial Adjustment
Model occurs if the dependent variable is non-stationary, which is usually the case with
economic series that continually increase (or decrease) over time. If this is the case, the
estimates obtained may be inconsistent and the standard significance tests misleading.
This is not a problem with the Error Correction model, since the dependent variable is
in differenced form, and thus generally stationary.

Stationarity can be tested with the Augmented Dickey-Fuller (ADF) Test, which
consists of regressing the 1st difference of a series on the level of the series lagged once,
lagged difference terms, a constant a trend. The ADF test is the test of the significance
of the lagged level term. If the coefficient is significantly different from zero, than the
hypothesis that the series contains a unit root is rejected, and stationarity can be
accepted. Thus a large negative test statistic suggests stationarity. If the series is not
stationary, or I(0), one must then test for the order of integration, or in other words, the
number of times the series must be differenced in order to obtain stationarity. The test
for integration of the first order, or I(1), involves regressing the second difference of the
series on its first difference, lagged second difference terms, a constant and trend. If the
coefficient of the lagged 1st difference term is significant, the hypothesis that the 1st


                                                      A-3
difference contains a unit root is rejected and the original series is I(1). Similar tests can
be performed for higher levels of integration if the 1st difference is not stationary.
However, most economic variables are generally found to be I(0) or I(1).

Given that the series are I(1), the Error Correction Model in equation (10) could be
estimated directly. Alternatively, a 2-step approach can be used. It could be shown that
if the variables are non-stationary and cointegrated, the long-run relationship could be
estimated directly from the static regression:

Qt = βX t + µ t                                                                        (11)

where β are the long-run parameters, and µ is a stochastic error term, which will be
stationary if Q and X are cointegrated. If this is the case, then equation (11) is termed
the cointegrating vector or regression. The hypothesis of cointegration can be tested by
examining the stationarity of µ using various statistical tests – the Dickey-Fuller test or
the Durbin-Watson test of the cointegrating regression (CRDW). If cointegration is
indicated, the residuals from the cointegration regression, µ , are used as an error
correction term in the dynamic Error-Correction Model, i.e., the term in brackets in
equation (10), and the following model is estimated:

∆QB ,t = + β 0 ∆X t + (ϕ − 1) µ t −1 .                                                 (12)

The short-run elasticities are determined by the parameters β0 and the feedback effect,
(ϕ -1), by the coefficient of µ. For the resulting model to have a plausible interpretation,
(ϕ -1) must be significantly negative and < 1 in absolute value, since ϕ must be positive.


A.4. STRUCTURAL MODEL

A structural model of bus use considers all the interactions determining bus patronage.
Apart from income and bus fares, here we consider only the effects of car ownership
and use and motoring costs. Given the aggregate nature of the data used to estimate the
model, service variables and alternative public transport modes are not included.

The basic model is a four-equation system:

J = α J + β JF F + γ JI I + β JM M + δ JC C
K = α K + β KF F + γ KI I + β KM M + δ KC C
                                                                                       (13)
C = α C + β CF F + γ CI I + β CM M
U = αU + β UF F + γ UI I + β UM M + δ UC C

where

J is bus journeys
K is bus passenger kilometres
C is car ownership


                                              A-4
U is car use in terms of passenger kilometres
F is the bus fare
I is income
M is motoring costs.

Assuming all variables are in log-form (so that the model is of the constant elasticity
type), the direct and total elasticities for bus journeys and car use are calculated as
follows. The total effect of, for example, motoring costs on bus journeys is made up of a
direct effect and of an indirect effect through the effect of motoring costs on car
ownership. Similarly, the total effect of bus fares on car use is also made up of a direct
effect and the effect of fare on car ownership. Any of these effects, however, may be
zero, which will be determined in the estimation.

Elasticity of:    With respect to:   Direct elasticity            Total elasticity
Bus journeys      Fare                           βJF              βJF + δJC βCF
                  Income                         γJI              γJI + δJC γCI
                  Car ownership                  δJC
                  Motoring costs                βJM               βJM + δJC βCM
Car use           Fare                          βUF               βUF + δUC βCF
                  Income                         γUI              γUI + δUC γCI
                  Car ownership                 δUC
                  Motoring costs                βUM               βUM + δUC βCM



Elasticities pertaining to the other variables could be derived in a similar fashion.

Since the equations (and the error terms) are related, the system must be estimated
simultaneously. Three-stage least squares techniques have been used.


A.5. ASYMMETRIC RESPONSE MODEL

The method used to analyse possible differences in response to rising and falling fares is
based on that used in Dargay and Gately (1997) to examine the issue of price-
reversibility. It is based on decomposing the variable of interest, in this case, the bus
fare. In order to distinguish between the responses to rising and falling income, the fare
variable Ft is decomposed into two monotonic variables: the cumulating series of fare
rises, Ft R , which is non-negative and non-decreasing, and the cumulating series of fare
falls, Ft F , which is non-positive and non-increasing. These are defined as follows:

       T
Ft R = ∑ max{0, Ft − Ft −1 }
      t =0


       T
Ft F = ∑ min{0, Ft − Ft −1 }                                                            (14)
      t =0




                                            A-5
where

Ft = F0 + Ft R + Ft F .

In the logarithmic specification, the decomposition is based on the logarithm of fares, so
that the Fs in the above equations are replaced by LnF.

By replacing the original fare variable in the estimated equation with Ft R and Ft F (or
with the log-decompositions) we obtain the asymmetric specification, which in the case
of the logarithmic model can be written as:

LnQt = α + β R LnFt R + β F Ln Ft F + γ Ln Z t                                         (15)

where βR and βF denote the response to rising and falling fares, respectively. If βR > βF
the response of bus patronage to rising fares will be greater than that to falling fares, and
vice-versa. If βR = βF the response of bus patronage will be the same to rising and to
falling fares, and the model will revert to the symmetric specification.

Clearly, the estimation of such an asymmetric model requires that fares have risen and
fallen over the observation period. If fares are generally constantly rising (in real terms),
there will not be a sufficient number of cases of falling fares to separately estimate the
response to falling fares. We will therefore not be able to statistically distinguish
between the effects of fare increases and fare reductions.


A.6. POOLED CROSS-SECTION TIME-SERIES MODEL

Pooling time-series and cross-section data is a technique often used to obtain more
reliable estimates of model parameters. It can be used when time-series data exist for a
number of individuals, firms, regions or countries, and when it can be assumed that the
relationship to be estimated and many of the parameters are the same for all of them. It
is particularly useful when only short data series are available. By combining the data in
the estimation procedure, the number of observations (and degrees of freedom) is
increased, thus improving the significance of the estimated parameters. It is also useful
when the variation over time in each individual data series is small. The variation
between individuals or regions may be greater, which will also serve to reduce the
variance of the estimates, providing greater reliability.

In the case of the bus data, pooling is advantageous for both of these reasons. The
number of time-series observations for each region is too little for reliable estimation of
elasticities. In addition, the variation – particularly in fares – is generally small over the
limited time period, but it is much greater between regions.

A time-series cross-section model can take various forms, depending on the
assumptions made about the similarity of the relationship to be estimated for the various
regions. Assume we have two regions, denoted by 1 and 2. Let YR t (R = 1, 2) denote the



                                                 A-6
dependent variable and for region R, and XR t and ZR t denote the independent variables
in the same fashion. The following two models could be estimated, one for each region.

Y1t = α1 + β1 X 1t + γ 1 Z1t
                                                                                      (16)
Y2 t = α 2 + β 2 X 2 t + γ 2 Z 2 t

As they stand, the two relationships are only similar in their specification, and the
parameters of the models – the α, β and γ - differ for the two regions. This is the most
unrestricted form and little is to be gained in estimating the two regions simultaneously
(or pooling them). However, if we can assume that at least some of the parameters are
the same for all regions, pooling will result in more reliable estimates. In the most
restricted form of the pooled model, it is assumed that all slope coefficients (the β and γ)
are the same for all regions, i.e. they have common slopes. The difference between
regions being represented by different intercepts (α). Such a model is termed a fixed-
effect model. An intermediate form of the model allows one or more (but not all) of the
slope parameters to vary across regions, along with the intercepts. This is generally the
most useful form, since parameters which can be thought to be the same for all regions
can be restrained to be so (thus improving the reliability of the estimates), while those
which might be thought to be different can be allowed to vary. In this way, statistical
tests could be used to test the equality of the parameters for the separate regions.

In the empirical work, we estimate two forms of the pooled model. One where only the
intercepts are region specific

QR t = α R + β FR t + γ Z R t                                                         (17)

where QRt is bus patronage, FRt is the bus fare, and ZRt are other explanatory variables in
region R in time t, αR is the region-specific intercept for region R, and β and γ are
parameters assumed to be the same for all regions. For a constant elasticity model, this
restriction implies that the elasticities are the same for all regions.

The second model also allows the coefficient of the fare variable (or the fare elasticity,
in the constant elasticity model) to be region specific:

QR t = α R + β R FR t + γ Z R t                                                       (18)

where βR is the coefficient relating to the fare variable for region R, and the coefficients,
γ, relating to all other variables Z are constrained to be equal for all regions.


A.7. VARIABLE ELASTICITY MODEL

The constant elasticity model is used for the majority of estimations. This is a model in
which all variables are in logarithmic form:

LnQR t = α R + β R LnFR t + γ LnZ R t .                                               (19)


                                            A-7
One of the questions we are interested in is whether or not the fare elasticity is constant,
i.e. if it’s the same for all fare levels or if it is itself related to the fare level. A simple
way of allowing the elasticity to be related to the fare level is to use an alternative
functional form in which the fare variable is specified in levels rather than logs:

LnQR t = α R + β R FR t + γ LnZ R t .                                                    (20)

The elasticities implied by this specification are derived as

         ∂Q F ∂LnQ
ε QF =        =    F =β F                                                                (21)
         ∂F Q   ∂F

so that the elasticity increases with increasing fare level. Since this model has the same
dependent variable as the constant elasticity model, the choice between them can be
made on the basis of simple statistical tests.




                                             A-8
    APPENDIX B

STATISTICAL APPENDIX
B.1.    NATIONAL GB: ERROR-CORRECTION MODEL

Table B.1.1. Stationarity (ADF) tests. All variables in log form.
                                      Levels    1st differences
Bus fare index                        -3.35     -4.91***
Fare per journey excl. CFR            -1.08     -2.62*
Fare per journey incl. CFR            -2.63     -4.85***
Bus journeys per capita               -2.61     -4.04***
Bus passenger kms per capita          -2.11     -3.61**
Income per capita                     -1.17     -3.37**
Cars per capita                       -3.22**   -4.02***
Car passenger kms per capita          -2.75*    -4.10***
Motoring price index                  -1.53     -3.08**

Non-stationarity rejected at the *10% level, ** 5% level, *** 1% level


Table B.1.2. Journeys per capita & Bus fare index.
Cointegrating Regression                          Cointegration accepted at the
Dependent variable: Ln(Journeys per capita)       *10%l, ** 5%, *** 1% level
Fare: Bus fare index                        Observations: 23

Variable                         Coefficient            Std. Error          T-Statistic

Constant                           12.44228             0.461536            26.95840
Ln(Fare)                          -0.879271             0.123584           -7.114758
Ln(Income)                        -0.446832             0.101097           -4.297203

Adjusted R-squared        0.977774              SSE                   0.018534
CRDW                      1.61***               ADF                  -3.02***

Restricted ECM
Dependent variable: ∆Ln(Journeys per capita)
Fare: Bus fare index                        Observations: 22

Variable                         Coefficient            Std. Error          T-Statistic

Constant                          -0.026784             0.007228           -3.705673
∆Ln(Fare)                         -0.338219             0.140767           -2.402686
∆Ln(Income)                        0.277191             0.193539            1.432225
EC(-1)                            -0.494085             0.172684           -2.861212

Adjusted R-squared         0.344292             SSE                  0.007363




                                                B-1
Table B.1.3. Journeys per capita & Fare per journey excluding CFR.
Cointegrating Regression                          Cointegration accepted at the
Dependent variable: Ln(Journeys per capita)       *10%, ** 5%, *** 1% level
Fare: Price per journey excl. CFR           Observations: 20

Variable                       Coefficient         Std. Error          T-Statistic

Constant                        11.09021           1.155898            9.594454
Ln(Fare)                       -0.624434           0.260050           -2.401206
Ln(Income)                     -0.800355           0.107916           -7.416480

Adjusted R-squared      0.931632             SSE                 0.029555
CRDW                    0.747***             ADF                -3.62***

Restricted ECM
Dependent variable: ∆Ln(Journeys per capita)
Fare: Price per journey excl. CFR           Observations: 19

Variable                       Coefficient         Std. Error          T-Statistic

Constant                       -0.034437           0.007643           -4.505877
∆Ln(Fare)                      -0.325709           0.196258           -1.659597
∆Ln(Income)                     0.411385           0.216760            1.897886
EC(-1)                         -0.401231           0.116896           -3.432368

Adjusted R-squared      0.438548             SSE                0.005687


Table B.1.4. Journeys per capita & Fare per journey including CFR.
Cointegrating Regression                          Cointegration accepted at the
Dependent variable: Ln(Journeys per capita)       *10%, ** 5%, *** 1% level
Fare: Price per journey incl. CFR           Observations: 27

Variable                       Coefficient         Std. Error          T-Statistic

Constant                        8.933125           0.896443            9.965077
Ln(Fare)                       -0.949173           0.127179           -7.463262
Ln(Income)                     -0.570455           0.091308           -6.247597

Adjusted R-squared      0.980375             SSE                 0.029555
CRDW                    1.259***             ADF                -3.09***

Restricted ECM
Dependent variable: ∆Ln(Journeys per capita)
Fare: Price per journey incl. CFR           Observations: 26

Variable                       Coefficient         Std. Error          T-Statistic

Constant                       -0.025836           0.005773           -4.475068
∆Ln(Fare)                      -0.407772           0.114523           -3.560625
∆Ln(Income)                     0.179787           0.146808            1.224643
EC(-1)                         -0.396148           0.130317           -3.039867

Adjusted R-squared      0.418985             SSE                0.007721




                                             B-2
Table B.1.5. Passenger kilometres per capita & Bus fare index.
Cointegrating Regression                         Cointegration accepted at the
Dependent variable: Ln(Passenger kms per capita) *10%, ** 5%, *** 1% level
Fare: Bus fare index                      Observations: 23

Variable                      Coefficient         Std. Error          T-Statistic

Constant                       11.20885           0.397736            28.18161
Ln(Fare)                      -0.708994           0.106501           -6.657188
Ln(Income)                    -0.145168           0.089608           -1.620026

Adjusted R-squared      0.954951            SSE                0.013770
CRDW                    0.89***             ADF                -2.23**

Restricted ECM
Dependent variable: ∆Ln(Passenger kms per capita)
Fare: Bus fare index                      Observations: 22

Variable                      Coefficient         Std. Error          T-Statistic

Constant                      -0.004151           0.002972           -1.396514
∆Ln(Fare)                     -0.190485           0.054440           -3.498993
∆Ln(Income)                    0.049222           0.081759            0.602034
EC(-1)                        -0.172751           0.081277           -2.125473

Adjusted R-squared      0.370833            SSE                0.001347


Table B.1.6. Passenger kilometres per capita & Fare per journey excluding CFR.
Cointegrating Regression                         Cointegration accepted at the
Dependent variable: Ln(Passenger kms per capita) *10%, ** 5%, *** 1% level
Fare: Price per journey excl. CFR         Observations: 20

Variable                      Coefficient         Std. Error          T-Statistic

Constant                       14.03025           1.752543            8.005653
Ln(Fare)                      -0.433228           0.380611           -1.138244
Ln(Income)                    -0.634215           0.066188           -9.582055

Adjusted R-squared      0.835807            SSE                 0.027857
CRDW                    0.550**             ADF                -3.62***

Restricted ECM
Dependent variable: ∆Ln(Passenger kms per capita)
Fare: Price per journey excl. CFR         Observations: 19

Variable                      Coefficient         Std. Error          T-Statistic

Constant                      -0.011639           0.002986           -3.898352
∆Ln(Fare)                     -0.183522           0.059899           -3.063852
∆Ln(Income)                    0.160746           0.089171            1.802677
EC(-1)                        -0.151355           0.049689           -3.046066



                                            B-3
Adjusted R-squared      0.518298            SSE                  0.000958

Table B.1.7. Passenger kilometres per capita & Fare per journey including CFR.
Cointegrating Regression                         Cointegration accepted at the
Dependent variable: Ln(Passenger kms per capita) *10%, ** 5%, *** 1% level
Fare: Price per journey incl. CFR         Observations: 27

Variable               Coefficient          Std. Error           T-Statistic

Constant                       15.21938             0.508241              29.94521
Ln(Fare)                      -0.919622             0.170559             -5.391796
Ln(Income)                    -0.540725             0.043943             -12.30505

Adjusted R-squared      0.948698            SSE                   0.023740
CRDW                    1.161***            ADF                  -3.09***

Restricted ECM
Dependent variable: ∆Ln(Passenger kms per capita)
Fare: Price per journey incl. CFR         Observations: 26

Variable                      Coefficient           Std. Error           T-Statistic

Constant                      -0.006429             0.002111             -3.044686
∆Ln(Fare)                     -0.199435             0.044668             -4.464852
∆Ln(Income)                    0.042310             0.060132              0.793625
EC(-1)                        -0.156778             0.056880             -2.756265

Adjusted R-squared      0.444652            SSE                  0.001345




                                            B-4
B.2.   NATIONAL GB: STRUCTURAL MODEL

Table B.2.1. Cointegrating regression. Fare: Bus fare index.
Cointegrating Regression                        Cointegration accepted at      the
                                                *10%, ** 5%, *** 1% level
                                              Observations: 22

Dependent variable: Ln(Bus passenger kms per capita)
                              Coefficient          Std. Error           T-Statistic
 Constant                      4.469149            1.949135             2.292888
 Ln(Fare)                        -0.6277           0.114379              -5.48785
 Ln(Income)                    0.476963            0.172329               2.76775
 Ln(Cars)                       -0.73258             0.21444             -3.41626

Adjusted R-squared      0.970539              SSE                 0.007126
CRDW                    1.65***               ADF                -5.09***

Dependent variable: Ln(Journeys per capita)
                              Coefficient           Std. Error          T-Statistic
 Constant                       6.538753            2.897382            2.256779
 Ln(Fare)                       -0.81561            0.169279             -4.81813
 Ln(Income)                     0.102027            0.255905            0.398692
 Ln(Cars)                       -0.64082            0.318809             -2.01005

Adjusted R-squared      0.974516              SSE                 0.015413
CRDW                    1.65***               ADF                -3.22***

Dependent variable: Ln(Cars per capita)
                               Coefficient          Std. Error          T-Statistic
 Constant                        -5.60259           0.780796             -7.17548
 Ln(Fare)                       0.416817             0.07866            5.298992
 Ln(Income)                     0.557767            0.068327            8.163174
 Ln(Motoring costs               -0.51461           0.113593             -4.53026

Adjusted R-squared      0.989678              SSE                 0.004451
CRDW                    1.45***               ADF                -2.64**

Dependent variable: Ln(Car passenger kms per capita)
                               Coefficient         Std. Error           T-Statistic
 Constant                       9.204065           1.676449             5.490216
 Ln(Fare)                       -0.03153           0.132308              -0.23827
 Ln(Income)                     0.393992           0.160689             2.451895
 Ln(Cars)                       0.809464           0.255772             3.164781
 Ln(Motoring costs)             -0.55053           0.170819              -3.22289

Adjusted R-squared      0.993294              SSE                 0.004649
CRDW                    1.66***               ADF                -3.49***




                                              B-5
Table B.2.2. Restricted ECM. Fare: Bus fare index.
Restricted ECM

                                             Observations: 22

Dependent variable: ∆Ln(Bus passenger kms per capita)
                        Coefficient        Std. Error            T-Statistic
 Constant                        -0.00412           0.002982               -1.38292
 ∆Ln(Fare)                       -0.32168           0.065962               -4.87682
 ∆Ln(Income)                        0.1382          0.092663              1.491414
 ∆Ln(Cars)                       -0.02725           0.143885                 -0.1894
 EC(-1)                          -0.40673           0.110462               -3.68205

Adjusted R-squared       0.333601            SSE                 0.001347

Dependent variable: ∆Ln(Journeys per capita)
                        Coefficient         Std. Error           T-Statistic
 Constant                          -0.0253             0.00704             -3.59366
 ∆Ln(Fare)                       -0.52439            0.162662              -3.22381
 ∆Ln(Income)                     0.378452            0.205363             1.842838
 ∆Ln(Cars)                       -0.05684            0.340399              -0.16697
 EC(-1)                          -0.62792            0.147708                -4.2511

Adjusted R-squared       0.375357            SSE                 0.006624

Dependent variable: ∆Ln(Cars per capita)
                        Coefficient          Std. Error          T-Statistic
 Constant                        0.010319             0.003441            2.998799
 ∆Ln(Fare)                       0.185163             0.062007            2.986157
 ∆Ln(Income)                     0.365753             0.094608            3.865993
 ∆Ln(Motoring costs                -0.3848            0.094986             -4.05113
 EC(-1)                          -0.65359             0.144601             -4.51999

Adjusted R-squared       0.597037            SSE                 0.002209

Dependent variable: ∆Ln(Car passenger kms per capita)
                        Coefficient        Std. Error            T-Statistic
 Constant                        0.002903           0.005522              0.525678
 ∆Ln(Fare)                         -0.0663          0.104622               -0.63366
 ∆Ln(Income)                     0.139734           0.165662                0.84349
 ∆Ln(Cars)                       0.942927              0.2938             3.209418
 ∆Ln(Motoring costs)             -0.43821           0.115777               -3.78497
 EC(-1)                          -0.76741           0.182778               -4.19862

Adjusted R-squared       0.682845            SSE                 0.004042




                                             B-6
B.3.     GB REGIONS: ERROR-CORRECTION MODEL

Table B.3.1. Constant elasticity model: common fare elasticity. Fare: bus
fare index.
Cointegrating Regression
Dependent variable: Ln(Journeys per capita)
Weighting variable: Population              Observations: 65

Variable                            Coefficient            Std. Error             T-Statistic

Ln(Fare)                            -0.880819               0.174689             -5.042208
Ln(Service)                          0.364669               0.164785              2.213000
Ln(Income)                          -0.643459               0.098604             -6.525685
London                               13.47360               0.438994              30.69203
Metropolitan areas                   13.05823               0.431752              30.24472
Shire counties                       12.21718               0.483273              25.28010
Scotland                             12.96729               0.443718              29.22416
Wales                                12.23766               0.466289              26.24483

Adjusted R-squared           0.999555             SSE                     0.311361
Tests for cointegration must be based on the separate regions. CRDW and ADF tests
require a greater number of observations than those available for each region and are
thus not presented.

Restricted ECM
Dependent variable: ∆Ln(Journeys per capita)
Weighting variable: Population              Observations: 55

Variable                            Coefficient            Std. Error             T-Statistic

∆Ln(Fare)                           -0.487352               0.094786             -5.141589
∆Ln(Service)                        -0.066553               0.044310             -1.501979
∆Ln(Income)                          0.265864               0.053873              4.935035
London                              -0.198280               0.070504             -2.812314
Metropolitan areas                   0.010539               0.021930              0.480576
Shire counties                      -0.022457               0.005506             -4.078745
Scotland                            -0.018462               0.002045             -9.026848
Wales                               -0.027575               0.016646             -1.656573
EC(-1)                               0.003611               0.054598              0.066129

Adjusted R-squared          0.621463              SSE                     0.032287




                                                   B-7
Table B.3.2. Constant elasticity model: area specific fare elasticity.
Fare: bus fare index.
Cointegrating Regression
Dependent variable: Ln(Journeys per capita)
Weighting variable: Population              Observations: 65

Variable                            Coefficient            Std. Error             T-Statistic

Ln(Service)                          0.248087               0.135625              1.829215
Ln(Income)                          -0.400673               0.088741             -4.515090
London                               6.995043               0.939518              7.445355
Metropolitan areas                   11.86167               0.351658              33.73071
Shire counties                       14.02666               0.457154              30.68254
Scotland                             11.46424               6.003562              1.909573
Wales                                4.490649               5.537227              0.810992
Ln(Fare)
 London                              0.182754               0.197324              0.926163
 Metropolitan areas                 -0.984542               0.084396             -11.66573
 Shire counties                     -1.671619               0.184552             -9.057702
 Scotland                           -0.917747               1.316594             -0.697062
 Wales                               0.426704               1.212597              0.351892

Adjusted R-squared          0.999728              SSE                     0.176895
Tests for cointegration must be based on the separate regions. CRDW and ADF tests
require a greater number of observations than those available for each region and are
thus not presented.

Restricted ECM
Dependent variable: ∆Ln(Journeys per capita)
Weighting variable: Population              Observations: 60

Variable                            Coefficient            Std. Error             T-Statistic

∆Ln(Service)                         0.331547               0.084025              3.945819
∆Ln(Income)                         -0.031289               0.046654             -0.670665
 London                              0.006981               0.014247              0.489971
 Metropolitan areas                 -0.021506               0.004988             -4.311881
 Shire counties                     -0.018264               0.003291             -5.548929
 Scotland                           -0.025147               0.023636             -1.063914
 Wales                              -0.022357               0.056067             -0.398760
∆Ln(Fare)
 London                             -0.200876               0.199727             -1.005752
 Metropolitan areas                 -0.600410               0.067273             -8.924961
 Shire counties                     -0.761923               0.366096             -2.081211
 Scotland                            1.995125               4.991371              0.399715
 Wales                              -1.218401               0.807115             -1.509576
EC(-1)                              -0.347043               0.109149             -3.179528

Adjusted R-squared          0.605474              SSE                     0.031011




                                                   B-8
Table B.3.3. Constant elasticity model: common fare elasticity.
Fare: fare per journey excluding CFR.
Cointegrating Regression
Dependent variable: Ln(Journeys per capita)
Weighting variable: Population              Observations: 60

Variable                            Coefficient            Std. Error             T-Statistic

Ln(Fare)                            -0.810337               0.116695             -6.944067
Ln(Service)                          0.805600               0.209259              3.849784
Ln(Income)                          -1.128620               0.178416             -6.325786
London                               11.39414               1.021236              11.15720
Metropolitan areas                   10.69583               0.918911              11.63968
Shire counties                       10.61734               1.019063              10.41873
Scotland                             10.77066               0.886539              12.14910
Wales                                10.38426               0.941858              11.02529

Adjusted R-squared           0.999791             SSE                     0.132728
Tests for cointegration must be based on the separate regions. CRDW and ADF tests
require a greater number of observations than those available for each region and are
thus not presented.

Restricted ECM
Dependent variable: ∆Ln(Journeys per capita)
Weighting variable: Population              Observations: 55

Variable                            Coefficient            Std. Error             T-Statistic

∆Ln(Fare)                           -0.218315               0.088702             -2.461209
∆Ln(Service)                         0.428794               0.099278              4.319123
∆Ln(Income)                         -0.274400               0.095496             -2.873403
London                               0.003535               0.024163              0.146318
Metropolitan areas                  -0.037455               0.008216             -4.559076
Shire counties                      -0.024649               0.002662             -9.260121
Scotland                            -0.031379               0.016958             -1.850394
Wales                               -0.025072               0.044392             -0.564794
EC(-1)                              -0.232696               0.108467             -2.145315

Adjusted R-squared          0.687225              SSE                     0.022913




                                                   B-9
Table B.3.4. Constant elasticity model: area specific fare elasticity.
Fare: fare per journey excluding CFR.
Cointegrating Regression
Dependent variable: Ln(Journeys per capita)
Weighting variable: Population              Observations: 60

Variable                            Coefficient            Std. Error             T-Statistic

Ln(Service)                          0.685882               0.200398              3.422604
Ln(Income)                          -1.007777               0.177618             -5.673831
London                               12.14205               1.000665              12.13398
Metropolitan areas                   10.17066               0.850803              11.95419
Shire counties                       9.770526               1.034339              9.446158
Scotland                             10.38739               0.906894              11.45381
Wales                                10.49596               1.651833              6.354132
Ln(Fare)
 London                              0.408425               0.372108              1.097597
 Metropolitan areas                 -0.761932               0.083079             -9.171203
 Shire counties                     -1.075102               0.120443             -8.926202
 Scotland                           -0.569499               0.298569             -1.907428
 Wales                               0.354068               2.004891              0.176602

Adjusted R-squared          0.999858              SSE                     0.083445
Tests for cointegration must be based on the separate regions. CRDW and ADF tests
require a greater number of observations than those available for each region and are
thus not presented.

Restricted ECM
Dependent variable: ∆Ln(Journeys per capita)
Weighting variable: Population              Observations: 54

Variable                            Coefficient            Std. Error             T-Statistic

∆Ln(Service)                         0.463589               0.075878              6.109685
∆Ln(Income)                         -0.293709               0.071440             -4.111287
 London                              0.005687               0.013259              0.428866
 Metropolitan areas                 -0.023891               0.006687             -3.572681
 Shire counties                     -0.026630               0.002450             -10.86883
 Scotland                           -0.029511               0.020660             -1.428410
 Wales                              -0.023995               0.035589             -0.674242
∆Ln(Fare)
 London                             -0.131098               0.301220             -0.435224
 Metropolitan areas                 -0.566152               0.102636             -5.516141
 Shire counties                     -0.124706               0.066244             -1.882517
 Scotland                           -0.306218               0.430239             -0.711739
 Wales                              -0.260367               0.896666             -0.290372
EC(-1)                              -0.289450               0.062450             -4.634900

Adjusted R-squared          0.728075              SSE                     0.0181888




                                                  B-10
B.4.     GB REGIONS: VARIABLE ELASTICITY ECM

Table B.4.1. Variable elasticity model: common fare elasticity.
Fare: fare per journey excluding CFR.
Cointegrating Regression
Dependent variable: Ln(Journeys per capita)
Weighting variable: Population              Observations: 60

Variable                            Coefficient            Std. Error             T-Statistic

Fare                                -1.875378               0.227165             -8.255567
Ln(Service)                          0.736039               0.206788              3.559384
Ln(Income)                          -1.039218               0.178651             -5.817039
London                               12.37307               0.878224              14.08874
Metropolitan areas                   11.71281               0.782734              14.96398
Shire counties                       11.56175               0.892509              12.95421
Scotland                             11.75633               0.759555              15.47790
Wales                                11.36024               0.816179              13.91880

Adjusted R-squared           0.999816             SSE                     0.116937
Tests for cointegration must be based on the separate regions. CRDW and ADF tests
require a greater number of observations than those available for each region and are
thus not presented.

Restricted ECM
Dependent variable: ∆Ln(Journeys per capita)
Weighting variable: Population              Observations: 55

Variable                            Coefficient            Std. Error             T-Statistic

∆(Fare)                             -0.324204               0.148465             -2.183701
∆Ln(Service)                         0.459260               0.098231              4.675315
∆Ln(Income)                         -0.287122               0.093861             -3.059005
London                               0.001216               0.023846              0.050981
Metropolitan areas                  -0.041362               0.007584             -5.453912
Shire counties                      -0.025959               0.002487             -10.43990
Scotland                            -0.032318               0.017982             -1.797247
Wales                               -0.025381               0.046204             -0.549312
EC(-1)                              -0.285511               0.116492             -2.450902

Adjusted R-squared          0.687738              SSE                     0.022875




                                                  B-11
B.5.     METROPOLITAN AREAS: ERROR-CORRECTION MODEL

Table B.5.1. Constant Elasticity Model: Common Fare Elasticity.
Fare: fare per journey excluding CFR.
Cointegrating Regression
Dependent variable: Ln(Journeys per capita)
Weighting variable: Population              Observations: 60

Variable                            Coefficient            Std. Error             T-Statistic

Ln(Fare)                             -0.44769               0.089389              -5.00831
Ln(Service)                          0.240959                0.13713              1.757165
Ln(Income)                           -1.26877               0.140296              -9.04353
Manchester                           14.52531               1.121897               12.9471
Merseyside                           14.49109               1.155199              12.54424
S. Yorkshire                         14.65919               1.130475              12.96728
W. Yorkshire                         14.61541               1.133311               12.8962
W. Midlands                          14.75155               1.140027              12.93965
Tyne & Wear                          14.79097               1.139384              12.98155

Adjusted R-squared          0.998985              SSE                     0.11701
Tests for cointegration must be based on the separate regions. CRDW and ADF tests
require a greater number of observations than those available for each region and are
thus not presented.

Restricted ECM
Dependent variable: ∆Ln(Journeys per capita)
Weighting variable: Population              Observations: 54

Variable                            Coefficient            Std. Error             T-Statistic

∆Ln(Fare)                            -0.23507               0.089182              -2.63584
∆Ln(Service)                         0.271715               0.073977              3.672977
∆Ln(Income)                          -0.20033               0.240775              -0.83201
Manchester                             -0.0309              0.010134                -3.0487
Merseyside                           -0.03363               0.020033              -1.67867
S. Yorkshire                         -0.03863               0.016724              -2.30986
W. Yorkshire                         -0.03315               0.013627              -2.43276
W. Midlands                          -0.02232               0.009784              -2.28119
Tyne & Wear                          -0.02621               0.015248              -1.71923
EC(-1)                               -0.50336                0.13479              -3.73438

Adjusted R-squared          0.425417              SSE                    0.047921




                                                  B-12
Table B.5.2. Constant elasticity model: area specific fare elasticity.
Fare: fare per journey excluding CFR.
Cointegrating Regression
Dependent variable: Ln(Journeys per capita)
Weighting variable: Population              Observations: 60

Variable                            Coefficient            Std. Error             T-Statistic

Ln(Service)                          0.220882               0.122507               1.803013
Ln(Income)                           -1.12897               0.134314               -8.40542
Manchester                           13.36018               0.922808               14.47775
Merseyside                           14.30091               0.831219               17.20474
S. Yorkshire                         13.37521               0.857034               15.60639
W. Yorkshire                         13.04234               0.978661               13.32673
W. Midlands                          12.85099               0.921848               13.94047
Tyne & Wear                          13.55565               0.877239               15.45262
Ln(Fare)
  Manchester                         -0.45183               0.127067               -3.55583
  Merseyside                         0.242505               0.215202               1.126868
  S. Yorkshire                       -0.56739               0.084243               -6.73508
  W. Yorkshire                       -0.83929               0.149523               -5.61315
  W. Midlands                        -1.07561               0.129264               -8.32104
  Tyne & Wear                        -0.51886               0.207891               -2.49584

Adjusted R-squared          0.999292              SSE                     0.073648
Tests for cointegration must be based on the separate regions. CRDW and ADF tests
require a greater number of observations than those available for each region and are
thus not presented.

Restricted ECM
Dependent variable: ∆Ln(Journeys per capita)
Weighting variable: Population              Observations: 54

Variable                            Coefficient            Std. Error             T-Statistic


∆Ln(Service)                         0.288661               0.052106               5.539891
∆Ln(Income)                            -0.3668              0.216843               -1.69153
Manchester                           -0.02634               0.008785               -2.99873
Merseyside                           -0.02249               0.012538               -1.79382
S. Yorkshire                         -0.03308               0.020948               -1.57929
W. Yorkshire                         -0.02572               0.016609               -1.54873
W. Midlands                          -0.01905               0.007113               -2.67815
Tyne & Wear                          -0.01446               0.020293               -0.71272
∆Ln(Fare)
  Manchester                         0.030715               0.085921               0.357475
  Merseyside                         -0.13497                0.11719               -1.15172
  S. Yorkshire                       -0.29605                0.13937               -2.12421
  W. Yorkshire                       -0.51947               0.336343               -1.54448
  W. Midlands                        -0.86096               0.156845               -5.48927
  Tyne & Wear                        -0.38742                0.14328               -2.70392
EC(-1)                               -0.79629               0.142307               -5.59556

Adjusted R-squared          0.611219              SSE                    0.02874




                                                  B-13
B.6.   METROPOLITAN AREAS: PARTIAL ADJUSTMENT MODEL

Table B.6.1. Constant elasticity model: common fare elasticity.
Fare: fare per journey excluding CFR.
Dependent variable: Ln(Journeys per capita)
Weighting variable: Population              Observations: 60

Variable                       Coefficient          Std. Error         T-Statistic

Ln(Journeys(-1))                 0.47232            0.062804            7.520586
Ln(Fare)                        -0.23419            0.073869            -3.17033
Ln(Service)                     0.354535            0.088026            4.027633
Ln(Income)                      -0.83829            0.098771            -8.48718
Manchester                      8.244534            0.974718            8.458378
Merseyside                       8.19732            0.987565            8.300534
S. Yorkshire                    8.234086            0.987982            8.334244
W. Yorkshire                    8.283281            0.985111            8.408475
W. Midlands                     8.376464            0.992112            8.443066
Tyne & Wear                     8.262821            1.001696            8.248833

Adjusted R-squared      0.999476             SSE                 0.059256




Table B.6.2. Constant elasticity model: area specific fare elasticity.
Fare: fare per journey excluding CFR.
Dependent variable: Ln(Journeys per capita)
Weighting variable: Population              Observations: 54

Variable                       Coefficient          Std. Error         T-Statistic

Ln(Journeys(-1))                0.400977            0.070477            5.689479
Ln(Service)                     0.382646            0.101628            3.765177
Ln(Income)                      -0.87524            0.097819            -8.94754
Manchester                      8.750126            0.932962            9.378871
Merseyside                      9.244258             0.95732            9.656396
S. Yorkshire                    8.663599            0.913864             9.48018
W. Yorkshire                    8.750568            0.919769            9.513871
W. Midlands                     8.106749            0.980724             8.26609
Tyne & Wear                     8.778721            0.893846            9.821292
Ln(Fare)
  Manchester                    -0.28103            0.104685            -2.68456
  Merseyside                    0.111703            0.173794             0.64273
  S. Yorkshire                  -0.35671            0.079994            -4.45928
  W. Yorkshire                  -0.32153            0.145728            -2.20638
  W. Midlands                   -0.94962            0.177523            -5.34926
  Tyne & Wear                   -0.28184            0.154955            -1.81887


Adjusted R-squared      0.999559             SSE                 0.044877



                                             B-14
B.7.    ENGLISH COUNTIES: PARTIAL ADJUSTMENT MODEL

Table B.7.1. Constant elasticity model: common fare elasticity.
Fare: fare per journey excluding CFR.
Dependent variable: Ln(Journeys per capita)
Weighting variable: Population              Observations: 414

Variable                       Coefficient            Std. Error           T-Statistic

Ln(Journeys(-1))                0.535468              0.054604              9.806420
Ln(Income)                     -0.308547              0.123893             -2.490435
Ln(Service)                     0.482277              0.068509              7.039622
Ln(Fare)                       -0.330207              0.060498             -5.458166
46 county intercepts         not reported


Adjusted R-squared      0.99979               SSE                  1.963088




Table B.7.2. Variable elasticity model: common fare elasticity.
Fare: fare per journey excluding CFR.
Dependent variable: Ln(Journeys per capita)
Weighting variable: Population                  Observations: 414

Variable                          Coefficient                 Std. Error                 T-Statistic

Ln(Journeys(-1))                    0.526960                  0.053487                    9.852088
Ln(Income)                         -0.329039                  0.117027                   -2.811640
Ln(Service)                         0.451349                  0.066182                    6.819838
Fare                               -0.746700                  0.105413                   -7.083543
46 county intercepts        Not reported


Adjusted R-squared     0.999797                 SSE                        1.889122




                                              B-15
Table B.7.3. Constant elasticity model: county specific fare elasticity. Fare: fare
per journey excluding CFR.
Dependent variable: Ln(Journeys per capita)
         Weighting variable: Population                   Observations: 414
        Variable                     Coefficient         Std. Error            T-Statistic
Ln(Journeys(-1))                      0.481107           0.064254               7.487550
Ln(Income)                           -0.354389           0.131736              -2.690143
Ln(Service)                           0.411433           0.082344               4.996509
Ln(Fare)
  Northumberland                     -0.059271           2.794657              -0.021209
  Cumbria                            -0.400974           0.649480              -0.617377
  Durham                              0.007823           0.617010               0.012678
  Tyne & Wear                        -0.485537           0.122517              -3.963029
  Cleveland                           0.104079           0.240156               0.433383
  North Yorkshire                    -0.211254           0.655608              -0.322227
  Lancashire                         -0.286139           0.235734              -1.213823
  West Yorkshire                     -0.498670           0.086075              -5.793425
  Humberside                         -1.213150           0.108289              -11.20289
  South Yorkshire                    -0.519440           0.102512              -5.067098
  Merseyside                          0.205034           0.161858               1.266752
  Manchester                         -0.423956           0.092531              -4.581794
  Cheshire                           -0.241701           0.661457              -0.365407
  Derbyshire                         -0.408768           0.229803              -1.778772
  Nottinghamshire                    -0.520729           0.161846              -3.217437
  Lincolnshire                       -0.162563           0.593890              -0.273725
  Staffordshire                      -0.862735           0.602158              -1.432739
  Shropshire                         -0.188319           0.387232              -0.486322
  Leicestershire                     -0.468234           0.211620              -2.212621
  Norfolk                            -1.609211           0.385344              -4.176036
  West Midlands                      -1.192169           0.119178              -10.00326
  Worcestershire                     -0.468155           0.432186              -1.083227
  Warwickshire                       -0.147450           0.349226              -0.422220
  Northamptonshire                   -0.410537           0.344150              -1.192901
  Cambridgeshire                     -1.081473           0.297933              -3.629917
  Suffolk                            -0.328507           0.412969              -0.795476
  Gloucestershire                    -0.073842           0.668328              -0.110487
  Oxfordshire                        -0.317426           0.169252              -1.875467
  Buckinghamshire                    -0.389929           0.396971              -0.982261
  Bedfordshire                       -0.578453           0.464498              -1.245331
  Hertfordshire                      -0.456508           0.229096              -1.992652
  Essex                              -0.344437           0.145289              -2.370695
  Avon                               -0.505227           0.198316              -2.547593
  Wiltshire                          -0.235281           0.637411              -0.369119
  Berkshire                          -0.475855           0.185558              -2.564454
  London                             -0.149393           0.081966              -1.822615
  Cornwall                           -0.663699           0.429290              -1.546038
  Devon                              -0.778672           0.299133              -2.603098
  Somerset                            1.245904           2.568363               0.485097
  Dorset                             -0.201642           0.632631              -0.318736
  Hampshire                          -0.617845           0.120037              -5.147106
  Surrey                             -1.204840           0.306348              -3.932913
  Kent                               -0.490439           0.147262              -3.330380
  West Sussex                        -0.052589           1.378850              -0.038139
  East Sussex                        -0.792323           0.290168              -2.730565
  Isle of Wight                      -0.600381           1.028702              -0.583629
46 county intercepts          Not reported
Adjusted R-squared       0.999802                  SSE              1.618074



                                              B-16
Table B.7.4. Variable elasticity model: county specific fare elasticity. Fare: fare per
journey excluding CFR.
Dependent variable: Ln(Journeys per capita)
         Weighting variable: Population                   Observations: 414
        Variable                     Coefficient         Std. Error            T-Statistic
Ln(Journeys(-1))                      0.479519           0.063759               7.520761
Ln(Income)                           -0.372383           0.131993              -2.821232
Ln(Service)                           0.407606           0.082500               4.940692
Fares
  Northumberland                     -0.079129           4.298525              -0.018408
  Cumbria                            -0.783245           1.305903              -0.599773
  Durham                             -0.006930           1.281061              -0.005409
  Tyne & Wear                        -1.640727           0.387668              -4.232302
  Cleveland                           0.321283           0.829711               0.387223
  North Yorkshire                    -0.363715           1.287308              -0.282539
  Lancashire                         -0.572874           0.462049              -1.239856
  West Yorkshire                     -1.388159           0.244382              -5.680287
  Humberside                         -2.089141           0.145510              -14.35738
  South Yorkshire                    -1.493589           0.293796              -5.083770
  Merseyside                          0.790974           0.646077               1.224273
  Manchester                         -0.946266           0.209235              -4.522497
  Cheshire                           -0.601861           1.385768              -0.434315
  Derbyshire                         -0.701550           0.396317              -1.770173
  Nottinghamshire                    -1.096933           0.346261              -3.167940
  Lincolnshire                       -0.394293           1.211414              -0.325481
  Staffordshire                      -1.627139           1.161096              -1.401382
  Shropshire                         -0.333476           0.823964              -0.404722
  Leicestershire                     -0.874389           0.382182              -2.287885
  Norfolk                            -2.453064           0.554332              -4.425260
  West Midlands                      -3.838953           0.386468              -9.933431
  Worcestershire                     -1.054852           0.973122              -1.083987
  Warwickshire                       -0.197118           0.510203              -0.386351
  Northamptonshire                   -0.730123           0.604113              -1.208586
  Cambridgeshire                     -1.233858           0.325887              -3.786156
  Suffolk                            -0.676154           0.843545              -0.801562
  Gloucestershire                    -0.149026           1.179241              -0.126374
  Oxfordshire                        -0.595850           0.267620              -2.226477
  Buckinghamshire                    -0.550196           0.549297              -1.001637
  Bedfordshire                       -0.754421           0.585951              -1.287516
  Hertfordshire                      -0.609577           0.357377              -1.705697
  Essex                              -0.491814           0.203950              -2.411448
  Avon                               -0.832924           0.324876              -2.563824
  Wiltshire                          -0.343555           1.022215              -0.336088
  Berkshire                          -0.833228           0.286279              -2.910548
  London                             -0.367362           0.257659              -1.425767
  Cornwall                           -0.993682           0.650796              -1.526871
  Devon                              -1.310979           0.478267              -2.741104
  Somerset                            2.024483           4.003801               0.505640
  Dorset                             -0.355659           1.008681              -0.352598
  Hampshire                          -1.139522           0.217063              -5.249741
  Surrey                             -1.556861           0.372774              -4.176419
  Kent                               -0.621915           0.181871              -3.419536
  West Sussex                        -0.109212           2.104869              -0.051885
  East Sussex                        -1.165767           0.424874              -2.743793
  Isle of Wight                      -0.679023           1.198103              -0.566749
46 county intercepts          Not reported
Adjusted R-squared       0.999802                  SSE              1.615323



                                              B-17
Table B. 7.5. Tests for various model formulations.
                                       Test         Probability      Conclusion
Tests for common fare
coefficients
Constant elasticity model              F = 1.51     Prob. = 0.02     Reject common fare
                                                                     coefficients
Variable elasticity model              F = 1.20     Prob. = 0.19     Cannot reject common fare
                                                                     coefficients
Tests for variable elasticity
model
Common fare coefficients               χ2 = 15.9    Prob. = 0.00     Reject constant elasticity model
County-specific fare coefficients      χ2 = 0.7     Prob. = 0.40     Cannot reject constant elasticity
                                                                     model




Table B.7.6. English Shire counties. Constant elasticity model: common fare
elasticity. Fare: fare per journey excluding CFR.
Dependent variable: Ln(Journeys per capita)
        Weighting variable: Population                              Observations: 414
       Variable                     Coefficient                    Std. Error              T-Statistic
Ln(Journeys(-1))                     0.274796                      0.045551                 6.032727
Ln(Income)                          -0.631913                      0.121710                -5.191977
Ln(Service)                          0.647828                      0.062654                 10.33976
Ln(Fare)                            -0.508866                      0.068736                -7.403150
39 county intercepts         Not reported

Adjusted R-squared          0.997880                  SSE                      1.828739




Table B.7.7. English Metropolitan areas. Constant elasticity model: common fare
elasticity. Fare: fare per journey excluding CFR.
Dependent variable: Ln(Journeys per capita)
        Weighting variable: Population                               Observations: 54
       Variable                     Coefficient                    Std. Error              T-Statistic
Ln(Journeys(-1))                     0.507415                      0.098196                5.167385
Ln(Income)                             -1.0232                      0.20668                 -4.95064
Ln(Service)                          0.352355                      0.089043                3.957144
Ln(Fare)                             -0.21358                      0.089731                 -2.38024
6 county intercepts          Not reported

Adjusted R-squared          0.999608                  SSE                      0.038622




                                                   B-18
B.8.    ENGLISH COUNTIES: ASYMMETRIC PRICE RESPONSE, PARTIAL
        ADJUSTMENT MODEL

Table B.8.1. Variable elasticity model: common fare elasticity. Fare: fare per
journey excluding CFR.
Dependent variable: Ln(Journeys per capita)
Weighting variable: Population                  Observations: 414

Variable                          Coefficient              Std. Error              T-Statistic

Ln(Journeys(-1))                    0.515692               0.060966                 8.458624
Ln(Income)                         -0.248830               0.152147                -1.635430
Ln(Service)                         0.492895               0.068804                 7.163773
Rising Fare                        -0.360240               0.087329                -4.125090
Falling Fare                       -0.272620               0.064083                -4.254130
46 county intercepts        Not reported

Adjusted R-squared     0.99979                  SSE                     1.953372




                                              B-19
B.9.    METROPOLITAN AREAS PTE DATA: TOTAL BUS JOURNEYS
        AND FULL-FARE BUS JOURNEYS


Table 9.1. Constant elasticity partial adjustment model. Common fare
elasticity. Dependent variable: total bus passenger journeys per capita.
Dependent variable: Ln(Total bus journeys per capita)
Weighting variable: Population                                           Observations: 58

Variable                     Coefficient                    Std. Error T-Statistic

Ln(Total journeys(-1))              0.536703                0.084897              6.321821
Ln(Income)                          -0.72116                0.160366              -4.49695
Ln(Service)                         0.202317                0.068682              2.945708
Ln(Fare)                            -0.23944                0.067287              -3.55843
West Midlands                       7.628168                1.626924              4.688705
Manchester                          7.545182                1.614538              4.673276
Mersey                              7.687212                1.631386              4.712076
South Yorkshire                     7.546625                1.612868              4.679009
West Yorkshire                       7.65236                 1.63102              4.691762
Tyne & Wear                         7.703142                1.640762              4.694856

Adjusted R-squared           0.99971           SSE                     0.031819



Table 9.2. Constant elasticity partial adjustment model. Common fare
elasticity. Dependent variable: full-fare bus passenger journeys per
capita.
Dependent variable: Ln(Full-fare bus journeys per capita)
Weighting variable: Population                    Observations: 58

Variable                     Coefficient       Std. Error              T-Statistic

Ln(Adult bus journeys(-1))          0.607802                0.075577              8.042154
Ln(Income)                          -0.67359                0.175428              -3.83968
Ln(Service)                         0.195516                0.065694              2.976174
Ln(Full-fare)                       -0.14773                0.052538              -2.81195
West Midlands                       6.877274                1.718167              4.002682
Manchester                          6.712244                 1.68773              3.977084
Merseyside                          6.912545                1.713239              4.034782
South Yorkshire                     6.743294                1.687388              3.996291
West Yorkshire                      6.893792                1.720817              4.006115
Tyne and Wear                       6.908422                1.715197              4.027771

Adjusted R-squared           0.999581          SSE                     0.037899




                                               B-20
B-21

								
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