Journal of Transport Economics and Policy, Volume 38, Part 3, September 2004, pp. 345–369
Urban Congestion Charging
A Second-Best Alternative
Georgina Santos
Address for correspondence: Dr Georgina Santos, Department of Applied Economics,
University of Cambridge, Cambridge CB3 9DE, UK. Support from the Economic and
Social Research Council (ESRC) under Grant R000223117, and the Department for
Transport, Local Government and the Regions (DTLR), former Department of the
Environment, Transport and the Regions, as well as from the British Academy, is
gratefully acknowledged. The author is indebted to David Newbery for invaluable
guidance and help. All mistakes that survived his corrections are the author’s sole
responsibility. The author is also grateful to David Reams from the Department for
Transport for fruitful discussions and constructive comments and to Laurent Rojey for
his help during his research placement in Cambridge, which gave origin to this paper.
The author is also grateful to two anonymous referees and to Dave Milne for help
and advice on SATURN first-best pricing. Provision of data by the following local
authorities and consultancies working for them is also gratefully acknowledged:
Director of the Environment and Transport Department of Cambridgeshire County
Council, WS Atkins, Herefordshire Council, Lincolnshire County Council, Symonds
Group, York City Council, Northamptonshire County Council, Kingston upon Hull
City Council, Bedfordshire County Council, and Norfolk County Council.
Abstract
Cordon tolls are simulated for eight English towns. The distributional effects and
environmental impacts are assessed. Although distributional effects vary across towns,
environmental impacts are positive in all cases. Benefits are compared to those that
would accrue from first-best charges. It is concluded that cordon tolls perform relatively
well.
Date of receipt of final manuscript: April 2004
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1. Introduction
The theoretical Pigouvian approach to the problem of traffic congestion
suggests that the negative externality should be internalised through the
introduction of a congestion charge equal to the marginal congestion
cost. This has been argued in numerous studies (Vickrey, 1955; Walters,
1961; Glaister, 1981; Newbery, 1990; Button, 1993; Yang and Huang,
1998; Button and Verhoef, 1998; Hau, 1998, Dodgson et al., 2002) and
the idea rests on sound microeconomic theory and of course goes back to
the neoclassical Cambridge economist, Arthur Pigou (Pigou, 1920).
Without questioning the legitimacy of marginal cost pricing,1 the problem
is that it has proved difficult to implement. In today’s technologically
advanced world the calculation of instant marginal cost pricing may not
be very difficult to envisage. Its cost effectiveness, however, would be
dubious and, most importantly, the transparency of such a system would
be at least arguable, as drivers would not know the congestion charge
they would be required to pay before starting their journey.2 Marginal
cost pricing would require highly differentiated pricing systems in time
and space, which would be expensive to provide and confusing to users
(Nash and Sansom, 2001).
Since marginal cost pricing is not very practical, transport economists
have lately devoted their efforts to the study of second-best3 alternatives
and in particular to the development of algorithms to find (second-best)
optimal toll levels and locations (Verhoef, 2002; May et al., 2002; Zhang
and Yang, 2004; Shepherd and Sumalee, 2004). This kind of work has
moved the theory forward but cannot be applied to actual complex
networks yet. De Palma et al. (2004) look at a related but slightly different
problem and explore the possibility of how to phase a toll system when
subsets of links are priced. They find that if a flat toll is applied the marginal
benefits of tolling successively more links are generally increasing, and
tolling of adjacent routes is preferred. If, on the other hand, a fine toll
that changes smoothly to deter queueing is used, it is better to toll a few
heavily congested and dispersed routes while leaving the rest of the network
1
However, introducing marginal cost pricing in the transport sector does not guarantee an efficient
outcome when there are externalities in other (related) sectors in the economy, which are not priced
according to marginal cost.
2
This could be in part overcome with screens at all priced roads showing the charge drivers would be
required to pay further down. Thus drivers could decide between paying the charge or using an
alternative toll-free road or lane. This solution might work on motorways or in big cities (indeed it is
used in the US) but it would be unlikely to work in English towns and cities where it is already difficult
to find alternative routes, given the high number of one-way streets and the narrowness of some of them.
3
‘‘Second-best’’ refers to the optimal policy when the true optimum (the first-best) is unavailable due to
constraints.
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Santos
Urban Congestion Charging
toll-free, at least during the early stages of the scheme (de Palma et al.,
2004). In order to derive these conclusions they use a very simple and
small network.
This paper simulates cordon tolls in eight English towns. Drivers may
choose not to make the trip when the charge applies or to use an alternative
route to avoid it. The system consists in charging a flat toll that maximises
the difference between the difference in benefits and the difference in costs
before and after the toll. Additional results for the environmental impacts
and distributional effects of cordon tolls, together with some further
considerations on level and design, are presented. The increase in social
surplus from these cordon tolls is also compared with the increase in
social surplus from first-best charges. The analysis is mainly applied and
involves simulation and assignment of traffic in towns and use of actual
data on network characteristics and trip matrices.
2. The Model
The potential impacts of the schemes were estimated using results from
SATURN (Simulation and Assignment of Traffic to Urban Road Networks), developed at the Institute for Transport Studies (ITS) at University
of Leeds (Van Vliet and Hall, 1997), used together with a batch file
procedure, SATTAX (SAT stands for SATURN and TAX, for tax), also
developed at ITS (Milne and Van Vliet, 1993).
The program estimates the ‘‘generalised cost’’ of trips as the sum of the
time cost and the vehicle operating cost:
GCij ¼ VOT timeij þ VOC distij
ð1Þ
where GCij is generalised cost in pence per passenger car unit (PCU)4 to go
from origin zone i to destination zone j, VOT is value of time in pence per
PCUmin, timeij is the time taken to complete the trip in minutes, VOC
is vehicle operating cost in pence per PCUkm, and distij is the distance
travelled to go from origin zone i to destination zone j, in km. Time and
distance vary according to the route chosen to go from origin zone i to
destination zone j but in equilibrium no trip maker can reduce his or her
GCij . VOC and VOT in this study were taken as 12.8 pence per PCUkm
and 25 pence per PCUmin (£15 per PCUhour) respectively, at 2002
prices. These values were computed as weighted averages taking into
account vehicle and fuel type, vehicle occupancies, trip purpose, and average
4
All vehicles were converted to PCUs before running the program.
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Journal of Transport Economics and Policy
Volume 38, Part 3
wages and value of leisure time, according to the guidelines of the Highways
Economics Note No. 2 (Highways Agency et al., 1996).5
The SATURN model simulates delays at junctions. Since these are the
major source of urban congestion, results reflect reality better than other
approaches such as the calculation of marginal costs on the basis of
(piece-wise linear) link speed-flow relationships.
The software requires a network file and a trip matrix to run the model
for a particular town. The network file contains a detailed description of the
network, including link capacities and characteristics of each junction
(priority, roundabouts, traffic signals, and so on). The trip matrix is an
origin-destination (O-D) matrix that contains the number of vehicles (or
PCUs) wishing to travel from origin zone i to destination zone j 6 in the
time period under consideration, which in this study was 8 to 9 am.
The software simulates and assigns traffic in urban road networks and
iterates until the equilibrium is reached as defined above. Instead of using
a simplified network as in May et al. (2002) or de Palma et al. (2004),
actual networks were used. Simplified networks usually have a small
number of links and junctions, and are very useful for theoretical research.
The aim of this study was more practical, and complex large networks for
eight English towns were used instead. The advantage of using actual
networks is that the results obtained are directly applicable to the town
in question, and not just a theoretical prediction that may or may not be
suitable for real world policies. Although not all links were included in
these models, the networks were fairly detailed, and reflected the network
layout of the towns quite well.7
SATTAX simulates a toll as a time penalty for crossing the cordon. The
time penalty required for any given toll will depend on the value of time
assumed (25 pence per PCUmin at 2002 prices in this study). Thus, a toll
of £2.50 per crossing would be modelled as a delay of 600 seconds.
SATTAX also simulates the effects of tolls, and models demand responses
to changes in trip costs. This is done by specifying a demand function and
an elasticity of trip demand with respect to the total cost of the trip. The
demand function was assumed to be constant elasticity and the elasticity
assumed was 0.7.8 Drivers’ response will be to pay the charge with no
5
The value of time varies with user’s income, time of the day, and trip purpose. For simplification a
weighted average representative of the morning peak has been taken. Sensitivity tests halving and
doubling VOT did not show big differences in the routes taken. Congestion costs expressed in time
units remained virtually unchanged.
6
The number of vehicles wishing to travel is the number of vehicles that start their trips. Some may not
finish within the period simulated due to congested conditions.
7
This was confirmed by the validation exercises carried out by the local authorities.
8
A discussion on elasticities and the reasons for choosing this value are provided below.
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Urban Congestion Charging
further change in travel behaviour, cancel the trip, or change route in order
to avoid the toll, resulting in fewer trips in the tolled area, although possibly
with more trips just outside the cordon. Cancelled trips will include trips
that take place at other (non-charged) periods, trips made by another
mode, or trips that are cancelled altogether.
3. The Data
The total number of trips, the average trip lengths, the areas in km2 and the
average speeds are all presented in Table 1. As will be explained later, the
cordoned area corresponds to the area where charges apply. The files to
run SATURN were all provided by the local authorities and consultancies
working for them.
4. Elasticities
The elasticity of demand with respect to generalised cost was assumed to be
0.7. This is in line with the literature and with experience from London,
although adjusted to take into account the lack of good public transport,
relative to London, that prevails in the study towns.
Dodgson et al. (2002), for example, summarise various studies for
Singapore suggesting point elasticities in the order of 0.12 to 0.35
with respect to congestion charges. These are (and so they should be)
lower than elasticities with respect to generalised costs. Shaffer and
Santos (2004) compute the elasticity of demand for trips by car in
London with respect to generalised costs after the London Congestion
Charge was implemented. They find it to be around 1.3 when vehicle
operating costs exclude fixed costs such as insurance and depreciation.
This short-run very high elasticity value picks up the fact that London
has a very good public transport system, which serves as a close substitute
to the car. For this reason, the elasticity assumed in this study was 0.7.
Using a lower value would underestimate the impacts from congestion
charging. In London, for example, traffic reduction has been higher and
revenues lower than expected, which means that elasticities might have
been underestimated prior to the implementation of the Scheme. Goodwin
(2003) suggests that elasticities were revised down by a sort of ‘‘ratchet’’
effect from one study to the next, probably because their authors wanted
to be conservative, and would always choose the lowest estimate.
349
350
51,581
47,080
42,471
27,747
40,431
33,903
24,644
15,383
Northampton
Kingston upon Hull
Cambridge
Lincoln
Norwich
York
Bedford
Hereford
15,049
15,834
16,581
13,737
14,831
11,690
14,717
8,069
Cordoned
area
5.3
7.7
6.4
5.2
9.4
6.6
3.3
4.3
Whole
network
1.1
2.0
1.9
1.8
0.7
1.3
1.9
1.4
Cordoned
area
AKT
(PCUkm per PCU)
99.8
111.7
65.5
72.0
99.0
62.4
46.4
66.5
0.7
1.0
1.6
1.0
2.0
1.2
1.5
0.5
Cordoned
area
Area in km2
Whole
network
Sources: number of trips: trip matrices provided by the local authorities and their consultants
AKT and average speeds: SATURN outputs
Areas: measured from maps
Whole
network
Town
Number of trips
(PCUs per hour)
15.9
22.0
38.2
30.8
36.0
41.3
28.4
30.6
Whole
network
11.8
14.1
16.3
15.4
15.9
14.0
24.6
15.9
Cordoned
area
Average speeds
Table 1
Number of Trips, Average Trip Lengths, Areas in km2 , and Average Speeds before Tolls
Journal of Transport Economics and Policy
Volume 38, Part 3
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Urban Congestion Charging
The value used in this study was therefore 0.7, although some sensitivity
analysis is reported below.
5. Cordon Tolls
The form of charging simulated in this study was an inbound cordon toll. In
a cordon toll scheme drivers pay to enter and/or leave a designated area,
usually the city centre, at all or some times of the day. Cordon tolls are transparent, as drivers know the charge beforehand, they are reliable and easy to
understand and use, they are relatively simple to implement and the technology has already been tested and is available for wide use. The charge does not
depend on the time taken or distance travelled within the charged area.
Cordon tolls can at best approximate marginal cost pricing. This is a
practical example of a second-best alternative to marginal cost pricing.
Discussions around second-best alternatives have become widespread
among researchers, and everyone is now so used to the idea that there
are studies on, for example, ‘‘optimal cordon tolls’’, such as those by
Verhoef (2002), Shepherd and Sumalee (2004), May et al. (2002), Mun
et al. (2003) and Zhang and Yang (2004).
Real world policies have also made use of second-best alternatives, such
as cordon tolls. The original Area Licensing Scheme (ALS) in Singapore,
implemented in 1975, was essentially a cordon toll. Vehicles entering the
7 km2 restricted zone, which covered most of the Central Business District,
were required to purchase and display a paper area licence on their
windscreen. Driving inside the zone without crossing the boundary could
be done free of charge. In this sense, the scheme was a cordon system
and not an area licence system.
The tolls in place in Bergen, Oslo, Trondheim, Kristiansand, and Stavanger, in Norway, though not conceived to manage demand, but rather to
finance road infrastructure, are also cordon tolls (Ramjerdi et al., 2004).
Although London has an area licensing scheme instead, Edinburgh is
currently considering the introduction of road pricing in the form of a
double cordon toll (Transport Initiatives Edinburgh, 2002). A daily
charge of £2 would be levied on vehicles crossing either one or both cordons
inbound. The proposed inner charging boundary surrounds the Old and
New Towns of Edinburgh that are covered by UNESCO World Heritage
Site designation. The proposed outer boundary is inside the outer city
bypass, at the edge of the built-up area.
In this study, inbound cordon tolls were simulated for eight English
towns. In the towns studied here, the charged area was defined as the city
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Journal of Transport Economics and Policy
centre of the town, usually delimited by what the local authority defines as
inner ring road, which is in all cases an A or B road.9 In the case of Northampton a smaller area than the one surrounded by the inner ring road was
cordoned, mainly because it is where most congestion takes place.
The optimal toll was defined as the toll that maximises benefits, defined
as the increase in social surplus. Social surplus was computed as the sum of
total utilities of all trips, minus the sum of total costs of all trips. The
disutility of paying a higher charge and the disutility of not making the
trip or making it at some other time are captured in the area under the
demand function, which is smaller after the toll scheme has been introduced.
The gross surplus of trips from each origin to each destination was
measured (in monetary units) by the area under the demand schedule for
such trips up to the actual level of traffic. The difference between drivers’
gross surplus before and after the introduction of the toll was computed
for each origin-destination pair and then summed over all such pairs to
give the overall change in gross surplus. The change in total costs was
obtained directly from the new cost matrix produced by SATTAX.
The change in social surplus was thus computed as the change in gross
surplus minus the change in costs:
X
P ð q0
N
X
cij ðqij Þ dqij ðSCijo SCij1 Þ;
ð2Þ
SS ¼
1
q1
1
where SS is change in social surplus, P is the number of O-D pairs, cij is
the average cost to go from origin zone i to destination zone j, measured in
pence per PCU, qij is the number of PCUs demanding a trip from origin
zone i to destination zone j, co is the original cost, qoij , the original
demand, Z is the demand elasticity with respect to the cost to go from i
to j, N is the total number of PCUs (assumed identical to the number of
trips), 0 indicates the original situation of no toll, and 1 indicates the
final situation in which one or two cordon tolls are introduced, and SC is
social cost, defined as:
SCij ¼ VOT timeij þ ðVOC VAT dutyÞ distij ;
ð3Þ
where SCij is the social cost in pence per PCU to go from origin zone i to
destination zone j, VAT is a weighted average of the Value Added Tax
on fuel and duties, and duty is a weighted average of the average fuel
duty paid by trip makers exclusive of VAT on duties. Individual social
costs are the generalised costs defined in equation (1) adjusted to make
them net of Value Added Tax (VAT) and fuel duties. VAT and fuel
9
In the UK A and B roads are main roads other than motorways.
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Urban Congestion Charging
Santos
duties influence drivers’ travel decisions, because time spent travelling is not
subject to those taxes. When it comes to choices it is relative prices that
matter. The price drivers pay for fuel includes fuel duties and VAT while
time taken does not. Therefore, excluding VAT and fuel duties from the
drivers’ relative prices would lead to an excessive ratio of time cost to
fuel cost, which would lead them to choose a longer but quicker route
where they spend more fuel than on a shorter alternative route but less
time because it is less congested. For this reason, VAT and fuel duties
have been included in the vehicle operating cost (VOC) with which drivers
are presented at the time of choosing a route, except for working vehicles,
which get a VAT rebate. Once drivers have made their decisions about
which route they will use to go from one origin to one destination total
costs added over all vehicles on the network can be computed. At this
point it is necessary to deduct taxes.
It should be noted that the meaning of the term ‘‘individual’’ is different
from the meaning of the term ‘‘private’’. Individual refers to trips from
origin zone i to destination zone j. Private and social refer to the inclusion
and exclusion of VAT and duties.
An additional benefit that was ignored in this study was the increase in
efficiency that would be derived from an optimal revenue allocation. The
interactions with other distorted markets such as the labour market were
also ignored. Parry and Bento (2001) and Van Dender (2003) analyse this
issue. Parry and Bento (2001) find that a congestion toll raises the overall
costs of commuting to work and discourages labour force participation.
The resulting welfare loss in the labour market can easily exceed the
Pigouvian welfare gain from internalising the congestion externality.
However, if the revenues from the toll are used to reduce labour taxes,
the net impact on labour supply is positive, and the overall welfare gain
from the congestion tax can increase by up to 100 per cent. Van Dender
(2003) models an urban transport system with cars and buses and
commuting and non-commuting trips. He finds that if tolls cannot be
differentiated according to trip purpose they generate substantial gains
only when labour is reduced.
In this study tolls were not differentiated according to trip purpose and
no reduction of labour taxes was considered. The proportion of commuting
trips used was the national average for all towns and cities in the UK
between 8 and 9 am. Thus, 94.5 per cent of all trips made during the
period modelled were assumed to be commuting trips. In this sense, the
research cited above indicates that introducing a cordon toll could discourage labour supply and the increase in social surplus could be more than
compensated by a decrease in welfare in the labour market. Similarly,
although computing this falls beyond the scope of this paper, it is worth
353
354
3.47
3.73
1.60
1.07
0.80
1.60
1.60
1.60
5.13
5.48
1.35
0.57
1.28
0.93
0.37
0.91
Benefit
(£m/year)
Source: Updated from Santos, Newbery and Rojey (2001)
AKT: average kilometres travelled per PCU
ATT: average travel time per PCU
Elasticity assumed: 0.7.
Northampton
Kingston upon Hull
Cambridge
Lincoln
Norwich
York
Bedford
Hereford
Town
Optimal toll
(£ to cross
the cordon)
8.96
9.65
2.98
1.66
1.78
1.98
2.88
1.95
Gross
Revenues
(£m/year)
1.7
1.8
2.2
2.9
1.4
2.1
7.7
2.1
Ratio
Revenue:
Benefit
0.2
1.6
1.1
0.6
1.6
2.5
1.0
1.4
AKT (%)
No. of
trips (%)
2.5
3.2
3.0
3.1
2.2
3.6
8.4
6.1
9.6
10.9
6.3
3.7
3.3
6.2
7.0
15.5
Changes in
ATT (%)
Table 2
Optimal Cordon Tolls and their Impacts at 2002 Prices
30.7
28.7
29.4
31.3
26.9
38.6
30.3
25.1
No. of cordon
crossings (%)
Journal of Transport Economics and Policy
Volume 38, Part 3
Urban Congestion Charging
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Figure 1
Increase in Annual Social Surplus at Different Toll Levels in Cambridge with an Elasticity of
0.7 at 2002 Prices
noting that if the revenues from the schemes simulated in this study were
used to reduce labour taxes, the gains presented here could be doubled.10
Table 2 presents the results of the simulations.
Average travel time, number of trips demanded and number of cordon
crossings decrease in all cases after the introduction of the toll. Average
kilometres driven may increase or decrease. Drivers who previously crossed
the cordon may use longer toll-free routes. Drivers who previously did not
cross the cordon, perhaps to avoid the heavily congested area, may now
decide to pay the charge and thus drive fewer kilometres. It is clear that
the reduction in average travel time would mainly come from the reduction
in the number of trips demanded (and consequently less congested
conditions) and from the re-allocation of traffic to less congested routes,
rather than from any reduction in the average kilometres travelled.
The tolls presented in Table 2 yield the highest increase in annual social
surplus. Other tolls would yield lower benefits, and they could even yield
losses, as Figure 1 shows.
10
If toll revenues were used to reduce labour taxes the optimal toll levels would probably be different.
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Journal of Transport Economics and Policy
Volume 38, Part 3
6. Sensitivity Analysis of Elasticities
The higher the demand elasticity is, the lower the charge required to reduce
demand is. More elastic demands require lower congestion tolls to achieve a
certain reduction in the number of trips. However, when the alternatives
available are not only to cancel the trip but also to change route, the
relationship between tolls and elasticities changes. For each town, while a
higher elasticity does indeed lead to a larger reduction in the number of
trips and, as a consequence of that, an even larger reduction in the
number of cordon crossings, the optimal cordon toll increases with the
elasticity. The only exception is Hereford. Although this may seem counterintuitive it should be noted that the optimal toll is not a toll that achieves a
certain reduction in the number of trips but a toll that maximises the
increase in social surplus. This increase results from two effects: change
of route and cancellation of the trip.
When there are not many alternative routes the dominating effect is that
drivers cancel their trips. In this case, the optimal toll decreases when the
elasticity increases. At the margin, if there are no alternative routes, the
only possible response is to cancel the trip, and the lower toll with a
higher elasticity principle applies.
When there are many alternative routes the dominating effect is the
change of route. In this case, if the toll is too high, the surrounding areas
will become congested and the average travel time and congestion costs
will increase. If the elasticity is high as well, enough drivers will cancel
the trip so that an increase in social surplus can be achieved. If the elasticity
is low and the charge is low not many drivers will be tolled off and because
the charge is low not many drivers will change route either.
If there is an error in the elasticity assumed, there will be an error in the
optimal toll estimated. Errors will lead to a choice of toll that no longer
maximises the increase in social surplus, and the loss in social surplus
from setting the wrong toll is the cost of the error. Santos, Newbery and
Rojey (2001) find that in seven of the eight towns they study, the cost of
the error from underestimating the elasticity is lower than that from
overestimating it. The exception is Hereford. As explained above, the
dominating effect in Hereford is the cancellation of trips because there
are few alternative routes.
When the dominating effect is the change of route and the elasticity is
overestimated the toll introduced will be higher than the toll that should
have been introduced. The reduction in the number of trips will be lower
than expected (because the elasticity is actually lower than the elasticity
assumed) and the number of remaining trips will be higher than expected.
The toll will be high and too many drivers will try to change route, causing
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Urban Congestion Charging
Santos
congestion outside the charged area and thus increasing travel costs. The
final benefits will be lower than expected for two reasons: (a) the reduction
in the number of trips will be lower than optimal, and (b) the reduction
in travel costs will be lower than optimal because congestion will increase
outside the charged area.
When the dominating effect is the change of route and the elasticity is
underestimated the toll introduced will be lower than the toll that should
have been introduced. The reduction in the number of trips will be higher
than expected (because the elasticity is actually higher than the elasticity
assumed) and the remaining trips will be fewer than expected. With a toll
lower than optimal not many drivers will change route. The final benefits
will be lower than expected for two reasons: (a) the reduction in the
number of trips will be higher than optimal (causing a decrease in the
sum of individual gross surpluses beyond the optimal decrease), and (b)
the reduction in the total costs will be lower than optimal because not
many drivers will change route and there will still be substantial congestion
inside the charged area.
When the dominating effect is the change of route the loss from overestimating the elasticity seems to be higher than the loss from underestimating it. In other words, too much traffic and too much diversion is
more costly than too little traffic and not enough diversion. The obvious
policy recommendation that derives from this finding is that if in doubt,
it seems to be better to assume a lower elasticity. Something should be
said about the generality of this statement. First, this is the result that
was found in the towns where the dominating effect was the change of
route, not in the one town where the dominating effect was the cancellation
of trips. Second, when the dominating effect is the cancellation of trips, the
main response to the charge will be a demand reduction. Under this
scenario, the cost of the error of underestimating the elasticity could be
greater, smaller, or equal to that of overestimating it. The cost of the
error will depend on the difference between the actual and the assumed
elasticity, the shape of the demand curve, the shape of the marginal
social cost function, and the shape of the marginal private cost function,
together with their slopes in the relevant sections of the curves.
7. Distributional Impacts
There has always been some concern on the potential regressive impacts
that road pricing could have and, as a consequence, the importance of
revenue allocation (Small, 1983; Morrison, 1986; Flowerdew, 1993;
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Journal of Transport Economics and Policy
Volume 38, Part 3
Richardson and Bae, 1998; Jones, 1998). Santos and Rojey (2004) show
that road pricing can be regressive, progressive, or neutral and that no
general conclusions can be drawn before a specific scheme is considered
and the social and geographical characteristics of the town in question
are carefully assessed.
A regressive tax is a tax that takes a larger percentage of the income of
low income people than of high income people. Although congestion
charges would not be taxes, they would still be regressive in the sense
that they would not vary with income (that is, the charge paid by drivers
would be the same regardless of their income). The £5 congestion charge
in London, for example, represents a larger percentage of the income of
low income people than of the income of high income people.
When implementing a cordon toll (or any scheme for that matter) policy
makers will be interested in determining whether the toll will be paid mainly
by higher or lower income groups. If, for example, the toll is mainly paid by
drivers with an income higher than the average income in a town, perhaps
because lower income drivers live and work outside the area where the
scheme operates, then the final impact in the town in question will not be
regressive. This of course does not mean that there may not be some
lower income drivers who will cross the cordon and pay the toll.
Santos and Rojey (2004) find that impacts are town specific and depend
on where people live, where people work, and what mode of transport they
use to go to work. Initial impacts may be progressive even before any
compensation scheme for losers is taken into account.
The indicators considered to assess the distributional effects of a cordon
toll scheme were the percentage of people crossing the cordon and their
income. Data sets for the Small Area Statistics and Local Base Statistics
from the 1991 Census of Population of Great Britain were retrieved.
The different geographical zones with which the SATURN model operates
were matched with the wards. Thus it was possible to estimate the
percentage of vehicles from each ward crossing the cordon.
The average income in each ward was approximated using the
distribution of occupations from the Census (http://census.ac.uk/casweb/)
and the average wage for each occupation reported in the New Earnings
Survey Part D (Office for National Statistics, 1998).11
11
SATURN/SATTAX do not input income information on the different zones and therefore demand
reduction and re-routeing depend on the elasticity and the availability of alternative routes only.
Even if different user classes were considered, with different elasticities and/or demand functions,
these would not be zone dependant and so it would not be possible to assume lower elasticities for
richer areas. As a result, the same demand function and elasticity value had to be assumed for all
trip makers.
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Santos
Urban Congestion Charging
From these results, the average proportion of people crossing the cordon
and the average earnings for each town were estimated. The percentage
deviation of the results for each ward from the average for the town
were then computed. The three towns whose effects were assessed are
Cambridge, Northampton, and Bedford. The reason for choosing these
towns was that the SATURN zones could be easily matched with the wards.
Wards can be split into four categories: low income and few crossings
(I), low income and many crossings (II), high income and few crossings
(III), high income and many crossings (IV). Categories (I) and (IV) are
progressive, categories (II) and (III) are regressive.
Five wards in Cambridge would experience progressive effects, whereas
nine would experience regressive effects. 37 per cent of the population in
Cambridge lives in the wards that would experience progressive effects
and 63 per cent lives in the wards that would experience regressive effects.
The overall effect of a cordon toll in Cambridge can therefore be expected
to be regressive.
Ten wards in Northampton would experience progressive effects, and
ten would experience regressive effects. 49 per cent of the population in
Northampton lives in the wards that would experience progressive effects
and 51 per cent lives in the wards that would experience regressive effects.
The overall effect would most probably be neutral.
Finally, in Bedford five wards containing 59 per cent of the population
would experience progressive effects and seven, containing 41 per cent of
the population would experience regressive effects. It can therefore be
concluded that if a cordon toll scheme was introduced in Bedford the
overall effects would be progressive.
Table 3 contains the breakdown of wards into the four categories
previously defined. It clearly shows that the distributional impact of
Table 3
Breakdown of Wards in Categories
Number (percentage %) of wards
Town
Cat. I
P
Cat. II
R
Cat. III
R
Cat. IV
P
Percentage population
experiencing regressive
effects (%)
Overall
effect
Cambridge
Northampton
Bedford
3 (23)
7 (34)
3 (28)
3 (24)
6 (26)
2 (18)
6 (39)
4 (25)
3 (23)
2 (14)
3 (15)
4 (31)
63
51
41
R
N
P
Source: Santos and Rojey (2004)
Key: Cat.: Category
R: Regressive
P: Progressive
N: Neutral
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Journal of Transport Economics and Policy
Volume 38, Part 3
cordon tolls varies considerably from town to town. In the three towns
studied the effects would be regressive, neutral, and progressive, even
before any compensation to losers or poorer groups is considered.
8. Double Cordons
It has been shown above that cordon tolls can increase social surplus if the
right toll is implemented. It is shown in this Section that a second outer
cordon implemented jointly with an inner cordon surrounding the city
centre enhances the increase in social surplus in comparison to a single
inner cordon. The benefit from a double cordon is on average 1.9 times
higher than the benefit from a single cordon in the towns studied here.
Level and location of cordon tolls are of crucial importance and
research has lately focused on those issues.
Mun et al. (2003), for example, estimate the optimal cordon pricing as
the optimal combination of cordon location and toll level. Their model is
theoretical and has one quite restrictive assumption: the destination of all
trips is the central business district.
Verhoef (2002) proposes an algorithm for finding the second-best
optimal levels of tolls and furthermore attempts to find a method for
choosing the optimal location of the cordon. His paper is mostly theoretical
but it shows that further research may inform policy makers and help them
with the decisions of where to toll and by how much.
May et al. (2002) succeed in developing a set of analytical procedures for
identifying the optimal locations for imposing charges and the optimal
charges at those points. Unfortunately the method they propose can only
be applied to very simple networks. Since their method cannot be used
for these towns, and since trying different cordon designs would be
computationally very demanding, given the detail and size of the networks
and trip matrices used, only one design was used in this study for each
(inner and outer) cordon. Benefits may be further improved by changing
the location of the toll points, and if a local authority was to pursue the
idea of introducing a cordon toll it is clear that many different designs
should be simulated before actually deciding on the one to implement.
Table 4 shows results for double cordons and compares them with
results for single cordons.
Since there is no method available for determining the optimal location
of the two cordons in actual networks yet, the location of the outer cordon
for these simulations was defined by the outer ring road when there was one
and by the geographical limits of the town when there was not.
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Santos
Urban Congestion Charging
Table 4
Optimal Tolls and Benefits for Single and Double Cordons at 2002 Prices
Single cordon
Northampton
Kingston upon Hull
Cambridge
Lincoln
Norwich
York
Bedford
Hereford
Double cordon
Toll
Benefit
(£m/year)
(a)
Toll inner
3.47
3.73
1.60
1.07
0.80
1.60
1.60
1.60
5.13
5.48
1.35
0.57
1.28
0.93
0.37
0.91
2.40
3.20
0.80
0.80
0.80
1.07
0.27
1.07
Toll outer
Benefit
(£m/year)
(b)
Ratio of
(b) to (a)
2.40
0.53
2.67
1.07
0.80
1.33
2.40
1.07
9.54
5.92
4.17
1.12
1.78
1.22
0.78
1.02
1.9
1.1
3.1
2.0
1.4
1.3
2.1
1.1
Source: Updated and expanded from Santos (2002)
Elasticity assumed: 0.7
The level of the toll is also important, as different inner and outer cordon
toll combinations yield different increases in social surplus. If incorrectly
chosen, there could be substantial losses, as shown in Figure 1. In the
absence of a secure method for finding the optimal combination for
actual networks, trial and error is the only viable method. Different
combinations were simulated. The toll level was varied across but not
within cordons.
The optimal combination could also be one in which different tolls are
charged at different points, even points belonging to the same cordon (inner
or outer). May et al. (2002) find that relaxing the requirement to have
uniform charges at all charging points can produce further increases in
benefits. This option was not tried in this study, mainly because the
number of simulations necessary would have increased significantly.
The towns studied here are not large enough to consider the introduction of three cordons. The MVA (1995), however, conducted tests allowing
for a third cordon in London. It was found that three cordon systems would
offer no advantage over variable bi-directional double cordons.
The problem, however, is that, even though the evidence presented in
Table 4 points in the direction of two cordons to achieve higher gains,
it is not clear that the costs of introducing a second cordon would be
justified by the potential increase in time savings. Specifically, a second
cordon would mean many more charging points, and the cost of this
would probably be higher than the increase in benefits.12
12
Quick calculations show that the benefit-cost ratio could be reduced by more than half.
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Journal of Transport Economics and Policy
Volume 38, Part 3
Introducing a second cordon could also bring some further distributional problems as drivers from villages surrounding the towns and crossing
the outer cordon would now be paying the toll. In a way, the local authority
would be exporting the charge. The town in question would be subsidised
by suburban residents and residents living in villages nearby (Arnott and
Grieson, 1981).
9. Environmental Impacts of Cordon Tolls
The theory of externalities has been widely used in environmental economics.
The environmental externality produced by road transport would be
internalised if road users paid a charge equal to the marginal environmental
cost (Baumol and Oates, 1988; Pearce and Turner, 1990). The question
addressed in this Section is a related but different problem: what would
be the environmental benefits that would derive from (second-best) optimal
cordon tolls?
Although cordon tolling may encourage more and/or longer trips
(Richardson and Bae, 1998), the simulations for the eight towns show
that in all cases there would be positive environmental benefits, at least
for the major health and global warming impacts. Given the very wide
range of environmental cost estimates of road transport emissions available
in the literature, the high estimates of the total environmental costs
presented below are about 15 times as high as the low estimates, showing
the considerable uncertainty attached to the figures. Fortunately, this
uncertainty has little practical effect, as even the high cost estimates are
modest compared to the traffic efficiency gains.
The main results of valuing the emissions for a single cordon are
reported in Santos, Rojey and Newbery (2000). Here the analysis is updated
and expanded to the case of double cordons.
The evaluation of emissions was based on the methodology described in
Chapter 7 of the EMEP/CORINAIR Atmospheric Emission Inventory
Guidebook (European Environment Agency, 1999). The emissions factors
were obtained by applying these formulae to the average speed obtained
from SATURN for each trip defined by its origin and destination.
National averages for vehicle age and power distribution were used for
all towns. The age distribution was derived from the National Travel
Survey 1993/1995 (Department of the Environment, Transport and the
Regions (DETR), 1996). The proportion of vehicles belonging to each
European class was deduced from the age of the vehicles. The power
distribution was derived from Transport Statistics Great Britain (DETR,
362
Urban Congestion Charging
Santos
1998). The proportions of vehicle types assumed to hold in each town were
taken from traffic flows monitored in Cambridge and provided by WS
Atkins on behalf of Cambridgeshire County Council.
Cold-start emissions were calculated using the average distance driven
in each town before the introduction of the toll and a temperature of
4.7 8C, which is the average minimum temperature recorded by Cambridge
Weather Station between 1961 and 1990 (Meteorological Office, at their
web site http://www.met-office.gov.uk/averages/19601991/sites/cambridge.
html).
Thus, emissions for each pollutant were estimated before and after the
introduction of the optimal toll. The pollutants considered were carbon
dioxide (CO2 ), carbon monoxide (CO), volatile organic compounds
(VOC), nitrogen oxide (NOx ), particulate matter (PM), methane (CH4 ),
nitrous oxide (N2 O), and ammonia (CH3 ).
The health costs of these emissions were estimated using the values
reported by McCubbin and Delucchi (1999). Estimates of the cost of
global warming due to CO2 emissions span a very wide range. Maddison
et al. (1996) use the shadow price of controlling the last unit of CO2 emitted.
They estimate it at £4.9/tonne of carbon (tC) at 2002 prices. The Royal
Commission on Environmental Pollution (1994) gives the value as £73.1/
tC, also at 2002 prices. Clarkson and Deyes (2002) review the literature
and conclude that £70/tC at 2000 values and prices is the value that
enjoys the greatest support in the literature. They also suggest increasing
it by £1/tC per year in real terms, which yields £72/tC for 2002 at 2000
prices, and £73.5/tC at 2002 prices. £4.9/tC and £73.5/tC were the figures
used in the present study as low and high estimates respectively. All
greenhouse gases were converted to CO2 equivalents.
According to McCubbin and Delucchi (1999), road traffic generates
pollution not only through motor vehicle emissions but also through
upstream emissions13 and road dust emission. This effect was taken into
account by multiplying the cost of the motor emissions by the ratio of
total cost (including motor, upstream, and road dust emissions) over
motor emissions cost for each pollutant, as given in McCubbin and
Delucchi (1999).
The corresponding monetary values of the reduction in emissions in the
eight towns are presented in Table 5. The table shows that, even when using
the highest estimate for pollution costs, the increase in benefit caused by the
13
Upstream emissions are pollutants associated with motor vehicles that do not come from the tailpipe.
For example, combustion, evaporation and leakage take place during storage, distribution and
refuelling of petrol (California Electric Transportation Coalition, www.evchargernews.com).
363
364
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Northampton
7.9
119.8
14.1
215.0
5.5
86.0
2.5
39.3
3.4
51.5
3.4
52.1
4.5
68.6
3.3
49.6
Single
14.9
225.5
14.6
223.7
13.4
204.7
4.1
63.4
8.4
129.4
5.3
81.9
7.3
112.0
5.4
83.6
Double
4.6
68.7
9.5
141.0
3.3
48.7
1.3
19.8
2.8
40.9
2.2
33.1
2.5
36.8
2.1
32.2
9.5
140.9
9.9
148.2
9.3
138.5
2.4
36.3
6.0
89.1
3.1
45.5
3.9
58.1
3.2
47.3
Double
Global warming
Single
Source: Updated and expanded from Santos, Rojey and Newbery (2000)
Elasticity assumed: 0.7
Hereford
Bedford
York
Norwich
Lincoln
Cambridge
Kingston upon Hull
Estimate
Town
Health
12.5
188.4
23.6
355.9
8.9
134.6
3.9
59.1
6.2
92.4
5.7
85.0
6.9
105.4
5.4
81.9
Single
Environmental benefit £’000 per year
Total
24.4
366.5
24.5
371.9
22.7
343.2
6.6
99.6
14.4
218.5
8.3
127.4
11.1
170.2
8.6
130.9
Double
Table 5
Reduction in Environmental Costs from Optimal Cordon Tolls at 2002 Prices
0.2
3.7
0.4
6.5
0.7
9.9
0.7
10.5
0.5
7.2
0.6
9.2
1.9
28.2
0.6
9.0
Single
0.3
3.8
0.4
6.3
0.5
8.2
0.6
8.9
0.8
12.3
0.7
10.5
1.4
21.8
0.8
12.8
Double
As % of transport
benefits
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Volume 38, Part 3
Urban Congestion Charging
Santos
reduction in emissions is small (typically less than 10 per cent) compared to
increases in social surplus. The two exceptions are Bedford and Hereford,
where, as shown in Table 4, there are large reductions in the number of trips
demanded. Although the environmental benefits increase with the introduction of a second outer cordon, when expressed as percentages of
transport benefits, there are no important differences between single and
double cordons.
In all cases the congestion toll, which maximises the increase in social
surplus, was the same toll that would both maximise the increase in
social surplus and the reduction in environmental costs. In other
words, when the toll was re-optimised to take account of environmental
externalities, the final results did not change. The reason for this is that
the environmental externality is very small in relation to the congestion
externality.
Daniel and Bekka (2000) simulate the effects of congestion tolls on
emissions of carbon monoxide, nitrogen oxide, and hydrocarbons. Their
results are not directly comparable with the results presented above because
they exclude some of the pollutants considered in the present study. They
simulate total and partial pricing. Partial pricing would be the nearest
comparable scenario to a cordon toll. They find that the benefits of
emissions reductions for partial network pricing are small relative to
benefits of congestion reduction. Even with a demand elasticity of 1,
they find benefits from emissions reductions to have a median value of
4.9 per cent, which is not out of line with the values presented in Table 5,
although any comparison should be made with much caution for the
reasons explained above.
10. Comparison with Benefits from First-best Charges
As explained at the beginning of the paper, first-best tolls are tolls that
charge for the marginal congestion cost. They therefore vary in space
and time. Although SATURN can in principle compute these first-best
tolls, in order to do so it needs to run with a buffer network. In this type
of network delays at junctions are not modelled and instead links are
assigned speed-flow relationships, which include the delays that occur at
junctions, even if these are not explicitly modelled. Notwithstanding that,
first-best tolls were computed for the eight study towns, together with the
increase in annual social surplus. The networks used to compute firstbest tolls in this study are simpler than the ones used to simulate cordon
tolls. The tolls vary according to link and traffic conditions, from £0 and
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Journal of Transport Economics and Policy
Table 6
Annual Increase in Social Surplus from First-best Charges and from Double
Cordons (£ million at 2002 prices)
Town
Northampton
Hull
Cambridge
Lincoln
Norwich
York
Bedford
Hereford
First-best (a)
Cordon (b)
Ratio of (a) to (b)
10.05
13.37
5.19
4.05
2.16
2.33
1.24
1.47
9.54
5.92
4.17
1.12
1.78
1.22
0.78
1.02
1.05
2.26
1.24
3.62
1.21
1.91
1.59
1.44
Source: Own calculations on the basis of SATURN results
Elasticity assumed: 0.7
£0.01 to almost £2 per link. As a research exercise, however, the increase
in social surplus was computed and can be compared with the one that
would derive from double cordons. Both estimates are presented in
Table 6. Even though the increase from first-best tolls is higher than the
increase in social surplus that would be obtained if a double cordon toll
was implemented, it is clear that it would not be cost effective. As stated
at the beginning of the paper, a first-best toll in every single link of a
town would simply be too expensive to implement, and the cost would be
higher than the gains.
Cordon tolls perform relatively well, and this is shown by the ratios,
which in most cases are below two. This is in line with Mun et al. (2003),
who build a theoretical model and conclude that cordon pricing attains
an economic welfare level very close to the first-best optimum.
11. Conclusions
The (second-best) optimal toll for single and double cordons has been
estimated for eight towns. Although the method is not based on marginal
cost pricing, the gains it yields are relatively high, when compared with
the first-best.
The distributional impacts for single cordons in three towns have been
assessed. Results show that these may be progressive, regressive, or neutral,
depending on where people live, where people work, and how they travel to
work. It was found that Bedford would have progressive impacts even
before any compensation scheme was taken into account.
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Urban Congestion Charging
A second outer cordon was found to enhance benefits. However, the
costs of introducing an outer cordon may not justify the gains and a careful
cost-benefit analysis would need to be undertaken before deciding on a
second cordon.
The environmental effects of single and double cordons were estimated.
These would be positive although very small compared to the transport
benefits.
Road pricing has been studied for several decades. The time has now
come where theory and practice need to be reconciled as politicians finally
agree that the way forward may entail some element of congestion
charging. The theoretical first-best model of marginal congestion pricing
cannot be applied but second-best cordon tolls can and it is shown in this
paper that the effects would be positive.
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