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The Effect of Transport Taxes on Society
Matts Andersson WSP
Christer Anderstig WSP
Håkan Berell WSP
Svante Berglund WSP
Jonas Eliasson KTH Royal Institute of Technology
Michael Lundholm Stockholm University
Tommy Lundgren SLU Swedish University of Agricultural Sciences
Roger Pyddoke VTI
Marcus Sundberg KTH Royal Institute of Technology
Jonas Westin KTH Royal Institute of Technology
Keywords congestion charges, fuel tax, kilometre tax, tax base, double dividend, socio economic, costbenefit analysis
JEL Codes R41, R48
ISBN: 978-91-980117-0-8
Centre for Transport Studies
SE-100 44 Stockholm
Sweden
www.cts.kth.se
Title: The Effect of Transport Taxes on Society
Authors: Matts Andersson (WSP), Christer Anderstig (WSP), Håkan Berell (WSP),
Svante Berglund (WSP), Jonas Eliasson (KTH Royal Institute of Technology),
Michael Lundholm (Stockholm University), Tommy Lundgren (SLU Swedish
University of Agricultural Sciences), Roger Pyddoke (VTI), Marcus Sundberg
(KTH Royal Institute of Technology), Jonas Westin (KTH Royal Institute of
Technology)
Keywords: congestion charges, fuel tax, kilometre tax, tax base, double dividend,
socio economic, cost-benefit analysis
JEL Codes: R41, R48
ISBN: 978-91-980117-0-8
Summary
Without investment costs, financial policy measures are almost by definition
socio-economically profitable if they push prices closer to the marginal cost. But
since most transport taxes include an investment cost the question is, as with
physical investments, if the benefits are larger than the costs. large part of the
benefit of transport taxes might be that the income can be used to lower other
taxes, which might have positive effects on the economy. This positive effect is
called “marginal cost of public funds” (MCPF) in the economic literature.
Sometimes it is argued though that the effect on the tax base cancels the
incomes from the policy measurement, meaning that the “double dividend”
(decrease in the externality and using the income to lower other, distortionary,
taxes) of environmental taxes does not exist.
The Swedish recommendations for transport CBA (ASEK) was until 2008 to
include the full double dividend effect in CBA for by multiplying the change in
tax revenue with MCPF. In 2007 evaluations of kilometre tax where done
including no double dividend effect using the tax base argument above. In the
last published recommendations (ASEK 4, 2008) is not clear on whether to
include the double dividend effect in the evaluation of economic policy
measures. Since the question of double dividend is crucial for the socio
economic profitability of most transport taxes it is highly desirable to clarify this
issue. This project aims at providing such clarification.
This report consists of five articles concerning CBA for transport taxes. The first
article gives survey of the literature. The other four articles are more case
oriented, analyzing the effects of congestion charges, fuel tax and kilometre tax.
This summary is meant to sum up all five articles in way that is accessible also
for nonscientists.
The project is financed by VINNOVA, CTS Centre for Transport Studies, VTI and
KTH Royal Institute of Technology. People from WSP (Matts Andersson, Christer
Anderstig, Svante Berglund, Håkan Berell), VTI (Roger Pyddoke), Stockholm
University (Michael Lundholm), KTH (Jonas Eliasson, Marcus Sundberg, Jonas
Westin) and SLU Swedish University of Agricultural Sciences (Tommy
Lundgren) have participated. Matts Andersson has been project leader.
Article 1: The treatment of changes in tax levels and new tax
instruments in transport sector cost-benefit analysis – A synthesis
The purpose of this paper is to survey theoretical and empirical findings
concerning the treatment of welfare costs for the revenue from taxes in costbenefit analysis. The main results are the following.
In situation with optimal taxes there is no double dividend effect, i.e. the only
benefit of the implementing/raising tax on an externality is the decrease in the
externality. Though, when taxes are not optimal there can be significant effect.
From an initial position where taxes are optimal, any small changes of levels
with balanced budget will result in tax base changes that cancel out any welfare
effects. For situation where taxes are not optimal there are trivially both gains
from introducing an externality correcting tax and from moving closer to
optimum. In the latter case, the effect from introducing tax instrument might
be that tax revenues can increase without welfare loss. This depends on how far
from optimum an initial situation is.
complete evaluation of MCPF would require
numerical social welfare
function which is not developed. In view of this lack one may use efficiency
based calculations of MCPF being aware that the desired redistributional effects
of taxes are not evaluated by this method.
Each tax instrument can, in principle, be associated with its own measure of
MCPF and each combination of tax instrument and form of public spending can,
in principle, also be associated with its own measure of MCPF. The multitude of
MCPF:s necessitates weighting process. As there are many measures it is no
surprise that there is quite wide interval of estimations for the MCPF, the
variation in the literature is caused by different measures of MCPF and
estimations done for different countries, time periods and tax instruments. An
important distinction is also between studies assuming that the public funds are
used for public good and those assuming lump-sum redistribution (the MCPF
will typically be smaller in the latter case). The estimations of MCPF:s are also
highly dependent on the labour supply elasticities associated with in particular
income tax rates for different income groups, especially the propensity of the
individuals not presently employed to get employment.
Article 2: Congestion charges and the labour market: “Wider
economic benefits” or “losses”?
The presence of distortive taxation and agglomeration benefits in the labour
market mean that there are benefits and losses not captured by standard costbenefit analyses of transport policy measures. Recent theoretical analyses have
raised concerns that the labour market effects of congestion charges may
constitute considerable losses in the form of reduced aggregate labour income,
over and above what is captured by the consumer surplus in the standard
analysis of congestion charges possibly to the extent that congestion charges
may reduce aggregate social welfare, contrary to conventional wisdom in
transport economics. The sign and size of these effects are an empirical
question, however. We investigate this issue by estimating the labour income
effects of the Stockholm congestion charges, using an estimated relationship
between workplace accessibility and labour income. Results show positive
effects on labour income, meaning that the “wider economic benefits” of this
system are in fact benefits, not losses. It turns out to be crucial that the model
accounts for value-of-time heterogeneity in the income/accessibility
relationship and in the calculation of generalized travel costs.
In this paper the estimated increase in labour income is 60 M€/year. Intuitively,
groups with high values of time get increased accessibility, while groups with
low values of time get decreased accessibility. Some travellers may also gain
accessibility due to network effects (“spillback” of congestion reductions). The
aggregate change in accessibility may be either positive or negative. But the
model estimations showed that changes in accessibility affects labour income
more for high-income groups than for low-income group. This is intuitively
plausible, since high values of time are correlated with high income and high
education, and such groups generally get higher wage premiums for increasing
work trip length. Hence, one may have positive effects on labour income even if
aggregate accessibility decreases.
The question in terms of the double dividend discussion could be formulated as
“will the decrease in labour income (the tax base investigated) neutralize the
dividend from using the revenues to lower other, distortionary, taxes?”. Since
the labour income increases the answer is that there is double dividend for the
Stockholm congestion charges.
The paper also analyses the effects of an increased fuel tax, designed to give the
same tax revenues as the congestion charges. In contrast to the congestion
charges, this does not give any appreciable travel time savings, so accessibility
decreases for all groups. Consequently, the fuel tax has quite different
consequences for labour income. While the congestion tax is estimated to
increase labour income with nearly 60 M€/year, the fuel tax is estimated to
decrease labour income with nearly 95 M€/year. The size of the decrease varies
between municipalities and between value-of-time categories in the same
municipality. This variation can mainly be explained by the variation in the car
modal share, which is linked to variation in land use pattern and supply of
public transport. In the case of the fuel tax it is clearly not correct to assume
full double dividend effect (ie. to just add tax revenue times MCPF to the
benefits). One needs to compare this tax base effect with the MCPF-effect.
Article 3: How to evaluate the welfare effects of congestion
charges?
common argument in the road pricing literature is that the way the revenues
from road toll are recycled is crucial for the overall welfare of the policy. An
early contribution (Parry and Bento, 2001) looked at welfare effects of
combination of road pricing and the redistribution of the revenues. lively
debate has considered the most welfare improving ways of using the revenue.
In this paper the results in 2001 are further developed by examining the effect
of introducing congestion tax under number of different budget neutral
revenue recycling policies is analyzed. The examined policies are to use all
revenues from the congestion tax to; an income tax reduction, an increased
public transit fare subsidy, an increased provision of public good, and lumpsum redistribution. These policies are also compared to budget neutral recalibration of all policy instruments. In addition to the theoretical expressions
for evaluation of these scenarios
number of numerical calculations are
presented.
The most important result is that if the initial situation is modeled as secondbest optimum with the restrictions that neither lump-sum nor congestion
taxation is available,
budget neutral change in any of the initially nonconstrained policy instruments will have the same welfare effect. This means
that any revenues from
marginal congestion tax will produce the same
welfare, regardless of which of the policy instruments the revenues are spent
on.
The consequences of starting from non-optimal policies are also examined,
resulting in that the initial point may influence the analysis significantly. If we
analyze model where we explicitly (or implicitly) assume that the taxes are
too high compared to social optimum, we will find that it is better to use the toll
revenues to lower other distortive taxes. If we on the other hand assume that
the public transport subsidy initially is below social optimum, it will be
preferable to recycle the revenues on increased subsidies. Differences in the
relative efficiency of different revenue recycling policies, especially for marginal
toll policies, are therefore more related to the initial model assumptions
regarding the initial situation than being direct feature of the road toll per se.
For non-marginal toll policies, interactions between the road toll and the other
policy instruments also need to be considered in the welfare analysis. For very
large toll levels, the reduced congestion in combination with the tax base effect
can for instance make the income tax cut out-perform the public transport
subsidy, even in situations where the both policies initially were equally good.
The type of general statements about how the revenues from road toll should
be spend to maximize welfare that can be found in the research literature is
problematic since the relative efficiency of different recycling policies so
strongly depend on the particular situation we analyze and what assumptions
we make regarding the efficiency of the initial policy instruments. The analysis
is also sensitive to what markets and interactions we include in the analysis and
whether we, for instance, include distributional considerations in the welfare
function or not.
Article 4: Welfare Effects of Congestion Pricing in a Population with
Continuously Distributed Value of Time
Interactions between the transport market and other distorted markets, such as
the labor market, can have large impact on the overall welfare effect of road
pricing policy. Many road pricing studies therefore try to incorporate effects
from other distorted markets in the analysis. critical assumption in many of
the previous analyses of congestion charges is that there only exists single
value of time. This is somewhat surprising since one of the main features of
congestion charge is that it sorts people related to their value of time, given the
existence of feasible transport alternatives. The purpose of the paper is to
analyze the labor market effect from congestion charge when commuters have
continuously distributed value of time. Using disaggregated demand model for
the individuals’ choice of travel mode, the paper studies the distributional
impact of different revenue recycling policies, and analyzes how the mode
choice self-selection mechanism affects the total welfare effect of congestion
charge. In stylized numerical example, the effect of three different revenue
recycling polices are analyzed; lump-sum transfer, labor tax cut, and
welfare maximizing readjustment policy.
Contrary to the general conclusion in many previous studies, the paper finds
that when the revenues from the congestion charge are recycled back to the
population, the overall effect welfare effect is positive, regardless if the revenues
are returned in lump-sum transfer or used to cut distortionary income taxes.
The analysis hence stresses the importance of recognizing that people have
different value of time and that this can have substantial effect on aggregate
labor supply and hence welfare. The reason for this is that the congestion
charge primary price out people (and trips) with low willingness to pay so that
people with higher willingness to pay can drive and work more. Disregarding
equity considerations, the congestion charge leads to more efficient use of the
available road space. The results also indicate that public transport subsidies
may increase labour supply more than the corresponding labour tax cuts. We
also find that even though the total welfare effect from the congestion charge for
marginal toll levels does not depend on the chosen form of revenue recycling,
the distributional impact of the policies can be significant.
Article 5: Kilometre or diesel tax in Sweden? A cost–benefit
analysis
The aim of this article is to examine to socio economic profitability of kilometre
and diesel tax. To suggestions are examined. The Swedish institution for
communication suggested kilometre tax of SEK per vehicle kilometre. This is
based on the external effects calculated to 1.4 SEK per km, out of which 0.4 SEK
is internalized by the energy tax. The Swedish opposition suggested that the CO
tax on fuel should be raised with 0.17 SEK per kilo CO 2, which implies that
the diesel tax increases with 2.64 0.17 0.45 SEK per litre diesel.
Examining the socio economic profitability and examining the tax base effect is
different sides of the same coin. As mentioned above discussions about tax base
effects are often based on analytical (i.e. non empirical) models assuming
optimal conditions. In this article we start out with an analytical model, but we
estimate the parameters/elasticities empirically on Swedish data.
The
estimations of the tax base, the marginal cost of public funds etc. are done with
both factor demand-model (FDM) and spatial general equilibrium (SCGE)
model (STRAGO). Since FDM and SCGE are two quite different approaches, an
aim of this study is also to compare these approaches.
Our calculation implies that the kilometre tax is socio economically profitable,
even very profitable in the FDM-based calculation. However when the
investment and administration cost is added, 350 MSEK per year according to
SIKA’s calculations, the profitability in the STRAGO-based calculation is slightly
negative. It could be noted though that our estimation of the decrease in
external effects is lower than SIKA’s, who estimates it to 180–400 MSEK per
year. Changing to SIKA’s valuation makes the calculation slightly positive.
There is obviously trade-off between making detailed calculation of one
market, as in the partial model, and capturing all effects but on
more
schematic level, which is done in the general equilibrium model. When we
estimate the tax base effect on private intermediate commodities (i.e. labour
and capital) with the FDM, the net social benefit is extremely positive; since the
net social benefit is approximately equal to the tax revenue from the kilometre
tax the revenue comes “for free”. The direction of the difference between the
partial (FDM) and the general equilibrium (STRAGO) estimates is logical since
the equilibrium effects most likely are negative. The in market effect might be
positive: increasing transport taxes makes firms replace transports with other
production factors. Equilibrium requires market to clear (which counteract the
in market effect) and increasing kilometre taxes on goods freight makes leisure
relatively cheaper (which makes labour supply go down). Even though the sign
of the difference between the model results is logical, it is hard to verify the size.
Our calculation for the diesel tax shows similar pattern, but since it requires
no investment or administration cost it is profitable in both calculations. It
should be mentioned though that our calculations of the external effects does
not capture the differences in benefits from kilometre tax compared to diesel
tax, i.e. the reasons for making the investment. The differences are that
kilometre tax can levied on all vehicles regardless of nationality (i.e. not
possible to avoid the tax by filling the tank abroad) and, most importantly, can
be differentiated very detailed (based on vehicle type, amount of people affected
by pollution etc.).
Main conclusions from the project
In an optimal, first best, world there is no double dividend from tax instruments.
In the real world though, it is an empirical question. This means that
microeconomic CBA, “measuring the benefits on the road” for economic policy
measures should be complemented with more specifically tailored models to
examine to tax base effects. Since MCPF and tax base effect most likely are larger
parts of the benefit for tax instruments than for physical investments the
combination of micro economic CBA and tailored models is more crucial here,
more so than for physical investments. Using both microeconomic CBA and
tailored model means that the result could not be added directly, avoiding
double counting is important.
Since physical investments are not treated in this project, our conclusions
concern only tax instruments (not, for example, weather to apply MCPF on
physical investments).
Our test of the effect congestion charges has on labour income showed
surplus. This means that the tax base increased, indicating that there is double
dividend (or even “triple”, since it is an increase). precise statement would
require examination of the other tax bases affected. The main explanation for
the positive result is that differentiated value of time is applied. Later applied in
our general equilibrium setting, contrary to the general conclusion in many
previous studies, we find that when the revenues from the congestion charge
are recycled back to the population the overall effect welfare on effect is
positive. This holds regardless if the revenues are returned in lump-sum
transfer or used to cut distortionary income taxes.
The fuel tax is estimated to decrease labour income with nearly 950 MSEK/year.
This is equivalent to tax revenue decrease of 332 MSEK/Year (assuming that
the tax is 35 percent of the change in labour income). The fuel tax is designed so
that the increase in tax revenue would be 800 MSEK/year. This means that the
decrease in labour income tax revenue is near half the size of the increase in the
fuel tax revenue. This in turn means that the MCPF effect for the fuel tax should
at least not fully be included in CBA. As with the congestion charges, precise
statement would require examination of other tax bases (mainly consumption
and the effect of more expensive business travels), but labour income is most
likely the largest tax base affected by fuel tax increase.
Both the kilometre and the diesel tax decreased the tax bases examined. Since
kilometre and diesel (fuel) tax do not lower transport cost by decreasing
congestion as congestion charges do, this is the expected result. The socio
economic profitability for both taxes is very high using the FDM result. Using the
STRAGO result, the profitability is lower. Since the results varied between
STRAGO and the FDM, no clear interpretation for the double dividend debate
could be made.
The discussion about tax base and MCPF effects also has implications for the
optimal level of the tax. The optimal level of the tax can be both higher and
lower than the first-best Pigouvian tax (ie. the marginal cost). The literature has
provided examples of where the optimal tax is higher, but it might also
theoretically be lower.
Table of content
1 The treatment of changes in transport sector taxes in
cost-benefit analysis
survey....................................................12
1.1 The marginal costs of public funds and the introduction of
new tax instruments ..................................................................................... 12
1.2 Modelling responses to tax changes and marginal costs of
public funds ...................................................................................................... 16
1.3 Welfare and tax base effects from externality correcting
taxes..................................................................................................................... 21
1.4 Road pricing (congestion tax) considerations........................ 24
1.5 Some geographical dimensions..................................................... 26
1.6 Summary and conclusion................................................................. 30
1.7 Acknowledgements ............................................................................ 32
1.8 References .............................................................................................. 33
2 Congestion charges and the labour market: “wider
economic benefits” or “losses”?.....................................................36
2.1 Introduction........................................................................................... 36
2.2 Literature................................................................................................ 38
2.3 The Stockholm congestion charging system ........................... 40
2.4 Modeling the relationship between income and
accessibility ...................................................................................................... 41
2.5 Effects of congestion charges on Labour income .................. 47
2.6 Conclusions............................................................................................ 50
2.7 References .............................................................................................. 52
3 How to evaluate the welfare effects of congestion
charges? .................................................................................................. 55
3.1 Introduction........................................................................................... 55
3.2 The model ............................................................................................... 58
3.3 Numerical experiments .................................................................... 63
3.4 Discussion............................................................................................... 71
3.5 Conclusions............................................................................................ 72
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3.6 Acknowledgements ............................................................................ 73
3.7 References .............................................................................................. 74
4 Welfare Effects of Congestion Pricing in Population
with Continuously Distributed Value of Time .........................75
4.1 Introduction........................................................................................... 76
4.2 Background............................................................................................ 77
4.3 Analytical model .................................................................................. 79
4.4 Numerical example............................................................................. 85
4.5 Concluding remarks ........................................................................... 93
4.6 Acknowledgements ............................................................................ 94
4.7 References .............................................................................................. 95
5 Kilometre or diesel tax in Sweden?
cost–benefit
analysis....................................................................................................97
5.1 Introduction........................................................................................... 97
5.2 Our two cases to be tested............................................................... 98
5.3 External Effects .................................................................................... 99
5.4 Model ..................................................................................................... 100
5.5 FDM ........................................................................................................ 102
5.6 STRAGO ................................................................................................ 104
5.7 Results................................................................................................... 105
5.8 Conclusions......................................................................................... 107
5.9 References ........................................................................................... 108
11
1
The treatment of changes in transport sector taxes in costbenefit analysis – A survey
Roger Pyddoke, VTI
Matts Andersson, WSP
Abstract
This paper was motivated by the analysis of introduction of new internalising
tax instruments in the Swedish transport sector. The purpose of the paper is to
survey the literature on welfare effects of taxes and discuss the implications for
the application of the concept of marginal cost of public funds (MCPF) in costbenefit analysis. The paper draws together some important observations for the
evaluation of internalising tax reforms. The consideration of the objectives of
income redistribution effects has decisive influence on the assessment of the
MCPF value. From an initial position where taxes are optimal, on the one hand,
any small changes of tax levels with balanced budget will result in tax base
changes that cancel out any welfare effects. For suboptimal taxes there are
trivially both gains from introducing an externality correcting tax and from
moving closer to tax system optimum. From pure efficiency perspective, on
the other hand, it is noted that from the reference point of second best
optimum without any correction of an externality, the introduction of
correcting tax, even larger than the first best correcting level, with simultaneous
budget balancing tax cuts of distortionary taxes, may yield welfare
improvements. The conclusion is that when evaluating tax reforms the effects
on tax bases as well as distributional effects need to be considered by general
equilibrium models rather than applying general MCPF factor to net aggregate
tax revenue from the reform.
1.1 The marginal costs of public funds and the introduction of new tax
instruments
The main question for this study is how tax revenue and the welfare effects of
changes in the tax system should be treated in cost-benefit analysis. The general
question is directed in particular to taxes intended internalize externalities in
the transport sector. This question was triggered by study from the Swedish
institute for transport and communications analysis (SIKA 2007) commissioned
by the Swedish government on the costs and benefits of kilometre taxation for
trucks. SIKA formulated two important assessments of the welfare costs of
kilometre taxation underlying their cost benefit analysis. The first assessment
was that tax revenues from the kilometre tax should not be increased with
welfare gain corresponding to the marginal cost of public funds (Skattefaktor 2)
(SIKA 2007 p. 45). The then current Swedish CBA practice in the transport
sector suggested that the welfare costs of new transport tax instruments should
be evaluated by the micro effects in the transport models and that the increased
tax revenues should be evaluated by the marginal cost of public funds (MCPF).
As the, then current, recommended value of MCPF equalled 1,3 this would have
12
implied that each extra krona of tax revenue could have an alternative value for
reducing the distortionary taxes larger than 1. SIKA (2007 p. 35) assessed the
calculable benefits of e.g. less wear and tear and less externalities associated
with the kilometre tax to be 180-400 million SEK per year and the system cost
to be 350 million SEK per year. In addition to this the welfare gain associated
with the MCPF effect from reducing other distortionary taxes was 8-900 million
SEK per year 1 The net from these three posts was thus in the range from 680 to
950 million SEK per year. The kilometre tax therefore initially appeared to be
welfare improving, but after assuming MCPF to be it is not.
At the same time as the cost-benefit rules suggested applying MCPF
the
already large literature on double dividends in the tax interaction literature (e.g.
Bovenberg 1999) suggested that there was are no additional benefits from
reducing other distortionary taxes when introducing or increasing suboptimal
internalising taxes. Invoking results from the tax interaction literature (and
citing Fullerton and Metcalf 2001) SIKA, therefore, chose not to count the
welfare gain from reducing other distortionary taxes, arguing that this gain may
be cancelled by equal reductions tax revenue caused by contractions of other
taxbases on account of the introduction of/increase in the internalising tax. In
the final instance SIKA argued that the uncertainty concerning these effects led
them to recommend not counting the welfare gains from reducing other
distortionary taxes, hence reducing the net from 50 to -170 million SEK per year
and therefore concluding that the kilometre tax was likely to have negative
welfare effects.
The second assessment (also formulated in SIKA rapport 2007:5 p. 46)
generalised the first assessment to other taxes motivated by external effects and
said that the welfare gain associated with the marginal cost of public funds for
other taxes (like the congestion tax) may not be valid either.
Both the assessments suggest that the tax base effects may perfectly cancel the
welfare gains from increased tax revenue.
related question is therefore if
there are other significant effects on tax bases that are not taken into account by
the travel demand models and hence cost-benefit analysis. further question
here is therefore to what extent improvements in accessibility in the transport
system through congestion charges may in turn lead to effects on income. This
effect can be expected to be larger if the values of travel time are differentiated.
The most recent value of travel time study in Sweden (WSP 2010) shows that
this is the case. The study indicates that there are substantial differences in
travel time valuations. This finding may have important implications for both
behaviour and valuation and consequently the assessment of the benefits from
e.g. congestion taxes.
The purpose of the project is to examine how the welfare costs of taxes or the
average marginal cost of public funds could be treated in cost-benefit analysis of
tax instruments for the internalisation of external effects in the transport sector.
For this purpose the paper synthesises four different fields of economic
1
Table on p. 46
13
literature. The first is the literature on marginal costs of public funds. In this
literature both theoretical and empirical analyses have been combined to assess
the costs of collecting public funds. The second is the closely linked tax
interaction literature concerning how different taxes interact and what their
total effects are. The third is the literature on the effects of pricing in transport,
e.g. road pricing and fuel taxes. The fourth, finally, concerns the effects of
income from increases in accessibility to potential employment. In the following
introduction we therefore present an overarching perspective of these
literature fields.
The issue of how to apply the marginal costs of public funds (MCPF) in costbenefit analysis entered the Swedish guidelines for the transport sectors costbenefit rule calculations in Kommunikationsdepartementet (1985)2 and was
again removed in SIKA (2008) partly because the EU financed project HEATCO
(2006) recommended using the MCPF=1 or practically disregarding it3 The
recommendations for the transport sector was originally intended to be used
primarily to analyse the effects from transport infrastructure projects, and to
some extent to other measures intended to influence transport flows. This
included for example changes in net public budget burdens caused from
changes in transport flows and the corresponding tax revenues from fuel taxes.
It was not, however, primarily thought as an instrument for the evaluation of
potential new or changes in existing, tax instruments.
The academic literature on MCPF has by 2010 developed to considerable
extent; see for example Dahlby (2008). Two main approaches exist in the
literature on the MCPF; the first calculating the welfare costs from changing
tax and simultaneously changing lump-sum redistribution while maintaining
budget balance and the second where the tax revenue instead is used for
public good while maintaining budget balance. The first approach implies
different measure for each tax instrument and the latter different measure for
each combination of tax instrument and public good.
There are number of well-established insights among which the following
were considered important:
i) Each tax instrument can, in principle, be associated with its own
measure of MCPF
2 The earliest reference to MCPF in Swedish government texts that
can find is
Kommunikationsdepartementet ”Investeringsplanering inom Transportsektorn” DsK 1985:4.
3 The HEATCO consortium (2006) argued that “a majority of EU national transport project
appraisal guidelines” do “not to include the marginal costs of public funds” and that there are
three good reasons for not doing so (p. 48):
The first being the large uncertainty about how large the marginal costs of public funds are
(0.62 1.75).
The second, that marginal costs of public funds are normally not considered when
evaluating public projects outside the transport sector, and that therefore inclusion in the
transport sector would bias decisions against transport.
The third, that in practice, the question of the inclusion might not be as important as it
might seem. Because only the best projects get financed, these projects tend to have high
rates of benefits to costs.
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ii)
Each combination of tax instrument and form of public spending can, in
principle, be associated with its own measure of MCPF (Hansson and
Stuart 1985)
iii) The multitude of MCPF:s necessitates weighting process
iv) As there are many measures it is no surprise that there is quite wide
interval of estimations for the MCPF, e.g. 1.15 to 2.52 in Kleven and
Kreiner (2003). The variation in the literature is caused by different
measures of MCPF and estimations done for different countries, time
periods and tax instruments.
v) The estimations of MCPF:s are also highly dependent on the labour
supply elasticities associated with in particular income tax rates for
different income groups. The question of how the propensity of the
individuals not presently employed to get employment may be very
important for the aggregate MCPF (Kleven and Kreiner 2006).
further insight in the literature on tax systems is that it is desirable to model
any tax system as the outcome of optimization. This implies interpreting given
tax system as balancing costs and benefits in many dimensions. In full social
welfare maximization sense this implies considering both efficiency and
distributional concerns. If tax system is modelled as inefficient this implies
some lack of representation of the process arriving at that particular form of tax
system. In an inefficient system it also becomes trivial to find efficiency gains.
The reasons for having “inefficiencies” should therefore ideally be underlying
conflicts on the distribution of income, property rights or other endowments, or
some lack of knowledge about the consequences of taxation. These
imperfections may also be associated with inertia in adapting to new insights
about the effects of taxation, technological developments or preferences. Even if
the tax system is considered as an equilibrium in political bargaining process
and the resulting system represents
compromise between different
preference this compromise still to some extent represents the underlying
preferences.
The underlying processes leading to new externality correcting taxation may in
many cases be complex and opaque. Even if new tax instrument appears to
deliver significant welfare gains the relative magnitude of the tax payments may
pose an obstacle. The Swedish and the international political experiences and
the academic debates on e.g. congestion charging have also demonstrated the
difficulties of establishing democratic acceptability and legitimacy (Hårsman
and Quigley 2010).
Independently of the development of the MCPF issue in cost-benefit analysis,
the question of tax reform also developed in Sweden. When the largest tax
reform in Swedish modern history in 1990-91 was evaluated in SOU 1995:104,
the issue of the dead weight losses from different tax instruments was also
addressed. The commission concluded that it was difficult to make precise
assessment of the dead weight losses from the tax system, as the calculations
are highly dependent on uncertain estimates of labour supply elasticities.
15
These difficulties do not necessarily preclude the possibility to obtain useful
information on the welfare effects of internalising taxes. In tax theory
distinction is made between situations where non-distortionary lump-sum
taxes are available, first-best and second-best where policy makers are
restricted to use distortionary taxes on labour and goods.
The basis for the internalisation of external effects is the first-best idea of
pricing activities with their marginal external costs at each time and place. For
this purpose it is useful to know how transport activities generate external
effects and consequently costs. An examination of transport pricing and taxation
reveals that the adopted tax levels do not correspond to approximately
calculated first-best levels (e.g. SIKA 2004). Available calculations are, however,
mostly partial and consider only some of the theoretically known trade-offs. It
therefore seems inevitable that real life choices are approximate and imperfect.
In addition to balancing the ultimate benefits from consumption and transport
second-best analysis balances the consequences from the use of different
distortive tax instruments. It is therefore important to know how behaviour and
demand is affected by the presence of externalities. This paper therefore further
presents research on how the introduction of congestion charges/taxes in
conjunction with optimal adaptions of other policy instruments, influences
welfare. In this part we review results of studies that have studied different uses
of the tax revenue.
central purpose is to compare how different schemes for
using revenue perform. Finally we examine the accessibility effects from
congestion taxes for those who continue to drive.
purpose is to look at
possible magnitudes of gains in income associated with improved accessibility
from reduced car flows.
The rest of the paper is organised as follows. In the following sections the
central results in four different literature fields are discussed and summarised.
Section presents models for the calculation of the marginal costs of public
funds. Section
covers the welfare and tax base effects from externality
correcting taxes. Section discusses results applied to the transport sector and
in particular congestion taxes. Section
goes on to consider further
geographical aspects associated with changes in accessibility. Finally Section
summarizes and concludes.
1.2 Modelling responses to tax changes and marginal costs of public
funds
Connecting the choices of transport to the governments’ choice of tax
instruments and tax levels introduces body of public economic considerations.
The focus is mostly on the efficiency aspects of collecting tax revenue for the
finance of public goods (e.g. Ballard and Fullerton 1992 for an overview, and
Harberger 1964 and Dasgupta and Stiglitz 1971 for early contributions). In the
early papers the public good is marginal lump-sum transfer. Ballard and
Fullerton 1992 distinguish between the Pigou-Harberger-Browning (PHB)
tradition and the Dasgupta-Stiglitz-Atkinson-Stern (DSAS) tradition. In the first
16
the tax revenues are used for lump-sum transfer to the households and in the
second the tax revenues are used for public good.
The theoretical experiments were initially conducted with assumptions of
identical individuals and budget balance. They emphasised that the optimal
amount of public goods depend on the welfare costs of raising revenue by
distortionary taxation. Central observations in these papers are that for the use
of public funds, it is necessary to evaluate changes in the level and structure of
taxes in terms of the general equilibrium and the income effects.
In Lundholm (2005a) the application of MCPF to cost-benefit analysis in the
transport sector is approached. Lundholm notes that Ballard and Fullerton
(1992) argue that the PHB-approach is not suited to use in CBA-context. They
argue for the DSAS-approach. In this approach the general equilibrium effects of
the public good are included in the welfare effects calculated as part of the
welfare effects of the tax.
Lundholm (2005a p. 11) summarises calculations from four papers with the
PHB-approach and three papers with the DSAS-approach. The calculated values
for MCPF in Sweden range from 1,05 to 36,4 for the PHB-approach and 0,71 to
7,1 for the DSAS-approach. This shows that the PHB-calculations generally are
above and that the DSAS-calculations may lie below 1.
The DSAS-approach is chosen by Hansson and Stuart (1985) who presented an
early calculation of MCPF by computing general equilibria in model calibrated
to Sweden. The main purpose was to calculate marginal cost of public funds
for an arbitrary tax system optimal or not. In this way the question of the
initial systems optimality is evaded. Welfare is represented by representative
consumer. In this model balanced budget experiments are conducted where tax
changes are accompanied by corresponding increases in public spending. The
taxes are labour and capital taxes and the public spending are, either stylized
public good not influencing private consumption or lump sum redistribution
of income. In Hansson and Stuart’s model it could in principle be possible to
compare welfare in scenarios with different trade-offs of private and public
consumption. Such calculations were however not conducted.
In summary (Lundholm 2005a) of the then current Swedish recommendations
(SIKA 2002) noted that the interpretation of the literature on MCPF seems to be
more in line with the PHB than the DSAS tradition. Neither SIKA nor Lundholm,
however, discussed the fact that in the transport sector cost-benefit guidelines,
most of the effects are represented by transport models. Such effects would
otherwise have to be modelled with computable general equilibrium model
(CGE), which in most cases would not have the high resolution provided by
transport models. The dilemma for transport studies is one of choosing
between, on the one hand, the high resolution in transport models and no
interaction with other household decisions or, on the other hand, little
resolution transport wise, but representation of interaction with e.g. labour
supply and other consumption decisions in CGE models.
17
This is also central observation in Sandmo (1998). Sandmo argues that when
the MCPF is to be used as practical tool by individual government agencies for
different projects, then the definition of the MCPF should not be project specific.
Therefore the effects of the public spending should not be included in the
definition of the MCPF as in the DSAS-approach but instead be incorporated on
the benefit side in the CBA and not double count them. The PHB estimates are
therefore more appropriate for this approach. Sandmo’s (1998) argument also
implies that the distributional consequences of taxation and public spending
would have to be taken account for in the cost benefit analyses of individual
agencies.
One avenue to theoretically considering wider set of consequences involves
representing heterogeneous individuals and using social welfare function. In
Sandmo (1998) marginal costs of public funds are analysed for optimal and nonoptimal taxes. central observation is that distributional consequences should
ideally be represented in calculation of the marginal costs of public funds.
With this perspective and the notion that taxes maximise social welfare, the
MCPF are equal for each tax instrument. When, on the other hand, taxes are not
optimal there may be several MCPF:s.
In Lundholm (2005b) the concept of marginal costs of public funds are analysed
in context of social welfare function, optimal and non-optimal taxes, and hence
in terms of social marginal value and costs. Lundholm generalises results in
Håkonsen (1998) derived for representative individual to
heterogeneous
population. For this context the social marginal costs of public funds are defined
as the ratio between the marginal shadow price of tax revenues and the average
social marginal utility of income in the economy.
central observation in the
context of optimal taxes and social welfare is that the social marginal costs of
public funds are 1, even if the taxes are highly distortionary. If, on the contrary,
taxes are not optimal, the social marginal costs of public funds may differ, and
need not be one. fundamental observation is therefore that in model with
optimal taxation there can be no welfare gains from small changes in current tax
instruments. This does not, however, exclude the possibility that new tax
instruments may yield welfare gains.
In Jacobs (2010) the marginal costs of public funds are examined in Mirrlees
(1971) framework with heterogenous agents, optimal redistributive taxes,
optimal provision of public goods and the marginal costs of public funds.
central analytical departure point is to conduct the analysis in terms of social
marginal value of private income and social marginal value of public income i.e.
in terms of social welfare function. In this system the tax parameters are
optimized and second best welfare optimum is characterized. The paper
iterates the result that in optimum the marginal cost of public funds is one.
Furthermore Jacobs (2010) demonstrates that within the chosen setting the
provision of public goods is also determined by distributional concerns, if the
willingness to pay for public goods is correlated with earning ability. In the
Mirrlees/Jacobs context the unit of measurement is social value of income. This
however makes it impossible to directly translate the value units into ordinary
18
monetary units, and the practitioner of cost-benefit analysis in the real world is
left on his own.
For practical cost-benefit purposes it is not clear what the computational
implications of these theoretical results are. The following tentative conclusions
are formulated here:
On the one hand the results indicate that the purpose to redistribute
income may account for some of the apparent inefficiencies observed for
purely efficiency based measures. On the other hand real world tax
systems are not likely to be optimal in all respects relevant for the
current majority. frequent reason being that adapting tax systems to
new circumstances may take time, implying that inefficiencies may
prevail.
Even though it is desirable to model taxes as optimal, distributional
considerations pose empirical requirements that (as far as we have
found) have not been met. This would for example imply estimating
social welfare functions.
In absence of well-defined preferences for distributional equality, it may
still be useful to define and measure the MCPF in terms of private
willingness to pay. This is also the path taken in the calculations in the
literature.
In Kleven and Kreiner (2006) an important extension to the previous models is
introduced. The authors note that the response in terms of the choice to work or
not may be more important than the response in terms of hours of work. Their
main purpose is to make an empirical contribution to the estimation of the
marginal costs of public funds for an arbitrary tax system and to examine how
sensitive such calculations are to variations in the assumptions about among
other parameters, the labour supply elasticities. The non-convexities in terms of
fixed costs for participation in the active work force are therefore modelled. For
some individuals this may imply that the choice to work may reduce welfare if
the rewards in terms of income and other welfare gains do not exceed the costs
incurred from working. An important extension is therefore to explicitly model
heterogeneity among individuals. Kleven and Kreiner therefore explicitly model
differences in individual skills (wage rates), fixed cost for work as well as
preferences. Therefore the total welfare effects are modelled by social welfare
function.
The purpose in Kleven and Kreiner (2006) is to calculate the marginal costs of
public funds and not to examine optimal tax structures or the optimality
properties of current tax structures. Therefore the authors do not examine
different taxes with respect to their excess burdens or distributional properties.
In principle, however,
model like Kleven and Kreiner’s allows for
examinations of welfare trade-off’s of different tax rates and transfers.
Kleven and Kreiner use model with the following form. The population is
divided in subgroups with the same income and preferences for all individuals
in each subgroup, but with heterogenous fixed cost to work q. The distribution
19
of is assumed to have the density function
(qi).
(qi and distribution function
The fixed cost to work may be thought of as the sum of generalized travel cost
and other fixed cost like clothing.
The travel cost is in turn determined by the location of the individuals residence
and work place.
Individual utility is specified as
vi (c,h) qi l(h>0)
Where vi is individual utility, is consumption,
of work and an indicator function.
hours of work,
the fixed cost
Taxes are represented by T(wih, z) where w is individual i’s wage rate and
shift parameter.
Budget constraint
(1-mi wi +Yi
where m is the marginal tax rate and Yi the virtual income Yi
miwi
T(wih, z).
In this context the taxes that optimise social welfare function subject to
individual responses to the taxes may be defined. Kleven and Kreiner (2006) in
the tradition of the literature on marginal cost of public funds however short cut
the optimal taxes to discuss the effects of any tax system. The central result is
that the effects from the individuals on the brink of choosing to participate in
the labour force may be substantial.
In Sundberg et.al. (2011) Hansson and Stuart’s (1985) calculations of the
marginal costs of public funds in the Swedish economy are updated and
extended. The purpose is to provide numerical calculation of the MCPF for cost
benefit analyses in regional computable general equilibrium model calibrated
for the Swedish economy. In this model consumption is represented as the
consumption of representative consumer in each region, the factor markets,
including the labour market, are represented as perfect market clearing markets
and production is represented by firms in monopolistic competition in different
sectors. In an earlier version of this model particular attention was paid to the
representation of freight transport costs as the model was developed to
represent the effects of freight kilometre taxes. In Sundberg et.al. (2011), the
model is further extended to represent both indirect taxes and taxes on labour
as well as public sector. This public sector is represented by expenditures in
an abstract public good. The calculated MCPF’s are showed to differ for value
added taxes, income taxes and capital. Furthermore the results differ for
20
different geographical regions. An average value for Sweden as whole is found
to be 1,32 which is close to the value previously used in Sweden.
The marginal costs of public funds are calculated with balanced budget where
tax income is spent either on
stylized public good or
lump sum
redistribution of income. further concern for this study is both to model
public sector with balanced budget and still to measure the marginal costs of
public funds without of the effects of the expenditures included in the measure.
This objective is motivated by the fact that the benefits of transport projects and
policies (i.e. investments in infrastructure as well as policy instruments like
kilometre taxes) are modelled and calculated to high degree of resolution.
1.3 Welfare and tax base effects from externality correcting taxes
In the tax interaction literature (e.g. Bovenberg 1999) the standard argument is
that increases of taxes motivated by previously external effects do only yield
welfare gain attributable to correction of the externality and no further welfare
gains. In recent analysis of the Swedish tax system this was formulated as
follows “when the initial indirect tax rates have been set in rational manner
from non-environmental viewpoint, there is no gain in employment and nonenvironmental welfare from revenue-neutral green tax reform that introduces
pollution taxes and uses the revenue to cut the labour income tax” (Birch
Sørensen 2010 p. 199). An alternative formulation of this insight is that in an
economy with optimal taxation except for one externality it is not possible to
generate welfare gains from introducing one further tax due to the fact that this
will decrease other tax bases The reason is that in the models where such effects
are studied, the labour supply and other tax base effects, cancel out. As argued
above, these adaptions are however, typically not accounted for in CBA
calculations.
But on the other hand “if for some reason the polluting goods were initially
under taxed even when one abstracts from their environmental effects for
example, if “dirty” goods carry lower initial tax rate than “clean” goods even
though the price elasticity of demand for the two types of goods is the same
then green tax reform would yield second dividend” (Birch Sørensen 2010 p.
199). This is possible, provided that the tax on dirty goods is brought closer to
the Ramsey rule for optimal indirect taxation from below. Formulated in tax
base terms this means that introducing an internalising tax in package to
improve, an otherwise sub optimal tax system, further tax revenue can be raised
without loss of welfare
In this context it is important to understand that the marginal costs of public
funds either as an aggregate measure, or as the vector of for example PHB
measures, typically is measure distinct from the total welfare effect from
introducing new tax instrument (e.g. congestion tax or kilometre tax) and
using the tax revenues to reduce other distortive taxes. The MCPF, not counting
the general equilibrium effects from government spending, will therefore (in the
PHB-tradition) be number larger than 1. Therefore it may be consistent to
have MCPF measure larger than 1, and tax base effects such that there will be
21
no welfare gains from introducing
lowering other taxes.
new tax instrument and simultaneously
The tax interaction literature points out two important factors determining the
results. The first of which is well known in the literature on marginal cost of
public funds is that the precise policy experiment conducted has decisive
effect on the calculated marginal costs of public funds and the second is the
degree to which the tax system in the starting point is not optimal. This raises
two possible reservations to the argument presented by Birch Sørensen. The
first reservation is that for cost-benefit analysis purposes we need to think
carefully about what policy context marginal cost of public funds is going to be
used. Are we for example going to assume point of departure with optimal
taxes or are we going to consider some imperfection in the initial situation. In
the first case there will be no extra cost of public funds whereas there will be in
the second. second reservation concerns the use of tax revenue. With optimal
public spending the social marginal benefit of public spending will equal its
social marginal costs. With less than optimal taxation and less spending,
multitude of possibilities arise and the analyst may have to be obliged to retreat
to some kind of averages for both marginal benefits and costs.
In
note Sundberg (2010b) points to some important but not obvious
conditions for Birch Sørensen’s (2010) model and argues that the result
therefore does not represent general condition but rather special case. The
conditions are that a) all government revenue is used as
lump-sum
redistribution to representative consumer and that b) the indirect tax rates
are assumed initially to be equal. Birch Sørensen (2010) (and Sundberg
(2010b)) show that in such simplified model it is impossible to influence
labour supply and hence there can be no second dividend. Sundberg (2010b)
however, goes on to argue that when the budget balance condition is relaxed,
increased tax incomes may be associated with increased spending in optimum.
In this extended model and assuming well behaved parameters Sundberg shows
that there will typically be second dividend when the labour tax can be
reduced on account of the introduction of
(small) internalising tax. In
Sundberg (2010a) the marginal costs of public funds are calculated in stylised
model of Sweden for three different tax instruments and for situation where
the tax revenue is assumed to generate public surplus. The magnitudes are
similar to Birch Sørensen’s (2010).
Similar such observations have been made earlier. In Mayeres and Proost
(2001) the results from earlier models were extended in four dimensions, by
introducing non-identical individuals, externalities that are non-separable from
consumption of private goods and the introduction of poll-taxes and public
abatement. Starting from an arbitrary initial position, the central policy
experiment is to increase the tax on an arbitrary good and to simultaneously
reduce the tax on another good in
situation that is not optimal. For
numerical example with starting point calibrated on Belgium and stylized
congestion charge, Mayeres and Proost (2001), demonstrate that that taxes on
consumption (corresponding to value added taxes), congestion taxes and off
peak taxes have marginal costs of public funds exceeding unity. With increasing
22
preferences for equality these MCPF’s decrease. Mayeres and Proost (2001)
proceed to examine if there is potential for welfare improving tax redistribution
between tax instruments. They show that for low preferences for equality
raise of the congestion tax combined with lower consumption tax is welfare
improving (which they call realising double dividend).
Note that in Mayeres and Proosts (2001) example the results are derived under
condition of recycling from an arbitrary point of departure. The question if
second best optimum can be improved upon by introducing new internalising
instrument is not considered.
In Jaeger (2011) some important extensions are made to the models and
analyses in the double dividend literature. Jaeger argues that the question of the
welfare effects from second-best, revenue-neutral environmental taxation has
been approached indirectly asking whether the second-best optimal
environmental tax is higher or lower than the first-best Pigouvian rate. Jaeger
further argues that more direct test suggested by Fullerton (1997) would be
more appropriate. Fullerton suggests framework where consumption goods
are taxed uniformly and where the optimal environmental tax is the difference
between the optimal tax on the dirty good and the optimal tax on clean good.
The test involves comparing the differences between the optimal tax on the
dirty good and the optimal tax on clean good in the first-best and the secondbest.
Jaeger defines reference first-best optimum as situation without commodity
taxation, and second-best case as situation where commodities are initially
equally taxed for fiscal purposes. The first-best optimum and the second-best
optimum differ because in the second-best setting there are two further costs
and benefits to be traded-off. In the second-best there are also fiscal effects to
consider in the form of revenue recycling effects and tax base effects. In
second step the tax on the externality generating good is raised and the tax of
the clean good is lowered in budget balance. Jaeger argues that the important
contribution of the double dividend literature is precisely the insight that the
revenue recycling and tax base effects matter. The first central result is that in
the second-best setting the marginal benefits from introducing
small
environmental tax will exceed those from those of introducing it in first-best
setting, but as the environmental tax is increased the revenue recycling benefits
decline, and the second is that in the second-best setting, raising the externality
tax will be welfare improving
Jaeger (2011) goes on to show that in basic model broadly consistent with the
U.S. economy second-best optimal tax for dirty good is higher than the firstbest Pigouvian tax by one-third. He also shows that in the basic model in the
second-best setting with initially only revenue raising taxes the first increments
to the environmental tax will initially be welfare improving. These new
theoretical results therefore place the question of the net welfare effects from
introducing an externality correcting tax on an empirical ground.
23
The cost benefit practice in Sweden for infrastructure investments implied
valuing changes in the net burden on the public budget by the marginal cost of
public funds. In typical road investment this would entail large cost to the
public for building road subtracting the increased revenues from petrol taxes
as road use increases. When the recommended MCPF equalled 1,3 this meant
that the cost from an increase in the net burden would have to be multiplied by
1,3. Applying this principle to the introduction of new tax instruments like
kilometre and congestion taxes or increases in the level of tax instruments like
the petrol tax appeared as straight forward. The double dividend literature
however indicated otherwise. Jaegers (2011) analysis however suggests that it
is likely that there are welfare gains to be had in addition to those arising from
first best correction of an externality by further increasing the taxes on
externalities and reducing other distortionary taxes.
In companion paper to Jacobs (2010), Jacobs and de Mooij (2011) optimal
Pigou taxes are derived. The central result is that, in optimum, the second-best
externality correcting tax should not be corrected for MCPF. If, however, an
externality generating commodity is more complementary to leisure than nonexternality generating commodities the tax should be adjusted for this.
To conclude we therefore formulate the following observations. The basic
results in the tax interaction literature are the following;
when indirect taxes initially have been optimally set, increases in taxes
motivated by externalities do only yield welfare gain attributable to the
reduction of externality
no further gain is generated due to that this decreases other tax bases
when taxes are not optimally set further tax revenue can be generated
without loss of welfare
Jaegers (2011) paper appears to contradict the two first statements in so
far as that, in
second-best setting, it may be possible to generate
benefits in addition to the externality correcting effects
furthermore, the second-best optimal taxes may be larger than the firstbest optimal levels
To assess tax effects in CBA context more specifically tailored models (eg.
Mayeres and Proost 2001 or Calthrop et.al. 2010) may have to be used. For tax
reforms having small effects on national labour supply the effects on the
aggregate measure of MCPF is likely to be small. Locally the interaction effects
on labour supply or consumption may be more substantial.
1.4 Road pricing (congestion tax) considerations
The literature on road (congestion) pricing and its welfare ramifications is now
considerable. An early contribution (Parry and Bento 2001) looked at welfare
effects of combination of road pricing and the redistribution of the revenues.
lively debate has considered the most welfare improving ways of using the
revenue. Several economists have argued for reduction of distortive taxes and
preferably labour taxes e.g. Mayeres and Proost (2001) and Parry and Bento
24
(2001). This touches directly on the question if the introduction of an efficient
Pigouvian externality correcting tax can improve welfare. Economists have
noted that how the revenue is used matters as well as the exact assumption
about the possible and desired variations in labour supply which in turn is
governed by rules, conventions and preferences.
Parry and Bento (2001) represents an early analysis of the interaction between
traffic congestion and labour supply in market distorted by taxes. In the line of
thinking from the marginal costs of public funds literature, Parry and Bento
(2001) study increases in congestion tax used to lower income tax, subsidise
public transit fares and lump sum transfers. In model with representative
household, the supply of number of workdays, commuting mode and
consumption is chosen. Furthermore the government’s budget constraint is
represented. No explicit optimization on the part of the government is
represented. The paper both presents some benchmark theoretical expressions
for household behaviour and the government’s budget balance. The authors
conclude that in their analysis, the introduction of congestion tax on workrelated traffic with revenues returned in the form of lump-sum transfers
reduces labour supply and the welfare loss can offset the welfare gain from the
congestion tax. In the case of using tax revenue to lower income taxes, labour
supply and welfare are increased.
In Westin (2011a) the results in Parry and Bento (2001) are further developed.
The most important consideration introduced by Westin is that he models the
initial situation as second-best optimum with the restrictions that neither
lump-sum nor congestion taxation are available. In addition to the theoretical
expressions for evaluation of these scenarios Westin presents numerical
calculations. The policies modelled are further re-optimisation of all the policy
instruments and compares this to budget neutral policies like putting all
revenue from the congestion tax into respectively; income tax reduction, public
transit fare subsidy increases, public good provision increases and lump-sum
redistribution. The results are that initially all policies yield the same welfare
effects. Obviously the re-optimising policy performs best. Less obvious is that
for larger congestion tax reductions the corresponding lowering of income taxes
out-performs the other non-optimising policies. Westin (2011a) also examines
the consequences of starting from non-optimal policies, and finds that the initial
point may influence the analysis significantly.
The distributional impacts of tax reforms have also received increasing
attention in economic research (Mayeres and Proost 2001). central reason for
this is that the revenues from externality correcting taxes in many cases may be
much larger than the value of the corrections. conclusion is that reform can
not be judged on efficiency and acceptability grounds alone. Instead wider
analysis of in particular the effects on labour markets is needed.
Westin (2011b) models road pricing in an area where there is congestion and
introduces some extensions. This is done in general equilibrium framework
with modal choice and heterogeneity of individuals which is represented as
25
distribution of the individual’s income earning capacity or wage rate, as well as
the value of time.
The central trade-off in the paper is how to use the revenue from congestion
price. The alternatives are increases in lump-sum transfers, public transport
subsidies and income tax cuts. These alternatives are compared to base case
where the marginal benefits from all three policy instruments are equal,
implying that social welfare is maximized before the congestion tax is
introduced.
The effects on social welfare are positive regardless of in which form the
revenue is recycled. The congestion charge also reduces the positive effects of
subsidy to public transport. In the model most individuals increase their labour
supply and gain from the introduction of the congestion but not the individuals
that change from car to public transport. They reduce their labour supply and
loose welfare.
The optimal adjustments of the instruments are largest for the public transport
subsidy. No combination of recycling instruments yields Pareto improvements
for all individuals. Adjusting the policy instruments also has different
consequences according to how welfare is measured. The results also indicate
that public transport subsidies may increase labour supply more than the
corresponding labour tax cuts.
1.5 Some geographical dimensions
Long term adaptions to transport changes
An important focus in classical labour supply studies are the short term
considerations where an individual makes her choice of labour supply and
consumption, given her place of residence, work place and education, as these
are considered as more inert in the short term. In longer term perspective all
these givens are considered to be subject to choice. The modelling of such
longer term choices makes for significant simplifications and assumptions in
order to represent the perceptions of future consequences.
Some of the longer term consequences of petrol and congestion taxes involve
adaptations in residential and work place location. In standard model for
residential location and commuting (Simpson and van der Veen, 1992) the
consumer choses
residence location depending on housing prices and
determining commuting time. This model therefore represents
trade-off
between land and commuting costs. In an extended model, time is included, now
implying trade-off between leisure, land and consumption. In such model
education is taken as given as are the market prices for land in different
locations. In further extension workplaces are assumed to be distributed in
space and wage gradient dependent on the distance from the city centre is
introduced.
Simpson and van der Veen (1992, p. 56) argue that
complete model of
residential and workplace choice requires “the introduction of the labour
26
market in urban space”. They show that some important implications can be
derived from simple model with two employment centres, central business
district and
suburban employment centre. In such
city with
smaller
suburban employment centre in relative terms will have
smaller wage
gradient because central city firms will have to pay larger premium to attract
larger proportion of suburban residents to central city jobs.
The standard model has been extended to include the effect of skill level on job
search behaviour in Simpson (1980). (See also Isacsson och Swärdh, 2007 for
recent empirical application for Sweden). Simpson argues that skill acquisition
broadens the spatial extent of job search because it is partly non-enterprisespecific and restricts job choice. Thus, skilled workers are likely to be less
responsive to local employment conditions than unskilled workers, contrary to
predictions based only on the value of commuting time from the more abstract
models referred to above. Simpson and van der Veen (1992) argue that crosssectional household data from London and Toronto support this argument.
In differentiated spatial model we could consider explicit assumptions on the
amounts of residential capacity and distribution of income earning capacities
among individuals. In
computational model
calculation of equilibrium
land/housing prices as well wages associated with certain location of firms
and jobs to workplaces could be performed.
model incorporating job location is formulated in Simpson and van der Veen
(1992).
max [q(h,j), x(h,j), l(h,j)]
s.t. p(h)q(h,j) x(h,j) w(j)l(h,j) w(j)T
[c(h,j) w(j)l(h,j)]
Where is distance of residence from the city centre, is the distance of the job
from the city centre, the amount of housing, the amount of Hicksian
composite commodity representing all other goods, p(h) is price gradient for
housing, w(j) is the wage rate at distance from the city centre c(h,j) is the cost
of commuting,
This model generates the following equilibrium conditions:
c
p
h
w
j
w t
j
h
q
c
j
w
(a)
j
L
(b)
Note that the wage rate varies by job location according to (b). Since c/
and t/
then w/
which means that the wage rate is decreasing with
27
the distance from the city centre. In this model the use of time is not modelled
separately.
In principle such model could be extended with congestion charge. Such
theoretical representation of
congestion problem should allow for the
following components: spatial representation of the choice of residence and
workplaces, link flows and congestion and its congestion externalities
determined by link flows and possibly from flows in adjacent links i.e.
congestion in one link creating congestion or delays in other links.
Extensions for education/training and search costs for labour and employers
are also possible.
How is search equilibrium affected by increased accessibility? Our conjecture
is that an increase in the accessibility to workplaces of high income earners will
increase their search area.
Some further steps towards extending models to improvements in productivity due
to positive agglomeration externalities
In Venables (2007) the implications of positive agglomeration externalities for
the evaluation of urban transport policies are analysed. The departure point is
the observation that urban centres tend to have higher factor productivity than
areas with lower employment density. Venables suggests that the evidence is
enough to accept the existence of positive city size/productivity relationship.
He also argues that the relationship suggests several ways in which transport
improvements may affect productivity. The exact mechanisms are however not
modelled. Venables (2007) however points to
more detailed survey of
empirical work on agglomeration economies Rosenthal and Strange (2004).
Accessibility effects from congestion and fuel taxes
Road use and fuel taxation have potentially two important consequences. On the
positive side such taxes may help to reduce negative externalities like air
pollution, accidents and congestion. The reduction of congestion will
consequently increase the accessibility, for those paying the congestion tax. On
the negative side it reduces accessibility and the real income of road users,
abstaining from using the roads on account of the congestion tax. As both the
negative externalities and the benefits from road use are unevenly
geographically distributed it makes sense to try to account for the geographical
distribution of consequences.
In this section we therefore survey results pertaining to how fuel and
congestion taxes in the Stockholm region affect accessibility and income.
Whereas the modelling of fuel taxes is straightforward, the modelling of the
effects of congestion taxes is more complicated.
The congestion tax in Stockholm which is charged for passing
cordon
encircling the inner city has been described and analysed in earlier papers
(Eliasson 2009 and Eliasson et.al. 2009). central result in the analysis of road
pricing is that for the welfare and distributional consequences the use of the tax
revenue is decisive. Here we focus however on the effects of the tax on mode
28
and route choice, the effects on congestion, time savings and distributional
aspects, and not on how the tax revenue is spent. In Stockholm only part (10
percent) of the total number of trips in Stockholm County are affected by the
congestion charge. This implies that large part of the population only is
affected insofar as the volume of traffic and if the use of public transport is
affected. In both cases accessibility to employment is affected.
Accessibility to employment may affect short run labour supply as well as more
long term search activities and leading to better matches in the labour market.
The resulting effects on income can be interpreted as the sum of the short term
effects arising within static equilibrium model and further effects due to
higher returns on search activities and productivity gains. Therefore we can not
attribute the whole of the effect on income to improved accessibility. With
good approximation of the general equilibrium effects we could regard the
remaining effect as an upper bound for the accessibility effect. Without an
overarching general equilibrium model well-defined effect is hard to quantify
in way that is compatible to the CBA-methodology.
In addition to theoretical analyses of the link between commuting time and
labour supply there are empirical studies. Gutiérrez-i-Puigarnau and van
Ommeren (2010) examine the effect of commuting distance on workers’ labour
supply patterns. They distinguish between weekly labour supply, the number of
workdays per week and the number of work hours per day. The answer to this
question has implications for how labour supply is affected by congestion tax
or fuel tax and how the tax revenues are used. For Germany Gutiérrez-iPuigarnau and van Ommeren (2010) find that distance has small positive
effect on daily and weekly labour supply, but no effect on the number of work
days. The effects are stronger, but still small, for females. The authors argue that
the results imply that the effects from policies affecting commuting costs on
labour supply are not likely to have strong effects on total welfare. They suggest
that budget-neutral recycling of revenue in terms of reductions of income
taxes may not be necessary to increase welfare.
In Anderstig et.al. (2011) the possible effects on labour income caused by
accessibility changes from congestion taxes and fuel taxes in the Stockholm
County are estimated. Based on recent Swedish estimations of value of travel
time (VTT), three categories of citizens with respectively low, medium and high
valuations are identified. For these categories the elasticity of income with
respect to change in accessibility are estimated. These are in turn used to
calculate effects on income from changes in accessibility due to the congestion
charge. The results suggest that the congestion tax system in Stockholm
generates considerable positive effects on labour income, if differences in VTT
are taken into account. For the category with high value the travel time savings
due to less congestion, are higher than the increase in monetary costs, due to
the congestion tax.
The congestion tax is estimated to result in total (net) effect on labour income
in the Stockholm County by nearly 620 MSEK, which represents an increase by
more than 0.2 %. fuel tax increase, designed to generate an increase in tax
29
revenues of about the same size as the congestion tax, has quite different
consequences for the income tax base. While the congestion tax is estimated to
generate an increase of income, the fuel tax is estimated to generate decrease
in income of about 950 MSEK, or reduction by nearly -0.4%.
As indicated above it is important to remember that these calculations do not
allow us to distinguish between the effects supposed to be captured by the
standard cost-benefit methods and possible further effects. The results however
indicate that the further effects may be positive and substantial and that simple
rules of thumb assuming that tax base effects cancel out are not likely to be true.
Furthermore an implication of these results is that, for cost-benefit calculations
of transport policies, the central interdependencies between labour markets
and transport markets have to be modelled in order to get the large effects right.
1.6 Summary and conclusion
In this paper we have surveyed central results from the economic literature
relevant to the assessment of welfare costs of taxes and how the effects from
changes in the net budget burden. This has been done with the special attention
to the tax instruments directed to the transport sector. Let us start with the
observation that some recent papers start with representation of the tax
system where the taxes are optimised to minimize the welfare costs of
generating the tax revenue. This was however not the case in early papers on
the marginal costs of public funds.
Marginal costs of public funds
fundamental value for the evaluation of changes in the net burden is the
average marginal costs of collecting public funds. In system where both the
expenses and the composition of the tax system are optimised, the marginal
costs of collecting one further monetary unit should equal the marginal benefits
of public spending. Therefore it should not be possible to increase welfare
neither by adjusting the tax system nor the expenses.
central result from the study of MCPF is that it is important to model both how
tax revenue is generated and how it is used. When the public funds are used for
public good, rather than lump-sum redistribution, the MCPF will typically be
smaller. This presents dilemma for transport economist wanting to do costbenefit calculations. Should the MCPF be calculated with general public good
in stylized model, or should the expenditures in the transport sector be
modelled with more resolution in traditional transport models? The
recommendation in Sandmo (1998) and in the official Swedish cost-benefit
guidelines for the transport sector is to choose the latter.
second central result is that in
case with optimal taxation, however
distortionary, the welfare losses from labour supply reductions are balanced by
distributional gains. These gains are typically not considered in purely efficiency
oriented calculations of MCPF. In order to quantify distributional gains in
monetary terms an estimated social welfare function would be required. In
absence of such measures efficiency based measures may still be useful.
30
Starting with Kleven and Kreiner (2003, 2006) it has been observed that the
elasticity of the decision to participate in the labour market with respect to after
tax income may have strong influence on the size of the calculated MCPF. This
suggests that for the calculation of MCPF better estimates of the participation
elasticities will be needed.
Tax interactions
The basic results in the tax interaction literature are the following; When
indirect taxes initially have been optimally set, increases in taxes motivated by
externalities do only yield welfare gain attributable to the correction of the
externality. In optimum no further gain is generated due to that this decreases
other tax bases. When taxes are not optimally set further tax revenue can be
generated without loss of welfare.
Jaegers (2011) paper appears to contradict the two first statements in so far as
that it may be possible to generate benefits in addition to the externality
correcting effects. Furthermore, the second-best optimal externality correcting
taxes may be larger than the first-best optimal levels.
To assess tax effects in CBA context more specifically tailored models (eg.
Mayeres and Proost 2001 or Calthrop et.al. 2010) may have to be used. For tax
reforms having small effects on national labour supply the effects on the
aggregate measure of MCPF is likely to be small. Locally the interaction effects
on labour supply or consumption may be more substantial.
Transport externalities
The central insights in early contributions (eg. Parry and Bento 2001 and
Mayeres and Proost 2001) were that road pricing on congested roads may have
important effects on labour supply and that the welfare effects in distorted
labour markets may be substantial. In these papers the authors assume an
arbitrary initial tax system and derive expressions for the welfare effects of
introducing congestion taxes.
In Westin (2011a) the results in Parry and Bento (2001) are extended. Westin
starts from second best optimum where tax levels and public spending are
optimised except for the absent congestion tax. He proceeds by numerical
calculations to show that initially all policy instruments perform equally but
that for larger changes re-optimising outperforms the other in delivering
welfare improvement. For the case when the initial tax system is not optimal,
and starting from differing starting points the effects may differ substantially. It
is also shown that re-optimisation of the tax instruments and the public
expenditures may imply an increase in government spending and
redistribution of the tax burden.
Accessibility effects from taxation in transportation
Taxation in transport has two broad effects. The first is that it increases the
costs of transportation, thereby reducing accessibility. The second is that by
reducing the demand for transportation it may at the same time reduce all kinds
31
of externalities. By reducing congestion
increase accessibility.
tax increase may therefore also
These effects are however not necessarily large in terms of labour supply. But
even small effects may be considerable in terms of the cost-benefit analysis for
the reform. In Anderstig et.al. (2011) the effects on income from accessibility
changes due to congestion taxes and fuel taxes in the Stockholm County are
estimated. The results suggest that the congestion tax system in Stockholm
generates positive effects on labour income. This is primarily due to time
savings for those with high value the travel time. The results therefor indicate
that simple rules of thumb assuming that tax base effects cancel out may not be
well based and that the central interdependencies between labour markets and
transport markets have to be modelled in order to evaluate the congestion tax
reform.
Conclusions for CBA-analysis of tax changes
In early recommendations for CBA calculations intended for the evaluation of
infrastructure, it has been common to suggest the use of MCPF factor as sort
of short cut for full scale general equilibrium calculations of the net cost of
public funds. This paper has surveyed papers suggesting that for taxes such
short cut may not be accurate enough. The presented examples show that tax
base effects can reinforce as well as reverse the results suggested by simplified
analysis. Therefore it cannot be recommended to use general MCPF number to
evaluate introduction or substantial changes in tax levels. The suggested
remedy is to use equilibrium modeling to represent the effects from taxation
and the use of tax revenue that have to be considered.
1.7 Acknowledgements
This project was financed by Vinnova and Centre for Transport Studies in
Stockholm. am grateful for comments from Björn Carlén and Jonas Eliasson,
and discussions with Jonas Westin and Marcus Sundberg.
32
1.8 References
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congestion charging trial 2006: Overview of effects’, Transportation
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when labor supply is endogenous and taxes are distortionary’, Munich
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work versus labor force participation’, Journal of Public Economics 90
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för resursanvändning offentlig kostnads–intäktsanalys, SIKA PM 2005:
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Proost (2001) ‘Marginal tax reform, externalities and income
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road pricing’, Scandinavian Journal of Economics 103(4) 645–71.
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agglomeration economies, in Henderson JV and Thisse JF (eds),
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Elsevier.
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of Public Economics, 70, pp. 365–38.
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van der Veen (1992), The Economics of Commuting and the
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35
2
Congestion charges and the labour market: “wider
economic benefits” or “losses”?
Christer Anderstig, WSP
Matts Andersson, WSP
Svante Berglund, WSP
Jonas Eliasson, KTH Royal Institute of Technology
Roger Pyddoke, VTI
Abstract
The presence of distortive taxation and agglomeration benefits in the labour
market means that there are benefits and losses not captured by standard
cost-benefit analyses of transport policy measures. Recent theoretical
analyses have raised concerns that the labour market effects of congestion
charges may constitute considerable losses in the form of reduced aggregate
labour income, over and above what is captured by the consumer surplus in
the standard analysis of congestion charges possibly to the extent that
congestion charges may reduce aggregate social welfare, contrary to
conventional wisdom in transport economics. The sign and size of these
effects are an empirical question, however. We investigate this issue by
estimating the labour income effects of the Stockholm congestion charges,
using an estimated relationship between workplace accessibility and labour
income. Results show positive effects on labour income, meaning that the
“wider economic benefits” of this system are in fact benefits, not losses. It
turns out to be crucial that the model accounts for value-of-time
heterogeneity in the income/accessibility relationship and in the calculation
of generalized travel costs.
2.1 Introduction
It is
well-established result within transport economics that congestion
charges can yield considerable social surplus in congested road systems. The
theoretical argument is obvious: pricing external congestion effects to make
user costs better reflect social marginal costs will in general result in positive
social surplus. Moreover, suggested or implemented real-world congestion
charging systems have also been shown to result in significant net social
surpluses, provided that investment and operations costs are not too high, and
provided that practical restrictions of the design of the charges are not too
severe.
However, the standard analysis is confined to effects within the transport
sector, i.e. travel times and travel costs as valued by travellers4 The standard
analysis implicitly assumes that effects in other sectors either do not exist or are
correctly priced, and thus can be disregarded. But the transport system is
4 In addition, environmental benefits such as reduced emissions and noise are often included.
These are almost always positive, though, so it does not change the line of reason here.
36
closely linked to the labour market, and the labour market is subject to several
market imperfections, such as distortive taxation, scale economies,
agglomeration benefits and imperfect competition, all of which create costs and
benefits which are external to the worker. In an influential paper, Parry and
Bento (Parry and Bento, 2001) showed that the increase in generalized travel
costs due to congestion charges may cause losses due to reduced labour supply
at the extensive margin which are large enough to cancel out the transportrelated benefits. This discussion has continued in stream of literature (Parry
and Bento, 2002)(Pilegaard and Fosgerau, 2008)(De Borger, 2009); (Van
Dender, 2003). Arnott (Arnott, 2007) makes
similar point related to
agglomeration effects.
This is the counterpart to the discussion of “wider economic benefits” in
transport CBA i.e., that there are benefits in the labour market that are not
captured by the standard transport appraisal framework. Distortive taxation
and external agglomeration benefits mean that worker will not perceive the
full social benefits of increasing working hours, going from unemployment to
work, or taking better paid job further away from home. Since standard
transport CBA only include consumer surplus as perceived by the
worker/traveller, standard appraisal will not capture any increases in profits or
tax revenues that are caused by an increase in working hours or productivity
hence the term “wider economic benefits”. The same goes for congestion
charges, but in this case the “wider economic benefits” may be losses, since
generalized travel costs usually increase by congestion charges (although this is
not always the case for all groups, as we will see later on). The problem, as
pointed out by Parry and Bento (Parry and Bento, 2001)(Parry and Bento,
2002), is that these losses may be significant in fact, they may be larger than
the benefits in the transport market.
In the Parry and Bento model, the effect of congestion charges on aggregate
labour income is always negative. This is because of two key assumptions: the
congestion charges increase the generalized travel costs for all travellers, and
labour supply only changes at the extensive margin. But once any of these
assumptions are relaxed, it is easy to get model where the sign of the labour
income effect is indeterminate (Westin, 2011a)(Westin, 2011b). First, as to how
generalized travel costs change, they may in fact decrease for some groups of
travellers. This may be because they have high values of time, or because of
network effects, i.e. congestion reductions “spilling back” on links that are
adjacent to the tolled ones. Heterogeneity in the value of travel time may be
caused by differences in wage or travel purpose. Typically, the “wider economic
benefits” associated with high-value-of-time trips can be expected to be larger,
since the wage gradient with respect to commuting radius tend to be higher for
high-income workers. Second, as to how labour supply adjusts, even if
generalized travel costs increase and hence decrease labour participation and
labour market matching, the decreased travel times for those still commuting by
car may lead to the number of working hours may go up. Summarizing, not just
the magnitude but also the sign of the labour income effects is indeterminate
from theoretical point of view. Determining the sign and size of the effects is
37
hence an empirical question, and the outcome is likely to be different depending
on the specific economic and geographic circumstances.
In this paper, we investigate this issue using an estimated relationship between
labour income and workplace accessibility. To reduce endogeneity and
confounding problems, the model is based on how changes in workplace
accessibility are related to changes in income, as opposed to the common
practice of cross-sectional estimation. We use accessibility measures taken from
large-scale transport model estimated on travel survey data. This means that
changes in the transport system will be properly captured by the accessibility
measure, and also ensures
high degree of behavioural realism. The
accessibility measures take heterogeneity in the value time into account. This is
crucial for evaluating effects of congestion charges, since whether the
generalized travel cost increase or decreases depends on the value of time. The
income/accessibility elasticity is also estimated separately for different valueof-time categories. It turns out, as one would expect, that the income effect of an
accessibility increase is larger for groups with higher values of time. Estimations
are based on “quasi-disaggregate” data, where individuals are grouped into
segments based on location and socioeconomic characteristics.
Since the sign of labour income effects is indeterminate from theoretical point
of view, one needs to study specific case to reach any conclusion. In this study,
we apply the model to the Stockholm congestion charging system. This also
enables us to calibrate traveller responses and travel time savings against
observed data. Eliasson (Eliasson, 2009a) presents cost-benefit analysis of the
congestion charging system. That study concludes that the system creates
social surplus, but also points out that labour market effects are not included. In
that sense, the present study can be viewed as complement to the CBA in
Eliasson (Eliasson, 2009a).
Section briefly summarizes the relevant literature. Section describes the
Stockholm congestion charges. Section describes the estimated relationship
between workplace accessibility and labour income. This is then applied in
section 5, where the effect on labour income of the Stockholm congestion
charges is estimated. Section concludes.
2.2 Literature
Agglomeration benefits, tax distortions and transport CBA
One of the cornerstones of “new economic geography” is the link between
accessibility and productivity. There are several theoretical reasons why
productivity is expected to increase with accessibility, often summarized in the
catchphrase “sharing, matching and learning” (Duranton and Puga, 2004). The
relation between accessibility and productivity is also well established
empirically (Rosenthal and Strange, 2004). Several studies have shown
connection between productivity and various measures of the spatial density of
economic activity, e.g. Ciccone and Hall (1996), Combes et al. (2008) and Groot
et al. (2011). In economic geography the effects of market accessibility on wages
have been studied on larger spatial scale by e.g. Redding and Venables (2004)
38
and Hering and Poncet (2010). If the results are to be used as complement to
standard transport appraisal, however, the agglomeration measure needs to be
sensitive to changes in the transport system, which density measures typically
are not. Studies using various measures of accessibility to labour include Kaliski
et al. (2000), Graham (2007a, 2007b, 2009), (Graham and Kim, 2008).
Hence, the existence of agglomeration benefits is well established. But
agglomeration benefits are only partially captured by standard transport
appraisal. To quote Graham and van Dender (2011): “Such benefits are in theory
additional to those captured in standard CBA because they are sourced from
increasing returns that are external to the firm and thus would not feature in
the willingness-to-pay approach that underpins calculations of consumer
surplus.” In other words, since agglomeration benefits are external to the
worker/traveller, they are not captured by the consumer surplus, and hence not
by standard CBA.
Agglomeration benefits are not the only external benefits of work-related
choices. Distortive taxation means that the worker will only perceive part of an
increase in wage, employment or working hours. Hence, such benefits are also
only partially captured by the consumer surplus used in CBA, as pointed out by
Forsyth (1980). Venables (2007) stress that when there is both distortive
taxation and agglomeration benefits, the external share of benefits will increase.
Calthrop et al. (2010) show that failure to account for distortions such as
agglomeration effects and tax distortions may cause severe errors in costbenefit analyses of transport improvements. So far, few countries have included
“wider economic benefits” in their standard CBA guidelines. One exception is
the UK CBA guidelines. The methodology and number of case studies are
summarized in Jenkins et al. (2011).
There are still comparatively few studies of precisely how much of total benefits
that is captured by transport CBA, however, and moreover, our understanding
of these relationships and the related econometrics are still limited, as pointed
out by Graham and van Dender (2011). They show that the estimated
relationship between accessibility and productivity is highly dependent on
model specification, indicating severe problems with confounding and
endogeneity.
Congestion pricing, labour market distortions and heterogeneity in the value of
time
Parry and Bento (2001, 2002) point out that congestion charge will affect
labour supply negatively at the extensive margin. Congestion charges may also
affect labour market matching negatively, since generalized travel costs
increase for many workers (depending on their value of time). In the ParryBento model, it is the income tax wedge that is the root of the problem, but such
problems may also be caused or exacerbated by the presence of (external)
agglomeration effects. Arnott (2007) points out that agglomeration externalities
may imply that the level of the optimal congestion tax is below the
corresponding congestion externality costs.
39
The quantitative estimates in Parry and Bento (2001) rest on the assumption
that an increase in travel costs caused by congestion charges will have similar
effects on labour supply as an increase of income taxes. general finding in
labour economics is that income tax changes have the greatest impact on labour
supply at the extensive margin, rather than at the intensive margin or through
matching effects (Kleven and Kreiner, 2006). However, it is not obvious that
introducing congestion charges affects labour supply in the same way that an
increased income tax would do. In our view, it seems unlikely that charge on
car drivers in urban cores during rush hours would lead to an appreciable
fraction of this population segment choosing to leave the labour force (i.e. adjust
at the extensive margin), especially in European conditions where typically
large majority of the low-skilled workers use other modes than car for
commuting trips to central areas during rush hours. Effects on matching (or
“destination choice” in transport model terminology) and working hours seem
to be more plausible adaptations.
If travellers have heterogeneous the values of time, then the standard analysis
of congestion charges will typically underestimate the benefits of the policy.
This was pointed out already by Vickrey (1969), but at the time, the
understanding of value-of-time heterogeneity as limited, and few attempts were
made to analyse what this meant for the quantitative results. Verhoef and Small
(2004) give detailed analysis of the issue. Proper estimation of value-of-time
distributions, together with socioeconomic explanatory variables, have been
made possible only recently (Fosgerau, 2006, 2007; Börjesson et al.,
forthcoming). In this paper, we use the results from the Swedish Value of Time
study, which was the first to successfully identify the full value-of-time
distribution (Börjesson et al., forthcoming; Börjesson and Eliasson, 2011).
2.3 The Stockholm congestion charging system
The City of Stockholm has around 0.8 million inhabitants, and is the central part
of the Stockholm county, with total of million inhabitants. Around 2/3 of the
City inhabitants live within the toll cordon, and the rest outside the cordon.
Because of its topology, with lots of water and well-preserved green wedges,
road congestion levels in Stockholm are high compared to the city’s moderate
size. Before the introduction of the congestion charges, the main roads arterials
leading to, from and within the city centre had congestion indices typically
averaging around 200% (i.e. three times the free-flow travel time).
The Stockholm congestion charging system consists of toll cordon around the
inner city (Figure 1), thereby reducing traffic through the main bottlenecks
located at the arterials leading into the inner city. The cost of passing the cordon
between 6.30 and 18.30 weekdays is 20 SEK (approx. 2€) during peak hours
(7:30–8:30, 16:30–18:00), 15 SEK during the shoulders of the peaks (30 min
before and after peak period) and 10 SEK during the rest of the charged period.
The charges were introduced in January 2006, and have reduced traffic across
the cordon by 22% during charged hours, with considerable reductions in
congestion levels as consequence. The effects have stayed remarkably stable,
increasing somewhat over time when controlling for inflation and growth in
40
population and car ownership (Börjesson et al., 2010). Eliasson (2009a)
provides cost-benefit analysis of the charges based on measurements of traffic
flows and travel times, calculating the value of travel time benefits to around 60
M€ per year. This can be compared to gross revenues of around 80 M€ per year.
The CBA uses standard transport appraisal framework, and hence explicitly
excludes “wider economic benefits” (or losses) in the form of labour market
effects apart from what is captured by work trip consumer surplus. The present
study hence complements the standard CBA in Eliasson (2009a). Travel time
benefits were calculated to be split in approximately equal shares between
commuting trips, leisure trips, business trips and freight transport (the two
latter categories are smaller in terms of traffic volumes but have higher values
of time). The calculations were based on uniform value of time for each traffic
category, and are hence likely to underestimate the true benefits.
The system, its history and its effects have been described in detail elsewhere.
description of the system and its effects can be found in Eliasson et al. (2009),
and experiences from the design and evaluation processes are described in
(2009b). Eliasson (2008) summarises the main lessons in terms of design,
effects, acceptability and political process. detailed account of the political
process can be found in Gullberg and Isaksson (2009).
Figure 1. The Stockholm congestion charging system. The dashed line is the charging
cordon, the dots are charging points and the solid line is the non-charged Essinge bypass.
2.4 Modeling the relationship between income and accessibility
In this section, we will estimate relationship between labour income and
workplace accessibility. Compared to many similar relationships reported in the
literature, the model estimated here differs in five ways:
1. It is estimated on differences across time rather than cross-sectional
data, thereby reducing the endogeneity problems that riddle crosssectional studies of accessibility/productivity relationships. After all,
41
2.
3.
4.
5.
correlation does not prove causality. If it is observed that highly
productive people and firms are more common in high-accessibility
locations is this because productive people and firms choose to locate
in such places (which they may do for several reasons), or have they
been made productive by the high-accessibility location? It is only the
latter mechanism that is relevant if we want to use an estimated
relationship to calculate accessibility benefits of an improvement in the
transport system. The model used here reduces this problem by relating
changes in income to changes in accessibility. To further reduce
endogeneity problems and isolate the impact of changes in the transport
system, the change in accessibility is decomposed into one part capturing
the change in employment in each zone, and one part capturing only the
change in generalized travel costs. It is the latter part that is used to
model the impact of the congestion charges.
It is estimated on “quasi-disaggregate” data. The entire population is
divided into segments based on location and socioeconomic
characteristics, and the average labour income is calculated for each such
segment. One such segment then constitutes one observation.
It is based on accessibility measures from transport model, rather than
density or size measures. If we want to capture the increase in
agglomeration effects due to transport investment, the measure of
agglomeration needs to be sensitive to changes in the transport system,
which size or density measures typically are not. It also has the benefit
that the accessibility measures are based on actual commuting behaviour
and actual, perceived generalized costs. Finally, it is an aggregation
across all modes based on actual mode shares.
Generalized travel costs account for heterogeneity in the value of travel
time. This turns out to be crucial for results. traveller with high value
of time will perceive that his generalized travel cost is reduced by
congestion charges, and vice versa. Ignoring this heterogeneity would
mean that one of the foremost benefits of congestion charges is ignored
that it “sorts” trips into high-value and low-value trips, and reduces the
latter while prioritizing the former.
The income/accessibility relationship is different depending on the value
of travel time of the segment. This also turns out to be important.
Segments with higher value of time (which is correlated with higher
income, although this is not the only factor) turn out to have much larger
income/accessibility elasticity than segments with low values of time.
This is natural, considering that the former segments are typically higher
educated and more specialized, and hence typically experience steeper
wage gradient when accepting longer commuting radius.
Model specification
The entire working population in the study area (4 million workers in Sweden,
1.8 million in the Mälaren Valley) is divided into segments, where each segment
is combination of age (7 categories), gender (2), ethnic origin (3), educational
level (4) and residential municipality (290 for Sweden, 86 for the Mälaren
42
Valley). The average income5 for each segment is observed for the years 1993
and 2002. This is regressed on initial accessibility (year 1985) and changes in
accessibility, one part due to changes in the transport system (1985-1997) and
one part due to changes in employment per zone (1993-2002). The choice of
years is mainly matter of data availability: in particular, getting detailed data
on historical transport systems is major effort6
Let E0s be the number of workplaces in municipality s at time (1985). c0rs is the
generalized travel cost between municipality r and s at time
(described
below), and is sensitivity parameter estimated in the transport model (see
below). Workplace accessibility of municipality r at time is then defined as
=
exp
)
The accessibility change due to changes in generalized travel costs is based on
the travel cost change 1985-1997, using employment data from 1993. The
change in accessibility due to changes in generalized travel costs is defined as
=
E exp(
E exp(
)
)
c0rs and c2rs are generalized costs in the years 1985 and 1997. E1s is the
employment in municipality s in 1993.
The accessibility change due to employment changes is based on the
employment change 1993-2002, using generalized travel costs from 1985. The
change in workplace accessibility due to changes in employment per zone is
defined as
exp(
exp(
=
)
)
is the number of workplaces in municipality s in the year 1993, while
the corresponding number in the year 2002.
is
With these variables, we can estimate
model for average income y3nr of
segment and zone at time (2002). Note that the income at time (1993) is
also included.
log(
)
log(
log(
)
)
log(
)
log(
)
“Income” means wage before taxes, excluding wage overhead costs.
We have also tested using income and employment data for the years 1985 and 1997, i.e. for
the same years as travel costs, with generally similar results.
5
6
43
The :s are vectors of dummy variables, and 2- 5 are the corresponding
parameter vectors. Later on, we will differentiate the accessibility variables by
value of time.
Above, we used generalized travel costs between municipalities. But the
transport model works with traffic zones, which are much smaller: typical sizes
are in the order of 0.1-1 km2 in built-up areas. Let cijm be generalized travel cost
between traffic zones and with mode m where
bijm is the monetary travel cost, the value of time, and tijm is the generalized
travel time (where waiting times and access times are weighted differently than
in-vehicle time). Relative time weights are taken from the traffic model LuTrans
LuTrans is large-scale transport model, version of the national transport
model SAMPERS (Algers and Beser, 2001) downscaled in certain respects
(primarily in the number of socioeconomic groups).
Generalized costs depend on the value time in two ways. Obviously, the value of
time enters the definition. But car travel costs and travel times in fact also
depend on the value of time, especially when road pricing is introduced, since
the route choice will be different depending on the value of time: drivers with
low value of time will be more willing to take detours to avoid tolls. To account
for this, segments are grouped into three equally sized categories according to
their value of time. The value of time for each category is taken to be the median
value of the lower, middle and upper third of the lognormal value-of-time
distribution estimated in the national Value of Time study (Börjesson and
Eliasson, 2011). For each origin zone, the share of the population belonging to
each value of time category is calculated, based on income, the number of
children and whether the zone is in Stockholm county (again using results from
Börjesson and Eliasson (2011)). Separate travel cost and travel time matrices
are then calculated for each category, by running the LuTrans model using the
three value-of-time categories in the network assignment step.
To calculate the generalized travel cost between municipalities r and s
generalized travel costs between traffic zones are weighted with traveling flows
Tijm. These are taken from the traffic model LuTrans
=
The notation
means that summation is taken over all traffic zones
belonging to municipality r
Estimation results
Estimation results are reported in Table 1. All models are estimated using OLS.
Model [1] is estimated on all of Sweden, without accounting for heterogeneity in
44
the value of time. The estimated elasticity of labour income with respect to
initial accessibility (log M0r), is 0.0447 while the estimate for the change in
accessibility due to changes in the transport system (log cMr is slightly lower,
0.03. The estimate for the change in accessibility due to changes in zonal
employment has no significant effect. These elasticities are in the expected
range; for example, Graham and van Dender (2011) state that studies relating
productivity to city size have typically yielded elasticities in the range 0.02-0.10;
Venables (2007) give similar range of 0.04-0.11. But as Graham and van
Dender (2011) point out, such aggregate elasticities are likely to be subject to
confounding and endogeneity effects. The estimation results presented here
attempts to control for these effects at least to some extent controlling for initial
accessibility and the change in the number of workplaces. The estimated effect
on final income from initial accessibility can be interpreted as capturing the
effect that high-income workplaces and people tend to move to highaccessibility locations. Not controlling for this would then be
source of
endogeneity bias.
Some of the estimation results indicate that there is unexplained heterogeneity:
in particular, the influence of initial income is conspicuously low one would
expect strong correlation between initial income and income in the next time
period. The socioeconomic variables show expected results: income increases
faster for middle-age, male, high-education and native-Sweden segments.
Model [2] is estimated only on municipalities in the Mälaren Valley Region,
which includes the Greater Stockholm region. While all parameters for
individual (segment) characteristics are very similar to [1], it can be noticed
that larger effects are indicated with respect to general accessibility and
transport-induced change in accessibility. This outcome is expected, as this
region includes the largest labour market region in Sweden, with better
opportunities for matching in the labour market than in other regions. This
result also implies that it can be questioned whether the elasticities are constant
over the sample.
Model [3] is also estimated on Mälaren Valley only, but the generalized costs in
the accessibility variables have been adjusted. Instead of using single value of
travel time taken from the transport model (as in [1] and [2]), the value of time
is different across segments. Segments are grouped into three value-of-time
categories as explained above, so the generalized travel cost will be different for
each segment. As result the elasticity increases from 0.044 to 0.053, while the
standard error is unchanged. This suggests that taking differences in the value
of travel time into account makes the generalized travel cost variable more
precise. However, this makes the assumption of constant elasticities across the
sample even more questionable.
Models [4a]-[4c] are separate models for each value-of-time category. Due to
collinearity number of dummy variables for segment characteristics have been
omitted in these equations. The estimates indicate that the elasticity with
7
This is about the same size as related estimate for UK, reported in Venables (2007).
45
respect to initial accessibility M0r and with respect to transport-induced
accessibility change cMr increases considerably with the value of time. This
confirms the expectation that workers with high income and higher education
tend to have better opportunities to benefit from the variety and specialization
offered by larger labour market. Moreover, the correlation between initial
income and final income is now much higher, also indicating better model fit.
Table
Estimated income equations for workers in Sweden and Mälaren Valley.
Dependent variable: log(income) 2002 (average per segment).
Model specification
[1]
Geographical region
Sweden
[2]
Mälaren
Valley
[3]
Mälaren
Valley
[4a]
Mälaren
Valley
All
All
All
Low VoT
Log Income 1993
0.282
0.328
0.324
0.671
0.823
0.947
0.013
0.025
0.025
0.021
0.034
0.027
Male
0.250
0.237
0.237
0.163
0.063
0.030
0.005
0.009
0.009
0.015
0.006
0.008
Age 21-30
0.520
0.480
0.484
0.028
-0.009
-0.013
0.016
0.031
0.031
0.014
0.010
0.018
Age 31-40
0.686
0.661
0.665
0.120
0.040
0.145
0.018
0.035
0.035
0.015
0.009
0.015
Age 41-50
0.775
0.745
0.749
0.209
0.085
0.158
0.019
0.037
0.037
0.016
0.009
0.015
Age 51-60
0.792
0.750
0.753
0.231
0.120
0.151
0.019
0.037
0.037
0.015
0.010
0.015
Age 61-70
0.596
0.562
0.566
0.017
0.034
0.034
Age 71+
0.257
0.223
0.224
0.017
0.027
0.026
Secondary education
0.120
0.107
0.107
0.004
0.006
0.006
Tertiary education < 3 years
0.128
0.121
0.121
0.004
0.007
0.007
Tertiary education
0.273
0.272
0.272
0.006
0.012
0.011
Native Sweden
0.130
0.148
0.149
0.030
0.095
0.136
0.004
0.006
0.006
0.010
0.008
0.010
Native other Nordic
0.120
0.131
0.131
0.051
0.070
0.121
0.005
0.007
0.007
0.012
0.009
0.014
0.044
0.051
0.052
0.019
0.024
0.037
0.001
0.002
0.002
0.005
0.003
0.003
-0.006
-0.110
-0.104
0.080
0.001
-0.036
0.024
0.054
0.054
0.136
0.070
0.088
0.030
0.044
0.053
0.025
0.029
0.062
0.004
0.006
0.006
0.016
0.008
0.011
4.108
3.730
3.749
2.239
1.159
-0.015
0.073
0.134
0.133
0.160
0.246
0.200
0.904
14817
0.909
5232
0.910
5232
0.758
1744
0.475
1744
0.713
1744
VoT Segment
3 years
0
Log M
r
Log
E Mr
Log
cMr
Constant
2
R
Number of observations
[4b]
Mälaren
Valley
Medium
VoT
[4c]
Mälaren
Valley
High VoT
Note: Standard errors (White heteroskedasticity-consistent) are reported under parameters; estimates in
bold are significant at the 95%-level; omitted categories for dummy variables are Female, Age<21, Primary
education, and non-Nordic native country.
46
2.5 Effects of congestion charges on Labour income
With the model described above, we can simulate the effects on aggregate
labour income of the introduction of the congestion charges. Accessibility
measures with and without the congestion charges are calculated using the
transport model LuTrans The changes in travel times due to the charges are
calibrated against travel time measurements from the situations before and
after the congestion charges (spring 2005 compared to spring 2006). Then, the
elasticities of labour income with respect to transport costs-related change in
accessibility (from models [4]-[6]) are used to assess the change in labour
income. Obviously, these effects do not happen at once: the calculation results
are indicative of what can be expected in the long run (such as the ten-year
period the estimation results are based on).
Figure illustrates the variation of the value of time the colours show the
share of the population in each zone belonging to the “high” value of time
category.
Figure 2. map of value-of-time variation: share of inhabitants belonging to the “high”
value-of-time category. The inner city of Stockholm is situated in the middle of the map.
47
Table shows the calculated change in labour income for each municipality and
value of time category. Note that whether the accessibility (and hence labour
income) increases or decreases varies with the value of time. For high values of
time, the decreased travel time is worth more than the increased travel cost, and
vice versa for low values of time. The sign of the accessibility change also varies
with location. For several municipalities, accessibility increases even for the
middle value of time category. One reason for this is network effects: when
traffic decreases all over the county, even many travellers that do not pay the
charge benefit from reduced congestion.
Table
2005.
The congestion tax system in Stockholm: Estimated effects on wage sum in
VTT category, share of
Effect on wage sum by VTT category
workers in municipality
Municipality
Danderyd
Low Medium
0.275
0.336
High
Low
Medium
High
Total Per capita
Total Per capita
Total Per capita
MSEK 1000 SEK
MSEK 1000 SEK
MSEK 1000 SEK
0.388
-3.3
-0.9
-3.6
-0.8
39.0
7.5
Stockholm
0.274
0.340
0.386
-14.7
-0.1
-31.3
-0.2
481.1
3.3
Nacka
0.292
0.338
0.370
-7.6
-0.7
-12.5
-0.9
42.5
2.9
Lidingö
0.299
0.339
0.362
-2.5
-0.4
-0.4
-0.1
18.0
2.6
Täby
0.283
0.334
0.384
-3.7
-0.4
-0.6
-0.1
24.5
2.2
Sollentuna
0.280
0.339
0.381
-0.9
-0.1
-0.8
-0.1
20.5
1.9
Järfälla
0.312
0.341
0.347
-0.7
-0.1
2.3
0.2
18.3
1.8
Solna
0.378
0.342
0.280
-7.2
-0.6
-12.2
-1.2
14.4
1.7
Sundbyberg
0.366
0.344
0.290
-2.3
-0.4
-4.2
-0.7
8.0
1.6
Huddinge
0.300
0.340
0.360
-1.3
-0.1
-2.0
-0.1
22.6
1.5
Upplands Väsby
0.314
0.343
0.344
-0.9
-0.2
-0.5
-0.1
7.2
1.1
Tyresö
0.283
0.340
0.376
-1.6
-0.3
-2.7
-0.4
7.3
1.0
Ekerö
0.256
0.340
0.404
-0.8
-0.3
-0.1
0.0
4.2
0.9
Värmdö
0.267
0.339
0.394
-1.4
-0.3
-1.4
-0.2
5.6
0.8
Vaxholm
0.273
0.339
0.388
-0.1
-0.1
0.4
0.2
1.5
0.7
Upplands-Bro
0.314
0.345
0.341
-0.2
-0.1
0.7
0.2
2.4
0.7
Botkyrka
0.327
0.342
0.331
-1.5
-0.1
-0.7
-0.1
7.1
0.6
Vallentuna
0.278
0.341
0.381
-0.3
-0.1
0.8
0.2
3.3
0.6
Österåker
0.272
0.338
0.391
-0.1
0.0
1.2
0.2
3.9
0.5
Haninge
0.313
0.343
0.344
-2.2
-0.2
-2.9
-0.2
5.0
0.4
Salem
0.280
0.341
0.379
-0.2
-0.1
-0.1
0.0
1.0
0.4
Sigtuna
0.314
0.344
0.343
-0.2
0.0
0.9
0.1
1.5
0.2
Norrtälje
0.331
0.345
0.324
0.2
0.0
0.1
0.0
1.4
0.2
Södertälje
0.339
0.343
0.318
-0.3
0.0
0.4
0.0
1.3
0.1
Nynäshamn
0.322
0.345
0.334
-0.1
0.0
0.0
0.0
0.4
0.1
0.0
0.2
0.1
0.1
0.1
Nykvarn
0.272
0.344
0.384
0.0
Total
0.294
0.340
0.366
-54.0
48
-69.0
741.9
The main conclusion is that the aggregate effect on labour income is in fact
positive, totalling 60 M€/year8 This is far from obvious, and it is impossible to
know whether this should be expected to be general result. Intuitively, groups
with high values of time get increased accessibility, while groups with low
values of time get decreased accessibility. Some travellers may also gain
accessibility due to network effects (“spillback” of congestion reductions). The
aggregate change in accessibility may be either positive or negative. But the
model estimations showed that changes in accessibility affects labour income
more for high-income groups than for low-income group. This is intuitively
plausible, since high values of time are correlated with high income and high
education, and such groups generally get higher wage premiums for increasing
work trip length. Hence, one may have positive effects on labour income even if
aggregate accessibility decreases.
As we argued at the outset, the sign of labour income effects is an empirical
question. In this case study, the effect on labour income turned out to be
positive. This is an interesting finding, since the literature on labour market
effects of congestion charges have often concluded that these will be negative,
usually on the basis of simplified theoretical models. Our results show that
reverse results may be obtained once the model allows for network effects,
heterogeneity in values of time, and heterogeneity in the relationship between
accessibility and labour income for different income/education segments.
Allowing for the two types of heterogeneity (in the value of time and in the
relationship between accessibility and income) is crucial. If model [2] is used,
where the travel costs and accessibility effects do not vary with the value of
time, the aggregate income effect changes from +62 M€/year to -17 M€/year.
Obviously, the size of the income effect should be regarded with caution for
several reasons. In particular, estimations of income/accessibility relationships
tend to be riddled with confounding and endogeneity bias. Results do suggest,
however, that the aggregate income effect from the Stockholm congestion
charges are positive and of considerable magnitude.
A comparison with an increased fuel tax
It is illuminating to compare the effects of the congestion charging system with
the effects of fuel tax, designed to give the same tax revenues. In contrast to
the congestion charges, this does not give any appreciable travel time savings,
so accessibility decreases for all groups. Consequently, the fuel tax has quite
different consequences for labour income.
The size of the decrease varies between municipalities and between value-oftime categories in the same municipality. This variation can mainly be explained
by the variation in the car modal share, which is linked to variation in land use
pattern and supply of public transport.
8 This includes the negative effect on the “low” value-of-time category, which is based on an
insignificant parameters estimate. Excluding this effect would increase the total effect and hence
strengthen the general conclusion.
49
While the congestion tax was estimated to increase labour income with over 60
M€/year, the fuel tax is estimated to decrease labour income with nearly 95
M€/year. On average, the estimated effect of the fuel tax is reduction of wage
sum by around 0.4% in each VTT category. However, there is considerable
variation between municipalities; the decrease in labour income is estimated to
vary between 0.1% and 1.1%.
2.6 Conclusions
In the standard theoretical model, it is clear that congestion charges will
generate social surplus. As shown in several studies (e.g. (Eliasson, 2009a)),
this will often also hold in the real world, even when technical costs have to be
covered and practical considerations place restrictions on the design of the
charges.
But in an economy with labour market imperfections such as distortive taxation
and agglomeration benefits, the “wider economic” effects of congestion charges
not captured by standard transport CBA may be negative. As shown by e.g.
(Parry and Bento, 2001), these negative effects may be so large that they cancel
the positive social surplus on the transport market. But the real effects of
congestion charges are complex and the mechanisms work in different
directions. Increased travel costs may reduce matching and labour
participation; improved travel times work in the opposite direction, and may
also increase working hours; different groups have different values of time, so
the sign of the change in generalized travel costs may be different for different
groups; and different groups will have different wage premiums with respect to
commuting radius and hence different relationships between accessibility and
income. This means that the sign of labour market effects is an empirical
question, likely to be different between different economic and geographical
conditions.
In this paper, we have assessed this by estimating relationship between
accessibility and income. The relationship takes differences in values of travel
time into account, and also that the income/accessibility elasticity may be
different for different groups. The estimation shows that categories with high
value of time have considerably stronger relationship between accessibility
and income than low value-of-time groups. Accessibility measures are
constructed using output and parameters from large-scale transport model,
making them consistent with observed travel behaviour. Previous studies on
labour market effects have often assumed that the reaction to congestion
charges will be similar to the reaction of change in income tax. Instead, we use
accessibility measures ultimately derived from observed travel behaviour,
through large-scale transport model.
Applying the estimated relationship to the Stockholm congestion charges, we
concluded that the labour market effects were in fact positive, amounting to
around 60 M€/year. This can be compared with gross revenues, which are
around 80 M€/year, the net consumer surplus, which is around -28 M€/year,
and the net social benefit (net of investment costs) of standard CBA, which is
50
around 65 M€/year (all figures are taken from (Eliasson, 2009a)). Hence, in this
case, labour market effects do not cancel the social surplus from transport
effects; in fact, they add significantly to it. Note, though, that the whole labour
income effect cannot be added to the transport CBA part of it is captured by
the work trip travel time benefits in the CBA, which accounts for around
quarter of the total travel time benefits.
51
2.7 References
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forecasting tool, in: Lundqvist, L., Mattsson, L.-G. (Eds.), National
Transportation Models Recent Developments and Prospects. Springer.
Arnott, R., 2007. Tolling with Agglomeration Externalities. Journal of Urban
Economics 62, 187-203.
De Borger, B., 2009. Commuting, congestion tolls and the structure of the labour
market: Optimal congestion pricing in wage bargaining model. Regional
Science and Urban Economics 39, 434-448.
Börjesson, M., Eliasson, J., 2011. Experiences from the Swedish Value of Time
study, CTS Working Paper. Centre for Transport Studies, Royal Institute
of Technology.
Börjesson, M., Eliasson, J., Hugosson, M., Brundell-Freij, K., 2010. The Stockholm
congestion charges four years on. Effects, acceptability and lessons
learnt., CTS Working paper. Centre for Transport Studies, Royal Institute
of Technology.
Börjesson, M., Fosgerau, M., Algers, S., forthcoming. Catching the tail empirical
identifications of value of time. Transportation Research Part A.
Calthrop, E., De Borger, B., Proost, S., 2010. Cost-benefit analysis of transport
investments in distorted economies. Transportation Research Part B:
Methodological 44, 850-869.
Ciccone, A., Hall, R.E., 1996. Productivity and the Density of Economic Activity.
The American Economic Review 86, 54-70.
Combes, P.P., Duranton, G., Gobillon, L., 2008. Spatial Wage Disparities: Sorting
Matters! Journal of Urban Economics 63, 723-742.
Van Dender, K., 2003. Transport Taxes with Multiple Trip Purposes. The
Scandinavian Journal of Economics 105, 295-310.
Duranton, G., Puga, D., 2004. Micro-foundations of urban agglomeration
economies, in: Handbook of Regional and Urban Economics, Vol. 4: Cities
and Geography. Elsevier, pp. 2063-2117.
Eliasson, J., 2008. Lessons from the Stockholm congestion charging trial.
Transport Policy 15, 395-404.
Eliasson, J., 2009a. cost-benefit analysis of the Stockholm congestion charging
system. Transportation Research Part A: Policy and Practice 43, 468-480.
Eliasson, J., 2009b. Expected and unexpected in the Stockholm Trial, in:
Gullberg, A., Isaksson, K. (Eds.), Congestion Taxes in City Traffic. Lessons
Learnt from the Stockholm Trial. Nordic Academic Press.
Eliasson, J., Hultkrantz, L., Nerhagen, L., Rosqvist, L.S., 2009. The Stockholm
congestion charging trial 2006: Overview of effects. Transportation
Research Part A: Policy and Practice 43, 240-250.
Forsyth, P.J., 1980. The Value of Time in an Economy with Taxation. Journal of
Transport Economics and Policy 14, 337.
Fosgerau, M., 2006. Investigating the distribution of the value of travel time
savings. Transportation Research Part B: Methodological 40, 688-707.
Fosgerau, M., 2007. Using nonparametrics to specify model to measure the
value of travel time. Transportation Research Part A: Policy and Practice
41, 842-856.
52
Graham, D.J., 2007a. Agglomeration, productivity and transport investment.
Journal of Transport Economics and Policy 41, 317-343.
Graham, D.J., 2007b. Variable returns to agglomeration and the effect of road
traffic congestion. Journal of Urban Economics 62, 103-120.
Graham, D.J., 2009. Identifying urbanisation and localisation externalities in
manufacturing and service industries. Papers in Regional Science 88, 6384.
Graham, D.J., van Dender, K., 2011. Estimating the agglomeration benefits of
transport investments: Some tests for stability. Transportation 38, 409426.
Graham, D.J., Kim, H.Y., 2008. An empirical analytical framework for
agglomeration economies. Annals of Regional Science 42, 267-289.
Groot, S.P.T., de Groot, H.L.F., Smit, M.J., 2011. Regional Wage Differences in the
Netherlands: Micro-Evidence on Agglomeration Externalities No. 2011050/3), Tinbergen Institute Discussion Paper. Tinbergen Institute.
Gullberg, A., Isaksson, K., 2009. The Stockholm Trial, in: Gullberg, A., Isaksson, K.
(Eds.), Congestion Taxes in City Traffic. Lessons Learnt from the
Stockholm Trial. Nordic Academic Press.
Hering, L., Poncet, S., 2010. Market Access and Individual Wages: Evidence from
China. The Review of Economics and Statistics 92, 145-159.
Jenkins, J., Colella, M., Salvucci, F., 2011. Agglomeration Benefits and
Transportation Projects. Transportation Research Record: Journal of the
Transportation Research Board 2221, 104-111.
Kaliski, J., Smith, S., Weisbrod, G., 2000. Major Corridor Investment-Benefit
Analysis System. Transportation Research Record 1732, 92-98.
Kleven, H.J., Kreiner, C.T., 2006. The marginal cost of public funds: Hours of
work versus labor force participation. Journal of Public Economics 90,
1955-1973.
Parry, I.W.H., Bento, A., 2001. Revenue Recycling and the Welfare Effects of Road
Pricing. Scandinavian Journal of Economics 103, 645-671.
Parry, I.W.H., Bento, A., 2002. Estimating the Welfare Effect of Congestion Taxes:
The Critical Importance of Other Distortions within the Transport
System. Journal of Urban Economics 51, 339-365.
Pilegaard, N., Fosgerau, M., 2008. Cost Benefit Analysis of
Transport
Improvement in the Case of Search Unemployment. Journal of Transport
Economics and Policy 42, 23-42.
Redding, S.J., Venables, A.J., 2004. Economic geography and International
Inequality. Journal of International Economics 62, 53-82.
Rosenthal, S.S., Strange, W.C., 2004. Evidence on the nature and sources of
agglomeration economies, in: Handbook of Regional and Urban
Economics. Elsevier, pp. 2119-2171.
Venables, A.J., 2007. Evaluating urban transport improvements: cost-benefit
analysis in the presence of agglomeration and income taxation. Journal of
Transport Economics and Policy 41, 173-188.
Verhoef, E.T., Small, K.A., 2004. Product Differentiation on Roads: Constrained
Congestion Pricing with Heterogeneous Users. Journal of Transport
Economics and Policy 38, 127-156.
Westin, J., 2011a. Welfare Effects of Road Pricing in
Population with
Continuously Distributed Value of Time.
53
Westin, J., 2011b. Labor Market Responses to Congestion Charges.
Vickrey, W.S., 1969. Congestion Theory and Transport Investment. The
American Economic Review 59, 251-260.
54
3
How to evaluate the welfare effects of congestion
charges?
Jonas Westin, KTH Royal Institute of Technology
Abstract
Interactions between the transport market and other interconnected markets
can have large effect on the welfare of road pricing policy or congestion
charge. An argument in the road pricing literature is therefore that the way the
revenues from road toll are recycled is crucial for the overall welfare of the
policy.
Using simple general equilibrium model we show that differences in the
relative efficiency of different revenue recycling policies, especially for marginal
toll policies, are more related to the initial model assumptions regarding the
initial situation than being direct feature of the road toll per se. For nonmarginal toll policies, interactions between the road toll and the other policy
instruments also need to be considered in the welfare analysis.
The contribution of the paper is to analyze how the welfare congestion charge
under different revenue recycling polices depends on whether the policy is
analyzed in balanced (optimal) or an unbalanced (not optimal) tax system.
The paper also extends previous research by also studying the effect of nonmarginal policies.
3.1 Introduction
Background
Interactions, both between the transport market and other interconnected
markets, and between different transport modes, can have large effect on the
welfare of road pricing policy such as congestion charge. Welfare may
therefore depend as much on indirect effects in other markets, as on direct
effects in the transport market. The full effect of road pricing policy can
therefore differ significantly from the effect predicted by first-best analysis
that ignores the spillover effects in other markets (Parry and Bento, 2002).
To analyze the welfare effect of road pricing policies, research literature has
emerged where general equilibrium models are used to capture interactions
between road pricing and pre-existing distortions in other interconnected
markets. One market that has been given special attention in this literature is
the labor market. The main argument is that since road pricing policy, such as
congestion charge, may raise the cost of work related commuting, it will
decrease employment at the extensive margin in similar way as raised
income tax. Parry and Bento (2001) even argue that the resulting losses in the
labor market from the road toll may exceed the welfare gain from the reduced
congestion externality in the transport market. However, if the collected toll
55
revenues are used to reduce other distortionary taxes, such as the labor tax,
double dividend can arise where the road pricing policy both increases welfare
in the transport market, and in the market where the distortionary tax is
reduced. The literature is hence related to the double-dividend debate and the
idea that it sometimes can be optimal from welfare perspective to tax negative
externalities higher than the partial equilibrium Pigouvian level, given that the
revenues are used to cut distortions elsewhere in the economy (see Bovenberg
1999; Parry and Oates 2000; Ballard and Don Fullerton 1992; Schwartz and
Repetto 2000; and Kim 2002).
An argument that is often found in the road pricing literature is therefore that
the way the revenues from congestion charge are recycled is crucial for the
overall welfare of the policy (Parry and Bento 2001; Van Dender 2003; De
Borger and Wuyts 2009; Fosgerau and Van Dender 2010). One reason for this is
that the value of the collected revenues often is larger than the value (in
monetary terms) of the time gains from the reduced congestion. During the
Stockholm congestion charging trial in 2006, the value of the shorter travel
times were for example estimated to be around two thirds of the collected toll
revenues (Eliasson 2009).
Comparing different revenue recycling schemes; labor tax cut is in general
preferred to lump-sum transfer, unless equity considerations are explicitly
included in the social welfare function as in Mayeres and Proost (2001). The
argument is related to the weak double-dividend claim, that an environmental
tax in general improves welfare more if the revenues are returned through cuts
in other distortionary taxes compared to being returned in lump-sum transfer
(see Goulder 1995; and Bovenberg 1999).
Using simple analytical model, Parry and Bento (2001) also find that the
efficiency gains are larger if the toll revenues are recycled through reduced
labor taxes than if the revenues are spend on increased public transport
subsidies. An opposite result is however found in De Borger and Wuyts (2009)
who argue that since labor tax cut and an increased public transport subsidy
have very different effects on congestion, it may be more efficient to recycle the
revenues via targeted public transport subsidy, than to use the revenues for
general reduction of distortionary labor taxes.
Interactions between different transport modes therefore complicate the
analysis. The economy of scale in the public transport system can for instance
be important for the overall welfare from policy that induces modal-shift
from car to public transport. troublesome implication of the conflicting results
in previous studies are that the estimated welfare effect and the relative
efficiency of different revenue recycling policies depend, not only on which
markets that are included in the analysis, but also on how the interactions
between different transport modes are modeled. However, as pointed out by
Rouwendal and Verhoef (2006), since many of the needed relationships can be
hard to measure, the optimal toll level as well as the total welfare effect can be
hard to assess empirically.
56
This has given rise to the question of how to evaluate the welfare effect of road
toll or congestion charge, especially in situations when it is uncertain how the
collected revenues are going to be spent? The question has practical
implications when it comes to how the welfare effects from road pricing policy
or congestion charge should be evaluated. If the chosen form of revenue
recycling is important for the overall welfare of the policy, then the revenues
recycling scheme must be included in the welfare analysis. If the chosen form of
revenue recycling is of less importance, simplified analysis using short-cut
rules may be enough.
The contribution of the paper to the literature is to analyze how the relative
efficiency of different revenue recycling polices depends on assumptions
regarding the initial tax system. The paper also extends previous research by
also studying the effect of non-marginal policies.
Conceptual Approach
The purpose of this paper is to study how interactions in the transport market
and other interconnected markets as well as interactions between the
congested road and the public transport system can affect the welfare effect of
congestion charge under number of different revenue recycling schemes. In
the study we both analyze marginal and non-marginal road pricing policies.
To analyze the welfare effects of yet non-existing road pricing policy, we need
to specify starting point from which to make the analysis, that is, the initial
values of policy instruments such as taxes, tolls and transfers. The choice of
starting point is important, especially when comparing different revenue
recycling polices, since it has large impact on the relative welfare effect of the
compared recycling policies. In the analysis, we will study the effect of
introducing new road toll on congested road. Hence, we consider situation
where the government previously was restricted from road tolls (by technical,
political or other reasons) but could choose the remaining policy instruments
freely, subject only to the governmental budget constraint.
The remaining policy instruments can either be chosen by specifying values for
each instrument individually, or being integrated in larger model calibration
procedure where both the policy instruments and the model parameters are
simultaneously chosen with respect to the whole model behavior. Since many
policy instruments give rise to distortions, we need to make
distinction
between initial situations where the distortions are balanced and situations
where they are unbalanced. That is, whether social welfare is maximized in the
constrained initial situation or not
Outline
The paper starts with theoretical background where the model is presented
together with an analysis of the welfare effects of road pricing policy under
different revenue recycling schemes. In the following section, three numerical
experiments are conducted to analyze the welfare effect of both marginal and
non-marginal toll policies, each using the same model but starting from
57
different initial situations. The last section summarizes the results and discusses
implications for policy analysis.
3.2 The model
To model the welfare effect of road pricing under different revenue recycling
schemes, modified version of the model presented in Parry and Bento (2001)
is used. We model static economy where homogenous population, modeled
as single representative agent, chooses labor supply and mode of transport to
get to work. In the model, simple traffic model is embedded in general
equilibrium framework. The agent gets utility from private consumption of
composite commodity, leisure, commuting and public good. Following Parry
and Bento (2001) and Van Dender (2003) we assume that labor supply is
chosen at the extensive margin and that the number of work trips is strictly
complementary to labor supply.9 We also assume that the daily work hours are
fixed, normalized to one and that the agent can choose labor supply at the
extensive margin without restriction. To get to work, the agent can choose
between three modes of transport; driving on congested road, using the public
transport system and driving on non-congested road.
difference between the model in this paper and the model in Parry and Bento
(2001) is that we in this paper use logit function to spread traffic over the
travel modes while Parry and Bento (2001) use CES demand function to do the
same thing.
The agent’s utility maximization problem
The agent’s utility maximization problem is decomposed into
two-stage
problem. First the agent chooses labor supply to maximize utility conditional on
chosen travel mode. Then the agent chooses the optimal mix of travel modes
based on the indirect utilities for all three transport modes.
The utility function conditional on travel mode
(
)
)
(
is given by:
( )
(1)
where
is private consumption,
is leisure, is public spending and
is
transport mode specific constant. The utility functions (. ) and (. ) are
assumed to be quasi-concave, continuous, twice differentiable, strictly
increasing and the same for all transport modes. The agent chooses
consumption and leisure to maximize utility subject to the following time
constraint:
(1 +
)
(2)
where
is the agent’s labor supply conditional on travel mode
is the total
time endowment in the analyzed period, and 1 +
is the time requirement for
one day of work and one commuting trip back and forth. The agent’s budget
constraint is:
9
This implies that the number of work days is directly proportional to the number of work trips.
58
]
=[
(3)
where is governmental lump-sum transfer, and
is the daily
net wage after income tax and cost for commuting where is the income tax,
is the toll (or subsidy) for transport mode
and
is the commuting cost for
the same mode.
When maximizing utility, the agent takes the travel time
public spending
and the governmental transfer as exogenous. By inserting the constraints on
time (2) and budget (3) into the conditional utility function (1) we can express
utility as function of conditional labor supply for all transport modes with
the constraint
0 From the first-order conditions for utility maximization,
we get the following relationship between consumption and leisure:
(
)
(1 +
(
0) = 0
)
=0
(4)
(5)
where = 0 if
> 0 Solving (4) and (5) we can express the representative
agent’s conditional indirect utility function
and conditional labor supply
given transport mode as function of the policy instruments (
), and
the travel time
In the outer maximization problem, the agent chooses the optimal mix of travel
modes. To capture that the agent prefers mix of travel modes,10 we use
random utility framework similar to the framework in Anas and Kim (1996) and
Anas and Liu (2007). Assuming that the preferences for certain transport
mode
is i.i.d. extreme value distributed, we can express the transport
demand as logit probability, see Train (2003).11 The mode share
for
transport mode is:
=
(6)
Note that public spending does not affect the mode choice since only utility
differences have an effect on the choice probabilities and ( ) is identical for all
transport modes. Since each work day requires one commuting trip, the total
number of trips
with mode is equal to:
(7)
where
is the chosen number of work days conditional on travel mode and
is the mode share for the same travel mode. Total labor supply is then equal
to:
=
(8)
From the properties of the logit-function, the indirect utility is finally given by:
10 Since the agent represent
homogenous population, the agent’s mix of travel modes can be
interpreted as the share of the population that chooses the different travel modes.
11 One interpretation of the probabilities is that the representative agent consists of
large
number of individuals with idiosyncratic taste constants for different travel modes.
59
)
= ln
(9)
We further assume that the agent works in competitive firm using labor as
single input to produce the consumption good. The marginal product of labor is
constant, independent of the chosen travel mode and normalized so that the
price of one unit of the consumption good is equal to one. This let us suppress
the equations for the firm from the general equilibrium model.
We assume that the agent can choose between three transport modes; driving
on congested road using public transport and driving on non-congested
{
} For the congested road, we use volume delay function
road i.e.
to capture the travel time as function of the total number of trips on the road
(
)
(10)
where the travel time on the congested road is an increasing function of the
( )
total number of trips, i.e.
> 0. This implies that the average number of
trips per day is assumed to be proportional to the total number of trips in the
period. The travel times for public transport
and for the non-congested road
are assumed to be constant.
The government’s welfare maximization problem
To maximize social welfare12 the government controls several policy
instruments. The government levies proportional tax on labor
toll on the
13
congested road
and subsidy on public transport . The tax on the noncongested road is normalized to zero, i.e. = 0.14 The toll and the subsidy are
paid on per trip basis. The government also produces public good and
have the option to give the agent lump-sum transfer
We assume that the
government cannot use lump-sum taxes, i.e
0 and that the tax, the toll, the
subsidy and the public good are non-negative, i.e.
0
0
0 and
0 The government can choose the policy instruments freely subject to the
following budget restriction:
(11)
To simplify the calculations we denote the collected revenues
+
From the agents utility maximization problem we can express
indirect utility, total labor supply, the demand for travel, and the collected
12 Since the model only contains
single representative agent and our primary interest is to
compare different policies we use the indirect utility (9) as measure of social welfare.
13 To simplify the analysis we define the public transport subsidy as negative transport tax, i.e.
Observe that we, without loss of generality, can normalize the tax on the third transport mode
to zero, i.e. = 0 since in combination with and can serve as perfect substitute to the
toll
If we removed the non-congested road, such that the agent only could choose between
the congested road and public transport, then the road toll and the subsidy in similar way
would be perfect substitutes. This implies that we instead of using congestion charge could
raise the income tax for everyone and compensate public transport commuters with an
increased subsidy.
14
60
revenues as functions of the policy instruments
time on the congested road
(
(
and
)
(
)
(12)
(13)
)
(14)
)
(
(
and the travel
)
(
Inserting (14) into (10) we obtain the travel time
instruments:
(
(15)
(16)
)
(17)
as
function of the policy
)
(18)
Assume now that the government wants to maximize social welfare given
with the restriction that
0 The Lagrangian for the
fixed road toll
government’s (constrained) welfare maximization problem is then:
(
(
)
0)
(19)
(
(
)
)
The first-order conditions for welfare maximization are:
+
+
+
+
=0
(20)
+
=0
(22)
+
+
=0
=0
(
0) = 0
)=0
(
=0
(21)
(23)
(24)
(25)
(26)
Combining (24) with the utility function (1) we see that:
where (
=
=
( )
(27)
is the marginal benefit of public spending
61
To further simplify the analysis we assume that the lump-sum transfer is zero
in optimum. The argument for doing so is that the government uses
distortionary taxes to finance public spending and that we assume that the
marginal benefit of the public good is larger than the marginal benefit of the
lump-sum transfer .15
Reformulating equation (20) and combining with (24):
(28)
we see that the marginal cost of public funds (
for labor tax
in
optimum, is equal to the marginal benefit of public spending (
). From
equation (22) we see in similar way that the marginal benefit of an increased
public transport subsidy (
also is equal to
(29)
In optimum, this implies that the welfare effect of marginal change in any of
the non-constrained policy instruments ( ,
is zero, given that the revenues
are used to increase the production of the public good
However, if the
revenues from the increased labor tax are used on any of the constrained
policy instrument ( , the welfare effect may differ from zero because of the
Lagrange multipliers and in conditions (21) and (23).
Revenue recycling and the welfare effects of road pricing
Assume now that we have an initial situation where the government prior to the
road pricing policy was restricted from using the road toll ( = 0), but has
chosen the remaining policy instruments to maximize social welfare by
balancing the distortions in the different markets.
What is then the welfare effect of marginal increase of the road toll
when
the revenues are used to increase public spending through
From the firstorder conditions (21) and (27) we see that:
+
+
(30)
The first term is the direct tax effect of increasing the road toll. Since the road
toll increases the cost of commuting to work, this has negative welfare effect,
i.e.
< 0 The second term corresponds to the welfare gain from the reduced
congestion. Given that the road toll increases the collected revenues, the third
term is also positive. The total welfare effect of the policy is equal to the
Lagrange multiplier
The first two terms can be interpreted as the direct
15 In theory there are situations where it would be optimal with
strictly positive lump-sum
transfer > 0 This could for instance happen if the marginal benefit of the public good is
negligible and there are other externalities that motivate the use of distortionary taxes (such as
congestion charge to reduce congestion).
62
welfare effect of the road toll while the third term depends on the chosen form
of revenue recycling. When the revenues are spend on increased public
spending
this term is equal to the marginal benefit of increased public
spending multiplied by the marginal change in revenues, i.e.
+
What if the revenues instead are used to cut the labor tax or increase the public
transport subsidy? Since
and
in the initial
no-toll situation, the welfare effect (at the margin) is the same regardless
whether the revenues are spend on labor tax cut
an increased public
transport subsidy
or increased public spending through
However, if the
revenues are returned in lump-sum transfer
the welfare effect can differ
because of the multiplier
3.3 Numerical experiments
In this section we use numerical model to analyze the welfare effect of
congestion charge under five different revenue recycling policies. The purpose
is both to illustrate how the relative performance of different revenue recycling
schemes may depend on the policy instruments in the initial situation, and to
analyze how interactions between different transport modes affect welfare for
non-marginal toll levels. In the model, we will also analyze how the welfare
maximizing choice of income tax, public transport subsidy, public spending and
lump-sum transfer depends on the chosen road toll for non-marginal toll levels.
To analyze how the efficiency of marginal road toll under different revenue
recycling policies depends on the initial taxation level, we will perform three
numerical experiments. In the first experiment we start from an initial situation
where the government has maximized social welfare in the absence of the
congestion charge. In the two subsequent experiments, we first study situation
where the initial level of public transport subsidy is set below its welfare
maximizing level and second, situation where the income tax is initially set
above the welfare maximizing level for the no-toll situation. The last experiment
therefore corresponds to the model in Parry and Bento (2001). Except for
different starting points, the same model is used in all experiments.
In the numerical model we assume that the agent has
function.
(
)
(
+(
)
)
CES-type of utility
(31)
where
is private consumption,
is leisure, is public spending and
is
16
transport mode specific constant. The parameter is equal to =
where
is the elasticity of substitution between consumption and leisure,
is the
agent’s marginal utility of the public good, and and are constants. For the
congested road, we use linear volume delay function
16
As in previous section we assume that the constant is i.i.d. extreme value distributed.
63
(32)
Inserting the constraints (2) and (3) into the utility function (31) and taking the
derivative, we can calculate the demand for consumption and leisure as
functions of the ratio between consumption and leisure
=
for the
chosen travel mode
Assuming we have an interior solution17 we get:
(
(
)=
)=(
(
)
The conditional indirect utility (conditional on
interior solution) is:
(
)
(
)
(35)
+(
(33)
)
(
)
chosen travel mode
(34)
and an
)
Using equations (6), (8) and (9) we can then calculate the demand for each
transport mode, total labor supply and social welfare.
The model parameters in the example are shown in Table 3.
Table 3: Model parameters in the numerical example
Parameter
Value
0.5
1.5
1.2
0.2
0.3
0.3
0.1
0.9
0.4
0.5
10
1.3
Starting from an optimal starting point
In the first experiment, we consider the situation where the government, prior
to the introduction of the road toll
has chosen the income tax
public
transport subsidy
lump-sum transfer and public good to maximize social
welfare given the governmental budget constraint (11). The initial welfare
maximization problem for the government can hence be formulated as follows:
17
0
64
(36)
This implies that the government maximizes social welfare given the budget
constraint (11) for congestion charge equal to zero.
First we note that the optimal lump-sum transfer is zero since distortionary
taxes are used to raise the money needed for public spending and the marginal
benefit of the public good is higher than the marginal benefit of positive
lump-sum transfer
This implies that the government, if possible, would use
lump-sum taxes instead of distortionary labor taxes to finance the public good
Figure shows contour plot of social welfare as function of the income tax
and the public transport subsidy
with the lump-sum transfer set to zero
and the public good given by the budget constraint (11). Since the public good
is assumed to be non-negative, this places restriction on the set of possible
policy parameters
for which
and
This is illustrated in the
figure by the white area in the lower right corner of the figure. The black dot
highlights the welfare maximizing choice of income tax and public transport
subsidy in the no-toll situation. We see that (in this example) social welfare is
maximized in the no-toll situation with the income tax set to 0.18, public
transport subsidy
equal to 0.061, public good set to 0.45 and lump-sum
transfer constrained to 0.
Figure 3: Contour plot of social welfare as
transport subsidy in the no-toll situation
function of the income tax and the public
From this optimal starting point we can then analyze the welfare effect of
introducing
road toll
on the congested road under different revenue
recycling policies. We will analyze five different recycling policies; the first
policy is to use the revenues to lower the income tax the second policy is to
increase the public transport subsidy
the third is to increase the public good
the forth is to return the additional revenues in lump-sum transfer and
65
the fifth recycling policy is to re-maximize the welfare maximization problem
(36) given the new road toll
Social welfare for the five recycling policies as
function of the road toll is shown in Figure 4.
Figure 4: Social welfare as function of the road toll for the five different revenue
recycling policies starting from an optimal starting point where all policy instruments
are chosen to maximize welfare in the no-toll situation
First, we see that for marginal toll levels, the road toll has the same welfare
effect, regardless if the revenues are used to lower the income tax increase the
public transport subsidy
or increase the consumption of the public good
The first three recycling policies also give the same welfare gain as the fifth
optimal readjustment policy. This stands in contradiction to the result from
previous studies where the choice of recycling policy was found to have
significant impact on the welfare effect of road toll. The only recycling policy
that does not produce the same effect is the lump-sum transfer recycling policy
(policy 4).
The reason behind the difference is that we in this model experiment, compared
to for instance the model in Parry and Bento (2001), have assumed that the
government has maximized welfare even before the road toll became available.
Since this implies that the marginal cost of public funds (e.g. the income tax in
the initial situation is equal to both the marginal benefit of public spending (e.g.
the public good
and the marginal benefit of public transport subsidies (e.g.
), all three recycling schemes will increase welfare with the same amount for
marginal toll levels. As could be seen from the analytical derivations, this is
general result that holds for all models what starts in an optimal initial situation
where the distortions are balanced.
For non-marginal toll levels the results are more in line with the results in
previous literature where the recycling policies were found to have different
performance. From Figure we see that when the toll increases, social welfare
increases more for both the lowered income tax recycling policy (policy 1) and
66
the increased public good (policy 3), compared to when the revenues are spend
on increased public transport subsidies (policy 2).
The reason, for this, is that road toll that reduces congestion also reduces the
need (and potential benefit) from public transport subsidy. This is because
part of the benefit from public transport subsidy comes from its ability to
reduce the congestion externality by attracting commuters to switch from car to
public transport. Recycling the revenues from congestion charge via an
increased public transport subsidy will therefore lead to situation with an
over-subsidized public transport system, given that the subsidy was set at its
optimal level in the initial no-toll situation. The welfare gain from recycling the
collected toll revenues through an increased public transport subsidy is
therefore smaller than both the increased public good and the labor tax cut
recycling policy. See Small (2004) for further discussion about interactions
between road pricing and public transport.
Comparing the income tax cut (policy 1) with the increased public good (policy
2) we see that the welfare gain for both policies in the example is similar. For
toll levels below 0.23 social welfare is improved more if the toll revenues are
spend on the public good and for toll levels above 0.23 welfare is higher for
the income tax cut The cause for this behavior is that the road toll has two
opposing effects. In particular for small toll levels, the road toll provides the
government with new and inexpensive source of revenue that the government
can use to increase the provision of the public good. The toll therefore initially
decreases the average marginal cost of public funds. But the road toll also
increases the distortions in the tax system by narrowing the tax base which
increases the cost of raising revenues through the income tax. This implies that
the marginal cost of public funds for the income tax increases. The relative
efficiency of the two recycling policies therefore depends on which of the two
effects that dominates. See for instance Bovenberg (1999) for an in depth
discussion on the topic. The results are also sensitive to changes in the model
parameters.
67
Figure 5: Marginal cost of public funds for the different policy instruments as
of the road toll for three different revenue recycling policies
function
In Figure 5, the marginal costs (and benefits) for the income tax (
), the
public good (
), the public transport subsidy (
and the congestion
charge (
), are shown as function of the toll level
for the optimal
readjustment policy (policy 5), the income tax cut recycling (policy 1) and the
increased public good policy (policy 3).
Since the tax system is balanced in the initial situation, the marginal costs and
benefits for all non-constrained policy instruments ( , and
are equal in the
no-toll situation. As the road toll increases, the marginal cost of the congestion
charge increases. For the remaining policy instruments, the effect depends on
how the revenues from the road toll are recycled. If the revenues are used to
increase the public good (policy 3),
increases compared to
If the
revenues on the other hand is recycled through an income tax cut (policy 1),
becomes lower than
When the revenues are spend on both
policy instruments, as in the optimal readjustment policy (policy 5),
and
continues to be equal for all toll levels
This shows that we to
maximize welfare in this example should spend the toll revenues one more than
one policy instrument. The optimal toll level is found where
intersects
with
The interactions between the policy parameters can also be examined by
studying how the optimal choice of policy instruments change when road toll
is introduced. From the constrained welfare maximization problem in (36) we
can express the optimal level of income tax
public transport subsidy
public good
and lump-sum transfer
as functions of the
chosen toll level
Assuming that the income tax, public transit subsidy, public
good and lump-sum transfer are at their welfare maximizing levels in the no-toll
situation; how does the introduction of the congestion charge affect these
68
optimal levels? For the numerical example, the change in the optimal parameter
levels as function of the road toll is shown in Figure 6.18
Figure 6: Change in optimal level of public good, public transport subsidy and income tax
compared to the no-toll situation as function of the road toll
First we see that the road toll decreases the optimal level of public transport
subsidy
which stresses the strong interplay between the two policy
instruments. The road toll also initially increases the optimal level of public
good
since it provides the government with new and inexpensive source
of revenue. For larger toll levels, the negative effect from the increased
distortions outweighs the positive effect of the additional source of revenue. To
compensate for the increased cost of collecting the public funds, the government
therefore decreases public spending, hence the optimal level of public good
decreases. Since the road toll increases the distortions in the tax system,
the optimal level of income tax
also decreases with the road toll.
Starting from a non-optimal starting point
In this section we will analyze two additional experiments where the initial
levels for the policy instruments differs from the optimal level studied in the
first experiment. In experiment number two, the public transport subsidy is set
below the initial welfare maximizing level, corresponding to situation where
the public transport system is under-subsidized in the initial no-toll situation.
motivation for this scenario is that among other Parry and Small (2009) argue
that even substantial levels of public transport subsidies can be efficient, even
when they are financed with distortionary income taxes. Compared to the
parameter setting in the first experiment, we set the public transport subsidy
to zero and adjust the public good
to keep the governmental budget (11)
balanced. In the third experiment, we study situation where the income tax
initially is too high compared to the welfare maximizing level in experiment
18
That is, we study
et cetera.
69
number one. This means that the marginal cost of public funds in the no-toll
situation is higher than the marginal benefit of public spending. The policy
instruments for the experiments are summarized in Table 4.
Table 4: Policy instruments in the initial situation for the three numerical experiments
Parameter
Experiment 1
Experimen 2
Experiment 3
0.18
0.18
0.25
0.061
0.00
0.061
0.00
0.00
0.00
0.45
0.52
0.65
0.00
0.00
0.00
Social welfare as function of the road toll for the first four revenue recycling
policies is shown below. Since we do not start from an optimal starting point,
we do not consider the optimal adjustment policy in these experiments. Figure
shows the result from experiment two and Figure shows the result from
experiment three.
Figure 7: Social welfare as function of the road toll for different revenue recycling
policies starting from situation with under-subsidized public transport in the no-toll
situation
70
Figure 8: Social welfare as function of the road toll for different revenue recycling
policies starting from situation with too high income tax compared to the welfare
maximizing level in the no-toll situation
3.4 Discussion
Comparing the three experiments we see that the initial choice of starting point
has large impact on the relative efficiency of the analyzed revenue recycling
policies for marginal toll levels. If we for example analyze model where the
public transport system is under-subsidized in the initial situation, we will most
likely come to the conclusion that welfare increases more at the margin, if the
toll revenues are spend on increasing the public transport subsidy compared to
lowering the income tax. This has however more to do with the initial model
assumption that the public transport system is under-subsidized in the no-toll
situation, and is not direct feature of the road toll per se. This also makes it
problematic to draw any general conclusions about the relative efficiency of
different revenue recycling policies, without explicitly including an analysis of
the initial situation from which the road toll is introduced. The relative
efficiency of different revenue recycling policies are therefore site specific and
will in general depend on number of things, not the least which costs and
benefits we include in the analysis. When analyzing the welfare effect of road
toll revenue recycling policy, it might therefore be good idea to separate the
direct welfare effect from the road toll from the indirect welfare effect from
general adjustment in the tax system.
For non-marginal policies, similar interaction patterns emerge in all three
experiments. The increased public transport subsidy recycling policy is for
larger toll levels less efficient than both the public good recycling policy and the
income tax cut recycling policy. Comparing the tax cut (policy 1) with the
increased public spending (policy 3) we also see that the ranking of the two
recycling policies are sensitive to the choice of starting point. This highlights the
difficulty of making general statements about the most efficient way of recycling
the revenues from road toll as is sometimes seen in the literature.
71
The whole revenue recycling approach can also be criticized from much
broader systems analytical perspective since it disregards the effect chosen
recycling policy may have on subsequent policies and decisions. If congestion
charging policy raises the cost of work related commuting, and this gives rise to
welfare loss in the labor market, it is clear that this loss should be included in
cost-benefit analysis of the policy. It is also clear that an appraisal of the
collected toll revenues needs to be included in the CBA. However, it is not
obvious that this appraisal should depend on the benefit of the particular
project that the revenues are earmarked for.
To assess the marginal welfare effect of recycling the revenues from
congestion charge on project instead of project B, we need to know whether
the non-selected project will be implemented anyway or not. Because if both
projects will be implemented regardless of what we do, the marginal benefit is
equal to the marginal cost of tax instrument that would have financed the
projects instead of the congestion charge. Without this knowledge, it may be
better to value the collected toll revenues more in terms of an “average”
marginal cost of public funds, instead of the marginal cost of particular project
or policy instrument.
One illustration of this problem is the Stockholm congestion charges, where the
collected toll revenues are earmarked for road investments (Eliasson et al.
2009). Because the road investments in Stockholm also are funded by other
national tax revenues, there is risk that the revenues from the congestion
charge reduce the regular funding from the national government. How we draw
the boundary of the system that we analyze is therefore important for an
analysis where we want to compare the relative efficiency of different revenue
recycling polices.
3.5 Conclusions
In the introduction we asked how the welfare effect of congestion charge or
road toll should be evaluated, especially in situations when we do not know how
the collected revenues are going to be spent. Assuming that the government has
maximized social welfare in the no-toll situation, there exists subset of nonconstrained policy instruments with the same marginal benefit. If we further
assume that public spending to some extent are financed through distortionary
income taxes (i.e. the income tax is included in the subset), we can use the
marginal cost of public funds for the income tax as proxy for the benefit of all
non-constrained policy instruments in the subset. That is, we can do the analysis
as if the marginal cost of public funds is equal to the marginal benefit of public
spending.
If the road toll is small compared to the rest of the economy, we can treat the
change as marginal and therefore do not explicitly need to know how the
revenues are going to be used within the subset of policy instruments. Instead
we can just use the marginal cost of public funds to calculate the value of the
collected revenues.
72
For larger non-marginal toll policies, the interactions between the road toll and
the other policy instruments become more important. Does the road toll for
instance reduce the need for public transport subsidies? Does the road toll
increase the distortions in the tax system which makes it more expensive to
collect money through the income tax? In this case we might consider lowering
the income tax to compensate for the increased distortions. Or, if the distortions
are small, then it might be more efficient to use the additional revenues to
increase public spending since the road toll provides the government with
new and relatively inexpensive source of revenue.
If we are not at optimum initially, introducing
road toll can give the
government an opportunity to make corrections in the tax system. However,
there might still be good idea to separate the welfare effect of the road toll
from the welfare effect of general tax adjustment, not least because it is
difficult to measure (and agree upon) all the costs and benefits in the whole tax
system and hence whether we are at optimum or not initially. And also, if we
create model with the assumption that the taxes in the initial situation are too
high compared to the benefits of spending them, and then introduce road
pricing policy only to find that it is more efficient to use the revenues to lower
the taxes than to increase public spending, what have we actually learned?
Without
thorough analysis of what initial situation we are in, it might
therefore make more sense to make the analysis as if the policy instruments in
the initial no-toll situation at least to some extent are balanced and can be
motivated on welfare maximizing principles.
To conclude, the type of general statements about how the revenues from road
toll should be spend to maximize welfare that can be found in the research
literature is problematic since the relative efficiency of different recycling
policies so strongly depend on the particular situation we analyze and what
assumptions we make regarding the efficiency of the initial policy instruments.
The analysis is also sensitive to what markets and interactions we include in the
analysis and whether we, for instance, include distributional considerations in
the welfare function or not.
For non-marginal policies we also need to consider how the road toll shifts for
instance the optimal level of taxes and subsidies. The interaction between the
public transport subsidy and the road toll stand out in this analysis, but the
results are sensitive to what interaction effects we include in the analysis and
how these are modeled.
3.6 Acknowledgements
The author wishes to thank Lars-Göran Mattsson, Jonas Eliasson, Marcus
Sundberg, Roger Pyddoke and Mattias Lundberg for helpful comments and
suggestions during the project.
This research was financed by the Swedish Transport Administration
(Trafikverket), the former Swedish Road Administration (Vägverket), the
Swedish Governmental Agency for Innovation Systems (VINNOVA), and the
Centre for Transport Studies (CTS), which is gratefully acknowledged.
73
3.7 References
Anas, A. Kim, I., 1996. General equilibrium models of polycentric urban land use with
endogenous congestion and job agglomeration. Journal of Urban Economics 40,
p.232-256(25).
Anas, A. Liu, Y., 2007. regional economy, land use, and transportation model (ReluTran©): formulation, algorithm design, and testing. Journal of Regional Science
47(3), p.415-455.
Ballard, C.L.
Don Fullerton, 1992. Distortionary taxes and the provision of public
goods. The Journal of Economic Perspectives 6(3), p.117-131.
Bovenberg, A.L., 1999. Green tax reforms and the double dividend: An updated reader’s
guide. International Tax and Public Finance 6(3), p.421-443.
De Borger, B.
Wuyts, B., 2009. Commuting, transport tax reform and the labour
market: Employer-paid parking and the relative efficiency of revenue recycling
instruments. Urban Studies 46(1), p.213 -233.
Eliasson, J., 2009. cost-benefit analysis of the Stockholm congestion charging system.
Transportation Research Part A: Policy and Practice 43(4), p.468-480.
Eliasson, J. et al., 2009. The Stockholm congestion charging trial 2006: Overview of
effects. Transportation Research Part A: Policy and Practice 43(3), p.240-250.
Fosgerau, M.
Van Dender, K., 2010. Road pricing with complication. OECD,
International
Transport
Forum
Available
at:
http://econpapers.repec.org/RePEc:oec:itfaaa:2010/2-en.
Goulder, L.H., 1995. Environmental taxation and the double dividend: reader’s guide.
International Tax and Public Finance 2(2), p.157-183-183.
Kim, S.R., 2002. Optimal environmental regulation in the presence of other taxes: The
role of non-separable preferences and technology. Contributions to Economic
Analysis Policy 1(1), p.1–25.
Mayeres, I.
Proost, S., 2001. Marginal tax reform, externalities and income
distribution. Journal of Public Economics 79(2), p.343-363.
Parry, I.W.H. Bento, A., 2002. Estimating the welfare effect of congestion taxes: The
critical importance of other distortions within the transport system. Journal of
Urban Economics 51(2), p.339-365.
Parry, I.W.H.
Bento, A., 2001. Revenue recycling and the welfare effects of road
pricing. The Scandinavian Journal of Economics 103(4), p.645-671.
Parry, I.W.H. Oates, W.E., 2000. Policy analysis in the presence of distorting taxes.
Journal of Policy Analysis and Management 19(4), p.603-613.
Parry, I.W.H. Small, K.A., 2009. Should urban transit subsidies be reduced? American
Economic Review 99(3), p.700–724.
Rouwendal, J. Verhoef, E.T., 2006. Basic economic principles of road pricing: From
theory to applications. Transport Policy 13(2), p.106-114.
Schwartz, J. Repetto, R., 2000. Nonseparable utility and the double dividend debate:
Reconsidering the tax-interaction effect. Environmental and Resource
Economics 15(2), p.149-157.
Small, K.A., 2004. 6. Road pricing and public transport. Road pricing: theory and
evidence p.133.
Train, K., 2003. Discrete choice methods with simulation first edition Cambridge
University Press, New York.
Van Dender, K., 2003. Transport taxes with multiple trip purposes. Scandinavian
Journal of Economics 105(2), p.295-310.
74
4
Welfare Effects of Congestion Pricing in a Population with
Continuously Distributed Value of Time
Jonas Westin, KTH Royal Institute of Technology
Abstract
Interactions between the transport market and other distorted markets, such as
the labor market, can have large impact on the overall welfare effect of road
pricing policy. Many road pricing studies therefore try to incorporate effects
from other distorted markets in the analysis. critical assumption in many of
the previous analyses of congestion charges is that there only exists single
value of time. This is somewhat surprising since one of the main features of
congestion charge is that it sorts people related to their value of time, given the
existence of feasible transport alternatives. The purpose of the paper is to
analyze the labor market effect from congestion charge when commuters have
continuously distributed value of time.
In the paper, simple traffic model is embedded within general equilibrium
framework where large number of heterogeneous individuals choose labor
supply and mode of transportation. Using disaggregated demand model for
the individuals’ choice of travel mode, the paper studies the distributional
impact of different revenue recycling policies, and analyzes how the mode
choice self-selection mechanism affects the total welfare effect of congestion
charge. In stylized numerical example, the effect of three different revenue
recycling polices are analyzed; lump-sum transfer, labor tax cut, and
welfare maximizing readjustment policy.
Contrary to the general conclusion in many previous studies, the paper finds
that when the revenues from the congestion charge are recycled back to the
population, the overall effect welfare effect is positive, regardless if the revenues
are returned in lump-sum transfer or used to cut distortionary income taxes.
For marginal toll levels, we also find that the total welfare effect of the
congestion charge does not depend on the chosen form of revenue recycling.
The distributional impact does however still depend on how the revenues are
used.
The congestion charge increases labor supply for the remaining car commuters,
but decreases labor supply for the individuals that change from car to public
transport because of the congestion charge. The effect on total labor supply is
hence ambiguous and depends on how the revenues are recycled. When the
revenues are used elsewhere in the economy, aggregate labor supply is found to
be positive. This indicates that the negative effect on labor supply from
congestion charge, found in many previous studies, might not generally hold.
75
4.1 Introduction
In standard textbook analysis of congestion charges, Pigouvian taxes are used
to adjust the price of car travel to its marginal social cost by incorporating the
congestion externality and reducing the associated delays. When all prices in
the economy are equal to their marginal costs, this pricing rule ensures
welfare improving Pareto efficient solution. This result does however not
necessarily hold if other interconnected markets in the economy are distorted,
as pointed out by Rouwendal and Verhoef (2006).
In response to this problem,
research literature has emerged where
interactions between the transport market and other distorted markets, such as
the labor market, are studied. Since congestion charge may raise the cost of
commuting to work, it can decrease employment at the extensive margin in
similar way as an income tax. The actual welfare effects of transport policy can
therefore be quite different from those predicted by first-best analysis that
ignores the spillover effects in other distorted markets (Parry and Bento, 2002).
It has even been shown that, without any form of revenue recycling, the
resulting welfare loss from the decreased employment can exceed the Pigouvian
welfare gain from internalizing the congestion externality (Parry and Bento,
2001).
critical assumption in many of the previous cost-benefit analyses of
congestion charges is that the whole population has single value of time. This
is problematic since one of the main features of congestion charge is that it
sorts people according to their value of time, given the existence of feasible
transport alternatives. In this paper we will instead of using representative
individual, consider population with continuous wage distribution and hence
continuously distributed value of time. The main contribution of this paper
compared to previous literature is that it studies the welfare effect and
distributional impact of congestion charge in population with endogenous
labor supply and heterogeneous value of time.
In the paper simple traffic model is embedded within general equilibrium
framework where large number of individuals choose labor supply at the
extensive margin and mode of transportation. The disaggregate travel demand
model makes it possible both to capture commuter heterogeneity and to analyze
how mode choice self-selection affects the costs and benefits of the congestion
charge under three different revenue recycling schemes. Special attention will
also be given to the distributional impact of the analyzed policies.
The model used in the paper is created with the Stockholm congestion charging
scheme in mind, but the framework can be applied to any city with well
developed public transport service. An important assumption in the model is
that car commuting is faster than public transport and that there exists strong
correlation between the value of time and choice of transport mode. The model
may therefore not be applicable to cities where almost everyone commutes by
public transport. In this paper the analysis is restricted to work related
76
commuting on single link, but the model framework can just as well be applied
to multi regional spatial CGE model.
The paper begins with
theoretical background presenting different
approaches for studying road pricing and congestion charges in distorted
economy. The background serves as foundation for the analytical framework
presented in the subsequent section. In this section we define the analytical
model and examine some of its analytical properties. The theory is illustrated in
numerical example where the welfare effect and distributional impact of
congestion charge are analyzed. The paper ends with some concluding remarks.
4.2 Background
Revenue recycling in a general equilibrium framework
To analyze the interaction between the transport market and other distorted
markets, an extensive literature has emerged where transport models are
embedded within general equilibrium framework. The general equilibrium
approach to road pricing is related to the double-dividend debate, the idea that
it can sometimes be optimal to tax negative externalities higher than at the
partial equilibrium Pigouvian level, if the revenues are used to cut distortionary
taxes elsewhere in the economy, see Goulder (1995) and Parry and Oates
(2000).
Parry and Bento (2001) use simple general equilibrium model to study how
the welfare effect from road toll on work related commuting depends on the
form of revenue recycling. In their model, single representative household
makes decisions about labor-leisure and transportation mode. Since
congestion charge in their model raises the cost of commuting to work, it affects
the net wage similar to an income tax and therefore decreases employment at
the extensive margin. If the revenues are returned in the form of lump-sum,
the authors find that the welfare loss in the labor market even can exceed the
Pigouvian welfare gain from internalizing the congestion externality. Comparing
this with two other recycling schemes, subsidized public transport and lowered
labor taxes, they find the latter the most preferable. For both these revenue
recycling schemes, the net welfare effect is found to be positive.
This basic model has been extended in many different directions. Van Dender
(2003) studies optimal tax structures in the case pricing can or cannot be
differentiated between trip purposes. Van Dender reaches results similar to
those of Parry and Bento but also stresses the importance of differentiating
between labor and leisure trips. Mayeres and Proost (1997) adopt theoretical
results from the optimal tax literature to road pricing, allowing them to study
optimal tax structures and revenue neutral tax reforms in tax system with
congestion type of externalities. Several studies have also tried to incorporate
these ideas into traditional cost-benefit analysis framework for transport
projects, adapted to allow for external distortions and market imperfections, see
Calthrop et al. (2010), Fosgerau and Pilegaard (2008) and Zhu et al. (2009). An
overview of the road pricing literature can be found in Fosgerau and Van
Dender (2010).
77
general conclusion in many of these models is that the way the revenues are
recycled is crucial for the total welfare of the policy (Van Dender, 2003).
recurrent policy recommendation in the literature is that the collected revenues
should be used to reduce distortive labor taxes rather than being spend on
increased public transport subsidies or returned in lump-sum transfer unless
equity considerations are explicitly included in the social welfare funtion, see
Mayeres and Proost (2001), Parry and Bento (2001) and Verhoef and Ubbels
(2002).
The labor supply effect can also be interpreted as location effect. decrease in
labor supply in model of work-related commuting between suburb and the
city centre can be interpreted as the commuters choosing to work at another
location than in the city centre. Effects on location and land use from transport
policy are for example modeled in Anas and Kim (1996), Eliasson and Mattsson
(2001) and Venables (2007), and Sundberg (2009) investigates regional effects
of different transport related infrastructure polices.
Equity effects and the distributional impact of a congestion charge
In partial-equilibrium studies of congestion pricing where only the direct effects
in the transport market are included in the analysis, the distributional impact is
often found to be regressive. This result does however not generally hold when
indirect effects are included in the analysis.
If the transport pricing policy is integrated in larger general fiscal policy,
congestion pricing may very well have progressive impact on welfare as
shown in de Palma and Lindsey (2004). Mayeres and Proost (2002) show that
the efficiency, equity and acceptability of congestion charging policy crucially
depend on how the revenues are used. Their main conclusion is that equity and
acceptability cannot be discussed only at the level of the transport market.
Instead, wider analysis is needed that includes the use of the revenues and its
effects. One reason for this is that the value of the collected charges is much
larger than the net benefits. Using the revenues to reduce public transport fares
will clearly have different distributional impact than labor tax cut or lumpsum replacement, as is illustrated in Berg (2007), Eliasson and Mattsson (2006)
and Mayeres and Proost (2001).
Several empirical studies of congestion charges have also empirically analyzed
welfare and equity effects of real congestion charging system. Karlström and
Franklin (2009) estimate the welfare effects of the Stockholm Trial for different
demographic groups including both the toll’s direct effect and effect in the form
behavioral adjustments as result of the toll. Disregarding the effect of revenue
recycling, they find small and regressive effect of the toll even though the
magnitude of the overall effect is not significant. For review of equity effects of
road pricing, see Levinson (2010).
The modal-choice approach to road pricing
Another modeling approach that has been used to study road pricing is mode
choice models, see Armelius (2005), Arnott and Yan (2000), Glazer and
78
Niskanen (2000), Hultkrantz and Liu (2009) and Small and Yan (2001). The
modal-choice approach is suited for transport systems with well developed
public transport system that can serve as substitute to commuting by car.
Armelius and Hultkrantz (2006) use modal-choice model in an ex-ante study
of the Stockholm congestion trial to estimate the welfare effects of road tolls. In
the model
working population with an exogenous wage distribution
commutes to work crossing road toll. To get to work individuals can choose
between two transport modes, fast and expensive mode (car) and slow and
cheap mode (public transport). Compared to the models in the previous section,
labor supply is constant so the individuals can only choose their transport mode
to maximize their utility. Given fixed income distribution, Armelius (2004)
shows that there exists unique break point income level such that people with
higher income choose car and those with lower income level choose public
transport. In the study Armelius finds that road toll affects the middle class the
most negative, while the winners are found both among people with high and
low income depending on how the revenues are recycled.
4.3 Analytical model
The model used in this paper extends the general equilibrium framework in
Parry and Bento (2001) with modal-choice model following Armelius and
Hultkrantz (2006).
simple traffic model is embedded within
general
equilibrium model where labor supply is endogenous and strictly
complementary to commuting. In the model, population of heterogeneous
individuals commutes between home and work in static economy.
First, we describe the commuters’ utility maximization problem and choice of
labor supply as function of an individual’s daily wage. Second, we turn the
model into general equilibrium model by deriving formulas for aggregate
labor supply, congestion and the governmental budget constraint.
Commuter utility maximization problem
Consider population of commuters with an exogenous daily wage distribution
) for
.19 Without loss of generality we normalize the size of the
( ) = 1 The utility function for each individual is
population to one, i.e.
(
) where the utility function is quasi-concave, strictly
given by
increasing and twice differentiable, is consumption of composite commodity
with price normalized to one, and is leisure measured as the total free time in
period with length
Every individual chooses the number of work days and mode of transportation
to maximize his or her utility subject to constraints in time and budget. The
daily work hours are assumed to be fixed and normalized to one. We also
assume that the individuals can choose the number of work days without
restriction, i.e. the job opportunities are unlimited. The individuals can choose
19 The wage distribution can be interpreted as
distribution of productivity. Assume that each
individual works at competitive firm with production function
where is number of
work days chosen by the individual and is the individual’s exogenous productivity. The
individual’s daily wage will hence be equal to his or her productivity
79
between two transport modes to get to work, fast mode (car) subject to
congestion and slow mode (public transport) with no congestion. Following
Parry and Bento (2001) and Van Dender (2003) we further assume that the
number of work trips is strictly complementary to labor supply, i.e. the number
of work days is directly proportional to the number of commuting trips.
commuting trip (back-and-forth) by car requires
units of time and costs
public transport trip takes
units of time and costs
We assume that the
travel time for car
in equilibrium is lower than the travel time for public
transport
and that the cost for car trip
is higher than the cost for
public transport trip .20 The government imposes proportional income tax
on labor, congestion charge on car commuting (cost for return trip) and
provides all individuals with lump-sum transfer
which is assumed to be
equally distributed in the population.
The utility maximization problem for an individual with
formulated as follows:
.
max
= [(
daily wage
)
(
]
] + [(
)
(1 + )
(1 + )
0,
0,
0,
0
(
)
)
(
)
can be
(1)
where
and
are the number of work days the individual commutes by car
and public transport. The individual’s total supply of labor is therefore
Since the size of the population is large, each individual takes the
travel times and the governmental lump-sum transfer as exogenous when
choosing travel mode and the number of work days.
Given these assumptions we can show that there exists unique modal-split
wage
that will split the population into two groups. All individuals with
daily wage lower than will only travel with public transport and those with
wage above will all choose car. To show this, we insert the time and budget
definitions into the utility function and use multipliers to capture the inequality
constraints on
and
We can then formulate the Karush-Kuhn-Tucker
conditions for the constrained optimization problem:
t)
u [(
u [(
t)
c
]
c ]
u (1 +
u (1 +
)
)
L
L
L
L
20
Since
=0
=0
0
0
0
0
=0
=0
(2)
and the commuters only value time and cost, car mode will only be used if
80
To solve this problem we need to consider four special cases. Assume first that
both multipliers are zero. This corresponds to an interior solution where both
we get:
transport modes are used. Solving (2) for
=
(
)
=
(
)
(3)
From equation (3) we see that an interior solution requires that the ratio
between consumption and leisure is equal for both transport modes, i.e.
(
)
(
)
( ) where ( ) =
( )
and ( ) =
Since both
ratios are linear in the daily wage
there exists unique solution to (3) as
(
)
has steeper slope than ( ) which is the case because of our
long as
previous assumptions that
For anyone to choose public transport, we
also need to assume that
>
Solving for the modal-split wage we get:
=
(
)(
(
)(
)
(
)
)
(4)
The second special case is when
= 0 and
> 0 From (2) we see that this
implies that
= 0 i.e. only car mode is used, and that:
Since
> 0 and
=
(
)
=
(
(
> 0 this implies that
)
(
)
)
+
(
<
(
)
(5)
)
Solving for
we see that this can only be true for
That is, for commuters with higher
wage than it is optimal to only commute by car.
In
similar way it can be shown that the third special case, where
> 0 and
= 0 only is valid for wages lower than the modal-split wage, i.e.
Finally, we have fourth special case where both
> 0 and
> 0 This
corresponds to situation where the individual chooses not to work at all, i.e.
= 0 and
=0
To maximize utility, every individual will choose the transport mode with the
highest ratio between consumption and leisure ( ) as function of his or her
daily wage Since we have assumed that the travel time by car is shorter than
the travel time by public transport, this means that all individuals with higher
wage than will only choose car, and all with lower wage than will only
choose public transport. The population is hence split into two distinct groups;
one only commuting by car and one only commuting by public transport.
Labor supply discontinuity
Conditional on chosen travel mode
the utility maximization problem in (1)
( )(
(
)
can be reformulated to the problem max
)
Given that the utility function is quasi-concave, strictly increasing and
twice differentiable in
and
there exists
unique solution
( )
( ) to this utility maximization problem for each
( )
(
)
and assuming that the
These demand functions are continuous in
81
substitution effect is greater than the income effect, the demand for leisure
( ) is also non-increasing in ( )
In previous section we saw that the choice of travel mode could be expressed
as function of the daily wage where ( ) = argmax ( ) ( ) Since
( ) are strictly increasing linear functions in
( ) and
and
both
( ) at the modal-split wage
( )
this implies that the demand for
leisure is
non-increasing continuous function for all
that is ( ) =
( ) where ( ) = max ( ) ( ) This also means that the demand
for leisure at the modal split wage is the same for both transport modes, that
( )
( )
is
From the time constraint, labor supply ( ) (number of work days conditional
on mode
can be calculated as function of leisure and travel time for the
chosen transport mode.
( )
( )=
(6)
Since
this creates positive discontinuity in the labor supply curve
( ) at the modal-split point depending on whether the individual travels by
car or by public transport.
( )
( )
( )=
( )
( )
=
(
(
)
)(
( )
)
> 0 (7)
The intuition behind the discontinuity in the labor supply curve
) is that an
individual with wage equal to the modal-split wage can use the time gain
from choosing car instead of public transport to work more, in order to fully
compensate for the higher commuting cost.
Since both ( ) and ( ) are non-decreasing in and the discontinuity is
strictly positive, this implies that sup
) < inf
) and labor supply
( ) (the number of work days using the optimal choice of travel mode for
wage
is non-decreasing in
Labor supply can therefore be expressed as
21
function of the daily wage.
( )=
( )
( )
( )
( )
(8)
Aggregate labor supply and congestion
To turn the model into general equilibrium model we need to formulate
expressions for aggregate labor supply and travel time on the congested road.
Total labor supply
can be calculated by aggregating the individual supply of
labor in the population, i.e.
21 Note that the optimal choice of labor supply at the modal-split wage is not unique. As long as
the daily wage distribution does not contain point mass at
this has no effect on total
welfare, aggregate labor supply and the congestion level.
82
=
( ) ( )
( ) ( )
=
( ) ( )
+
(9)
where
is the modal-split point and ( ) is the wage distribution function.
Because we have assumed that labor supply is strictly complementary to
commuting, total labor supply is also equal to the total number of car and public
transport trips, i.e.
Since road usage is subject to congestion, we assume that the car travel time
i.e.
is an increasing function of the total number of car trips
(
)
( ) ( )
(10)
(. ) is volume delay function giving the average travel time as
where
function of the total number of car trips in the period. To keep the model simple,
we assume that both travel time
and travel cost
for public transport is
i.e. we neglect the
independent of the number of public transport users
Mohring effect.
Welfare and equity
To measure social welfare, we use an aggregate equivalent variation. From the
utility maximization problem (1) we can calculate the indirect utility function
for an individual with daily wage as function of the exogenous parameters.22
( )
(
)
(11)
Using the indirect utility function we define the equivalent variation of policy
as the lump-sum payment
that makes an individual indifferent between the
situation before and after the policy has been implemented. We define the
( ) for an individual with wage as:
equivalent variation
( )
(
)
(12)
The total welfare change of policy can then be calculated as the lump-sum
payment needed to make everyone in the population indifferent between the
before and after situation, that is:
=
( ) ( )
(13)
As an alternative welfare measure we will also study the population’s total gross
wage
which can be calculated as:
=
( ) ( )
(14)
Since we assume that each individual’s daily wage
is equal to his or her
productivity, the total gross wage is equal to the total private production.
To evaluate the distributional impact of the analyzed policies, we will use two
inequality measures; the Gini measure which is scale invariant and the Kolm
measure which is translation invariant. Scale invariance (or relative inequality
aversion) and translation invariance (or absolute inequality aversion) is
22 Observe that although the travel time
and the lump-sum transfer
are treated as
exogenous by the individuals, they are actually endogenous in the general equilibrium model.
83
associated with different views of inequality. Definitions of the measures can be
found in Ramjerdi (2006). Because welfare is calculated as an equivalent
variation from the initial situation, we can only analyze the inequality of the
change in welfare and not the inequality of the absolute welfare levels before
and after the policy.
Governmental spending and budget restriction
Public spending can be modeled in several ways. Ballard and Don Fullerton
(1992) distinguish between two common approaches; the Pigou-HarbergerBrowning approach and the Stiglitz-Dasgupta-Atkinson-Stern approach. In the
first approach, focus lies on comparing distortionary tax instruments with equal
revenue yield. Public spending in this setting is often modeled as
redistributive lump-sum transfer back to the taxpayers. This makes the
approach better suited for analyzing the composition of the tax system, rather
than being used to evaluate the overall level of taxation. In the second approach,
the focus is instead on finding conditions for the optimal provision of public
goods, given that the production must be financed through distortionary taxes.
Parry and Bento (2000, 2001) and Van Dender (2003) all study situations
where the government returns the tax revenues through lump-sum transfers.
When analyzing revenue neutral tax reforms, this can be feasible method. The
assumption is however problematic when we want to evaluate the welfare
effects of policies that are not revenue neutral, such as when the toll revenues
are recycled through an increased lump-sum transfer. The reason is that if we
want to evaluate the welfare effect associated with
change in the
governmental expenditures, and thus the overall level of taxation, we also need
to model the benefits associated with public spending, in addition to the costs of
distortionary taxation.
Unless distributional considerations are explicitly included in the welfare
function, as in Mayeres and Proost (2001), it is difficult to motivate why
rational government would impose distortionary income taxes only to return
the revenues back to the tax payers in lump-sum transfer. This is also the
problem with the standard textbook assumption in Parry and Bento (2001).
When comparing different revenue recycling schemes, they find that it is
preferable to recycle the collected toll revenues from
congestion charge
through
reduced labor tax rather than through an increased lump-sum
transfer or an increased public transport subsidy. This has however more to do
with the fact that the marginal benefit of public spending (effectuated through
lump-sum transfer or public transport subsidy) in their chosen base case
scenario is lower than the marginal cost of public funds (from the distortionary
income tax) as long as the income tax is set above zero. That means that the
government even without congestion charge can improve welfare by lowering
the distortionary income tax at the expense of reduced lump-sum transfer;
then it is also clear that any additional revenues from congestion charge
should be spent on decreasing distortionary taxes, rather than on increasing
public spending. This issue is further discussed in paper in this thesis.
Instead, the idea in this paper is to study deviations from point where all tax
instruments, except the congestion charge, are optimally chosen. This allows us
84
to separate the welfare effect of the congestion charge from the welfare effect of
general adjustment of the governmental policy instruments. This welfare
effect can then be combined with the welfare effect from general adjustment
of the policy instruments in the cases where we believe that the policy
instruments ( and in the initial situation are not optimally chosen.
Since we want to study situation that resembles reality, we need to create
model where the optimal income tax is set above zero. To do this, we assume
that the government uses
production function to produce the lump-sum
23
transfer. The governmental budget restriction is therefore given by:
( )
(15)
(16)
+
where is the governmental lump-sum transfer to each individual, (. ) is
strictly increasing governmental production function,
is the population’s
total gross wage, and is the collected tax revenues from the labor tax and the
congestion charge.
The reason for including governmental production function, and not just
assuming that the government only redistributes the collected taxes, is that we
want to allow for adjustments of the marginal benefit of public funds in the no
toll situation without including explicit equity considerations into our welfare
function to motivate the redistribution. By choosing an income tax and
corresponding lump-sum transfer that maximizes social welfare, we can isolate
the welfare effects of congestion charge from the welfare effect of general
adjustment of the other policy instruments.
4.4 Numerical example
From the analytical expression (4) we see that since
congestion charge
increases the cost of commuting by car, it will shift the modal-split wage
upwards, increasing the share of public transport commuters in the population.
This will in turn reduce congestion and the travel time among the remaining car
commuters. The congestion charge therefore has two counteracting effects on
labor supply for the remaining car commuters, direct negative effect from the
increase commuting cost, and an indirect positive effect from the reduced travel
time. To calculate the total labor market response from congestion charge we
both need to consider the effect from the modal-shift and the change in labor
supply for the remaining car commuters. To illustrate the full effect on labor
supply from congestion charge we will study numerical example.
The model in the numerical example is calibrated using stylized data from the
Stockholm congestion charging trial. In the numerical example we will analyze
and compare five different policy scenarios against base case scenario with no
congestion charge. The base case scenario (B) is chosen so that the government
maximizes social welfare given that the congestion charge is set to zero, i.e.
23 An interpretation of the governmental production function is that the government uses the
collected revenues to buy composite commodity from the competitive firms from which it
produces governmental commodity which is perfect substitute to private consumption.
85
= 0 Assuming that the government has strict budget constraint, we can
frame the problem as choosing an optimal income tax and lump-sum transfer to
maximize social welfare given that the congestion charge is equal to zero, i.e.
{
}
In the first two policy scenarios, (G) and (T), the collected toll revenues from the
congestion charge are recycled back to the population through an increased
lump-sum transfer
and through an income tax cut. These two scenarios
correspond to the first two revenue recycling polices in Parry and Bento (2001).
In the lump-sum scenario, the collected toll revenues are recycled through an
increased lump-sum transfer while keeping the income tax constant, i.e.
{
), } The new transfer
) is calculated by keeping the income
tax constant at the reference level
and adjusting the lump-sum transfer so
that the governmental budget constraint holds for the chosen congestion charge
in the new equilibrium. In the labor tax cut scenario, the new tax rate
)
in similar way depends on how much the labor tax can be changed without
exceeding the governmental budget constraint, given fixed level of public
}
spending
and the chosen congestion charge i.e. {
),
In the third policy scenario (GT), both the income tax and the lump-sum transfer
are readjusted to maximize social welfare given the new congestion charge
and the governmental budget constraint, i.e. { ( ) ( ) } By studying how
the optimal choice of policy instruments changes when we introduce
congestion charge, we get measure of the interaction between the congestion
charge and the remaining policy instruments for non-marginal changes in
The first three policy scenarios are evaluated using daily congestion charge of
(corresponding to charge of 2.5€ in the morning peak and 2.5€ in the
afternoon peak). In the fourth scenario (O), the model is evaluated using the
welfare maximizing congestion charge and the corresponding welfare
maximizing choice of policy instruments, i.e. { ( ) ( ) } Finally we include
fifth policy scenario (N) where the collected revenues are not recycled back to
} Since the toll revenues are used elsewhere in the
the commuters, i.e. {
economy and we no longer have an equilibrium, welfare is not measured for this
scenario.
Calibration and choice of base case scenario
To calibrate the model numerically we need to specify the daily income
distribution, set parameter values to the income tax, travel costs, travel times
and specify functional forms for the volume delay function and the utility
function. To keep the simulation simple, we assume that the daily wage
distribution follows uniform distribution between
and 500 €, and that all
individuals have Cobb-Douglas type of utility functions:
(
)
)
(17)
where the parameter is assumed to be equal for all individuals. For volume
delay function we use the Bureau of Public Roads function from 1964 which is
widely used volume delay function, see Spiess (1990). The function is given by:
86
where
(
)
1 + 0.15
is the free-flow travel time and
(18)
is road capacity constant.
To compare the impact of the chosen policies, we need to specify the base case
scenario from which we make the comparisons. The choice of base case scenario
is important since it have large effect on the relative performance of the
different revenue recycling policies. To separate the welfare effect of the
congestion charge from the welfare effect of
general adjustment of the
remaining governmental policy instruments, we need to choose base case
scenario where the marginal costs are equal to the marginal benefits of the
different policy instruments in the initial situation (except for the congestion
charge). This implies that the government chooses income tax and lump-sum
transfer to maximize social welfare in the model, given that the congestion
charge is set to zero. Assuming that the government has
strict budget
constraint, we can frame the problem as choosing an optimal income tax
to
maximize social welfare where the lump-sum
is given by the governmental
budget constraints (15) and (16) and is zero.
Since social welfare in the model is measured as an equivalent variation, the
measure depends on what initial situation we measure the equivalence from. To
find the set of policy instruments that maximizes social welfare we therefore
search for
base case scenario with
local maximum in the measured
equivalent variation. The base case scenario is chosen so that the modal-split
wage splits the population into two equal parts. To set the optimal income tax
above zero we also need to adjust the governmental production function to
increase the marginal benefit of the lump-sum transfer. To simplify the analyze
we assume that the governmental production function has constant return to
scale, i.e.
)=
The calibrated parameters are summarized in Table 5.
Table 5: Summary of model parameters for the numerical example
Parameter
Value
Daily income distribution, minimum wage
€
Daily income distribution, maximum wage
500 €
Car cost
10 €/return trip
Public transport cost
3.3 €/return trip
Utility parameter
0.36
Public transport travel time
0.1875 units of time (90 min/return trip)
Car free-flow travel time
0.0833 units of time (40 min/return trip)
Car road capacity constant
0.2667 return trips/day
units of time (1 day)
Time endowment
Governmental production function parameter
1.3
Income tax in base case scenario
25.4%
Lump-sum transfer in base case scenario
60.45 €
87
Simulation results
Labor supply discontinuity
Figure shows labor supply ( ) as function of the daily wage for the base
case scenario and for congestion charge of
(price for return-trip) where
the revenues are recycled back to the population through labor tax cut (the
second policy scenario). Because travel mode in the model is chosen as
function of the daily wage, the population is split into two distinct groups; one
group only commuting by public transport and one group only commuting by
car. Since individuals with high wage choose to work more if they commute by
car than by public transport, this creates discontinuity in the labor supply
curve at the modal-split wage
The congestion charge increases the cost of commuting by car which will shift
the modal-split point to higher daily wage level, hence increasing the share of
public transport commuters. The congestion charge also has direct negative
effect on labor supply for the car commuters since it decreases the net wage in
similar way as an increased income tax. The negative labor supply effect is
however outbalanced by the shorter travel time, which both shifts the modalsplit wage downwards and stimulates labor supply among the remaining car
commuters. However, even though the total number of car trips decreases
because of the congestion charge, aggregate labor supply increases.
Labor supply
(full time equivalent work days)
0,9
0,8
0,7
0,6
0,5
0,4
Base case scenario (B)
0,3
Income tax cut scenario (T)
0,2
0,1
0,0
0
100
200
300
400
500
Daily wage (€)
Figure 9: Labor supply as function of the daily wage for the base case scenario (B) and
for the income tax cut scenario (T) with congestion charge of
for return-trip.
The welfare effect of congestion charge
Figure 10 depicts total welfare as function of the congestion charge for the
three different recycling policies. The congestion charge initially increases
welfare with similar amount regardless of how the collected revenues are
recycled back to the economy. This stands in contrast to the results in Parry and
Bento (2001) where the lump-sum recycling scheme was found to have
negative effect on total welfare due to increased losses in the labor market. The
reason behind the difference is that we in this model, compared to the model by
Parry and Bento, have chosen an initial starting point where the marginal
88
benefit of public funds (e.g. the governmental lump-sum transfer) is equal to the
marginal cost of public funds (e.g. the income tax). Setting the congestion charge
too high will on the other hand reduce total welfare for all recycling polices. In
the model, welfare is maximized with daily congestion charge of 13.46 (i.e.
the total congestion charge for return trip) given that all policy instruments
are adjusted in an optimal way.
We also see that the lump-sum transfer recycling policy lags behind for
congestion charges above 10 €. With
lower level of congestion (higher
congestion charge), the marginal benefit of policies that increase labor supply
(at the expense of an increased number of car trips) increases, compared to
policies that primarily reduce congestion. Since the lump-sum transfer has
negative impact on labor supply, while the income tax instead stimulates people
to work more, this is part of the explanation for why the performance of the two
policies differ for higher toll levels.
5
4
Welfare (€)
3
2
Lump-sum transfer
recycling policy
1
Income tax cut recycling
policy
0
-1
Optimal adjustment
recycling policy
-2
-3
0
5
10
15
Congestion charge (€)
20
25
Figure 10: Welfare measured as an equivalent variation from the base case scenario as
function of the congestion charge when the revenues are recycled through an income
tax cut, lump-sum transfer and with an optimal adjustment of both the income tax and
the lump-sum transfer.
Table
gives numerical values for welfare, equity, aggregate labor supply,
modal-split point and car travel time for all five policy scenarios. The congestion
charge in scenario one, two, three and five are
and the congestion charge in
the fourth scenario are set at the welfare maximizing level 13.46 €.
Although car travel time, and hence congestion, is reduced, regardless of how
the toll revenues are used, the increased lump-sum recycling scheme is clearly
the most effective policy for reducing congestion because of its negative effect
on labor supply. The income tax cut has the opposite effect since the increased
net wage both stimulates labor supply directly and increases the share of car
commuters in the population.
Compared to the base case scenario (B); aggregate labor supply increases for
both the income tax cut scenario (T) and the welfare maximizing scenario (O),
89
but decreases when the revenues are recycled back through an increased lumpsum transfer (G). However, when the revenues are not recycled back to the
commuters (N), the effect on aggregate labor supply is also positive. This
indicates that the congestion charge per se does not have negative effect on
labor supply. Instead the negative labor supply effect comes from the increased
lump-sum transfer and the underlying model assumption that an increased
lump-sum transfer has negative effect on labor supply.
Table 6: Scenario summary for the base case scenario and the four policy scenarios
Base case Lump-sum
scenario
transfer
(B)
scenario
(G)
Income
tax
cut
scenario
(T)
Optimal
adjustment
scenario
(GT)
Welfare
maximizing
scenario
(O)
No
recycling
scenario
(N)
-
2.688 €
2.670 €
2.690 €
4.415 €
-
wage 183.2 €
183.7 €
186.3 €
184.3 €
189.5 €
185.6 €
-
0.1124
0.4621
0.1744
0.5618
-
Kolm ( = 0.1)
Aggregate
labor 0.589 days
supply
0.0186
0.585 days
0.2301
0.598 days
0.0406
0.588 days
0.8871
0.610 days
0.594 days
Modal-split point
250.7 €
284.2 €
284.4 €
284.3 €
342.3 €
285.4 €
Car travel time
69.2 min
58.1 min
58.7 min
58.2 min
46.37 min
58.2 min
Lump-sum
60.45 €
62.89 €
60.45 €
62.37 €
59.11 €
60.45 €
Income tax
25.38%
25.38%
24.01%
25.08%
22.08%
25.38%
Welfare
Total
gross
Gini coefficient
Congestion charge
€
€
€
€
13.46 €
The distributional impact of congestion charge
Using the model we can also analyze the distributional impact of congestion
charge. Figure 11 shows welfare as
function of the daily wage in the
population. To clarify the discussion, the population is divided into four
different groups (I,II,III,IV); group consists of people with the lowest wage that
do not commute; group II contains public transport commuters; group III
consists of car commuters in the base case scenario that switch to public
transport because of the policy; and group IV consists of the car commuters that
remain to drive car to work after the policy. Observe that the dividing lines
between the groups depend on the parameters and do therefore differ between
the scenarios.
As can be seen from the figure, the distributional impact of the congestion
charge strongly depends on the chosen form of revenue recycling. In the
example, people on low income (group and II) benefit more from increased
public spending compared to labor tax cut, while people on high income
(group II and IV) have opposite preferences. We also see that although the
commuters with the highest income pay most of the charges; they also gain
most from the congestion charge, regardless of how the revenues are recycled.
When the collected revenues are recycled through increased lump-sum
90
€
transfers, the relative losers are found among those switching from car to public
transport (group III) and in the group of remaining car drivers with the lowest
daily wage (leftmost part of group IV).
From the inequality measures in Table we see that the welfare gains from the
congestion charge is more unequal when the revenues are recycled through an
income tax cut (T) than through lump-sum transfer (G). This is because both
the tax cut and the time gains benefit those with the highest wages most. For
small toll levels, the optimal readjustment policy also spreads welfare more
equally than the income tax cut. For larger toll levels, inequality increases.
Figure 11 also reveals that the welfare maximizing scenario (O) is not even
Pareto improving. The reason for this is that the congestion charge narrows the
tax base which increases the marginal cost of public funds; to improve welfare
the government therefore decreases public spending (i.e. the transfer
to
compensate for the increased distortions in the tax system. See Bovenberg
(1999) for an in depth discussion on the topic. The analysis hence highlights the
importance of also including equity aspects when analyzing the welfare effects
of transport policy, especially if one is interested in the distributional impact
and political acceptance of the analyzed policy.
10
Welfare (€)
8
I
II
III
IV
6
Lump-sum transfer
scenario (G)
4
Income tax cut scenario
(T)
2
Optimal adjustment
scenario (GT)
0
Welfare maximizing
policy scenario(O)
-2
0
100
200
300
Daily wage (€)
400
500
Figure 11: Welfare as function of daily wage measured as an equivalent variation from
the base case scenario and the four analyzed policy scenarios.
In Figure 12 the difference in labor supply compared to the base case scenario
as function of the daily wage is shown. While all schemes increase labor
supply for individuals on high income (group IV), the effect varies more among
low-income earners (group II) depending on the recycling policy. Labor supply
is also negative, regardless of how the revenues are recycled, for the part of the
population that changes from car to public transport as
result of the
congestion charge (group III). From the figure we also see that the indirect
effect on labor supply from the chosen form of revenue recycling is larger than
the direct effect on labor supply from the congestion charges. This also explains
why the change in total labor supply, as summarized in Table 6, is positive for
91
both the labor tax cut (T) and the no recycling scenario (N), but negative for the
increased lump-sum transfer scenario (G).
Difference in labor supply
(full time equivalent work days)
0,06
Lump-sum transfer
scenario (G)
0,04
I
II
III
IV
0,02
Labor tax cut scenario (T)
0,00
Optimal adjustment
scenario (GT)
-0,02
Welfare maximizing
scenario (O)
No recycling scenario (N)
-0,04
0
100
200
300
Daily wage (€)
400
500
Figure 12: Differences in labor supply as function of daily wage for the five policy
scenarios compared to the base case scenario.
Sensitivity analysis
To analyze the sensitivity of the numerical results, we vary key parameters,
recalibrate the policy instruments in the base case scenario to maximize welfare
without congestion charge, and then study the welfare effect of the three
different revenue recycling policies for small increase in the toll level. In the
numerical example, small congestion charge was found to produce positive
welfare for all three revenue recycling policies. This result is robust to changes
in the model parameters as long as the initial level of congestion in the no-toll
situation is not too low. Reducing the road capacity increases the welfare of the
congestion charge since the congestion is more severe in the before toll
situation.
For marginal changes in the congestion charge, the welfare gain from
congestion charge does not depend on how the collected revenues are recycled.
As long as the income tax and lump-sum transfer are set at their optimal levels
in the no toll situation, this result is also robust to changes in the model
parameters. For non-marginal changes we saw that the labor tax cut performed
better than the increased lump-sum transfer. By changing the parameter values
of the model we can make the lump-sum transfer policy increase welfare more
than the labor tax cut. This means that the relative performance24 of the
different revenue recycling policies for non-marginal toll levels is not robust to
changes in the underlying assumptions about key parameter values.
In the example we assume that the governmental policy instruments (
,0
in the base case scenario are chosen to maximize social welfare. This means that
24
etc.
92
the marginal cost of the income tax is equal to the marginal benefit of the lumpsum transfer in the initial situation. Relaxing this restriction results in
situation where the indirect welfare effect from spending the collected revenues
even for marginal toll levels depends on the used recycling policy. If the income
tax for instance is set above its optimal level in the no toll situation, the
government can increase welfare by reducing the tax at the expense of
decreased public spending.
recycling policy that reduces the income tax
towards its optimal (lower) level will therefore improve total welfare more than
recycling policy that increases public spending. The relative performance of
the analyzed revenue recycling polices is therefore sensitive to changes in the
initial calibration of the remaining policy instruments in the no toll situation.
4.5 Concluding remarks
In the paper, all analyzed revenue recycling policies has positive effect on the
total welfare, regardless if the revenues are returned in lump-sum transfer or
used to cut distortionary income taxes. The welfare gain from the lump-sum
recycling policy is also found to be more or less equal to the labor tax cut policy
for small toll levels. This stands in contrast to earlier studies where the
efficiency loss in the labor market is found to exceed the welfare gains from
internalizing the congestion externalities in the transport market. Two main
reasons behind this result are; first that we study
population with
heterogeneous value of time, and second that our analysis starts from initial
no-toll situation where the policy instruments (except the congestion charge)
are optimally chosen to maximize social welfare.
The analysis hence stresses the importance of recognizing that people have
different value of time and that this can have substantial effect on aggregate
labor supply and hence welfare. The reason for this is that the congestion
charge primary price out people (and trips) with low willingness to pay so that
people with higher willingness to pay can drive and work more. Disregarding
equity considerations, the congestion charge leads to more efficient use of the
available road space.
From the numerical analysis we also saw that the congestion charge only had
direct negative effect on labor supply for the car commuters that changed from
car to public transport because of the congestion charge. For the car commuters
that continued to commute by car after the congestion charge, the effect on
labor supply was positive. For the public transport commuters, the effect on
labor supply depended on the revenue recycling policy. The effect on total labor
supply from the congestion charge was hence ambiguous and mainly depended
on how the revenues were used.
The chosen revenue recycling policy also had large effect on the distributional
impact of the congestion charges. If the collected revenues were recycled
through an income tax cut, car commuters in the highest wage group that
remained to drive car got most of the welfare gain compared to the no-toll
situation, while if the revenues were used to increase public spending through
an increased lump-sum transfer, the welfare gains were more proportionally
spread across the population.
93
critique of the model is that the modal choice approach used in this paper
tends to overestimate the correlation between an individual’s daily gross wage
and his or her mode choice. Without this strong correlation, some of the results
will be smaller. Nevertheless, user heterogeneity and self selection cannot be
completely ignored when studying congestion pricing, and, as has been shown
in this paper, can have substantial effect on labor supply, welfare and the
distributional impact of congestion charge.
4.6 Acknowledgements
The author wishes to thank Lars-Göran Mattsson, Jonas Eliasson, Marcus
Sundberg and Stef Proost for helpful, yet challenging, comments on the
manuscript. The research was financially supported by the Swedish Transport
Administration (Trafikverket), the former Swedish Road Administration
(Vägverket) and the Swedish Governmental Agency for Innovation Systems
(VINNOVA).
94
4.7 References
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with endogenous congestion and job agglomeration', Journal of Urban
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avoidance and congestion tolls, Doctoral dissertation, Department of
Economics, Uppsala universitet, Uppsala.
Armelius, H. (2005): 'An integrated approach to urban road pricing', Journal of
Transport Economics and Policy, 39, 75-92.
Armelius, H., and Hultkrantz, L. (2006): 'The politico-economic link between public
transport and road pricing: An ex-ante study of the Stockholm road-pricing
trial', Transport Policy, 13, 162-172.
Arnott, R., and Yan, A. (2000): 'The two-mode problem: Second-best pricing and
capacity', Review of Urban and Regional Development Studies, 12, 170-199.
Ballard, C.L., and Don Fullerton (1992): 'Distortionary taxes and the provision of public
goods', The Journal of Economic Perspectives, 6, 117-131.
Berg, C. (2007): 'Household transport demand in CGE-framework', Environmental
and Resource Economics, 37, 573-597.
Bovenberg, A.L. (1999): 'Green tax reforms and the double dividend: An updated
reader's guide', International Tax and Public Finance, 6, 421-443.
Calthrop, E., De Borger, B., and Proost, S. (2010): 'Cost-benefit analysis of transport
investments in distorted economies', Transportation Research Part B:
Methodological, 44, 850-869.
Eliasson, J., and Mattsson, L. (2001): 'Transport and location effects of road pricing:
simulation approach', Journal of Transport Economics and Policy, 35, 417456(40).
Eliasson, J., and Mattsson, L. (2006): 'Equity effects of congestion pricing: Quantitative
methodology and case study for Stockholm', Transportation Research Part A:
Policy and Practice, 40, 602-620.
Fosgerau, M., and Pilegaard, N. (2008): 'Cost benefit analysis of
transport
improvement in the case of search unemployment', Journal of Transport
Economics and Policy, 42, 23-42.
Fosgerau, M., and Van Dender, K. (2010): 'Road pricing with complication', OECD,
International Transport Forum.
Glazer, A., and Niskanen, E. (2000): 'Which consumers benefit from congestion tolls?',
Journal of Transport Economics and Policy, 34, 43–53.
Goulder, L.H. (1995): 'Environmental taxation and the double dividend:
reader's
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Hultkrantz, L., and Liu, X. (2009): 'Sterilized Congestion Charges. Model Analysis of
the Reduced Impact of The Stockholm Road Toll', Presented at the International
Transport Economics Conference, Minneapolis, Minnesota State University,
June 15-16.
Karlström, A., and Franklin, J.P. (2009): 'Behavioral adjustments and equity effects of
congestion pricing: Analysis of morning commutes during the Stockholm Trial',
Transportation Research Part A: Policy and Practice, 43, 283-296.
Levinson, D. (2010): 'Equity effects of road pricing: review', Transport Reviews:
Transnational Transdisciplinary Journal, 30, 33 57.
Mayeres, I., and Proost, S. (1997): 'Optimal tax and public investment rules for
congestion type of externalities', Scandinavian Journal of Economics 99, 261279.
Mayeres, I., and Proost, S. (2001): 'Marginal tax reform, externalities and income
distribution', Journal of Public Economics, 79, 343-363.
95
Mayeres, I., and Proost, S. (2002): 'Reforming transport pricing: an economist’s
perspective on equity, efficiency and acceptability', Center for Economic
Studies-KU Leuven.
de Palma, A., and Lindsey, R. (2004): 'Congestion pricing with heterogeneous travelers:
general-equilibrium welfare analysis', Networks and Spatial Economics,
4, 135-160.
Parry, I.W.H., and Bento, A. (2000): 'Tax deductions, environmental policy, and the
"double dividend" hypothesis', Journal of Environmental Economics and
Management, 39, 67-96.
Parry, I.W.H., and Bento, A. (2001): 'Revenue recycling and the welfare effects of road
pricing', The Scandinavian Journal of Economics, 103, 645-671.
Parry, I.W.H., and Bento, A. (2002): 'Estimating the welfare effect of congestion taxes:
The critical importance of other distortions within the transport system',
Journal of Urban Economics, 51, 339-365.
Parry, I.W.H., and Oates, W.E. (2000): 'Policy analysis in the presence of distorting
taxes', Journal of Policy Analysis and Management, 19, 603-613.
Ramjerdi, F. (2006): 'Equity measures and their performance in transportation',
Transportation Research Record: Journal of the Transportation Research Board,
1983, 67-74.
Rouwendal, J., and Verhoef, E.T. (2006): 'Basic economic principles of road pricing:
From theory to applications', Transport Policy, 13, 106-114.
Small, K.A., and Yan, J. (2001): 'The value of "value pricing" of roads: Second-best
pricing and product differentiation', Journal of Urban Economics, 49, 310-336.
Spiess, H. (1990): 'Technical note--conical volume-delay functions', TRANSPORTATION
SCIENCE, 24, 153-158.
Sundberg, M. (2009): Essays on spatial economies and organization, Doctoral
dissertation, Department of Transport and Economics, Royal Institute of
Technology, Stockholm.
Van Dender, K. (2003): 'Transport taxes with multiple trip purposes', Scandinavian
Journal of Economics, 105, 295-310.
Venables, A.J. (2007): 'Evaluating urban transport improvements: Cost-benefit analysis
in the presence of agglomeration and income taxation', Journal of Transport
Economics and Policy, 41, 173-188(16).
Verhoef, E.T., and Ubbels, B. (2002): 'Using transport pricing revenues: Efficiency and
acceptability', MD-PIT Working paper 4, Free University Amsterdam.
Zhu, X., Van Ommeren, J., and Rietveld, P. (2009): 'Indirect benefits of infrastructure
improvement in the case of an imperfect labor market', Transportation
Research Part B: Methodological, 43, 57-72.
96
5
Kilometre or diesel tax in Sweden? A cost–benefit analysis
Michael Lundholm, Stockholm University
Matts Andersson, WSP
Tommy Lundgren, SLU Swedish University of Agricultural Sciences
Markus Sandberg, KTH Royal Institute of Technology
Introduction
Without investment costs, financial policy tools are almost by definition socioeconomically profitable if they push prices closer to the marginal cost. But since
most financial policy measures include an investment cost the question is, as
with physical investments, if the benefits are bigger than the costs. large part
of the benefit of financial policy measures might be that the income can be used
to lower other taxes, which might have positive effects on the economy. This
positive effect is called “marginal cost of public funds” in the economic
literature. Many articles have argued though that the effect on the tax base
cancels the incomes from the policy measurement, meaning that the “double
dividend” of environmental taxes does not exist.
The aim of this article is to do cost benefit analysis of the fuel and kilometre
taxes. In doing this we estimate the taxe base effect and compare it with the
mcpf effect. Most of the literature in this area is based on analytical models, for
example assuming an optimal tax system. We start out with an analytical model,
but we estimate the parameters/elasticities empirically on Swedish data. The
estimations of the tax base, the marginal cost of public funds etc are done with
both factor demand-model (FDM) and spatial general equilibrium (SCGE)
model (STRAGO). Since FEM and SCGE are two quite different approaches, an
aim of this study is also to compare these approaches.
The outline of the article is as follows. First we describe our two cases to be
tested and analyse their effects on transport costs. To calculate the
97
effect on transport costs, we use a model developed in an earlier project. After that our analytical general equilibrium model, including the parameters
to be estimated, is presented. Our estimation/simulation tools FDM and
STRAGO are then described. Since this article contains one cost model and
two models for estimation/simulation, the model presentations are made
very short (readers looking for an in depth knowledge of the models are
directed to presentations in earlier articles and reports). Finally we test our
two cases based on parameters from FDM and STRAGO.
2
Our two cases to be tested
The introduction of taxes in the transport sector is typically motivated by
a mix of allocation and fiscal reasons in line with Pigouvian taxation and
Ramsey taxation.1 In the particular case of a kilometre tax, the Pigouvian
rationale is fundamental since it internalizes externalities that are not sufficiently accounted for in present prices, including other taxes. The relevant
externalities to internalize are primarily emissions to the air except Carbon
Dioxide (CO2 ) emissions and road deformation. For heavy goods vehicles,
emissions and road deformation are both highly correlated with transport
distance. CO2 is the main externality that is corrected with the diesel tax.
Diesel consumption correlates perfectly with CO2 emissions, given the carbon content of the fuel.
Although the aim of the article is not to give judgements on specific
suggestions we have tried to choose the most politically relevant suggestions
for kilometre tax and diesel tax in Sweden. Most people advocating for
kilometre tax in Sweden support the suggestion by the Swedish institution
for communication analysis to set the tax to 1 SEK per vehicle kilometre.2
This is based on the external effects calculated to 1.4 SEK per km, out
of which 0.4 SEK is internalized by the energy tax. The most relevant
suggestion for raised diesel tax is the opposition’s suggestion to raise the
CO2 tax on fuel with 0.17 SEK per kilo CO2 , which implies that the diesel
tax increases with 2.64 × 0.17 ≈ 0.45 SEK per litre diesel.
A model is used to calculate the effects of the kilometre tax and the
increased fuel tax on the total transportation costs per truck kilometre.3
The kilometre tax results in a cost increase of 6.6 percent, and the increased
fuel tax in an increase of 1.5 percent. The effect on total transportation
cost for each commodity group depends on the share of road transport,
which differs from 10 to 95 percent for the 12 commodity groups in the
1
Pigou (1920); Ramsey (1927), Diamond and Mirrlees (1971a,b) and Mirrlees (1971).
SIKA (2007).
3
The model was originally developed in 2006 for Swedish EPA (Naturvårdsverket,
2007) and is described thoroughly in that report. The basis is data from the Swedish
transport administration, the Swedish tax administration, the Swedish petroleum institute
and Svenska åkeriförbundet. During this project the indata has been updated.
2
2
Swedish goods transport model.4 Assuming that the cost increase does not
affect mode choice the change in total cost could be calculated as cost per
kilometre times the share done by truck. This results in the cost change
caused by the kilometre tax varying from 0.7 to 6.3 percent respective 0.1
to 1.4 percent for the increase in fuel tax. The truck market share and the
result for each product are shown in Table 1 on page 3.
Table 1: Truck market share and effects on products.
Market
Effect
Effect
Product
share
km-tax
diesel
truck (%)
(%)
tax (%)
1 Agricultural products
0.81
+5.4
+1.2
2 Unprocessed lumber
0.68
+4.5
+1.0
3 Processed wood products
0.88
+5.8
+1.3
4 Foodstuffs
0.95
+6.3
+1.4
5 Crude petroleum
0.36
+2.4
+0.5
6 Petroleum products
0.30
+2.0
+0.4
7 Iron ore and metal waste
0.10
+0.7
+0.1
8 Metal products
0.17
+1.1
+0.3
9 Paper and pulp
0.25
+1.6
+0.4
10 Earth, stone and build
0.69
+4.6
+1.0
11 Chemicals
0.62
+4.1
+0.9
12 Manufactured ind. prod.
0.73
+4.8
+1.1
Sum
0.55
3
External effects
SIKA (2007) has valued of the external effects to 2.4 SEK per vehicle kilometre. As mentioned above we use SIKA’s recommendation for kilometre
tax (1 SEK per vehicle kilometre). To be consistent we therefore use SIKA’s
valuation of the external effects as well. The relation between the valuation
of external effects and the tax is as follows. CO2 stands for 1 SEK (of the
2.4 SEK). Since CO2 emissions are better internalized with fuel tax, this is
not included in the recommendation for kilometre tax. Of the remaining
1.4 SEK, 0.4 SEK is assumed to be internalized by the energy tax, leaving
1 SEK for the kilometre tax.
Valuing CO2 emissions to 1 SEK per vehicle kilometre is based on a CO2
valuation of 1 SEK per kilo and an assumption that the fuel consumption is
4
The statistics has been retrieved from SIKA’s publications, where the commodity
groups have been converted from NST/R to the 12 commodity groups that is used in the
STAN-model (a freight forecast model).
3
0.4 litre per kilometre. The official Swedish valuation of CO2 is 1.5 SEK per
kilo (SIKA, 2009). In the kilometre tax report SIKA has chosen a valuation
matching the CO2 part of the fuel tax. Both 1.5 and 1 are high valuations
in an international perspective, we have chosen to use SIKA’s valuation
anyway to be consistent and since valuation of CO2 is not the focus of this
paper.
Out of the 2.4 SEK 0.11 SEK is costs for deformation and wear. Including
these effects, the total value of the decrease in externalities therefore is 2.29
SEK per vehicle kilometre. However, it turns out that this effect is marginal
and we therefore do not take into account the reduction in the cost for
deformation and wear in the theoretical analysis as well as in the CBA
calculations.
4
Model
The purpose of this section is to set up a simple framework in which we
will be able to analyse a change a the tax system as a cost–benefit decision. Focus is to identify the different types of effects that will occur. The
consider a government which use distortionary taxation and lump sum redistribution is available. The model is a general equilibrium model, but as
a simplification we disregard from redistribution and have a representative
agent. There is constant returns to scale (no pure profits) and the number of
firms normalized to one). Private goods are either consumption commodities
consumed by the representative agent or intermediate commodities used by
the representative firm to produce consumption commodities. There is no
public production. One intermediate commodity is assumed to be “dirty”
and affect a negative environmental externality, which in turn affects consumption but not production directly. These assumptions then implies that
all goods are taxable, that a pure profits tax is unnecessary since profits
are zero due to constant returns to scale and that differential taxation on
inputs in the private sector is not used. The legal incidence on consumption
commodities are on the representative household and on intermediaries on
the representative firm. The general character is similar to Diamond and
Mirrlees (1971a).
Assume a representative individual economy with standard consumer
preferences over private consumption goods x, and the environmental externality Ê described by the utility function u. Facing the consumer price
vector q = p + t the consumer’s utility maximisation problem is
max
x
u(x, y, Ê) s.t.
n
X
(pi + ti ) xi ≤ y,
(1)
i=0
where y is a public lump sum transfer. The solution is the vector Marshallian
demand functions x∗ (p + t, y, Ê) ∈ Rn+1 . Let the indirect utility function
4
be υ(p + t, y, Ê) := u(x∗ (p + t, y, Ê), Ê). Roy’s identity is
∂υ
∂qk
= −λx∗k (p +
t, y, Ê) ∀k = 0, . . . , c, where λ is the marginal utility of income in the optimal
point.
Private consumption goods are produced competitively according to a
constant returns to scale production technology F (v, w) = 0, where v is the
n + m + 1 dimensional output vector of private consumption and intermediary goods and w the m dimensional input vector of private intermediary
goods. Let C be the set of private consumption goods and I the set of private intermediary goods. Intermediate goods face the specific taxes τ with
legal incidence on producers. In a long run competitive equilibrium the optimum output vector v∗ (p, τ ) and input vector w∗ (p, τ ) are determined.
The externality is assumed to depend on one dirty intermediate commodity,
denoted wD , such that E (wD ).
The equilibrium conditions then are
x∗i (p + t, y, Ê) = vi∗ (p − τ )
wi∗ (p
− τ) =
vi∗ (p
Ê = E
∀i ∈ C,
− τ)
∗
(wD
(p
∀i ∈ I, and
− τ )) .
(2a)
(2b)
(2c)
Consider now a government that considers to increase the level taxation of an intermediate good (dτ
taxes unchanged,
Pk > 0),∗ leaving
P all other
∗
subject to a balanced budget, i∈C ti xi + i∈I τi wi = y, and the equilibrium conditions (2). To balance the budget the transfer to households is
changed (dy 6= 0). Therefore, there will be only two the control variables;
i.e., p (τk , y). Note that in the following Ê denotes the equilibrium quantity
of the environmental externality.
The welfare effect we want to evaluate is
dυ =
dυ
dυ
dτk +
dy.
dτk
dy
(3)
Rearranging and using Roy’s identity we get
X ∂pi
1 dυ
1 ∂υ dE
=−
x∗i
+
+
λ dτk
∂τk
λ ∂ Ê dτk
i∈C
1−
X
i∈C
∂pi
x∗i
1 ∂υ dE
+
∂y
λ ∂ Ê dy
Differentiating the budget set and rearranging we get
P
P
dx∗
dw∗
wk∗ + i∈C ti dτki + i∈I τi dτki
µy
dy
=
=
,
∗
∗
P
P
dx
dw
i
i
dτk
µ τk
1−
ti
−
τi
i∈C
i∈I
dy
!
dy
. (4)
dτk
(5)
dy
where the last equality follows from the standard definition of social marginal
welfare of tax revenue.5
P
P
dx∗
dw∗
That is, µy = λ/ 1 − i∈C ti dyi − i∈I τi dyi is the social marginal welfare of tax
revenue from lump sum taxation etc.
5
5
Combining, rearranging and using that MCPFx = µx /λ we get
!
X ∂pi
dυ
∂υ
dE
1
MCPFτk
= −
x∗i
+
MCPFτk
dτk
∂τk
λ ∂ Ê dτk
i∈C
!
X ∂pi
1 ∂υ dE
∗
MCPFy .
+
+ 1−
xi
∂y
λ ∂ Ê dy
(6)
i∈C
5
FDM
The econometric modelling approach is the same as in Hammar et al. (2008,
2011), which both use a partial equilibrium factor demand model to study
the impact of a kilometre tax on Swedish industry.6 The model is based
on standard micro-economic foundations. We assume (1) that the objective
of each individual firm is to maximize profits, (2) that each individual firm
operates in a competitive environment, and (3) that each individual firm
has access to a technology that transforms a number of inputs into a single
output. Assumption (1) implies, inter alia, that the firm chooses production
level and input demands simultaneously. Furthermore, assumption (2) implies that all input and output prices are exogenous to the firm. Assumption
(3) implies that we can describe the technology with a production function.
The profit function derived from these assumptions has the usual properties, implying it is increasing in output price, and non-increasing in input
prices. Applying Hotelling’s lemma to the specified profit function, we obtain supply and demand as functions of all prices. In order to obtain an
operational form of the demand system we need to specify an empirical
functional form for the profit function. Like Hammar et al. (2008, 2011) we
have chosen to use the normalized quadratic profit function.
From theory it follows that the own price supply effect is positive, whereas
the effect on supply from an increase in any input price is negative. The
own price demand effect is negative, whereas the cross price effects cannot
be determined a priori. The sign of the cross price effect will depend on
the technology, and on whether inputs are substitutes or complements in
production.
5.1
Data
The data set is a firm level unbalanced panel covering the 1990–2001 period.
It contains plants with more than five employees and is classified according
to the industry standard and includes plant level data on output (sales),
input data on (quantities and values) labour, electricity and fuels used,
gross investment, and transport costs. In the official data on transport costs
6
For more detailed background on factor demand modelling and the specific approach
used, see the references in Hammar et al. (2008, 2011).
6
there is no disaggregating between modes of transport. We handle this
shortcoming by dividing the total transport costs according to information
on the average share of road transports that are used in respective industry.
We have consequently scaled the transport data to reflect the direct road
transport cost shares in the different sectors of manufacturing.
The proxy for road transport demand is constructed by dividing the
scaled transport costs by a price index for heavy vehicle transports (more
on this index below). Fuels are aggregated into a single variable (70–80 per
cent fossil fuels in aggregate the variable). Capital stock is calculated from
data on investment, value added, and salary paid to employees. Assuming
that value added is compensation to labour and capital (salaries plus capital
costs), we extract the capital stock residually.
Output price indices are sector specific, meaning that we have one output
price index for each industry. Firm specific input prices can be calculated
from the costs for labour, electricity, and fuels. Price of transports and
capital are not firm specific. The calculations of these indices are based
on national and industry based indices, respectively (taken from Statistics
Sweden, producer price index section at www.scb.se), which seems plausible
considering that firms have limited opportunities to affect the prices for
capital (global market) and transports significantly.
For the transport price we use a weighted index containing price indices
for labour cost (for employees in the heavy vehicle transport sector), cost
of capital, and diesel (used as fuel in heavy transportation vehicles), and a
consumer price index reflecting the price development of other costs. The
weights used here are 42 per cent for labour, 15 per cent for capital, 26 per
cent for fuel, and 17 per cent for other costs.7
5.2
Partial vs. general equilibrium
In a partial equilibrium setting, like the factor demand model presented
above, policy changes, such as a kilometre tax, do not explicitly generate
general equilibrium effects. That is, policy changes have effects only on the
prices of those inputs directly affected by the specific policy. For example, an
introduction of a kilometre tax translates directly and fully into an upward
price change in heavy road transports. No other prices are assumed to
change. This may be realistic in some cases, and less realistic in others. For
example, significant increases in the road transport price will most likely
affect the labour market. Increased transportation costs may affect labour
demand, which in turn may affect the labour market and wage rates. In the
end, this will affect the overall cost. The model we use here cannot track
these types of general equilibrium effects, but the reader should be aware
7
The weights were supplied by TRANSEK (now WSP?), a consulting firm focusing
on the transport sector, and are based on the cost of operating a heavy vehicle in road
transportation.
7
that they do exist to some degree. To account for all interactive effects
between all sectors and markets, a computable general equilibrium model
(CGE) would be more suitable. However, this type of model is not without
flaws either and the modelling approach used in this analysis certainly has
some benefits compared to a CGE. For example, the parameters used in the
simulation have been estimated using very detailed micro-panel data, and
the massive amount of information it contains is important to consider when
choosing between different modelling approaches. It should, however, be
stressed that even though we have the data, we cannot study each company
separately. The effects from, for example, price changes are to be interpreted
as effects for a group of firms, or as a mean effect for a specific group of firms.
6
STRAGO
STRAGO (Swedish Trade of Goods, SCGE model calibrated to Sweden) is
a spatial computable general equilibrium model of the Swedish economy. In
the model, the economic activity that takes place in Sweden is divided between nine different regions, and fourteen different sectors/industries. The
economic activities in the different regions induce both interregional and
interindustry trade, which requires transports. Similar to the partial equilibrium factor demand model, the equilibrium model described here is based
on standard micro-economic foundations. The model includes descriptions
of the actions of both firms and households, as well as the interactions of
these actors on different markets. One of the main focuses of the model is to
capture the interdependencies between transport costs on goods trade and
the spatially distributed economic activities. In this model, goods transport
is considered to be a derived demand. That is, transport demand is derived
from the need to move goods from one location to another, from the suppliers to the demanders of the goods. The model is built on the framework of
monopolistic competition.
We will now give a somewhat more extensive description of the model,
yet for a full description of the model (Sundberg, 2009, see). Regarding the
firms, it is assumed that they act under monopolistic competition. Hence,
they maximize profits by choosing their output price and optimal mix of
inputs. The inputs to production are intermediate inputs, i.e. goods, possibly purchased from any region and sector, as well as primary inputs in the
form of capital and labour. The monopolistically competitive firms maximize their profits, yet in equilibrium we have zero profits due to competition.
The zero profit condition yields the level of output of each firm, while market demand determines the number of active firms in any particular region
and industry.
In each region there is a representative household, which is assumed to
behave as if it is utility maximizing. The household earns its income through
8
provision of primary inputs to the firms in the form of labour and capital.
The household use all its income on expenditures on the provided goods,
which are consumed, but also benefit from leisure.
All markets are assumed to be in equilibrium. In the model, all prices
adjust to the point where supply meets demand on all markets. Labour markets clear, such that the households’ supply of labour is equal to the firms’
demand for labour, the same holds for the capital market. Goods markets
clear, the supply of output from any firm is demanded as a consumption
good by the households, as an intermediate input to production in other
firms, or it is exported to some foreign country. The goods markets clearing
conditions determine the number of active firms in every region and sector.
Finally, the model is calibrated to Swedish data such that the National
Input/Output structure, representing inter sectoral trade and use of primary
input factors as well as final demands, are replicated. The regional distribution of production is also calibrated. Both the National I/O-table and the
regional distribution of production are taken from the National Accounts.
The transport costs are calibrated to reflect the distribution of transport
costs between the different types of goods as given by the Samgods model.
7
Results
The source for estimating the different effects A–E is the STRAGO model
since FDM only can estimate the indirect effects on the tax base caused by
the change in indirect taxation (effect C). Therefore we here present two
different CBA’s, with alternative measures for effect C (CBA 1 and CBA
2). CBA 1 is only based on STRAGO whereas in CBA 2 the indirect effect
on the indirect tax revenues are exchanged for the estimate from FDM. The
two different CBA’s are made for both the kilometre tax (Table 2 on page
10) and the diesel/CO2 tax (Table 3 on page 11).
The net social benefit is calculated as follows:
net social benefit = MCPF (A + B + C) − D + E
where MCPF = 1.32 is also calculated by STRAGO.8 The change in the
external effects (E) has been calculated by taking the change in transported
kilometres times 2.4 (SEK/km) which is our estimated external cost per
vehicle kilometre.
The results for the kilometre tax and CO2 -tax differ in magnitude, simply
because the kilometre tax represents a larger tax increase, in absolute terms,
on transports. In relative terms the two different tax instruments have
similar effects. This is an expected result since fuel consumption and vehicle
8
Note that we can calculate the “instrument specific” MCPF for the two tax instruments. In the absence of fixed costs they are given by (D-E)/(A+B+C), which equals
1.18 in CBA 1A, and 1.17 in CBA 2A.
9
Table 2: Results for the kilometre tax (SEK million)
Effect
A
B
C
D
E
Net social benefit
CBA 1A
3 202
-94
-1130
2 419
84
276
CBA 2A
3 202
-194
965
2 419
84
2 909
kilometres are highly correlated. See cost changes for the two policies in
Table 1 on page 3.
Given the valuation of 2.4 per vehicle kilometre and the calculated decrease in vehicle kilometres being 35 million kilometres in the case of the
kilometre tax and 7.9 million kilometres in the case of the diesel tax, the
value of the decrease in external effects is 84 million SEK for the kilometre
tax and 19 million SEK for the diesel tax. The reduced cost for deformation and wear (0.11 SEK per vehicle kilometre) would reduce the external
effects to 80.1 and 18.9 million SEK respectively; a difference so small that
we disregard from the effect.
In CBA 1A and CBA 1B, completely performed by means of the STRAGO
model, we have a strong direct effect (A), while indirect effects on the tax
base (B) are small. The indirect tax base effect on private intermediates
(C) differs between CBA 1 and CBA 2. In the STRAGO model we have
equilibrium outcomes where higher taxes on transports induce lower tax
incomes from intermediates such as labour and capital. There are many
forces within the economy that may tip the effect in C either in a negative
or a positive direction. Take labour for instance, increasing transport based
taxes motivates firms to shift towards using more labour in production in
favour of transported goods. If this demand for labour is met it would actually expand the labour tax base. On the other hand, equilibrium requires
demand and supply of labour to equilibrate, labour markets clear. From
the households’ perspective, increasing transport-taxes on goods makes free
time, or leisure, relatively cheap. Thus, the households may shift their consumption toward leisure, which implies that labour supply goes down. Such
an effect reduces the labour tax base. Taking both demand and supply side
effects into account, in summary, we have a negative equilibrium effect on
the tax base of private intermediates.
10
Table 3: Results for the diesel/CO2 tax (SEK million)
Effect
A
B
C
D
E
Net social benefit
8
CBA 1B
721
-204
-253
542
19
68
CBA 2B
721
-204
542
19
Conclusions
Our calculation implies that the kilometre tax is socio economically profitable. However when the investment and administration cost is added, 350
MSEK per year according to SIKA’s calculations,9 the profitability in the
STRAGO-based calculation is slightly negative. It could be noted though
that our estimation of the decrease in external effects is lower than SIKA’s,
who estimates it to 180-400 MSEK per year. Changing to SIKA’s valuation
makes the calculation slightly positive. When we estimate the tax base effect on private intermediate commodities (“C” in our analytical model, i.e.
Labour and capital) with the FDM, the net social benefit is extremely positive; since the net social benefit is approximately equal to the tax revenue
from the kilometre tax the revenue comes “for free”.
The direction of the difference between the partial (FDM) and the general equilibrium (STRAGO) estimates is logical since the equilibrium effects
most likely are negative. The in market effect might be positive: increasing
transport taxes makes firms replace transports with other production factors. Equilibrium requires market to clear (which counteract the in market
effect) and increasing transport taxes makes leisure relatively cheaper (which
makes labour supply go down). Even though the sign of the difference is
logical, it is hard to verify the size. There is obviously a trade-off between
making a detailed calculation of one market and capturing all effects but on
a more schematic way.
Our calculation for the diesel tax shows a similar pattern, but since it
requires no investment cost it is profitable in both calculations. It should
be mentioned though that our calculations of the external effects does not
capture the differences in benefits from a kilometre tax compared to a fuel
tax, i.e. the reasons for making the investment. The differences are that
a kilometre tax can levied from all vehicles regardless of nationality (where
the tank is filled) and, most importantly, can be differentiated very detailed
9
SIKA (2007).
11
(based on vehicle type, amount of people affected by pollution etc.).
It is now well established in the literature that there in an optimal, first
best, world is no double dividend from tax instruments. In the real world
though, it is an empirical question. Our tests of the kilometre and diesel
taxes imply that the critical issue for the existence of a double dividend is
the effect on other production factors.
References
Diamond PA, Mirrlees JA (1971a). “Optimal Taxation and Public Provision
1: Production Efficiency.” American Economic Review, 61, 8–27.
Diamond PA, Mirrlees JA (1971b). “Optimal Taxation and Public Provision
2: Tax Rules.” American Economic Review, 61, 261–78.
Hammar HT, Lundgren T, Sjöström M (2008). “The significance of transport costs in Swedish forest industry.” Journal of Transport Economics
and Policy, 42, 83–104.
Hammar HT, Lundgren T, Sjöström M, Andersson M (2011). “The Kilometer Tax and Swedish Industry.” Applied Economics, 43, 2907–2917.
Mirrlees JA (1971). “An Exploration in the Theory of Optimum Income
Taxation.” Review of Economic Studies, 38, 135–208.
Naturvårdsverket (2007). “Klimat, transporter och regioner. En studie om
målkonflikter och målsynergier.” Technical report. URL http://www.
naturvardsverket.se/Documents/publikationer/620-5710-3.pdf.
Pigou AC (1920). The Economics of Welfare. MacMillan and Company,
London.
Ramsey FP (1927). “A Contribution to the Theory of Taxation.” Economic
Journal, 37, 47–61.
SIKA (2007). “Kilometerskatt för lastbilar. Kompletterande analyser. Redovisning av ett tilläggsuppdrag från regeringen.” Technical report,
Statens institut för kommunikationsanalys. URL http://www.trafa.se/
document/sr_2007_5.pdf.
SIKA (2009). “Person- och godstransporter på järnväg, tredje kvartalet
2007. Kvartalststatistik.” Technical report, Statens institut för kommunikationsanalys. URL http://www.trafa.se/document/ss_2008_3.
pdf.
Sundberg M (2009). The Development of STRAGO - With application to
a kilometer tax, pp. xx–yy. Department of Transport and Economics,
12
Royal Institute of Technology, Stockholm. ISBN 978-91-85539-43-7. Diss.
Stockholm : Kungliga Tekniska högskolan, 2009, URL http://urn.kb.
se/resolve?urn=urn:nbn:se:kth:diva-10540.
13
Centrum för transportstudier är ett forskningscentrum vid KTH
ett samarbete
mellan KTH, VTI, WSP Analys
Strategi, Internationella Handelshögskolan
Jönköping, Trafikanalys, Trafikverket, Vectura och VINNOVA. Forskningsfältet
omfattar bland annat samhällsekonomisk analys, hållbara transportsystem,
prognosmodeller, trafiksimulering, transportsystemets finansiering och organisation,
samspelet mellan transportsystem och regional ekonomi samt trafikanters beteenden
och värderingar. Centret är en tioårig satsning med en total finansiering från parterna
på uppåt 250 miljoner kr, oräknat tillkommande externa uppdrag. Verksamheten
sysselsätter motsvarande minst 20 heltidstjänster, oräknat de många forskare vid de
olika parterna som har sin finansiering på annat sätt, och har en gemensam
lokalisering på KTH:s campus.
The Centre for Transport Studies is new research centre at KTH
cooperation
between KTH, VTI, WSP Analysis Strategy, Jönköping International Business School,
Transport Analysis, Transport Administration, Vectura and VINNOVA. The research
area includes cost-benefit analysis, sustainable transport systems, transport
modelling, simulation, financing and organisation, interactions between the transport
system and the regional economy, and travellers’ behaviour and valuations. The
Centre is
ten-year project comprising almost 250 million SEK, not counting
additional research grants. The centre employs around 20 full-time equivalents, in
addition to the researchers at the partners funded in other ways, and has joint
location at KTH campus.
Centre for Transport Studies
SE-100 44 Stockholm
Sweden
www.cts.kth.se