Healthy climate, healthy bodies: Optimal fuel taxation and physical activity [original]

Accepted: 15 September 2023

DOI: 10.1111/ecca.12497

ORIGINAL ARTICLE

Healthy climate, healthy bodies: Optimal fuel

taxation and physical activity

Inge van den Bijgaart1David Klenert2Linus Mattauch3,4,5

Simona Sulikova5

1Utrecht University, Utrecht, Netherlands

2Joint Research Centre, European Commission,

Seville, Spain

3Technical University of Berlin, Berlin,

Germany

4Potsdam Institute for Climate Impact

Research - member of the Leibniz Association,

Potsdam, Germany

5University of Oxford, Oxford, United

Kingdom

Correspondence

Linus Mattauch Faculty of Economics and

Management, Technical University of Berlin

Email: linus.ma[email protected]

Passenger transport has significant externalities, including

carbon emissions and air pollution. Public health research

has identified additional social gains from active travel,

due to the health benefits of physical exercise. Per mile,

these benefits greatly exceed the external costs from car

use. We introduce active travel into an optimal fuel taxa-

tion model and characterize analytically the second-best

optimal fuel tax. We find that accounting for active travel

benefits increases the optimal fuel tax by 44% in the USA

and 38% in the UK. Fuel taxes should be implemented

jointly with other policies aimed at increasing the uptake

of active travel.

1INTRODUCTION

Transport policies need to balance the economic gains from passenger vehicle use with a large

number of significant externalities, including air pollution, accidents, congestion and climate

change. For example, in the USA and the UK, the transport sector is the largest contributor of

greenhouse-gas emissions (Hockstad and Hanel 2018;Gabbatiss2018). Increased active travel

such as cycling and walking—even to the nearest public transport stop—can reduce these exter-

nalities, especially in urban areas. In addition, the physical exercise involved in active travel is

highly beneficial for public health, especially given high rates of inactivity and obesity in many

societies. Previous scenario-based modelling in public health research has indicated that the

health benefits of active travel exceed those from abating emissions and air pollution of private

vehicles (Woodcock et al. 2009; De Hartog et al. 2010). For example, Woodcock et al. (2009) find

that an increased active travel scenario would avoid 530 premature deaths per million population

in London annually, while a low-carbon motor vehicles scenario would save only 17.

Surprisingly, economists have yet to examine the significance of the health benefits from

active travel for optimal regulation of urban transport. While they can be assumed to know that

exercise is good for health in general, most citizens are not aware of the full extent to which it

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Economica. 2024;91:93–122. wileyonlinelibrary.com/journal/ecca 93

94 ECONOMICA

provides health benefits (Fredriksson et al. 2018). Furthermore, the effectiveness of simple inter-

ventions such as reminders or initial payments to attend a gym (Calzolari and Nardotto 2017;

Charness and Gneezy 2009) and evidence of overspending on gym contracts (DellaVigna

and Malmendier 2006) point to self-control problems and an underappreciation of the health

benefits of exercise. One might think that health benefits of active travel are a local phenomenon,

which has limited relevance for transport policy at the macro level. It is, however, yet to be

determined how fuel taxes, or more targeted instruments, should be set to reap these health

benefits in addition to mitigating the externalities of car use.

In this paper, we examine a novel economic effect by adding an active travel mode to a

model of transport externalities from car use. Households respond to higher fuel taxes by buying

more fuel-efficient cars and reducing car travel, but do not fully internalize the health benefits of

switching to active travel modes. We confirm that on a per mile basis, the monetary value of the

health benefits from active travel exceeds the social costs of unregulated externalities of carbon

emissions, air pollution, congestion and accidents by up to two orders of magnitude. First-best

policy would thus involve a large subsidy to promote active travel (at least absent health policy

to increase activity levels in general). Without such subsidies, we derive the second-best optimal

fuel tax that corrects for the externalities and the unrealized health benefits. We examine the dif-

ference for the tax rule, and quantify the appropriate tax rate when including or excluding health

benefits from active travel.

Our main finding is that the optimal tax increases by 44% in the USA, and 38% in the UK,

when health benefits from physical exercise are included. The second-best optimal fuel tax for

the USA is $12.92 per gallon, and $8.99 per gallon without physical inactivity costs, while the

current1rate in the USA is $0.50 per gallon (US Energy Information Administration 2023). The

optimal fuel tax for the UK is $6.31 per gallon, which is higher than the current rate of $3.82 per

gallon (RAC 2023). Without physical activity costs, the second-best optimal tax would be $4.56

per gallon.2

Our main contribution is to show that the health benefits from active travel are so significant

that they should change the second-best fuel tax—the most archetypal, widely used, and very

effective instrument of transport regulation. To be clear, other transport policies such as conges-

tion charges, adequate walking and cycling pathways, and parking fees will be better suited to

promoting active travel than fuel taxes (see the final subsection of Section 3, on first-best poli-

cies). Furthermore, they can better address concerns about the negative impacts that increasing

fuel prices have on low-income households, as they can be differentiated between locations.

Analysing which mix of fuel- or mileage-based taxes and more local instruments, such as urban

infrastructure overhaul, are feasible to best achieve sustainable mobility (Banister 2008) requires

geographical context and is beyond scope of our approach.

This paper builds on three distinct strands of the literature.

First, a large body studies optimal levels of fuel taxes, and which externalities should be

addressed by them (van Essen et al. 2019). In addition to generating government revenue,

fuel taxes are typically used for the purpose of reducing most forms of non-priced costs of

transport—for example, the externalities of carbon dioxide and particulate matter, or reducing

congestion by raising the cost of driving. Parry and Small (2005) derive the optimal gasoline

taxes for the USA and the UK, accounting for congestion, accidents, carbon emissions and air

pollution, and Antón-Sarabia and Hernández-Trillo (2014) apply this framework to Mexico.

Sterner (2012) compares the optimality of fuel taxes in Europe and the USA, concluding that fuel

taxes vary considerably between countries. They are inefficiently low in most European countries

(Santos 2017). Yet the optimal fuel tax literature has so far not considered the health benefits

from active travel.

Second, the field of public health, starting with Woodcock et al. (2009), has identified high

social benefits from active travel over and above the benefits from abating emissions and air pol-

lution of private vehicles (De Hartog et al. 2010; Wolkinger et al. 2018). To the majority of the

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HEALTHY CLIMATE, HEALTHY BODIES 95

population, increasing physical activity outweighs the negative impacts of increased exposure to

air pollution (Tainio et al. 2016). This is due to the overwhelmingly sedentary lifestyles in both

the UK and the USA, making physical inactivity a leading risk factor for 6 of the 10 largest

causes of death worldwide (World Health Organization 2019). Most UK adults do not exercise

regularly (37% never, 16% less than once a week, 57% admit they never do activity strenuous

enough to be out of breath; European Commission 2018). This leads to significant costs, includ-

ing higher rates of disease incidence, lower quality of life, loss of income, excess healthcare costs,

and productivity losses in the workplace. Meeting the minimum recommendations of 150 minutes

of moderate-intensity physical activity per week can reduce the risk of cognitive impairment and

dementia, depression, hypertension, several kinds of cancer, type 2 diabetes, and cardiovascular

disease (Davies et al. 2019). We build on the valuation methods in public health to quantify the

welfare cost of travel that is inactive.

Third, behavioural public economics research has elaborated on the important role of

‘internalities’ in various domains of public policy (Allcott and Sunstein 2015). An ‘inter-

nality’ occurs when an individual imposes a significant cost on herself due to behavioural

failures, broadly understood as being prevented from acting according to her true motiva-

tion. As these private costs are imposed only or mainly on oneself—which is true for lack

of physical activity—they fall outside the definition of an externality. Nonetheless, govern-

ments regulate internalities when scientific evidence substantiates them. Internality taxes have

been applied to the market for smoking (Gruber and K˝

oszegi 2004), gym memberships and

exercise (in the form of subsidies; DellaVigna and Malmendier 2006), sugary drinks (Allcott

et al. 2019a,b) and the energy and automobile market (Allcott and Wozny 2014; Allcott

and Sunstein 2015), where they also interact with environmental externalities. In the lat-

ter case, the interaction leads to a behavioural–environmental second-best problem (Shogren

and Taylor 2008).3‘Sin taxes’—surcharges on prices of goods of which people consume

too much because of internalities—have been modelled as either simple extensions of a

Pigouvian tax (O’Donoghue and Rabin 2006) or complex interactions between taxes and

individuals’ heuristics and decisions, to achieve an optimal outcome in second-best settings

(Allcott et al. 2014).

However, this body of literature has not considered the internality of physical inactivity in

urban transport. Walking, cycling and switching to public transport are considered ways in

which people can achieve ‘appropriate’ levels of physical activity as prescribed by public health

guidelines (Gibson-Moore 2019; Office of the Surgeon General 2015). People generally under-

value the contribution of physical exercise to their long-term health (Zamir and Teichman 2014).

There are two behavioural biases behind this undervaluation, which lead to insufficient levels of

exercise and further health impacts: imperfect information and insufficient self-control (Allcott

et al. 2019b). This reinforces the case for building active travel into commuting routines.

Our contribution is threefold. First, we introduce a physical-activity-related health internal-

ity into an established framework of transport decisions (Parry and Small 2005), and use this

behavioural–environmental framework to provide an analytical solution for the second-best opti-

mal fuel tax. Second, we provide an updated quantification of the external costs of travel provided

by Parry and Small (2005), considering recent research and global climate policy goals, and com-

plement this with a quantification of the health benefits of active travel. For example, updating the

carbon price estimates increases the contribution of fuel pollution to the optimal fuel tax by two

orders of magnitude. Congestion costs have also risen more significantly than accident costs since

the year 2000. In the USA, though not in the UK, the Ramsey tax component contributes more

than the individual externalities to the optimal fuel tax. Third, in terms of policy implications,

we contribute to evaluating fuel taxes as opposed to other policies. We confirm that raising the

propensity of consumers to switch to active travel modes can impact greatly the appropriate fuel

tax: the demand for vehicle miles travelled (VMT) is so inelastic that increasing the appropriate

96 ECONOMICA

elasticities to their upper bound found in the literature raises the fuel tax by up to 58% for the

UK and 78% for the USA.

To be clear, our paper does not aim for a complete characterization of first-best policy

instruments to address the underappreciation of physical activity, including information

provision, commitment devices and direct monetary incentives by health providers. Rather,

our contribution is more modest: insofar as there remains uninternalized valuation of physical

activity from direct attempts to reduce it, we show how it affects optimal transport policy through

fuel taxation.4

While local policies are attractive for addressing specific transport externalities, we focus on

fuel taxes to show that the health benefits of active travel matter even for getting the macro level of

optimal transport regulation right. Fuel taxes have some advantages over more specific transport

policies. First, they can be implemented with relatively small administrative costs compared to

other policies, since most countries already have fuel taxes in place and levels would only have

to be adjusted accordingly. Second, fuel taxes have a proven track record of reducing carbon

emissions (Bento et al. 2009;Sterner2012;OECD2019; Bretschger and Grieg 2020). Third,

they generate government revenue—which remains true if more electric vehicles in the future

will prompt a switch from fuel- to mileage-based road taxes. This revenue could be used either

for green spending, for instance on low-carbon transport infrastructure, or for compensating

households that are especially affected by the tax (Bento et al. 2009). Both measures could make

the public more supportive of fuel- or mileage-based taxation (Klenert et al. 2018).

The analysis is organized as follows. Section 2describes the analytical model, which includes

the standard externalities of road transport and the behavioural failure of ignoring health ben-

efits. We derive an analytical result for the optimal fuel tax. Section 3explains our choice of

parametrisation for quantifying second-best fuel taxes and drawing implications for first-best

options. Section 4presents the quantitative results on fuel tax levels, and traces sensitivity

and welfare effects. Section 5discusses limitations of our analysis and explains the context of

our result on fuel taxes in transport economics and policy. Section 6concludes with policy

implications.

2 ANALYTICAL FRAMEWORK

2.1 Model

To explore how the fuel tax might be adjusted optimally to account for health benefits of public

transport, we extend Parry and Small (2005) to include active travel decisions and associated

health benefits. We take advantage of the fact that in certain settings, internalities can be treated

as extensions of externalities (O’Donoghue and Rabin 2006).

We consider a representative agent with the utility function

U=u(𝜓(C,M,Tin,Tac,G),N)−𝜑(P)−𝛿(A)+𝜉(Q),(1)

where Cis the quantity of numeraire consumption, Mis total distance travelled, Tin and Tac

are total time travelled using active and inactive modes respectively, Gis exogenous government

spending, and Nis leisure, with UC,UM,UG,UN>0andUTin ,UTac <0, where the subscript

denotes a partial derivative. The level of pollution is denoted by P, while Acaptures accidents,

and health is denoted by Q. As in Parry and Small (2005), we assume that u(⋅)and 𝜓(⋅)are

quasi-concave, and 𝜑(⋅)and 𝛿(⋅)are convex. The functions 𝜑(⋅)and 𝛿(⋅)capture the disutility

from pollution and accidents, respectively. We add the concave function 𝜉(⋅), which captures the

positive utility from health Q.5

HEALTHY CLIMATE, HEALTHY BODIES 97

Total travel Mcan be separated into two components, inactive travel Min and active

travel Mac:

M=Min +Mac.(2)

Inactive travel denotes travel using modes that require very little physical activity, most impor-

tantly using the car. Active travel instead captures walking and cycling. We also consider

public transport as an active mode of travel, as it typically requires the individual to walk or

bike to the bus stop, tram stop or train station, in some cases providing up to 30% of daily

exercise recommendations (Besser and Dannenberg 2005). As such, active travel requires spend-

ing S, which will be specified further below. Inactive travel distance Min requires fuel F,and

other travel inputs H:Min =𝜒(F,H). In line with Parry and Small (2005), we assume that

Min is homogeneous of degree one with respect to its inputs. This specification allows for

multiple channels of substitution. For instance, as fuel prices increase, the agent can decide

to: (i) reduce total distance travelled M; (ii) spend more on other inactive travel inputs,

H, such as purchasing a vehicle with higher fuel economy; or (iii) increase active travel

distance Mac.

The agent spends time Tin in inactive travel. For a given distance Min,thistimeisincreasing

in the amount of congestion on roads, which we take as an increasing function of the population

average inactive miles travelled, Min:

Tin =𝜋in(Min)Min,(3)

where 𝜋in

Min >0. Here, 𝜋in is equal to the inverse of the speed of inactive travel, which we assume

the agent takes as exogenous. In equilibrium, Min =Min. For active travel, we abstract from

congestion,6and model time travelled as directly proportional to distance:

Tac =𝜋acMac,(4)

with 𝜋ac the inverse of speed from active mobility. Only inactive travel contributes to pollution, in

the form of both carbon dioxide emissions and local air pollution. Carbon emissions are directly

proportional to fuel use. To capture local air pollution effects, inactive miles travelled offer a

better proxy (Hitchcock et al. 2014).7This allows us to write

P=Pf(F)+Pm(Min),(5)

with Pf

F>0andPm

Min >0. We also assume that the agent will take pollution as given; she will not

internalize the effect of travel decisions on the population averages Fand Min.

Both active and inactive travel are subject to accident risk. We assume that agents internalize

own accident risk and separate accident costs associated with active and inactive travel. For inac-

tive travel, accident costs are increasing with the amount of travel. As travel increases, the agent

also imposes an ‘accident externality’ upon other users: the higher average travel Min,themore

likely a road user will be involved in an accident. For active travel, we similarly assume that higher

travel increases the number of, and thereby costs of, accidents. Yet roads that are busier with cars

tend to be more dangerous to both cyclists and pedestrians. Conversely, there exists a so-called

‘safety in numbers’ effect: more cyclists on the road tend to make cycling safer overall (Elvik and

Bjørnskau 2017; Kahlmeier et al. 2017). Hence we assume that the accident costs associated with

active travel are increasing in the average amount of inactive travel Min, and decreasing in average

active travel Mac.Thisgives

98 ECONOMICA

A=Ain(Min,Min)+Aac(Mac,Min,Mac),(6)

with Ain

Min >0andAin

Min >0. Likewise, Aac

Mac >0andAac

Min >0, while Aac

Mac <0.

We assume that active travel is conducive to health. To capture this, we write health as a

function of active travel:

Q=Q(Mac,O),(7)

where Oare other forms of exercise,8with QMac >0andQO>0. We assume that the agent

considers only a constant share 𝜔∈[0,1]of Qas relevant in her optimization problem. Instead

of considering actual health Q, she considers ‘perceived health’ Qper:

Qper =𝜔Q+

Q,(8)

where the agent considers 

Qas outside of her control, while in reality, 

Q=(1−𝜔)Q. Whenever

𝜔<1, equation (8) represents the notion that the individual underestimates the effect of exercise

on health. This underestimation is consistent with substantive evidence that individuals do not

fully appreciate the positive effects of activity-related health (see the subsubsection ‘Rate of health

internalization, 𝜔’ in Section 3), and is also underscored by the existence of policy interventions

encouraging healthy behaviours.9

With equation (8), we adopt a specification of limited attention proposed by DellaVigna

(2009), which assumes that the direct benefit of completing travel (in active mode, Mac)is

‘visible’, while the health benefit Qfrom active travel is ‘opaque’. This seems justified as many

citizens are largely unaware of the high health benefits of even short walks (Fredriksson

et al. 2018; Bennett et al. 2009). Alternatively, the unrealized health benefits from active

travel could represent a case of time-inconsistent preferences (Laibson 1997; O’Donoghue and

Rabin 1999), where citizens highly value their health, but repeatedly postpone undertaking

exercise (DellaVigna and Malmendier 2006). This can be captured by an equivalent formula-

tion of equation (8) in our static model, as the assumption of time-inconsistent preferences

implies that an activity level less than desirable in the long term is pursued at any point

in time.

The agent’s budget constraint is given by

C+(pf+tf)F+phH+poO+S=w(1−tl)L,(9)

where pf+tfis the consumer price of fuel, phis the price of other inactive travel inputs, and

pois the price of other forms of exercise.10 In addition, active travel requires the agent to spend

on items such as a bicycle or public transport. We denote by Sany such spending on active

travel (with normalized price), with S=S(Mac),S(0)=0andSMac >0. Finally, we denote the

gross wage rate by w, and the labour tax rate by tl. The total amount of time available is

given by L, which is allocated to labour L,leisureN, and time spent travelling Tin and Tac,

such that

L+N+Tin +Tac =L.(10)

In the remainder of this paper, we assume that all prices are exogenous and constant. The fuel

tax tfwill be set by the policymaker. The proceeds of the fuel tax will be used to fund government

spending G. The labour tax will in turn be set such that the government budget constraint is

binding:

G=tfF+tlwL.(11)

HEALTHY CLIMATE, HEALTHY BODIES 99

Throughout, we assume that there exists a unique and interior equilibrium, where the

agent chooses strictly positive levels of C,F,H,Mac,Oand L,andthatGis such

that tl>0.

2.2 Second-best fuel tax

In the setup above, an increase in fuel use is associated with carbon emissions. Additionally,

higher fuel use increases the number of miles travelled, which increases local pollution, as well

as congestion and accident risk. All these effects are not internalized by the representative agent,

who takes them as given. On their own, these externalities already justify the introduction of a

positive ‘externality tax’ on fuel. Such a tax will be welfare-improving, as it forces the agent to

internalize (part of) the externality. In addition to the externalities, our framework also features

an ‘internality’: whenever 𝜔<1, the agent underestimates the extent to which higher levels of

activetraveldeliverpositivehealthbenefits. Consequently, the choicesofMac and O, andresulting

Q, may be suboptimally low.

Our aim is to quantify how the consideration of these health benefits of active travel affects the

welfare-maximizing (optimal) fuel tax. For this purpose, we derive the solution for the optimal

fuel tax tf∗, and calibrate its value. We present the full derivation of tf∗in Online Appendix A,

where we obtain the result

tf∗=ZPF+[ZPMin +ZC+ZAMin ](−dMin∕dtf

−dF∕dtf)+ZAMac (−dMac∕dtf

−dF∕dtf)(12)

−(1−𝜔)

ZQ(−dQ∕dtf

−dF∕dtf)−wtl(−dL∕dtf

−dF∕dtf).

Here, we define

ZPF≡𝜑P

𝜇IPf

F,ZPMin ≡𝜑P

𝜇IPm

Min ,ZC≡Γin𝜋in

Min Min,

and

ZAMin ≡𝛿A

𝜇I[Ain

Min +Aac

Min ],ZAMac ≡𝛿A

𝜇IAac

Mac ,

ZQ≡𝜉Q

𝜇I,

with Γin ≡w(1−tl)−𝜓Tin ∕𝜓C.

Equation (12) characterizes the optimal fuel tax. This tax is equal to the sum of uninternal-

ized costs associated with fuel use. The first term in equation (12), ZPF, is the direct pollution

externality of fuel use. It is equal to the marginal cost of pollution 𝜑P, multiplied by the effect of

additional fuel use on pollution Pf

F, and converted to consumption units using the shadow value

of income 𝜇I.

Next, higher fuel use is associated with more inactive miles travelled. The marginal external-

ity cost of inactive miles travelled is captured by ZPMin +ZC+ZAMin , the cost associated with

increased air pollution, congestion and accidents, respectively.11 The contribution of these costs

to the magnitude of the optimal fuel tax depends on the marginal effect of a fuel tax increase

on miles travelled relative to the marginal effect on fuel use. If the reduction in fuel use due to

higher fuel taxes is associated with a small reduction in miles travelled (small (−dMin∕dtf)∕(−

dF∕dtf)), then only a small portion of the externality costs associated with miles travelled can

(implicitly) be attributed to fuel use.

100 ECONOMICA

Likewise, fuel taxes may lead to changes in active travel distance, which is associated with

accident externalities, with cost ZAMac . The contribution of those costs to the optimal fuel tax

then depends on the relative response of active travel to fuel taxes: (−dMac∕dtf)∕(−dF∕dtf).

Our main effect of interest is (1−𝜔)

ZQ(dQ∕dtf)∕(−dF∕dtf): the adjustment of the opti-

mal fuel tax to the health internality. Here, 

ZQis the marginal value of additional health, with

(1−𝜔)the uninternalized portion; see subsubsections ‘Cost of inactivity, ZQ’ and ‘Rate of health

internalization, 𝜔’ in the first subsection of Section 2. As can be seen from equation (12), a high

value of 

ZQdoes not automatically imply that once health internalities are accounted for, the

optimal fuel tax is adjusted much; this is the case only if the fuel tax is an effective tool to increase

health Q. Following equation (7), fuel taxes can affect health through two channels: by changing

active travel Mac, or through other forms of exercise O. The interpretation of the final term is

similar. Fuel taxes may also affect labour supply. Even though the agent takes into account that

higher labour supply increases income, she does not internalize the positive effect of increased

labour on the government budget. This effect is equal to the wage, multiplied by the labour tax

rate wtl. Its contribution to the optimal fuel tax is larger when the increase in labour supply in

response to higher fuel taxes is higher.

In the next section, we quantify the optimal tax tfand the effect of considering the

health benefits of active travel on it. To facilitate this quantification, we further manipulate

equation (12)to

tf∗=MEC

1+MEB +tl(pf+tf)

1−tl

𝜀c

LL(1−𝜂MinI)

−𝜂FF (13)

+tl

1−tl[𝜀LL −𝜀c

LL(1−𝜂MinI)]ZC𝛽Min Min

with 𝜀c

LL and 𝜀LL the compensated and uncompensated labour supply elasticity (and MEC,

MEB defined below). Akin to Parry and Small (2005), this optimal tax is separated into three

components.

The first component of equation (13) is the ‘adjusted Pigouvian tax’, equal to the marginal

external cost associated to fuel use, corrected by the marginal excess burden of labour taxation.

The marginal external cost (MEC) of fuel use is given by

MEC ≡ZPF+[ZC+ZAMin +ZPMin ]𝛽Min Min

F(14)

+[ZAMac −(1−𝜔)(1−𝜍)ZQ]𝛽Mac Mac

with ZQ≡(𝜉Q∕𝜇I)QMac the marginal value of active travel through induced changes in health.

This latter term is corrected by a factor (1−𝜍), which captures the unrealized share of health

benefit from increased active travel due to crowding out of other exercise O:

𝜍≡−QO

QMac [dO∕dtf

dMac∕dtf].

We use the following ratios of fuel and income price elasticities to capture the indirect benefits of

fuel taxes through inactive and active distance travelled and health:12

𝛽Min ≡𝜂MinF

𝜂FF ,𝛽

Mac ≡𝜂MacF

𝜂FF ,(15)

HEALTHY CLIMATE, HEALTHY BODIES 101

with 𝜂XF the fuel price elasticity of X∈{F,Min,Mac},and𝜂MinIthe income elasticity of inactive

travel. The marginal excess burden (MEB) is commonly defined as

MEB ≡(tl∕(1−tl))𝜀LL

1−(tl∕(1−tl))𝜀LL .(16)

The second component of equation (13) is the ‘Ramsey tax’: fuel taxes raise revenues, which are

used to finance government spending. This component commands a positive tax on fuel even in

the absence of external costs. The third component is the ‘congestion feedback’: a reduction in

travel due to fuel taxation reduces congestion, freeing up time for labour. This creates a positive

welfare effect as long as labour is taxed at a positive rate (tl>0), and as such increases the optimal

fuel tax.

3FUEL TAX COMPONENTS

In this section, we explain how we choose the parameter values for the quantification of the

optimal fuel tax. We specify a central value and a plausible range. Table 1summarizes the main

parameter values, and Figure 1provides a graphical representation of the social costs Zexpressed

in 2022 USD. We compare our parametrization of social cost to Parry and Small (2005), and state

the implications for first-best policy. We base our values on the most recent available publications

or official datasets.

Table 1and Figure 1highlight that the social cost of inactivity is one to two orders of

magnitude larger than that of the second-largest social cost: congestion. While this difference is

TABLE 1 Parameter Values Used for Optimal Fuel Tax Calculation and Sensitivity Analyses

USA UK

Parameter Central value Range Central value Range

Baseline fuel efficiency Min,0∕F024 28

Fuel pollution (CO2), per gallon ZPF160 [74,347.5]150 [69,323]

Distance pollution (air), per mile ZPM5.4 [1.2,10.7]4.3 [1.2,9.6]

Congestion, per mile ZC11.9 [3.6,16.7]6[0.1,8.7]

Accidents, inactive, per mile ZAMin 7.6 [2.4,21.5]1.9 [1.2,2.7]

Accidents, active, per mile ZAMac 6.3 [1.8,17.9]1.9 [1.4,3.1]

Inactivity, per mile ZQ825 [481.1,1192.7]291.3 [174.4,815.4]

Rate of health internalization 𝜔0.5 [0.3,0.7]0.5 [0.3,0.7]

Fuel price elasticity 𝜂FF −0.36 [−0.21,−0.75]−0.48 [−0.3,−0.9]

VMT-fuel price elasticity 𝜂MinF−0.25 [−0.05,−0.3]−0.35 [−0.2,−0.5]

Income elasticity of inactive travel 𝜂MinI0.4 [0.02,0.6]0.61 [0.3,0.8]

Cross-elasticity of active travel 𝜂MacF0.19 [0.06,0.31]0.19 [0.06,0.31]

Current tax rate on gasolineat0

f50.2 n.a. 381.7 n.a.

Notes: aIncludes VAT for the UK but not the USA.

All values apart from fuel efficiency are provided in 2022 USD cents using the end 2022 exchange rates 1 GBP =1.21 USD, and either

per mile or per US gallon. Baseline fuel efficiency is provided in miles travelled per US gallon. Min,0and F0denote intensive miles

travelled and fuel used at the initial gasoline tax rate. Justification for the social cost values is given in the subsubsections ‘External cost

of carbon emissions (fuel pollution), ZPF’ to ‘Rate of health internalization, 𝜔’ in the first subsection of Section 3.

102 ECONOMICA

FIGURE 1 Social costs of personal car travel in US cents per mile in 2022 prices, fuel pollution in US cents per

gallon; own calculations. Notes: Distance pollution comprises local air pollution; fuel pollution accounts for climate

damages.

in part due to the difference in travel time between motorized transport and walking or cycling,

it signals the potential importance of health benefits for optimal fuel taxes.

3.1 Parametrization

3.1.1 Baseline fuel efficiency and elasticities

•Baseline fuel efficiency and taxes.WesetMin,0∕F0according to average fuel efficiency of the

UK and US vehicle fleets. The US average was 24 miles per gallon in 2016 (Federal Highway

Administration 2018), and the UK average was 28 miles per gallon (Department for Transport

(DfT) 2018b). These values have not changed substantially since 2016, as more energy-efficient

cars are counterbalanced by the greater adoption of sports utility vehicles in both countries.

The difference in fuel efficiency is due to a smaller average size of the UK private vehicle fleet,

and a higher proportion of diesel cars, which have a higher average fuel economy. The social

cost estimates of carbon emission and air pollution per mile account for the fleet composition.

Baseline (current) fuel tax levels are calculated differently for the two countries. For the UK,

it is the sum of the fuel, excise and value-added taxes. For the USA, it is the average over the

different federal and state taxes.

•Fuel price elasticities. Based on Dieler et al. (2015) and Litman (2013), we choose a fuel price

elasticity 𝜂FF =−0.38 for the USA as a central estimate. This is slightly less elastic than the

UK value −0.45, where there are more public transport options. The elasticities of inactive

miles travelled (VMT) with respect to fuel price 𝜂MinFare calibrated at −0.25 in the USA,

and −0.35 in the UK.13

To our knowledge, very few direct estimates of the cross-elasticity of active travel (walking

and cycling), with respect to the fuel price 𝜂MacF, exist. Instead, we utilize primarily estimates

HEALTHY CLIMATE, HEALTHY BODIES 103

of the cross-elasticity of public transport with respect to fuel price (Litman 2019). The use of

public transit requires getting to and from stations, often on foot or by an alternative active

mode, and certain public transit investments have been found to be an effective way of increas-

ing active travel (Reis et al. 2016). We adopt a range 0.06–0.31 for 𝜂MacF, with central value

0.185 for both the USA and the UK. We conduct a further sensitivity analysis for the UK,

where we increase the possible range of 𝜂MacFby an additional standard deviation (see Section

B.2 of the Online Appendix).

•Income elasticity of inactive travel. The elasticity of inactive travel demand with respect to

income, 𝜂MinI, is calibrated at 0.4 (0.02–0.6) for the USA, and 0.605 (0.3–0.8) in the UK. We

use long-term elasticities where possible to allow for mode shifts and other behaviour changes.

Further details and a full list of references on fuel price and income elasticities can be found

in Section B.2 of the Online Appendix.

•Labour supply elasticities. For the compensated and uncompensated labour supply elasticities,

𝜀c

LL and 𝜀LL, we adopt the same values as Parry and Small (2005). These estimates fall in

between the more recent estimates by Bargain et al. (2011) and Erosa et al. (2016).

3.1.2 External cost of carbon emissions (fuel pollution), ZPF

The external costs of fuel use are the cost of carbon emissions and associated climate damages.

We derive our central estimate and range of plausible values from a large body of literature

(see Section B.3 of the Online Appendix for a full overview). We multiply the value of climate

change costs per tonne of CO2emitted by the amount of CO2emitted per gallon of fuel burnt,

weighted by fuel type consumption in both countries (diesel/gasoline) to derive an average value

of fuel pollution costs per gallon of fuel.14 With a social cost of carbon $158 per tCO2and range

$73–343 per tCO2, the central estimate for the USA is 160 cents per gallon, with range 74–348

cents per gallon. The central estimate for the UK is 150 cents per gallon, with range 69–326 cents

per gallon.

Carbon emissions per gallon are subsequently converted into per mile units by dividing by

baseline fuel efficiency as presented in Table 1. Throughout, we abstract from any effects of fuel

taxation on the cost of carbon.

3.1.3 External cost of air pollution (distance pollution), ZPin

Local air pollution is caused by car tyre and break wear emissions of PM2.5and PM10,which

are approximately proportional to miles travelled, and by gases from incomplete fuel combustion

processes. For the USA, estimates of the cost of air pollution per mile range from high value

$0.089 (OECD 2015) to extremely low value $0.007 (Muller et al. 2011), with several values in

between, for example, $0.03 in Mashayekh et al. (2011), and $0.06 in Parry et al. (2014). To reflect

this uncertainty, we adopt values $0.012, $0.054 and $0.107 as the low, central and high estimates

for the USA, respectively.

For the UK, national project evaluations use a value $0.036 per mile (Hitchcock et al. 2014).

OECD (2015) reports a high value $0.08 per mile travelled, while the average for a passenger

car in the EU is estimated at $0.009 per mile for gasoline and $0.033 per mile for diesel cars.

Reflecting the 55–45% split between gasoline and diesel cars in the UK, and updated costs of air

pollution (Birchby et al. 2019), we adopt values $0.012, $0.043 and $0.096 as the low, central and

high estimates.

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104 ECONOMICA

3.1.4 External cost of congestion, ZC

Congestion is defined as the travel delay due to crowding of roads. For the USA, we adopt the

values of Inrix (2019a), which provides a central value $0.119 per mile, and range $0.036–0.167

per mile. In the UK, we follow Inrix (2019b) and set the per-mile congestion costs at $0.06, with

lower and upper bounds $0.001 and $0.087, respectively.

3.1.5 External cost of accidents, ZAMin and ZAMac

There are two components to accident costs: the internalized cost of knowing and accounting for

the risk of getting into a crash (see Useche et al. (2019)andCornagoet al. (2023) for empirical

support); and the external cost of the increased risk of causing an accident imposed on others by

travelling.15 Hence using the full cost of accidents per mile driven would overestimate the size of

the accident externality. Instead, we adopt the approach by Lemp and Kockelman (2008), who

estimate the external costs of transport in the USA and assume that 50% of accident costs are

external.16

Using accident data and cost estimates from the report by Blincoe et al. (2015), we find that

accident costs attributable to inactive modes of transport, ZAMin , amount to $0.076 per mile,

with range $0.024–0.215 per mile for the USA. Accident costs attributable to active modes of

transport, ZAMac , amount to $0.063 per mile, with range $0.018–0.179 per mile. The relatively

high accident cost attributed to active transport modes is due to the proportionately higher death

rate per mile travelled for active modes.

In the UK, ZAMin amounts to $0.019 per mile, with range $0.012–0.027 per mile. Accident

costs attributable to active modes of transport, ZAMac , amount to $0.019 per mile as well, with

range $0.014–0.027 per mile (DfT 2018a).

3.1.6 Cost of inactivity, ZQ

The health benefits of exercise are well known to be the most substantial health-related impact

of active travel, dwarfing air pollution or accident effects. For example, De Hartog et al. (2010)

estimate, for the Netherlands, that people shifting from car to bicycle for short trips lose 7 days

of life due to traffic accidents, and 21 days of life due to air pollution, but gain 8 months of

life due to physical activity. This relationship is confirmed for Global North countries, where

road safety is much better compared to many Global South cities (Woodcock et al. 2017;Garcia

et al. 2021). Our analysis requires translating such benefits into monetary values for the USA and

the UK.

First, health benefits comprise all mortality- and morbidity-reducing effects. Second, there

may be productivity benefits, due to a reduction in absenteeism (taking sick leave), and pre-

senteeism (being at work but having lower productivity due to illness). Third, better health

reduces (public) health system costs. Depending on the characteristics of the health system (and

the extent to which the individual bears the cost of absenteeism), the costs can be labelled

as private or external. In the remainder of the analysis, we focus on the value of unrealized

private health benefits only, as they are much larger than the direct productivity gains to the

economy.

In order to calculate the marginal value of the private health benefits from physical activity

for the UK and the USA, we used the Health Economic Assessment Tool (HEAT) developed

by the World Health Organization (Kahlmeier et al. 2017). HEAT calculates the value of the

changes in mortality arising from a specified change in walking and cycling for travel purposes.17

HEALTHY CLIMATE, HEALTHY BODIES 105

Further details regarding the HEAT model, inputs and corresponding data sources can be found

in Section B.4 of the Online Appendix.

We convert the HEAT output to an estimate of the health benefit per mile of active travel. We

obtained a central ZQvalue $8.25 per mile for the USA, with range $4.81–11.93 per mile. For

the UK, this value is $2.91 per mile, with range $1.74–8.15 per mile. The UK–USA discrepancy

has two sources: higher value of statistical life estimates for the USA, and higher US baseline

mortality rates for younger members of the population.

3.1.7 Rate of health internalization, 𝝎

The extent to which individuals internalize the health benefits of exercise and active travel is

captured by the parameter 𝜔. Estimating internalities is inherently empirically complex, and as a

consequence there are relatively few well-identified empirical estimates regarding the size of the

internality. Examples of studies that are informative about the size of the internality are Haase

et al. (2004), Coups et al. (2008) and Bennett et al. (2009), who find that individuals underestimate

the probability of disease associated with physical inactivity.

To obtain a proxy for 𝜔, we consider three types of studies: first, stated preference sur-

veys of cyclists/pedestrians and drivers on their reasoning for choosing that particular mode

of transport (see Table 2); second, surveys asking the general population about their knowl-

edge of the health benefits of physical activity (see Table 3); and third, results from experiments

and policies aimed at incentivizing health behaviour (see Table 4). While they find substan-

tial variation in the extent to which individuals do, or do not, internalize health benefits

of physical activities, these studies provide overwhelming evidence that this internalization is

incomplete, that is, 𝜔<1. In Section B.5 of the Online Appendix,wesummarizethedetails

of the studies listed in Tables 2–4. Based on this exercise, we choose a central value 0.5 and

range 0.3–0.7 for 𝜔, to be transparent about the broad range of estimates and their high

uncertainty.

3.1.8 Crowding out of other exercise, 𝝇

The empirical literature shows little to no effect of fuel taxes on other forms of exercise O. Specif-

ically, the review by Wanner et al. (2012) finds no systematic evidence in favour of crowding in

or out, and more recent studies generally suggest that exercise through active travel is additive,

rather than crowding out other forms of exercise (Dons et al. 2018;Foleyet al. 2015;Laere-

mans et al. 2017; Martin et al. 2015;Paniket al. 2019). Based on this, we set 𝜍=0, implying that

active travel is the only channel through which fuel taxation affects health. While the evidence in

Martin et al. (2015) could also justify low positive values of 𝜍, the sensitivity analysis for the rate

TABLE 2 Studies of Stated Reasons for Walking and Cycling Regularly

𝜔Question Source

0.52 Factors affecting cycling Börjesson and Eliasson (2012)

0.82 Factors affecting cycling to work Fernández-Heredia et al. (2014)

0.42–0.94 Factors affecting cycling to work De Souza et al. (2014)

0.68 Factors affecting cycling De Geus et al. (2008)

0.38 Factors affecting cycling Useche et al. (2019)

106 ECONOMICA

TABLE 3 Studies of Health Awareness Used for the Calculation of the Rate of Health Internalization

𝜔Question Source

0.4–0.6 Link with heart disease Haase et al. (2004)

0.6 Link with cancer Oh et al. (2010)

0.15 Link with cancer Coups et al. (2008)

0.3 Link with cancer Keighley et al. (2004)

0.5 Link with diabetes San Diego and Merz (2020)

0.2–0.8 Probabilities of developing diseases Fredriksson et al. (2018)

0.5 Knowledge of weekly guidelines Morrow Jr et al. (2004)

0.33 Knowledge of weekly guidelines Bennett et al. (2009)

0.01 Knowledge of weekly guidelines Kay et al. (2014)

0.44 How much movement is needed Fredriksson et al. (2018)

0.22 Knowledge of weekly guidelines Piercy et al. (2020)

0.5 Knowledge of own activity levels Ronda et al. (2001)

0.4–0.6 Knowledge of own activity levels Godino et al. (2014)

TABLE 4 Studies of Behaviour Bias Used for the Calculation of the Rate of Health Internalization

𝜔Question Source

– Overprojection of gym attendance DellaVigna and Malmendier (2006)

– Overprojection of gym attendance Acland and Levy (2015)

0.57–0.7 Response to incentive & commitment Charness and Gneezy (2009)

0.65 Response to incentive & commitment Royer et al. (2015)

1 Response to commitment Carrera et al. (2018)

of health internalization 𝜔also applies for varying 𝜍. The reason is that an increase in 𝜍has an

effect on the optimal tax equivalent to an increase in 𝜔(see equation (14)).

3.2 Social cost comparison to Parry and Small (2005)

Figure 2specifies the parametrization of social costs in Parry and Small (2005) in US cents per

mile travelled and updated to 2022 prices. A comparison of Figures 1and 2reveals that in par-

ticular, the social cost of carbon, and therefore the fuel pollution component of the fuel tax,

has increased in value. While it was a minor component of the optimal fuel tax in Parry and

Small (2005), it contributes significantly to the tax in our parametrization. In addition, while

Parry and Small (2005) estimated UK congestion costs at twice the value of the US congestion

cost, our parametrization based on Inrix (2019a,b) reverses these values. Going beyond Parry

and Small (2005), we show that the social cost of inactivity is at least an order of magnitude larger

than all the passenger transport externalities (see Table 1and Figure 1).

HEALTHY CLIMATE, HEALTHY BODIES 107

FIGURE 2 Social costs of personal car travel in US cents per mile in 2022 prices; Parry and Small (2005)

calculations.

3.3 Implications for first-best policy

Table 1and Figure 1permit a quantitative conclusion about first-best policy. In a first-best world,

there exist appropriate policy instruments to address all market failures, as well as non-distortive

(e.g. lump-sum) taxes to generate government revenues. One can verify that under these

assumptions, the optimal carbon (fuel) tax is equal to the cost of fuel pollution ZPF. Similarly,

the socially optimal level of the price instruments for all other externalities (and internality, by

analogy, that is paying individuals for active travel and other exercise) are at their respective

Pigouvian levels. For the internality, this Pigouvian level is equal to the social cost of inactivity,

multiplied by the uninternalized share (1 −𝜔). On a per-mile basis, this means that a first-best

subsidy paid to individuals for incentivizing active travel modes would be at a much higher level

than any of the tax levels for the externalities, or indeed, the sum of all other externality taxes.18

4QUANTITATIVE RESULTS

4.1 Second-best optimal fuel tax rates

We use equations (13)–(15) and the parameter estimates provided in Table 1to calculate the

optimal fuel tax.19 An increase in fuel taxation will reduce fuel use and inactive miles travelled,

which will in turn affect the optimal tax through equation (14). To account for those effects, we

follow Parry and Small (2005), and endogenize F,Min and Mac in our numerical solution (see

Section B.6 of the Online Appendix).

We find an optimal fuel tax $6.31 per gallon of fuel in the UK, which is significantly

higher than the current fuel tax.20 In the USA, the optimal fuel tax amounts to $12.92 per

gallon of fuel, which is more than twenty times the current (population-weighted) average fuel

tax across the fifty states. Table 5lists the optimal tax levels and their decomposition. This

decomposition shows that costs associated with physical inactivity, congestion and fuel pollution

108 ECONOMICA

TABLE 5 Central Calculations of the Optimal Fuel Tax Rate

Cost, USD cents per gallon USA UK

Fuel efficiency, Min∕F28.4 29.3

Adjusted Pigouvian tax:

Pollution, fuel-related, ZPF160 150

Pollution, distance-related, ZPMin 𝛽Min Min∕F107 92

Congestion, ZC𝛽Min Min∕F235 128

Accidents, inactive, ZAMin 𝛽Min Min∕F150 41

Accidents, active, ZAMac 𝛽Mac Mac∕F−5−2

Physical inactivity, (1−𝜔)ZQ𝛽Mac Mac∕F305 159

Adjustment to MEC for excess burden −89 −51

Ramsey tax 430 108

Congestion feedback −14

Optimal fuel tax rate with physical activity, tf∗

11292 631

Optimal fuel tax rate without physical activity 899 456

Naive fuel tax rate 758 492

Parry and Small optimal tax rate 177 235

Actual (2023) tax rate 50 382

Notes: Based on equations (13)and(14), the optimal rate is the adjusted Pigouvian tax, adjustments for the excess burden, the Ramsey

tax, and the congestion feedback, combined. The naive rate is given by MECF(excluding the health internality) from equation (14)with

Min∕F=Min,0∕F0,𝛽Min =1and𝛽Mac =−1.

are the main contributors to the adjusted Pigouvian tax, albeit it is somewhat reduced due to

the compensation for the marginal excess burden of labour taxation. Ramsey taxes are substan-

tial, especially in the USA; the congestion feedback does not influence the optimal fuel tax rate

significantly.

Including physical activity increases the UK fuel tax by 38%, and the US fuel tax by 44%.

Although this increase is significantly smaller than the pure per-mile social cost of physical inac-

tivity, the inactivity component is still the largest contributor to the MEC part of the tax. Even

without including physical activity, we obtain an optimal fuel tax that is two to five times the

tax computed by Parry and Small (2005) (adjusted to 2022 values), which is due to much higher

current values on social cost of carbon predominantly.

Consistent with both Parry and Small (2005) and Santos (2017), we find that for the USA,

the second-largest externality component of the second-best optimal fuel tax is congestion. For

the UK, the contribution of fuel pollution (CO2) exceeds the contribution of congestion. This is

despite the fact that London, whose congestion impacts are 28 times higher than the EU average

(Cookson 2016), greatly influences the congestion costs for the UK.

Fuel pollution is a substantial contributor to optimal fuel taxes as the social cost of car-

bon has increased significantly over the last two decades, reflecting increasing estimated climate

damages (see the second subsubsection of the first subsection of Section 3). Contrary to Parry

and Small (2005), air pollution costs for both countries contribute less to the fuel tax than

carbon emissions. This is due primarily to increasingly stringent fuel air pollutant emissions

standards.

HEALTHY CLIMATE, HEALTHY BODIES 109

In the USA, traffic accidents are associated with a far higher per-mile cost, even though the

rates of traffic injuries are very similar in both countries. This is explained by a higher nominal

value that is attached to human life in the USA,21 and leads to a fuel tax component due to the

inactive travel accident externality of inactive travel that is considerably higher in the USA than

in the UK.

In addition to the second-best optimal tax, we compute the ‘naive’ tax rate, which is based

on three assumptions. First, in absolute terms, all 𝛽terms are equal to 1; that is, both active and

inactive miles travelled are equally responsive to fuel taxation as fuel use. Second, the feedback

of tax-induced changes in fuel use and miles travelled to the tax rate is ignored. Third, interac-

tions of the fuel tax with the labour tax, as well as the Ramsey component, are abstracted from.

Instead, the only relevant components to the tax are the external effects of car use. The naive rate

thus mimics common practice in transport and cost–benefit analysis evaluations.22 In our central

calculations, 𝛽Min =0.69 (USA) or 𝛽Min =0.73 (UK), and 𝛽Mac =−0.51 (USA) or 𝛽Mac =−0.39

(UK). Values 𝛽Min <1 are due to a low fuel price elasticity of inactive travel, 𝜂MinF. This reflects

the very inelastic demand for VMT, meaning that most reduction in fuel use comes from increases

in fuel economy of driving and the vehicle fleet, not reductions in distances covered in cars. Thus

mileage-related externalities (air pollution, congestion and accidents) are all inflated in the naive

fuel tax calculation.

Treating fuel efficiency, fuel consumption and distance travelled as endogenous, rather than

exogenous, in the second-best optimal fuel tax calculation causes fuel consumption to fall by

42.5% and 15.6% in the USA and UK, respectively. Inactive travel Min falls slightly less, by 32%

in the USA, and this is more than compensated for by an increase of 33% in active travel. In

the UK, inactive travel also falls by less than fuel consumption, by 11.6%. However, as active

travel increases by only 6.7%, total travel in the UK falls. The change is more drastic in the USA

because of the low fuel efficiency of motor vehicles, and higher contingent valuation of people’s

time and lives, resulting in a bigger Pigouvian tax. In the UK, the current tax level is much closer

to the optimal level. The fuel efficiency of motor vehicles in the UK therefore does not change

much in response to moving to the optimal level, and the endogenous solution does not change

the optimum level significantly.

4.2 Welfare effects

The welfare gain of implementing the second-best optimal fuel tax is presented in Table 6.We

use the current tax rate as a benchmark, and consider a fuel tax that does, and does not, take

into account active travel benefits. All gains are expressed as a share of current fuel expendi-

ture. The analytical derivation of the welfare benefit is discussed in Section B.7 of the Online

Appendix. The welfare gain of implementing the second-best optimal tax that accounts for the

health internality is 115% for the USA, but only 4% for the UK. Contrary to the UK, in the

USA, any increase in the fuel tax yields significant welfare improvements. This difference is pri-

marily due to the very low current US fuel tax, while the UK fuel tax is already closer to the

optimal rate.

Additionally, we present the changes in active and inactive miles travelled following the

change in the fuel tax. In the UK, the small change in the fuel tax results in relatively small

changes in distance travelled. In the USA, however, the fuel price changes are large, and induce

a substantial shift from inactive to active miles.23

Finally, we compute the effect of the tax increase on mortality through increased active

travel using the HEAT tool, described in the subsubsection ‘Cost of inactivity, ZQ’ of the first

subsection of Section 3, and Section B.4 of the Online Appendix. Increases in active travel

save lives only by improving health from increasing exercise (see also Section B.8 of the Online

Appendix).24 Due to a larger tax increase and larger population size, lives saved are greatest in

110 ECONOMICA

TABLE 6 Welfare Effects of Fuel Taxation

Fuel tax type Rate (cents Welfare Min Mac Annual Lives per $ per

per gallon) change change change lives 100,000 population

USA

tf∗1292 114.68% −31.95% 32.96% 6262 saved 0.24

tf, excl. health 899 63.98% −26.91% 26.11% 4960 saved 0.28

tf∗631 3.93% −11.61% 6.74% 280 saved 0.25

tf, excl. health 456 0.40% −4.12% 2.25% 93 saved 0.28

Notes: Welfare effects calculated relative to the current fuel tax rate, expressed as a percentage of current fuel expenditure (approximately

$1800 in the USA, and $1500 per person per year in the UK, according to household expenditure surveys (US Bureau of Labor

Statistics 2019; Office for National Statistics 2019). The current US fuel tax rate is $0.50 per gallon, and the current UK fuel tax rate is

$3.82 per gallon. The last column reports the number of lives saved due to increased active travel per a one dollar change in the tax, per

100,000 population.

the USA: setting the fuel tax at its optimal level saves 6262 lives each year. The difference of

0.24 versus 0.25 lives saved per unit tax change, per a unit of 100,000 population in the USA

and UK, respectively, is negligible, largely due to the cross-elasticity of active travel. The gain

is achieved by increasing active travel by 0.03 and 0.11 miles per day for the UK and the USA,

respectively.

4.3 Sensitivity analysis

In Figure 3, we illustrate the sensitivity of the second-best optimal fuel tax with respect to the

elasticities and rate of health internalization, keeping all other parameters at their central values

(denoted X in the graphs). Figure B.2 in the Online Appendix presents additional results where

we vary the cost parameters Z. Importantly, as the potential rate crowding out (1−𝜍)is directly

multiplicative with the rate of internalization (1−𝜔)in our model (see equation (14)), we do not

carry out sensitivity analysis around the degreeof crowding out. If a value of crowding out greater

than zero should be tested (see the final subsubsection of the first subsection of Section 3), this is

equivalent to greater internalization. Further details and figures can be found in Section B.9 of

the Online Appendix.

For both the UK and the USA, the fuel tax is most sensitive to 𝜂FF , the fuel price elas-

ticity. This elasticity affects the optimal fuel tax directly through 𝛽Min and 𝛽Mac in the MEC

component (see equation (14)), and indirectly by governing the response of fuel use Fto the

introduction of the fuel tax. Jointly, this results in a positive relationship between the fuel price

elasticity and the optimal fuel tax, as shown in Figure 3. Using the upper or lower bound of

the fuel price elasticity, as opposed to the central value, can either increase or decrease the fuel

tax by as much as 75%. Varying the cross-elasticity of active travel 𝜂MacFhas a similar, though

smaller, effect. Conversely, the net effect of the elasticity of inactive travel (VMT) with respect to

the fuel prices, 𝜂MinF, on the fuel tax is negative. Using the upper bound instead of the central

value for 𝜂MinFreduces the fuel tax by up to 70%; using the lower bound instead has a notice-

ably smaller effect. The income elasticity of inactive travel affects the fuel tax, especially for the

USA. This effect materializes via the Ramsey tax component, which is comparatively large for

the USA to begin with (see Table 5). The fuel tax is relatively insensitive to the rate of health

internalization.

HEALTHY CLIMATE, HEALTHY BODIES 111

5.Health internalisation rate

3.VMT−fuel price elasticity 4.Income elasticity of inactive travel

1.Fuel price elasticity 2.Cross elasticity of active travel

0.3 0.4 0.5 0.6 0.7

−0.5 −0.4 −0.3 −0.2 −0.1 0.2 0.4 0.6 0.8

−0.8 −0.6 −0.4 −0.2 0.10 0.15 0.20 0.25 0.30

500

1000

1500

2000

500

1000

1500

2000

500

1000

1500

2000

Value

Optimal tax, cents/gallon

Country

FIGURE 3 Sensitivity of the fuel tax to relevant elasticities and the rate of health internalization.

The fuel tax in both the USA and the UK increases approximately linearly with all social cost

parameters and the cost of inactivity (i.e. ZPF,ZAMin ,ZAMac ,ZPMin ,ZCand ZQ), reacting most

strongly to ZPF, fuel pollution, that is, the social cost of carbon. For more details, see Section B.9

of the Online Appendix.

Figure 4presents the results of a Latin hypercube parameter sensitivity analysis using the

pse package in R (Chalom and de Prado 2015). We varied parameters for external costs and the

elasticities using 20 values drawn at random from a uniform distribution, and allowed fuel use

and mileage to be generated endogenously. The function was run 200 times, with 50 bootstrap

112 ECONOMICA

0.00

0.25

0.50

0.75

1.00

0 500 1000 1500 2000

Tax, cents/gallon

Probability <= X

FIGURE 4 Cumulative distribution function of optimal fuel tax values for both the USA and the UK.

replicates. For the USA, the optimal fuel tax is less than 0.01% likely to be below the current 50

cents per gallon. For the UK, the optimal fuel tax is below the current fuel tax of 382 cents per

gallon with a 2% probability.

5DISCUSSION

This paper shows that it may be costly to societies not to reap the health benefits from choosing

travel modes that lead to more physical activity. Including these benefits in an analysis of optimal

fuel taxation demonstrates that the optimal fuel tax increases significantly, although to a lesser

extent than one might expect based on assessments of the benefits of active travel measured in

public health. Here, we discuss how our findings align with current thought on optimal transport

policy, and subsequently discuss limitations of our approach.

Experts on urban transport policy have long argued for a mix of ‘push’ and ‘pull’ factors to

reduce efficiently societal costs from car use (Pucher and Buehler 2007; Creutzig and He 2009).

‘Push measures’ discourage car use and include fuel or road pricing and parking fees; ‘pull mea-

sures’ encourage uptake of other forms of transport by making them more attractive. Our study

considers explicitly only a fuel tax, but a number of conclusions about other policy instruments

may be drawn.

First, both active and inactive miles travelled are relatively inelastic to the fuel tax. This

not only affects the second-best optimal level, but also implies that a fuel tax on its own is not

an ideal instrument for reducing mileage-related externalities.25 Parry and Small (2005) suggest

that using a VMT tax for all externalities other than carbon emissions would be preferable.

Indeed, there is renewed academic interest in alternative road pricing mechanisms, such as con-

gestion or GPS-based charging, cordon pricing, optimal toll pricing or real-time road pricing

(see Guo et al. 2017;Cramtonet al. 2018; Bjertnæs 2019; Arlinghaus et al. 2023). However,

HEALTHY CLIMATE, HEALTHY BODIES 113

ideal externality-correcting mechanisms have not been implemented widely, and most plans to

introduce congestion charging are advancing slowly. The benefit of the fuel tax over a congestion

charge is that a fuel tax can, at least indirectly, address all large externalities caused by driving

concurrently, and be used to generate a broader revenue base for the government (Rietveld and

van Woudenberg 2005). It also encourages improvements in the fuel economy of the fleet by

encouraging the purchase of more efficient new cars, and in some cases, more fuel-efficient driving

patterns (Dhondt et al. 2013; Bjertnæs 2019).

Second, our study has further implications for policies encouraging active transport. Akin

to congestion charges, a straightforward public finance approach could involve a direct subsidy

foractivemodesoftravel(Wardmanet al. 2007; Employee Benefits Scheme 2020) or indirect

subsidies in the form of suitable cycling and washing facilities for employees that would improve

the comfort of cycling relative to driving (Useche et al. 2019).

Appropriate active travel infrastructure may, however, be a more important ‘pull’ measure to

make walking and cycling attractive. Car-free city centres, bicycle lane networks and improve-

ments in public transport provision will increase the mode share of active travel (Pucher and

Buehler 2007; Buehler and Pucher 2012; Gössling 2013; Kraus and Koch 2021). For example,

in a study of 167 European cities, Mueller et al. (2018) find that increasing bicycle lane infras-

tructure in urban areas up to 315 km per 100,000 inhabitants increases the mode share of cycling

up to 24.7%. Further, the lack of appropriate street lighting, and badly maintained roads and

cycle lanes, have all been identified as factors impeding active commuting (Yang et al. 2017;Fed-

eral Highway Administration 2019). Investing in cycling infrastructure has not been considered

a significant investment strategy until recently, and infrastructure cost assessments have not been

including it in their analyses (van Essen et al. 2011). Due to the large differences in the effective-

ness of cycling infrastructure investments, or alternatively soft, information-based measures, it is

difficult to estimate their effectiveness relative to a fuel tax change.

Our optimal tax result signals that the extent to which an increase in fuel taxes is welfare

enhancing is constrained by the presence of viable low-carbon alternatives (high 𝛽terms). This

result was also demonstrated by Martens (2016), and (in part) justifies the grievances of the Gilets

Jaunes in France and similar movements. Conversely, this implies that improvements in infras-

tructure designed for active travel and public transport as discussed above could further support

increased fuel taxation.26 While greater willingness of citizens to switch to active travel in par-

ticular would manifest itself in a higher responsiveness of active travel to fuel taxation, 𝜂MacF,it

would likely also result in higher active miles travelled Mac, lower fuel use F, and higher (absolute)

elasticities 𝜂MinF. From equations (13)–(15), all of these effects would justify higher fuel taxes.

A full characterization of the ‘pull effect’, would include the public good charac-

teristics of infrastructure—everyone benefits from safer and more comfortable cycling

infrastructure—which will lead individuals to derive more utility from active travel and there-

fore ‘pull’ them into these modes. This channel is not considered in our model and yet could

lead to either higher or lower second-best optimal fuel taxes (Siegmeier 2016), once infrastructure

changes are seen as an additional policy instrument rather than an exogenous change in elastici-

ties (similar to Bovenberg and van der Ploeg 1994). In other words, as improved public transport

infrastructure moves active travel decisions closer to optimal decisions, it may reduce the need

for and value of higher fuel taxes as captured through ZQ. We believe that this is a crucial area

for further work.

We note a number of limitations to our study: health manifests itself only as an internality

within the utility function, though there is evidence that health–labour feedback loops might

exist,specifically betweenphysicalactivityand productivity(Proper et al. 2006), and presenteeism

(Pereira et al. 2015). We abstract from these effects in our analysis; if anything, including such

effects would strengthen the case for including health benefits from active travel in transport

policy assessments. Also, our model is not designed for an accurate assessment of the potential

114 ECONOMICA

of subsidizing non-travel-related physical exercise, in part because it is not straightforward to

include a time cost of such ’other exercise.

Furthermore, our estimate of the degree of internalization is arguably crude: that levels of

inactivity vary between countries merits further empirical studies of the rate of internaliza-

tion and its determinants. It is, for instance, conceivable that the rate of internalization may be

affected by (tax) policy, transport infrastructure and geography. There also exists evidence that

in particular, interventions that support planning and commitment for exercise are effective in

increasing exercise levels (Charness and Gneezy 2009;Royeret al. 2015). While such interven-

tions would arguably reduce the internality, as long as they do not lead to full internalization,

a rationale for including health benefits in the optimal fuel tax computation remains. This said,

we would like to stress that the model framework is ignorant about the determinants of the

rate of internalization. Insofar as this is influenced by alternative interventions such as informa-

tional campaigns or access to commitment devices, the optimal fuel tax is affected. This could

include health policy interventions to generally increase levels of exercise (say, mandated track-

ing of total exercise through step counters and appropriate fiscal incentives by health insurance

companies). As such, our analysis does not rule out the relevance of alternative policy inter-

ventions; rather, it highlights the implications of any remaining internalities for optimal fuel

taxation.

Further, we do not consider distributional concerns of the policy instruments, especially

related to income, location or race (see Bento et al. 2009; Tessum et al. 2019;Creutziget al. 2020).

In the context of fuel taxation with health internalities, at least five types of distributional effects

are at play: first, the fact that relative spending on transport fuels differs with income (Grainger

and Kolstad 2010;Sterner2012); second, the empirical observation that fuel price elasticities

depend on household income levels and that this relationship also depends on the country anal-

ysed (Wang and Chen 2014; Mattioli et al. 2018); third, the decreasing incidence of obesity,

sedentariness and related diseases such as diabetes and cardiovascular diseases with increasing

income (Ameye and Swinnen 2019; Eurostat 2022;Levine2011); fourth, the fact that transport

and commuting times might also vary by income (Dargay and Van Ommeren 2005; Plaut 2006);

fifth, heterogeneity in extent of internalization across income levels (Allcott et al. (2019a), for

instance, find greater behavioural bias for low-income households).

In sum, the distributional effects of an increased fuel tax (at least in terms of utility and

health outcomes) can go both ways, and the resulting overall effect is not clear ex ante.Asthe

relative spending on transport fuels differs with income, some households will be hit harder by

the tax. This will not be mitigated by their demand reactions, as lower-income households in

the UK and the USA appear to have smaller elasticities, which might exacerbate the regressive

effect of a price increase in terms of disposable income. In addition, households with longer com-

muting times would be affected disproportionately by the tax. On the contrary, when looking at

health and utility outcomes, both in the UK and the USA, lower income quintiles show a higher

prevalence of obesity and related diseases such as diabetes, so could benefit more from the reduc-

tion in negative health outcomes. As the main focus of our paper is on how the inclusion of a

health internality changes the optimal fuel tax, and because heterogeneity in a model of opti-

mal fuel taxation without health internalities has already been explored in Bento et al. (2009),

modelling heterogeneity explicitly goes beyond the scope of this paper. However, future research

should examine the trade-off between harming poorer households by fuel taxes and related

instruments, and high health benefits from generating more physical activity, as pioneered by

Allcott et al. (2019a).

Further, we do not model explicitly pre-existing regulation such as fuel efficiency standards,

which are an important element in current transport regulation (Greene 2011). Assuming sep-

arable utility in leisure and the social costs contributes to analytical tractability and allows for

direct comparison to Parry and Small (2005), yet is also restrictive and therefore a significant

limitation. Finally, we combine public transport with walking and cycling as an active mode of

HEALTHY CLIMATE, HEALTHY BODIES 115

transport, and so omit recent trends in urban travel such as ride-hailing and sharing apps such

as Uber, or the increasing popularity of e-scooters.

6CONCLUSION

This paper shows that optimal fuel tax rates increase significantly if the health benefits from

increased active travel, such as reduced rates of diabetes, cardiovascular diseases, dementia and

depression are not fully internalized by citizens. Building on the established framework developed

by Parry and Small (2005), we present an assessment of optimal fuel taxation when an internality

through physical inactivity is also considered in the tax design.

We confirm the main conclusion of a large body of research in public health that, per mile

travelled, the social costs of inactivity dominate the social costs from transport externalities by

an order of magnitude. We examine how this fact changes the appropriate second-best opti-

mal fuel tax, which targets active travel health benefits only indirectly. We conclude that the

second-best optimal fuel tax increases from $4.56 to $6.31 per gallon in the UK, and from $8.99

to $12.92 per gallon in the USA. Due to the inelastic demand for vehicle miles travelled and

low cross-elasticity of active travel, the tax rate increases by less than the value of the per-mile

internality.

In contrast to Parry and Small (2005), we find that the fuel tax rate in the UK is too low

when the health benefits from active travel are accounted for. We confirm that even without these

benefits, in the USA, fuel is significantly undertaxed: it significantly exceeds the current average

fuel tax rate across the 50 states, as well as the previous estimate by Parry and Small (2005).

Over the past two decades, the economic costs of damage to human health (air pollution and

accident externalities) have risen significantly; more time is being spent in congestion on US

roads, and the value of time has also risen faster than inflation. Further, the social cost of carbon

estimates that we derived from the literature ($73–343 per tCO2) are now several times higher

than the values Parry and Small used in 2005 ($11.9 per tCO2, $0.5–47.3 per tCO2in 2022

prices). Whereas pollution linked to carbon emissions once contributed the least to their Pigou-

vian tax component, it is the largest component after congestion and inactivity according to our

estimates.

The main contribution of our analysis is that the significant health benefits from active travel

imply that fuel taxes should be increased—in absence of introducing more targeted policies. Fuel

taxes are an established instrument for addressing all social costs of transport, but beyond our

specific formal analysis demonstrating the importance of health benefits for overall transport

policy, we remain neutral about how much of the desirable changes in mobility patterns should

come from fuel price increases (and how much from specifically targeted, local policies) in actual

policymaking. Rather, we see this as central for future research. The modest relevance of a fuel

tax on an individual’s decision to walk or cycle indicates that the fuel tax may not be the most

appropriate policy instrument to encourage active travel.

The last point is reinforced by noting that optimal US fuel tax can be deemed politically

unrealistic, especially due to concerns of car-dependency of low-income households. Targeted

measures to increase the relative price of car travel, such as congestion charges, and measures

aimed at reducing barriers to other modes of transport, such as building better active travel

infrastructure, will permit societies to reap the high health benefits. Congestion charging would

be effective in both the UK and the USA for this purpose (Cramton et al. 2018). The USA specif-

ically would benefit from more public transit infrastructure that would result in more active trips

as people reach the transit stops by foot or bicycle. The UK, characterized by denser cities, would

especially benefit from improved urban infrastructure for walking and cycling. Nonetheless, with-

out an associated change in the price signal in the form of a fuel tax rise or congestion charge,

116 ECONOMICA

infrastructure investment is unlikely to lead to sufficient changes in travel decisions on its own

(Pucher et al. 2010; Buehler et al. 2017). Different policies at multiple levels are needed to realize

meaningful change in passenger transport.

ACKNOWLEDGMENTS

We thank seminar audiences in Berlin, Dublin, Osaka, Oxford, Paris, Siena, at EAERE, IIPF,

LAGV, and Elizabeth Baldwin, Geir Bjertnaes, Christian Brand, Felix Creutzig, Bart DeFloor,

Marc Fleurbaey, Franziska Funke, Reyer Gerlagh, Cameron Hepburn, Zarko Kalamov, Sebas-

tian Kraus, Ian Parry, Ryan Rafaty, Gregor Schwerhoff and Jiaxin Zhao for helpful comments,

and Leona Tenkhoff for research assistance. Linus Mattauch thanks the Robert Bosch Foun-

dation for financial support. Simona Sulikova was supported by the Martin Filko and Kellogg

Progress stipends.

Klenert declares that he works as an economist at the Joint Research Centre of the European

Commission. Sulikova declares that she is currently employed at the Ministry of Finance of the

Slovak Republic, where she works on evaluating infrastructure projects. Van den Bijgaart and

Mattauch declare that they have no competing interests. The views expressed are purely those of

the authors and may not in any circumstances be regarded as stating an official position of the

European Commission. Open Access funding enabled and organized by Projekt DEAL.

ENDNOTES

1‘Current’ values are correct as at January 2023.

2Sensitivity analysis shows that the second-best optimal tax varies significantly within the range of realistic parameter

values, from $6 per gallon to $23 per gallon for the USA, and from $4.75 per gallon to $11.25 per gallon for the UK.

3Chetty (2015), Bhargava and Loewenstein (2015), Allcott and Sunstein (2015), and Allcott et al. (2019b) all provide

more extensive discussions of why regulating internalities is desirable, arguing that the complexity of choices that

people face, and large internal costs in, for example, health and energy efficiency, warrant the greater use of behavioural

economics in regulation.

4Accounting for the physical health benefits from active travel increases further the gap between actual and optimal

fuel taxes. It may be argued that, especially in the US case, realizing such an increase is politically unrealistic in the

foreseeable future. Still, our result indicates that current fuel tax rates are further below their desirable levels than

previously thought, which implies that fuel tax increases have greater benefits.

5Equation (1) models the utility from health and leisure as separable. As a consequence, any improvement in health

will leave the labour–leisure trade-off unaffected.

6Even though large passenger volumes can congest public transport, this does not typically increase travel time. Bicycle

paths do not generally get congested to the extent that travel time increases. Still, congestion on roads may increase

travel time of buses, for example. In Section C.1 of the Online Appendix, we present an extension accounting for such

effects.

7Substantial emissions of particulate matter from transport are due to tyre, brake and road abrasion, rather than fuel

consumption. Fuel emissions contribute mostly to noxious gas emissions such as NOxand ozone.

8Note that any adverse effect of pollution on health is already subsumed in 𝜑(P).

9Additionally, publicly financed healthcare systems and moral hazard in health insurance imply that individuals may

not bear the full cost of unhealthy decisions.

10 We take poas exogenous, and thus abstract from any effects of fuel taxes on cost incurred for other exercise. Section

C.2 of the Online Appendix discusses an extension where other exercise requires travel (e.g. to reach a gym).

11 The term Γin in ZCcaptures the notion that congestion is costly for two reasons: it creates a direct disutility (see

equation (1)) and reduces time available to allocate to labour (see equation (10)).

12 The 𝛽terms are equal to the response of miles travelled to fuel taxes relative to the response in fuel taxes. As such,

they capture the relative effectiveness of fuel taxes in inducing changes in miles travelled, both active and inactive.

13 The lower fuel price elasticity of miles travelled as compared to the fuel price elasticity of fuel use is explained by the

fact that the most significant response of an increase in fuel price is typically not reduction in the distance travelled by

people, but rather upgrading to a higher-fuel-economy car (Coglianese et al. 2017).

14 As fuel mix is almost exclusively gasoline in the USA but approximately half and half gasoline and diesel in the UK,

the marginal cost of climate damages per gallon of fuel is not the same in both countries.

15 We abstract from behavioural approaches to how exactly accident risk is valued under uncertainty, including impli-

cations of overconfidence and focusing on outcomes rather than probabilities, as our analysis does not model risk

explicitly (Svenson 1981; de Blaeij and van Vuuren 2003; Mattauch et al. 2016).

HEALTHY CLIMATE, HEALTHY BODIES 117

16 To determine the external cost of accidents associated with inactive travel, we consider all costs associated with

car-on-car and car-on-pedestrian accidents, as well as 50% of the car-on-cyclist accident costs. Similarly for active

travel, we include pedestrian-only and cyclist-on-pedestrian accident costs, and the remaining half of the car-on-cyclist

accident costs.

17 HEAT is designed as a practitioner-oriented tool for health impact assessments. More complex assessments could

quantify the effect of exercise on morbidity as well as mortality. Our results are therefore likely to be conservative

estimates of the health benefits of physical activity.

18 For comparison to second best see Section 3, and for the policy implications of that comparison see Section 5.

19 We used R for all computations. Code available at https://github.com/ssulikova1/optimalfueltax.

20 The total tax on UK fuel includes VAT (116 cents per gallon) and fuel duty (265 cents per gallon). In the USA,

value-added and other indirect taxes are not levied on fuel.

21 To be clear, it is a standard feature that national income affects the value of statistical life, as this represents an oppor-

tunity cost of saving lives. The analysis abstracts from a dimension of redistribution across countries. See the second

subsection of Section 4for a presentation of effects in terms of lives saved instead.

22 In applied transportation research, the differences between the responsiveness of fuel consumption to fuel prices, and

miles travelled to fuel prices, are often disregarded, and assumed to be unitary. Multiplying externalities only by fuel

efficiency, and not by the responsiveness of VMT to fuel price, is considered the naive approach in the literature, and

can sometimes lead to a doubling of the optimal fuel tax estimation (Newbery et al. 1995).

23 However, as we used constant fuel price elasticities to calculate these changes, these results should be interpreted with

caution. It is unlikely that a 20-fold increase in the fuel tax in the USA would induce the same rate of response as a

20% increase in the tax.

24 HEAT computes only the lives saved due to an increase in active travel. Higher fuel taxation also reduces inactive

miles travelled, which reduces air pollution and vehicle traffic fatalities. As we do not capture these effects, the values

reported in Table 6can be considered a lower bound for the lives saved due to the tax increase.

25 Standalone marginal increases in fuel taxes are unlikely to spur significant behaviour change in drivers, because the

response to a fuel tax is to alter fuel consumption, but not to reduce the amount or distances travelled by car—the

demand for VMT is more inelastic than the demand for fuel (Gillingham and Munk-Nielsen 2019).

26 Future research could investigate how cost–benefit analysis of a public transport infrastructure project changes once

health benefits are taken into account. Such an analysis should note that the health benefits are distributed unevenly

across the population.

ORCID

Inge van den Bijgaart https://orcid.org/0000-0003-0180-8792

Linus Mattauch https://orcid.org/0000-0002-8900-3827

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SUPPORTING INFORMATION

Additional supporting information can be found online in the Supporting Information section

at the end of this article.

How to cite this article: van den Bijgaart, I., Klenert, D., Mattauch, L. and Sulikova, S.

(2024). Healthy climate, healthy bodies: Optimal fuel taxation and physical activity.

Economica,91(361), 93–122. https://doi.org/10.1111/ecca.12497