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Automation and theValue of Time in
Passenger Transport

Discussion Paper

176

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Mogens Fosgerau
University of Copenhagen, Denmark

176

Roundtable

Automation and theValue of Time in
Passenger Transport

Discussion Paper

Mogens Fosgerau
University of Copenhagen, Denmark

The International Transport ForumThe International Transport Forum is an intergovernmental organisation with 60 member countries. It
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Comments on Discussion Papers are welcome.
Cite this work as: Fosgerau, M. (2019), “Automation and the Value of Time in Passenger Transport”,
International Transport Forum Discussion Papers, No. 2019/10, OECD Publishing, Paris.

AUTOMATION AND THE VALUE OF TIME IN PASSENGER TRANSPORT | DISCUSSION PAPER NO. 2019/10 | ITF ROUNDTABLE 176

Acknowledgements

The author would like to thank Rebecca Overgaard Udsen for her comments on an earlier draft.

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Table of contents
Introduction ........................................................................................................................................ 5
The value of travel time for private travel............................................................................................ 6
In-vehicle work productivity ............................................................................................................ 7
In-vehicle leisure productivity ......................................................................................................... 8
In-vehicle productivity ..................................................................................................................... 9
Business travel..................................................................................................................................... 9
Basic analysis of congestion pricing ................................................................................................... 10
Dynamic models ............................................................................................................................ 11
Congested demand peaks ............................................................................................................. 13
Travel time variability .................................................................................................................... 14
Monocentric cities............................................................................................................................. 15
Some observations on self-driving cars.............................................................................................. 16
The value of travel time in a self-driving car ................................................................................. 16
Willingness-to-pay for self-driving technology .............................................................................. 17
Small travel time savings ................................................................................................................... 17
Conclusions ....................................................................................................................................... 18
References ........................................................................................................................................ 21

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Introduction
New technology is emerging that promises to free car drivers from driving, allowing them to use their invehicle time for other purposes. Similarly, mobile devices allow public transport users to spend their timein transit more productively than before. Travel time, then, is becoming less costly for travellers, thus
lessening the value of reducing it.
The impact of technology on the productivity of travel time depends on the characteristics of thetransport mode. Laptops and mobile internet have increased the productivity of time spent in planes,
trains and even buses1. Travel time can be spent on work (of the kind that can be done on a laptop or
similar), playing games, watching movies, etc. Comfort is of great importance, of course: productivity isclearly low in a crowded bus or train. Car manufacturers promise a future in which car drivers are freed
from driving, effectively turning car drivers into car passengers. But what are the policy implications fromthis broad change?
To a large extent, transport policy focuses on the trade-off of money for time. This is particularly true forthe provision of infrastructure, where money is spent in order to save travel time for travellers. Hence,the value of travel time is vital for assessing transport policy. The core of the economic evaluation of an
infrastructure project is to translate the consequences of travel times into an aggregate monetary valuethat can be compared with the cost of the project.
The same is true for congestion pricing, which one might say is about making travellers pay for spending
other people’s time. It is also true for the pricing of transport facilities (e.g. ferries, bridges), wheretravellers’ willingness to pay depends on how much travel time they might save.
Individual travel choices are guided by the value of travel time. This does not require that travellers beconscious of any such number. However, the choices travellers make between routes and transportmodes generally involve active trade-offs of travel time and comfort against monetary costs. Suchchoices, then, implicitly incorporate their underlying value of travel time. More broadly, the decision to
travel or not is affected by the cost of travel time.
Through the value of travel time, transport policy connects to fundamental urban policy issues. The
attractiveness of locations depends significantly on their accessibility to other locations through thetransport system. Property values and urban densities fluctuate according to changes in travel times andcosts brought about by transport policy.
Value of travel time is derived from first principles in a microeconomic framework that assumes a
consumer cares about leisure and consumption. Assuming that time spent traveling is not completely
available for work or leisure, reducing travel time has value when the time gained can be used for suchactivities. This framework allows us to predict the effect of making travel time more productive, that
increasing the productivity of travel time will decrease the value of travel time.
The theory established in this paper will distinguish between the productivity of time allocated for workand that allocated for leisure during travel. This will help determine whether people choose to work orpartake in leisure activities while traveling. The paper will discuss the individual willingness to pay to savetravel time. It is concerned with the private value of time rather than the social. This allows for anagnostic view (for the present purpose) of how individual values should be aggregated to social values.2
The next section derives the value of private travel time and examines the implications of enabling invehicle time to be used productively. A discussion on business travel will follow. With this in place, the© OECD/ITF 20195

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paper will undertake a basic static analysis of congestion pricing and will discuss the implications ofincreased in-vehicle productivity. This will then be extended to dynamic models that take the timing oftrips into account, examining rush hour traffic and travel time variability. A brief discussion on the impact
on urban form, using the monocentric city framework will follow. The paper will then make someobservations that are relevant for providing high-level rough estimates of the willingness-to-pay for selfdriving technology. It will revisit an old issue in the valuation of travel time: the value of small travel timesavings, particularly whether or not all time savings should be treated equally, regardless of their size
(despite increased in-vehicle productivity). The paper ends with a summary of the policy-relevant
implications that can be drawn from the analysis.

The value of travel time for private travel
The basic microeconomic theory3 underlying the value of travel time is based on the utility maximisation
problem of a consumer who allocates his4 time to various activities. The consumer cares about
consumption, how much time he spends at work, on leisure and on travel. Work time is rewarded at a
fixed wage rate (net after tax) that determines the monetary budget. The time required for travel isexogenously determined, while the allocation of time between work and leisure is chosen by the
consumer within the available time budget.
This paper will establish the basic microeconomic model for this problem and derive the value of travel
time within this context. This basis can later be extended to include possibilities for working andproducing leisure while in transit. For concreteness, the paper will focus on car drivers, noting that thesame theory applies to other modes of transport.
Suppose, then, that the consumer maximises utility
U(C,tL ,tW ,tD ),where C, tL , tW and tD represent consumption, leisure time, time spent at work and time spent driving.
The consumer faces a number of constraints. The first is that the total time spent at work, in leisureactivities or driving is limited by the total time available, T=tW +tL +tD. Second, the time spent driving
cannot be less than the time it takes to cover some exogenously given distance, tD ≥t0 . Third, time spentworking is paid at the (net after tax) rate w.

This basic model leads to the familiar conclusion that the value of travel time isw+

U tW U tD
- ,
UC UC

where U and its subscripts denote the marginal utilities for consumption, work or driving time. This
expression is discussed in more detail below.

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Decreasing the time required for travel is valuable for the consumer as it relaxes the time budget
constraint. The consumer reallocates the time saved in some proportion to work or leisure. More leisuretime is always desirable, ceteris paribus. Time spent at work affects utility directly (depends on how niceis it to be at work) or indirectly, by allowing more consumption of goods.
The value of travel time is the willingness to pay to reduce travel time. It has three components in thisanalysis. The basis is the wage rate, net after tax. The second component is the marginal willingness to
pay to increase work time. This component concerns only the effect on utility of spending time at work,
i.e. how pleasant (or not) it is to work. It does not comprise the effect that more work enables moreconsumption. The third component is the marginal willingness to pay to decrease travel time, again
holding everything else constant.
The last two components combine into the difference in marginal willingness to pay for time working
relative to time spent travelling. If the marginal utilities of work time and travel time are equal, then thevalue of travel time is just the wage rate, as the last two terms cancel each other out. If working is nicer
than travelling, then the consumer is willing to pay more than the wage rate to reduce travel time.
Conversely, if travelling is nicer than working, then the consumer is willing to pay less than the wage rate
to reduce travel time.
In addition, the rational consumer balances work and leisure and, therefore, additional leisure time has
the same value as additional work time. This is a very useful observation. It means the wage rate, which
is observable, can be used to measure the value of additional leisure time.
This theory in place, it is possible to compare the value of travel time in two different modes of transportthat are not equally comfortable. The marginal willingness to pay to reduce travel time is lower in the
more comfortable mode. Accordingly, the value of travel time is lower in the more comfortable mode.
A meta-study of estimates of the value of travel time from 389 European studies (Wardman,
Chintakayala and de Jong, 2016) finds values of travel time for non-business trips in the range 32-64% of
the gross wage rate. For studies conducted since 2001, they find a rate of 44% for commuting, 54% forother non-business travel purposes, and 43% for those studies that did not segment by travel purpose.
Taking into account that the top bracket marginal income tax rates is roughly around 50% in Western
Europe and that high income individuals are over-represented in the total distance driven on roads, it
may be suggested that the value of travel time tends to be close to but lower than the net wage rate. 5
This, in turn, suggests that the marginal utility of work time is less than the marginal utility of in-vehicle
time, i.e. for most people, driving tends to be nicer than working.
This basic theory assumes that it is not possible to work during travel. However, if sufficiently advanced
self-driving cars become generally available, they will enable car drivers to carry out other activities,
whether they are work or leisure related, while driving. Of course, this has long been possible on trains
and buses and increasingly so with expanding mobile internet availability.

In-vehicle work productivity
Were the model extended to include the possibility of working while driving, one would assume thefollowing utility
U(C,tL ,tW ,tD +tDW ).
Doing so assumes that working while driving and just driving are perfect substitutes. The benefit ofworking while in transit is assumed to arise since working time while driving (tDW ) is productive. One© OECD/ITF 20197

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supposes that consumption is a function net wage rate and time spent on productive work, i.e.
w∙(tW +αW tDW ), where αW 0<αW ≤1, is the productivity while driving relative to productivity at work. The
closer αW is to one, the closer the productivity working in the car is to productivity at work.
A straightforward analysis of this extended model shows that consumers switch completely to working
while driving, i.e. tD =0 and tDW =t0. This is intuitive, as working pays a wage while just driving does not. By
assumption, consumers are otherwise indifferent between working or not while driving. The value oftravel time becomes(1-αW )w+

UtW -UtD
UC,

which is exactly the same as in the case without the possibility of working while driving, except the wage
rate is multiplied by the difference between productivity at work and in the car. The previous result isreproduced if productivity 𝛼𝑊 is zero, while the wage rate drops out of the value of travel time if working
while driving is as productive as working at work.

In-vehicle leisure productivity
There is also the possibility that time in transit may be used to participate in leisure activities. One may,for example, watch a film while driving. Sleeping can also be called a leisure activity and counts as a
productive use of travel time. To account for this, the model must be extended as
U(C,L,tW ,tD +tDW +tDL ) ,where now tDL is time spent partaking in a leisure activity while driving and the various time uses whiledriving are still perfect substitutes. This extended model supposes that the in-vehicle productivity ofleisure time is a factor αL of the productivity of leisure time elsewhere.
As before, working while driving and just driving are perfect substitutes. Whether the consumer will workor partake in a leisure activity depends on what time use yields the highest marginal utility. The
consumer will produce leisure if
αW UC w<αL UL ,which happens if the wage is low or if leisure can be produced more effectively than work. The same
inequality may be written as
Ut

αW <αL +αW UW .
L

Then, if time at work has no direct impact on utility, the choice between work and leisure is solely
determined by the relative size of the productivities. The choice is tilted towards leisure if time at work
has a direct positive effect on utility and vice versa if it has a negative effect. This is intuitive: if time spent
at work is not pleasant, then it makes sense to conduct that work elsewhere if the opportunity exists.
The leisure-producing consumer has a value of travel time that is(1-αL )w+

(1-αL )UtW -UtDUC.

As leisure production while driving becomes increasingly productive, the wage term gradually drops outof the expression for the value of travel time. At the same time, the influence of the marginal utility of

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working at work also gradually drops out. If travel time was fully productive, then the value of travel time
would only reflect the pure comfort effect of driving.

In-vehicle productivity
The main take-away from this analysis can be isolated by ignoring the component of the value of travel
time derived from the difference in marginal utility between time spent at work and time spent in thecar. The value of travel time is then limited to the net wage rate, multiplied by a factor that expresses the
productivity difference between time use out of the car and time use in the car. The value of travel timein the simplest case is just(1-α)w ,where α is the productivity of time in the car relative to the productivity of time out of the car.
Without imposing further assumptions, one cannot determine from this theory whether people will tend
to work or partake in leisure activities during travel, nor the influence of income on that decision. This isan empirical issue.

Business travel
It is easier to assess the value of travel time for business travel, understood as any travel during work,than it is to assess the value of travel time for people travelling outside working hours. The traditional
cost savings approach assumes that travel time is completely unproductive and that time not spent
travelling is used productively. Workers are assumed to derive the same utility whether they work or
travel during work hours. In that case, the value of business travel time is simply the gross wage rate, i.e.
the cost to the employer per unit of employee time. The gross wage rate should be in market prices tobe comparable to the consumer willingness-to-pay. That is, it should include value-added tax as well asother indirect taxes, such that it corresponds to the savings to consumers from productivity gains due toreduced transport costs. This embodies an assumption of perfect competition, which might be anadequate approximation for the present purpose.
With the cost savings approach, the introduction of driverless cars would have no impact on the value ofbusiness travel time. This is clearly unreasonable and the problem is that the cost savings approachassumes that travel time is completely unproductive.
The Hensher approach (1977) goes to the other extreme, taking an engineering-style approach toaccount for many relationships that could affect the value of business travel time. It decomposes thevalue into the following components: the gross wage rate, multiplied by the proportion of travel timethat is unproductive (this takes into account that the business traveller may produce work or leisureduring travel); the value of resting during travel (this takes into account that the business traveller may
use travel time for restitution to become more productive after the trip); the worker’s willingness-to-pay© OECD/ITF 20199

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for converting business travel time not spent in leisure activities into working time; and the worker’s
willingness-to-pay for converting business travel time spent in leisure activities into leisure time.
It seems the full Hensher formula is not applied in any appraisal guidelines in any country. The reason isthat the formula is complicated and requires numbers to be assigned to a range of somewhat elusive
concepts. It is safer to rely more on a number that can be credibly observed, namely the wage rate.
Most applications treat business travellers as zombies, whose personal willingness-to-pay for reducing
travel time should be ignored. This avoids the serious problems that arise in assessing their willingnessto-pay for travel time savings for which they do not, in fact, pay.
Removing the corresponding items from the Hensher formula and simplifying it a bit leaves a formulathat can be written (1-α)W, where α is the share of travel time that is productive (for work, not leisure)and W is the gross wage rate. This is essentially the same as the expression (1-α)w derived in the earlier
section, except that the analysis there concerns private travel and w is the net wage rate.
In conclusion, private and business travel may be treated in much the same way, with the exception thatthe value of private travel time is based on the net wage rate while the value of business travel time isbased on the gross wage rate. It follows from this observation that the willingness-to-pay for technologythat increases in-vehicle work productivity will be higher for business travel.

Basic analysis of congestion pricing
This section considers the effect of increased productivity of travel time on the basic analysis ofcongestion pricing. The economic argument behind congestion pricing is as follows.
Every potential traveller has some willingness-to-pay (expressed in monetary units) for a trip. The
potential traveller travels if the cost of travel is less than her willingness-to-pay. If it is not, she does not.
The number of travellers, then, is inversely related to a trip’s cost: cheaper travel implies more travel.
The price of the trip depends first on the number of travellers, N, through the supply function S(N),which gives the travel time of a trip and takes into account that congestion causes the travel time toincrease if the number of travellers increases. This quantity is multiplied by the value of travel time(1-α)w and added to a toll 𝜏 that may be zero. The cost of a trip, then, is(1-α)wS(N)+τ ,and the number of travellers adjusts such that it equals the number of potential travellers whose
willingness-to-pay is greater than the cost of the trip. All of these attain a positive benefit of traveling, ora surplus, which is their willingness-to-pay less the trip cost.
Now consider a social planner aiming to maximise welfare. Welfare is defined as the sum of thewillingness-to-pay over all travellers less their total travel time cost, i.e. as the total net benefit gained
from traveling. In other words, the social planner aims to maximise the benefit derived from the ablity totravel. The social planner will set the toll 𝜏 at the level that maximises welfare.

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Important to note is that the aim of tolling is not just to reduce traffic. Were that the case, it would be a
lot easier to simply remove road capacity. On the contrary, the point of congestion tolling is to maximise
the benefit derived from the transport system.
Toll payment does not affect aggregate welfare directly, as the loss for travellers is exactly offset by acorresponding gain for the rest of society. The toll has two indirect effects on welfare. First, it
discourages some from traveling and these individuals then lose their willingness-to-pay for traveling.
Second, the remaining travellers experience reduced congestion and this is the source of gain fromcongestion tolling. The social planner will increase the toll to the point where the gain from further
increasing the toll is exactly offset by losses to those discouraged from traveling. This means that the
optimal toll isτ=N(1-α)wS'(N).
The optimal toll does not remove congestion. It ensures that the willingness-to-pay of the marginal
traveller is exactly equal to the congestion cost that traveller imposes on the other travellers. The
optimal does not in any way guarantee that travellers as a group gain from tolling. Generally, they will
lose. It is only when the benefit associated with the toll revenue is added that there is a net welfare gain.
The transfer away from travellers may easily be larger than the gain.
As in-vehicle productivity 𝛼 increases, traffic volume is also likely to increase, even when the optimal toll
is applied. In other words, the optimal traffic volume increases as in-vehicle productivity increases.

Dynamic models
The previous analysis is static and represents time as nothing more than a quantity; it does not take into
account the timing of trips. A dynamic model is needed to analyse a number of issues related to travel
time. The notion of scheduling utility can be applied to build such a model.
Consider now a traveller calculating the timing of a single trip. The traveller has a scheduling utilityU(tdep , tarr ) that ranks all possible ways the trip can be timed.6 For simplicity, the scheduling utility ismoney-metric, such that the utility difference between two potential outcomes is a monetary value.
There are several approaches to formulate a scheduling utility. Different approaches will have different
impacts on how the effect of increasing the productivity of in-vehicle time may be included.
The first approach assumes the traveller accumulates utility prior to the trip at the decreasing rate u1 (t)until the time of departure. Similarly, the traveller accumulates utility at the destination at the increasingrate u2 (t) after the time of arrival. The scheduling utility can then be written in terms of utility rates7 ast

U(tdep ,tarr )= ∫ dep u1 (t)dt+ ∫t u2 (t)dt .
arr

(1)

Figure 1 illustrates this formula. The scheduling utility expresses that the traveller would like to stay athome as long as possible, everything else equal, and also that he would like to be at work as early as
possible, everything else equal.
The traveller chooses departure time to balance these two goals. If travel time is fixed at 𝑡0 , the optimal
departure time is u1 (tdep )=u2 (tdep +t0 ). The value of travel time is the utility rate at the optimal
departure time, u1 (tdep ). It is clear that the value of travel time increases with trip length in this model.

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Figure 1. Utility rates

Vickrey (1969) bottleneck model applied this kind of scheduling utility to analyse congested demand
peaks. The Small (1982) analysis of commute scheduling and congestion also used it. It is also applied toassign a value to travel time variability (Engelson and Fosgerau, 2016).
The second approach uses insights from the static model set the foundation for considering the impact
of increasing the in-vehicle productivity of work or leisure. The scheduling utility rates should beunderstood as differences from the utility rate that is achieved while travelling (Oort, 1969). Lacking an
explicit theory that links the static and dynamic models, one option is to simply suppose that utility rates
in the scheduling model are multiplied by the productivity difference (1-α). An increase in in-vehicle
productivity would then translate directly into a decrease in the value of travel time.8
The decrease would be proportionally the same for all trip lengths if the in-vehicle productivity is
independent of the trip length. However, it seems more likely that the in-vehicle productivity is higher
for longer trips, since longer trips allow for activities that require more time. This could be, e.g., watchinga TV show or performing work-related tasks. The range of activities that are possible on shorter trips ismore limited. These considerations suggest that the value of travel time decreases more on long trips.
The third approach assumes that scheduling utility is the sum of two terms: one that is related just totravel time and one that is related just to the arrival time9, i.e.
U(tdep ,tarr )=Utt (tarr -tdep ) +Uarr (tarr ) ,(2)

where Utt is decreasing and Uarr is concave with maximum at some preferred arrival time.10 Within thismodel one may also suppose, for example, that in-vehicle productivity affects only the first term, as in
the static model, but not the second. The two different versions will hereafter be referred to as Model 1
and Model 2.
Model 1 is separable in departure and arrival times. Both terms are scaled by (1-α).
Model 2 is separable in travel time and arrival time. Only the travel time term is scaled by (1-α).

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The two models are equivalent when the travel time term Utt (tarr -tdep ) in Model 2 is linear, except for
the way in-vehicle productivity is included.

Congested demand peaks
Increased in-vehicle productivity is likely to have an impact on congested demand peaks. In a generalversion of the Vickrey (1969) bottleneck model, commuters with similar scheduling utility have to pass abottleneck on their way to work. Ideally, many commuters would travel at the same time, but this is notpossible since the bottleneck capacity is limited. This capacity constraint causes a queue to build astravellers arrive at the bottleneck at a faster rate than they can pass through it. The queue diminishes
gradually at the end of the demand peak, when the arrival rate is smaller than the bottleneck capacity.
The bottleneck model considers an equilibrium where each commuter has chosen her optimal departuretime, taking the behaviour of the other commuters as given. Early commuters achieve a short travel
time, but pay by departing when their utility rate at home is high and arriving while their utility rate atwork is low. They would prefer to depart and arrive later, but commuters departing later pay for theirmore convenient departure and arrival times by spending more time queueing. This correlation isreversed at the other side of the demand peak. Later commuters spend less time queueing but pay withlater departure and arrival times. They would have preferred earlier departure and arrival times, but only
if it had been possible without increasing travel time.
The duration of the congested demand peak is determined solely by the number of commuters and thebottleneck capacity. Increasing the productivity of in-vehicle time therefore has no direct impact on thisduration. The effect of in-vehicle productivity depends on the model of scheduling preferences.


In Model 1, if increasing in-vehicle time productivity translates into a proportional decrease inutility rates, then there is also no direct impact on the beginning and the end times of thecongested demand peak. The evolution of travel time over the peak is given by a differential
equation that depends on a ratio of utility rates. Multiplying these utility rates by a constantrelative change (1-α) makes no difference for this differential equation. Thus the basic
prediction of this model is that increasing in-vehicle time productivity has no direct impact on
the queueing delay at any time during the demand peak. However, the equilibrium scheduling
utility of commuters will increase, which will generally induce more commuting. Taking this into
account, one may expect that the duration and height of the congested demand peak will
increase as α increases.

In Model 2, increasing in-vehicle productivity does not affect the arrival time term. The travel
time is the same for the first and the last commuters in the peak, therefore the arrival time term
determines the timing of the peak. Hence, in-vehicle productivity has no direct impact on thetiming of the peak. Commuters that travel in the middle of the peak pay for their moreconvenient arrival times with longer travel time. As increasing in-vehicle productivity reduces thecost of queueing, the amount of queueing must increase to maintain equilibrium. The
equilibrium scheduling utility of commuters will increase, but less than in Model 1, so perhaps
the induced increase in the demand for commuting will be smaller than in Model 1.

Van den Berg and Verhoef (2016) undertake a more extensive analysis of the impact of self-driving cars
on congestion in a bottleneck setting based on the assumptions of the present Model 2, i.e. where
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related to arrival time. The main point of their analysis is to allow the share of self-driving cars to varyfrom 0 to 100%. With some share of cars being self-driving, heterogeneity is introduced, with the drivers
in the self-driving cars having lower value of travel time but the same disutility of inconvenient arrival
time as drivers in the manually-driven cars. The length of the demand peak is determined by thescheduling utility of arrival time and is hence unaffected in this first extension. However, people indriverless cars may use their in-vehicle time productively and hence have lower value of travel time.
Therefore, they are better able to tolerate queueing and these drivers will then occupy the middle partof the demand peak where queues will be longer than if all cars were manually driven. The shoulders of
the peak will be occupied by manually-driven cars and their situation will be essentially unchanged
relative to the situation without driverless cars.
This conclusion changes, however, if the reduced travel cost for driverless cars induces more traffic.
Drivers in manually-driven cars will then be crowded out of the most attractive trip timings and the peak
will begin sooner and end later, with manually-driven cars still occupying the shoulders of the peak.
Van den Berg and Verhoef consider an opposing effect, namely that a high share of self-driving cars may
increase capacity and thereby contribute to reducing congestion by reducing the length of the demand
peak. This effect benefits all drivers, regardless of whether they use a driverless car or not.

Travel time variability
Traffic congestion not only causes delays; it also causes travel times to be random from the traveller’s
point of view. Empirical evidence shows that a large share of average delays is due to irregular delays
caused by random events. It is relevant for prediction and policy evaluation to be able to assign a value
to reducing travel time variability. This is often done using models that are based on a notion ofscheduling utility (Engelson and Fosgerau, 2016).
In this paper μ represents the mean travel time and σ the standard deviation of travel time. It further
assumes (as a rough approximation to facilitate analysis) that the travel time distribution is independentof the departure time. These models suppose that each traveller chooses departure time to maximise
the expected scheduling utility, taking into account that travel time is random with some distribution
known by the traveller.11 Then the value of changing the variability of travel time can be derived.12 Thisvalue allows that travellers compensate for changes in the random distribution of travel times bychanging their departure time.
There are two main formulations of scheduling preferences that lead to simple expressions for the valueof travel time variability: the step model, and the slope model. Both are special cases of Model 1 and thestep model is also a special case of Model 2.
In the step model, the value of time is a constant while utility decreases linearly the more travellers
arrive earlier or later than a given preferred arrival time. Holding the standardised travel time
distribution fixed, Fosgerau and Karlstrom (2010) show that the scheduling utility is linear in the standard
deviation of travel time, with a slope that depends only on the penalty for early or late arrival.
The impact of increased in-vehicle productivity, then, depends on whether Model 1 or Model 2 isapplied. In Model 1, in-vehicle productivity scales the whole scheduling utility and hence the value oftravel time variability. In Model 2, on the other hand, in-vehicle productivity scales only the travel time
term. Therefore, the value of travel time variability is unaffected.

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Whether Model 1 or Model 2 is more appropriate is thus very important. As travel time becomes moreproductive, one of two things will happen, depending on the model chosen: either travel time variability
maintains its importance relative to travel time itself, or travel time variability retains its importance
while the importance of travel time diminishes.
These conclusions apply to other measures of travel time variability than the standard deviation,
provided that one accepts either Model 1 or 2 as theoretical foundation, and that these measures areproportional to the standard deviation. This includes the difference between two specific quantiles of thetravel time distribution (Small, Winston and Yan, 2005), the difference between a quantile and the mean
travel time, the buffer time index (FHA, 2006), and the mean lateness.
The main alternative to the step model is the slope model, which also leads to a tractable expression for
the value of travel time variability. This model is a special case of Model 1, in which utility rates varylinearly over time. If the utility rate at the origin is constant, then, mathematically, it is also a special caseof Model 2.
In this model, the marginal utility per unit of travel time variance is constant, equal to the slope of theutility rate at the destination. The more important are deviations in arrival time: the larger is the value oftravel time variance.
The effect of a change in in-vehicle productivity depends on which interpretation of the model is correct.
In Model 1, larger in-vehicle productivity leads to lower value of travel time variability, where there is noeffect in Model 2.

Monocentric cities
This section discusses the impact of increasing in-vehicle productivity on urban form using the classic
monocentric city model (Alonso, 1964). The model describes a stylised city with a central business
district in which all employment takes place. Residents choose where to live and how much of theirincome to spend on housing and consumption. In the simplest version of the model, residents are taken
to be identical. Then various conclusions may be derived concerning an equilibrium where all residents
attain the same utility level.
The main stylised fact emerging from the monocentric city model is that the residential density
decreases with the distance from the centre. Residents face a trade-off between transport costs andhousing costs. Near the centre, transport costs are low but the cost of housing is high. Consequently,
residents there consume less housing and the residential density is higher. Further out, transport costs
are higher but housing costs lower. This allows each resident to occupy more space and, therefore, theresidential density is lower. Altogether, the model predicts that the residential density decreases as thetransport cost to the city centre increases. As the transport cost is positively related to distance, thedensity gradient with respect to distance is negative.
A general decrease in transport costs due to increased in-vehicle productivity will then make the density
gradient less steep. Holding the city population constant, one may expect that the residential density
decreases near the centre and increases further out. Cities will become more sprawled.

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There is a balancing mechanism, however, which is that reduced transport costs allow cities to becomelarger. Due to agglomeration forces, one may predict that large cities will attract population from smaller
cities and become even larger, while smaller cities will lose population (Rappaport, 2016).
These conclusions carry over to the case of the bottleneck model, which takes into account thatcongestion is dynamic (Gubins and Verhoef, 2014; Fosgerau, Kim and Ranjan, 2018).

Some observations on self-driving cars
The value of travel time in a self-driving car
What will the value of travel time be in a self-driving car? Self-driving cars currently are not widely
available yet, so the trade-offs between time and money made by travellers in such vehicles cannot be
observed. Instead, other comparisons may reveal something about the value of freeing drivers’ timespent travelling.
In stated preference data from the Danish value of time study, respondents completed choice exercises
both for the current mode of transport as well as for an alternative mode (Fosgerau, Hjorth and LykJensen, 2010). This design makes it possible to compare the value of travel time in different transportmodes for the same individual. This comparison is important, as confirmed by the study, because of thefact that people self-select into travel modes affected by their value of travel time making it impossible
to infer modal differences from simple differences in the average value of travel time across modes.
The study’s main finding on comfort effects is that current bus passengers retain their (low) value oftravel time in different alternative modes. It seems that only respondents with high value of travel time
are affected by the experiment mode. Among those, the value of travel time is significantly lower in cars
than in trains, which is consistent with cars being more comfortable than trains. There is no evidence
that the value of travel time is lower in trains due to the ability to conduct activities other than driving.
Hence, this study does not support the idea that car drivers have significant willingness-to-pay for nothaving to drive. It should be considered, however, that the data in the Fosgerau, Hjorth and Lyk-Jensen
study are from 2004 and the present availability of mobile technology may change the conclusion.
Comparing car drivers to car passengers (in manually driven cars) is also informative. Self-driving
technology will enable car drivers to behave like car passengers. The higher potential in-vehicle
productivity of car passengers should then be reflected in a lower value of time. There are, however,other factors influencing the difference in the value of travel time between car drivers and car
passengers. First, the car driver is unlikely to be randomly designated: the selection of who drives the car
will most likely correlates with the individual value of travel time. Second, a car passenger is not thesame as a single user of a self-driving car.
There are not many studies of the passenger value of travel time. The consensus seems to be that car
passengers value travel time at about 75% of the rate of car drivers, even if that assessment does nottake into account the interactions between the occupants of a car (Ho et al., 2015). Such a difference inthe value of travel time is not universally found. For example, a recent large-stated preference study in

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Copenhagen (Lu et al., 2018) found no difference between car drivers and passengers in the value oftravel time. These studies do not control for self-selection, so it is possible that any difference between
drivers and passengers is due to a tendency for the driver to be the person with the highest value oftravel time. Altogether, these observations suggest an upper bound of 25% for the reduction in the valueof travel time from not having to drive. This suggests that α=0.25 is a large number.

Willingness-to-pay for self-driving technology
Self-driving cars are coming, it seems, although it will probably take many years before they have an
impact on traffic volume. As there is very limited experience with self-driving cars, any conclusions
regarding their impact on the value of travel time will be highly speculative. It is still worth putting somethoughts forward to stimulate further thinking and discussion.
One can try to make a small back-of-the-envelope calculation to get some idea about the potential
willingness-to-pay for self-driving technology. One can estimate the total cost of the time spent driving a
car during its lifetime and use that figure to suggest an upper bound for the willingness-to-pay for fully
self-driving technology.
If a car drives 300 000 km at a time cost (for the driver) of EUR 10 per hour and an average speed of
60 km per hour, that time is worth EUR 50 000, or perhaps just EUR 25 000, allowing for discounting.
Taking such a figure as the willingness-to-pay for self-driving technology is, of course, extreme. It
supposes that all driving time can be converted to fully productive use such that travel time will cease to
be a constraint at all. Less extremely, self-driving technology will more likely lead to some productivity
increase and only for some of the kilometres driven by the car. If we suppose that the willingness-to-pay
were 10% of the value of travel time for 50% of the kilometres, which does not sound unrealistic, thenthe estimated total willingness-to-pay would be just EUR 1 250.
This simple analysis suggests that self-driving technology will have to become very cheap in order tobreak through at a large scale. This is much lower than the price that is currently anticipated.

Small travel time savings
The issue of small travel time savings has two parts. The first is that large, and hence valuable, aggregate
savings of travel time, which may result from certain transport projects, is actually composed of lots ofsmall travel time savings of a few seconds. These small travel time savings may seem virtually worthlessfrom the perspective of current individual travellers. Thus it may seem paradoxical that they are assigned
a large value in the aggregate. The second part is that stated preference data seem to support that small
travel time savings are worth less per minute than large travel time savings. As a result, some havesuggested that small travel time savings below a certain threshold should not be included in cost-benefit
analysis at all.
Regarding the first part, the established and well-founded point of view is that this objection to valuing
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may have difficulty seeing how they could use a few extra seconds. However, as the goal is to evaluate
long-term effects, the short-term perspective of individual travellers with committed activity schedules isjust not relevant. Furthermore, evaluating small and large time savings differently is nonsensical, as anylarge project can be decomposed into a sequence of small projects.
An increase in the productivity of in-vehicle time would not have any effect on this discussion. The
conclusion would remain that small and large time savings should be assigned the same value for policy
evaluation purposes.
Regarding the second part, evidence from stated preference data shows that small time differences arevalued less than large time differences. This is inconsistent with neoclassical utility maximisation but
consistent with reference point effects according to prospect theory (De Borger and Fosgerau, 2008). For
anything but the very short-term, reference points are irrelevant; therefore any effect deriving fromreference points is also irrelevant. The main takeaway from this research is that: 1) stated preference
data are highly problematic for measuring the value of travel time because of these reference point
effects; and 2) it is strongly advisable to develop revealed preference data and methods for measuring
the value of travel time.
To conclude, small travel time savings is unrelated to the effect of increasing in-vehicle productivity.

Conclusions
Driverless technology and mobile communication technology promise to increase the ability of travellers
to perform productive activities while travelling. The unsurprising theoretical prediction that follows isthat this will be reflected in a lower willingness-to-pay of travellers for reducing travel time, i.e. a lower
value of travel time. This is true for both private and business travel.
The first-order effect of this is to reduce the case for investing in infrastructure in order to reduce travel
times. However, the reduction in the cost of travelling will induce more traffic and the net effect on thebenefits of infrastructure investment is ambiguous.
The economic efficiency argument for road pricing is unchanged. Increased in-vehicle productivity willlead to increased traffic volume, even in the presence of the optimal congestion toll. The optimalcongestion toll may increase or decrease as in-vehicle time becomes more productive. A reduction in thevalue of travel time will not have a direct effect on the duration of commuting peaks. Driverless cars willtend to concentrate in the middle of the peaks and queue lengths may increase due to the reduced costof travel time. A large share of driverless cars may improve capacity, thereby reducing travel cost foreverybody. This will induce more traffic. It is possible that users of non-driverless cars will be worse off.
The value of travel time variability may or may not be reduced by increased in-vehicle productivity. Thereare competing theories and little empirical evidence to distinguish between them. There is no indication,
however, that the value of travel time variability will increase.
The impact of increased in-vehicle productivity on urban form is a tendency for cities to become moredispersed in relative terms. Larger cities may become even larger and it is possible that some large cities

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will become denser at all distances from the centre. These effects hinge on the assumption that thevalue of travel time will actually decrease. One can guess how much by comparing the value of time incars to that in buses and trains and by comparing car drivers to car passengers. Evidence suggests thatthe reduction in the value of travel time due to increased in-vehicle productivity might be less than 25%.
Taking into account how much time a car is actually driven and making some back-of-the-envelope
calculations suggests that the average willingness-to-pay for self-driving technology might be as low as
EUR 1 000 to 2 000. This is very low compared to the current predictions of the cost of providing selfdriving technology. This, in turn, suggests that the market share of self-driving cars will be fairly small.

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Notes
1 This paragraph was in fact written on a laptop in a plane and with (partially successful) internet access during the flight.
2 Mackie, Jara-Diaz and Fowkes (2001), Gálvez and Jara-Diaz (1998)
3 The microeconomic formulation of the theory of the value of travel time savings was fundamentally formulated by Becker (1965), Johnson(1966), Oort (1969), and DeSerpa (1971). Jara-Diaz (2000) provides a review.
4 Gender of representative person was chosen at random.
5 Considering the arguments made in this paper and elsewhere, it would be good practice to report the value of travel time relative to the net
wage rate.
6 It would be of interest to have a theory that unifies the static and the dynamic perspectives on the value of travel time.
7 This generic form for scheduling utility was first formulated by Vickrey (1973). It can be derived from a broader model in which consumers
derive utility from leisure and consumption, and travel time (Fosgerau and Small, 2017).
8 This observation indicates that it would be nice to have a more extensive theory that could account for the idea that in-vehicle time is moreproductive on longer trips. The static and dynamic models, as formulated here, do not allow such an effect to be represented.
9 This paper ignores the symmetric possibility that scheduling utility could be separable in travel time and departure time.
10 Like the first formulation above, this formulation generalises the popular α-β-γ preferences (Vickrey, 1969; Small, 1982; Arnott, de Palma andLindsey, 1993).
11 What travellers really know and take into account is an important issue. Fosgerau and Jiang (2017) present a model in which travellers choose
how much information to acquire.
12 Using the envelope theorem.

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Automation and the Value of Time in
Passenger TransportThis paper reiterates the basic principles and rationale for valuing
travel time savings. It explains the type of impacts that the valuationof travel time savings intends to capture and discusses whether andhow those fundamental principles continue to hold with automationand increased possibility of productive time use while travelling. The
paper also discusses implications for traffic management and urban
form that follow from increased in-vehicle productivity.

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Published: 10/2019 | Photo credit: Shutterstock/metamorworks

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