Road infrastructure and public bus transport service provision under different funding schemes: A simulation analysis

Transportation Research Part A 125 (2019) 89–105

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Transportation Research Part A journal homepage: www.elsevier.com/locate/tra

Road infrastructure and public bus transport service provision under different funding schemes: A simulation analysis

T

Nicolás Pavóna, Luis Ignacio Rizzib,

⁎

a b

MSc Transport Engineering, Pontificia Universidad Católica de Chile, Chile Departamento de Ingeniería de Transporte y Logística, Pontificia Universidad Católica de Chile, Casilla 306, Código 105, Santiago 22, Chile

ARTICLE INFO

ABSTRACT

Keywords: Road capacity Congestion pricing Public transport subsidies Urban transport externalities Equity

There is a large and still growing literature on road pricing; there is also a large literature on public transport pricing and provision. However, the integration of these subtopics with the subtopic of road capacity provision as a unified topic is very small (Lindsey, 2012). Therefore, we seek to gain a better understanding of the interplay of transport pricing, transport service provision, cost recovery, together with an explicit consideration of equity in a unified fashion. To do so, we carry out a simulation analysis, as theoretical results in second-best contexts are not clean and depend on assumptions on relevant parameters. Under the assumptions of parameters typical of a city like Santiago de Chile, the most relevant conclusions of this research are the following. First, if road infrastructure provision and its pricing are jointly determined, road infrastructure provision is lower when adequately priced through user charges, with car speeds in the peak period increasing very close to free-flow speeds. Second, if user charges are designed to achieve cost recovery of road investments, public bus transport ridership will increase, taking full advantage of social economies of scale. Third, welfare redistribution through transport market interventions is limited. Fourth, if car use is subsidised, most of the benefits, if not all, of subsidising public transport are undone. Fifth, if road pricing were to be implemented in actual urban contexts, reallocation of road space away from private vehicles (even road closure) could become a reality, especially in denser parts of cities.

1. Introduction Despite the large amount of urban space allocated to road infrastructure, travel delays are a day-to-day feature of most cities. Urban motorised transport also creates several other externalities such as risk of accidents, air pollution, noise pollution, segregation, visual impacts, CO2 emissions, etc. Economists strongly advocate for comprehensive road pricing as the most suitable travel demand management strategy to deal with these urban transport problems (Newbery, 1994), however its implementation is very limited worldwide. Given the difficulty of implementing road pricing, governments and transport authorities need to resort to other means of taxation to finance the construction and maintenance of roads. This leads to the involvement of different government bodies in the ⁎

Corresponding author. E-mail address: [email protected] (L.I. Rizzi).

https://doi.org/10.1016/j.tra.2019.05.001 Received 30 August 2018; Received in revised form 22 April 2019; Accepted 1 May 2019 Available online 21 May 2019 0965-8564/ © 2019 Elsevier Ltd. All rights reserved.

Transportation Research Part A 125 (2019) 89–105

N. Pavón and L.I. Rizzi

provision of transport services, usually without adequate coordination. Consequently, a disconnection arises between road construction and road maintenance management, on the one hand, and travel demand management, on the other hand1. The unavailability of widespread road pricing creates several inefficiencies. First, the amount of space allocated to roads will not be (near) optimal, especially if funding for road construction and maintenance is weakly linked to the intensity of car usage. Most likely, this results in over-provision of road infrastructure. Second, with distorted prices of car usage, subsidising public transport becomes necessary to redress the imbalance between public and private transport to same extent. Third, a higher modal share of private car will engender greater production of negative externalities. There is a large and still growing literature on road pricing; there is also a large literature on public transport pricing and provision. However, there is very little work studying the integration of these subtopics with the subtopic of road capacity provision as acknowledged in Lindsey (2012), who expertly reviews the theory of congestion pricing and the relationship between optimal congestion tolls and optimal road capacity. This bias in the literature may be due to the fact road capacity is usually decided by administrative criteria without close regard to its pricing. In many countries, income inequality is an important concern and while fiscal policy could help mitigate it in principle, its scope is limited, partly because of the distortions so introduced2. Hence, transport decision makers could contribute to lessen the extent of inequality through the pricing of transport services, e.g. by subsidising public transport. The main goal of this article is to gain a better understanding of the interplay of transport pricing, road infrastructure provision, public bus service provision, cost recovery and equity in a unified fashion. Our focus on the provision of road capacity in combination with other instruments is what sets this research apart from previous literature. This type of analysis should be relevant for tackling traffic congestion and its concomitant effects. It should also be valuable to (i) put into perspective how current road transport policies fare against alternative scenarios in terms of level of service, production of externalities and equity and (ii) provide benchmarks for decision makers to guide future urban transport policy, including reallocation of road space away from private cars. We developed a simple general equilibrium model to determine the effects of different transport funding mechanisms on infrastructure provision, departure time, mode choice, level of service, production of an externality (air pollution) and welfare redistribution. Regarding the latter topic, the only available means for redistributing welfare is through transport pricing. The only taxes we allowed are a fuel tax or a flat tax on generalized consumption (that excludes transport expenditures). These taxes may be used to fund transport services wholly or partially. The explicit consideration of different pricing/funding mechanisms gives raise to many different scenarios. We solved each scenario by means of simulation: solving analytically each scenario would be complex and, based on experience from single mode scenarios, many theoretical results (e.g. the level of infrastructure provision) would not be clean and solutions would depend on assumptions on relevant parameters (Lindsey, 2012; Rizzi, 2014). Our model is representative to some extent of cities like Santiago, Chile. We developed the model having in mind these features: a compact city, making possible a dense network of public bus transport; peak hours concentrated in periods of the day; a highly right skewed income distribution; high-income people who have a higher preference for using the car; and a tax collection system depending mainly on indirect taxes, e.g. value added tax. The most relevant conclusions of this research are the following. First, if road infrastructure provision and its pricing are jointly determined, road infrastructure provision is lower when adequately priced through user charges, with car speeds in the peak period increasing very close to free-flow speeds, reducing travel delays, fuel consumption and other negative externalities. Second, if user charges are designed to achieve cost recovery of road investments, public transport ridership will increase, taking full advantage of economies of scale in the provision of bus services. Third, welfare redistribution through transport markets is limited. To do so, it is a sine qua non that road user charges (road tolls or fuel taxes) are designed to achieve full cost recovery of infrastructure costs, as only then subsidising public transport would contribute to welfare redistribution. Fourth, if road space is provided free of charge to car users, the benefits of subsidising public transport are undone: not only welfare redistribution gains disappear, but total welfare goes down; even worse, more and more space needs to be allocated to roads for the use of private cars. Fifth, if road pricing were to be implemented in actual urban contexts, private cars would require less road space, making it possible to reallocate space to active transport modes, ampler bus stops and even road closure could become a likely option. The rest of this article is organised this way. Section 2 contains a brief literature review. Section 3 presents the model to carry out the simulations and Section 4 describes the different scenarios to evaluate. Section 5 presents the most relevant parameters of the model. Section 6 presents results and sensitivity analyses, and Section 7 closes the article with discussions of our main findings and its implications. 2. A brief literature review There is a very well-known theorem stating that under constant economies of scale in road construction and homogeneity of degree zero of travel times in traffic flows and capacity, roads that are optimally designed and priced will generate enough earnings 1 In Chile, The Ministry of Housing and Urbanism is in charge of road construction and maintenance in cities through its regional agencies. The Ministry of Transport and Telecommunication and the municipalities are mainly responsible for managing travel demand. The fuel tax is the most relevant payment made by motorists related to intensity of car usage. The Congress levies taxes on gasoline and diesel that cannot be earmarked for transport expenditures. 2 Equity is at the heart of distortionary taxation (Mayeres and Proost, 2001).

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to recover exactly the capital costs of infrastructure (including the opportunity costs of capital). In this case, road tolls should be levied equal to the marginal external cost of driving (Mohring and Harwitz, 1962). This result is known as the self-financing theorem (Small and Verhoef, 2007; Verhoef and Mohring, 2009; Lindsey, 2012). There are very few attempts to generalize the above result when the pricing instrument is other than a road toll, for instance a fuel tax, or when the road infrastructure is financed from general taxation. Lindsey (2012) provides an algebraic example on how to determine the optimal infrastructure level when road pricing is suboptimal within a partial equilibrium framework. He concludes that “(W)ithout specific assumptions about the user cost and demand functions it is not possible to determine … whether second-best capacity is larger or smaller than first-best capacity”. This result crops up several times in the transport economics literature (Wilson, 1983; D’Ouville and McDonald, 1990; Arnott et al., 1993; and Rizzi, 2014). These authors conclude that, under sensible assumptions, road infrastructure provision, in second best settings, should be greater than in a first best setting. Rizzi (2014) is one attempt to extend the analysis of the Mohring-Harwitz theorem to include other means of funding beyond road tolls3. Specifically, he considers fuel taxes and a (purchase) tax on generalised consumption as alternative means of funding. His analysis introduces the effect of fuel efficiency (Parry and Small, 2005) and equity considerations. Regarding equity, he assumes that the only means to re-distribute welfare is through the pricing of roads. To accommodate all these effects, he needs to move from a partial equilibrium to a general equilibrium analysis. As in previous research, he could not obtain a clean theoretical result in terms of road infrastructure provision when switching from road tolls to other funding instruments. However, by means of simulation he could show that, under plausible empirical assumptions, infrastructure provision is greater when consumption taxes are in place. He also shows how different funding mechanisms affect equity. The extension of this type of analysis when, in addition to private car, public transport is present is also small. Basso and Silva (2014; Section 2 and Table 1) provide a detailed overview of the literature on transport pricing when a public transport mode is available in the mode choice mix. In all the articles they review, the provision of road infrastructure is held fixed and most of them ignore equity considerations. Two other relevant papers could be added to those reported by Basso and Silva (2014): Parry and Timilsina (2010) and Russo (2015), but again none of them addresses the interplay of pricing, road provision and equity in a unified fashion. In the 70s and 80s there were many authors concerned about the effect of different management objectives in public bus transport. Examples of this are, among many others, articles by Nash (1978), Frankena (1981) and Glaister and Collings (1978). These investigations sought to understand what instructions public transport operators should follow. The debate was, partly, about market efficiency versus welfare maximisation. This will be present in our research, although not in the way these authors addressed the topic. They analysed the effect of different managerial objectives with regard to fare, level of service and subsidies, but without integrating the analysis with road infrastructure provision, mode choice and equity. Regarding distributional aspects, Levinson (2010) reviews the literature about the equity dimension of different road pricing schemes. This literature, however, does not analyse the interplay of road infrastructure provision and pricing regarding equity; nor does it consider the type of inequality seen in developing countries that is more severe than that observed in developed countries. 3. The model We first provide an overview of the model. We model a representative stretch of the road network of a city where both private car and public buses are available. Land-use patterns are assumed exogenous so no feedback response to location decision are allowed for. Origins, destinations and trip length are distributed over the space in such a way that this stretch of the road network is representative of the whole network in terms of modal split, passenger flows and level of service. Regarding the time dimension, the model only considers the morning commute, assuming a peak hour with two off-peak identical hours on either side. Consumers derive utility from consumption of a generalised good and the enjoyment of leisure time. Travelling also yields utility and this utility depends on the joint choice of departure time and mode of traveling. Making trips, however, entails spending money and time not allocated to consumption and leisure. Travelling in the peak and by car is most attractive. Consumers may also decide not to travel at all; if they travel, they only make one trip. To avoid complicating our model in excess, we postulate that travelling provides utility per se, departing from the typical assumption that travel is a derived demand providing negative utility. One possible justification could be that people travel to work and interact with other persons/colleagues and this social interaction is the main source of this positive utility. For instance, working at the office with colleagues, face to face, would yield more utility than working at home. Our model incorporates three externalities. Congestion gives raise to travel delays and extra fuel consumption: the more cars are on the street, the greater the time to complete a trip and the consumption of fuel will be. In addition, as all trips are made by polluting motorised modes, air quality deteriorates affecting everybody’s utility negatively. Regarding fuel consumption, fuel efficiency is a feature of the model. The model considers three types of consumers according to income: low-income, middle-income and high-income people. Consumers work a fixed time schedule and their income is given and spent on a generalized good and trip making. A fixed time working schedule is a most sensible assumption in the context of South American countries (Jara Díaz and Farah, 1987)4. 3 Wilson (1983) and D’Ouville and McDonald (1990) are earlier attempts to generalise the Mohring-Harwitz theorem when the pricing instrument is other than a road toll. See a literature review in Rizzi (2014). 4 In Chile, 68 percent of the working population are full time workers under a fixed-schedule job contract (Rau, 2012; Castex and Sepúlveda,

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The planner maximises a utilitarian social welfare function. She has to decide i) the level of road infrastructure provision, ii) the level of service of public buses (frequency and capacity) and iii) the amount of charges to collect to fund the provision of transport services. The planner could establish road tolls, bus fares, fuel taxes and taxes on consumption. She could also decide to implement different budget constraints for the provision of roads and public bus services or implement a joint budget constraint. If the planner wants to redistribute welfare, the only means to do so is by subsidising the price of transport but without being able to charge negative prices. She cannot implement individual lump-sum taxes. To redistribute welfare, she can establish cross-subsidies between modes or she can introduce a tax on generalised consumption to subsidise travel. Our model does not consider targeted subsidies to, e.g., low- income people. Labour income tax is not a feature of the model. In a country like Chile, those who actually pay some labour income tax are in the very highest percentiles of the personal income distribution (Engel et al., 1999), severely limiting its revenue potential. Engel et al. (1999) showed that when taking into account the cost of tax collection and deadweight loss, broad-based proportional taxes become more desirable. Actually, in Chile, indirect taxes raise more money than labour income taxes. This led us to consider a tax on consumption rather than a labour income tax5. We now proceed to describe the model in full detail. 3.1. Individual utility function The utility function is separable and entropic in the travel component (Small and Verhoef, 2007):

Un = 1

n(

l

(

n n l (ln l

n n )) ) l

+

n (X n )m

+

1

n n l (ln l

n(

l

(

nLn

E n n )) l

l

n (ln lin i li

n n) li )

(1)

Superscript n indexes type of consumers (n = 1, 2, 3; low-income, middle-income and high-income respectively); θ represents the utility of consuming one unit of the generalised good X and m is an exponent between 0 and 1 to reflect decreasing marginal utility of consumption. The value of m is the same for everybody. π is the marginal utility of leisure time L and ϖ is the marginal disutility from deteriorated air quality E (or air pollution). In Eq. (1), the fourth and fifth entropy terms correspond to the travel demand model. These entropy terms define a nested logit demand model, as in Basso and Silva (2014). This model encompasses two decisions. First, consumers decide the time of departure (peak or off-peak) or not to travel. ρ is a parameter influencing this choice and κl are positive numbers reflecting the preferences for travelling in period l (l = peak, off-peak or not to travel). We impose κpeak > κoff-peak to represent people’s preferences for travelling in the peak (the most desired departure time). Also κoff-peak > κno_travel as we assume people prefer travelling in the off-peak to not travelling. The higher nest (higher hierarchy) of the nested logit model represents this decision. The second decision is about the mode of travel. Parameter β governs this decision and parameters γli (i = private car, public bus) describe travellers’ preferences for different modes at different times of the day - private car being prefered to public bus. The second nest (lower hierarchy) models the choice of travel mode conditioned on departure time. In Eq. (1), δl (l = peak, off peak and no travel) is the marginal logit probability of choosing a period of the day and δli is the nested logit joint probability of choosing mode i (i = private car, bus) in time period l. We impose 0 < ρ ≤ β for internal consistency of the nested logit model. Regarding the duration of the morning commute, it has three hours. The second hour is the most preferred travel time, the peak period and it is preceded and followed by a first and third hour that represent the off-peak period. The two off-peak hours are identical in terms of utility and level of service. Consumers face three constraints. The budget constraint simply says that expenditure equals income: n l, car

pX X n +

((pg g + tolll, car ) K¯ + pcap ) +

l (peak; off peak )

n ¯ l, bus pl, bus K l (peak; off peak )

= In

(2)

pX is the price of the generalised good and could include an ad valorem tax; without the ad valorem tax, pX = 1. g is gasoline consumption per kilometre for private cars and pg is the price of gasoline. This price could include a tax component if fuel taxes are levied. tolll,car is the road toll per kilometre; pl,bus is the price of a bus trip per kilometre. The last two values could differ by time of the day. K¯ is the average trip length and pcap the capital cost of using the car. I is income: as we considered a typical daily morning commute, income is given by the pro rata corresponding to half a day. The next equation determines the time budget constraint: n ¯ l, auto tl, car K

Ln + l (peak; off peak )

n ¯ l, bus tl, bus K

+

¯ =T +W

l (peak; off peak )

(3)

¯ is fixed working time and tl,car and tl,bus are the travel times per kilometre by car and bus respectively. tl,bus L is leisure time, W (footnote continued) 2014). This figure would increase a few percentage points if it included hired workers employed in private households for domestic services. 5 In developed countries, the proportion of workers who pay labour income taxes is substantially higher. Actually, this tax raises more money than consumption taxes. This is why, in the developed countries tradition, labour income tax rates and the decision on how many hours to work are modelled in analyses of this type. Russo (2015) provides one of the most accomplished theoretical analyses on the interaction between labour income taxes, the choice of how many hours to work, commuting mode choice, pricing of transport services and equity. 92

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includes access and waiting time. The last two constraints force consumers to choose only one alternative (including not to travel): n l

n li

= 1,

l

=

n l

(4)

i

Consumers maximise Eq. (1), subject to constraints (2), (3) and (4). Their only decision variables are the values of X, δl and δli. Actually, one of these will be redundant: upon deciding on δl and δli, the value of X is automatically solved. Eq. (3) can be easily incorporated in Eq. (1) by replacing the value of leisure time L from the very same constraint. The Lagrange multiplier associated to the budget constraint, λn, gives the marginal utility of income and the value of saving a unit of time is equal to πn/λn. 3.2. Travel time Travel time depends on the flow of cars and buses sharing the roads. Letting Nn denominate the total number of people in each n category, total car flow (CF) per period is given by Eq. (5): n n l, car N ,

CFl =

l = peak, off peak

(5)

n

We assume that car occupancy equals one (1). The bus flow equals its frequency (fr), but a bus clearly contributes more to congestion than a car by an equivalence factor feq that depends on the size of the bus or its passenger capacity, kb. Bus frequency could differ by time of day. The following macroscopic volume-to-capacity equation gives the travel time per kilometre by car in a particular period of the day (the l subscript is removed):

tcar = t 0 1 +

n n N n c

+ feq (kb ) fr RK

(6)

α and ζ are parameters belonging to the volume-to-capacity function, t0 is free flow travel time and RK is road capacity. This function is homogenous of degree zero in volume and capacity. As buses have to come to a complete standstill at bus stops and spend time permitting boarding and alighting, travel time per kilometer by bus is necessarily greater than by car. Also, riding a bus requires accessing and waiting for it. The next equation formalises these phenomena (the l subscript is removed):

tbus K¯ = taccess + twait + tcar K¯ + fo kb tb + ts Bs K¯

(7)

fo is the occupancy factor for buses and it is the only way to limit crowdedness in the model, as crowdedness is not an attribute of the utility function. The lower this factor is, the less crowded the bus will travel. tb represents the time it takes a passenger to board the bus. Bs is the number of bus stops per kilometre and ts the extra time a bus needs to decelerate on arrival at and to accelerate on departure from the bus stop. Bus passengers need to wait for the bus to arrive at the bus stop. taccess represents access time; waiting time, twait, is given by Eq. (8), where φ is a factor that accounts for service regularity6:

twait =

(8)

fr

The frequency of the bus services is defined by the amount of people travelling by bus divided by effective capacity, that is,

fr =

n

n n l, bus N

(9)

fo kbus

Eq. (9) states that if the demand for bus services increases, the frequency of the service also increases, contributing to increasing scale economies in the provision of bus services, the Mohring effect. The Mohring effect is a positive externality among bus users as a new bus rider contributes to a higher frequency and so the rest of bus riders have to wait a little less (Mohring, 1972). Multiplying the frequency of the bus service by average trip distance K¯ yields the total amount of kilometres made by buses. Last, if we multiply the time to complete one cycle (round trip plus time needed at the bus terminal to ready the bus for the next cycle, tcycle) times the frequency, we obtain the size of the bus fleet. As there are two periods of the day, size fleet is determined by Eq. (10):

B = Max (tcycle _peak frpeak; tcycle _off

(10)

peak froff peak )

3.3. Fuel consumption Fuel consumption is a U-shaped function of speed with a minimum at an intermediate speed. As we are only concerned with congested urban traffic conditions for which speeds are below the speed corresponding to the minimum point of the fuel consumption 6

If time between successive buses were perfectly regular, the value of φ would be 0.5. 93

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function, we can safely assume fuel consumption to be decreasing in speed. This equation computes fuel consumption per kilometre:

g=

a + b + c vel + d vel2 vel

pg pg , n _tax

g

.

(11)

On the first term on the right hand side of the equation, vel denotes speed and a, b, c and d are parameters such that fuel consumption increases with lower speeds (UK DOT, 2014). The second term on the right hand side of equation defines the effect of price on fuel efficiency. Pg,n_tax represents the cost of fuel without taxes and ηg, the own-price demand elasticity of fuel consumption. Hence, when fuel is taxed, the price increase induces a higher fuel efficiency that, in turn, negatively affects the base of the fuel tax (Parry and Small, 2005). We adopt similar functions for the consumption of gasoline and diesel. 3.4. Cost of transport services There are two cost functions. There is one equation for the cost of road infrastructure provision. We assume a very simple cost function: (12)

C (RK ) = w RK K¯

w is the cost of infrastructure or road capacity per unit of time per unit of distance. A unit of time is the three-hour period corresponding to the morning commute; the unit of distance is a kilometre. This cost function assumes perfect divisibility and exhibits constant economies of scale. The second cost function is for buses and it has two components. The first component comprises variable costs and depends on kilometres. The second component includes the capital costs of buses that depend on the number of buses and on their size. The next equation determines total bus service costs:

C (Bus ) =

(pd dl + vcl, v + tolll, bus ) Kl, bus + Cbus (kb) B

(13)

l

Variable costs depend on i) diesel consumption per kilometre (d), ii) the price of diesel (pd), iii) other variable costs other than diesel (vc), iv) road tolls per kilometre for buses (tolll,bus) and v) total bus kilometres travelled within the stretch of the network considered for the analysis, Kl,bus. Fixed capital costs equal the capital cost of a bus as a function of size Cbus(kb) times the number of buses B. 3.5. Externalities To simplify the model, externalities (E) equal total fuel consumption from motorised vehicles. This amounts to consider that externalities are proportional to fuel consumption7. Implicitly, we only consider emissions of local pollutants, such as PM and O3. The factor ξ accounts for the higher emissions of local pollutants from diesel compared to gasoline. The main assumptions in this formulation are that (i) externalities correlate perfectly with fuel consumption and (ii) total emissions during the morning commute determine the amount of externalities to which people are exposed. Emissions represent a public bad since its ‘consumption’ is nonrival. Eq. (14) gives total emissions.

gK¯

E= l (peak; off peak )

n n l, car N

+ dKl,bus fl

(14)

n

3.6. Planner’s objective function The social welfare function is the sum of individual indirect utility functions V –the utilitarian social welfare function:

SWF ({U n}) =

N nV n

(15)

n

The planner maximises the above equation, subject to budget and feasibility constraints. Feasibility constraints, among others, include non-negativity constraints. 4. Scenarios to evaluate In this section, we describe the scenarios we evaluated. There are two types of transport services to be provided: roads and public 7 Parry and Timilsina (2010) make a similar assumption for emissions in Mexico City, based on the facts that emissions control equipment deteriorates over the vehicle life and that people can evade emissions inspections for in-use vehicles. See their footnote 13. In Santiago, Chile, controls are strict, but still we believe this general assumption is a good starting point for our simulation analysis. As an opposite case, Parry and Small (2005) consider local externalities to be related to driven kilometres as given by emissions norms per kilometre.

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buses. Each transport service could be provided separately –two transport agencies with their own budget constraint– or jointly –one transport agency with only one budget constraint. In Santiago, there are different transport agencies for road provision and public bus provision. As an opposite, Transport for London is one agency for London’s transport system. The London example affords an extra degree of freedom that, if well managed, could lead to a higher level of welfare. Transport services could be funded through road tolls, fuel taxes, bus fares or consumption taxes. Different funding mechanisms will have different impacts in terms of distortions or inefficiencies that, in turn, will affect welfare. We also created a Reference Scenario that intends to represent a status quo situation for comparison. This reference scenario will correspond to a maximization problem with some fixed parameters as road capacity, the fuel tax and the bus fare. The part of costs not covered by user charges will be subsidised through a tax on consumption. We did not create a first best scenario as a first best scenario would require, in addition to marginal social cost pricing, individualised lump sum transfers to achieve equality of the social marginal utility of consumption of every individual (Sandmo, 1998). To wrap up, each scenario implements different pricing policies from the user standpoint. Different pricing policies will provide different incentives that would affect the decision of time departure/not to travel and the decision of mode choice through Eqs. (1)–(4). These individual decisions, in turn, will affect the planer’s decisions on road infrastructure provision and bus level of service to maximise social welfare according to Eq. (15). Hence, different scenarios will bring about different transport outcomes. 4.1. Scenario I – Two transport agencies, full cost recovery, differentiated pricing by time of day Road tolls are designed to recover the costs of road infrastructure. The capital and operational expenses of buses are recovered through fares charged to bus passengers. Decision variables are i) road tolls differentiated by time of day, ii) bus fares differentiated by time of day, iii) frequency by time of day and capacity of buses and iv) road infrastructure provision. This scenario would be the closest to an “efficiency” scenario, with minimal concern for equity. 4.2. Scenario II – Two transport agencies, full cost recovery, homogeneous pricing by time of day In this scenario, the same road toll and the same bus fare are levied in the peak and the off-peak periods. Decision variables are i) road tolls fixed throughout the whole period, ii) bus fares fixed throughout the whole period, iii) frequency by time of day and capacity of buses and iv) road infrastructure provision. This scenario permits to contrast the effect of differentiated pricing by time of day versus homogeneous pricing. 4.3. Scenario III – One transport agency, full cost recovery, cross subsidies among transport modes In this scenario, there is only one transport agency as if the road agency and the public bus agency have been merged into a metropolitan transport agency. Bus fares are the same throughout the day, but road tolls adjust to demand by time of day. Decision variables are i) road tolls differentiated by time of day, ii) bus fare, the same for both periods, iii) frequency by time of day and capacity of buses and iv) road infrastructure provision. This scenario would allow the transport agency to address equity concerns through cross subsidies between travellers from different modes. 4.4. Scenario IV – One transport agency, full cost recovery, cross subsidies among transport modes, fuel taxes substituting for road tolls The same as Scenario III, with a fuel tax substituting for road tolls. Decision variables are i) fuel taxes, ii) bus fare, the same for both periods, iii) frequency by time of day and capacity of buses and iv) road infrastructure provision. As speeds differ between the peak and the off-peak, the fuel tax will also differ when translated to a charge per kilometre. This scenario permits to study the impact of funding road investments from fuel taxes. 4.5. Scenario V – Two transport agencies, full cost recovery for roads, available subsidies for public transport This scenario is analogous to Scenario I, but public transport is provided free of charge and funded through consumption taxes. Decision variables are (i) road tolls by time of day; (ii) consumption tax, (iii) frequency by time of day and capacity of buses and (iv) road infrastructure provision. In this scenario, the bus agency has more leeway to be concerned with equity as they can rely on subsidies to cover costs. 4.6. Scenario VI – Two transport agencies, free provision of road space, available subsidies for public transport In this scenario, the use of roads is free of costs and funded through consumption taxes. Capital and operational public bus expenses could be funded through fares, subsidies or a mix of fares and subsidies. Therefore, the bus fare, the same throughout the day, is left as a decision variable, being feasible to charge a zero price. Decision variables are (i) the consumption tax, (ii) the bus fare, (iii) frequency and capacity of buses and (iv) road infrastructure provision. This scenario is a polar case, where roads are provided free of charge and subsidies are made available for the bus agency if necessary. 95

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4.7. Reference scenario This scenario considers conditions similar to current policy in Santiago as well as in many other cities: no road pricing, subsidized public transport, road infrastructure financed via fuel and consumption taxes. We fix capacity at 4,500 vehicles per hour. The cost of road infrastructure is payed through consumption taxes and fuel taxes, with fuel taxes not higher than a value representative of a realistic level. The costs of bus services are partly payed through bus fares that cannot exceed a realistic value. A tax on consumption is implemented to pay the balance of costs not covered by fuel taxes nor bus fares. In this scenario, we do not intend to replicate exact current transport conditions in Santiago. Table 1 allows the reader to glance at all scenarios in a more friendly fashion. Table 1 Summary characteristics of each scenario. Characteristic

Scenario I

Scenario II

Scenario III

Scenario IV

Scenario V

Scenario VI

Reference Scenario

Road tolls by time of day Bus fares by time of day Fuel tax Consumption tax Subsidies for roads Subsidies for buses Full cost recovery - roads Full cost Recover –buses Full cost recovery with cross subsidies between modes Road and Bus agencies

Different Different – – – – √ √ – Separated

Same Same – – – – √ √ – Separated

Different Same – – – – – – √ Integrated

– Same √ – – – – – √ Integrated

Different Different – √

– Same – √ √ √ – – – Separated

– Same √ √ √ √ – – – Separated

√ √ – – Separated

The sign ‘√’ means the characteristic is present in the corresponding scenario; the sign ‘–’ means the characteristic is absent.

5. Model parameters In this section, we present the parameters of the model. We selected most of these parameters from data from the Metropolitan Santiago, Chile. We assume an average trip 10 km long; that is, K¯ = 10 km. 5.1. Population and income parameters The monthly income per strata amounts to CLP 338,480, CLP 557,373 and CLP 1,223,906 for low-income, middle-income and high-income people respectively. These values are taken from official statistics from the year 2011 (MDS, 2011) and updated to 2016 prices8. To make these incomes consistent with our modelling period (one commuting period), we divide these values by 60 (30 days times 2 commuting periods per day) to arrive to a per-commuting-period income values of CLP 5,700, CLP 9,300 and CLP 20,500 for low-income, middle-income and high-income people respectively. We consider a reference population of 21,000 people, stratifying it according to income: 25 percent of the population is lowincome people, 60 percent is middle-income people and 15 percent is high-income. This distribution of income is representative of that of Metropolitan Santiago for 2011 (MDS, 2011). This reference population together with the assumed road capacity for the reference scenario generate traffic conditions representative of a status quo situation. 5.2. Bus ridership Given our reference population of 21,000 commuters, we assumed that three (3) bus lines serve the stretch of the network under consideration, each line serving different origin-destination pairs. In terms of ridership, frequency and capacity the three bus lines operate in the same way. Implicitly, we assume the bus stops of different lines are located separately, contributing to less traffic conflicts. In terms of the working of the model, the assumption of three operating bus lines requires to multiply Eq. (8) and Eq. (10) by three and to divide Eq. (9) by three. We made the assumption of three operating bus lines to increase realism. Assuming only one bus line serving all riders would result in very high passenger loads, very high frequencies and very high capacity buses, artificially biasing results against the private car.

8 Taking as a reference date June 30st 2016, these are the rates of exchange for the Chilean peso: 1 EUR = CLP 734.58 and 1 USD = CLP 661.49. In Chile, rates of exchange float freely and can vary greatly through time upwardly or downwardly.

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5.3. Utility function parameters The parameters of leisure time (πs) in the utility function are related to the value of travel time savings. Fernández y De Cea Ingenieros (2005) calibrated the model ESTRAUS in use by SECTRA, the Transport Planning Office within the Chilean Ministry of Transport and Telecommunications. ESTRAUS is a four-step classical transport model calibrated for the city of Santiago, Chile, using data from travel surveys and vehicle and passenger counts. A component of this model is the modal split logit sub-model. As a result of this sub-model, a minute of waiting time and of access time are 1.93 and 3.63 times as onerous as a minute of in-vehicle travel time. With regard to the time-of-departure decision, we adjusted the values of ρ and κl (l = peak, off peak) to reproduce likely patterns of the morning commute. The values of κl are such that people prefer travelling in the peak to travelling in the off-peak to not travelling. The cost parameter of the nested logit model is given by the marginal utility of consumption of the generalized good that is decreasing throughout; hence, this parameter is endogenous in the model. This marginal utility is a function of the parameters m – the same for everybody – and θ. The parameter m is equal to 0.8, and we chose the values of θ –a different one for each level of income– to approximate the values of travel-time savings estimated for different strata for the city of Santiago. Regarding the disutility of externalities, we chose a value of ϖ so that it contributes to disutility levels around one and two per cent for each income strata, in the Reference Scenario. It is the same value of ϖ for the three strata. 5.4. Volume to capacity function and travel times Travel times are given by Eq. (6) with parameters α = 1.447 and ζ = 7.644 calibrated for mixed-traffic urban streets of Metropolitan Santiago (Fernández y De Cea Ingenieros, 2005) and a free flow speed of 40 km/h. For buses, we considered bus stops separated by 500 m and boarding and alighting times of 2.5 s per rider. The time ts accounting for deceleration and acceleration at the bus stop is 16.5 s (Tirachini, 2013). The value of φ is 0.5, assuming perfect regularity. For every bus passenger, access time to and from the bus stop is 6 min (Silva, 2010). As for the bus equivalence factor to convert buses to light vehicle units in the volume-tocapacity function, we used the following formula: feq = 1.65 + 0.0114 kb, adapted from Pavón (2017). We assumed a value for the bus occupancy factor parameter fo equal to 0.75 throughout the morning commute. As this parameter constrains the total number of people travelling on a bus –resulting in less crowded buses–, its effect will be to increase frequency and, indirectly, capital and operating costs. 5.5. Fuel consumption The parameters of the fuel consumption functions corresponding to the first term on the right hand side of Eq. (11) were taken from UK DOT (2014, Table 10). The value of ηg, the demand price elasticity of fuel consumption, is −0.2 (Rizzi, 2014). The cost of a litre of gasoline and diesel are CLP 302 and CLP 270 respectively. These values were derived by taking the retail price of fuel in Chile (June 2016) and deducting all taxes. 5.6. Capital costs of buses and cars Capital costs of buses, expressed as CLP/hour-bus, and variable costs, vc, of buses, expressed as CLP/km-bus are given by the following two equations (Pavón, 2017): (16)

Cbus (k ) = 5, 423.6 + 22.6 kb; vc = 2.3kb

Bus capacity kb is constrained at 120 passengers per bus. The capital cost of a private car was calculated from the best-selling car in 2016 in Chile, whose approximate cost was around CLP 7 million. We assume a car is fully depreciated over a period of ten years to arrive to a cost-of-capital value of CLP 960 per half a day. Under the assumption of our model, anyone willing to pay this per-half-day cost of capital will have access to private car; in other words, the decision to travel by car for commuting implicitly means renting it. We made this assumption to avoid the need to model the decision to purchase a car that would complicate matters unnecessarily. We took the cost of road infrastructure provision from Archer and Glaister (2006). This value is available in their Table 20, column ‘London’, row ‘incur’. When converted to a value per veh-km/h per unit of capacity it equals CLP 499. We multiply this value by three to take into account the duration of the morning commute of three hours. 6. Results We carried out our simulations using the optimization solver Knitro developed by Artelys©. We used the option ‘Multistart’ that generates multiple feasible initial solutions in the search of a global maximum. The reader should interpret results qualitatively as the focus of this research is on understanding the implications of different transport policies on transport outcomes and welfare. 9 We updated this value by the UK inflation (https://www.bankofengland.co.uk/monetary-policy/inflation/inflation-calculator) and then converted it to CLP.

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Table 2 Departure time and mode choice probabilities. Scenario I

Scenario II

Scenario III

Scenario IV

Scenario V

Scenario VI

Reference Scenario

Peak Off-peak* No travel

31% 60% 9%

41% 49% 10%

40% 51% 9%

41% 50% 10%

40% 52% 8%

44% 50% 7%

35% 55% 9%

Low-income people, peak share Low-income people, off-peak share* Low-income people, no travel

30% 59% 11%

40% 49% 11%

40% 49% 11%

40% 49% 11%

41% 50% 9%

45% 47% 8%

40% 50% 11%

Middle-income people, peak share Middle-income people, off-peak share* Middle-income people, no travel

32% 60% 9%

42% 49% 9%

41% 50% 9%

41% 50% 9%

41% 51% 7%

45% 49% 6%

36% 56% 9%

High-income people, peak share High-income people, off-peak share* High-income people, no travel

30% 62% 8%

40% 51% 9%

36% 55% 9%

39% 51% 10%

36% 56% 8%

38% 56% 6%

28% 64% 8%

Peak Bus Share - peak Car Share - peak Low-income people, bus share Low-income people, car share Middle-income people, bus share Middle-income people, car share High-income people, bus share High-income people, car share

64% 36% 88% 12% 62% 38% 30% 70%

72% 28% 93% 7% 72% 28% 38% 62%

82% 18% 96% 4% 83% 17% 50% 50%

79% 21% 95% 5% 80% 20% 46% 54%

81% 19% 96% 4% 82% 18% 50% 50%

21% 79% 40% 60% 16% 84% 8% 92%

41% 59% 68% 32% 34% 66% 14% 86%

Off-peak Bus Share Car Share Low-income people, bus share Low-income people, car share Middle-income people, bus share Middle-income people, car share High-income people, bus share High-income people, car share

67% 33% 95% 5% 68% 32% 21% 79%

88% 12% 99% 1% 93% 7% 50% 50%

74% 26% 97% 3% 78% 22% 26% 74%

90% 10% 100% 0% 95% 5% 56% 44%

74% 26% 97% 3% 78% 22% 26% 74%

53% 47% 88% 12% 51% 49% 14% 86%

57% 43% 92% 8% 57% 43% 15% 85%

Scenario I – Two transport agencies, full cost recovery, differentiated pricing by time of day. Scenario II – Two transport agencies, full cost recovery, homogeneous pricing by time of day. Scenario III – One transport agency, full cost recovery, cross subsidies among transport modes. Scenario IV – One transport agency, full cost recovery, cross subsidies among transport modes, fuel taxes substituting for road tolls. Scenario V – Two transport agencies, full cost recovery for roads, available subsidies for public transport. Scenario VI – Two transport agencies, free provision of road space, available subsidies for public transport. * These probabilities should be divided by two (2) to arrive to probabilities for each off-peak one-hour period.

Table 2 and Table 3 show the results of the simulations for all scenarios. Table 2 depicts all marginal and conditional probabilities corresponding to the nested logit travel demand model. Table 3 shows results regarding level of service, prices, emissions, welfare and values of travel time savings (VTTS). Regarding the validity of the simulations, we already said we are not trying to replicate the exact average traffic conditions in Santiago. Having this in mind, we first checked the VTTS and compared them to those estimated for Metropolitan Santiago. These values are endogenous as the marginal utility of income is given by the marginal utility of consumption that, in turn, depends on the solution of the model. Therefore, the calibrated VTTSs provide a measure of the reasonableness of our simulations. Across all simulations, the median VTTSs are 380 CLP/h, 1,591 CLP/h and 3,105 CLP/h for low-income, middle-income and high-income people, respectively (Table 2). These values are lower, but still in line with those estimated for Metropolitan Santiago (Fernández y De Cea Ingenieros, 2005). If we compare these values as a percentage of hourly earnings – calculated as monthly income divided by 22 working days per month and by 9 working hours a day –, these values are 22 percent, 57 percent and 50 percent for low-income, middle income and high-income people, respectively. The percentages for middle income and high-income people are within the range of those reported in the literature (Small and Verhoef, 2007). Regarding low-income people, evidence from Metropolitan Santiago suggests their VTTS is much lower than the value obtained by a linear-in-income approximation of the VTTS of middle- or high-income people. They are indeed willing to incur greater total travel time to save a few pesos. As another reference point about the calibration of the model, the estimated own price elasticity for the bus in the peak is −0.43, a value in line with those reported by Parry and Small (2009). For the Reference Scenario, car speed in the peak is 16 km/h, a value consistent with speeds observed in the CBD of Metropolitan Santiago in peak periods (Universidad Alberto Hurtado, 2014, Fig. 27). In addition, as the volume to capacity quotient is very high in the peak, with a high car mode split, roads cannot accommodate more travellers and many of them need to switch their departure time to the off-peak. 98

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Table 3 Level of service, prices, emissions and welfare.

Road capacity (veh/h) Car speed, peak (km/h) Car speed, off-peak (km/h) Bus speeds, peak (km/h) Bus speed, off-peak (km/h) Bus frequency, peak (bus/h) Bus frequency, off-peak (bus/h) Bus capacity (pax) Car road toll, peak (CLP/km) Car road toll, off-peak (CLP/km) Gasoline tax (CLP/l) Tax on generalised good (CLP) Bus fare, peak (CLP/km) Bus fare, off-peak (CLP/km) Total emissions, peak (eq_l) Total emissions, off-peak* (eq_l) Total welfare Low-income people. individual welfare Middle-income people. individual High-income people. individual welfare Low-income people VTTS Middle-income people VTTS High-income people VTTS

Scenario I

Scenario II

Scenario III

Scenario IV

Scenario V

Scenario VI

Reference Scenario

3,919 38 39 22 22 19 19 97 160 36 – – 78 10 1,966 3,456 814,566 28.3 38.1 59.2 379 1,582 3,103

3,757 37 40 21 22 25 18 109 139 139 – – 38 38 2,126 1,505 810,891 28.3 37.9 58.6 379 1,588 3,102

2,605 37 39 21 21 26 15 116 160 86 – – 33 33 1,523 2,384 813,231 28.4 38.0 58.9 380 1,589 3,102

2,843 36 40 20 22 26 18 115 – – 2,237 – 35 35 1,734 1,361 811,225 28.4 37.9 58.5 380 1,591 3,105

2,726 37 39 21 21 27 16 114 132 57 – 0.031 0 0 1,586 2,476 813,776 28.8 38.0 58.3 394 1,638 3,189

8,246 25 40 18 24 13 18 68 – – – 0.078 0 0 6,057 3,919 800,613 28.1 37.5 57.2 403 1,684 3,310

4,500 16 39 12 22 14 15 96 – – 600 0,019 30 30 4,830 3,889 800,054 27.9 37.3 58.0 383 1,601 3,152

eq_l: stands for equivalent litre. (Diesel fuel consumption by buses is multiplied by a factor to account for the higher level of local emissions.) VTTS: value of travel time savings. Taking as a reference date June 30st 2016, these are the rates of exchange for the Chilean peso: 1 EUR = CLP 734.58 and 1 USD = CLP 661.49. Scenario I – Two transport agencies, full cost recovery, differentiated pricing by time of day. Scenario II – Two transport agencies, full cost recovery, homogeneous pricing by time of day. Scenario III – One transport agency, full cost recovery, cross subsidies among transport modes. Scenario IV – One transport agency, full cost recovery, cross subsidies among transport modes, fuel taxes substituting for road tolls. Scenario V – Two transport agencies, full cost recovery for roads, available subsidies for public transport. Scenario VI – Two transport agencies, free provision of road space, available subsidies for public transport. * This value is the sum of the emissions of the two one-hour off-peak periods.

6.1. Road capacity, bus capacity and level of service The greatest level of road infrastructure, 8,246 veh/h, is built when roads are provided free of cost, Scenario VI. In all the other five scenarios, road infrastructure provision falls by a factor of 2.1 to 3.2 compared to Scenario VI. The lowest level of road provision corresponds to Scenario III, with only one transport agency, cross subsidies among transport modes and road tolls differentiated by time of day. Scenario IV –with fuel taxes replacing road tolls– and Scenario V –road tolls and free public transport– follow closely. In the Reference Scenario, car speeds are low in the peak, reaching 16 km/h. In this scenario, the off-peak speed is 39 km/h. Notwithstanding the greater road capacity provision of Scenario VI, car speeds only increase to 25 km/h in the peak. In the off-peak, speeds are those of free-flow. In all other Scenarios, speeds in the peak are two to four km/h below the free-flow speed, whereas in the off-peak speeds are those of free-flow or one km/h below, even for the Reference Scenario. In the peak period, the highest speeds, by a tiny margin, correspond to those scenarios where road tolls discriminate by time of the day. Bus speeds are lower than car speeds, the main reason being deceleration and acceleration at stops, and boarding and alighting of passengers. Once again, the Reference Scenario achieves the lowest peak bus speed, at 12 km/h. Then again, the second lowest peak bus speed corresponds to Scenario VI, at 18 km/h. In all other scenarios, peak bus speeds increase to around 20–22 km/h. Off-peak speeds reach 21–24 km/h in all scenarios. In two scenarios, Scenario VI and the Reference Scenario, frequencies are greater in the off-peak. As numerous travellers drive the car in the peak because it is under-priced, the volume-to-capacity ratio increases, reducing speeds and making buses very slow in the peak. Hence, many travellers postpone departure to the off-peak period, with lower traffic flows that permit greater bus speeds and frequencies. In all other scenarios, frequencies are higher in the peak. Scenarios II to V provide the highest frequencies in the peak, between 25 and 27 services per hour, with average waiting times somewhat greater than a minute, almost exhausting the Mohring effect. In the off-peak, frequencies decrease, with a minimum at 15 services per hour (Scenario III and Reference Scenario) and a maximum at 19 services per hour (Scenario I). The highest average waiting time is never greater than two minutes. Bus capacity does vary in each scenario. In Scenario VI, bus capacity is the lowest, at 68 passengers per bus. The highest bus capacity corresponds to Scenario III, at 116 passengers per bus. Bus capacity is quite close to this value in Scenarios IV and V, but it never reaches the constraining value of 120. These results are quite different to those of Basso and Silva (2014) for their simulations for Santiago. In their case, bus capacity is 153 passengers per bus or even higher depending on the simulated scenario. We attribute this difference to their assumption that one bus line serves all bus riders. 99

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6.2. Departure time and modal split In all simulations, those who travel in the peak are between 31 percent and 44 percent of total population. Scenario VI (free provision of road space) has the greatest value: as transport services are subsidized, people travel more in the peak as it provides greater utility. In the Reference Scenario, those who travel in the peak are 35 percent of the population. As mode choice is biased towards the car, the volume-to-capacity relation is high, speed is low and therefore many users switch their departure time to the offpeak. The lowest value of peak travel is 31 percent in Scenario I. The proportion of people who do not travel varies from 7 percent to 10 percent, the lowest value corresponding to Scenario VI. In all scenarios, and more so in the Reference Scenario, high-income people travel the least in the peak. This result is typical in the literature of Vickrey-type models (Vickrey, 1969), where in the absence of tolls, those with the highest VTTS avoid traveling during the most congested periods (Newell, 1987; Arnott et al., 1994). In this type of model, users with high VTTS prefer to incur low schedule delay costs rather than high travel time costs. In our model, however, there are no schedule delay costs; put simply, highVTTS users prefer to avoid travelling at that time of the day where travel delays are greater. In Scenario VI, where roads are provided free of cost, modal split is tilted to the car, especially during the peak, with car usage at 79 percent of total trips. This value is even higher than the one corresponding to the Reference Scenario. Free provision of roads results in very high road usage, even for middle- and low-income people. In Scenarios I to V, car share is much lower both in the peak and in the off- peak, with maximum values in Scenario I at 36 percent and 33 percent in the peak and the off-peak, respectively. Joint optimization of road capacity, bus fleet and pricing of transport services results in higher use of public transport, a most sensible result for consolidated, dense urban areas. As an expected result, the higher personal income is, the higher the probability of choosing car is; the opposite happens with the probability of choosing the bus. For low-income people, the probability of choosing the car in Scenarios I to V is never higher than 12 percent, both in the peak and in the off-peak. In Scenario VI and in the Reference Scenario, the probabilities of low-income people choosing the car in the peak are 60 percent and 32 percent respectively10. In the same scenarios, these probabilities go down to 12 percent and eight percent in the off-peak. As we will see later, this is by no means an indication that the welfare of low-income people has increased. 6.3. Air pollution externalities It is worth remembering that i) emissions correlate perfectly with fuel consumption and ii) total emissions throughout the morning period affect utility negatively. Hence, the best way to deal with this externality is through a fuel tax (Parry and Small, 2005). Total emissions change notably among different scenarios. In Scenario VI, where transport services are free of cost, emissions are at their greatest value. The second worst situation takes place in the Reference Scenario. In all the other scenarios, emissions fall significantly. In Scenario IV, where fuel taxes are charged and there is a single transport agency, emissions are at their lowest value. A result worth commenting is how emissions change between Scenario I and Scenario II and between Scenario III and Scenario IV. In both cases, in the first scenario road tolls are adjusted by time of the day, whereas in the second scenario, the levy is the same in the peak and in the off-peak. In both cases, when moving to the second scenario, total emissions fall and they fall more strongly in the offpeak due to the comparatively higher road tolls levied at this time of the day. 6.4. User charges When road tolls for private cars are implemented by time of day, there is a high variation in their magnitude, the off-peak value being significantly lower, providing an incentive to switch to car travel in the off-peak. This incentive is lost when road tolls remain the same by time of day. Road tolls for buses and diesel tax are always zero: by charging the full cost of road construction on light vehicles, the road agency is able to redistribute welfare favouring low-income people11. As these levies are always zero, we do not show them in Table 3. As to the value of road charges, in Scenario I, road tolls are CLP 160 and CLP 36 per kilometre in the peak and the off-peak respectively. Bus fares per kilometre are CLP 78 and CLP 10 in the peak and the off-peak respectively. When moving to Scenario II, road tolls and bus fare per kilometre are CLP 139 and CLP 38 respectively –no price discrimination between times of the day. In Scenario IV, the gasoline tax per litre is CLP 2,237 and bus fares, at any time of the day, are CLP 35 per kilometre. For the peak and off-peak period, the gasoline tax turns out to be a ‘quasi’ road toll per kilometre of CLP 114 and CLP 111 respectively. Despite the fuel tax being able to adjust by time of day as ‘quasi’ road toll, the adjustment falls short of what would be optimal as in Scenario I. To put all these values in perspective, low-income, middle-income and high-income people's incomes per modelling period are CLP 5,700, CLP 9,300 and CLP 20,500 respectively –and remember an average one-way trip is 10 km long. Scenario VI result regarding bus fares deserves an explanation. In this scenario, roads are used free of charge. Therefore, mode 10 From this, one can infer that services like Uber that make the use of private rides more accessible, could subtract ridership from buses not only from high- or middle-income earners, but also from low-income people if no road pricing is in place. Remember, we consider the per-trip capital costs of car usage, as if car users could rent the car for the day. 11 Actually, this is one reason put forward for the lower diesel tax rate in Chile. The diesel tax rate is one-fourth of the gasoline tax rate.

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share is heavily tilted towards cars. This, in turn, exerts very high pressure on road construction and on deteriorated air quality. The only means to attenuate, to some extent, car demand is by means of subsidising public transport, to the point that it is provided free of charge. 6.5. Welfare and equity In the model, the only way to redistribute welfare is through transport interventions that affect the price of transport services and/ or the price of generalized consumption. Pricing of transport services indirectly affects the total amount of emissions representing a public bad that generates a negative externality. The Reference Scenario provides the lowest total welfare. In this Scenario, low-income people and middle-income people achieve their lowest welfare and high-income people their second lowest level –second to Scenario VI. Scenario VI, where transport services are provided free of charge and funded through consumption taxes, achieves the second lowest total welfare. In this scenario, middleincome and low-income people are marginally better off than in the Reference Scenario, but worse off than in all other scenarios. Despite high-income people contributing proportionally more to total tax collection, they benefit from both free roads and free public buses, making the consumption tax not progressive enough. Scenario I provides the maximum total welfare. In this scenario, two different transport agencies provide transport services, each of them having to cover their costs through user charges. This scenario also provides the highest welfare levels for middle-income people and high-income people at the expense of the welfare of low-income people. Scenario V achieves the second highest total welfare. In this scenario, i) public transport is free of charge and funded through consumption taxes and ii) road users pay a toll by time of day. This Scenario favours low-income people who achieve their highest welfare at the expense of the welfare of high-income people. Regarding middle-income people, they are almost the same as in Scenario I. In Scenario V, the consumption tax becomes highly progressive: high-income people contribute the most to tax collection and the tax itself is spent on public transport that is mainly used by middle-income and low-income people. Redistribution would have been higher if negative bus fares could be charged; however, we did not allow for this option. Compared to the Reference Scenario, Scenario V achieves a welfare improvement of 0.4 percent, 1.8 percent and 2.9 percent for high-income people, middle-income people and low-income people, respectively. Different scenarios affect the welfare of different income groups in different ways. This is a headline result that also showed up in Rizzi (2014). For instance, following the leximin principle (Sen, 2017), social choice among scenarios would favour the one providing the highest welfare to the worst-off individual; in our case, Scenario V. Simple majority rule will result in Scenario I being the preferred social alternative. As a last observation, the impact in terms of welfare of different scenarios is relatively small: redistribution through transport markets would not correct huge differences in personal income. Even worse, blunt subsidization as in Scenario VI makes everybody worse off. 6.6. Sensitivity analysis We performed two sets of sensitivity analyses. In the first set, we subjected four variables of the model to a sensitivity analysis to better understand their impact on the results. We carried out this sensitivity analysis only for Scenario I and Scenario V. We considered, in turn, i) an increase in the cost of infrastructure, ii) an increase in the preference for commuting in the peak, ii) an increase in the disutility from emissions, and iv) a modification in the value of ζ in the travel delay equation. We started doubling the cost of infrastructure. When doing so, bus ridership increases drastically and road infrastructure falls notably in both Scenario I and Scenario V to 997 veh/h and 1,003 veh/h, respectively. This leads to very high road tolls, making car use a luxury almost exclusively for few high-income people; car share in the peak is less than eight percent in both scenarios. Most people travel by public bus, whose frequency increases by more than 25 percent. Air quality also improves notably. In terms of welfare redistribution, we observe the same pattern as before between the two scenarios. We then increased the preference for travelling in the peak period by increasing the value κpeak by the same amount for the three income types. This amounts to an increase in the value of κpeak of 26 percent on average for the three income strata. Surprisingly, doing so results in a moderate decrease in road infrastructure provision of around three percent in both scenarios. In both scenarios, the greater amount of people travelling in the peak are accommodated through increased bus frequencies. In the peak, bus frequencies increase by 35 percent and 72 percent for Scenario I and Scenario V respectively. At the same time, road tolls go up in the peak by approximately 20–22 percent to incentivise a modal shift to buses. Once again, there are no significant changes in terms of car speeds and bus commercial speeds. When doubling the disutility of externalities from air pollution, in Scenario I, results are almost the same as when the cost of infrastructure was doubled: road infrastructure provision is reduced significantly as well as car share. In Scenario V, however, there is only a moderate reduction (five percent) in road infrastructure provision, accompanied by a ten percent increase in road tolls. This was enough to reduce car usage by 19 percent and 28 percent in the peak and the off-peak, respectively. The contrast between Scenario I and Scenario V, in terms of road infrastructure provision and mode share, stands out. We hypothesize the following explanation. In Scenario V, increasing road tolls by 10 percent is enough to deter many travellers from using the car as, in this scenario, the consumption tax is being used aggressively to provide free public transport. Welfare redistribution makes low-income people better off, attenuating the need to reduce emissions to the extreme required in Scenario I. In Scenario I, the only way to improve the welfare of low-income people, and indirectly everybody’s welfare, is through lower emissions, as bad air quality is a non101

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rival good, so a more aggressive stance against car usage should be adopted. Our next sensitivity analysis refers to the values of the volume-to-capacity function. We changed the value of ζ to 4, as this value is typically used in this type of analysis (Parry and Strand, 2012; Basso and Silva, 2014). Decreasing the value of ζ leads to greater travel delays at volume levels below capacity utilization, making congestion more severe. In Scenario I, there is a 15 percent reduction of road infrastructure provision. Road tolls are increased by 23 percent and 117 percent in the peak and the off-peak, respectively, with bus fares almost the same. Speeds are a shade lower in both periods. In terms of modal split, car usage goes down by around 42 percent in both peak and off-peak periods. Reducing the value of ζ from 7.644 to 4 makes travel delays higher at lower levels of vehicle flow, favouring the use of public bus. For Scenario V, road infrastructure falls very slightly, road tolls are increased slightly and car usage diminishes approximately by 30 percent in both periods. In terms of the distribution of departure period by time of the day and no travel, proportions remain almost the same in both scenarios. Once again, we believe that as in Scenario V, as there are more channels to maximise social welfare, the change in the ζ parameter has less of an impact in terms of road infrastructure provision than in Scenario I. In the second set of sensitivity analyses, we studied the impact of three policies. First, we ran a simulation assuming road infrastructure provision fixed at 4500 veh/h and the presence of two agencies: one for managing roads and another one for managing public buses. These two agencies must recover all their costs through user charges. Roads are financed through fuel taxes and buses through fares. This Scenario is quite similar to Scenario II with fuel taxes substituting for road tolls and, of course, with road infrastructure fixed. In this new scenario, total welfare increases notably, surpassing that of Scenario VI and coming quite close to the value corresponding to Scenario II. Therefore, optimal pricing alone, without the optimal provision of road infrastructure, would lead the economy to a relevant increase in the welfare of all agents. Basso and Silva (2014) also found this result in their simulations, where road infrastructure is always fixed. Second, we wanted to make a direct comparison between road tolls and fuel taxes. Because of fuel efficiency, fuel taxes are imperfect substitutes for road tolls (Parry and Small, 2005; Rizzi, 2014). To analyse the impact of fuel efficiency in our simulations, we also ran a different version of Scenario II, with fuel taxes substituting for fixed road tolls throughout the day, permitting a fair comparison between fuel taxes and road tolls. Our model considers two main externalities. The first externality is travel delays and the best pricing instrument to deal with it is a road toll depending on the level of congestion. The second externality is air pollution and the optimal way to deal with it is by means of a fuel tax. When comparing both simulations, we observe an increase of eight percent in the provision of infrastructure, in the modified Scenario II. This leads to an increase in car share of two percent in both the peak and the off-peak and to slightly higher emissions. Despite these changes in this new Scenario II, total welfare decreases by a tiny amount, but high-income people are marginally better off, two results also obtained in Rizzi (2014). The interplay between the two externalities makes fuel efficiency have a minimal impact on total welfare, although the transport outcomes change in a visible way. Therefore, if travel delays are the most acute externality in terms of marginal external costs, and only one pricing instrument could be implemented, a uniform road toll would bring about a higher social welfare. When comparing the results in the above paragraph with those reported by Parry and Small (2005), we find similarities and dissimilarities. Like them, we arrived at the conclusion that a road toll is a better pricing instrument in terms of welfare maximisation than a fuel tax, as the marginal external costs of travel delays exceed those from emissions. However, in terms of the amount of the increase in total welfare, our result does not yield as high an increase as theirs. The modelling settings present several differences that could explain this dissimilarity. Parry and Small (2005) assume a fixed amount of infrastructure and public transport is not present in their model nor equity considerations. Third and last, we ran a new Scenario I where income redistribution is performed in a lump-sum fashion. High-income people's income is taxed with a five percent levy to be redistributed to low-income people. This amount of money increases low-income people’s income by 11 percent. Low-income people would spend this lump-sum transfer to maximise their personal utility. Middleincome people’s income remains the same. This scenario achieves the highest total welfare and the highest impact on low-income people’s welfare. Low-income people see their welfare increased by six percent whereas high-income people’s welfare falls 3.4 percent. In this new Scenario I, low-income people are travelling the same but consuming more. It is greater consumption that increases low-income people’s welfare, not travelling more. 7. Discussion If the provision and pricing of road capacity are jointly determined, with road users paying the cost of infrastructure (through road tolls or fuel taxes), the amount of required urban road space diminishes. In our simulations, we observe substantial reductions in road capacity when moving from a scenario with no user charges to scenarios with user charges. This result is not new in the literature. For example, De Lara et al. (2013) considered a monocentric city, where people commute to the city centre, only by car, where all economic activity is located. In their model, congestion technology is the same as in ours. They considered one time period, one type of consumer (household) and roads could be funded through road tolls responsive to traffic conditions or a poll tax. They showed that when moving from no road tolls –roads funded through poll taxes– to first best road tolls, the amount of urban space allocated to roads is reduced by 20 percent and average travel times, by 13 percent12. As we did not design a first best scenario, we made a crude comparison by contrasting Scenario I with Scenario VI. In our simulations, we observe greater reductions of both road 12 In their model, location –and as a consequence population density– depends on the funding scheme; therefore, first best road pricing also achieves lower average travel distance.

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infrastructure provision (53 percent) and travel times (36 percent in the peak). Most likely, this is so because we included public transport in the analysis, which they did not. Using Vickrey’s model, Arnott et al. (1993) show that optimal demand management also results in a lower requirement of road capacity of 25 percent for their best-guess demand elasticity. We also show that, when road capacity is jointly designed and priced, travel times are greatly reduced even at peak times of the day. We could interpret this result as the static counterpart of that obtained in Vickrey’s dynamic model. In Vickrey’s model, congestion technology is that of a vertical queue: vehicles arrive at a server and their travel time depends on the number of vehicles in front of them at the server. Once the vehicle is ‘served’, travel times are those corresponding to free-flow speeds. If optimal tolls adjust continuously to traffic demand, wasted travel time in queues is brought down to zero (Vickrey, 1969). In our static model, travel delays are not eliminated, but are substantially reduced. By reducing travel time, fuel consumption is lowered, reducing in turn pollution externalities. Designing adequate user charges will level the playing field for buses, increasing public bus modal share. A higher bus ridership contributes to a more efficient use of the road infrastructure as more travellers could travel at the same time of day, thus allowing more users to depart at their preferred time. In case there is a very strong preference for travelling in the peak, differentiated pricing among time of the day and between modes is the adequate tool to tackle this situation. Building more road infrastructure would not necessarily make society better off. Different scenarios lead to different transport and welfare outcomes. Depending on the scenario, the transport outlooks do vary significantly. However, in terms of total welfare and equity, variations are narrow. The possibility of addressing equity issues through transport pricing is limited13 and populist policies that tend to underprice private transport, even if public transport is subsidised, would do more harm than good. There are indeed smarter fiscal policies, outside the transport realm, to improve the welfare of lowincome and middle-income people14. If, due to political reasons, targeted fiscal policy could not be implemented to address equity concerns, the transport planner could still do something. Scenario V provides a blueprint for action. On the one hand, public transport is free and used mainly by lowincome and middle-income people. On the other hand, public transport capital and operational expenses are covered with the proceeds of consumption taxes. These consumption taxes are paid in the same proportion by everybody, with the bulk of the revenues accruing from the consumption of high-income people. At the same time, car drivers pay the costs of road infrastructure provision through road tolls. Thus, when comprehensively analysed, the provision of free public transport funded through consumption taxes is a progressive policy. Another alternative is Scenario III or Scenario IV, where all transport services are provided by the same transport agency and revenues from road pricing cross subsidize, at least partially, public transport expenses. This contributes to the welfare of low-income people. If road pricing were to be implemented, a comparison between the Reference Scenario and the other scenarios allows us to infer that reallocation of road space away from private car could be a sensible strategy in denser parts of cities, provided our modelling assumptions represent real-life conditions to some extent. This phenomenon, for example, has been observed in Central London, where road pricing was instituted, public transport was reinforced and some road space was reconverted to provide room for nonmotorized transport (Badstuber, 2018). We strongly believe that under current transport demand and management conditions –where car users do not pay the full cost of motoring– most cities have built road infrastructure in excess. We have already said that either charging road tolls or fuel taxes would lead to a more rational use of private transport. Notwithstanding this, there are certainly differences between these two pricing instruments. First, road tolls can be easily implemented as a function of time and space, whereas fuel taxes could not. Hence, to address travel delays, road tolls are a better pricing instrument. Second, fuel taxes are a better pricing instrument to cope with externalities related to fuel consumption as local pollutant emissions and CO2 emissions. Third, fuel efficiency does play a role in terms of the transport outcome according to our sensitivity analysis. When moving to fuel taxes, the amount of roads to be built increases. Establishing fuel taxes could also be slightly regressive, favouring high-income people (Rizzi, 2014). Another relevant policy conclusion from our simulations is that if road user charges are in place, the need for dedicated bus lanes does not arise since speeds in the peak are very close to free-flow speeds. With dedicated bus lanes, commercial bus speeds would only increase two or three kilometres per hour, making the measure much less effective. In other words, dedicated bus lanes in dense urban areas could be thought of as a traffic management solution to ward off congestion from public transport in a political context where road pricing is not feasible. Interestingly, Basso and Silva (2014) also conclude that congestion pricing helps to achieve greater levels of welfare than dedicated bus lanes. They recommend policy makers to try establishing road pricing in the first place, and if this policy were not possible, then try introducing dedicated bus lanes. What is definitely relevant, however, in terms of bus commercial speeds, is a smart bus stop management. In our model, people board the bus in a single queue. Investment in bus and bus stop designs and/or payment mechanisms that speed up the process of boarding and alighting will contribute to higher commercial speeds. We also implicitly assumed in our modelling a type of vertical queue of buses at bus stops. If we link this point with what we said above about reallocation of road space, it may well be that some of the road space that could be saved through adequate pricing needs to be re-allocated to the provision of roadside space for bus bays. We close the paper providing a few caveats about this research. First, we developed our model having in mind capital cities of South American countries like Santiago or Buenos Aires and the functioning of the tax systems of these countries. These cities have a

13

If negative bus fares were an option, the room for redistribution would certainly increase. Lowering the cost of transport could lead to positive external agglomeration economies and facilitate low-income people’s access to the job market. Our model does not consider these features. 14

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very dense and expanded urban center (CBD), making possible the availability of public buses that exhaust Mohring scale economies. Many of our conclusions may not apply directly to other types of cities or even to suburban areas of the cities we have in mind. Second, the benefits of free public transport should be weighed against labour unions power that could ensue. If labour unions demanded very strict labour conditions or very high benefits, these could result in greater than optimal subsidies and poor service quality, reversing potential benefits in terms of equity and welfare as in Scenario V. Third, regarding the implementation of user charges, we are ignoring the administrative costs of road toll collections and of fuel tax collection. The costs of the latter are usually lower as they are collected through motor-vehicle fuel wholesale distributors, whereas road tolls need to be levied on each individual driver. We also ignore the fact that road tolls are usually charged by local authorities and fuel taxes by the central government (De Borger and Proost, 2012). Fourth, from a methodological point of view, the main limitation of our analysis is the treatment of travel delays. Nowadays, macroscopic fundamental diagram models are starting to dominate the formal treatment of the economics of traffic congestion (Daganzo and Geroliminis, 2008; Fosgerau, 2015). Future analysis of the interaction between pricing and transport service provision should incorporate this type of modelling. A starting point in that direction is the analysis by Gonzales (2015). Acknowledgements We greatly benefited from comments from Leo Basso and Hugo Silva throughout this research. We are indebted to Antonio Russo for reading and commenting a first draft of this article. We also thank the comments and suggestions of three anonymous referees that substantially contributed to improve the quality and readability of the article. All errors, of course, are our own responsibility. We recognize financial support from project FONDECYT 1170903 and the Institute in Complex Engineering Systems (CONICYT: FBO816). Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.tra.2019.05.001. References Archer, C., Glaister, S., 2006. Investing in Roads: Pricing. Retrieved from. Costs and New Capacity, Independent Transport commission. Arnott, R., de Palma, A., Lindsey, R., 1993. A structural model of peak- period congestion: A traffic bottleneck with elastic demand. Am. Econ. Rev. 83 (1), 161–179. Arnott, R., de Palma, A., Lindsey, R., 1994. The welfare effects of congestion tolls with heterogeneous commuters. J. Transp. Econ. Policy 28 (2), 139–161. Badstuber, N., 2018. London's Congestion Charge Is Showing Its Age. Retrieved from, Citylab. Basso, L., Silva, H., 2014. Efficiency and substitutability of transit subsidies and other urban transport policies. Am. Econ. J.: Econ. Policy 6, 1–33. Castex, G., Sepúlveda, F., 2014. Caracterización del mercado laboral en Chile y su evolución en los últimos 25 años. Banco Central de Chile Working Paper No. 728 (in Spanish). http://www.bcentral.cl/documents/20143/32019/bcch_archivo_096426_es.pdf/05e74c34-13dd-51cc-936f-b193a0b5fb14. D'ouville, E.L., McDonald, J.F., 1990. Optimal road capacity with a suboptimal congestion toll. J. Urban Econ. 28, 34–49. Daganzo, C., Geroliminis, N., 2008. An analytical approximation for the macroscopic fundamental diagram of urban traffic. Transp. Res. Part B 42, 771–781. De Borger, B., Proost, S., 2012. Transport policy competition between governments: a selective survey of the literature. Econ. Transport. 35–48. De Lara, M., de Palma, A., Kilani, M., Piperno, S., 2013. Congestion pricing and long term urban form: Application to Paris region. Regional Sci. Urban Econ. 43, 282–295. Engel, E., Galetovic, A., Raddatz, C., 1999. Taxes and income distribution in Chile: some unpleasant redistributive arithmetic. J. Dev. Econ. 59 (1), 155–192. Fernández y De Cea Ingenieros, 2005. Análisis y actualización del modelo ESTRAUS, Informe Ejecutivo. Final Report for Secretaria Interministerial de Planificación de Transporte (SECTRA). Santiago, Chile (in Spanish). Fosgerau, M., 2015. Congestion in the bathtub. Econ. Transport. 4, 241–255. Frankena, M.W., 1981. The effects of alternative urban transit subsidy formulas. J. Publ. Econ. 15, 337–348. Glaister, S., Collings, R., 1978. Maximisation of passenger miles in theory and practice. J. Transp. Econ. Policy 12, 304–321. Gonzales, E.J., 2015. Coordinated pricing for cars and transit in cities with hypercongestion. Econ. Transport. 4, 64–81. Jara Díaz, S., Farah, M., 1987. Transport demand and users' benefits with fixed income: The goods/leisure trade off revisited. Transp. Res. Part B 21, 165–170. Levinson, D., 2010. Equity effects of road pricing: a review. Transp. Rev. 30, 33–57. Lindsey, R., 2012. Road pricing and investment. Econ. Transport. 1, 49–63. Mayeres, I., Proost, S., 2001. Marginal tax reform, externalities and income distribution. J. Publ. Econ. 79, 343–363. MDS, Ministerio de Desarrollo Social, 2011. Encuesta de Caracterización Socioeconómica Nacional. (in Spanish). Mohring, H., 1972. Optimization and scale economies in urban bus transportation. Am. Econ. Rev. 62, 591–604. Mohring, H., Harwitz, M., 1962. Highway Benefits: An Analytical Framework. Northwestern University Press, Evanston, Illinois. Nash, C., 1978. Management objective, fares and service levels in bus transport. J. Transp. Econ. Policy 12, 70–85. Newbery, D.M., 1994. Pricing and congestion: economic principles relevant to pricing roads. In: Layard, R., Glaister, S. (Eds.), Cost-Benefit Analysis, second ed. Cambridge University Press, Cambridge. Newell, G., 1987. The morning commute for nonidentical travelers. Transport. Sci. 21, 74–88. Parry, I.W.H., Small, K.A., 2005. Does britain or the united states have the right gasoline tax? Am. Econ. Rev. 95 (4), 1276–1289. Parry, I.W.H., Small, K.A., 2009. Should urban transit subsidies be reduced? Am. Econ. Rev. 99 (3), 700–724. Parry, I., Strand, J., 2012. International fuel tax assessment: an application to Chile. Environ. Dev. Econ. 17, 127–144. https://doi.org/10.1017/S1355770X11000404. Parry, I., Timilsina, G., 2010. How should passenger travel in Mexico City be priced? J. Urban Econ. 68, 167–182. Pavón, N., 2017. Tarificación y Provisión de Infraestructura Vial y Servicios de Transporte Público: el Impacto de Diferentes Mecanismos de Financiamiento. Thesis, School of Engineering, Pontificia Universidad Católica de Chile, MSc (in Spanish). Rau, T. (2012) Flexibilidad de la jornada laboral en Chile: una tarea pendiente. Centro de Políticas Públicas UC Working Paper No. 50. (in Spanish). Rizzi, L.I., 2014. Simple model of road infrastructure financing: the impact of different road user charges. J. Transp. Econ. Policy 48, 35–51. Russo, A., 2015. Pricing of transport networks, redistribution, and optimal taxation. J. Publ. Econ. Theory 17, 605–640. Sandmo, 1998. Redistribution and the marginal cost of public funds. J. Publ. Econ. 70, 365–382. Sen, A., 2017. Collective choice and social welfare, Expanded Edition. Penguin Books. Silva, H., 2010. Análisis Microeconómico de Políticas para Combatir la Congestión Vial. Thesis, Department of Civil Engineering, Universidad de Chile, MSc (in Spanish).

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Small, K.A., Verhoef, E.T., 2007. The Economics of Urban Transportation. Routledge, London. Tirachini, A., 2013. Estimation of travel time and the benefits of upgrading the fare payment technology in urban bus services. Transp. Res. Part C 30, 239–256. UK DOT, Department for Transport United Kingdom, 2014. Values of Time and Vehicle Operating Costs. Transport Analysis Guidance (TAG) Unit 3.5.6. Available at http://webarchive.nationalarchives.gov.uk/20140304110038/http://www.dft.gov.uk/webtag/documents/expert/pdf/U3_5_6-Jan-2014.pdf. Universidad Alberto Hurtado, 2014. Encuesta Origen Destino de Viajes 2012. Available at. Santiago, Chile. In Spanish, Final Report for Secretaria Interministerial de Planificación de Transporte (SECTRA). Verhoef, E.T., Mohring, H., 2009. Self-financing roads. Int. J. Sustain. Transport. 3, 293–311. https://doi.org/10.1080/15568310802259940. Vickrey, W., 1969. Congestion theory and transport investment. Am. Econ. Rev. 59, 251–260. Wilson, J.D., 1983. Optimal road capacity in the presence of unpriced congestion. J. Urban Econ. 13, 337–357.

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