Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form

Transportation Research Part B xxx (2015) xxx–xxx

Contents lists available at ScienceDirect

Transportation Research Part B journal homepage: www.elsevier.com/locate/trb

Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form q Martijn I. Dröes a,b,c,⇑, Piet Rietveld c a

Amsterdam Business School, Faculty of Economics and Business, University of Amsterdam, Plantage Muidergracht 12, 1018 TV Amsterdam, The Netherlands Amsterdam School of Real Estate, Jollemanhof 5, 1019 GW Amsterdam, The Netherlands c Department of Spatial Economics, Faculty of Economics and Business Administration, VU University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands b

a r t i c l e

i n f o

Article history: Received 21 April 2014 Received in revised form 3 July 2015 Accepted 4 July 2015 Available online xxxx Keywords: General equilibrium Public transport Land use model Railway Sorting

a b s t r a c t We examine the effect of spatial differences in access to a railway network on both urbanization and road congestion in a typical ‘transport corridor between cities’ setup. Using a spatial urban equilibrium model, we find that if the number of access nodes, i.e. stations, is limited, stations contribute to the degree of urbanization. The total effect on road congestion, however, is small. By contrast, if stations are omnipresent there is little effect on urban spatial structure, but a considerable decrease in congestion. This suggests there is a policy trade-off between congestion and urbanization which crucially depends on the type of railway network. We find similar results for a within-city metro network. The key methodological contribution is that, besides the dependence between mode choice and where to work/live, the model allows for differences in the degree of substitutability – local competition – between transport modes. We find that an increase in the substitutability between car travel and railway travel substantially decreases the congestion reduction benefits of a dense railway network. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Roads have had a considerable impact on urban spatial structure. Baum-Snow (2007a), for instance, finds that without the interstate highway system there would have been more clustering of population (city growth) in the United States. In other words, highways caused suburbanization. This result is particularly interesting given the concerns about urban sprawl and, more recently, the decline of certain urban areas (Glaeser, 1998). In many countries, such as the European countries, but also relatively poor countries, railway travel is an important alternative mode of transport. The yearly passenger-km of rail transport in the EU, for instance, is about 398 billion. Only in India and China the amount of travel by railroads is higher,

q We would like to thank Jos van Ommeren, Hans Koster, Ioannis Tikoudis, seminar participants of the TOD Southwing 2013 international seminar and NARSC 2013 conference for valuable comments. In addition, we are very grateful that Alex Anas provided comments and the programming code he used in Anas and Rhee (2006). This work has benefited from a NWO (DBR) research grant. This article is in memory of Piet Rietveld, who has passed away on November 1, 2013. ⇑ Corresponding author. Tel.: +31 20 5255414, +31 20 5982291. E-mail addresses: [email protected], [email protected] (M.I. Dröes).

http://dx.doi.org/10.1016/j.trb.2015.07.004 0191-2615/Ó 2015 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

2

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

978 billion km and 815 billion km, respectively. By contrast, it is only 9.5 billion km in the US (UIC, 2011). This raises a question about the role of railway travel in determining urban economic outcomes. To understand the added impact of railway travel on the urban economy it is important to highlight two aspects of such travel that differ from travel via roads. First, supply of railway services is discrete by nature. That is, access to the railway network goes through a train station while access to the road network is nearly continuous. As such, the spatial allocation of train stations has a direct effect on the distribution of population across space (urbanization). Second, railway travel provides an alternative to travel by car, at least to some degree, and, consequently, interacts with the level of road congestion. This interaction depends, however, on the spatial structure of the railway network and the degree of mode substitutability. The aim of this paper is to examine the interaction between urbanization and road congestion in relation to spatial differences in access to a public transport (railway) network and to highlight the role of mode substitutability as a key determining factor in explaining urbanization and congestion outcomes. We model travel in a generic transport corridor based on the computable spatial urban equilibrium model of Anas and Kim (1996), Anas and Xu (1999), and Anas and Rhee (2006), in the rest of this paper referred to as the Anas model. We measure urbanization by population density and congestion by the difference between the free-flow vehicle speed and the actual vehicle speed inside the corridor. There are a variety of land use/transport models currently used in the literature. On the one end of the spectrum there is the mathematically elegant, analytically traceable, general equilibrium model of Lucas and Rossi-Hansberg (2002). They model the urban economy of a circular city. Based on this model it is possible to prove that a spatial equilibrium exists, but at the cost of imposing functional form restrictions and only considering a limited number of choice variables. In addition, changes in the parameters of the model can lead to widely different urban outcomes. On the other end of the spectrum there are the partial equilibrium transport models, such as used by Tirachini, among others, in the literature on urban bus transportation (i.e. Tirachini et al., 2014, 2011, 2010; Tirachini, 2014; Tirachini and Hensher, 2011). Transport in these models is often modeled in much detail, but the location of population and transport demand is typically fixed (i.e. travel occurs toward a predefined central business district, CBD). These models can teach us a lot about transport behavior/systems, but less about the interaction with the rest of the urban economy.1 The Anas model lies somewhere in between these two extremes. It is flexible enough to allow for a highly non-linear formulation of consumption, production, and travel behavior (a discrete number of zones/stations). The model, however, needs to be solved numerically. Although travel behavior itself is modeled in less detail, there is interaction with other parts of the urban economy. Due to a (multinomial) logit formulation of the origin–destination (OD) choices, changes in the parameter values result in a smooth change in urban outcomes. In sum, the Anas model is ideally suited for our research purposes. Travel in the standard Anas model, however, occurs by road only. We extend the model by allowing individuals to travel by train – depending on the availability of a station – or car within the same OD pair. This essentially makes car and train competing modes, which we model by a nested logit formulation of the OD (work/live) choice and mode choice. The effect of network design on urbanization and congestion, and the role of substitutability – local competition – between the two modes, is explicitly discussed. There is ample empirical evidence that mode choices are correlated. Koppelman and Wen (1998), for example, examine different nested logit models and find some evidence that train and car are within a single nest for the Toronto-Montreal corridor.2 Moreover, not allowing mode choices to be correlated, basically using a multinomial logit structure, can lead to an incorrect estimate of the impact of rail service improvements on rail ridership (Forinash and Koppelman, 1993; Bhat, 1995). The multinomial logit approach is, for example, used in the transport model of Tirachini et al. (2014), but also by Anas and Liu (2007), Anas and Hiramatsu (2013), and Tscharaktschiew and Hirte (2012). The latter three studies add a second layer of multinomial logit probabilities to also model the commuting, origin–destination, choice. The commuting and transport mode choices are only linked through endogenous travel times/costs. The nested logit we add to the Anas model essentially implies that individuals jointly choose where to work/live and which mode to use based on a broader set of economic variables (i.e. goods consumption, leisure/work, housing/land consumption, which depends on full economic income, travel times, etc.). Moreover, within each OD pair the mode choices are allowed to be correlated. This seems to be more in line with the actual choice problem faced by individuals and it allows us to examine the interaction between urbanization and congestion in relation to mode access and mode competition simultaneously. To summarize, although the benefits and empirical relevance of the nested logit model is evident, it has not, as of yet, found its way into the more formal models of transport and urban land use.3 The results in this paper show there is a trade-off between congestion and urbanization which crucially depends on the structure of the railway network and the degree of mode substitutability. First, we find that when the number of access 1 Transport models are, in some instances, also linked to a wider collection of partial equilibrium models describing other parts of the urban economy (e.g. labor market, housing market). There are many of such combined urban models (for an overview, see Wegener, 2004). Typically, these models can, for example, predict land use for every 100 m grid cell within a particular country/region and, as such, are a very popular tool for policy analysis. These models are, however, typically based on a large number of reduced form equations (the underlying economic choices are no longer directly modeled). In these models, it is virtually impossible to identify the underlying mechanisms that lead to a particular outcome, something we are particularly interested in. 2 For a discussion of the different nested logit (transport choice) models, see Wen and Koppelman (2001). For a broader discussion of transport modeling and logit models, see Ortúzar and Willumsen (2001). 3 One particular reason is that it is a highly non-linear approach, which makes it difficult to get clean analytical results. Specifically, it requires the simultaneous modeling/interaction of congestion, urbanization, and railway travel (discrete access), substantially increasing the dimensionality and non-linearity of the model.

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

3

points is limited population density around stations is 5.8% higher in comparison with a situation in which there is only travel by car. Since travel time by train is relatively low, workers have an incentive to reside in a location that is distant from the place of work and in close proximity to a train station. Population clusters because access to the railway network is clustered. Instead, if train stations are present in all geographical areas, we do not find a sizeable effect on population density but a substantial decrease in congestion: 35.6% relative to benchmark equilibrium in which travel only occurs by car. In essence, travel by train is just like travel by car: access to the railway network is more or less continuous across space. We find similar results for a within-city metro network. Second, our results indicate that the degree to which railway accessibility decreases congestion highly depends on the degree of mode substitutability. In our specific urban setup, going from no correlation to a strong degree of correlation between mode choices decreases the effectiveness of rail (dense network of stations) to reduce congestion by about 15 percentage points. Similarly, the increase in population density (few stations) goes from 5.8% to 1.1% when mode substitutability increases. This paper belongs to a long-standing literature on transportation systems and urban land use.4 It relates to the literature on transit-oriented development, which promotes the more efficient integration of land use and rail transit (see Calthorpe, 1993; Bernick and Cervero, 1997), and the literature on sorting into catchment areas (see, for example, Voith, 1991). Although there have been a lot of models that have focused on the role and impact of car travel (e.g. Anas and Rhee, 2006; Baum-Snow, 2007b), there has also been a growing literature on models that focus on public transport (see Li et al., 2011). In particular, our paper relates to the literature on urban bus transportation. Travel by train is much like travel on a dedicated busway. Tirachini et al. (2010), for example, use a radial line (toward CBD) approach to compare bus versus railway travel and find that a high standard bus service is most cost-effective. Rail may be preferred as long as trains run substantially faster than buses. Related is the work of Tirachini (2014), who examines optimal bus stop spacing. There are several studies that have used a spatial urban equilibrium model to investigate the effect of railway travel on the urban economy. Anas and Moses (1979), for example, were one of the first to investigate the role of multimodality in a spatial urban land use model by allowing travel to occur on a dense network of roads versus an expressway/mass transit line. They find that different cost characteristics can lead to different forms of the market area of the two transport modes. Kanemoto (1984) shows that competing railways do not lead to optimal pricing and investment decisions (for the effect of side businesses, see Kanemoto and Kiyono, 1995). More recently, using the Anas model and a typical German city setup, Tscharaktschiew and Hirte (2012) find that subsidies to public transport result in suburbanization (but no urban sprawl). All of these studies have in common that stations and their spatial allocation, as well as mode substitutability, are abstracted from. Our study specifically focuses on these aspects. There is also quite some empirical literature about the impact of rail-based public transport on urbanization and economic activity. Levinson (2008), for example, shows that rail stations have resulted in higher population density in the suburbs of London and increased commercial development in the city center. King (2011) finds that subway construction followed population and commercial development and has resulted in decentralization in New York away from lower Manhattan. Atack and Margo (2011) discuss, from a historical perspective, that the creation of farm land (land use) in the US is directly related to the coming of the railroad to the Midwest. Garcia-López (2012) finds that railroads led to increased population growth in suburban areas in Barcelona. Baum-Snow et al. (2013) show that each additional radial and ring railroad decreases central city GDP in China. These empirical papers typically focus on one aspect of the urban economy, assuming that the rest of the economy stays fixed. However, to understand the effect of railway travel on urban spatial structure it is important to examine the interaction between different parts of the urban system and to identify the underlying mechanisms that drive the urban economic outcomes; exactly what our paper aims to achieve. The remainder of this paper is structured as follows. Section 2 presents the model. Section 3 discusses the parameters and solution procedure. Section 4 shows the results. Section 5 contains a discussion of the limitations and future research. Section 6 concludes.

2. The model 2.1. Modeling approach We model a transport corridor reflecting travel between cities and consisting of several zones, which is in line with the initial model of Anas and Kim (1996). In accordance with many previous studies (for an overview, see Li et al., 2011) travel occurs on a single line (linear network geometry) through the center of the corridor.5 The crucial addition is that for each OD pair individuals are allowed to choose which transport mode to use. Where to work/live (the formation of cities) and how, and how much, to commute are endogenously determined. In that sense, the model is more general than the classic monocentric city model with a fixed CBD: a mixed land use (production, residential, infrastructure) is allowed in each zone. Prices are established in markets for goods, land, and labor and balance the urban economy. 4 For an overview of the literature on urban spatial structure, see Anas et al. (1998). For infrastructure investment and the impact of (rail)roads on urban spatial structure, see Baum-Snow et al. (2013). For an overview of bus/train related transport models, see Li et al. (2011). 5 There is a gradual shift in the literature to a more full-fledged network approach, see for example the transport model of Zubieta (1998) or Jara-Díaz and Gschwender (2003). For an urban economic model, see Anas and Hiramatsu (2013).

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

4

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

We start with the US (car only) parameter setup of Anas and Rhee (2006) because (1) the properties of the resulting urban equilibrium have already been extensively described and (2) we can use the outcomes as benchmark.6 We aim to show that adding a simple equation for railway travel times can lead to substantially different urban outcomes. As such, we add an equation reflecting the main elements of railway travel (access/egress, in-vehicle time, and waiting times at stations) that is linked to the model through a nested logit equation and examine how the urban economic results change. This approach allows us to single-out the effect of railway travel on congestion and urbanization outcomes. We present a case in which rail is accessible in all zones and one in which rail is only present in a few selected zones to highlight the role of network design. These cases represent two extremes of a continuum of possible network structures. Subsequently, we examine how the urbanization and congestion results change with the degree of substitutability between railway travel and car travel. To confirm that our results hold in a variety of setups (e.g. European consumption pattern, circular city metro, different train speeds), we perform several robustness checks. Finally, we end with a bird’s eye view on the limitations of the model and future research opportunities (i.e. incorporating agglomeration externalities, the potential to do a full-fledged welfare analysis, linking of origin–destinations through multiple routes, and the possibility to allow for endogenous network formation). 2.2. Spatial structure and actors We follow Anas and Kim (1996) by modeling a closed economy. Moreover, land is separated into Z equally-sized zones (see Fig. 1). We distinguish between three types of economic actors: workers, firms, and the government. There is a population of N workers. Each worker lives and is employed in one of the zones. Workers travel within and across zones to work and consume. In each zone firms produce goods that are consumed by workers. The government imposes a head tax on the workers to finance (rail) roads. The three actors interact with each other through the product market, labor market, and land market. The economic behavior of each actor is discussed in the following subsections. For an exact list of the endogenous variables that are modeled, see Table A1 in the Appendix A. 2.3. Workers Each worker has a home location (zone) i, work location j, and commutes using transport mode t (car or train) and derives utility Uijt from consumption zijvt, bought in zone v, lot size (land) qijt, leisure time lijt, and an idiosyncratic component uijt, reflecting heterogeneity in tastes7:

X q U ijt ¼ a ln zijv t

!1=q þ b ln qijt þ c ln lijt þ uijt :

ð1Þ

v

The goods sub-utility function has a constant elasticity of substitution equal to q/(1  q). We assume a + b + c = 1. Since P q the marginal utility of each good conditional on the commuting arrangement i, j and transport mode t, azijqv1 n zijnt , goes to t = infinity when the consumption of that good goes to zero, workers consume from each zone. This captures the worker’s ‘‘taste for variety’’.8 Workers maximize utility subject to a budget constraint:

X pijv zijv t þ ri qijt þ wi lijt ¼ Xijt ;

ð2Þ

v

where full endowment income equals Xijt = wjH  2dwjgijt + D, H is the total time in hours in a month available to a worker, wj is the wage rate, d is the number of work days per month, gijt is the one-way commuting time, and D is land revenue, with P D = 1/N krkAk  h, where Ak denotes the land area at zone k, rk is the land rent, and h is a head tax imposed by the government. Hence, there is equal ownership of land and there are no absentee landlords. The left-hand side of Eq. (2) captures expenditure on consumption, lot size, and leisure, where pijv is a composite price: pijv = pv + 2fwjgiv, which is the sum of the price of the consumption good pv and the opportunity costs of travel time wjgiv, where giv is the one-way travel time between the residential location i and shopping location v, and we assume that all shopping occurs by car (i.e. g iv ¼ g iv 0 car0 ). The term 2f scales the cost of travel, where f is the exogenous number of trips per year to purchase a unit of consumption. 6 This type of model is usually either calibrated to represent a particular city/region (e.g. Chicago, see Anas and Hiramatsu, 2013) or to represent the typical American (Anas and Rhee, 2006) or, for example, German (Tscharaktschiew and Hirte, 2012) urban economy. The former approach raises questions about the generalizability of the results, the latter about the practical applicability. We use a generic setup (the latter approach) and examine the sensitivity of the results to changes in the parameter values in order to show that the results hold in a wide variety of setups. 7 As such, there is only one type of household, but based on the idiosyncratic component of utility there is a distribution of work-live location (commute) and transport mode choices. For the impact of different types of households on urban economic outcomes in the Anas model, see Tscharaktschiew and Hirte (2010a). 8 The fact that the consumer shops in every zone is determined by the specification of utility. The commuting arrangement and the amount of shopping (and shopping flows through the conversion factor f) are endogenously determined by the model.

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

5

Fig. 1. Distribution of land in the transport corridor.

Given the Cobb–Douglas utility function, the Marshallian demands for consumption zijvt, lot size qijt, and leisure lijt are of the following form: q1Þ Xijt pij1=ð v

zijv t ¼ a P

q=ðq1Þ ;

n pijn

qijt ¼ b

Xijt ri

;

lijt ¼ c

Xijt wj

:

ð3Þ

In comparison to the standard Anas model, these variables are now transport mode specific because full endowment income and travel times are mode specific. 2.4. Where to work, live, and the choice of transport mode Each worker has a specific chance to live in i, work in j, and use transport mode t. To elaborate, the indirect utility is Vijt + uijt, where Vijt is the optimized value of the deterministic part of the utility function. The worker chooses the commuting arrangement i,j and transport mode t with the highest utility. In the nested logit approach these choices are nested. Workers choose the commuting arrangement and within the commuting arrangement they make the transport mode choice. The joint choice probability Wijt is modeled in the nested logit form as follows9:

Wijt ¼

P expðkV ijt =vij Þð l expðkV ijl =vij ÞÞvij 1 ; P P vnm n;m ð l expðkV nml =vnm ÞÞ

ð4Þ

where the parameter vij captures the correlation between the random part of utility of each joint commuting arrangement and transport mode choice within a particular transport mode nest.10 If vij = 1, an assumption we will make in the base analysis, this correlation is zero and the probabilities collapse to multinomial logit probabilities. If there is also only one transport mode (i.e. car), the probabilities collapse to the Anas and Rhee (2006) multinomial logit probabilities, where k is the dispersion (scaling) parameter. If k ! 1 choices are deterministic. If k ! 0 choices are completely random. In essence, k balances the role of the deterministic versus the idiosyncratic part of utility and, as such, determines the sensitivity of the location and mode choices to changes in the economic variables/parameters. As long as choices are not entirely deterministic, there is a smoothed change in urban outcomes when the parameters are changed. In essence, the nested logit model allows both the work/live location choice and transport choice to be interdependent and, conditional on each work/live location choice, the transport mode choices can be correlated. In case of two separate multinomial logit structures (i.e. Anas and Liu, 2007), this is not allowed. Moreover, if each determinant of utility would have been modeled (i.e. not only consumption, lot size, and leisure) it would be reasonable to assume (an assumption made in the standard Anas model) that the idiosyncratic part of utility is not correlated, but independently and identically distributed (i.i.d.). The same applies if the decision makers (workers) do not consider car and train as substitutes. Given the specific form of utility in the Anas model and the empirical evidence on correlated mode choices (see Section 1), however, the nested logit structure seems to be an appropriate modeling choice.11 2.5. Travel times Assume that travel occurs on a straight line through the zones. Interzonal travel occurs from the center of each zone, while intrazonal travel occurs toward the center of a zone. The commuting time g ij0 car0 and the shopping travel time g iv 0 car0 are the same if the origin and destination are the same (i.e. travel time does not depend on the purpose of the trip), and they are fully determined by the time (hours) to travel one kilometer by car g i0 car0 . Specifically, the intrazonal travel time g ii0 car0 is P Di g i0 car0 =2, where Di is the length of the zone, and the interzonal travel time g ij0 car0 equals ðDi g i0 car0 þ Dj g j0 car0 Þ=2 þ n Dn g n0 car0 , 12 where i – j and n = {i + 1, j  1}. The time to travel one kilometer by car g i0 car0 is determined by the congestion function13:

  c  F0 0 ; g i0 car0 ¼ a 1 þ b i car K i0 car0

ð5Þ

9 The probabilities add up to one. This implies that each worker works and lives within the transport corridor (no inside–outside commuting) and travels either by car or by train (no outside options). 10 The actual correlation is a non-linear decreasing function of vij. 11 Still, correlations across nests are not allowed. See Ortúzar and Willumsen (2001) for a discussion of more generalized models. 12 Interzonal travel is across half a zone in the origin and destination zone plus the travel times through all intermediate zones. 13 The model does not allow for peak hour congestion.

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

6

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

where K i0 car0 is the road capacity based on the land allocated to roads Ri0 car0 (i.e. K i0 car0 ¼ fRi0 car0 ), a, b, and c are congestion parameters, and two-way zonal traffic flows F i0 car0 are defined as:

F i0 car0 ¼ F ii0 car0 þ

i1 X Z X X ðF in0 car0 þ F ni0 car0 Þ þ 2 ðF km0 car0 þ F mk0 car0 Þ; i–n

ð6Þ

k¼1 m¼iþ1

where the zonal traffic consists of three terms: the intrazonal traffic flows, the flows going to and leaving from the center of zone i, and the traffic passing through zone i (assumed to travel a full zone length, flows are multiplied by two).14 In Eq. (6), s the total daily flow by car F in0 car0 between some location pair i,n equals F w in0 car0 þ F in0 car0 where the destination zone n is either the 0 work location j or the shopping location v and the expected number of one-way commuting trips is F w ij0 car0 ¼ N Wij car0 , and the P expected number of one-way shopping trips is F siv 0 car0 ¼ N 1d j;t Wijt fzijv t .15 If there is a train station in a zone, it is located in the center of the zone. If both zone i and j have a train station, workers can use the train to commute between these two stations. The intrazonal travel time by train g ij0 train0 is directly determined by the train speed in kilometers per hour, trainspeed, and distance between the origin and destination zone:

g ij0 train0 ¼

    X Di Dj Di Dj Dn 2þ 2þ þ þ þ #Stopsij ; / / train speed train speed train speed n

where i – j and n = {i + 1, j  1} and



Di /

þ

Dj /

.

ð7Þ

2 captures the time to travel to and from the train station (access/egress) by

foot/bicycle.16 Hence, / can be interpreted as a station accessibility parameter. The term #Stopsij captures the fixed ’waiting time’ effect of the number of stops between i and j on travel time. It includes waiting time at the origin and destination zone (i.e. it takes time for the train to arrive and to board/exit the train). In essence, the waiting time added to Eq. (7) ensures that each additional node (station) in the network has an effect on travel occurring from the other nodes. In addition, if a train runs between i and j, we assume that it stops at all stations that are in between i and j. This implies that workers either use a local train (in the ‘many stations’ case) or express train (in the ‘few stations’ case) to go to work. The impact of a hybrid system of local and express trains is further discussed in the limitations and future research section. Finally, the travel time by train in Eq. (7) does not depend on the number of passengers. This implies there is no congestion (crowding) at stations or inside trains (infinite rail network capacity), an assumption that is, for instance, also made by Tscharaktschiew and Hirte (2012). We will discuss the impact of this assumption in more detail in the limitations section. In addition, for a discussion about congestion inside versus outside buses and the impact on the optimal frequency of bus services, see Tirachini et al. (2014). 2.6. Government budget The government finances the land allocated (exogenously) to roads, Ri0 car0 , and railways, Ri0 train0 , by levying a head tax h on the workers:

Nh ¼

X X r i Ri0 car0 þ r i Ri0 train0 : i

ð8Þ

i

This makes the government a passive player in this model. As mentioned, the head tax decreases the land revenues that are redistributed among the workers. 2.7. Producers Goods are sold in the center of each zone. Hence, there are Z goods. Firms produce these Z goods in quantity Xv. Firms maximize profit, pvXv  wvMvrvQv, where Mv is labor input, Qv is land input, and with X v ¼ EMdv Q lv , where E is a technology parameter and d + l = 1 captures the constant returns to scale production technology. There is perfect competition, every firm is a price taker, and there are a lot of small firms (i.e. the exact number of firms is indeterminate).17,18 In this case, firms make zero profits and the conditional labor and land demands are

Mv ¼

dpv X v ; wv

Qv ¼

lpv X v rv

:

ð9Þ

14

For the edge zones the third term is zero. We aggregate consumption over all commuting transport modes and possible work locations. Shopping only occurs during work days and does not take any additional time besides travel time. 16 Workers are allowed to travel to the train station within their zone of residence for working purposes (internal travel). This reflects that work locations are usually close to public transport hubs. 17 Since firms are price takers, supply is fully price elastic. As a result, the level of production is determined by consumption demand. Hence, the location of firms in this model is ultimately determined by consumption. 18 Note that it is implicitly assumed that consumption and output prices are equal because there are no taxes (for an example of the impact of taxes in this type of model, see Tscharaktschiew and Hirte, 2012). In addition, there is no intermediate use (inter-industry trade) in this model (for an example with trade, see Anas and Kim, 1996). 15

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

7

2.8. General equilibrium Product prices pv, wages wj, and land rents ri are determined by the following market clearing conditions:

N

X

Wijt zijv t  X v ¼ 0 ðproduct marketÞ

i;j;t

Mj  N N

X

X

Wijt ðH  T ijt  lijt Þ ¼ 0 ðlabor marketÞ

i;t

ð10Þ

X Wijt qijt þ Q i þ Ri;t  Ai ¼ 0 ðland marketÞ; t

j;t

P

where Tijt = 2dgijt + v2givfzijvt is the total travel time (commuting and shopping) and H  Tijt  lijt is the remaining time available for work. The prices defined by Eq. (10) are assumed to be independent of the transport mode (i.e. demand and supply are summed across transport modes).

3. Parameters and solution procedure 3.1. Parameters Table 1 contains an overview of all parameter values and exogenous model inputs. To calculate the base equilibrium (only car travel), we mainly take the parameters of Anas and Rhee (2006), except for the spatial structure of the land, the land allocated to roads, and the value of the dispersion parameter k (see discussion below). We change these parameters in such a way that it is in line with travel in a transport corridor (instead of a circular city). We set several additional parameters associated with railway travel. Although most of the parameter values are straightforward, we will show several robustness checks in the results section. The remainder of this section contains a discussion of the main parameter values and what these values imply for travel inside the transport corridor. We assume there is a population of 5000 workers. Note that this is just a matter of scaling. It is possible to directly interpret the results in terms of 500 or 50,000 workers.19 In essence, what is modeled are the choices (probabilities) of a representative consumer. However, for expositional purposes – we want to talk about flows, population densities, station use – we use a fixed population of workers. The transport corridor consists of 11 equally-sized zones. Although this does not sound as much, it implies that each of the endogenous variables that are i, j (t = car only) specific reflects 121 (11 ⁄ 11) observed outcomes, which needs to be solved by an equal amount of equations. Much like a regression equation, each of the observed outcomes of an endogenous variable is captured by a single equation (with the appropriate subscripts). There are 21 endogenous variables, which in case of the base equilibrium results in a number of 3719 observed outcomes (equations), which suffices for our modeling purposes. Moreover, it implies that we will only report some key descriptive statistics that characterize the urban economic equilibrium. Each zone is assumed to be 5 km long by 0.5 km wide. Consequently, if a station is present, the station catchment area equals the size of a zone (2.5 km2).20 Moreover, it implies that the total length of the transport corridor is 55 km, which is much larger than a typical city21, about three times the highway corridor used by Anas and Kim (1996) and Anas and Xu (1999), and approximately the distance between Washington DC and Baltimore. We use such a relatively large distance because it is in line with a situation in which travel occurs between cities. In addition, car and rail are typically considered competing modes at longer distances. Given the Cobb–Douglas form of the utility function, the utility parameters can directly be interpreted as consumption shares. Accordingly, workers are assumed to spend 36% of their (full endowment) income on consumption, 15% on land (lot size), and 49% on leisure (a = 0.36, b = 0.15, c = 0.49).22 These preference parameters are important because they determine the weighting of the different elements of the utility function which, as mentioned, determines location and transport mode choices. The preference parameters are in line with the typical consumption pattern of a US household.23 It is, however, 19 Anas and Rhee (2006), for example, multiply the number of workers by an (exogenous) number of family members and by the number of wedges that fit inside the modeled circular city, resulting in a total modeled population of 1.8 million residents. 20 There is considerable debate about the exact catchment area of a station. For a discussion, see Curtis et al. (2009). 21 The typical US circular city of Anas and Rhee (2006) has a radius of 8 km (with suburbs 22.5 km). According to the US Census Bureau, as of the 1st of January 2010, Washington DC has, for example, an approximate land area of 172 km, which corresponds to a radius of about 4 km. 22 Similarly, given the Cobb–Douglas form of production, the (cost) share of labor in production is assumed to be 86%. According to the US national accounts (BEA, 2014), the compensation of employees as part of national income (excluding firm profits, interest income, and taxes) is about 82% in 2013 (it was 86% in 2002, see Anas and Rhee, 2006). In the model, the remainder of costs is assumed to be the result of the production factor land. 23 In particular, assume that full endowment income is about 65,000 dollars. Expenditure on consumption (including food, apparel and services, transportation, health care, and cash contributions) is about 22,500 dollars and expenditure on housing is about 17,000 dollars (see BLS, 2014). Hence, 35% of income is spent on consumption. Assuming that 60% of housing expenditure is paid to obtain land (60% is in between the land value to price ratio of metropolitan areas in 2004, see Davis and Palumbo, 2007), about 16% of income is spent on land. In the model, the remainder (49%) is assumed to be leisure expenditure. These values are very close to the Anas and Rhee (2006) setup.

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

8

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx Table 1 Parameters. Transport corridor (symmetric around central zone) Z = 11 zones Length of zones in km (1) 5, (2) 5, (3) 5, (4) 5, (5) 5, (6) 5 Area in km2 (vertical width, 500 m) (1) 2.5, (2) 2.5, (3) 2.5, (4) 2.5, (5) 2.5, (6) 2.5 Land allocated to roads (percentage): (1) 5, (2) 5, (3) 5, (4) 5, (5) 5, (6) 5 Consumer equations

a = 0.36 income share of consumption goods b = 0.15 income share spent on rented lot size q

c = 0.49 income share of leisure q = 0.6 relates to elasticity of substitution between commodities H = 500 h per month time endowment d = 500/24 work days per month 1 f ¼ 13 the number of trips to purchase one unit of consumption k ¼ 12:0 the degree that tastes are idiosyncratic (0 = random) N = 5000 workers Producer equations d = 0.86 labor cost share l = 0.14 land cost share E = 1 scale factor Transport equations a = 1/(45 ⁄ 1.6093) hours per km, inverse of free of congestion traffic speed b = 50 strength of traffic flow to capacity in congestion function c = 2 strength of traffic flows to capacity in congestion function f = 1.1 parameter that converts roads to road capacity in a zone Additional parameters for railway travel

vij = 1 captures the correlation between random utilities (1 = no correlation) / = 15 speed in km/h to get to the train station by foot/bicycle train speed = 100 speed in km/h of travel via train # = 2.5/60 time in hours spent on waiting time after each train stop (2.5 min) Land allocated to railroads (percentage): (1) 1.0, (2) 1.0, (3) 1.0, (4) 1.0, (5) 1.0, (6) 1.0 Note: There are no parameters for the market clearing conditions and government budget.

substantially different from the consumption pattern of a European household (see Tscharaktschiew and Hirte, 2012). We will show how the results change using European consumption preferences in the sensitivity analysis. The congestion function parameters, see Eq. (5), are set in such a way that the average free-flow speed is about 70 km/h, which includes time driving around the neighborhood to get on/off the highway, and is in between the free-flow speed of a secondary road with high frictions (40 km/h) and a highway (120 km/h) (see Akçelik, 1991). The land allocated to roads is assumed to be 5%, which is much lower than found in a typical city. Anas and Xu (1999) assume that the percentage of roads inside their modeled transport corridor is 6% and it ranges between one percent in the suburbs to about 50% in the center of the circular city modeled by Anas and Rhee (2006). For the total of the US it is about one percent (Nickerson et al., 2007). It is about 25% for Washington DC (city center), 30% for cities like Amsterdam, Paris, and London, and 35% for New York, although for the suburbs it is typically smaller than 15% (UN-Habitat, 2013). Importantly, the amount of roads that is used in the model implies that the average speed in the base equilibrium is about 60 km/h, which suggests that we are examining travel behavior inside a corridor that has a moderate degree of congestion. We will show some results of a much more congested circular city, as well as a case where there is more land allocated to roads, in the sensitivity section. We set k at 12. As mentioned, k reflects the sensitivity of choices to changes in the variables (such as travel times). It is an important variable that is difficult to calibrate. Anas and Kim (1996) set k at 1, Anas and Xu (1999) at 5, Anas and Rhee (2006) at 4, Tscharaktschiew and Hirte (2010a) at 10, and Tscharaktschiew and Hirte (2010b, 2012) at 5. Travel flows typically decrease when the distance between origin and destination increases. We set the value of k in such a way that there is a reasonable distance decay of travel flows.24 In particular, Fig. 2 contains the base equilibrium commuting flow from zone 1 to 11 relative to the flow from zone 6 to zone 1 for different values of k. Fig. 2 indicates that, at a k of 12, a doubling of the travel distance (from 25 km to 50 km) results in a 25% decrease in travel flows. More importantly, we will show that our main results (trade-off urbanization, congestion) will hold for different values of k. Finally, there are several parameters that determine railway travel. It is assumed that the average speed at which to travel toward or from a train station (e.g. by bicycle) is 15 km/h (see for example, Jensen et al., 2010). Land allocated to railroads is

24

For a discussion of different forms of the commuting distance decay function, see Halás et al. (2014).

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

9

set at one percent, which is lower than the land allocated to roads, but higher than typically found in the US (see Nickerson et al., 2007).25 Waiting time at stations is fixed at 2.5 min.26 In the base analysis, the correlation between the random utilities equals one. This implies that the joint commuting and transport mode probabilities are of the multinomial logit form (i.e. we first focus on the effect of railway travel and subsequently show results for different degrees of mode substitutability). Average train speed is set at 100 km/h, which is much higher than assumed by Tirachini et al. (2010) and Li et al. (2011) (i.e. they use a train speed of about 40 km/h), and it is more in line with a situation in which travel occurs between cities. From a US perspective, 100 km/h (75 mph) is relatively fast,27 it is more in line with train speeds in Europe,28 and substantially slower than high-speed rail, which is typically considered to go faster than 200 km/h. Such high-speed transport corridors are currently being considered as part of the High-Speed Intercity Passenger Rail Program (see U.S. Department of Transportation, 2014). Since train speed determines the extent to which rail competes with car travel, we will report urbanization and congestion outcomes based on different train speeds in the sensitivity section. Even though the above railway travel setup is very simple and stylized, we show that the urban economic results differ substantially after the introduction of railway travel in the model.

3.2. Solution procedure We need to solve 20 (blocks of) equations. Given the dimensionality of the endogenous variables (again, see Table A1 in the Appendix A), the total number of single equations is 3720 in the base equilibrium.29 According to Walras’ law, if n  1 markets clear, see the equations in (10), the nth market also clears. Given that we will only examine symmetric equilibria (i.e. the results of zone 11 are the same as that of zone 1), there are two market equations that are redundant. Consequently, without loss of generality, we can normalize these two outcomes. We follow Anas and Rhee (2006) by normalizing the edge zone rents to 0.25 in such a way that monetary income is around 40,000 dollars (30,000 euros). Still, we have to solve the remaining 3718 equations. Anas and Rhee (2006) use their own iterative procedure that minimizes the (maximum) slack in the equations (variables).30 Instead, we reprogrammed the model in the optimization software GAMS (full-fledged GAMS code) and reformulate the system of non-linear equations as a non-linear programming (NLP) problem.31 In essence, this implies that we add an additional auxiliary equation (the total number of equations thus becomes 3719) to help in solving the system of equations. It turns out that this facilitates the solution procedure considerably and allows us to run different versions of the model with relative ease. As an additional equation, we use the expected (log-sum) welfare function. That is, we maximize32:

welfare ¼ 1=k ln

X

expðkV ijt Þ:

ð11Þ

ijt

We will report this welfare measure for each of the three cases (car travel only, stations in all zones, limited number of stations). Welfare (utility) in itself is not that informative, since it is only defined up to some scale. Consequently, we also report the compensating variation relative to the base equilibrium of the cases that allow for railway travel. In essence, the compensating variation is the amount of income that needs to be subtracted from full endowment income in case of railway travel in such a way that welfare (keeping all else fixed) equals the welfare of the base case. If railway travel improves welfare, the compensating variation measure should be positive. Finally, to show that the system of equations is appropriately solved (no leakages) we also report whether Walras’ law holds (land market clearing) for each of the cases. That is, excess demand of the land market in zone 1 (and 11) should be (close to) zero. 25 Note that this land allocation does not play an important role in the model, since railroads are a relatively small part of total land and it does not directly affect railway travel times. In the model, the railway track lies directly next to the highway going through the center of the zones. 26 Waiting time can vary considerably. Nie and Hansen (2005), for example, find that dwelling time of trains at one particular station in the Netherlands ranges between 20 s and 12 min, with average dwelling time ranging between 150 and 170 s. 27 Amtrak’s Acela Express, considered to be one of the fastest trains in the US, has an average speed of about 68 mph (including stops) between Washington and Boston, but can go as fast as an average speed of 110 mph from Philadelphia to Washington, although speeds around train stations are substantially lower (see RealTransit, 2014). 28 In the UK, for example, average train speed is in between 60 and 65 mph, but it is substantially higher for intercity services (for an international comparison, see Rutzen and Walton, 2011). One particular reason that train speed is faster in Europe is that in Europe dedicated railway tracks are typically used, while intercity rail travel in the US is more based on sharing tracks (rights-of-way of the tracks). 29 The exact total number of endogenous solutions (equations) depends on the i, j and t dimensions of the variables and the restrictions imposed on the model (e.g. normalization prices, number of train stations). In the results section we report the exact number of equations for the case with rail. 30 Alex Anas graciously provided us with the (GAMS) code he used in Anas and Rhee (2006). 31 This allows us to use the built-in algorithms to solve the model. The algorithm that we use is based on the Generalized Reduced Gradient (GRG) method. The benefit of our approach is that we utilize the first and second order conditions (Jacobian and Hessian matrices) to find the optimum, using some standard convergence criteria (more robust procedure) and, consequently, the number of iterations before convergence is relatively low. Moreover, it is easier to incorporate restrictions on (the dimensionality of) the equations, which is necessary to examine the impact of the spatial differences in the allocation of train stations on urban economic outcomes. 32 Note that this welfare measure is not an outcome of the model. It does, however, teach us something about the solutions of the model: this type of model favors solutions with a higher aggregate welfare.

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

10

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

Decrease in flows, doublibg the distance

40% 35% 30% 25% 20% 15% 10% 5% 0%

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

λ Fig. 2. Distance decay of commuting flows.

4. Results As mentioned, we run three versions of the model. First, we calculate the base equilibrium, which is similar to the equilibrium of Anas and Kim (1996), Anas and Xu (1999), and Anas and Rhee (2006) in which commuting only occurs by car.33 Second, we report results of the urban equilibrium in case railway travel is added to the model (train stations in all zones). Finally, we show the result in case access to the railway network is restricted (to zones 1, 6, and 11). Table 2 contains the main urban economic descriptive statistics. We also report some results that are specific to zones 1–6 (again, the equilibria are symmetric). We focus on population density (residents/km2) and road congestion (difference between free-flow speed and actual speed). We are particularly interested to find out to what extent these urban metrics change between the three cases. 4.1. Base equilibrium Table 2, column 1, labeled ‘no trains’, shows the base equilibrium results. Disposable income is 42,176 dollars. Workers shop and commute about half an hour per day (total is about one hour). Although the differences across zones are relatively small, population density – based on the number of workers living in a particular zone – is relatively high in zones 4, 5, and 6 (hence, also in 7 and 8). Population density is 185.4, 187.3, and 187.9 residents per km2 in these zones, respectively.34 Workers have a tendency to live in the center of the corridor because of its relative position (connectivity) inside the corridor. The population density over the whole transport corridor is 181.8 (5000/27.5) residents per km2. This is relatively low in comparison to an actual city.35 Note, however, that the level of population density in itself is not that informative. We are particularly interested in how this urban metric changes in case there is railway travel. Job density shows a similar spatial pattern as population density. The job-housing balance is very close to one in each zone, which suggests that jobs and residences are balanced across zones. Hence, the model does not say much about (changes in) urban sprawl across space (in the model firms follow people and people follow firms).36 The fact that the center of the corridor, from a spatial position point of view, is a relatively good place to work and live is also reflected by the (weighted) average distance of outward commutes, which is 21.8 km in zone 1 versus 13.0 km in zone 6. The commuting flow between zones 1 and 6 is 38 and the flow between the edge zones 1 and 11 is 29, which is about 25% lower. Again, this reflects the distance decay in commuting flows as distance between the origin and destination increases. The center of the corridor acts as a bottleneck in terms of travel flows. In particular, the car speed (i.e. the inverse of the time to travel one km, see the congestion function in Eq. (5)) in zone 6 is 60.7 km/h. The edge zones are relatively uncongested with a traffic speed of 72.0 km/h, which is very close to the free-flow vehicle speed of 72.4 km/h. The weighted (by traffic flows) average of car speed in the corridor is 64.1 km/h, suggesting that there is a mild to moderate degree of congestion in the corridor. The average speed is 8.3 km/h (11.4%) less than the free-flow traffic speed. As mentioned, we focus on the extent to which this measure of congestion changes after introducing railway travel in the model. 4.2. The impact of railway travel on urbanization and congestion In Table 2, columns 2 and 3, the urban economic equilibrium outcomes are presented, in which workers can use the train to go to work either by a dense network of railway stations (column 2) or by a scarce network of stations (column 3) with 33

That is, t = {car}, Eq. (7) is excluded, and there is no land allocated to railroads. To calculate population density we calculate the workers that live in zone i by aggregating the probability matrix, see Eq. (4), by the j and t dimension for each zone i and multiplying by the total number of workers. The land area in each zone is used as benchmark. 35 In the circular city of Anas and Rhee (2006), for example, the density in zone 6 is about 1800 workers per km2. We will show results of the circular city in the sensitivity analysis. 36 Baum-Snow (2013), however, finds that each radial highway displaces 16% of central city population in the US to suburbs, but the effect on jobs is only 6%. This suggests that the transport system can also play an important role in the creation/reduction of urban sprawl. 34

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

11

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx Table 2 The spatial equilibrium in a transport corridor: urbanization versus congestion.

Main urban metrics

Zones

Population density: (Residents/km2)

1 2 3 4 5 6 Tot. 1 2 3 4 5 6 Tot. 1 2 3 4 5 6 Tot.

Job density: (Workers/km2)

Vehicle speed (km/h): (Free-flow speed is 72.4 km/h)

Other urban metrics Average distance outward commute in km

Commuting time (1 = h) Shopping time (1 = h) Daily commuting flow zone 1–6 Daily commuting flow zone 6–1 Daily commuting flow zone 1–11 Percentage train use Disposable income (dollars) Welfare (utils/worker) Comp. variation ($/worker/month) Walras’ law (land market zone 1) Number of eq./iterations

(1) No trains (base equilibrium)

(2) Train stations in all zones

(3) Train stations in zones 1, 6, and 11

173.0 178.1 182.3 185.4 187.3 187.9 181.8 174.3 178.7 182.2 184.8 186.4 187.0 181.8 72.0 69.3 66.0 63.1 61.3 60.7 64.1

172.6 178.1 182.4 185.5 187.4 188.1 181.8 174.0 178.7 182.3 184.9 186.5 187.1 181.8 72.2 70.5 68.4 66.5 65.2 64.8 67.1

183.5 174.3 178.4 181.4 183.2 198.5 181.8 184.3 175.1 178.5 181.0 182.6 197.1 181.8 72.0 69.5 66.3 63.6 61.8 61.2 64.5

Car 1 2 3 4 5 6

Train

21.8 18.3 15.8 14.2 13.3 13.0 0.517 0.475 38 38 29 42,176 6.978 <|1 ⁄ 103| 3719/24

Car

Train

Car

Train

22.0 18.4 15.9 14.3 13.4 13.1 0.496 0.449 22 23 17

20.5 17.3 15.1 13.6 12.8 12.5 1.260

21.9 18.2 15.7 14.1 13.2 12.9 0.510 0.473 31 31 23

19.4

15 15 11

41.7 42,025 7.022 300 <|1 ⁄ 103| 5897/49

14.5 0.976 24 24 20

5.0 39,997 6.980 390 <|1 ⁄ 103| 3881/35

Notes: Population and job density are measured in workers per km2. The job/population density for the whole transport corridor (total jobs or population divided by total land area) is reported under the line ‘Tot.’ (for speed this is the weighted average, by transport flows). Shopping/commuting time is in hours per day per worker.

stations only present in a few selected zones. Our main findings regarding urbanization and congestion are summarized in Fig. 3. Fig. 3 reports the percentage change, relative to the base equilibrium, in congestion (free-flow speed minus average speed) and the weighted (by population) average population density around train stations. That is, in case of three stations, the weighted average summarizes the population density across the three zones. We find that in case of many stations, there is a considerable decrease in congestion (35.6%) relative to the base equilibrium. There is, however, almost no change in urban spatial structure. By contrast, if stations are only present in a few strategically selected areas, the two edges and the center of the corridor, there is a considerable increase in the degree of urbanization (5.8%) around those stations. There is also a decrease in congestion of 4.4%, but this is relatively small in comparison to the case with stations in all zones. The remainder of this section discusses the two cases in more detail. Table 2, column 2, reports the results of the urban equilibrium where railway travel is added as a separate mode of transport. Stations are present in all zones. As mentioned, this setup is much in line with a case in which travel occurs via local train (light rail). About 41.7% of the population uses the train to go to work. Nevertheless, due to the relatively high travel times by train (1.260 h, on average, in case of commuting), most workers still use the car to commute (58.3%). Table 3 contains a decomposition of the railway travel time by number of stops (including the origin and destination). Below 8 stops, the largest component of travel time of rail passengers is access/egress time. In case of 8 stops or more, the in vehicle travel time is the largest component in total travel time. Waiting times are also a substantial part of travel time. Even though the waiting time in each zone is limited, having a train station in each zone results in an accumulation of waiting time for longer trips. In essence, the results in Table 3 imply that, although railway travel in itself is quite efficient (low net travel time), the access/egress and waiting time associated with railway travel makes this mode of transport relatively unattractive. Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx 5.8%

40%

35.6%

Decrease in congeson

35%

6% 5%

30% 4%

25% 20%

3%

15%

2%

10% 1%

4.4%

5%

<0.1%

0%

Increase in populaon density

12

congeson urbanizaon

0% many staons

few staons

Fig. 3. Congestion versus urbanization. Notes: This figure presents percentage changes relative to the base equilibrium. Congestion is measured by the difference between free-flow and the weighted (by transport flows) average speed in the transport corridor. Population density is in residents/km2. The figure reports the change in the weighted (by population) average population density around stations.

Table 3 Decomposition of travel time between train stations by number of stops. Stops

2

3

4

5

6

7

8

9

10

11

Nominal Access/egress Travel time Waiting time Total

0.333 0.050 0.083 0.375

0.333 0.100 0.125 0.442

0.333 0.150 0.167 0.508

0.333 0.200 0.208 0.575

0.333 0.250 0.250 0.642

0.333 0.300 0.293 0.708

0.333 0.350 0.333 0.775

0.333 0.400 0.375 0.842

0.333 0.450 0.417 0.908

0.333 0.500 0.458 0.975

Percentage Access/egress Travel time Waiting time Total

71.5 10.7 17.8 100

59.7 17.9 22.4 100

51.2 23.1 25.7 100

44.9 27.0 28.1 100

40.0 30.0 30.0 100

36.0 32.4 31.6 100

32.8 34.4 32.8 100

30.1 36.1 33.8 100

27.8 37.5 34.8 100

25.8 38.7 35.5 100

Notes: A travel time of 1 is equivalent to one hour. Travel time by train is symmetric by number of stops (i.e. travel time between zones 1 and 3 is equal to travel time between zones 3 and 5). Stops include the stop at the origin and destination.

Regardless of the relative unattractiveness (high travel times) of the train, it is accessible in all zones and the use of railway travel, as such, remains relatively high. Railway provides transport for the masses. This can explain why congestion inside the transport corridor is much less than when workers only have the opportunity to travel by car. Accordingly, the average speed increases to about 67.1 km/h. This is also reflected by a decrease in shopping and commuting time by car to 0.449 and 0.496, respectively. Speed increases most in the central zone; the ‘bottleneck’ type of congestion is alleviated by the introduction of public transport. Even though railway travel has an indirect effect on road congestion, in contrast to travel by bus (see Tirachini et al., 2014), for example, the effect on congestion is still considerable. By contrast, the results in Table 2, column 2, indicate that the spatial pattern in terms of population and work remains virtually unchanged relative to the base equilibrium. Apparently, railway travel, in our particular setup, is just like travel by car – access is widely available. There is a new mode of travel, but it does not induce workers to reallocate toward another home or another job. Table 2, column 3, contains the urban results when train stations are only available in zones 1, 6, and 11. In essence, we restrict the dimensionality of the variables (system of equations) in such a way that railway travel can only occur between zones that have a station. The number of equations, therefore, decreases from 5897 (stations in all zones) to 3881, but it is still more than in the base case (3719). Since travel distances by train are longer relative to column 2, travel can be interpreted as travel via express/intercity train. Even with a stylized and simple formulation of railway travel, we see an interesting spatial pattern emerging. Population density peaks in zones 1, 6, and 11, the zones in which the railway network is accessible (a similar pattern holds with regard to jobs: a polycentric structure emerges, in contrast to the classic single CBD). Note that these results imply that it is not necessarily the number of ingoing, outgoing, tracks that determines urban economic outcomes (i.e. Baum-Snow et al., 2013), but that also the number of stations and where they are located are important factors. The clustering of population and jobs into 3 cities/urbanized areas has several causes. First, the part of the population that wants to use the train, even though this is only 5.0%, all clusters around a relatively limited number of train stations (access points). That is, since access to train stations is spatially clustered, the population that wants to use the train also gets clustered (spatial sorting into catchment areas). Interestingly, the use of stations in zones 1, 6, and 11 goes up in comparison to the case where train stations are omnipresent. Specifically, the flows from zone 1 to 6 (and vice versa) go up from 15 to 24, an increase of 60%. From zone 1 to 11 the commuting flows almost double relative to the base equilibrium. Nevertheless, because overall train use is relatively low, congestion only decreases marginally.

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

13

Second, the regions with railway access become more attractive places to work and shop, partly due to an increased variety of goods, but also due to a more competitive travel time (i.e. railway commuting time goes from 1.260 to 0.976, while car travel times go up a bit). The spatial structure of train stations has an effect on urbanization and congestion outcomes because each additional station affects travel times of the other stations. Therefore, from a travel time perspective, less is more. These results are in line with the idea that railway travel makes cities with access to the railway network more attractive (comparative advantage), as long as the total number of train stations is limited. Due to railroads people find it easier to spatially differentiate where they work versus where they live. Moreover, besides the rail travel flows, car commuting flows and consumption peak in those zones which have access to the railway network. That is, Marshallian demand is 3.3% higher in zone 1 and 11 (3.1% for zone 6) in comparison to the base equilibrium. Train stations (railway travel) have a broader impact on the urban economy than just the effect on population (job) density alone. This reflects that stations, especially large intercity stations, are typically multifunctional locations around which there is a clustering of jobs, shops, and other economic activities. It implies that not necessarily the marginal effect of an additional station, as is focused on in many empirical studies, is key, but that the total effect, including the impact on other parts of the urban economy and of other train stations, is important. Finally, there remains an additional interesting aspect of the results we find. In particular, from a broader welfare perspective, it turns out that the introduction of railway travel improves welfare. The compensating variation is 300 dollars per worker per month in case railway travel is available in all zones. Interestingly, the compensating variation is higher, about 390 dollars per worker per month, in case there are only a few strategically placed train stations. It holds, then, from a broader welfare perspective it is not true that building more stations (more accessibility) is necessarily better. To make a more complete comparison, however, it would be necessary to also include the externalities of congestion (CO2, accident costs, health costs), the benefits of urbanization (agglomeration externalities), and the difference in infrastructure costs based on the type of railway network (number of stations, tracks). To summarize, what we have found in this section implies that access to railway travel, at least when this access is limited across space, results in an increase of population (and job) density. The fact that population only clusters when the supply of train stations is limited suggests that, if train stations are used to combat urban decline, they should be used in moderation. Instead, our results indicate that to obtain a decrease in congestion having a relatively large number of access points to the railway network is most useful.37

4.3. The role of mode substitutability If modes are non-substitutable they can still compete in terms of passengers, but passengers are less likely to switch between modes based on (time) cost considerations. An increase in the nested logit mode choice correlation coefficient makes the model more sensitive to differences between modes. An increase in the mode correlation can, therefore, be interpreted as an increase in competition between the two modes (local competition within the corridor). If goods are better substitutes they are also more in competition with each other. It turns out that the correlation between mode choices has a substantial impact on the urban economic outcomes, especially on the congestion results in case there are relatively many stations. In particular, Fig. 4 shows the road congestion benefits at varying degrees of mode substitutability. As the general level of mode correlation increases from no correlation (vij = 1) to a strong degree of correlation (vij = 0.3) the congestion reduction benefits as a result of a dense station network decrease considerably from 35.6% (the base results) to 20.3% (note that the effect is non-linear). In essence, travel by train is not as efficient, in terms of travel times, as travel by car. Thus, if the substitutability between the modes increases, there will be fewer workers willing to commute by train, although due to the idiosyncratic preferences there will always be some. As such, there will be a crowding out of the reduction benefits. We find similar effects in case stations are only present in zones 1, 6, and 11. The congestion reduction benefits decrease from 4.4% to 2.4%. Also, the impact of rail travel on urbanization in this case decreases from 5.8% to 1.1%. In sum, the results indicate that it is important to take the substitutability of transport modes into account when considering (rail) infrastructure investment.

4.4. Sensitivity analysis In this section, several robustness checks are reported. The results are presented in Table 4. In general, the results (trade-off congestion and urbanization) seem to hold in a variety of different setups. First, we change the idiosyncratic preference parameter from k ¼ 12:0 to k ¼ 4:0 and to k ¼ 20:0. In case idiosyncratic preferences play a larger role (i.e. k ¼ 4:0), the congestion reduction benefits become a bit larger, 41%, in the many stations case. In case of a few stations, the reduction is 5.6% and the increase in population 11.1%. For k ¼ 20:0, the results are similar. Congestion is reduced by 30.6%, but only by 3.7% if there are stations in only a few zones. Interestingly, the urbanization effects become less, 3.8%. 37 Interestingly, this result suggests that public transport (railway travel) may well act as a second-best solution to congestion tolls (the standard solution to reduce congestion, see Anas and Rhee, 2006).

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

14

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

Decrease in road congeson

40% 35% 30% 25% 20% 15% 1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

Correlaon mode choices ( χij = 1, no correlaon) Fig. 4. Mode choice correlation and congestion reduction due to a dense station network.

Table 4 Sensitivity analysis (% change relative to base equilibrium). Main results Train in all zones Congestion reduction Pop. dens. increase Train zones 1, 6, 11 Congestion reduction Pop. dens. increase

35.6% 0% 4.4% 5.8% Idiosyncratic preferences:

Train in all zones Congestion reduction Pop. dens. increase Train zones 1, 6, 11 Congestion reduction Pop. dens. increase

k = 12.0 ? k = 4.0

k = 12.0 ? k = 20.0

41.0% 0%

30.6% 0%

5.6% 11.1%

3.7% 3.8%

A European setup: a = 0.36, b = 0.15, c = 0.49, q = 0.6 ? a = 0.40, b = 0.21, c = 0.39, q = 0.6 Train in all zones Congestion reduction Pop. dens. increase Train zones 1, 6, 11 Congestion reduction Pop. dens. increase

33.6% 0% 4.1% 4.7% Train speed:

Train in all zones Congestion reduction Pop. dens. increase Train zones 1, 6, 11 Congestion reduction Pop. dens. increase Land allocated to roads: Train in all zones Congestion reduction Pop. dens. increase Train zones 1, 6, 11 Congestion reduction Pop. dens. increase

100 km/h ? 50 km/h

100 km/h ? 200 km/h

33.4% 0%

36.7% 0%

4.0% 5.2%

4.6% 6.2%

5% ? 1%

5% ? 10%

14% 0%

38.4% 0%

1.5% 7.5%

4.9% 5.8%

A circular city: rectangular zones ? circular wedge Train in all zones Congestion reduction Pop. dens. increase Train zones 1, 6, 11 Congestion reduction Pop. dens. increase

30.6% 0.6% 4.5% 63.6%

Notes: This table presents percentage changes relative to the base equilibrium. Congestion is measured by the difference between free-flow and the weighted (by transport flows) average speed in the transport corridor. Population density is in residents/km2. The table reports the change in the weighted (by population) average population density around stations.

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

15

Fig. 5. Distribution of land in a circular city.

Second, we use preference parameters (consumption shares) that are in line with a European setup, instead of a US setup. That is, the income share of consumption and housing increases to 40% and 21% (a = 0.40, b = 0.21), respectively, and the share of leisure decreases to 39% (c = 0.39). These parameters are used by Tscharaktschiew and Hirte (2012) and are in line with consumption shares in a typical German city. We again find that, although the spatial patterns shift somewhat, the trade-off between congestion and urbanization is still there. Third, the extent to which the train is a viable alternative to travel by car depends on the speed of the train. Up to now, we assumed the same train speed for the local and express train case. Table 4 shows a case in which the speed is 50 km/h, more in line with the local train case, and the results when the speed is 200 km/h. The results show that if the train speed is slower the congestion reduction benefits decrease a bit and they become higher if the train goes faster. The same applies to the increase in population density. The general pattern of the results, however, remains remarkably stable. Fourth, an important assumption is the amount of land allocated to roads, since the amount of roads directly determines congestion. In the case that only one percent of land consists of roads there is a considerable increase in congestion inside the corridor. In particular, the average speed decreases from 64.1 km/h to 26.2 km/h, which suggests that the corridor is heavily congested. Interestingly, the percentage of road congestion reduction decreases considerably relative to our base results (many stations case). The difference of the actual speed with the free-flow speed is so substantial that a bit more vehicle speed results in only a relatively small congestion reduction effect. The urbanization effect, if there are only stations in zones 1, 6, and 11, becomes a bit stronger. Workers want to live close to a train station to avoid the excessive congestion. In case the land allocated to roads is increased to 10%, the results stay very close to our main results. With a 5% road allocation, traffic speed was already close to the free-flow speed, so increasing the amount of roads even further does not affect our results much. An alternative way to introduce more congestion in the model is by changing the spatial structure of the land. In particular, we also calculated the results in case the land structure represents a circular city (see Fig. 5). The rectangular patches of land are replaced by two circular wedges originating from the center of zone 6. The angle of each wedge is three degrees. The horizontal width of the zones is 3.22 km (2 miles) and 8.05 km (5 miles) for the edge zones. The land area of the two wedges is 13.3 km2 and the total area of the circular city is 797 km2. The percentage of land allocated to roads is relatively high in the center (27.5% in zone 6) and low at the edges (0.7% in zone 1 or 11). The idiosyncratic preferences are set at k ¼ 4:0 and we use the same railway travel parameters as before, except the train speed is lowered to 50 km/h, which is in line with the typical speed of a metro/light rail. The base equilibrium is a replication of the Anas and Rhee (2006) equilibrium. The vehicle speed is 44.5 km/h. Population density ranges from 215 residents/km2 to 1848 residents/km2 in the center of the circular city and average commuting time is 42 min. The congestion and urbanization outcomes reported in Table 4 suggest that the results within cities are similar to the results between cities. There is still a trade-off between congestion and urbanization. The railway network with train stations in all zones resembles a metro network in which lines originate from the center and there are many access nodes. Such a network is, for instance, currently present in Moscow. In this case, we do not find large effects on the degree of urbanization in different zones, but we do find a substantial decrease in congestion of about 30.6% relative to the benchmark case. This is very much in line with the base results. The main difference is that the absolute level of the decrease in congestion is much larger within the circular city than in the transport corridor. Instead, if access to the railway network is limited which, for example, resembles the metro network in Los Angeles (i.e. lines still originate from the center, there are not many access nodes, nodes are not clustered), population again peaks in zones 1, 6, and 11. The effect on population density is much higher than in the transport corridor. Apparently, the effects are amplified within cities. Accessibility (travel times) – an essential determinant in the Anas model – is more restricted in cities than in the transport corridor.

5. Limitations and future research In this section, we suggest several directions for future research. First, it is now well appreciated that agglomeration economies play an important role in the formation of cities (see Glaeser and Gottlieb, 2009). Although the Anas model incorporates that consumers value the variety of goods, which is in line with Krugman (1991), there are no economies of scale in production. Ogawa and Fujita (1982), or more recently, Lucas and Rossi-Hansberg (2002), use models in which the level of production is directly dependent on the density of firms. In these models, cities form as a result of agglomeration externalities and not necessarily due to differences in travel times. We would expect that the clustering of population and firms as a result of train stations would be more pronounced if there are agglomeration externalities. It would be interesting to examine to what extent cities in this case are affected by public transport, making a distinction between within (metro) versus between (train) city dynamics. In addition, although the model incorporates the negative effect of extra train stations on travel times, there are no direct positive (e.g. cultural heritage) or negative (e.g. crime, environmental) externalities as a result of having a train station in a particular region. Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

16

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

A second direction for future research would be to extend the model by using a network approach. In this paper, travel occurs on a line through the transport corridor, which consists out of a limited number of zones. The potential broader implications of our results, from a transport corridor to a national railway network, are best understood using some examples. France, for instance, has a relatively low density railway network centered around Paris and focusing on the high-speed TGV. There is about 31,000 km of railway track, 3000 train stations, while the total land area is 640,000 km2 (UIC, 2011). The percentage of total population living in urban areas, a measure of urbanization, is 86%.38 By contrast, the INRIX index, a measure of congestion intensity, is 15.9 in France.39 Instead, Germany has a hybrid system with a combination of high speed lines and regular lines, a relatively low level of congestion (INRIX index of 12.2) and a high degree of urbanization (74% of the population lives in urban areas). The results in this paper suggest that, at least in part, these differences in urbanization and congestion can be explained by the differences in railway network density and the type of railway network. In addition, many cities are accessible through multiple paths (via train, car, airplane, etc.). Jara-Díaz and Gschwender (2003), for example, create a transport model and compare direct lines against a transfer-based transit system (i.e. connections between non-aligned OD pairs). Zubieta (1998) shows a network model of a city (applied to the city of Santiago) and examines competition between bus companies. The system of cities approach has also been used by Anas and Pines (2013) to examine the role of fiscal and zoning policies to help finance local public goods. Anas and Liu (2007) combine the Anas model with a separate transport model (algorithm) for the Chicago MSA. Anas and Hiramatsu (2013) use this model to examine optimal cordon tolling in Chicago.40 The main issue is that the network approach increases the dimensionality of the system of equations (in our case i,j,t dimension), especially in case of a large number of nodes (and choices), which makes it hard to solve such models. A third research direction relates to the effect of zoning regulations on the urban structure of cities. The model in this paper shows the effects of railway travel on population density and the mechanism through which these effects are obtained. If, at the extreme, zoning regulations are binding in all zones, the effects on the population would be zero. This suggests a potential overestimation of the changes in population density in our model. A potential solution would be to use a Kuhn–Tucker type of approach and reformulate the system of equations in such a way that it represents a mixed complementarity problem (often used in CGE analysis). Alternatively, Anas and Pines (2013) show a model in which lot size is determined by the government and consumers bid to obtain a particular lot.41 Moreover, it would be interesting to examine the supply and spatial allocation of train stations in more detail (i.e. endogenous network formation). In particular, the allocation of train stations in this paper is exogenous. It would be interesting to look at different spatial patterns of railway accessibility, including a hybrid system of high-speed and regular lines, the welfare implications of different spatial patterns, and under which conditions such patterns emerge. The general equilibrium framework used in this paper only shows the direction of congestion/urbanization effects, given the railway network, but not the underlying time dynamics (i.e. for a dynamic approach, see Zubieta, 1998). In addition, the local/national government usually plays an important role in the creation of public transport hubs. It would be interesting to investigate whether the supply of public transport should be centralized or decentralized. There is some research in this direction in relation to travel by car (De Borger et al., 2005, 2007). To incorporate this feature, we would need to make a clear distinction between (the cost of) the supply of train stations and the supply of railway services (ticket fares). In combination with the full infrastructure costs of the rail network (see, for example, Tirachini et al., 2010) and the externalities of congestion (i.e. CO2) and agglomeration, it would be possible to do a more full-fledged welfare analysis of different network structures. Finally, we have used a relatively simple formulation of (railway) travel. It would be interesting to add more detail, such as peak-hour traffic congestion, the operating costs of trains/stations, different fare systems, and the monetary costs of travel (ticket prices). Moreover, crowding inside stations and trains (especially during peak hour) could lead to additional waiting time and disutility of going by train (see Tirachini et al., 2014). This could potentially reduce the extend of the congestion and urbanization effects found in this paper. Although we do include a fixed waiting time in the train travel time equation, the waiting time might be endogenous based on traffic flows. Mohring (1972), for example, shows an optimal frequency rule based on service frequencies and waiting times. At least, the type of model that has been used in this study has the potential to be extended to handle such details. To summarize, although the model differs substantially from a typical transport model, it shows great potential to be further extended in such a direction, resulting in a better connection between the urban economic and transport literature. The results in our paper suggest that the fusion between both disciplines shows an interesting potential to generate new, intriguing results that are also important for transportation scientists.

6. Conclusions We have used a unified modeling framework to examine the impact of the spatial allocation of train stations and mode substitutability on both congestion and urbanization in a transport corridor. Urban land use models have mostly been used 38

World development indicators 2012 (www.worldbank.org). The INRIX index measures the percentage increase in average travel time during peak hours. An index value of zero means no congestion (www.scorecard. inrix.com). 40 In addition, the effect of (rail-based) public transport on congestion may depend on the type of highway network between/within cities. Nitzsche and Tscharaktschiew (2013), for instance, find that roads with speed restrictions can have entirely different effects on congestion and welfare than roads without (or just local) restrictions. It would be interesting to examine urbanization and congestion in the context of a system of roads versus a system of railroads. 41 For a discussion of different zoning regimes on land use and land prices, see Debrezion et al. (2007). 39

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

17

to analyze the effect of travel by road on the allocation of jobs and residences. Although these models have significantly increased our understanding about urban land use patterns, and in particular the development of cities, the focus on travel by roads makes these models mainly applicable to countries such as the United States. The results in this paper show that train stations positively affect the degree of urbanization in the area in which the train station is located if the number of train stations is limited. Because access is limited – emphasizing the discrete nature of railway accessibility – the effects are clustered around train stations. In particular, population density is about 5.8% higher in areas with access to railway travel. We find similar results for job density. In addition, we find that commuting flows between areas with a train station are larger in comparison with both the base equilibrium (only car) and the equilibrium with full access to train stations in all geographical zones. This result is in line with the idea that railway travel makes it easier for households to differentiate between the place of residence and the place of work. Limiting the availability of railway travel results in a comparative advantage in terms of goods and travel times for those regions with access to the railway network. However, in this case, we do not find large effects on congestion. In contrast, if access to railway travel is relatively abundant, we find an average decrease in congestion of about 35.6%, but little effect on the degree of urbanization (urban spatial structure). These results suggest that there is a trade-off between congestion and urbanization. This trade-off seems to hold in a wide variety of setups, including a circular city setup. The results, however, did indicate that especially the congestion reduction benefits of a dense network of stations are severely reduced if the substitutability between car and train is higher. The degree of substitutability, therefore, seems to be an important aspect to include in infrastructure investment decisions. Finally, the results in this paper have several implications for policies regarding rail-based public transport. First, it is evident that the accessibility to public transport has broader implications on the urban economy than just the effects on travel time, or population density for that matter, which is the focus of many empirical studies. Not the marginal effect of an additional station is necessarily important, but also the total effect. Second, public transport is not a goal in itself. The purpose of producing public transport determines how access to public transport is to be allocated across space. Policies aiming to reduce congestion by means of public transport are best served by a large number of transport hubs, although it should be carefully taken into consideration to what extent rail-based public transport is actually a substitute for other modes of transport. Instead, if the aim is to create a clustering of population or jobs, to mitigate urban decline or, for instance, to foster agglomeration economies, policy makers should carefully evaluate not only the amount of access points, but also the spatial allocation of those points. A limited number of strategically placed stations may be more effective in strengthening the economy in certain areas than a large number of stations randomly allocated across space.

Appendix A Table A1 Endogenous variables. Consumer zijvt consumption of goods qijt consumption of lot size lijt consumption of leisure Xijt full endowment income D land dividend Vijt indirect utility Producer Mv labor demand Qv land demand Xv production of goods Travel gijt travel time Wijt origin–destination probability matrix F in0 car0 total flows by car (shopping and working) between zones F i0 car0 total flows by car in a zone (internal, crossing, and ending/beginning in the zone) g i0 car0 congestion (time to cross one kilometer) by car Tijt total travel time Government h head tax to finance (rail)roads Market pv product prices (effective price) pijv composite price of goods (including travel time) wj wages ri land rents Objective welfare welfare measure

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

18

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

References Akçelik, R., 1991. Travel time functions for transport planning purposes: Davidson’s function, its time-dependent form and an alternative travel time function. Australian Road Research 21, 49–59. Anas, A., Arnott, R., Small, K.A., 1998. Urban spatial structure. Journal of Economic Literature 36, 1426–1464. Anas, A., Hiramatsu, T., 2013. The economics of cording tolling: general equilibrium and welfare analysis. Economics of Transportation 2, 18–37. Anas, A., Kim, I., 1996. General equilibrium models of polycentric urban land use with endogenous congestion and job agglomeration. Journal of Urban Economics 40, 232–256. Anas, A., Liu, Y., 2007. A regional economy, land use, and transportation model (RELU-TRAN): formulation, algorithm design, and testing. Journal of Regional Science 47, 415–455. Anas, A., Pines, D., 2013. Public goods and congestion in a system of cities: how do fiscal and zoning policies improve efficiency. Journal of Economic Geography 13, 649–676. Anas, A., Moses, L.N., 1979. Mode choice, transport structure and urban land use. Journal of Urban Economics 6, 228–246. Anas, A., Rhee, H.-J., 2006. Curbing excess sprawl with congestion tolls and urban boundaries. Regional Science and Urban Economics 36, 510–541. Anas, A., Xu, R., 1999. Congestion, land use, and job dispersion: a general equilibrium model. Journal of Urban Economics 45, 451–473. Atack, J., Margo, R.A., 2011. The impact of access to rail transportation on agricultural improvement. The Journal of Transport and Land Use 4, 5–18. Baum-Snow, N., 2007a. Did highways cause suburbanization. Quarterly Journal of Economics 122, 775–805. Baum-Snow, N., 2007b. Suburbanization and transportation in the monocentric model. Journal of Urban Economics 62, 405–423. Baum-Snow, N., 2013. Urban Transport Expansions, Employment Decentralization, and the Spatial Scope of Agglomeration Economies. Brown University Working Paper. Baum-Snow, N., Brandt, L., Henderson, J.V., Turner, M.A., Zhang, Q., 2013. Roads, Railroads, and Decentralization of Chinese Cities. Brown University Working Paper. BEA, 2014. Gross Domestic Product: Third Quarter 2014, News Release, Tuesday, December 23, 2014. Bernick, M., Cervero, R., 1997. Transit Villages in the Twenty-first Century. McGraw-Hill, New York. Bhat, C.R., 1995. A heteroscedastic extreme value model of intercity travel mode choice. Transportation Research Part B 29, 471–483. BLS, 2014. Consumer Expenditure – 2013. News Release, Tuesday, September 9, 2014. Calthorpe, P., 1993. The Next American Metropolis: Ecology, Community, and the American Dream. Princeton Architectural Press, New York. Curtis, C., Renne, J.L., Bertolini, L., 2009. Transit Oriented Development: Making it Happen. Ashgate Publishing Company, Burlington, USA. Davis, M.A., Palumbo, M.G., 2007. The price of residential land in large US cities. Journal of Urban Economics 63, 352–384. De Borger, B., Dunkerley, F., Proost, S., 2007. Strategic investment and pricing decisions in a congested transport corridor. Journal of Urban Economics 62, 294–316. De Borger, B., Proost, S., Van Dender, K., 2005. Congestion and tax competition in a parallel network. European Economic Review 49, 2013–2040. Debrezion, G., Pels, E., Rietveld, P., 2007. The effects of railway investment in a polycentric city: a comparison of competitive and segmented land markets. Environment and Planning 39, 2048–2067. Forinash, C.V., Koppelman, F.S., 1993. Application and interpretation of nested logit models of intercity mode choice. In: Innovations in Travel Behavior Analysis, Demand Forecasting, and Modeling Networks, Transportation Research Record No. 1413. National Academy Press, Washington D.C.. Garcia-López, M.A., 2012. Urban spatial structure, suburbanization and transportation in Barcelona. Journal of Urban Economics 72, 176–190. Glaeser, E.L., Gottlieb, J.D., 2009. The wealth of cities: agglomeration economies and spatial equilibrium in the United States. Journal of Economic Literature 47, 983–1028. Glaeser, E.L., 1998. Are cities dying? Journal of Economic Perspectives 12, 139–160. Halás, M., Klapka, P., Kladivo, P., 2014. Distance-decay functions for daily travel-to-work flows. Journal of Transport Geography 35, 107–119. Jara-Díaz, S.R., Gschwender, A., 2003. From the single line model to the spatial structure of transit services. Journal of Transport Economics and Policy 37, 261–277. Jensen, P., Rouquier, J.B., Ovtracht, N., Robardet, C., 2010. Characterizing the speed and paths of shared bicycle use in Lyon. Transportation Research Part D 15, 522–524. Kanemoto, Y., 1984. Pricing and investment policies in a system of competitive commuter railways. The Review of Economic Studies 51, 665–681. Kanemoto, Y., Kiyono, K., 1995. Regulation and commuter railways and spatial development. Regional Science and Urban Economics 25, 377–394. King, D., 2011. Estimating the effect of subway growth on New York City land uses. The Journal of Transport and Land Use 4, 19–32. Koppelman, F.S., Wen, C., 1998. Alternative nested logit models: structure, properties, and estimation. Transportation Research Part B 32, 289–298. Krugman, P., 1991. Increasing returns and economic geography. Journal of Political Economy 99, 483–499. Levinson, D., 2008. Density and dispersion: the co-development of land use and rail in London. Journal of Economic Geography 8, 55–77. Li, Z.C., Lam, W.H.K., Wong, S.C., Sumalee, A., 2011. Design of a rail transit line for profit maximization in a linear transport corridor. Procedia Social and Behavioral Sciences 17, 82–112. Lucas, R.E., Rossi-Hansberg, E., 2002. On the internal structure of cities. Econometrica 70, 1445–1476. Mohring, H., 1972. Optimization and scale economies in urban bus transportation. The American Economic Review 62, 591–604. Nie, L., Hansen, I.A., 2005. System analysis of train operations and track occupancy at railway stations. European Journal of Transport and Infrastructure Research 5, 31–54. Nitzsche, E., Tscharaktschiew, S., 2013. Efficiency of speed limits in cities: a spatial computable general equilibrium assessment. Transportation Research Part A 56, 23–48. Nickerson, C., Ebel, R., Borchers, A., Carriazo, F., Major Uses of Land in the United States, 2007. EIB-89, U.S. Department of Agriculture, Economic Research Service, December 2011. Ortúzar, J. de D., Willumsen, L.G., 2001. Modelling Transport. John Wiley & Sons, West Sussex, England. Ogawa, H., Fujita, M., 1982. Multiple equilibria and structural transition of non-monocentric urban configurations. Regional Science and Urban Economics 12, 161–196. RealTransit, 2014. Planning for a New Corridor. Research Report, October 2014. Rutzen, B., Walton, C.M., 2011. High Speed Rail: A Study of International Practices and Identification. Research Report SWUTC/11/476660-00071-1. Tirachini, A., 2014. The economics and engineering of bus stops: spacing, design and congestion. Transportation Research Part A 59, 37–57. Tirachini, A., Cortés, C.E., Jara-Díaz, S.R., 2011. Optimal design and benefits of a short turning strategy for a bus corridor. Transportation 38, 169–189. Tirachini, A., Hensher, D.A., 2011. Bus congestion, optimal infrastructure investment and the choice of a fare collection system in dedicated bus corridors. Transportation Research Part B 45, 828–844. Tirachini, A., Hensher, D.A., Jara-Diáz, S.R., 2010. Comparing operator and users costs of light rail, heavy rail and bus rapid transit over a radial public transport network. Research in Transportation Economics 29, 231–242. Tirachini, A., Hensher, D.A., Rose, J.M., 2014. Multimodal pricing and optimal design of urban public transport: the interplay between traffic congestion and bus crowding. Transportation Research Part B 61, 33–54. Tscharaktschiew, S., Hirte, G., 2010a. How does the household structure shape the urban economy. Regional Science and Urban Economics 40, 498–516. Tscharaktschiew, S., Hirte, G., 2010b. The drawbacks and opportunities of carbon charges in metropolitan areas – a spatial general equilibrium approach. Ecological Economics 70, 339–357. Tscharaktschiew, S., Hirte, G., 2012. Should subsidies to urban passenger transport be increased? A spatial CGE analysis for a German metropolitan area. Transportation Research Part A 46, 285–309.

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004

M.I. Dröes, P. Rietveld / Transportation Research Part B xxx (2015) xxx–xxx

19

UIC, 2011. Synopsis 2011. Available from The International Union of Railways Website (www.uic.org). UN-Habitat, 2013. Streets as Public Spaces and Drivers of Urban Prosperity. Research Report HS/060/13E. U.S. Department of Transportation, 2014. Higher Speed Freight Truck Market Analysis. Technical Report, DOT/FRA/ORD-3/32. Voith, R., 1991. Transportation, sorting and house values. Real Estate Economics 19, 117–137. Wegener, M., 2004. Overview of land-use transport models. In: Handbook of Transport Geography and Spatial Systems, vol. 5, pp. 127–146. Wen, C.H., Koppelman, F.S., 2001. The generalized nested logit model. Transportation Research Part B 35, 627–641. Zubieta, L., 1998. A network equilibrium model for oligopolistic competition in city bus services. Transportation Research Part B 32, 413–422.

Please cite this article in press as: Dröes, M.I., Rietveld, P. Rail-based public transport and urban spatial structure: The interplay between network design, congestion and urban form. Transportation Research Part B (2015), http://dx.doi.org/10.1016/j.trb.2015.07.004