Public transport and urban structure

Highlights

• We model the role of public transit in shaping the structure of a monocentric city.

• Public transport stations induce non-monotonic gradients on prices and densities.

• The model reproduces observed patterns of modal and income mixing along the city.

• We simulate the effect of a pollution toll on the urban structure and modal shares.

• With a pollution toll, a smaller city with a larger public transit network arises.

Abstract

Public transport is central to commuting in most cities. This paper studies the role of public transportation in shaping the urban structure. Its main contribution is to propose a tractable model as a tool to study urban regulations and transport policies in the long-run. Using the classic monocentric city framework, we model public transport as a mode that can only be accessed by walking to a set of stops. By incorporating a discrete transport mode choice and income heterogeneity, the model remains simple yet can reproduce non-monotonous urban gradients observed in cities with public transport, and well-observed spatial patterns of sorting by income and use of public transport. For example, it can reproduce an inverted U-shape of transit usage along the city. To highlight the relevance of the model, we study the effects of pricing pollution externalities together with extending the public transportation network on the urban structure.

Introduction

Transportation and commuting are central to the theory of cities and urban structure. Early works from Alonso (1964), Mills (1967), and Muth (1969) developed the starting point of the modern urban economics literature in what is called the monocentric city model. In that model, production takes place at the Central Business District (CBD), where all jobs are located. The core of the model is that residents consume a numeraire good, housing, and must commute. As commuting costs increase with distance to the CBD, the differences in these costs along the city must be balanced by differences in the price of living space and consumption of housing (Brueckner, 1987). For this reason, land and rental prices, as well as population density, should decrease with distance to the CBD, and dwelling size should increase with distance to the CBD. This model has been extended in many directions, for example, to study amenities (Brueckner et al., 1999), local public goods (de Bartolome and Ross, 2003), landscape preferences (Turner, 2005), and the institutional frictions in land markets related to slums (Henderson et al., 2020), among others. See Duranton and Puga (2015) for an extensive review.

Public transport is essential to commuting in many cities around the world. For example, the share of public transport trips is 28% in 25 of the European largest cities, while the share of private car trips was 33% in 2015 (EMTA, 2015).¹ The use of public transport is arguably more important in developing countries. The average share of trips made by public transport in 15 of the largest cities in Latin America was 43% in 2009, significantly higher than the share made by car, which was 28% (CAF, 2010). The public transport system’s features and technology affects commuting costs and, thus, following the argument of its central importance, it should change the urban structure.

This paper studies the role of public transport in shaping cities, through a novel use of the monocentric city model. We focus on three crucial aspects of the urban structure: (i) use of public and private transport according to location; (ii) spatial sorting of different income groups, and (iii) how housing price, land price, dwelling sizes, population density, and structural density (floor-to-area ratio) change with distance to the central business district. We show that the model provides significant predictory power regarding several (ir)regularities that are usually observed in cities with high use of public transport. When cities differ in commuting costs components, their structure and use of public transport will be different. For example, the discrete nature of stations in space allows us to obtain the inverted U-shape of public transport usage along the city that has been identified in some metropolis. The main contribution of the paper is, therefore, to propose a tractable model that is a useful tool to address the efficiency and impact of transport policies in the long-run.

The literature about the role of transportation on the urban structure of cities is extensive. As this paper, some contributions have developed modifications of the monocentric city model to study population density and urban sprawl. For instance, Baum-Snow (2007) introduces radial highways into the model, retaining the primary standard results, but suggesting that this transportation infrastructure causes suburbanization. Kim (2012) incorporates vehicle size choice, arguing that as commuting cost per mile increases the city tends to expand, as opposed to the predictions of the standard model. In a later study, Kim (2016) includes negative externalities into his model of vehicle size choice, showing a positive relationship between population density and fuel-efficiency (closely related to vehicle size) when externalities are priced.

Unlike these contributions, our paper allows residents to choose among commuting by car, public transport, or foot. Certainly, there are studies that incorporate other modes of transportation into the standard monocentric city model. For example, Baum-Snow et al. (2005) study the effect of the incorporation of a rail transit line on ridership and modal shifts through making assumptions about the relative speeds of the transportation modes. Other papers have studied the role of public transit on explaining the sorting of residents by income in a city (LeRoy and Sonstelie, 1983, Glaeser et al., 2008, Su and DeSalvo, 2008). In particular, Glaeser et al. (2008) argue that “the primary reason for central city poverty is public transportation”. However, in all these studies, the modeling of public transport is quite simple; indeed, public transport is simply modeled as a car that is slower and less expensive. The consequences of the simplification are that the patterns of car and public transport usage are reduced to a small number of segregated zones where either one or the other mode is dominant. Our modeling of public transportation allows for more complex patterns that are relevant when studying transport taxes, emissions, vehicle-kilometer traveled, among other key outcomes.

More recently, a growing body of studies have developed quantitative urban models to study more comprehensively the implications of public transport improvements (see, e.g., Tsivanidis, 2019; Severen, 2018). For instance, Tsivanidis (2019) develops a model where multiple skill groups of workers have non-homothetic preferences over transit modes and residential locations. By taking into account time savings but also reallocation and general equilibrium effects, this study shows that a large change in the public transit infrastructure (Transmilenio) in Bogota, Colombia benefited high-skilled workers more because time savings did not compensate for price adjustments which hurt low-skilled workers more. As opposed to these quantitative urban models, our approach takes advantage of its micro-modeling feature to allow for more detailed analyses such as studying the effect on housing price changes in smaller areas than a census-tract, or boarding externalities at public transport stations.

On the other hand, the transport economics literature has modeled public transportation in a significantly more detailed way to study its optimal level of service, the efficient pricing scheme, or agglomeration externalities such as crowding and congestion (see, e.g., Hörcher et al., 2020). Furthermore, many studies have investigated the efficiency of policies such as subsidization, bus lanes, car congestion pricing, and combinations thereof in the case of interaction between modes of transportation (for recent studies, see, e.g., Proost and Van Dender, 2008; Parry and Small, 2009; Kutzbach, 2009; David and Foucart, 2014; and Basso and Silva, 2014). Nevertheless, this strand of the literature has adopted a short-run view by assuming that the housing market and location of households is exogenously fixed.² Our paper contributes to this literature by providing a framework to assess such transportation policies when public transportation and patterns of mode usage and income along the city are interrelated.

Our paper also contributes to the literature on the benefits of better access to transportation to consumers. There is ample empirical evidence that households value improved accessibility, and several studies have estimated the effect of closer proximity to a rail station on prices (e.g., McMillen and McDonald, 2004; Gibbons and Machin, 2005; Billings, 2011; Diao et al., 2017). Other papers have studied the effect of transportation accessibility improvements on employment and population density. For example, using the opening of a rail transit line in France (the Regional Express Rail, henceforth RER) as a natural experiment, Garcia-López et al. (2017a) show an increase in employment and population density in municipalities located close to the network. Mayer and Trevien (2017) also study the RER opening and show a similar effect on employment, no effect on population density, and a rise in the likelihood of high-skilled residents living near a RER station. Motivated by this evidence, Garcia-López et al. (2017b) delve into the effects of rail transit improvements in Paris between 1968 and 2010, and show an increase in employment subcenters formation. Yet, the theory suggests that the average impact may mask significant heterogeneity concerning overall accessibility (or proximity to the CBD). Our theoretical model delivers price elasticities with respect to the distance to the station that change with distance to the CBD depending on structural parameters. Thus, it can shed light on how the effect of closer proximity changes along a transport corridor such as a rail line.

The discrete nature of the stops and the fact that people may walk downstream or upstream to access public transport drives the action and predictory power while remaining a rather simple model.³ The non-monotonic commuting costs induce non-monotonic gradients with peaks in prices (as in Fig. 1), population density, and structural density at stations, where dwelling sizes are smaller. These predictions have been suggested in the literature, for example, by Duranton and Puga (2015), and modeled in the context of complementary public transport modes, where people take buses to train stations but car is not available as an alternative mode (Kilani et al., 2010).

However, it is the combination of detailed modeling of public transport, a simple discrete choice model between car and transit, and income heterogeneity that makes the model stand out. Our model predicts that the use of cars can appear all along the city and not only in long stretches of the city, where that mode dominates without any use of public transport, as currently available models predict. We also show that the presence of public transport can break the ordered sorting from the models without the need to have multiple modes of transportation. Our model with only public transportation and two income-groups has a large amount of mixing at the level of the distance between stops because, as the price gradients are non-monotonic due to the access cost to the stations, price bids can cross multiple times.⁴

Finally, even though it is not the main purpose of the paper, we study the policy of pricing pollution externalities and extending the public transportation network. We compare the untolled city with the resulting equilibrium when the marginal external cost per km is charged, the revenues are distributed among residents and public transport service is extended as long as it has demand. We find that the optimally tolled city is 8% more compact, the modal share of car trips is 15 percentage points lower, and 35% fewer kilometers are driven. The demand for public transportation is larger and 4.5 additional km of transit are provided, which had no demand in the untolled city. We also obtain that the utility achieved by both income groups is lower.

Nevertheless, the difference in rental prices and population density is the prediction where our model significantly differs from previous ones. As our model can have more mixing along the city than traditional models, the changes in prices and density that follow the implementation of a policy have a more significant dispersion. Besides the macro-changes that would be observed in a simpler monocentric model with two zones, it predicts changes due to the presence of stations and changes in the income group. For example, within five kilometers the policy induces changes in household density that are very different over space and can range from an increase of 17% to a decrease of 13%. These results highlight the relevance of the model and the potential it has for future policy analysis.

The rest of the paper is organized as follows. Section 2 introduces the monocentric city model with public transport and characterizes the urban structure equilibrium. Section 3 extends the analysis by including the interaction between public and private transport on the urban structure and explores the implications of our model in the sorting of residents by income. Section 5 concludes.