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Bikeability and the induced demand for cycling
\paragraph*{Author contributions}{Author contributions: M.F designed research; M.P performed research; M.F., M.\L., M.P., and T.K.R. analyzed data; M.F., M.\L., M.P., and T.K.R. wrote the paper.}
{Promotion of bicycle use has received considerable global attention. In addition to reducing the impact of urban transportation on climate, it will help to improve public health, and reduce traffic congestion, noise, and air pollution. Provision of bicycle-friendly infrastructure is a primary means to achieving this. Using a large dataset of observed bicycle trip trajectories and fine-grained network data covering the city of Copenhagen, Denmark, this study finds a large effect of infrastructure provision on the volume of bicycle traffic.}
Copenhagen has extensive bicycle infrastructure and a high level of bicycle usage for everyday urban travel CSC:18. We have a dataset of unprecedented size available, comprising 218,489 bicycle trajectories in Copenhagen obtained from users of Hövding airbag helmets Hovdingdata. Matching these trajectories with very detailed network information (see Figure (ref)) allows us to track the observed bicycle route choices across a range of infrastructure and land use types.
To make inference regarding the factors influencing bicyclists' choice of routes, we must compare the observed chosen routes to the possible alternatives. However, the number of possible routes between two points in a large network is extremely large and impossible to enumerate. To overcome this, we exploit the recently proposed perturbed utility route choice model Fosgerau2021a, which allows the entire network to be taken into account while being computationally feasible.
The estimated route choice model indicates very substantial variation in the subjective cost of using various infrastructure types. The subjective cost per meter traveled on the most attractive infrastructure type, a cycleway, designated as a cycle superhighway, and located in a green area, is seven times lower than the subjective cost of cycling on a residential road.
Bicycle infrastructure can therefore considerably affect the subjective cost of cycling and thereby the volume of bicycle use. We relate the number of trips in each origin-destination (OD) pair to the subjective cost from the route choice model. Employing a variant of the gravity model Wilson1967, we find a clear relationship whereby lower subjective cost is associated with a higher number of bicycle trips. We use this model to simulate a range of counterfactual scenarios, exploring the impact of the bicycle network on the volume of bicycle use.
We employ the perturbed utility route choice model Fosgerau2021a, which is a perturbed utility model McFadden2012,Fudenberg2015,Allen2019, adapted to describe the route choice through a network. For each OD pair, the predicted behaviour of bicyclists is a vector $x\in \mathbb{R}^{|\mathcal{E}|}_+$ that represents the distribution of flow across the network links $e\in\mathcal{E}$. The model assumes that the observed flow $x$ minimizes a convex cost function under the constraint that the flow $x$ is physically consistent with a flow of mass one through the network from origin to destination. The cost does not involve monetary elements but is a subjective cost that represents the bicyclists' preferences for various infrastructure types. The cost function has the form
where $l_e$ are the link lengths, $x_e$ are the link flows, and link cost rates are specified as $c_e=z_e' \beta$, where $z_e$ is a vector of link characteristics and $\beta$ is a vector of the parameters to be estimated. The perturbation function $F(\cdot):\mathbb{R}_+ \rightarrow \mathbb{R}$ is defined as $F(x_e) = (1+x_e) \ln{(1+x_e)} -x_e$, which is a convex function with $F(0)=F'(0)=0$. The perturbation term provides incentive to distribute flow on more than one route, while allowing the cost-minimizing flow to be zero on most links.
The materials and methods section explains the data and estimation methods, and further details are provided in the SI Appendix. The full specification of the vector of link characteristics $z_e$ and the corresponding parameter estimates are given in SI Appendix Table (ref).
Figure (ref) shows the estimated link cost rates on a map of the network. The main bicycle network is clearly visible and seems to be quite dense and well connected. Such maps may be used by urban planners to suggest areas where the bicycle network could be improved. The specification of the cost rate comprises variables that indicate the type of infrastructure for each link in the network, including information about the type of bicycle infrastructure, and the nearby land use. We discuss the most important parameters in turn.
The reference category is residential roads without bicycle infrastructure in low-rise urban areas. Compared with the reference, bicyclists associate a 11% higher cost rate with large roads (roads with at least two lanes in one direction), whereas the difference to medium roads (roads with at most one lane in each direction) is small and statistically insignificant.
Provision of dedicated bicycle infrastructure quite substantially reduces the subjective cost of bicycling. Cycleways (bicycle paths in own trace) reduce the subjective cost by 20%. On residential and medium roads, bicycle lanes, whether protected or just painted, reduce the cost rate by 14% and 22%, respectively. The type of bicycle lane has a considerable effect on the cost rate for the large roads category: painted bicycle lanes have only a small and statistically insignificant effect, whereas protected bicycle lanes reduce the cost rate by 34%. It makes clear intuitive sense that the impact of bicycle lanes is larger, the larger the road is, and only protected lanes affect the largest roads where car traffic is heavier.
A number of routes are branded as so-called cycle superhighways. This is a label given to high-quality, continuous bicycle routes, that cater to commuter cyclists liu2019practitioners. Additional routes are planned to become cycle superhighways in the future, but have not yet received the label Visionsplan2017. We estimate a cost rate reduction of 12%, both for the actual and the planned cycle superhighway links. This suggests that the routes included in the cycle superhighway network were ex ante attractive and that the transformation from planned to actual cycle superhighway does not yield any additional cost reductions beyond those already accounted for at the link level.
The model also includes parameters accounting for interactions between the type of infrastructure and the neighboring land use. The cost rate is much reduced for cycleways in industrial areas (48%) or green areas (53%). It makes intuitive sense that cycleways in green areas may be pleasant. Another potential explanation which also applies for industrial areas is the attractiveness of isolation from heavy traffic.
In summary, provision of bicycle-friendly infrastructure has a substantial effect on route choice. We shall see below that this translates into a substantial effect on the number of bicycle trips.
We set up a gravity model to measure the association between the number of bicycle trips in each OD pair and the characteristics of the bicycle network. The route choice model parameter estimates show that the characteristics of the network significantly affect the subjective cost of using the links of the network. Therefore, the route choice model can be used to compute the subjective cost of traveling by bicycle in any given OD pair, thereby aggregating the network information in a model-consistent manner.
Let $\hat c ^{od} = \sum_{e \in \mathcal{E}} l_e \left(c_e \hat x_e^{od} + F(\hat x_e^{od}) \right)$ be the subjective cost associated with the cost-minimizing flow $\hat x ^{od}$ connecting origin $o$ to destination $d$ and let $Y^{od}$ be the observed number of trips in the OD relation $od$. We assume that $Y^{od}$ follows a Poisson distribution with expectation given as a log-linear function of the cost:
where $\delta$ is a constant, and $\eta_o$ and $\gamma_d$ are constants for each origin and destination, respectively, except one. The constants account for the total bicycle traffic volume out of each origin and the total volume into each destination. The demand function $D$ is expected to be downward sloping, such that higher cost implies less volume. We specify $D$ to be continuous and piecewise linear with the number of pieces chosen by eye-balling.
Figure (ref) shows the estimated demand function. The figure also shows a bootstrapped pointwise confidence band for the estimate of the demand function. The confidence band is very tight at small values of $\hat c ^{od}$ and is wider at larger values where observations are fewer. From the estimated demand function, we can compute the implied demand elasticity as a function of the cost. We find that the demand elasticity decreases almost linearly from 0 to about -6.5 as the cost increases from 0 to 7. A 10% increase in the cost of a short trip thus has very little impact on the number of bicycle trips while it reduces the number of trips by up to 65% for the longest trips.
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We now exploit our model to simulate the impact of general counterfactual changes to the bicycle-relevant network to illustrate how much bicycle infrastructure has contributed to encouraging bicycling in Copenhagen. These results may be of interestfor other cities aiming to improve or expand their bicycle-relevant network.
Table (ref) summarizes the results for the counterfactual scenarios. We compute the change in consumer surplus for bicyclists as well as the change in external cost owing to health and accidents. We have scaled the gravity model output such that the base scenario reflects the total number of kilometers traveled by bicycle in the region. A full economic evaluation of constructing bicycle infrastructure would also need to take into account construction costs, the effects on travel times by car, and the induced effects on climate, accidents, noise, and air pollution.
The first counterfactual simulates a situation where all 1,427.8 km of bicycle lanes and all cycle superhighway classifications have been removed. On average, this increases the subjective cost of bicycling by 34.3% per km, which induces a decrease of 37.0% in the number of bicycle trips and 46.8% in the total distance traveled by bicycle. The bootstrapped confidence intervals indicate that these numbers are quite precisely determined. Relative to the situation without bicycle lanes, the simulation thus suggests that the provision of bicycle lanes has induced an increase in bicycle use by 59% (trips) and 88% (total distance traveled).
To measure the loss to bicyclists in the counterfactual scenario compared with the base scenario, we have computed the change in the consumer surplus Mas-Colell1995. To convert this number from subjective cost units to monetary values, we first apply the sample average speed to convert the subjective cost to time units, and then apply the official Danish value of travel time Enhedspriser2022 to convert from time units to monetary units. Our results suggest a decrease in consumer surplus of €174.1M per year.
Bicycling is associated with both health benefits and accident risk DeHartog2010,Oja2011. The official Danish guidelines for cost-benefit analysis suggest a net external benefit owing to health and accidents of 0.91 EUR per bicycle km Enhedspriser2022. Applying this figure, we estimate the welfare loss induced by removing the bicycle lane network through health and accidents to be €435.3M per year. In total we find a loss of €609.4M per year or €0.427M annually per km of bicycle lane if all bicycle lanes were removed.
In the second counterfactual, we convert the 407.0 km of protected lanes on large roads to painted lanes, while maintaining the cycle superhighway classifications. This increases the subjective cost of bicycling by 7.1% on average, which in turn induces 9.9% less bicycle trips and 13.7% less kilometers travelled by bicycle. We find that downgrading protected lanes leads to an annual loss of €44.8M of consumer surplus and an annual loss due to health and accidents of €127.8M. In total, we compute an annual loss of €172.6M€ or €0.424M per km of protected bicycle lane.
The third counterfactual removes the existing and planned cycle superhighway classifications. We interpret this as representing the effect of no longer having long, connected bicycle routes. The change involves 333.7 km of cycle superhighway routes and leads to an average increase of 12.8% in the subjective cost, which induces a 16.8% decrease in the number of trips and 22.8% decrease in the number of kilometers traveled by bicycle. Removing the route-level features that constitute the cycle superhighways is associated with a annual total loss of €288.1M or €0.864M per lane km.
In all three counterfactuals, we find that the total distance traveled by bicycle responds relatively more than the number of trips. This means that the number of long bicycle trips responds more than the number of short trips, in line with our observation that the demand elasticity increases with the trip cost.
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We find substantial impact of the provision of bicycle-relevant infrastructure on the subjective cost and the volume of cycling. We work at a very fine level of resolution, which allows us to distinguish between a large number of infrastructure types. This is first-order important, as we find a difference in the subjective cost of cycling of more than a factor eight between the best and the worst infrastructure types. Thus, the type and the location of infrastructure are very important.
The counterfactual simulations performed in this study illustrate the effect of broad changes to the bicycle network. These results may be of interest when considering the consequences of expanding the bicycle network in cities with less bicycle infrastructure than Copenhagen. We find that the existing bicycle network in Copenhagen has led to a substantial increase of about 90% in distance traveled by bicycles. These changes can be interpreted as representing short-term effects, as they hold constant the fixed effects associated with origins and destinations. In the longer term, location patterns can be expected to adapt to improvements in the bicycle network, making the long-term effect of a network improvement larger than the short-term effect. Previous research supports the broad conclusion that bicycle infrastructure induces more bicycle traffic Pucher2009,buehler2016bikeway,Aldred2019a,Kraus2021.
From the counterfactual scenarios, we have calculated the net benefit of bicycle lane provision associated with the change in subjective cost, health, and accidents to be €420k--440k per lane km per year. According to ECF2021, construction costs are in the range €0.5M--1.5M per lane km.\footnote{Lower if the numbers in ECF2021 pertain to route km.} The estimated benefit associated with cycle superhighway status is greater, €860k per km per year, although it relates only to route-level features, holding link-level features constant. As construction costs are incurred once but benefits accrue year by year, these results indicate that the provision of well-located and high-quality bicycle infrastructure can easily generate a positive net present value in a standard cost-benefit analysis.
Copenhagen already has extensive bicycle infrastructure, so the effect of additional infrastructure may be smaller. On the other hand, we find a large net benefit of cycle superhighways, which may arise from having long and connected bicycle routes. This means that limited investments can potentially lead to large net benefits by improving overall connectivity of the bicycle network. Maps such as Figure (ref) can be used to identify candidate locations for such investments.
We have combined a very large database of observed bicycle trajectories and a very fine-grained representation of the bicycle-relevant network with a modeling approach that allows us to take the entire network into account. Our model can be applied to predict the effect of providing specific infrastructure in specific places. Similar analyses can be undertaken for other cities. In such analyses, however, the main obstacle is obtaining sufficient data on observed route choices similar to the Hövding dataset used in this study.
This is the first study of its kind, so there is much scope for future research. On the bicycle front, it is of interest to estimate similar models using datasets from other cities to consolidate and extend the conclusions regarding the impact of bicycle infrastructure on bicycle demand. Another research avenue is investigating datasets sampled by different means or from different kinds of users to check the robustness of our conclusions.
On the methodological front, a general research agenda can be formulated for the perturbed utility route choice model, with a view to applications to bicycle traffic or other traffic through complex networks. The most important point here, we think, is to develop approaches that allow the estimation of the models at the level of individual trajectories. This would make it possible to avoid the data loss associated with the aggregation of data to the OD level and allows the inclusion of individual-level information. Another related avenue is to develop solution methods for the cost minimization problem in (ref) that make it feasible to work with meta-networks where link-pairs take the place of links. This would allow turn movements to be represented and hence allow to take into account, for example the cost of left turns and crossing roads with car traffic.
Figure (ref) shows the raw data from our sample of GPS traces of bicycle trips, collected in Greater Copenhagen Hovdingdata. Figure (ref) presents the corresponding views of the road and dedicated bicycle network, using Open Street Map data OpenStreetMapdata. Copenhagen has an extensive bicycle network with many cycleways, especially outside central Copenhagen. In central Copenhagen there is a dense network of protected bicycle tracks and many non-protected bicycle lanes.\footnote{See SI Appendix (ref)(ref) for definitions of the various infrastructure types.}
SI Appendix (ref)(ref)-(ref) describes how we processed our data. In brief, the pre-processed dataset of 218,489 GPS trajectories collected from 8,588 individuals were map-matched to the Copenhagen bicycle network using software presented in Haunert2012. Our estimator for the route choice model requires trips to be aggregated such that each included OD pair has at least two distinct observed trajectories. Therefore, we applied an algorithm that trims individual trajectories at both ends such that the trimmed trajectories have a small number of origins and destinations in common. Our analyses are based on data with 200 origins and 200 destinations, which represents a compromise between including most of the observed trajectories and avoiding many OD pairs with only a small number of observations. Robustness check with 100 and 400 origins and destinations did not indicate problems; see SI Appendix Section (ref)(ref). We use the data for all OD pairs that are more than 1 km apart and have at least two distinct individual route choice observations per OD. Our estimation data comprise 152,323 trimmed trips from 7,672 individuals.
A directed network comprising nodes and links $(\mathcal{V},\mathcal{E}) $ is described by the incidence matrix $A$ with elements $a_{ve}=1$ if $v$ is the origin node of link $e$, $-1$ if it is the destination node, and $0$ otherwise. A set of OD pairs $\mathcal{B}$ is represented in terms of OD demand vectors $b \in \mathcal{B} \subset \mathbb{R}^{|\mathcal{V}|}$, where $b_v = 1$ indicates the origin node of trip $b$, $b_v = -1$ indicates the destination node and $b_v = 0$ otherwise. The flow conservation constraint $Ax=b$ ensures that a non-negative flow vector $x \in \mathbb{R}_+^{|\mathcal{E}|}$ is physically consistent with demand $b$ through the network.
The perturbed utility route choice model holds that the flow vector $\hat x ^b$ for bicyclists with demand $b$ minimizes the cost function in (ref) under the flow constraint $A\hat{x}^b=b$. Fosgerau et al. Fosgerau2021a show that this model generates very reasonable substitution patterns. Moreover, the model directly applies to the complete network, without a need to specify a choice set of route alternatives.
Given (noisy) observations of flow vectors, Fosgerau et al. Fosgerau2021a transform the active first-order conditions for the cost minimization problem to a linear regression equation that directly leads to an estimate of $\beta$. There is an active first-order condition for each link with positive observed flow. The transformation eliminates Lagrange multipliers corresponding to the flow conservation constraints at each node of the network. The data for the regression comprises many observations for each OD pair, which enables standard errors to be clustered by OD pair.
Figure (ref) plots the total observed link flow ($x_e^{\bm\cdot} = \sum_{o\in \mathcal{O}} \sum_{d \in \mathcal{D}} x_e^{od}$) against the total predicted link flow ($\hat x_e^{\bm\cdot} = \sum_{o\in \mathcal{O}} \sum_{d \in \mathcal{D}} \hat x_e^{od}$) for each link $e \in \mathcal{E}$ across all origins and destinations. A perfect prediction would exactly follow the $45^\circ$ line. We find that a non-parametric regression line quite closely tracks the $45^\circ$ line. This is satisfactory, especially considering that the route choice model uses only 28 parameters. The correlation (defined in the SI Appendix (ref)) between $x^{\bm\cdot}$ and $\hat x^{\bm\cdot}$, is $ \rho(x^{\bm\cdot}, \hat x ^{\bm\cdot}) = 0.8894$.
SI Appendix (ref)(ref) comprises a range of validation tests of the route choice model.
{This research is funded by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 740369). We thank Michel Bierlaire, Mike Smith, seminar participants at the Tinbergen Institute in Amsterdam, conference audiences at the 7\textsuperscript{th} International Choice Modelling Conference in Reykjavik, and the 10\textsuperscript{th} Symposium of the European Association for Research in Transportation (hEART) in Leuven for comments.}
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