Congestion pricing 1: theory & history🍋

Long advocated by economists, but with a mixed history of implementation

The draft Government Policy Statement on Land Transport, issued in March 2024, states that new legislation will “… allow for time-of-use charging on the most congested parts of New Zealand’s road network, helping to reduce congestion and maximise use of existing assets.”

Ever since Pigou,¹ Walters,² and Vickrey,³ economists have advocated congestion pricing to deal with the negative externality of driving on congested roads. The externality arises because, although drivers take into account the cost (to them) of road congestion when making trip decisions, they tend not to take into account the cost they impose on other drivers.

An analysis of the effects of congestion pricing is not straight-forward. In this post I hope to inform discussion by outlining some of the issues and the conclusions that economists have come to. I draw mainly from an article by Kenneth Small.⁴ It will be followed up by a second post focused on the practicalities of implementation.

Livingstone Range, Fiordland National Park. Dave Heatley

Congestion is an externality

Pricing the congestion externality would change drivers’ consideration of the various alternatives they face, such as to drive at a different time, take a different route, take public transport or stay home.

Contrary to public perceptions, pricing will not necessarily reduce demand. The bottleneck model, first formulated by Vickrey and further elaborated by others (in particular Arnott, de Palma & Lindsey⁵), has provided significant new insights and computational tools for understanding many features of congestion and the pricing thereof.

The bottleneck model

Congestion happens at bottlenecks — those parts of the roading system with limited capacity (compared to the capacity before and after the bottleneck), and where that capacity is less than demand. When queues form at bottlenecks, drivers waste time either by sitting in the queue, or because they arrive at their destination too early. Arriving too early can happen because drivers departed early so as to avoid the congestion, or if they get through the queue more quickly than they expected.

The cost of arriving too early or too late is known as a scheduling cost. Indeed, the most important insight of this literature is the role that scheduling costs play in the aggregate travel time costs — exactly 50% of the total aggregate travel time costs, in the simplest version of the bottleneck model. This contrasts with the intuition of and normal rhetoric regarding congestion, both of which focus on the cost of time wasted while driving slowly. Scheduling costs cannot be measured directly by observing travel time.

Queues form because of a mismatch between demand and road capacity. But if some drivers’ arrival at the bottleneck is pushed forward or delayed, so that the arrival times match the rate at which vehicles pass through the bottleneck, then the queues can be avoided. An optimal price structure that incentivises this can be readily computed. It will consist of a toll rising linearly from the time when the queue would first start building (in the absence of a price) and reaches its maximum when the queue would be at its peak, decreasing after that. The optimal price depends on how much drivers value their time, i.e. how much they value avoiding scheduling costs, given that under an optimal time-varying congestion toll there is no queueing.

The main insights that this model provides include:

• Travel time captures only one of the two major sources of congestion cost, the other being the scheduling cost.,

• Optimal time-varying pricing completely eliminates queueing costs.

• In the simple model, pricing reduces aggregate travel costs (travel time plus scheduling) exactly by half.

• Nobody is either better or worse off privately because of the toll.

• The toll revenue is pure public benefit (strictly Pareto improving).

• The self-financing theorem of Mohring & Harwitz,⁶ derived from a static model, applies here too, i.e. that an efficiently designed road can be fully financed from optimal user charges.

Hendrickson & Kocur,⁷ and subsequent papers by other authors, analyse the consequences of relaxing the rather restrictive assumptions of the simple model above, by discussing more complicated scenarios (for example two roads merging before a bottleneck, populations with heterogeneous values of time, multiple appointment times, pay-lanes, etc). The basic insights mostly continue to be the same – see the literature review by Small⁸.

One interesting problem is breaking behaviour, where drivers wait before an expected increase in the toll if the toll payment saved outweighs the travel time and schedule delay cost incurred by waiting. This can happen particularly (but not only) if the pricing schedule has discreet steps in it, and results in a loss of efficiency, which is greater the fewer the number of steps, but can be avoided by replacing location-based toll collection schemes with more sophisticated systems with charges proportional to distance driven. Comprehensive, per-kilometre road-pricing schemes have other advantages, including more complete network coverage and greater spatial/geographical equity (Lindsey, van den Berg & Verhoef⁹).

International experience

Congestion charging has been implemented with varying degrees of success in Singapore, London and Stockholm. Other schemes, for example Dubai and Gothenburg, were less successful.

There is a long list of failed schemes:

• Netherlands (full network charging): public opposition due to perceived cost of implementation and lack of belief that it would benefit motorists.

• Edinburgh (double cordon): too many objectives (e.g. improving urban amenity, raise revenue), lots of exemptions

• Manchester (double cordon)

• New York (tolling the untolled East River crossings): cordon seen as arbitrary and unjust, fear of negative impacts.

• Helsinki (mixed and changing objectives, seen as unfair)

• Oslo (current system designed to raise revenue was to be changed to a congestion scheme)

• Dublin, Hong Kong and Copenhagen

Singapore has arguably the best scheme: First introduced in 1975, there are now around 80 charging points throughout the city, each with its own pricing schedule. Drivers pay as they pass a charging point, each one has multiple charging steps throughout the day, the price at each charging point is adjusted every three months in light of average traffic speeds over the preceding 3 months at that point (for each daily time period). If the average speed drops below a certain level, the price is increased, and vice versa. This makes it clear to the public that the purpose is to manage congestion (as defined by traffic speed), and not revenue raising.¹⁰

The pricing schedule of one charging point in Singapore.

Stockholm undertook a 7-month congestion tax trial in 2006. This was not popular initially, but at the end of the trial a referendum was held and the scheme was made permanent in 2007.¹¹

My assessment

A common view (mostly amongst non-economists) is that congestion pricing will deter drivers with low values of time from using the road, and switch to other roads, to public transport, to less convenient travel times, or to forego travelling. A common demand is for public transport to be improved before a congestion charge is introduced, and for schemes to be established to compensate losers (especially low income losers). As outlined above, the existing literature does not provide support for these views, and is much more encouraging of outcomes.

Nevertheless, it may be that in real life things are more complicated than suggested by the existing literature. Pricing schemes that change prices continuously in real time are internationally unprecedented and may seem too radical for political acceptability; the road networks of many cities are vastly more complicated than simple bottlenecks; and demand fluctuates in unpredictable ways, making both pricing schedules and trip planning difficult.

Moreover, decision-makers find it difficult not to load a scheme with multiple, potentially conflicting objectives, in particular revenue raising and allowing exemptions for certain interest groups.

While there are solutions to most of these issues, the result of even a successful practical congestion pricing scheme is likely to be less tidy and to produce periods when the charge is too high or too low, and therefore potentially produce some losers as well as winners.

By Dieter Katz

Read more: Congestion pricing 2: alternatives🍋

Unnamed lake near Jaquirey Pass, Fiordland National Park. Dave Heatley

1. Pigou, A.C.: Wealth and Welfare, 1^st edition, 1920.

2. Walters, A.A., “The Theory and Measurement of Private and Social Cost of Highway Congestion,” Econometrica, October 1961, 29, 676-99.

3. Vickrey, W.S., Congestion theory and transport investment, Amer. Econ. Rev. 59, 251-261 (1969).

4. Small, K.A., 2015. The Bottleneck Model: An Assessment and Interpretation.

5. Arnott, R., de Palma, A., & Lindsey, R., 1990. Economics of a bottleneck. Journal of Urban Economics 27, 111-130.

Arnott, R., de Palma, A., & Lindsey, R., 1991. A temporal and spatial equilibrium analysis of commuter parking. Journal of Public Economics 45, 301-335.

Arnott, R., de Palma, A., & Lindsey, R., 1993. A structural model of peak-period congestion: A traffic bottleneck with elastic demand. American Economic Review 83, 161-179.

6. Mohring, H., & Harwitz, M., 1962. Highway benefits: An analytical framework. Northwestern University Press, Evanston, Illinois.

7. Hendrickson, C. Kocur, G., 1981. Schedule delay and departure time decisions in a deterministic model. Transportation Science 15, 62-77.

8. Small, K.A., 2015. The Bottleneck Model: An Assessment and Interpretation.

9. Lindsey, C.R., van den Berg, V.A.C., & Verhoef, E.T., 2012. Step tolling with bottleneck queuing congestion. Journal of Urban Economics 72(1), 46–59.

10. See Wikipedia article https://en.wikipedia.org/wiki/Electronic_Road_Pricing.

11. See Wikipedia article https://en.wikipedia.org/wiki/Stockholm_congestion_tax.