Welfare evaluation with a road capacity constraint

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Abstract

Severe traffic congestion in and around many cities across the world has resulted in programmes of extensive road building and other capacity increasing projects. But traffic congestion has often not fallen in the long run and neither has journey speed increased. Demand for peak period road travel, particularly by car, has grown so strongly that increases in road capacity have been quickly matched by increased road use. This paper develops a model of a road network characterised by insatiable road passenger (car and bus) demand. The model parameters are calibrated on a typical urban road network, and a number of simulations conducted to determine social welfare after the introduction of a road capacity constraint into the optimisation process. The empirical results have an important policy implication for the evaluation of projects that increase road capacity, namely that standard methods of cost-benefit analysis may tend to overestimate the net benefits of such projects by a significant amount. Although the model is developed in the context of roads and road traffic congestion, it could also be applied to air travel.

Introduction

Road traffic congestion is a major problem in and around cities throughout the world, from Los Angeles to London, from Beijing to Bangkok. On the M25, the London orbital motorway built originally to solve chronic traffic delays around the capital, some ten million vehicles a month are involved in traffic jams and the average total tailback during peak periods has increased to 80 miles. By 2011 it is estimated that the average business motorist in Britain will spend 14 days a year sitting in traffic jams.1 Traffic congestion in developing countries can be even worse because of the high concentration of industrial and commercial activity within capital and other major cities. In the Southeast Asian cities of Bangkok, Jakarta and Manila, for example, infrastructure provision and traffic management has barely coped with the pace of economic growth and the rapid motorisation generated by it (Kubota, 1996).

Even in less extreme cases the provision of more road space has often failed to satisfy the demand for higher speeds. To take one of many possible cases, the road network in Britain increased by over 20% in the post-war period, yet average urban peak (and off-peak) traffic speeds generally fell. Even where the expansion of road capacity was much higher than average, as in the outer London area, traffic speeds still fell. Between 1968–70 and 1994–97 the average traffic speed in this area for the morning peak period declined from 33 to 27.4 km/h (DETR, 2000, Table 4.14). There is no shortage of evidence to show that similar (or worse) stories can be told elsewhere.

The problem is that increased road capacity does not relieve traffic congestion if there is substantial suppressed demand for peak period road space. Road building or improvement in this context simply allows the suppressed demand to become actual demand. Demand may not only be suppressed but also insatiable, in the sense that increases in road capacity over long periods of time are continuously matched by increases in road traffic, as in the case of the M25.

It is this insatiability that imparts a unique character to peak period road transport demand. Other economic activities may be subject to periodic bottlenecks and delays, but it is not easy to think of situations, at least if we exclude non-market economies,2 where demand pushes so strongly and persistently against supply for so many years. Downs, 1962, Downs, 1992 has documented the “fundamental law of traffic congestion” in the United States, and the view that “you cannot build your way out of traffic congestion” has recently been given more support by the Surface Transportation Policy Project (1998). In a report based on 15 years of data covering 70 US metropolitan areas, it concluded that areas with high levels of road capacity investment did no better at easing congestion than areas with lower investment levels. Hansen and Huang (1997), using panel data for California urban areas for 1973–1990, also find that increasing road capacity has a strong traffic inducing effect, particularly at the metropolitan level.

Hensher and Brewer (2001, p. 184) remark more generally that “There is so much latent demand for car travel at peak periods … that whatever capacity we can feasibly expect to build, or that can be freed up by enticing a few drivers off the road, will quickly become filled by people who are now being deterred only by congestion itself ” (author’s italics). This statement is particularly relevant here. First, its emphasis on the importance of road capacity constraints, rather than budget constraints, is consistent both with the main theme of this paper and with empirical observation. Between 1953 and 1996, real per capita incomes increased by 158% in Britain, but real motoring costs (including purchase and running costs) actually fell by 34% (Romilly et al., 2001). Given these opposite movements in income and the price of car use, it is hardly surprising that traffic congestion is still a serious problem. Second, the statement implies that road capacity constraints are nearly always binding: increases in road capacity are quickly filled by increases in road use. From a modelling perspective, the implication is that a road capacity constraint should form an integral part in modelling insatiable road passenger travel demand.

But one must ask the question: why is demand insatiable? Assuming that the demand for car use is not completely price inelastic, the answer must depend on price. If the price of car use could be increased sufficiently to ration demand to the available road space, then the issues of demand insatiability and capacity constraints would not arise. The fact that they exist in some circumstances is indicative of a failure of the price mechanism or, in the case of most major transport infrastructure, the failure or inability of the relevant transport authorities to increase price to the required level. In a modelling sense, the specification of a road capacity constraint can be viewed as an alternative way of modelling this “sticky” or non-optimal price effect.

Hansen and Huang (1997, p. 205) observe that “The relationship between road supply and road use is crucial to the appraisal of urban road construction programmes. If the effect is strong, urban road construction becomes very hard to justify in light of its enormous cost, marginal congestion reduction benefit, and probable adverse environmental and energy consequences.” By the inclusion of a road capacity constraint our model addresses the appraisal issue, provides new results concerning road travel demand and social welfare, and also gives an alternative perspective on the standard cost-benefit approach to the evaluation of road building or other capacity-increasing projects. The model has the advantage that it can be calibrated using a relatively small number of parameters, the values of which are widely used in the transport modelling literature.

The paper confines itself to the two main modes of road passenger travel: car and bus. These modes are clear alternatives in the sense that the first represents a preference for a higher price/higher quality mode of travel, and the second for a lower price but lower quality mode. In this sense the model can in theory also be applied to air travel, where passengers have a choice between business and economy class and where, at least in the UK, increasing demand has run up against the problem of capacity constraints in the form of shortages of runway space.

The remainder of the paper is structured as follows. Section 2 provides a description of the model assumptions and key results. Section 3 develops an operational version of this model to determine the welfare effects of varying road capacity. Section 4 discusses the choice of appropriate parameter values to calibrate the model, and Section 5 uses these values to generate simulation results. A summary and concluding remarks are provided in Section 6.

Section snippets

General remarks

The preceding observations can be summarised as follows. In the short term, transport authorities build more roads3 to reduce traffic congestion and increase journey speeds

Model specification

The model equations are specified in linear form, which simplifies the derivation and interpretation of optimality and sufficiency conditions. Alternative specifications are not considered in this paper but there is justification for the use of the linear specification. Walters (1961, fn. 7) cites empirical evidence to suggest that it is superior to the log-linear specification for road user costs. Additionally, there is empirical evidence to indicate that the relationship between speed and

Model calibration

The theoretical long run model developed in Section 3 must be calibrated on a specific set of road traffic conditions. There are a number of possibilities, but the one most useful for our purposes is the peak period case given in Table 4 of De Borger et al. (1996), henceforth termed the reference case. Starting from actual traffic conditions and mode prices, this case provides calculations of short run optimal peak period prices, marginal social costs, traffic flows and speeds for private and

Model simulation

The values from the reference case in Section 4 are inserted in our model equations to derive the net social benefit with and without a road capacity constraint, assuming optimal prices, costs and quantities. The results, together with the initial (exogenous) and derived constant values, are summarised in Table 1. The key result is for net social benefit, which is $11.82 million per peak period day without a road capacity constraint, but only $9.54 million with a constraint. Thus a failure to

Summary and concluding remarks

Historical experience in many parts of the world suggests that increasing road capacity has not always reduced traffic congestion in the long run, where this time period can extend for decades rather than a few years. Road passenger transport in the peak period may often be characterised, perhaps uniquely, by insatiable demand in the sense that car use continually pushes up against the limits of whatever road capacity is supplied. If this constraint (or policy negation effect) is recognised and

Acknowledgements

The author would like to thank Keith Cowling, Gianluigi Giorgioni, Paul Hare and two anonymous referees for comments on earlier drafts of this paper. Remaining errors are the responsibility of the author.

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