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Article Excerpt
I. INTRODUCTION
Urban motorists are well acquainted with the frustrations of traffic congestion. As Calfee and Winston (1998) put it, "Everyone knows the toll congestion can take on drivers' nerves. And everyone knows how costly it can be in terms of wasted time and lost productivity." This statement illustrates two distinct externalities that are generated during a typical rush-hour commute. First, congested travel is simply unpleasant. (1) Second, congested travel means delayed travel. Economists have devoted considerable attention to estimating travel delay externalities, and the marginal value of travel time savings--often referred to as the "value of time" (VOT)--typically dominates the estimation of highway improvement benefits (Small 1992). The sheer unpleasantness of congestion, however, has received little attention presumably because it is difficult to quantify or even observe. Yet, it may represent a substantial portion of the wedge between the social and the private costs of highway travel. For example, consider this familiar scenario: a ball game or concert lets out, spectators flock to their vehicles, and parking lot gridlock ensues. Several motorists decide to stay put, turn on the radio, and "wait it out." For these motorists, the cost of delayed travel is dominated by another distinct cost--one that is difficult to observe but is certainly palpable. For rush-hour commuters, schedule delay costs are too large for most motorists to wait it out and this additional congestion cost must be incurred. There is no conventional label for such costs, so the term "white-knuckle costs" is introduced here to describe them. (2)
The existence of white-knuckle costs helps to explain a recurring finding that the value of time increases with the severity of congestion (Hensher 2001; Small et al. 1999; Wardman 2001). For instance, Wardman's (2001) meta-analysis of several VOT studies finds that time spent in congested traffic is valued 48% more highly than time spent in free-flowing conditions, suggesting that "more difficult driving conditions linked with greater stress, frustration, and perhaps travel-time uncertainty, lead to higher time valuations." The finding provides an initial gauge on the size of these white-knuckle costs and suggests that traditional VOT estimates may reflect them to some extent. How successfully these VOT estimates capture white-knuckle costs, however, depends on the degree to which they are correlated with travel delay costs. Unfortunately, in such studies, no precise method has been offered for disentangling travel delay and white-knuckle influences. As such, there has been no way to determine how closely VOT estimates approximate the value of both reduced travel time and relief from other knuckle-whitening factors. Moreover, separate estimates would allow for a more thorough understanding of how the "stress and frustration" of congestion compare to the travel delays it causes.
This paper exploits a unique set of toll road data to obtain separate estimates for travel delay and white-knuckle costs so that their magnitudes can be compared. This is accomplished by analyzing the real-world trade-offs that rush-hour commuters make between congested travel and uncongested travel for a fee, holding constant the influence of travel times on this choice. (3) The basic idea is that both travel times and unobservable influences such as stress and frustration naturally increase with congestion. By simultaneously estimating the influences of congestion and travel time on route choice, the resulting value of reduced congestion is purified of travel time influences, thus revealing the value of nontime factors that cause white knuckles. Likewise, the value of time is purified of white-knuckle influences, revealing the pure opportunity cost of motorists' time. Applying these valuations to a suitable travel cost framework yields separate estimates of travel delay externalities and white-knuckle externalities, where the latter measures the unobservable externalities that motorists generate during congested travel. This paper also uses the same data to obtain traditional VOT estimates in order to measure how closely they approximate the joint value of delays and white knuckles.
Estimation results suggest that travel delay and white-knuckle externalities together amount to $1.86 per vehicle-mile during an urban rush-hour commute in Southern California. Of this, $0.99 is attributable to travel delays and $0.87 represents white-knuckle costs. In other words, unobservables such as stress and frustration generate 47% of the congestion externalities borne by rush-hour commuters; it suggests taking white-knuckle costs seriously when formulating road pricing and investment policies. Traditional value-of-time estimates are also obtained implying a travel delay externality of $1.58 per vehicle-mile. Using the combined travel delay and white-knuckle externality estimate of $1.86 as a benchmark suggests that about 85% of this combined externality can be captured using common procedures for estimating the value of time.
The paper proceeds as follows. Section II develops a simple travel cost framework to formally describe travel delay and white-knuckle externalities. Section III describes the empirical setting and estimation procedures used to obtain valuation and external cost estimates. Results are discussed in Section IV, followed by a few concluding remarks in Section V.
II. TRAVEL DELAY AND WHITE-KNUCKLE EXTERNALITIES
This paper's empirical strategy relies on the ability to estimate how motorists respond to varying levels of traffic congestion and travel times, which calls for a brief review of congestion principles. In this study, traffic congestion is characterized by traffic "density," defined as the number of vehicles per unit of space on a road at some point in time. Density is suitable for measuring the influences of congestion because it provides motorists with a direct sense of how "crowded" conditions are and, perhaps, how frustrating they might be. For example, bumper-to-bumper conditions indicate high traffic density. However, density is a stock quantity, which is not suitable for measuring economic costs. But the influences of density can be readily mapped into a flow quantity, traffic "volume," defined as the number of vehicles passing a given point per unit of time. Density is also related to travel time because vehicle speeds fall monotonically with density; this relationship demonstrates why travel times and traffic densities are often highly statistically correlated and provides insight on why the nontime costs of congestion might be reflected in value-of-time estimates.
The explicit relationship between volume (V), density (D), and speed (S) is defined by the "fundamental" equation of traffic flow (Haight 1963; Hall 2002):
(1) V = DS(D),
where [partial derivative]S/[partial derivative]D [less than or equal to] 0. (4) It will be useful for later analysis to describe how traffic density changes with traffic volume. Applying the implicit function theorem to Equation (1) yields
(2) [partial derivative]D/[partial derivative]V = 1/[S(1 + [[epsilon].sub.S,D])] > 0.
where [[epsilon].sub.S,D] [equivalent to] ([partial derivative]S/[partial derivative]D)(D/S) is the elasticity of speed with respect to density. (5)
Rearranging Equation (1) allows density to be expressed as D(V) and travel time, T, to be expressed as T = T(D(V)), noting that travel time is simply the inverse of speed. This allows for modeling congestion costs as functions of the flow quantity, traffic volume (following Walters 1961). (6) To proceed, consider a fixed commute period lasting q hours. Abstracting from money costs, let c = c[T(D(V)),D(V)] represent the private cost that each motorist faces during this commute, where [partial derivative]c/[partial derivative]T > and [partial derivative]c/[partial derivative]D > 0. This expression indicates that private cost...
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