Optimal congestion taxes in a time allocation model

Abstract

The purpose of this paper is to study optimal congestion taxes in a time-allocation framework. This makes it possible to distinguish taxes on inputs in the production of car trips and taxes on transport as an activity. Moreover, the model allows us to consider the implications of treating transport as a demand, derived from other activities. We extend several well known tax rules from the public finance literature and carefully interpret the implications for the optimal tax treatment of passenger transport services. The main findings of the paper are the following. First, if governments are limited to taxing market inputs into transport trip production, the time-allocation framework: (i) provides an argument for taxing congestion below marginal external cost, (ii) implies a favourable tax treatment for time-saving devices such as GPS, and (iii) provides a previously unnoticed argument for public transport subsidies. Second, if the government has access to perfect road pricing that directly taxes transport as an activity, all previous results disappear. Third, in the absence of perfect road pricing, the activity-specific congestion attracted by employment centres, by shopping centres or by large sports and cultural events should be corrected via higher taxes on market inputs in these activities (e.g., entry tickets, parking fees, etc.).

Introduction

In this paper, we consider optimal taxes for passenger transport services in a time-allocation framework, allowing for potential substitution between market inputs and time in the production of trips. We first derive optimal tax rules under the assumption that the government cannot directly tax car transport, but only has access to taxes on the market inputs into car trip production (gasoline, maintenance, etc.). We then compare the results with optimal tax rules when the government does have the possibility to impose direct taxes on car transport via, e.g., a system of road pricing. To facilitate the interpretation of our findings, we relate the optimal tax expressions to several well known tax rules that have shaped economists’ thinking about optimal commodity taxes, including the Diamond and Mirrlees, 1971a, Diamond and Mirrlees, 1971b efficiency theorem, Ramsey (1927) taxation and the Corlett and Hague (1953) rule. Moreover, the time-allocation framework allows us to study the implications of treating transport demand as a derived demand from other activities. The derived-demand nature of transport is often emphasized, but the relevant implications for the optimal taxation of congestion have not formally been analyzed.

In the sixties, a series of seminal papers and monographs – including, among others, Walters, 1961, Mohrung and Harwitz, 1962, Strotz et al., 1965, Marchand, 1968, Vickrey, 1969 – initiated a large literature on congestion pricing. This literature has been extended in several directions. For example, a variety of second best considerations were incorporated into the analysis (e.g., Verhoef et al., 1996, Small and Yan, 2001), the implications of the interaction of transport policies with the labour market for congestion tolls were explicitly recognized (Parry and Bento, 2001, Van Dender, 2003), and the consequences of agglomeration economies for congestion policies were carefully studied (see, e.g., Safirova, 2002). Moreover, several authors emphasized the importance of congestion for trip scheduling decisions by road users and investigated the implications of schedule delay for congestion policies (Small, 1982, Arnott et al., 1993). Finally, the role of other pricing instruments has received considerable attention, in case optimal road tolls can for some reason not be implemented (Fullerton and Mohr, 2003, Parry and Small, 2005, De Borger and Mayeres, 2007).

Although the literature surveyed above has greatly increased our understanding of the congestion problem and how to deal with it, it has not considered the problem within a formal time-allocation framework. The purpose of the current paper is to reconsider the problem of optimal congestion taxes within the time allocation setting originally developed by Becker (1965), and recently embedded in an optimal tax framework by Kleven et al., 2000, Kleven, 2004. We have two specific reasons for doing so. First, existing models of optimal congestion taxes typically assume that the time it takes to make a particular car trip depends on congestion levels but that, conditional on traffic levels, travel time is exogenous to the individual road user (see, among many others, Verhoef et al., 1996, Mayeres and Proost, 1997, Parry and Bento, 2001). However, recent technological developments suggest the existence of additional substitution possibilities between money and time. Indeed, drivers can invest in time-saving devices such as GPS and ATIS; spending on these market inputs reduces the time it takes to make a trip. Moreover, Verhoef and Rouwendal (2004) have questioned the exogeneity of the traditional speed-flow relation on other grounds. They argue that, if one interprets travel speed as ‘average’ speed over an entire trip, drivers do have the opportunity to optimally select speed at given traffic flows. The available empirical evidence in fact widely supports the existence of a trade-off between time and monetary spending. For example, fuel use has been empirically found to be directly related to speed over quite a relevant range (see, e.g. Rouwendal, 1996). Furthermore, Fosgerau (2005) reports that, conditional on traffic levels, drivers with better cars drive faster. In addition, it is well known that people spend time looking for a parking spot in order to save on parking costs (Anderson and De Palma, 2004). Although the importance of these substitution possibilities between money and time deserves further empirical analysis, the question arises whether such potential substitution has implications for the optimal tax treatment of passenger transport, given the presence of road congestion.¹

A second reason for reconsidering congestion taxes in a time-allocation framework is that, although all introductory textbooks on transport economics (see, e.g., Button, 1993) start out by emphasizing the derived nature of transport demand, existing models have not formally exploited this derived-demand nature. They either treat transport demand as a final demand (e.g., Verhoef et al., 1996), or they assume perfect complementarity with labour supply (e.g., Parry and Bento, 2001). The Becker–Kleven time-allocation framework is the ideal vehicle to deal with transport as derived from various activities, and to study the role of taxes on transport and on other market inputs in transport-using activities under different assumptions on the nature of congestion (e.g., is it the joint consequence of multiple activities, or is it activity-specific?) and on the available tax instruments (e.g., is an activity-specific congestion toll possible or not?). As we will show, taking account of the derived-demand nature of transport has a number of highly intuitive implications that, although probably not surprising to specialists in the field, have never formally been derived before.

The main findings of this paper are easily summarized as follows. First, if governments are limited to taxing market inputs (such as gasoline, car maintenance, car accessories) into the production of car trips, the time-allocation framework provides an argument for taxing congestion below the marginal external congestion cost. It also implies a favourable tax treatment for time-saving devices such as GPS and it suggests reducing public transport fares. Second, however, all these results disappear if road pricing is available. Market inputs in transport production should then neither be taxed nor subsidized. The intuition is that the road toll does not distort the choice of time versus commodity inputs in trip production, so that the extra stimulus of lower taxes on time-saving devices disappears. Similarly, the argument in favour of lower public transport fares disappears. We will argue that these findings are easily understood by reconsidering several famous results in the public economics literature in a household production framework, and allowing for congestion. Third, we show that explicitly treating transport demand as derived from activities implies a useful role for taxes on other market inputs in transport-using activities whenever optimal activity-specific congestion tolls are not possible. Not surprisingly, the tax structure raises taxes on inputs of activities that generate a lot of transport. The results imply, in the absence of perfect road pricing, partially correcting the congestion attracted by employment centres, by shopping centres or by large sports and cultural events via higher taxes on market inputs in these activities (e.g., parking, entry tickets, etc.).

The paper has several obvious limitations. First, the focus on time allocation and congestion implies that we ignore other externalities, such as pollution and accident risks. Environmental pollution could be easily introduced but does not affect the findings of the current paper. Ignoring accident risks is not entirely innocuous, however, as it is well known that accident risk and congestion are not unrelated (see, e.g., Verhoef and Rouwendal, 2004). Moreover, insurance against accident risks raises issues of moral hazard, in the sense that drivers may take less care in avoiding accidents and the associated damage than they would in the absence of insurance. Moral hazard has clear implications for the optimal tax treatment of driving that are ignored in the current paper. For example, since driving cannot be taxed directly, Arnott and Stiglitz (1986) suggest taxing complements and subsidizing substitutes to driving to cope with moral hazard. They argue in favour of taxing gasoline and cars (to reduce driving), subsidizing maintenance (to make driving less risky) and, assuming that moral hazard is less pronounced for other modes than for car use, subsidizing alternative modes. Second, the time-allocation framework we use throughout the paper is a direct extension of Becker, 1965, Kleven et al., 2000, Kleven, 2004, despite the criticism of, e.g., Boadway and Gahvari, 2006, Gahvari, 2007.² These authors make the useful distinction between ‘labour substitutes’ (goods for which consumption time yields negative utility) and ‘leisure substitutes’ (time yields positive utility). They argue that the Becker–Kleven model implicitly assumes that all taxed commodities are labour substitutes, and that the optimal tax rules look quite different if goods happen to be leisure substitutes.³ However, for the large majority of trips people do consider the time spent in transport as unpleasant, so that this restriction seems rather innocuous for our purposes. Moreover, the Becker–Kleven activity approach is especially attractive from another perspective, highly relevant for this paper: unlike the Boadway-Gahvari model, it allows for substitution in the production of transport activities, and it provides a simple and direct way to study transport demand as derived from the demand for particular other activities. A third important limitation of this paper is the set of tax instruments considered. Throughout the paper, we follow the standard Ramsey approach. This implies that we exclude lump-sum taxes (such as head taxes) and focus on linear commodity taxes.⁴ Moreover, we ignore heterogeneity and distributive concerns. Finally, there are no income taxes in the model.⁵

To keep the analysis as transparent as possible, we study the role of the time dimension of transport trips for optimal taxes and the implications of transport as derived from other activities sequentially. The structure of the paper is therefore the following. In Section 2 we present the simplest version of the time allocation model. Transport is viewed as an activity that requires time and commodity inputs and that generates a congestion externality. It is assumed that the government is restricted to taxing market inputs. Section 3 reconsiders the optimal commodity tax structure when the government does have the instruments to tax the transport activity directly, through a system of road pricing. In Section 4 we formulate a model that treats transport demand as derived from other activities, and we discuss the implications for dealing with congestion. Finally, Section 5 concludes.