Vincent A.C. van den Berg

Congestion pricing in a road and rail network with heterogeneous values of time and schedule delay

We analyse congestion pricing in a road and rail network, where the two modes are imperfect substitutes. On the road there is bottleneck congestion; in each train there is crowding congestion. We model two dimensions of preference heterogeneity; these two dimensions have opposite effects on the welfare impact of congestion pricing and lead to different distributional effects. The distributional effects also differ between road and rail. On the road, pricing is generally more beneficial with a higher value of time or schedule delay. In the train, pricing has no distributional effects or is less beneficial with a higher value.

On the Existence and Uniqueness of Equilibrium in the Bottleneck Model with Atomic Users

This paper investigates the existence and uniqueness of equilibrium in the Vickrey bottleneck model when each user controls a positive fraction of total traffic. Users simultaneously choose departure schedules for their vehicle fleets. Each user internalizes the congestion cost that each of its vehicles imposes on other vehicles in its fleet. We establish three results. First, a pure strategy Nash equilibrium (PSNE) may not exist. Second, if a PSNE does exist, identical users may incur appreciably di fferent equilibrium costs. Finally, a multiplicity of PSNE can exist in which no queuing occurs but departures begin earlier or later than in the system optimum. The order in which users depart can be suboptimal as well. Nevertheless, by internalizing self-imposed congestion costs individual users can realize much, and possibly all, of the potential cost savings from either centralized traffic control or time-varying congestion tolls.

Why Congestion Tolling Could be Good for the Consumer: The Effects of Heterogeneity in the Values of Schedule Delay and Time on the Effects of Tolling

In studying congestion tolling, it is important to account for heterogeneity in preferences of drivers, as ignoring it can bias the welfare gains. We analyse the effects of tolling, in the bottleneck model, with continuous heterogeneity in the value of time and schedule delay. The welfare gain of a time-variant toll increases with heterogeneity in the value of schedule delay. With heterogeneity, tolling makes the arrival ordering more efficient, and this lowers scheduling costs. If there is not much more heterogeneity in the value of time than in the value of schedule delay, then first-best tolling decreases the generalised price for most users. In our model, first-best tolling is not most detrimental for the lowest values of time and schedule delay: it raises prices more for users with an average value of schedule delay and a slightly larger value of time. Further, the lowest values of time are among those who gain most from a public pay-lane.

Biases in Willingness-to-Pay Measures from Multinomial Logit Estimates Due to Unobserved Heterogeneity

It is a common finding in empirical discrete choice studies that the estimated mean relative values of the coefficients (i.e. WTPs) from multinomial logit (MNL) estimations differ from those calculated using mixed logit estimations, where the mixed logit has the better statistical fit. However, it is less clear under exactly what circumstances such differences arise, whether they are important, and if they can be seen as biases in the WTP estimates from MNL. We use datasets created by Monte Carlo simulation to test, in a controlled environment, the effects of the different possible sources of bias on the accuracy of WTPs estimated by MNL. Consistent with earlier research we find that random unobserved heterogeneity in the marginal utilities does not in itself biases the MNL estimates. Furthermore, whether or not the unobserved heterogeneity is symmetrically shaped also does not affect the accuracy of the WTP estimates of MNL. However, we find that if two heterogeneous marginal utilities are correlated then the WTPs from MNL may be biased. If the correlation between the marginal utilities is negative, then the bias in the MNL estimate is negative, whereas if the correlation is positive the bias is positive.

Inequality in military expenditures and the Samuelson rule

In this paper, we show that standard measures used in the income inequality literature, the Lorenz curve and the associated Gini‐index, can successfully be applied to the distribution of defence spending across countries. Secondly, we use the Samuelson rule to explain the distribution of military expenditures across countries over time. According to the constant defence burden interpretation of the Samuelson rule, corresponding to the diagonal in the Lorenz diagram, the defence burdens should be equal across countries. It is shown that about three quarters of the variation in military expenditures can be explained by the Samuelson rule. We then go beyond the Samuelson rule to see which countries spend much more or less than predicted and investigate which other factors may influence the defence burden.

Step Tolling with Price Sensitive Demand: Why More Steps in the Toll Makes the Consumer Better Off

Most dynamic models of congestion pricing use fully time-variant tolls. However, in practice, tolls are uniform over the day or at most have a few steps. Such uniform and step tolls have received surprisingly little attention from the literature. Moreover, most models that do study them assume that demand is insensitive to price. This seems an empirically questionable assumption that, as this paper finds, strongly affects the implications of step tolling for the consumer. First-best tolling has no effect on the generalized price, and thus leaves the consumer equally well off as without tolling. Conversely, under price-sensitive demand, step tolling increases the price and lowers the number of users, making consumers worse off. The more steps the step toll has, the closer it approximates the first-best toll, thereby increasing the welfare gain and making consumers better off. This makes it important for real-world tolls to have as many steps as possible: this not only raises welfare, but also increases the political acceptability of the scheme by making consumers better off.Most dynamic models of congestion pricing use fully time-variant tolls. However, in practice, tolls are uniform over the day or at most have a few steps. Such uniform and step tolls have received surprisingly little attention from the literature. Moreover, most models that do study them assume that demand is insensitive to price. This seems an empirically questionable assumption that, as this paper finds, strongly affects the implications of step tolling for the consumer. First-best tolling has no effect on the generalised price, and thus leaves the consumer equally well off as without tolling. Conversely, under price-sensitive demand, step tolling increases the price and lowers the number of users, making consumers worse off. The more steps the step toll has, the closer it approximates the first-best toll, thereby increasing the welfare gain and making consumers better off. This makes it important for real-world tolls to have as many steps as possible: this not only raises welfare, but also increases the political acceptability of the scheme by making consumers better off.

Auctions for private congestible infrastructures

This paper investigates regulation by auctions of private supply of congestible infrastructures in two networks settings: 1) two serial facilities, where the consumer has to use both in order to consume; and 2) two parallel facilities that are imperfect substitutes. There are four market structures: a monopoly and 3 duopolies that differ in how firms interact. The effects of an auction depend on what the bidders compete. With a bid auction, the bidders compete on how much money they transfer to the government. This auction leads to the same outcome as the unregulated game (for a given market structure), since this gives the maximum profit to transfer. An auction on the capacity of a facility leads to an even lower welfare than no regulation, because firms set very high capacities and usage fees. Conversely, an auction on generalised price or number of users leads to the first-best outcome. Moreover, these two auctions are robust: they attain the first-best regardless of whether the facilities are auctioned off to a single firm or to two firms, and for all market and network structures. On the contrary, the performances (relative to the first-best) of the bid and capacity auctions strongly depend on these considerations.

Private Road Networks with Uncertain Demand

We study the efficiency of private supply of roads under demand uncertainty and evaluate various regulatory policies. Due to demand uncertainty, capacity is decided before demand is known but tolls can be adjusted after demand is known. Policy implications can differ from those under deterministic demand. For instance, for serial links, the toll in the second-best zero-profit case is no longer equal to the marginal external congestion cost. In the first-best scenario, the capacity under uncertain demand is higher than that under the deterministic demand of the same expected value, though self-financing still holds in expected terms. Regulation by perfect competitive auction cannot replicate the second-best zero-profit result and thus leads to a lower welfare, whereas without uncertainty various forms of competitive auctions can attain this second-best optimum. For more complex networks, when private firms add capacity in turn, contrary to the case without demand uncertainty, some form of auction performs better than others with demand uncertainty.

The total size of an airline and the quality of its flights

We examine the relationship between the total size of an airline and its service quality by analysing over 4.8 million domestic flights within the USA in 2016. The total size of an airline is measured by its total market share, total amount of assets or total number of full-time equivalent employees. Delays are a widely used proxy for service quality and the most common category of airline customer complaints. Numerous regressions have been estimated using arrival delay time and whether a flight arrives on time as dependent variables. The regressors of main interest were the total airline size and the degree of competition on the route and airport. We control for weather, congestion, date, and characteristics of the airport, flight and airplane. The results suggest that the larger the total size of an airline, the smaller its average delay time and delay occurrence. Hence, larger airlines seem to offer a higher quality in terms of delays. We also find that an origin airport with less competition may lead to more delays. Surprisingly, a less competitive route may reduce delays.

Complementary Alliances with Endogenous Fleets and Load Factors

This paper analyzes the effect of carrier collaboration on fleet capacity, fleet structures in terms of the number and the size of vehicles, and load factors. The model features complementary networks, scheduling, price elastic demands, and demand uncertainty. For the case of a given number of vehicles, the analysis shows that carrier collaboration increases vehicle sizes (thus, fleet capacity) if marginal seat costs are low while fleet capacity remains unchanged if marginal seat costs are high. If both vehicle sizes and vehicle numbers can be varied, then collaboration will always increase vehicle numbers and fleet capacity, while the effects on vehicle sizes and, thus, also load factors, are ambiguous and therewith hard to predict. Numerical simulations indicate that collaboration increases expected load factors also when the number of vehicles is endogenous.