Bayesian Estimation of the Value of Travel Time Savings: Application to Freight Transport in France

Bayesian Estimation of the Value of Travel Time Savings: Application to Freight Transport in France


A Nunez, LET, University of Lyon, FR


We apply Bayesian Monte Carlo Markov Chain procedures to estimate the value of time in freight transport in France.


In this paper we apply Bayesian Monte Carlo Markov Chain procedures to estimate the value of time in freight transport in France. We conjugate the information of a revealed preference survey including 1027 vehicles with a previous study of the value of time using classic estimation, as a source of prior information.

The value of travel time savings (VTTS) is probably the most important concept in transport economics. It allows to estimate the modal share and the optimal pricing of a new link or service, and in evaluation, time savings, valuated through the value of time, uses to account for the main part of a transport project benefit. Despite its importance, few convergences were reached about the size, distribution, and determinants of the value of time. Although there is a large literature available today on the passengers? value of time, allowing for a good interpretation and quantification of it, studies on the value of time of freight transport are very scarce. The reasons for the little research in freight transport compared to passengers are due to many reasons, specially the number of agents involved in the supply chain, and so in the modal and itinerary choice, and the interrelations between then.

One of the main issues regarding the value of time is its distribution over the population. Logit is by far the widest used model for estimation of discrete choice models and the derivation of the value of time. Its popularity is due to the fact that the formula of choice probabilities takes a closed form and is readily interpretable with good results related in literature. Classic models like logit allow for the determination of a VTTS point estimate but not its distribution. This is a very restrictive assumption both in terms of modelling and interpretation of results.

Advances in software and hardware performance have allowed to rapid simulation. Simulation methods have been largely used in finance and economics. In this way a partial simulation partial closed form discrete choice model called mixed logit has been used in many recent applications allowing for distributed parameters. Mixed logit is estimated by maximum simulated likelihood, which can sometimes lead to convergence problems, especially with lognormals distributions, currently used in value of time estimations.

Furthermore, the introduction of prior knowledge is intrinsic to even the classic analysis. First, the analyst usually has some priors about the result (i.e. one should expect that the value of travel time to be positive and to lay within a reasonable set) and second, the set of hypothesis and parameters need to the estimation of mixed logit models like the form of the distributions and the starting values indirectly represent a prior hypothesis.

Bayesian estimations have some strong advantages compared to the classical techniques; they allow for distributed coefficients but the estimation does not require any maximization, rather, draws from the posterior are taken until convergence is achieved, avoiding convergence problems and sample sizes necessary to achieve the convergence are substantially smaller. Moreover, they can properly integrate a priori knowledge on the parameters.

In this paper we discuss a number of issues related to the estimation and the interpretation of results in practical estimations of the value of time in transport; we identify sources of systematic and random taste variations; we then propose a comparison of the different methods without using relevant prior information; we measure the benefit of integrating a prior distribution of VTTS and finally we provide a robust estimation of the value of travel time for the freight transport in France. Results show that Bayesian estimations based on a prior knowledge leads to more sound and robust results; furthermore we find that values used currently in France should be reviewed upwards.


Association for European Transport