Assuring finite moments for willingness to pay in random coefficient models

Random coefficient models such as mixed logit are increasingly being used to allow for random heterogeneity in willingness to pay (WTP) measures. In the most commonly used specifications, the distribution of WTP for an attribute is derived from the distribution of the ratio of individual coefficients. Since the cost coefficient enters the denominator, its distribution plays a major role in the distribution of WTP. Depending on the choice of distribution for the cost coefficient, and its implied range, the distribution of WTP may or may not have finite moments. In this paper, we identify a criterion to determine whether, with a given distribution for the cost coefficient, the distribution of WTP has finite moments. Using this criterion, we show that some popular distributions used for the cost coefficient in random coefficient models, including normal, truncated normal, uniform and triangular, imply infinite moments for the distribution of WTP, even if truncated or bounded at zero. We also point out that relying on simulation approaches to obtain moments of WTP from the estimated distribution of the cost and attribute coefficients can mask the issue by giving finite moments when the true ones are infinite.     

Cost and time damping: evidence from aggregate rail direct demand models

There is a significant body of evidence from both disaggregate choice modelling literature and practical travel demand forecasting that the responsiveness to cost and possibly to time diminishes with journey length. This has, in Britain at least, been termed ‘Cost Damping’, and is recognised in guidance issued by the UK Department for Transport. However, the consistency of the effect across modes and data types has not been established. Cost damping, if it exists, affects both the forecasting of demand and our understanding of behaviour. This paper aims to investigate the evidence for cost and time damping in rail demand using aggregate rail ticket sales data. The rail ticket sales data in Britain has, for many years, formed the basis of analysis of a wide range of impacts of rail demand. It records the number of tickets sold between station pairs, and it is generally felt to provide a reasonably accurate reflection of travel demand. However, the consistency of these direct demand models with choice modelling and highway demand model structures has not been investigated. Rail direct demand models estimated by ticket sales data indicate only slight variation in the fare elasticity with distance, as is evidenced in the largest meta-analysis of price elasticities conducted to date (Wardman in J Transp Econ Policy 48(3):367–384, 2014). This study of UK elasticities shows strong variation between urban and inter-urban trips, presumably a segmentation at least in part by purpose, but less remaining variation by trip length. A lack of variation by length supports the hypothesis of cost damping, because constant cost sensitivity would imply that fare elasticity would increase strongly with distance, because of the increasing impact of higher fares at longer distances. In this paper we indicate that rail direct demand models have some consistency of behavioural paradigm with utility based choice models used in highway planning. We go on to use rail demand data to estimate time and fare elasticities in the context of various cost damping functions. Our empirical contribution is to estimate time elasticities on a basis directly comparable with cost elasticities and to show that the phenomenon of cost damping is strongly present in ticket sales data. This finding implies that cost damping should be included in models intended for multimodal analysis, which may otherwise give incorrect predictions.     

VTT or VTTS: a note on terminology for value of travel time work

Transportation - The value of travel time (VTT) can be said to be the most important number in transport economics, and its estimation has been the topic of extensive academic and applied work....     

A critical appraisal of the use of simple time-money trade-offs for appraisal value of travel time measures

Transportation - Stated choice surveys have established themselves as the preferred approach for value of travel time elicitation with the help of choice models. However, major differences exist in...     

The opening of the Amsterdam Ring Road

This paper presents the results of a major before-and-after study carried out to establish the short term effects of the removal of a severe bottleneck in the road network around Amsterdam. An important focus in the study was on measuring changes in the timing of travel, as well as changes in route choice, mode choice, destination choice and frequency of travel. The results of the study indicated that, in the short run, there was little or no change in mode choice, nor was there significant emergence of new induced trips. On the other hand, large shifts in time of travel as well as route choice were reported, emphasising the importance of alterations to the timing and routes of existing trips when congestion is relieved, and the need to consider the benefits these bring in evaluating the impact of any road investment.     

Using ordered attitudinal indicators in a latent variable choice model: a study of the impact of security on rail travel behaviour

There is growing interest in the use of models that recognise the role of individuals’ attitudes and perceptions in choice behaviour. Rather than relying on simple linear approaches or a potentially bias-inducing deterministic approach based on incorporating stated attitudinal indicators directly in the choice model, researchers have recently recognised the latent nature of attitudes. The uptake of such latent attitude models in applied work has however been slow, while a number of overly simplistic assumptions are also commonly made. In this article, we present an application of jointly estimated attitudinal and choice models to a real-world transport study, looking at the role of latent attitudes in a rail travel context. Our results show the impact that concern with privacy, liberty and security, and distrust of business, technology and authority have on the desire for rail travel in the face of increased security measures, as well as for universal security checks. Alongside demonstrating the applicability of the model in applied work, we also address a number of theoretical issues. We first show the equivalence of two different normalisations discussed in the literature. Unlike many other latent attitude studies, we explicitly recognise the repeated choice nature of the data. Finally, the main methodological contribution comes in replacing the typically used continuous model for attitudinal response by an ordered logit structure which more correctly accounts for the ordinal nature of the indicators.     

Estimating choice models containing attraction variables

The paper presents a family of disaggregate choice models, which are shown to be equivalent to many of the aggregate models commonly used in planning studies. A brief summary is given of the method that has been developed for estimating the parameters of these models. A generalisation is then introduced in which variables representing the attractiveness in terms of size or quantity of each alternative are allowed to enter the model. It is shown that the form in which these variables enter the model requires a more general estimation algorithm than is commonly used, and such an algorithm is presented. A series of practical tests of the new algorithm is described.     

Impact of family in-home quality time on person travel demand

This paper introduces the concept of Primary Family Priority Time (PFPT), which represents a high priority household decision to spend time together for in-home activities. PFPT is incorporated into a fully specified and operational activity based discrete choice model system for Copenhagen, called COMPAS, using the DaySim software platform. Structural tests and estimation results identify two important findings. First, PFPT has a place high in the model hierarchy, and second, strong interactions exist between PFPT and the other day level activity components of the model system. Forecasts are generated for a road pricing and congestion scenario by COMPAS and a comparison version of the model system that excludes PFPT. COMPAS with PFPT exhibits less mode changing and time-of-day shifting in response to pricing and congestion than the comparison version.     

Impacts of an emission based private car taxation policy - First year ex-post analysis

This paper assesses the impacts of a targeted policy designed to influence car purchasing trends towards lower CO₂ emitting vehicles. Vehicle registration tax and annual motor tax rates in Ireland changed in July 2008 from being based on engine size to emissions performance of cars. This paper provides a one year ex-post analysis of the first year of the tax change, tracking the change in purchasing trends arising from the measure related to specific CO₂ emissions, engine size and fuel, and the implications for car prices, CO₂ emissions abatement, and revenue gathered. While engine efficiency improvements had been offset by purchasing trends towards larger and generally less efficient cars in the past, with the average MJ/km remaining constant from 2000 to 2007, this analysis shows that in the first year of the new taxation system the average specific emissions of new cars fell by 13% to 145 g/km. This was brought about, not by a reduction in engine size, but rather through a significant shift to diesel cars. Despite an unexpected reduction in car sales due to a recession in 2008, the policy measure has had a larger than anticipated impact on CO₂ emissions, calculated to be 5.9 ktCO₂ in the first year of the measure. The strong price signal did however result in a 33% reduction in tax revenue from VRT, in financial terms amounting to a drop of €166 million compared to a baseline situation.