Estimation of value of travel-time savings using mixed logit models

TLDR: In this paper, the authors discuss some of the issues that arise with the computation of the implied value of travel-time savings in the case of discrete choice models allowing for random taste heterogeneity.

Abstract: In this paper, we discuss some of the issues that arise with the computation of the implied value of travel-time savings in the case of discrete choice models allowing for random taste heterogeneity. We specifically look at the case of models producing a non-zero probability of positive travel-time coefficients, and discuss the consistency of such estimates with theories of rational economic behaviour. We then describe how the presence of unobserved travel-experience attributes or conjoint activities can bias the estimation of the travel-time coefficient, and can lead to false conclusions with regards to the existence of negative valuations of travel-time savings. We note that while it is important not to interpret such estimates as travel-time coefficients per se, it is nevertheless similarly important to allow such effects to manifest themselves; as such, the use of distributions with fixed bounds is inappropriate. On the other hand, the use of unbounded distributions can lead to further problems, as their shape (especially in the case of symmetrical distributions) can falsely imply the presence of positive estimates. We note that a preferable solution is to use bounded distributions where the bounds are estimated from the data during model calibration. This allows for the effects of data impurities or model misspecifications to manifest themselves, while reducing the risk of bias as a result of the shape of the distribution. To conclude, a brief application is conducted to support the theoretical claims made in the paper.

Figures

Table 1: Estimates for MNL and MMNL models (t-statistics in brackets)

Table 2: 95% percentile intervals for distribution of value of travel-time savings ($/hour)

Frequently asked questions

Q1. What distribution was used for the generation of the travel-time coefficients?

For the generation of the travel-time coefficients, a Normal distribution truncated at zero was used, thus allowing for a group of people who are indifferent to changes in travel-time (zero VTTS). 

Q2. What is the known example of a distribution with a fixed bound?

The best known example of a distribution with a fixed bound is the Lognormal distribution, which is the most common choice of distribution for coefficients with an explicit sign assumption in MMNL models. 

Q3. What was the process used to determine the chosen alternative?

A process based on random draws was then used to determine the chosen alternative with the help of the calculated choice-probabilities. 

Q4. How many individualspecific travel-time coefficients were produced?

rather than using simulation over this distribution in the calculation of the choice probabilities for the different alternatives and observations, a separate draw from this distribution was produced for each observation, leading to 4,306 individualspecific travel-time coefficients. 

Q5. What is the effect of allowing for positive values of TT?

The results of this analysis show the effect of allowing for positive values of βTT , with a lower 95% percentile limit on the VTTS of -$75.78 per hour when using the Normal distribution. 

Q6. What is the purpose of this paper?

The objective of this paper is to highlight one of several critical issues arising in the computation of VTTS in MMNL models; the possibility of obtaining results that indicate a non-zero share of respondents with negative valuations of travel-time savings. 

Q7. What are the main issues associated with the VTTS estimation using MMNL models?

They are related to the difficulty of maintaining consistency between the theoretical assumptions on which the models are based, the actual behaviour of decision-makers, and the data collection and model specification constraints. 

Q8. What is the way to estimate the travel time coefficients?

if all attempts to obtain strictly negative travel-time coefficients fail, modellers should acknowledge the potential impact of unobservables on their estimates, and an appropriate re-labelling of the coefficients is desirable to avoid any confusion. 

Q9. What is the recent attempt to disentangle the two components of the VTTS?

The authors are aware of only one recent attempt (Jara-Diaz & Guevara 2003) to disentangle these two components of the VTTS, where the empirical results reported suggested that for the sample of Chilean commuters studied, the VTTS was dominated by the strongly negative utility associated with the travel-time experience itself. 

Q10. What is the way to justify the use of a normal distribution for travel-time coefficient?

12It is sometimes tempting to justify the use of an unbounded distribution (e.g. Normal) for travel-time coefficients, and an implied positive probability of non-negative coefficient values, by the better model fit obtained with this distribution.