## Identifying the Value of Travel Time Distribution ? Evidence from the Swedish Value of Time Study 2008

### Authors

M Börjesson, M Fosgerau, S Algers, DTU Transport, DK

### Description

This paper reports the estimation of the Swedish value of time study. We find that extending the VVT bids, as compared to the Danish study, enable us to observe the whole VTT distribution, leaving much less uncertainty in the estimated mean VTT.

### Abstract

Two main problems are associated with estimation of the mean and distribution of the value of travel time (VTT). One is that the range of the bids should be extended over the support of the VTT distribution. Another one is that the mean may be very sensitive to parametric assumptions on the form of the distribution. Based on experience from the Danish value of time study, the Swedish 2008 value of time study was designed to better capture the expected VTT distribution by extending the bid range. Another innovation was to ask respondents about their maximum willingness to pay (be compensated for) for a certain time gain (loss). This gave a means to identify a suitable truncation point. The main finding in this study is that extending the bids enabled us to observe the whole VTT distribution, leaving much less uncertainty as to the form of the VTT distribution.

The 2008 Swedish VTT study has drawn on the findings from the Danish VTT study. In this paper, we report the findings of the Swedish value of time study with regards to model specification and estimation. Although the study comprises not only car but also the bus and train modes, we limit the analysis to the car mode in this paper.

A key issue is that in order to estimate the mean and other moments of the VTT distribution, we need to observe the entire distribution. In other words, the range of the bids should be extended over the support of the VTT distribution such that the estimated VTT is bounded by the data. If not, then only a part of the distribution is observed so that the moments of the VVT distribution cannot be estimated without further assumptions. In the Danish case, 13 percent of the observations did not reject the highest bid offered. This is one of reasons for why the estimated mean VTT was found so sensitive to the assumption about the distributional form (Fosgerau 2006).

Analysing the choices made in the present study, it turns out that there are only 15 out of 1317 drivers who rejected all bids. At the outset of the study, it was feared that although the bid range was extended, a significant share of respondents would still accept all bids as an experimental artefact, and thereby just push the unobserved part of the VTT distribution further away. Our result is assuring and shows that respondents behavior is consistent with the theory. It thus seems that the gap between the bid range and the VTT distribution endpoint is practically closed. The CV question responses from the 15 rejecting all bids range from 137 ? 1500000 SEK/h. Nine responses are below 1500 SEK. It is of course difficult to assess the accuracy and seriousness of these answers, and we only use them to perform sensitivity tests with respect to truncation of the VTT distribution.

Performing a non-parametric regression of the cumulative distribution function of VTT, we find that most respondents have a VTT less than 200 SEK/h. At the end of the bid range, we miss only a small percentage, although this gap does not seem to be significant.

Local logit regression is used to visualise the properties of the data. Applying local-logit regression shows that a model which estimates the ratio of the marginal utilites of time and cost directly describes the data better than the more traditional linear-in-utility model.

Performing a parametric estimation of VTT, while including covariates, we test a log-normal distribution of the VTT against a more flexible distribution. The flexible model generalises the base model by allowing the distribution of VTT to be flexible using the approach of Fosgerau and Bierlaire (2007) such that distribution of VTT is allowed to vary around the parametric distribution.

As in the case with the non-parametric estimation, we need to observe the entire VTT distribution to be able to compute the mean (and other moments) of VTT distribution. This is more easily achieved applying a model including covariates, since the covariates now also contribute to creating variation. Estimating this parametric model, we are able to observe the whole VTT distribution. We also find that the lognormal formulation of the VTT distribution is rejected against a semiparametric generalization. Still, the resulting mean VTT does not differ very much between the two models.

#### Publisher

Association for European Transport