Abstract
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. Numerous papers use the term “value of travel time savings”, or VTTS. The addition of the word “savings” has not arisen suddenly but goes back to the 1970s, and has also been used in the titles of national studies. The addition of ‘savings’ is in our view incorrect, misleading and unhelpful. Unlike money, time cannot be stored or borrowed—there is no piggy bank for spare minutes. In addition, the modelling approaches used for many of the more advanced VTT studies in fact produce valuations that are ‘bracketed’ between gains and losses in time, and an average between these gains and losses, typically the geometric mean, is then used as the VTT. It is then clear that the value obtained from this averaging cannot be described as the value of time savings (or reductions), as it includes the higher value of losses (i.e. increases) as well. To exemplify the magnitude of our theoretical points, we show how for the 2015 UK VTT study, using the bracketed value for commuters and labelling it as a VTTS implies an overestimation by a factor of more than 2.
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Notes
We acknowledge that the widespread use by governments of monetary valuations of time is not uncontroversial but this is not the topic of the present work, which takes its use as given and seeks to improve terminology and interpretation. Similarly, we do not discuss how VTT is used.
The numbers would be higher if we also included studies using the term “value of time” as opposed to “value of travel time”.
In the simplest terms, we have that \(\left| {\beta_{time\,increase} } \right| \ge \left| {\beta_{time\,reduction} } \right|\) and \(\left| {\beta_{cost\,increase} } \right| \ge \left| {\beta_{cost\,reduction} } \right|\), so that with \(WTA = {{\left| {\beta_{time\,increase} } \right|} \mathord{\left/ {\vphantom {{\left| {\beta_{time\,increase} } \right|} {\left| {\beta_{cost\,reduction} } \right|}}} \right. \kern-0pt} {\left| {\beta_{cost\,reduction} } \right|}}\) and \(WTP = {{\left| {\beta_{time\,reduction} } \right|} \mathord{\left/ {\vphantom {{\left| {\beta_{time\,reduction} } \right|} {\left|\beta_{cost\,increase} \right|}}} \right. \kern-0pt} {\left|\beta_{cost\,increase}\right| }}\), we see that \(WTA \ge WTP\).
For the interested reader, these values are obtained as follows, based on Hess et al. (2017). We have that the value of a change in attribute \(x\) relative to a base value \(x_{0}\) is given by \(v\left( {\Delta x} \right) = S\left( {\Delta x} \right).\exp \left( {\eta S\left( {\Delta x} \right)} \right) \cdot \left| {\Delta x} \right|^{\alpha }\), where \(\Delta x = x - x_{0}\), \(\alpha = 1 - \beta - \gamma S\left( {\Delta x} \right)\), \(S\left( {\Delta x} \right)\) is the sign of \(\Delta x\), \(\eta\) gives the difference of gain value and loss value (with \(\eta > 0\) showing that losses are valued more strongly than gains), \(\beta\) allows the impact of gains and losses to be non-linear and \(\gamma\) allows the non-linearity of value to be different for gains and losses. With \(\theta\) giving the underlying VTT, we then have from Hess et al. (2017) that when taking the geometric mean of gains and losses, \(VTT = \theta^{\kappa } |\Delta t|^{\kappa - 1}\), where \(\kappa = {{\left( {1 - \beta_{t} } \right)} \mathord{\left/ {\vphantom {{\left( {1 - \beta_{t} } \right)} {\left( {1 - \beta_{c} } \right)}}} \right. \kern-0pt} {\left( {1 - \beta_{c} } \right)}}\). On the other hand, if we look separately at gains and losses, then we have that \(VTTG = \frac{{\left( {\exp \left( { - \eta_{T} - \eta_{C} } \right)\left| {\theta \Delta t^{ - } } \right|^{{\alpha_{t}^{ - } }} } \right)^{{\frac{1}{{\alpha_{C}^{ + } }}}} }}{{\left| {\Delta t^{ - } } \right|}}\) and \(VTTL = \frac{{\left( {\exp \left( {\eta_{T} + \eta_{C} } \right)\left| {\theta \Delta t^{ + } } \right|^{{\alpha_{t}^{ + } }} } \right)^{{\frac{1}{{\alpha_{C}^{ - } }}}} }}{{\left| {\Delta t^{ + } } \right|}}\), where the + and – superscripts on \(\Delta t\) and \(\alpha_{T}\) and \(\alpha_{C}\) reflect the different signs of changes.
It should be noted that for the three valuations in Table 1 that are for “all modes”, the presented bracketed value does not correspond to the geometric mean of the presented values of gains and losses. This is a result of the values being obtained as weighted averages across models for different modes. The bracketed value is in each case the weighted average of bracketed values from models for individual modes. The values for gains and losses we present are the weighted averages across models that would be used if using only the gains or losses value.
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Acknowledgements
The authors acknowledge the financial support by the European Research Council through the consolidator grant 615596-DECISIONS. We are also grateful for feedback from Thijs Dekker. While the results reported in the paper are based on a study commissioned by the UK Department for Transport, the opinions and any omissions in this paper remain the responsibility of the authors.
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A. D.: literature review and manuscript writing. S. H.: additional empirical work and manuscript writing.
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Daly, A., Hess, S. VTT or VTTS: a note on terminology for value of travel time work. Transportation 47, 1359–1364 (2020). https://doi.org/10.1007/s11116-018-9966-4
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DOI: https://doi.org/10.1007/s11116-018-9966-4