Testing the slope model of scheduling preferences on stated preference data

- Our work is one of few applications of the slope model to investigate the preferences of car drivers towards travel time variability.
- We compare valuations of travel time and travel time variability in a scheduling model (the slope model) and its reduced form. We find largely comparable value-of-time estimates between the two models, which are consistent with values from other studies. However, the implied valuations of travel time variability are very different between the two models.
- We expand on previous studies (e.g. Bojesson et al. , 2012) by i) using a similar design both for the scheduling and reduced-form choice experiments to allow for a direct comparison of the two models and ii) examining the implications of different model assumptions.
- The key finding of the paper is that, despite a better designed experiment, we are not able to empirically support the theoretical equivalence between the two models. Moreover, this conclusion is robust to the various sensitivity checks we perform by relaxing central model assumptions.
- We provide a detailed account of factors potentially generating the observed discrepancy.
- We recommend performing analysis using revealed preference data to avoid possible hypothetical bias from stated choice experiments.

The valuation of travel time variability is derived either from a structural model, given information on departure time, or directly from a reduced-form model where departure time is assumed to be optimally chosen. The two models are theoretically equivalent under certain assumptions, hence are expected to yield similar results. We use stated preference data to compare the valuation of travel time variability under a structural model where trip-timing preferences are defined in terms of time-dependent utility rates, the “slope model”, against its reduced-form model. Two choice experiments are used that are identical except one has a fixed departure time while the other allows respondents to choose departure time freely. The empirical results in this paper do not support the theoretical equivalence of the two models as the implied value of travel time variability under the reduced-form model is an order of magnitude larger. This finding, which is robust to various specification tests, is in line with a recent Swedish study by Börjesson, Eliasson and Franklin [Transportation Research Part B: Methodological, 46(7), 855-873 (2012)]. Since our data allows a direct comparison of the two approaches, we are able to rule out some potential explanations lined up by past research for the observed discrepancy between the two models.