Income effects, cost damping and the value of time: theoretical properties embedded within practical travel choice models

Mackie et al. (Values of travel time savings in the UK. Report to Department for Transport. Institute for Transport Studies, University of Leeds & John Bates Services, Leeds and Abingdon, 2003) proposed an identity relating the value of time (VoT) for commute and leisure travel to income and travel cost, reporting the prevalence of ‘cost damping’ (i.e. the phenomenon where VoT increases as travel cost increases). This identity (or a variant thereof) has been adopted within official methods for estimating VoT in the UK, Switzerland and The Netherlands. The present paper shows that Mackie et al.’s identity: (i) implies linear preferences, not strictly convex preferences as reported by Mackie et al.; (ii) complies with homogeneity and symmetry by construction; (iii) complies with adding-up if and only if VoT is unit elastic with respect to income; (iv) complies with negativity if VoT is unit elastic or greater with respect to income; (v) violates both adding-up and negativity in the case of the 2003 UK national VoT study. We propose alternative identities which comply with adding-up and homogeneity by construction, and offer comparable fit to Mackie et al.’s identity on the UK VoT dataset. We also find that the imposition of adding-up and negativity on Mackie et al.’s identity, through appropriate constraint on model estimation, leads to an increase of around 20% in valuations from the 2003 UK dataset.