The Relationship of Cost Sensitivity and Trip Length

The Relationship of Cost Sensitivity and Trip Length


A Daly, RAND Europe, UK


Presentation and discussion of appropriate functional forms for the representation of marginal cost and time impacts over varying distances.


A recurring feature of recent travel demand modelling studies is the focus on variation of the sensitivity of travellers to changes in travel cost or travel time. Specifically, it has consistently been found that sensitivity appears to decline as trip length increases. A wide range of theories have been advanced to explain the effect and a similarly wide range of functions have been tried in practice to incorporate this variation into the models used in planning studies.

The questions that naturally arises in these circumstances are whether such variation is justified empirically and what are the implications of the choice of particular functional forms. A paper presented at the 2006 ETC (Daly and Hyman) showed that pure economic theory was quite weak in discriminating between potential forms. However, there are other considerations, based on empirical or forecasting considerations, that can be used to indicate which functional forms can be used to represent time or cost sensitivity.

The empirical considerations are based primarily on cross-sectional model estimation results, since it is difficult to imagine that longitudinal data would be adequate to distinguish differential impacts by trip length. However, in model estimation, the role of trip length variables, such as the road distance, is open to different interpretations. It is possible that such variables represent a ?pure? separation effect, for example that they are reflecting traveller?s knowledge about the existence of opportunities. However, it is also possible that a distance variable that appears to be significant in model estimation is actually reflecting a travel time or cost for which distance is a ?proxy?. The paper discusses the circumstances in which pure or proxy effects could be attached to the distance variable.

Forecasting considerations are also relevant, as the assumption of particular functional forms can be important in determining how models behave when forecasting for scenarios substantially different from the present. Even though the economic theory is not very strong, it does rule out some models that have been used in practice, e.g. where utility increases with increasing cost(!). Sharper tests may be formulated, such as requiring that the total distance driven would decrease with an increase in fuel price, which are not strictly economic in nature but which may be considered as formulations of common sense. These tests also allow us to identify unsatisfactory features of other models that have been used in practice.

Summarising, the paper puts forward a restricted range of model forms which would satisfy the tests that are discussed and shows that these models can indeed represent the range of varying cost sensitivities that have been found in practice.


Association for European Transport