Improving the Treatment of Cost in Large Scale Models

Improving the Treatment of Cost in Large Scale Models


J Fox, A Daly, B Patruni, RAND Europe, UK


This paper discusses a number of improvements to large-scale models to improve their policy forecasts. In particular, the issue of the appropriate cost formulation is explored, particularly the effect on the model elasticity.


The elasticity of transport models, that is to say the responsiveness of models to policies expressed in terms of changes in travel costs and times is often used as a test of the ?realism?, i.e. validity, of the models. However, statistical estimation of the relevant parameter of the models will be determined by fitting the length of journeys and, while this will tend to yield a reasonable elasticity, this will not always happen. One interpretation of this problem is that, in most models, the functional form is assumed a priori, which means that the model is not sufficiently flexible to meet both objectives. In particular, elasticity with respect to cost is often an issue.

The functional forms that have most often been used in these models are linear and logarithmic. If maximum likelihood methods are used for estimation, models where cost is represented logarithmically tend to perform better than models based on linear cost. However, log cost models tend to give elasticities that appear too low, while linear cost models give values that are often too high.

It has been argued for some time (particularly by Gaudry) that a more flexible functional form should be used for these functions and the Box-Cox (or Box-Tukey) transformation has been advocated. However, these transformations are unfamiliar to transportation engineers and present technical difficulty in modelling because of the power functions they imply. An alternative is to use both logarithmic and linear functions. Providing both these functions have the correct sign (!), their combination covers the same range of functional shapes as the power transformations, while the resulting functions are both comprehensible and convenient to use.

The paper presents the results of analyses using mixed linear and logarithmic functions in two major conurbations in England: Greater Manchester and West Midlands (the latter centred on Birmingham). It shows how the use of these functions improves the fit of the models to the data and produces elasticities that are considerably more plausible. In addition, the values of time that are implied by the models are also more reasonable, an unexpected bonus of the approach. The use of data from two major conurbations allows the models to be compared and contrasted, giving a broader basis for the claims that are made.

The paper also discusses some model specification issues where lessons have been learnt from Manchester and the West Midlands. The first is the treatment of intrazonal movements, where using a ?nearest neighbour? assumption can have an impact the model elasticity and values-of-time, as well as improving the model fit. The issue of how best to treat car costs is discussed, with discussion of findings of how best to allocate total car costs between drivers and passengers, and the impact of different assumptions regarding the perception of non-fuel costs. Finally, a technical issue about the treatment of small or zero costs with a logarithmic form is discussed.


Association for European Transport