Cost damping and functional form in transport models

Transport models allowing for cost damping are characterised by marginally decreasing cost sensitivities in demand. As a result, cost damping is a model extension of the simple linear-in-cost model requiring an appropriate non-linear link function between utility and cost. The link function may take different forms and be represented as a non-linear-in-parameter form such as the well-known Box–Cox function. However, it could also be specified as non-linear-in-cost but linear-in-parameter forms, which are easier to estimate and improve model fit without increasing the number of parameters. The specific contributions of the paper are as follows. Firstly, we discuss the phenomenon of cost damping in details and specifically why it occurs. Secondly, we provide a test of damping and an easy assessment of the (linear) damping rate for any variable by estimating two auxiliary linear models. This turns out to be an important guidance as the damping rate largely dictates which link functions are appropriate for the data. Thirdly, inspired by the Box–Cox function, we propose alternative linear-in-parameter link functions, some of which are based on interpolation of approximate Box–Cox end points, and others which are inspired by Taylor Expansions. The different functions are tested in simulation experiments and subsequently in a large-scale demand model based on more than 22,000 revealed preference observations. It is concluded that the use of properly specified linear-in-parameter functions gives good data fit and sometimes even outperforms the Box–Cox functions without increasing the number of parameters.