Confidence intervals to bound the value of time

Abstract

Abstract The derivation of a subjective value of time (SVT) requires finding the marginal rate of substitution between travel time and cost in a travel choice model. In the typical case of models with linear-in-parameters utility functions, the SVT is equal to the ratio between the parameters of travel time and cost. However, since model estimation yields an estimator of the true values of their parameters (with a certain probability distribution), the computed SVT is also an estimator with another probability distribution; then, it is important to devise a method to incorporate the randomness of the estimated SVT in project evaluation. In this paper, we consider this problem rigorously and propose methods to replace the typical SVT point estimates by the construction of confidence intervals for a certain probability level. This allows, in addition, to estimate the SVT limits (lower and upper) which may be used in sensitivity analyses of the calculation of project revenues in transport infrastructure investment. The paper proposes two forms for building these intervals: the t -test and the LR-test, and discusses the construction of intervals for Multinomial Logit (MNL), Hierarchical Logit (HL) and Box–Cox Logit (BCL) models. We use two samples where the values of the level-of-service attributes have been measured with an unusually high degree of precision. Other methods proposed in the literature are also studied (simulation of multivariate normal variates (MVNS), SVT normal approximation (NA), and re-sampling techniques) using the above data, and their advantages and disadvantages are analysed. In addition, the effects of different modelling elements on the size and quality of the constructed intervals are scrutinised, such as model specification, sample size and individual income. Finally, the proposed methods are compared and recommendations about the use of each one in practice are indicated.