Income, Time Effects and Direct Preferences in a Multimodal Choice Context: Application of Mixed RP/SP Models with Non-Linear Utilities

Transport problems typically involve at least two types of constraints, on income and on time. Therefore, the indirect utility function depends either on the income available after having subtracted the cost of the discrete alternative and on the free time left after having worked and travelled by each competing option. In the typical linear-in-the-attributes and in-the-parameters specification, that represents the first grade approximation of the indirect utility function, the effect of income and time constraints cancel out and only the cost and time of the alternatives matter in the comparison between them. From a microeconomic point of view this is equivalent to assume that income and time effects could be disregarded; which is not always the case. To account for these effects the utility function should include second order attributes; however, in non-linear utility functions it may not be easy to distinguish among several effects that could be relevant: direct preferences for good and leisure, and simple interactions between attributes other than income and time effects. This paper analyses these effects from a theoretical point of view focusing on the possible confounding problem in detecting income and time effects. We use a dataset collected for a modal choice context and containing both revealed and stated preference data, and estimate several NL models examining the effect of the different second-order terms on detecting income and time effects. We compared specifications including square cost and time attributes, interactions between time and cost, cost divided by the income available to be spent on free time, and time multiplied by free time. Our results confirm the strong effect of direct preferences for goods and leisure time on choice, and the potential confounding effect between quadratic attributes and other non-linear omitted terms. Finally, we also found that care should be taken in highlighting income and time effects using mixed data sources, since confounding effects can occur when non-linearities are accounted for in both data sets.