## The Amazing Sensitivity of the Value of Time Savings to Income Dependent Utility Functions

### Authors

S Jara-Diaz, M Munizaga, Universidad de Chile, CL

### Description

We show that estimates of the value of travel time savings vary dramatically when using a cost/income variable. The problem is explored through simulation and properties of the max log likelihood coefficient estimates.

### Abstract

This paper shows a very serious problem arising from the estimation of the subjective value of travel time savings (SVTTS) from discrete choice models. We show that this value can be dramatically different depending on the treatment of the cost over income variable, say an expenditure rate specification against a linear in cost specification of utility, even segmented by income. The theoretical exploration of this unpleasant property was motivated by empirical evidence using data from Santiago and Valparaiso, where discrete mode choice models using a cost over income variable yielded average SVTTS ten times larger than the linear in cost models for the same population data. This is important indeed as a cost/income variable has been justified in many forms within a consumer behaviour framework (expenditure or wage rate models).

In this paper we first formulate the problem in terms of two specifications of utility, one where the cost variable is included with a linear effect in the utility function, and another where the same cost variable is divided into an income variable, whose variation accross individuals seems to be causing the described effect on the estimation of the SVTTS. We use real data from a corridor in Santiago in order to simulate the variation in income around the observed average. We show that the average SVTTS increases ten times as the coefficient of variation of income increases from 0 to 0.3 only, keeping everything else constant; we also show that this happened basically due to the variation of the marginal utility of income estimate. In order to explore this relation, we generate the explicit equations for the first order conditions behind the maximisation of the log-likelihood that commands the estimation of cost and time coefficients. The system is examined qualitatively and an expression for the parameters as a function of data is formulated for the binomial case using the implicit function theorem. As the derivative of the parameters is not possible to interpret clearly, the behaviour of the coefficients and the SVTTS is simulated, showing that this seems to be a structural weakness of the model.

#### Publisher

Association for European Transport