## On the Approximation Bias to Benefit Measures in Discrete Choice Models

### Authors

C Bowen, J de D Ortuzar, L I Rizzi, Pontificia Universidad Catolica de Chile, CL

### Description

We study the bias associated to using approximations for calculating transport benefits. Significant bias arise when using the usual methods applied in practice, but no significant bias found if income effects are not considered.

### Abstract

The problem of travel demand analysis and valuation of attribute changes can be complex in practice. Among other things, demand is influenced by the availability of alternatives to make the trip. When consumers are considered utility maximisers and improvements can be expressed as a reduction in an element of their travel costs, the willingness-to-pay (WTP) of a consumer is measured by the Hicksian consumer surplus attached to the equivalent cost change and the social benefit is given by the sum of the WTP of individual consumers. In practice, calculation problems arise due to individuals? heterogeneity in tastes and/or to the presence of income effect; in fact, this prevented finding an exact benefit measure, even for fairly simple choice models as the multinomial and nested logit functions, for many years. The plot thickens considerably if less restrictive forms such as mixed logit must be used.

In this paper we study the bias associated to using different approximations to the calculation of benefits in transport project evaluation. For this, we generated a simulated data bank which reproduces the real behavior of a revealed preference sample of individuals choosing mode in journey-to-work trips. Then, exact measures of welfare were calculated for three policies with different degrees of impact on individual decisions, and results were compared with estimations of the benefits corresponding to a series of simpler, but less precise methods, usually applied in practice. In particular, we found significant bias when the classical logit models, which are restrictive in terms of heterogeneity, were considered. Significant biases also arise if the correct formula for the case of marginal changes is applied in the presence of non-marginal policies. In the first case, the proportional error does not depend on the size of the policies, but in the second one it grows with their impact.

A second empirical application considered the simulation of another data bank, allowing for nonlinear utilities in income. Interestingly, in this case we found no significant bias if income effect was not considered. Neither did we find a systematic relation between the bias and the size of the policy under consideration. A caveat might be that in the real data set used to construct the simulated population, the importance of the income related variable in explaining the choice of mode was fairly limited (i.e. around 10% of total utility).

#### Publisher

Association for European Transport