## Another Test of the Theory of Reference-dependent Preferences: the Trade off Between Money and Time

### Authors

Mogens Fosgerau, Danish Transport Research Institute, DK; Bruno de Borger, University of Antwerp, BE

### Description

I test whether there is room for utility maximisation in SP data where effects attributable to prospect theory are strong. If not, then measurement of the WTP for time from such data is questionable.

### Abstract

We consider stated preference data in a simple design common to the Danish, Dutch and UK value of time studies. These designs involve only two variables: time and cost, and are thus particularly simple to analyse.

The issue in brief is the following: We would like to interpret the data within a model of utility maximisation in order to derive measures of willingness-to-pay (WTP) that can be used in cost-benefit analysis. However, it turns out that the data do not fit within this paradigm since there are strong effects that can rather be interpreted in terms of prospect theory (Kahneman & Tversky 1979). Thus measurement of WTP does not make immediate sense.

In this paper I will test the viability of the following proposition:

?The effects of prospect theory are confined to certain choices involving trade-offs with the reference situation and/or small travel time changes. Choices with large travel time changes and not involving the reference situation can be interpreted in terms of utility maximisation and WTP measurement makes sense for these choices.?

This interpretation would fit with an interpretation of prospect theory which loosely says that, although they try, people are simply not very good at maximising their utility and that they apply heuristics which may fail in certain situations. This view is supported by recent evidence in Plott & Zeiler (2005) and List (2004).

The stakes on this issue are rather high. If the above proposition can be accepted against the data, then we can proceed with measuring the WTP for time and apply the results in cost-benefit analyses. If not, then it is by no means certain that this kind of exercise makes sense.

Going into more detail, each choice situation involves a time difference and a cost difference. The ratio of these is the boundary value of time (VOT). Under utility maximisation, individual choices would reveal whether the individual VOT is smaller or larger than the boundary VOT. With a sequence of choice situations with changing boundary VOTs it would be possible to determine a narrow range for the individual VOT.

However, it turns out that the choices of most individuals are inconsistent with this model. In fact, most individuals are seemingly happy to accept a high price for time in some situations and reject a low price for time in other situations. Choice specific errors (maximisation errors) would have to play a very large role in order to reconcile the data with utility maximisation.

Now prospect theory holds that the WTP for time savings relative to the reference should be less than the WTA for time increases. This effect is strong in the data. Prospect theory also predicts the effect found in the data that small time changes are valued less per minute than large time changes.

Prospect theory says nothing about the situation where respondents can choose between either a time saving or a cost reduction (gain-gain). Prospect theory also says nothing about the converse situation involving a choice between a time increase or a cost increase (loss-loss). Empirically, the VOT for these two situations turns out to be in between the WTP and the WTA.

The proposition stated above holds that the prospect theory effects are confined to comparisons with the reference and/or small time changes and that utility maximisation holds otherwise. We can test this proposition by testing whether the individual VOT stabilises at the same value for gain-gain or loss-loss choices as the time change increases. The paper carries out this test using state-of-the-art econometrics. The paper further tests whether the prospect theory effects can be described by a few variables. If so, then all the data can be used to measure the WTP. Finally, the resulting VOT estimates can be held up against individual income as an external validity check against the objection that stated preference choices are hypothetical and may be disconnected from real behaviour.

Kahneman, D. & Tversky, A. 1979, "Prospect Theory: An Analysis of Decision under Risk", Econometrica, vol. 47, no. 2, pp. 263-292.

List, J. A. 2004, "Neoclassical Theory Versus Prospect Theory: Evidence from the Marketplace", Econometrica, vol. 72, no. 2, pp. 615-625.

Plott, C. R. & Zeiler, K. 2005, "The Willingness to Pay?Willingness to Accept Gap, the "Endowment Effect," Subject Misconceptions, and Experimental Procedures for Eliciting Valuations", The American Economic Review, vol. 95, no. 3, pp. 530-545.

#### Publisher

Association for European Transport