International Choice Modelling Conference, International Choice Modelling Conference 2017

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Subjective Beliefs about the Willingness to Pay for Travel Time Savings
Vinayak V Dixit, Neeraj Saxena, Rico Krueger, Taha H. Rashidi

Last modified: 28 March 2017


1. Motivation

The willingness-to-pay for (WTP) for travel time savings constitutes an important measure to value transportation projects and assets. A widely used method to elicit preferences for travel time savings is through stated choice (SC) experiments, which hinge on respondents making choices over competing alternatives (e.g. Louviere et al., 2000). The WTP is modelled assuming structural distributions over errors in the choice tasks, and often a logit or mixed logit models are used to represent this. However, there has been very limited work in actually attempting to elicit this distribution and evaluate the error distributions. To do this we use novel methods from experimental economics (Dixit et al. 2015) to elicit these values and characterize the error distributions.

2. Objective

Overall, our research is concerned with the question of how to elicit error distributions in choice to provide more precise estimates on WTP. More specifically, we conjecture that the knowledge of respondents’ subjective beliefs over their own WTP for an attribute may provide insights into these error distributions.

The notion of subjective beliefs refers to an individuals’ subjective evaluation of a latent or uncertain quantity or attribute. Subjective beliefs are commonly considered in experimental economics and psychology. It is argued that measurements of subjective beliefs are of informational value, when the quantity of attribute of interest is difficult to measure directly or when the discrepancy of subjective beliefs and objective measurements may provide additional insights into individuals’ perceptions and decision-making processes (Andersen et al., 2011; Dixit et al. 2014; Dixit 2013).

In this vein, we hypothesise that a discrepancy may exist between the WTP for travel time savings estimated using the choice task and the individuals’ subjective beliefs about the WTP for travel time, and this discrepancy would help infer error distributions. Furthermore, we posit that the parameters characterising individual belief distributions are functions of socio-demographics and individual risk attitudes.

3. Method

To test our hypothesis, we pursue the following methodological approach:

  • We devise and implement an incentive-compatible mechanism to elicit subjective beliefs over WTP at the individual level.
  • We contrast subjective belief distributions with parameter estimates obtained from standard SC methods.

3.1 Experimental design

An incentivised experiment implements the incentive-compatible mechanism. The experiment comprises three stages:

1. Stated choice experiment: The first stage of the experiment features a standard stated choice experiment, which requires participants to choose between two unlabelled alternatives, which are characterised by two attributes, namely delay time and toll cost. For each subject an auxiliary measure of their WTP is obtained, by determining the narrowest WTP interval that is bounded by the respondents’ choices. This auxiliary WTP measure is required as an input for the third stage of the experiment.

2. Lottery choice tasks: Holt’s and Laury’s (2002) lottery choice task is used to approximate respondents’ risk attitudes. The tasks require subjects to make choices over a series of scenarios, whereby each scenario consists of two lotteries. One of the scenarios is randomly selected for payoff and the selected lottery is played out.

3. Subjective belief elicitation: In the final stage of the experiment, the incentive-compatible mechanism to elicit respondents’ subjective beliefs over their own WTP was implemented. The design of this task is inspired by Andersen et al. (2011), who used a similar question type to elicit individuals’ subjective beliefs over the probability distribution of an uncertain outcome of an event. Figure 1 visualises the task, as it is implemented in our experiment. Respondents are presented an array of slider bars, whereby each bar corresponds to a WTP interval with a width of one AU$ per minute. The slider bar on the very left of the array represents a WTP of zero to one AU$ per minute; the slider bar on the very right represents a WTP of nine to ten AU$ per minute. Respondents are endowed a budget of 100 experimental currency units (ECU), whereby ten ECU correspond to one AU$. Subsequently, respondents are asked to allocate ECUs to the WTP intervals, which according to their subjective belief correspond to their WTP for a travel time reduction of either ten, twenty, thirty or forty minutes. Respondents’ pay-off for this task is determined by the number of tokens allocated to the interval corresponding to their auxiliary WTP value, which was elicited in the first task of the experiment.

Figure 1: An illustration of subjective belief elicitation task

3.2 Data analysis

We make inferences on the experimental data, employing a threefold approach:

  1. We estimate the parameters characterising WTP distributions on the sample level based on the stated choice data of stage one of the experiment (Train, 2003).
  2. We develop a bi-level hierarchical Bayes model to analyse the subjective belief data of the final step of the experiment. At the lower level, we estimate the parameters characterising subjective belief distributions at the individual level and consider socio-demographic information and measurement of individual risk attitudes as covariates to explain these parameters. At the upper level, we estimate the parameters of the hyper-distribution, from which the individual-level parameters are drawn.
  3. Ultimately, we contrast the parameters estimates obtained in the first two steps.

4. Statement of contribution

The objective of this study is to investigate whether a significant discrepancy exists between the WTP estimated through the choice task and the subjective beliefs about WTP for travel time savings. We further use these differences to elicit error distributions in choice tasks. Moreover, this study tests whether socio-demographics and measurements of individual risk attitudes can explain inter-personal differences in subjective belief distributions. Our preliminary results support our hypothesise, as we find that individuals’ subjective belief distributions differ significantly from WTP estimates obtained from standard SC methods. We argue that supplementing existing SC approaches with information about respondents’ subjective beliefs with regard to attributes of interest could help provide more precise values on WTP.


Andersen, S., Fountain, J., Harrison, G.W., Hole, A.R., Rutström, E.E., 2011. Inferring beliefs as subjectively imprecise probabilities. Theory Decis. 73, 161–184. doi:10.1007/s11238-011-9276-1

Dixit, V. V., R. C. Harb, J. Martínez-Correa and E. E. Rutström (2015) “Measuring risk aversion to guide transportation policy: Contexts, incentives, and respondents” Transportation Research Part A: Policy and Practice, Volume 80, October 2015, Pages 15-34

Dixit, V. V., G. W. Harrison and E. E. Rutström (2014) “Estimating the subjective risks of driving simulator accidents.” Accident Analysis and Prevention, vol. 62, pp. 63 – 78.

Holt, C.A., Laury, S.K., 2002. Risk Aversion and Incentive Effects. Am. Econ. Rev. 92, 1644–1655.

Louviere, J.J., Hensher, D.A., Swait, J.D., 2000. Stated Choice Methods: Analysis and Applications, 1\textsuperscriptst. ed. Cambridge University Press.

Train, K.E., 2003. Discrete Choice Methods with Simulation. Cambridge University Press.

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