Simulation Techniques to Obtain Confidence Intervals for Willingness to Pay Measures

We obtain confidence intervals for willingness-to-pay (WTP) measures derived from a mode choice model estimated to analyse travel demand for suburban trips in the two main interurban corridors in Gran Canaria island, using a mixed RP/SP data base. We considered a specification of the systematic utility that incorporates income effect and interactions among socioeconomic variables and level-of-service attributes, as well as between travel cost and frequency. As our model provides rather complex expressions of the marginal utilities, we simulated the distribution of the WTP (in general, unknown) from a multivariate Normal distribution of the parameter vector. For every random draw of the parameter vector, the corresponding simulation of the WTP was obtained applying the sample enumeration method to the individuals in the RP database. The extremes of the confidence interval were determined by the percentiles on this distribution. After trying different simulation strategies we observed that the size of the intervals was strongly affected by the outliers of the simulation as well as by the magnitude of the simulated parameters. In all cases analysed, the simulated distribution of the corresponding WTP measure presented an asymmetric shape that was very similar for the two model specifications considered. This is consistent with previous findings using a radically different approach. We also observed that the upper extreme of the confidence interval for the value of time in private transport presented a very unstable behaviour as the number of random draws varied.