Confidence Intervals For Willingness-To-Pay And Beyond: A Comparative Analysis

The aim of this research is to investigate and develop methods for building confidence intervals (CIs) for parameter functions of discrete choice models, with a special focus on the CIs for willingness-to-pay measures. CIs are more than simply statistical measures. Rather, they are a convenient and easily understood means by which the variability of a parameter or sample statistic can be reported, especially because they can be presented graphically. CIs should be reported for all random statistics, and especially so in applied work where one cannot assume that the estimated parameter would exactly equal the true (unknown) parameter. Yet, when presenting willingness-to-pay values, the CIs are often neglected. This is partially because building CIs for willingness-topay values is not a trivial task, due to the possibility of discontinuity in the willingness-to-pay measure and its unknown probability distribution a priori. In addition, the methods used to build these intervals are debated greatly, with no consensus as to the best method to use. This research consolidates the contradictory results and presents reasons for the disparity currently present in the literature. It also extends the work of building CIs beyond willingness-to-pay measures to other parameter functions; in particular, this research demonstrates how CIs can be built for the probability that an airline passenger cancels his ticket. The methods of building CIs are studied using Monte Carlo simulations and case studies. Results indicate that when sample sizes or the price parameter is large (i.e. there are fewer chances for discontinuity to occur), all the preference space methods studied work equally well. However, under weak identification (when the price parameter is small), the Fieller method performs best. Hence, in general, the Fieller method should be the preferred method for building CIs for willingness-to-pay values. This research also proposes the use of the Bayesian post-processing method to build CIs. This method, though a viable option, is not often discussed. The Bayesian method also has an edge over the other methods studied for several reasons, including the ease of constructing individual CIs and the ability to incorporate factors such as historical data into the model