Bayesian Analysis of Interval Data Contingent Valuation Models and Pricing Policies

The general aim of a contingent valuation survey is to elicit the willingness to pay (WTP) of respondents for some (public) commodity without a clear market price. This could be a program to protect some environmental resource, or (as in our application) the access to a recreational area of particular interest. Such data have peculiarities like the presence of zero WTP and the fact that observations can be in the form of intervals for WTP, rather than point observations. We propose a Bayesian statistical analysis of WTP as a function of individual characteristics of the respondents which formally incorporates this structure of the data. The zero observations are handled through a probit model, and inference on the positive observations will be conditional on the observed intervals. The model for the positive observations will be of a log-linear form with possibly skewed and fat-tailed error distributions. We consider model uncertainty and pay particular attention to the predictive distribution of WTP, from which we derive expected revenue if a certain entry price were asked. The latter is an important tool for deriving pricing policies.