Sequential choice designs to estimate the heterogeneity distribution of willingness-to-pay

Two prominent approaches exist nowadays for estimating the distribution of willingness-to-pay (WTP) based on choice experiments. One is to work in the usual preference space in which the random utility model is expressed in terms of partworths. These partworths or utility coefficients are estimated together with their distribution. The WTP and the corresponding heterogeneity distribution of WTP is derived from these results. The other approach reformulates the utility in terms of WTP (called WTP-space) and estimates the WTP and the heterogeneity distribution of WTP directly. Though often used, working in preference space has severe drawbacks as it often leads to WTP-distributions with long flat tails, infinite moments and therefore many extreme values. By moving to WTP-space, authors have tried to improve the estimation of WTP and its distribution from a modeling perspective. In this paper we will further improve the estimation of individual level WTP and corresponding heterogeneity distribution by designing the choice sets more efficiently. We will generate individual sequential choice designs in WTP space. The use of this sequential approach is motivated by findings of Yu et al. (2011) who show that this approach allows for superior estimation of the utility coefficients and their distribution. The key feature of this approach is that it uses Bayesian methods to generate individually optimized choice sets sequentially based on prior information of each individual which is further updated after each choice made. Based on a simulation study in which we compare the efficiency of this sequential design procedure with several non-sequential choice designs, we can conclude that the sequential approach improves the estimation results substantially.