Two-Step Approach to Self-Selected Interval Data in Elicitation Surveys

We propose a novel two-step approach to elicitation in surveys and provide supporting statistical theory for the models suggested. The essential idea is to combine self-selected intervals in a first step and then employ brackets generated from the intervals in a second step. In this way we combine the advantages of selfselected intervals, mainly related to the fact that individuals often fi nd it difficult to report a precise point-estimate of a quantity of interest, with the documented usefulness of brackets. Because the brackets are generated from the first sample we sidestep the thorny problem of the optimal design of brackets and additional assumptions on dependency between the self-selected intervals and their points of interest. Our set-up necessitates development of new statistical models. First, we propose a stopping rule for sampling in the first step. Second, Theorem 1 proves that the proposed non-parametric ML-estimator of the underlying distribution function is consistent. Third, a special recursion for quick estimation of the ML-estimators is suggested. Theorem 2 shows that the accuracy of the estimator can be consistently estimated by resampling. Fourth, we have developed an R-package for efficient application of the method. We illustrate the approach using the problem of eliciting willingness-to-pay for a public good.