WP 2016-01 Recovering Subjective Probability Distributions

Posted On February 2, 2016
Categories Working Papers, WP 2016

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AUTHORS: Glenn W. Harrison and Eric R. Ulm

ABSTRACT: An individual reports subjective beliefs over continuous events using a proper scoring rule, such as the Quadratic Scoring Rule. Under mild additional assumption, it is known that these reports reflect latent subjective beliefs if the individual is risk neutral and obeys Subjective Expected Utility (SEU) theory. It is also known that these reports are close to latent subjective beliefs if the individual obeys SEU and has a concave utility function in the range typically observed. We extend these results in three ways. First, we show how to fully recover latent subjective beliefs if the individual obeys SEU and has any concave utility function. Second, we demonstrate how to fully recover latent subjective beliefs if the individual is known to distort probabilities into decision weights using Rank Dependent Utility theory. We illustrate these theoretical results with an example drawn from an incentivized experiment eliciting beliefs over longevity risk for men. Third, we generalize all results for the complete class of proper scoring rules. These theoretical results and empirical applications significantly widen the domain of applicability of proper scoring rules for eliciting latent subject belief distributions.