Theory and Decision

, Volume 73, Issue 1, pp 161-184

First online:

Inferring beliefs as subjectively imprecise probabilities

  • Steffen AndersenAffiliated withDepartment of Economics, Copenhagen Business School
  • , John FountainAffiliated withDepartment of Economics, University of Canterbury
  • , Glenn W. HarrisonAffiliated withDepartment of Risk Management & Insurance and Center for the Economic Analysis of Risk, Robinson College of Business, Georgia State University Email author 
  • , Arne Risa HoleAffiliated withDepartment of Economics, University of Sheffield
  • , E. Elisabet RutströmAffiliated withRobinson College of Business and Department of Economics, Andrew Young School of Policy Studies, Georgia State University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other and then a series of betting choices in which the subject is presented with a range of bookies offering odds on the outcome of some event that the subject has a belief over. Knowledge of the risk attitudes of subjects conditions the inferences about subjective beliefs. Maximum simulated likelihood methods are used to estimate a structural model in which subjects employ subjective beliefs to make bets. We present evidence that some subjective probabilities are indeed best characterized as probability distributions with non-zero variance.


Subjective risk Subjective beliefs Random coefficients Non-linear mixed logit Experiments