Theory and Decision

, Volume 73, Issue 1, pp 161–184

Inferring beliefs as subjectively imprecise probabilities


  • Steffen Andersen
    • Department of EconomicsCopenhagen Business School
  • John Fountain
    • Department of EconomicsUniversity of Canterbury
    • Department of Risk Management & Insurance and Center for the Economic Analysis of Risk, Robinson College of BusinessGeorgia State University
  • Arne Risa Hole
    • Department of EconomicsUniversity of Sheffield
  • E. Elisabet Rutström
    • Robinson College of Business and Department of Economics, Andrew Young School of Policy StudiesGeorgia State University

DOI: 10.1007/s11238-011-9276-1

Cite this article as:
Andersen, S., Fountain, J., Harrison, G.W. et al. Theory Decis (2012) 73: 161. doi:10.1007/s11238-011-9276-1


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 riskSubjective beliefsRandom coefficientsNon-linear mixed logitExperiments

Copyright information

© Springer Science+Business Media, LLC. 2011