Theory and Decision

, Volume 73, Issue 1, pp 161–184

Inferring beliefs as subjectively imprecise probabilities

  • Steffen Andersen
  • John Fountain
  • Glenn W. Harrison
  • Arne Risa Hole
  • E. Elisabet Rutström

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

Authors and Affiliations

  • Steffen Andersen
    • 1
  • John Fountain
    • 2
  • Glenn W. Harrison
    • 3
  • Arne Risa Hole
    • 4
  • E. Elisabet Rutström
    • 5
  1. 1.Department of EconomicsCopenhagen Business SchoolCopenhagenDenmark
  2. 2.Department of EconomicsUniversity of CanterburyChristchurchNew Zealand
  3. 3.Department of Risk Management & Insurance and Center for the Economic Analysis of Risk, Robinson College of BusinessGeorgia State UniversityAtlantaUSA
  4. 4.Department of EconomicsUniversity of SheffieldSheffieldUK
  5. 5.Robinson College of Business and Department of Economics, Andrew Young School of Policy StudiesGeorgia State UniversityAtlantaUSA