Inferring beliefs as subjectively imprecise probabilities

• Published in: Theory and decision Vol. 73; no. 1; pp. 161 - 184
• Main Authors: Andersen, Steffen, Fountain, John, Harrison, Glenn W., Hole, Arne Risa, Rutström, E. Elisabet
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Boston Springer US 01-07-2012; Springer; Springer Nature B.V
• Subjects: Applied sciences; Attitudes; Behavioral/Experimental Economics; Belief & doubt; Betting; Coefficients; Computer simulation; Decision theory. Utility theory; Design of experiments; Econometrics; Economic models; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; Estimates; Estimating techniques; Estimation; Exact sciences and technology; Expected utility; Experiments; Finance; Gambling; Game Theory; Imprecise probabilities; Insurance; Lotteries; Management; Mathematical models; Mathematics; Maximum likelihood; Mixed logit; Model structures; Non-linear mixed logit; Normal distribution; Operational research and scientific management; Operational research. Management science; Operations Research/Decision Theory; Parametric inference; Population; Probability; Probability and statistics; Probability distribution; Probability theory; Random coefficients; Risk; Risk attitude; Risk perception; Risk theory; Sciences and techniques of general use; Simulated likelihood; Social and Behav. Sciences; Standard deviation; Statistics; Statistics for Business; Structural economics; Structural models; Studies; Subjective beliefs; Subjective probability; Subjective risk; Subjectivity; Tasks; Subjective beliefs; Non-linear mixed logit; Subjective risk; Experiments; Random coefficients; Belief; Imprecise probability; Attitude; Inference; Probability distribution; Risk analysis; Gambling game; Standards; Subjective probability; Logistic regression; Uncertain system; Lottery; Structural model; Gamble; Maximum likelihood
• ISSN: 0040-5833; 1573-7187; 1573-7187
• 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.