Eliciting Beliefs: Proper Scoring Rules, Incentives, Stakes and Hedging

Accurate measurements of probabilistic beliefs have become increasingly important both in practice and in academia. Introduced by statisticians in the 1950s to promote truthful reports in simple environments, Proper Scoring Rules (PSR) are now arguably the most popular incentivized mechanisms to elicit an agent's beliefs. This paper generalizes the analysis of PSR to richer environments relevant to economists. More speci…cally, we combine theory and experiment to study how beliefs reported with a PSR may be biased when i) the PSR payments are increased, ii) the agent has a financial stake in the event she is predicting, and iii) the agent can hedge her prediction by taking an additional action. Our results reveal complex distortions of reported beliefs, thereby raising concerns about the ability of PSR to recover truthful beliefs in general economic environments.

The Value of a Statistical Life under Ambiguity Aversion

We show that ambiguity aversion increases the value of a statistical life as soon as the marginal utility of wealth is higher if alive than dead. The intuition is that ambiguity aversion has a similar effect as an increase in the perceived baseline mortality risk, and thus operates as the “dead anyway” effect. We suggest, however, that ambiguity aversion should usually have a modest effect on the prevention of ambiguous mortality risks within benefit-cost analysis, and can hardly justify the substantial “ambiguity premium” apparently embodied in environmental policy-making.ambiguity, value-of-a-statistical-life, uncertainty, risk-aversion, willingness-to-pay, benefit-cost analysis, environmental risk, health policy

Overbidding in Independant Private-Values Auctions and Misperception of Probabilities

We conduct an experiment to test whether probability misperception may be a possible alternative to risk aversion to explain overbidding in independent first-price private-values auctions. The experimental outcomes indicate that subjects underestimate their probability of winning the auction, and indeed overbid. Yet, when provided with feed-back on the precision of their predictions, subjects learn first to predict their probability of winning correctly, and second to curb-down significantly overbidding. The structural estimation of different behavioral models suggests that i) subjects are heterogenous with respect to risk preferences and probability perceptions, ii) subjects tend to best-respond to their stated beliefs, and iii) although necessary to explain fully behavior, risk aversion appears to play a lesser role than previously believed. Finally, our experimental findings are shown to be consistent with a standard theoretical auction model combining risk aversion and misperception of probabilities. Nous menons une expérience pour évaluer si le fait qu'un sujet évalue mal ses probabilités de gagner peut être une hypothèse alternative à l’aversion au risque pour expliquer les surenchères lors d'enchères indépendantes privées au premier prix. Les résultats expérimentaux montrent, en effet, que les sujets sous-estiment leurs probabilités de gagner l'enchère et ont tendance à surenchérir. Cependant, lorsqu'on leur présente plus de précisions sur leurs prédictions, les sujets apprennent d'abord à prédire correctement leurs probabilités de gagner, puis à limiter considérablement la surenchère. L'estimation de différents modèles du comportement suggère que i) les sujets sont hétérogènes par rapport à leurs préférences du risque et leurs perceptions des probabilités, ii) les sujets choisissent leur meilleure réponse conditionnellement aux croyances qu’ils révèlent, et iii) bien que nécessaire pour expliquer pleinement le comportement des sujets, l'aversion au risque semble jouer un rôle moins important que prévu. Finalement, nos résultats expérimentaux sont consistants avec un modèle théorique d'enchères standard qui combine l'aversion au risque et la mauvaise perception des probabilités.auctions, misperception of probabilities, overbidding, risk-aversion, aversion au risque, enchères, mauvaise perception des probabilités, surenchère