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People’s beliefs about everyday events are both of theoreti-cal interest in their own right and an important ingredient inmodel building—especially in Bayesian cognitive models ofphenomena such as logical reasoning, future predictions, andlanguage use. Here, we explore several recently used methodsfor measuring subjective beliefs about unidimensional contigu-ous properties, such as the likely price of a new watch. Asa first step towards a way of assessing and comparing beliefelicitation methods, we use hierarchical Bayesian modeling forinferring likely population-level beliefs as the central tendencyof participants’ individual-level beliefs. Three different depen-dent measures are considered: (i) slider ratings of (relative)likelihood of intervals of values, (ii) a give-a-number task, and(iii) choice of the more likely of two intervals of values. Ourresults suggest that using averaged normalized slider ratingsfor binned quantities is a practical and fairly good approxima-tor of inferred population-level beliefs.

We show that consumption-based asset pricing models with time-separable preferences generate realistic amounts of stock price volatility if one allows for small deviations from rational expectations. Rational investors with subjective beliefs about price behavior optimally learn from past price observations. This imparts momentum and mean reversion into stock prices. The model quantitatively accounts for the volatility of returns, the volatility and persistence of the price-dividend ratio, and the predictability of long-horizon returns. It passes a formal statistical test for the overall fit of a set of moments provided one excludes the equity premium.

What are the behavioral effects of voluntary self-protection in situations where the probabilities are unknown to the agent? Virtually all naturally occurring environments of risk management involve subjective probabilities, and many allow decision makers to voluntarily mitigate risk using self-protection activities. To examine this environment we design a laboratory experiment in which incomplete information about probabilities is generated in a naturalistic way from the perspective of decision makers, but where the experimenter has complete information. Specifically, we use virtual simulations of property that is at risk of destruction from simulated wild fires. Using direct belief elicitation mechanisms we find that subjective beliefs over high and low risk scenarios underestimate the shift. Thus, predictions of voluntary self-protection activities based on such data would estimate a suboptimal willingness to invest. However, when offering subjects’ self-protection opportunities, their choices indicate that they over-estimate the risk reducing effects and would in fact be willing to pay more than if they knew the objective probabilities. These findings have direct implications for the normative evaluation of risk management policies when risk perception is subjective.

What are the behavioral effects of voluntary self-protection in situations where the probabilities are unknown to the agent? Virtually all naturally occurring environments of risk management involve subjective probabilities, and many allow decision makers to voluntarily mitigate risk using self-protection activities. To examine this environment we design a laboratory experiment in which incomplete information about probabilities is generated in a naturalistic way from the perspective of decision makers, but where the experimenter has complete information. Specifically, we use virtual simulations of property that is at risk of destruction from simulated wild fires. Using direct belief elicitation mechanisms we find that subjective beliefs over high and low risk scenarios underestimate the shift. Thus, predictions of voluntary self-protection activities based on such data would estimate a suboptimal willingness to invest. However, when offering subjects’ self-protection opportunities, their choices indicate that they over-estimate the risk reducing effects and would in fact be willing to pay more than if they knew the objective probabilities. These findings have direct implications for the normative evaluation of risk management policies when risk perception is subjective.

What are the behavioral effects of voluntary self-protection in situations where the probabilities are unknown to the agent? Virtually all naturally occurring environments of risk management involve subjective probabilities, and many allow decision makers to voluntarily mitigate risk using self-protection activities. To examine this environment we design a laboratory experiment in which incomplete information about probabilities is generated in a naturalistic way from the perspective of decision makers, but where the experimenter has complete information. Specifically, we use virtual simulations of property that is at risk of destruction from simulated wild fires. Using direct belief elicitation mechanisms we find that subjective beliefs over high and low risk scenarios underestimate the shift. Thus, predictions of voluntary self-protection activities based on such data would estimate a suboptimal willingness to invest. However, when offering subjects’ self-protection opportunities, their choices indicate that they over-estimate the risk reducing effects and would in fact be willing to pay more than if they knew the objective probabilities. These findings have direct implications for the normative evaluation of risk management policies when risk perception is subjective.

What are the behavioral effects of voluntary self-protection in situations where the probabilities are unknown to the agent? Virtually all naturally occurring environments of risk management involve subjective probabilities, and many allow decision makers to voluntarily mitigate risk using self-protection activities. To examine this environment we design a laboratory experiment in which incomplete information about probabilities is generated in a naturalistic way from the perspective of decision makers, but where the experimenter has complete information. Specifically, we use virtual simulations of property that is at risk of destruction from simulated wild fires. Using direct belief elicitation mechanisms we find that subjective beliefs over high and low risk scenarios underestimate the shift. Thus, predictions of voluntary self-protection activities based on such data would estimate a suboptimal willingness to invest. However, when offering subjects’ self-protection opportunities, their choices indicate that they over-estimate the risk reducing effects and would in fact be willing to pay more than if they knew the objective probabilities. These findings have direct implications for the normative evaluation of risk management policies when risk perception is subjective.

What are the behavioral effects of voluntary self-protection in situations where the probabilities are unknown to the agent? Virtually all naturally occurring environments of risk management involve subjective probabilities, and many allow decision makers to voluntarily mitigate risk using self-protection activities. To examine this environment we design a laboratory experiment in which incomplete information about probabilities is generated in a naturalistic way from the perspective of decision makers, but where the experimenter has complete information. Specifically, we use virtual simulations of property that is at risk of destruction from simulated wild fires. Using direct belief elicitation mechanisms we find that subjective beliefs over high and low risk scenarios underestimate the shift. Thus, predictions of voluntary self-protection activities based on such data would estimate a suboptimal willingness to invest. However, when offering subjects’ self-protection opportunities, their choices indicate that they over-estimate the risk reducing effects and would in fact be willing to pay more than if they knew the objective probabilities. These findings have direct implications for the normative evaluation of risk management policies when risk perception is subjective.

We examine the subjective risks of driving behavior using a controlled virtual reality experiment. Use of a driving simulator allows us to observe choices over risky alternatives that are presented to the individual in a naturalistic manner, with many of the cues one would find in the field. However, the use of a simulator allows us the type of controls one expects from a laboratory environment. The subject was tasked with making a left-hand turn into incoming traffic, and the experimenter controlled the headways of oncoming traffic. Subjects were rewarded for making a successful turn, and lost income if they crashed. The experimental design provided opportunities for subjects to develop subjective beliefs about when it would be safe to turn, and it also elicited their attitudes towards risk. A simple structural model explains behavior, and showed evidence of heterogeneity in both the subjective beliefs that subjects formed and their risk attitudes. We find that subjective beliefs change with experience in the task and the driver's skill. A significant difference was observed in the perceived probability to successfully turn among the inexperienced drivers who did and did not crash even though there was no significant difference in drivers' risk attitudes among the two groups. We use experimental economics to design controlled, incentive compatible tasks that provide an opportunity to evaluate the impact on driver safety of subject's subjective beliefs about when it would be safe to turn as well as their attitudes towards risk. This method could be used to help insurance companies determine risk premia associated with risk attitudes or beliefs of crashing, to better incentivize safe driving.

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.

The paper incorporates qualitative differences of probabilistic beliefs into a rational (or normatively motivated) decision framework. Probabilistic beliefs can range from objective probabilities to pure guesstimates. The decision maker in the present model takes into account his confidence in beliefs when evaluating general uncertain situations. From an axiomatic point of view, the approach stays as close as possible to the widespread von Neumann-Morgenstern framework. The resulting representation uses only basic tools from risk analysis, but employs them recursively. The paper extends the concept of smooth ambiguity aversion to a more general notion of aversion to the subjectivity of belief. As a special case, the framework permits a threefold disentanglement of intertemporal substitutability, Arrow-Pratt risk aversion, and smooth ambiguity aversion. A decision maker’s preferences can nest a variety of widespread decision criteria, which are selected according to his confidence in the uncertainty assessment of a particular setting.

The paper analyzes the discount rate under uncertainty. The analysis complements the probabilistic characterization of uncertainty by a measure of confidence. Special cases of the model comprise discounting under smooth ambiguity aversion as well as discounting under a disentanglement of risk aversion from aversion to intertemporal substitution. The paper characterizes the general class of preferences for which uncertainty implies a reduction of the discount rate. It also characterizes how the more comprehensive description of uncertainty changes the discount rate with respect to the standard model. The paper relates different results in the literature by switching between different risk measures. It presents a parametric extension of the Ramsey discounting formula that takes into account confidence into future growth estimates and a measure of aversion to the lack of confidence. If confidence decreases in the futurity of the growth forecast, the discount rates have a falling term structure even in the case of an iid growth process.

The paper incorporates qualitative differences of probabilistic beliefs into a rational (or normatively motivated) decision framework. Probabilistic beliefs can range from objective probabilities to pure guesstimates. The decision maker in the present model takes into account his confidence in beliefs when evaluating general uncertain situations. From an axiomatic point of view, the approach stays as close as possible to the widespread von Neumann-Morgenstern framework. The resulting representation uses only basic tools from risk analysis, but employs them recursively. The paper extends the concept of smooth ambiguity aversion to a more general notion of aversion to the subjectivity of belief. As a special case, the framework permits a threefold disentanglement of intertemporal substitutability, Arrow-Pratt risk aversion, and smooth ambiguity aversion. A decision maker’s preferences can nest a variety of widespread decision criteria, which are selected according to his confidence in the uncertainty assessment of a particular setting.

The paper analyzes the discount rate under uncertainty. The analysis complements the probabilistic characterization of uncertainty by a measure of confidence. Special cases of the model comprise discounting under smooth ambiguity aversion as well as discounting under a disentanglement of risk aversion from aversion to intertemporal substitution. The paper characterizes the general class of preferences for which uncertainty implies a reduction of the discount rate. It also characterizes how the more comprehensive description of uncertainty changes the discount rate with respect to the standard model. The paper relates different results in the literature by switching between different risk measures. It presents a parametric extension of the Ramsey discounting formula that takes into account confidence into future growth estimates and a measure of aversion to the lack of confidence. If confidence decreases in the futurity of the growth forecast, the discount rates have a falling term structure even in the case of an iid growth process.