Individual vs. couple behavior: an experimental investigation of risk preferences

In this article, we elicit both individuals’ and couples’ preferences assuming prospect theory (PT) as a general theoretical framework for decision under risk. Our experimental method, based on certainty equivalents, allows to infer measurements of utility and probability weighting at the individual level and at the couple level. Our main results are twofold. First, risk attitude for couples is compatible with PT and incorporates deviations from expected utility similar to those found in individual decision making. Second, couples’ attitudes towards risk are found to be consistent with a mix of individual attitudes, women being more influent on couples’ preferences at low probability levels.     

Error Propagation in the Elicitation of Utility and Probability Weighting Functions

Elicitation methods in decision-making under risk allow us to infer the utilities of outcomes as well as the probability weights from the observed preferences of an individual. An optimally efficient elicitation method is proposed, which takes the inevitable distortion of preferences by random errors into account and minimizes the effect of such errors on the inferred utility and probability weighting functions. Under mild assumptions, the optimally efficient method for eliciting utilities and probability weights is the following three-stage procedure. First, a probability is elicited whose subjective weight is one half. Second, the utility function is elicited through the midpoint chaining certainty equivalent method using the probability elicited at the first stage. Finally, the probability weighting function is elicited through the probability equivalent method.     

Probabilistic Insurance

Probabilistic insurance is an insurance policy involving a small probability that the consumer will not be reimbursed. Survey data suggest that people dislike probabilistic insurance and demand more than a 20% reduction in the premium to compensate for a 1% default risk. While these preferences are intuitively appealing they are difficult to reconcile with expected utility theory. Under highly plausible assumptions about the utility function, willingness to pay for probabilistic insurance should be very close to willingness to pay for standard insurance less the default risk. However, the reluctance to buy probabilistic insurance is predicted by the weighting function of prospect theory. This finding highlights the potential role of the weighting function to explain insurance.     

Viewing the future through a warped lens: Why uncertainty generates hyperbolic discounting

A large body of experimental research has demonstrated that, on average, people violate the axioms of expected utility theory as well as of discounted utility theory. In particular, aggregate behavior is best characterized by probability distortions and hyperbolic discounting. But is it the same people who are prone to these behaviors? Based on an experiment with salient monetary incentives we demonstrate that there is a strong and significant relationship between greater departures from linear probability weighting and the degree of decreasing discount rates at the level of individual behavior. We argue that this relationship can be rationalized by the uncertainty inherent in any future event, linking discounting behavior directly to risk preferences. Consequently, decreasing discount rates may be generated by people’s proneness to probability distortions.     

A parametric analysis of prospect theory’s functionals for the general population

This article presents the results of an experiment that completely measures the utility function and probability weighting function for different positive and negative monetary outcomes, using a representative sample of N = 1,935 from the general public. The results confirm earlier findings in the lab, suggesting that utility is less pronounced than what is found in classical measurements where expected utility is assumed. Utility for losses is found to be convex, consistent with diminishing sensitivity, and the obtained loss-aversion coefficient of 1.6 is moderate but in agreement with contemporary evidence. The estimated probability weighting functions have an inverse-S shape and they imply pessimism in both domains. These results show that probability weighting is also an important phenomenon in the general population. Women and lower educated individuals are found to be more risk averse, in agreement with common findings. In contrast to previous studies that ascribed gender differences in risk attitudes solely to differences in the degree utility curvature, however, our results show that this finding is primarily driven by loss aversion and, for women, also by a more pessimistic psychological response toward the probability of obtaining the best possible outcome.     

Heterogeneity in life-duration preferences: Are risky recreationists really more risk loving?

We conduct multiple price list experiments that elicit life duration risk preferences from amateur auto racers, technical rock climbers, SCUBA divers, and a student control group. We posit a preference function that allows for risk aversion and probability weighting. We are particularly interested in whether the behavior of risk takers, such as risky recreationists or smokers, is best explained by a risk-tolerant utility function or if immunity to possibility bias arising from overweighting of low probabilities is a more important motivator of the choice to engage in risky activities. We find that amateur auto racers are more rational than either students or other risky recreationists because they are less likely to overemphasize low-probability events. Women, older subjects, and rock climbers are more susceptible to possibility bias than others, making them likely to overinvest in disease treatments that have a low probability of success.     

What can multiple price lists really tell us about risk preferences?

Multiple price lists have emerged as a simple and popular method for eliciting risk preferences. Despite their popularity, a key downside of multiple price lists has not been widely recognized — namely that the approach is unlikely to generate sufficient information to accurately identify different dimensions of risk preferences. The most popular theories of decision making under risk posit that preferences for risk are driven by a combination of two factors: the curvature of the utility function and the extent to which probabilities are weighted non-linearly. In this paper, we show that the widely used multiple price list introduced by Holt and Laury (The American Economic Review 92(5) 1644–1655 2002) is likely more accurate at eliciting the shape of the probability weighting function, and we construct a different multiple price list that is likely more accurate at eliciting the shape of the utility function. We show that by combining information from different multiple price lists, greater predictive performance can be achieved.     

Risk preferences of Australian academics: where retirement funds are invested tells the story

Risk preferences of Australian academics are elicited by analyzing the aggregate distribution of their retirement funds (superannuation) across available investment options. Not more than 10 % of retirement funds are invested as if their owners maximize expected utility under the assumption of constant relative risk aversion with an empirically plausible level of risk aversion. An implausibly high level of risk aversion is required to rationalize any investment into bonds when stocks are available. Not more than 36.54 % of all investments can be rationalized by a model of loss averse preferences. Moreover, the levels of loss aversion typically reported in the experimental studies imply overinvestment in bonds, which is not observed in the data. Up to 67.18 % of all investments can be rationalized by rank-dependent utility or Yaari’s (Econometrica 55:95–115 1987) dual model with empirically plausible parameters. A median Australian academic behaves as if maximizing rank-dependent utility with parameter \(\gamma \in [0.76, 0.79]\) in a Tversky and Kahneman (J Risk Uncertain 5:297–323 1992) probability weighting function.     

Mean utility preserving increases in risk for state dependent utility functions

This paper defines the concept of a mean utility preserving spread across states (MUPSAS) for state dependent utility functions and analyzes the behavioural impact of shifts in the probability distribution of wealth across states such that overall mean utility is preserved. The main result provides an alternative way of ranking state dependent utility functions according to their degree of risk aversion (thus extending Kami's theorem of comparative risk aversion) and establishes a link between increases in risk and risk aversion for state dependent preferences. In a portfolio problem where preferences and the rate of return of the risky venture are state dependent, we find sufficient conditions to determine the impact of a MUPSAS on the optimal share of the portfolio invested in the risky asset.

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Gender, Financial Risk, and Probability Weights

Women are commonly stereotyped as more risk averse than men in financial decision making. In this paper we examine whether this stereotype reflects gender differences in actual risk-taking behavior by means of a laboratory experiment with monetary incentives. Gender differences in risk taking may be due to differences in valuations of outcomes or in probability weights. The results of our experiment indicate that value functions do not differ significantly between men and women. Men and women differ in their probability weighting schemes, however. In general, women tend to be less sensitive to probability changes. They also tend to underestimate large probabilities of gains more strongly than do men. This effect is particularly pronounced when the decisions are framed in investment terms. As a result, women appear to be more risk averse than men in specific circumstances.     

The two faces of independence: betweenness and homotheticity

This paper shows that expected utility belongs to the intersection of models satisfying betweenness and a homotheticity condition for risky choice. Betweenness models can accommodate variable risk attitudes, originally highlighted by the Allais paradox, by restricting indifference curves to be linear while allowing non-parallelism. Homotheticity, in contrast, restricts indifference curves to be parallel while permitting non-linearities, such as those highlighted by inverse-S probability weighting. Data from an experiment indicate that approximately 2/3s of participants satisfied homotheticity. Of this group, about half satisfied the expected utility hypothesis. The other half violated expected utility and therefore betweenness. These results indicate that homothetic preferences, and in particular those violating betweenness, can be empirically relevant for decision making under risk.

     

Common ratio using delay

We present an experiment in which we add a common delay in a choice between two risky prospects. The results show that delay produces the same change in preferences as in the well-documented common ratio effect in risky lotteries. The added common delay acts as if the probabilities were divided by some common ratio. Moreover, we show that there is a strong magnitude effect, in the sense that the effect of delay depends on the magnitude of the outcome. The results are consistent with the recently introduced probability time trade-off (PTT) model by Baucells and Heukamp. We present a parameterization of the model based on the experimental results, showing that the value function exhibits increasing relative risk aversion, the weighting function is s-shaped, and the intrinsic discount rate is decreasing.     

Emotional balance and probability weighting

We find suggestive evidence that emotional balance has an impact on probability weighting incremental to demographic controls. Specifically, low negative affectivity (implying high emotional balance) tends to be a characteristic of those whose probability weighting functions exhibit lower curvature and more neutral elevation. In other words, emotional balance seems to push people in the direction of normative expected utility theory.     

Comparing risk preferences over financial and environmental lotteries

This paper investigates whether preferences over environmental risks are best modeled using probability-weighted utility functions or can be reasonably approximated by expected utility (EU) or subjective EU models as is typically assumed. I elicit risk attitudes in the financial and environmental domains using multiple-price list experiment. I examine how subjects?? behavioral, attitudinal, and demographic characteristics affect their probability weighting functions first for financial risks, then for oil-spill risks. I find that most subjects tend to overweight extreme positive outcomes relative to expected utility in both the environmental and financial domains. Subjects are more likely to overemphasize low probability, extreme environmental outcomes than low probability, extreme financial outcomes, leading subjects to offer more support for mitigating environmental gambles than financial gambles with the same odds and equivalent outcomes. I conclude that EU models are likely to underestimate subjects?? willingness to pay for environmental cleanup programs or policies with uncertain outcomes.     

Separating curvature and elevation: A parametric probability weighting function

This paper presents a preference foundation for a two-parameter family of probability weighting functions. We provide a theoretical link between the well-established notions of probabilistic risk attitudes (i.e., optimism and pessimism) used in economics and the important independent measures for individual behavior used in the psychology literature (i.e., curvature and elevation). One of the parameters in our model measures curvature and represents the diminishing effect of optimism and pessimism when moving away from extreme probabilities 0 and 1. The other parameter measures elevation and represents the relative strength of optimism vs. pessimism. Our empirical analysis indicates that the new weighting function fits elicited probability weights well, and that it can explain differences in the treatment of probabilities for gains compared to that for probabilities of losses.     

At the nexus of risk and time preferences: An experimental investigation

Although many economic decisions involve choices between uncertain outcomes occurring at different times, most theoretical and empirical work restricts attention to one dimension or another. In this paper, we investigate whether both risk and time preferences can be represented by a single parameter. We collect experimental data to estimate models which allows for a disentanglement of risk and time preferences. Results reveal that the discounted expected utility model assumption, that risk and time preferences can be explained by a single parameter, is not supported by the data. The model estimates imply people prefer to delay the resolution of risky outcomes.     

Estimating Risk Attitudes using Lotteries: A Large Sample Approach

Attitudes towards risk play a major role in many economic decisions. In empirical studies it is quite often assumed that attitudes towards risk do not vary across individuals. This paper questions this assumption and analyses which factors influence an individual's risk attitude. Based on questions on lotteries in a large household survey we first semiparametrically estimate an index for risk aversion. We only make weak assumptions about the underlying decision process and our estimation method allows for generalisations of expected utility. We then estimate a structural model based on Cumulative Prospect Theory. Expected utility is strongly rejected and both the value function and the probability weighting function vary significantly with (among other things) age, income, and wealth of the individual.     

Does Learning Diminish Violations of Independence, Coalescing and Monotonicity?

Violations of expected utility theory are sometimes attributed to imprecise preferences interacting with a lack of learning opportunity in the experimental laboratory. This paper reports an experimental test of whether a learning opportunity which engenders accurate probability assessments, by enhancing understanding of the meaning of stated probability information, causes anomalous behaviour to diminish. The data show that whilst in some cases expected utility maximising behaviour increases with the learning opportunity, so too do systematic violations. Therefore, there should be no presumption that anomalous behaviour under risk is transient and that discovered preferences will be appropriately described by expected utility theory.     

源于身份的隔阂:人口多样性、社会信任与犯罪

本文以2014年中国劳动力动态调查（CLDS）数据为基础，构建了一个人口多样性指数，并将其与288个城市的数据相匹配，检验了人口多样性与犯罪率之间的关系。实证结果表明，人口多样性是导致城市犯罪率上升的原因之一，且这一发现是稳健的。作用机制检验结果表明，社会信任是一个重要的中介变量，即人口多样性通过削弱社会信任水平导致犯罪率的上升。进一步，从地区制度环境和民生支出水平两个角度展开的实证检验发现，产权保护越完善、民众对法庭越有信心，政府在公共教育和社会保障上的财政支出越高，人口多样性对犯罪率的影响越弱，说明良好的制度和较高的社会福利支出具有显著的犯罪治理效应。本文的发现为城市化进程中我国各级政府的犯罪治理政策选择提供了经验证据，有助于科学把握犯罪治理的着力点。