Anticipated regret as an explanation of uncertainty aversion

The paper provides a psychological explanation of uncertainty aversion based on the fear of regret. We capture an agent’s regret using a reference-dependent utility function in which the agent’s utility depends on the performance of his chosen option relative to the performance of the option that would have been best ex post. An uncertain option is represented as a compound lottery. The basic idea is that selecting a compound lottery reveals information, which alters the ex post assessment of what the best choice would have been, inducing regret. We provide sufficient conditions under which regret implies uncertainty aversion in the sense of quasi-concave preferences over compound lotteries.     

Past experience of uncertainty affects risk aversion

In an experiment with more than 500 participants we study how past experience of uncertainty (imperfect knowledge of the state space) affects risk preferences. Participants in our experiment choose between a sure outcome and a lottery in 32 periods. All treatments are exactly identical in periods 17–32 but differ in periods 1–16. In the early periods of the risk treatment there is perfect information about the lottery; in the ambiguity Treatment participants perfectly know the outcome space but not the associated probabilities; in the unawareness treatment participants have imperfect knowledge about both outcomes and probabilities. We observe strong treatment effects on behavior in periods 17–32. In particular, participants who have been exposed to an environment with very imperfect knowledge of the state space subsequently choose lotteries with high (low) variance less (more) often compared to other participants. Estimating individual risk attitudes from choices in periods 17–32 we find that the distribution of risk attitude parameters across our treatments can be ranked in terms of first order stochastic dominance. Our results show how exposure to environments with different degrees of uncertainty can affect individuals’ subsequent risk-taking behavior.     

Loss aversion

Loss aversion is traditionally defined in the context of lotteries over monetary payoffs. This paper extends the notion of loss aversion to a more general setup where outcomes (consequences) may not be measurable in monetary terms and people may have fuzzy preferences over lotteries, i.e., they may choose in a probabilistic manner. The implications of loss aversion are discussed for expected utility theory and rank-dependent utility theory as well as for popular models of probabilistic choice such as the constant error/tremble model and a strong utility model (that includes the Fechner model of random errors and Luce choice model as special cases).     

Group and individual risk preferences: A lottery-choice experiment with self-employed and salaried workers

This paper focuses on decision making under risk, comparing group and individual risk preferences in a lottery-choice experiment. In the individual treatment, subjects make choices individually; in the group treatment, each subject placed in a group made lottery choice via voting. In the choice treatment, subjects choose whether to be on their own or in a group. The originality of this research lies in the fact that we introduced variability in socio-demographic characteristics by recruiting salaried and self-employed workers. Our main findings indicate that groups are more likely than individuals to choose safe lotteries. Our results also show that individuals risk attitude is correlated with both the type and the sector of employment.     

Lotteries, Sunspots, and Incentive Constraints

We study a prototypical class of exchange economies with private information and indivisibilities. We establish an equivalence between lottery equilibria and sunspot equilibria and show that the welfare and existence theorems hold. To establish these results, we introduce the concept of the stand-in consumer economy, which is a standard, convex, finite consumer, finite good, pure exchange economy. With decreasing absolute risk aversion and no indivisibilities, we prove that no lotteries are actually used in equilibrium. We provide a simple numerical example with increasing absolute risk aversion in which lotteries are necessarily used in equilibrium. We also show how the equilibrium allocation in this example can be implemented in a sunspot equilibrium. Journal of Economic Literature Classification Numbers: D11, D50, D82.     

Free riders and the optimal prize in public‐good funding lotteries

We prove the existence and uniqueness of an equilibrium in a game where players, whose preferences exhibit constant absolute risk aversion or constant relative risk aversion, contribute to a public good via lottery‐ticket purchases. Contrasting models with risk neutrality, we show that an equilibrium with a strictly positive amount of the public good may not exist without a sufficient number of participants who are not too risk‐averse. We show that players who are more risk‐averse purchase fewer lottery tickets and are more likely to free ride in equilibrium. In fact, it is possible for free riders to place a larger value on the public good than do those who contribute. In a symmetric equilibrium, we show that an upper bound exists for the amount of the public good, even though there are infinitely many participants. Furthermore, we derive a lottery prize that maximizes the amount of the public good in a symmetric equilibrium and find that such a prize always results in an overprovision of the public good.     

Reducing ambiguity in lotteries: evidence from a field experiment

Ambiguity about the chances of winning represents a key aspect in lotteries. By means of a controlled field experiment, we exogenously vary the degree of ambiguity about the winning chances of lotteries organized to incentivize the contribution for a public good. In one treatment, people have been simply informed about the maximum number of potential participants (i.e. the number of lottery tickets released). In a second treatment, this information has been omitted as in all traditional lotteries. Our general finding shows that simply reducing the degree of ambiguity of the lottery leads to a sizable and significant increase (67%) in the participation rate. This result is robust to alternative prize configurations.     

Charitable Lottery Structure and Fund Raising: Theory and Evidence

Do fixed-prize charitable lotteries generate more net revenue than do revenue-dependent lotteries? I present the results of an experiment designed to test a theoretical prediction of the relationship between the prize structure of a lottery funding a public good and individuals' participation in the lottery. I find that a fixed-prize lottery configuration induces significantly greater participation and a significantly higher level of public good funding than does a revenue-dependent lottery.     

Probabilistic risk aversion with an arbitrary outcome set

This paper analyzes risk aversion when outcomes/consequences may not be measurable in monetary terms and people have fuzzy preferences over lotteries, i.e. they choose in a probabilistic manner. The paper shows that comparative risk aversion is well defined in a constant error/tremble model but not in a strong utility model.     

The economic analysis of lotteries

This paper considers policy issues arising in the design, regulation and taxation of lotteries, focusing on the market for an on-line lottery game. Demand determines who buys lottery tickets and in what quantities. The design of lotteries affects the terms on which tickets are supplied.
UK data suggest that its lottery may be priced too high to maximize lottery revenue – more revenue might be raised if the proportion of sales allocated to tax and other levies were smaller.
Having established the positive economics of lotteries, the paper then assesses their welfare implications. Pari-mutuel lotteries enjoy scale economies and, as natural monopolies, are invariably run either by government agencies or a regulated licensee. I estimate consumer surplus and identify the excess burden that arises from existing (over)taxation of lotteries. The large price elasticity of demand implies that revenue raised from the lottery is raised very inefficiently. Moreover, the demand for lottery tickets is inferior (and there is some evidence that such games are contagious and addictive). So using lotteries as a vehicle for raising revenue is extremely regressive. Finally, I consider other policy implications: induced effects on charitable giving and on other forms of gambling; the impact on the government budget; perceptions of risk; and distributional considerations.     

On the Evaluation of Options on Lotteries: An Experimental Study

We present the results of a comparative experimental study of the evaluation of simple lotteries and call/put/insurance options on these lotteries. The main findings and conclusions are:

(a) The observed bidding patterns depend on the type of asset under evaluation. In particular, subject behavior when buying or selling a basic lottery seems much more cautious than their behavior when buying or selling options on that lottery.

(b) The observed bidding patterns also depend on subject positions with respect to the underlying asset. In particular, the bids for buying lotteries and options long are statistically uncorrelated with the bids for selling the same lotteries and options short.

(c) Subjects with extreme risk attitudes are more inclined to violate basic no-arbitrage conditions (like the call-put parity) when bidding for the different lotteries.

We demonstrate that it is difficult to reconcile the experimental evidence with mainstream theories on individual decision and choice (although we find strong support for prospect theory in some parts of the data). We conclude that the evaluation of options on lotteries is context-dependent and subtler than perceived by existing theories.     

Lottery expenses and charitable contributions – Taiwan's experience

Individuals’ contributions are affected by their lottery outlays if they consider their spending of lottery funds on charities to be a substitute for or a complement to their direct charitable contributions. This study investigates the effect of lottery outlays on charitable contributions based on the experience of lottery introduction in Taiwan. The estimates reveal that lottery outlays exert a positive effect on charitable contributions while the quantitative impact is significant. This study thus provides evidence ameliorating the pessimistic prospect that people may reduce their direct charitable contributions when they spend more on lotteries. Possible explanations for the positive effect are also discussed.     

A theory of subjective compound lotteries

We develop a Savage-type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries. Our theory permits issue preference; that is, agents may not be indifferent among gambles that yield the same probability distribution if they depend on different issues. Hence, we establish subjective foundations for the Anscombe-Aumann framework and other models with two different types of probabilities. We define second-order risk as risk that resolves in the first stage of the compound lottery and show that uncertainty aversion implies aversion to second-order risk which implies issue preference and behavior consistent with the Ellsberg paradox.     

Multi-dimensional skills,specialization, and oligopolistic competition in higher education

This paper develops a differentiated products model of school competition that distinguishes among different dimensions that matter in the skill acquisition process. The model predicts that when identical schools compete for students, specialization may arise as a competition strategy. This serves rich students' education goals well. Poorer students, however, may attend schools with specializations that do not cater to their relative strengths. By doing so, these poorer students complement the weaknesses of the richer students through peer effects and receive financial aid in return. The empirical analysis provides strong support for the model's predictions about within-school implications of specialization.     

Equity or intention: it is the thought that counts

Economists theorize how and when other-regarding behavior determines experimental outcomes. Two approaches are: (1) explicitly model fairness—intentions matter and (2) use inequity aversion as a proxy for fairness—only the outcome matters. The first approach is consistent with people behaving as though they think, “He was as fair as he could be; do not punish him”. The second approach is consistent with people behaving as though they think, “Despite his best efforts, the outcome was inequitable; punish him”. The results of this experiment are consistent with the fairness-based model, that is, “It is the thought that counts”.     

Comparing risk aversion in a probability triangle

An agent's acceptance set consists of the probability distributions preferred to the status quo. One agent is more risk averse than another if the more risk averse agent's acceptance set is a proper subset of the less risk averse agent's acceptance set. An agent's odds premium expresses the odds in favor of winning the largest cash prize in a lottery over the best and worst alternatives that is indifferent to the the agent's initial wealth. Comparisons of two agents odds premia completely characterizes the risk aversion relations between them when facing lotteries in a probability triangle. The result applies to expected utility and some non-expected utility theories. Received: December 30, 1998; revised version: February 10, 1999     

The influence of spouses on household decision making under risk: an experiment in rural China

We study household decision making in a high-stakes experiment with a random sample of households in rural China. Spouses have to choose between risky lotteries, first separately and then jointly. We find that spouses’ individual risk preferences are more similar the richer the household and the higher the wife’s relative income contribution. A couple’s joint decision is typically very similar to the husband’s preferences, but women who contribute relatively more to the household income, women in high-income households, and women with communist party membership have a stronger influence on the joint decision.     

On the Interaction of Risk and Time Preferences: An Experimental Study

Experimental studies of risk and time preference typically focus on one of the two phenomena. The goal of this paper is to investigate the (possible) correlation between subjects' attitude to risk and their time preference. For this sake we ask 61 subjects to price a simple lottery in three different scenarios. At the first, the lottery premium is paid 'now'. At the second, it is paid 'later'. At the third, it is paid 'even later'. By comparing the certainty equivalents offered by the subjects for the three lotteries, we test how time and risk preferences are interrelated. Since the time interval between 'now' and 'later' is the same as between 'later' and 'even later', we also test the hypothesis of hyperbolic discounting. The main result is a statistically significant negative correlation between subjects' degrees of risk aversion and their (implicit) discount factors. Moreover, we show that the negative correlation is independent of the method used to elicit certainty equivalents (willingness to pay versus willingness to accept).     

An International Comparison and Analysis of Lotteries and the Distribution of Lottery Expenditures

Lotteries are found in nearly half of the world's countries, with annual worldwide lottery ticket sales topping $115 billion. Despite the global presence of lottery games, there has been little research conducted on any international aspect of lotteries. This paper presents the first-ever examination and comparison of lottery games from around the world. Differences in both absolute and relative lottery expenditures are presented. Estimates for the income elasticity of demand for lottery tickets provide evidence on the distributional burden of lottery expenditures. These estimates consider each country by continental location and country income level. Further analysis reveals that lower income countries could adopt Lotto games in order to increase revenues. Recognizing that the distributional impact of lottery games is one of the greatest concerns surrounding lotteries, it is shown that the introduction of Lotto games does not significantly affect the distributional burden of lottery ticket expenditures. Given the international scope of lotteries and the availability of international lottery game data, the paper concludes by discussing future research on international lottery games.