Forecasting risk attitudes: An experimental study using actual and forecast gamble choices

We develop and evaluate a simple gamble-choice task to measure attitudes toward risk, and apply this measure to examine differences in risk attitudes of male and female university students. In addition, we examine stereotyping by asking whether a person's sex is read as a signal of risk preference. Subjects choose which of five 50/50 gambles they wish to play. The gambles include one sure thing; the remaining four increase (linearly) in expected payoff and risk. Each subject also is asked to guess which of the five gambles each of the other subjects chose, and is paid for correct guesses. The experiment is conducted under three different frames: an abstract frame where the two highest-payoff gambles carry the possibility of losses, an abstract frame with no losses, and an investment frame that mirrors the payoff structure of the former. We find that women are significantly more risk averse than men in all three settings, and predictions of both women and men tend to confirm this difference. While average guesses reflect the average difference in choices, only 27 percent of guesses are accurate, which is slightly higher than chance.     

Ambiguity aversion among student subjects: the role of probability interval and emotional parameters

In the literature on decision-making under uncertainty, it has been shown that decision-makers tend to prefer taking gambles with known-risk probabilities (pure risk) over equivalent gambles with ambiguous probabilities. This article contributes to the ongoing discussion in the literature on cognitive and non-cognitive covariates of ambiguity aversion. Through a series of experiments, it finds that subjects are more ambiguity-averse to prospects with wide probability intervals than to an equivalent prospect with narrow intervals, and that subjects’ inherent trust, happiness and level of optimism affect the level of ambiguity aversion.     

A rational,economic model of paygo tax rates

We argue that paygo rates are determined by a representative agent and a benevolent government jointly maximizing the expected life-time utility of the agent. The distributions of labor and capital income are calculated from national data on real GDP, real wages and the real return to capital since 1950. With uniform risk aversion, predicted rates explain 83% of the variance of observed rates. The globalization of capital markets would lead to convergence of paygo rates. Our results are immune to crises like 2008.     

Risk Attitudes of Children and Adults: Choices Over Small and Large Probability Gains and Losses

In this paper we examine how risk attitudes change with age. We present participants from age 5 to 64 with choices between simple gambles and the expected value of the gambles. The gambles are over both gains and losses, and vary in the probability of the non-zero payoff. Surprisingly, we find that many participants are risk seeking when faced with high-probability prospects over gains and risk averse when faced with small-probability prospects. Over losses we find the exact opposite. Children's choices are consistent with the underweighting of low-probability events and the overweighting of high-probability ones. This tendency diminishes with age, and on average adults appear to use the objective probability when evaluating risky prospects.     

Increases in risk aversion and the distribution of portfolio payoffs

Oliver Hart proved the impossibility of deriving general comparative static properties in portfolio weights. Instead, we derive new comparative statics for the distribution of payoffs: A is less risk averse than B iff A?s payoff is always distributed as B?s payoff plus a non-negative random variable plus conditional-mean-zero noise. If either agent has nonincreasing absolute risk aversion, the non-negative part can be chosen to be constant. The main result also holds in some incomplete markets with two assets or two-fund separation, and in multiple periods for a mixture of payoff distributions over time (but not at every point in time).     

Knightian decision theory and econometric inferences

An uncertainty averse Knightian decision maker has a set of probability distributions over outcomes and chooses something other than the status quo only if the change increases the expected payoff according to all the distributions. It is possible to define a standardized degree of uncertainty aversion. To each such degree, there corresponds a set of prior distributions over the parameters of a Gaussian linear regression model, these priors being centered on a uniform prior. The set of posterior means corresponding to this set of priors has the same properties as a standard confidence region.     

An examination of the effect of messages on cooperation under double-blind and single-blind payoff procedures

Previous research has suggested that communication and especially promises increase cooperation in laboratory experiments. This has been taken as evidence for internal motivations such as guilt aversion or preference for promise keeping. The goal of this paper was to examine messages under a double-blind payoff procedure to test the alternative explanation that promise keeping is due to external influence and reputational concerns. Employing a 2×2 design, we find no evidence that communication increases the overall level of cooperation in our experiments with double-blind payoff procedures. However, we also find no evidence that communication impacts cooperation in our experiments with single-blind payoff procedures. Further, the payoff procedure does not appear to impact aggregate cooperation.     

ON THE PRICE AND STRUCTURAL EFFICIENCY IN FARRELL'S MODEL

The paper develops a mean variance model to characterize the price efficiency at the firm level in Farrell's model and shows how risk aversion may affect this measure. Problems of estimating the structural efficiency at the industry level are also discussed and it is shown that this involves a comparison between efficiency distributions of two or more industries. Two empirical applications for the two efficiency measures are also discussed.     

Parimutuel contests with strategic risk-sensitive bettors

Existing models in the parimutuel betting literature typically explain betting data by either assuming a single, representative bettor with certain risk preferences or by assuming that a number of risk neutral bettors compete strategically within a game theoretic framework. We construct a theoretical framework of parimutuel markets in which we model both strategic interaction and individual bettor risk preferences, distinguishing between sophisticated insiders and recreational outsiders. We solve this model analytically for the optimal insider betting amount in a static symmetric Nash equilibrium. A new data set of 126 million individual horse race bets in New Zealand from 2006 to 2014 allows us to calibrate the model. We find that insiders (those betting $100 or more) outperform outsiders by 7.5% in terms of realized returns. The best fit of the model to the data is obtained when insiders are assumed to be risk neutral and to have an information advantage of 0.08 in probability terms. This finding provides empirical support for the common assumption of risk neutrality in strategic interaction models of parimutuel betting.     

An Experimental Study of Risk Aversion in Decision-making Under Uncertainty

This paper presents the findings of an experimental study of risk aversion in decision making under uncertainty. When presented with a series of gambles, subjects determined the certainty-equivalent wealth of each gamble. Risk aversion was measured by the Markowitz risk premium of the decision. The fixed effects regression model indicates the significant influence of the first three moments of a probability distribution in determining the risk premium. These results lend support to the rules of mean-variance and third-degree stochastic dominance. The extent of influence is also affected by the individual’s age, but not by gender, wealth or schooling.     

The effects of risk preferences in mixed-strategy equilibria of games

We consider the effects of risk preferences in mixed-strategy equilibria of 2×2 games, provided such equilibria exist. We identify sufficient conditions under which the expected payoff in the mixed equilibrium increases or decreases with the degree of risk aversion. We find that (at least moderate degrees of) risk aversion will frequently be beneficial in mixed equilibria.     

Output and wages with inequality averse agents

Abstract.  We analyse a two‐task work environment with risk‐neutral but inequality averse individuals. For the agent employed in task 2 effort is verifiable, while in task 1 it is not. Accordingly, agent 1 receives an incentive contract that, owing to his wealth constraint, leads to a rent that the other agent resents. We show that greater inequality aversion unambiguously decreases total output and therefore average labour productivity. More specifically, inequality aversion reduces effort, wage, and payoff of agent 1. Effects on wage and effort of agent 2 depend on whether effort levels across tasks are substitutes or complements in the firm's output function. JEL classification: D2, J3     

How sensitive are bargaining outcomes to changes in disagreement payoffs?

We use a human-subjects experiment to investigate how bargaining outcomes are affected by changes in bargainers’ disagreement payoffs. Subjects bargain against changing opponents, with randomly drawn asymmetric disagreement outcomes that vary over plays of the game, and with complete information about disagreement payoffs and the cake size. We find that subjects only respond about half as much as theoretically predicted to changes in their own disagreement payoff and to changes in their opponent’s disagreement payoff. This effect is observed in a standard Nash demand game and a related unstructured bargaining game, in both early and late rounds, and is robust to moderate changes in stake sizes. We show theoretically that standard models of expected utility maximisation are unable to account for this under-responsiveness, even when generalised to allow for risk aversion. We also show that quantal-response equilibrium has, at best, mixed success in characterising our results. However, a simple model of other-regarding preferences can explain our main results.     

‘A Fair Suck of the Sauce Bottle’ or What Do You Mean by Inequality?*

The literature on the economics of inequality conventionally uses the utilitarian social welfare function as a tool for comparing income distributions. This approach usually suppresses the distinction between two types of ‘inequality aversion’. The formal analysis of these two types is examined and the results of an informal survey are reported.     

Observational equivalence and nonequivalence of subjective and robust mean–variance preferences

We identify the conditions where robust mean–variance preferences, which capture ambiguity aversion, are observationally nonequivalent to subjective mean–variance preferences. Conversely, we also provide an example showing that observational equivalence holds regardless of the degree of ambiguity aversion.     

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.     

实际汇率与就业--基于内生劳动力供给的跨期均衡分析

文章在个体跨期最优模型中引入内生劳动力供给,并同时假定对资本流动存在限制,以此来分析实际汇率变动对就业的影响。结果发现:只有当消费者对商品消费的相对风险规避程度比较大,即消费的跨期替代弹性比较小时,本币实际贬值才会促进就业的增加,反之贬值会使就业减少。考虑到中国当前的具体情况,消费者商品消费的相对风险规避程度会比较大,因而人民币实际贬值会有利于就业。对中国的实证分析支持了这一结论,且该实证分析通过了实际汇率的超外生性检验。鉴于从长期来看中国消费者的相对风险规避程度有下降的趋势,过分的依赖于低币值的汇率政策来解决失业问题是不可行的。     

Rotating Savings and Credit Associations When Participants are Risk Averse*

We model rotating savings and credit associations (Roscas) among risk‐averse participants who experience privately observed income shocks. A random Rosca is not advantageous, whereas a bidding Rosca is if temporal risk aversion is less pronounced than static risk aversion. The payoff scheme of a bidding Rosca facilitates risk sharing in the presence of information asymmetries. The risk‐sharing performance of a simple arrangement where a group of homogenous individuals runs several bidding Roscas simultaneously is as good as that of a linear risk‐sharing contract, and is more enforceable because it carries a fixed rather than a variable contribution.     

Monotone imitation

We analyze the social learning process of a group of individuals who have limited information about the payoff distributions of each action. We say that a behavioral rule is first-order monotone (FOM) if the number of individuals who play actions with first-order stochastic dominant payoff distributions is expected to increase in any environment. We provide a characterization of FOM rules. Both Imitate if Better and Schlag’s (J Econ Theory 78:130–156, 1998) Proportional Imitation rule are FOM. No FOM rule is dominant in the sense of having the best performance in every environment.     

New light on the longshot bias

The longshot bias is the tendency for bettors to put more money on horses with long odds than is justified by their objective probability of winning: thus favourites win more often than projected by their odds. This challenges normative assumptions as it means the return increases with the probability of winning. Even though the longshot bias is well-known, it has defied authoritative explanation. This article draws on studies of the longshot bias over 50 years across four continents to show that its nature is consistent with two bettor populations. One is risk-averse, knowledgeable about winners, backs favourites, believes in the gambler's fallacy, and has a positive expected return. The other, a larger group is risk loving, backs longshots, believes in hot hands, and has a significant, negative expected return. The crossover between the two groups occurs where the probability of a positive result is about 0.2. This matches the transition from risk aversion to risk embrace which has been found in a variety of behavioural studies.