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.     

Marginal risk aversion and preferences in a betting market

An individual's behavioural attitudes toward variance and non-symmetry in the payoff distributions of pari-mutuel gambles are empirically examined using the von Neumann - Morgenstern expected utility of wealth paradigm. Preferences over payoff distributions for a representative bettor are estimated from observed payoffs at a greyhound racetrack. The results indicate that the representative bettor exhibits increasing absolute risk aversion and, given that the representative bettor is locally non-satiated with regard to wealth, exhibits preference for variance and aversion to positive skewness in the payoff distributions of the gambles examined.     

Is households’ risk attitude robust to different experimental payoffs?

We compared risk attitudes among rural people in Tanzania and Kenya using an experimental design where payoffs were defined and quantified in maize and milk production. About 42% of the sample revealed different risk attitude between the two payoff types. The difference was mainly explained by household livelihood strategy, geographical location and ethnicity. Hence, appropriate pay-off metrics differ across contexts and different metrics may provide noncomparable results that does not reflect intrinsic risk attitude.     

EXPLAINING ATTITUDES TOWARDS AMBIGUITY: AN EXPERIMENTAL TEST OF THE COMPARATIVE IGNORANCE HYPOTHESIS

Many theories have been put forward to explain attitudes towards ambiguity. This paper reports on an experiment designed to test for the existence of Comparative Ignorance when it is tested over events with a range of different likelihoods. A total of 93 subjects valued a series of gambles, one of which was played out for real. The results do not lend support to the theory, although the relationship between risk and ambiguity does appear to correspond with other theories and previous empirical work.     

Regret minimization in repeated matrix games with variable stage duration

Regret minimization in repeated matrix games has been extensively studied ever since Hannan's seminal paper [Hannan, J., 1957. Approximation to Bayes risk in repeated play. In: Dresher, M., Tucker, A.W., Wolfe, P. (Eds.), Contributions to the Theory of Games, vol. III. Ann. of Math. Stud., vol. 39, Princeton Univ. Press, Princeton, NJ, pp. 97–193]. Several classes of no-regret strategies now exist; such strategies secure a long-term average payoff as high as could be obtained by the fixed action that is best, in hindsight, against the observed action sequence of the opponent. We consider an extension of this framework to repeated games with variable stage duration, where the duration of each stage may depend on actions of both players, and the performance measure of interest is the average payoff per unit time. We start by showing that no-regret strategies, in the above sense, do not exist in general. Consequently, we consider two classes of adaptive strategies, one based on Blackwell's approachability theorem and the other on calibrated play, and examine their performance guarantees. We further provide sufficient conditions for existence of no-regret strategies in this model.     

Coordination cycles

Players repeatedly face a coordination problem in a dynamic global game. By choosing a risky action (invest) instead of waiting, players risk instantaneous losses as well as a loss of payoffs from future stages, in which they cannot participate if they go bankrupt. Thus, the total strategic risk associated with investment in a particular stage depends on the expected continuation payoff. High continuation payoff makes investment today more risky and therefore harder to coordinate on, which decreases today's payoff. Thus, expectation of successful coordination tomorrow undermines successful coordination today, which leads to fluctuations of equilibrium behavior even if the underlying economic fundamentals happen to be the same across the rounds. The dynamic game inherits the equilibrium uniqueness of the underlying static global game.     

Risk preferences under acute stress

Many important decisions are made under stress and they often involve risky alternatives. There has been ample evidence that stress influences decision making, but still very little is known about whether individual attitudes to risk change with exposure to acute stress. To directly evaluate the causal effect of psychosocial stress on risk attitudes, we adopt an experimental approach in which we randomly expose participants to a stressor in the form of a standard laboratory stress-induction procedure: the Trier Social Stress Test for Groups. Risk preferences are elicited using a multiple price list format that has been previously shown to predict risk-oriented behavior out of the laboratory. Using three different measures (salivary cortisol levels, heart rate and multidimensional mood questionnaire scores), we show that stress was successfully induced on the treatment group. Our main result is that for men, the exposure to a stressor (intention-to-treat effect, ITT) and the exogenously induced psychosocial stress (the average treatment effect on the treated, ATT) significantly increase risk aversion when controlling for their personal characteristics. The estimated treatment difference in certainty equivalents is equivalent to 69 % (ITT) and 89 % (ATT) of the gender-difference in the control group. The effect on women goes in the same direction, but is weaker and insignificant.     

An Axiomatization of Nash Equilibria in Economic Situations

We consider the class of all abstract economies with convex and compact strategy sets, continuous and quasi-concave payoff functions, and continuous and convex-valued feasibility correspondences. We prove that the Nash correspondence is the unique solution on the foregoing class of abstract economies that satisfies nonemptiness, rationality in one-person economies, and consistency.Journal of Economic LiteratureClassification Numbers: C72, D50.     

Diverse beliefs and time variability of risk premia

Why do risk premia vary over time? We examine this problem theoretically and empirically by studying the effect of market belief on risk premia. Individual belief is taken as a fundamental primitive state variable. Market belief is observable; it is central to the empirical evaluation and we show how to measure it. Our asset pricing model is familiar from the noisy REE literature but we adapt it to an economy with diverse beliefs. We derive equilibrium asset prices and implied risk premium. Our approach permits a closed form solution of prices; hence we trace the exact effect of market belief on the time variability of asset prices and risk premia. We test empirically the theoretical conclusions. Our main result is that, above the effect of business cycles on risk premia, fluctuations in market belief have significant independent effect on the time variability of risk premia. We study the premia on long positions in Federal Funds Futures, 3- and 6-month Treasury Bills (T-Bills). The annual mean risk premium on holding such assets for 1?C12?months is about 40?C60 basis points and we find that, on average, the component of market belief in the risk premium exceeds 50% of the mean. Since time variability of market belief is large, this component frequently exceeds 50% of the mean premium. This component is larger the shorter is the holding period of an asset and it dominates the premium for very short holding returns of less than 2?months. As to the structure of the premium we show that when the market holds abnormally favorable belief about the future payoff of an asset the market views the long position as less risky hence the risk premium on that asset declines. More generally, periods of market optimism (i.e. ??bull?? markets) are shown to be periods when the market risk premium is low while in periods of pessimism (i.e. ??bear?? markets) the market??s risk premium is high. Fluctuations in risk premia are thus inversely related to the degree of market optimism about future prospects of asset payoffs. This effect is strong and economically very significant.     

Measuring Strategic Uncertainty in Coordination Games

This paper proposes a method to measure strategic uncertainty by eliciting certainty equivalents analogous to measuring risk attitudes in lotteries. We apply this method by conducting experiments on a class of one-shot coordination games with strategic complementarities and choices between simple lotteries and sure payoff alternatives, both framed in a similar way. Despite the multiplicity of equilibria in the coordination games, aggregate behaviour is fairly predictable. The pure or mixed Nash equilibria cannot describe subjects' behaviour. We present two global games with private information about monetary payoffs and about risk aversion. While previous literature treats the parameters of a global game as given, we estimate them and show that both models describe observed behaviour well. The global-game selection for vanishing noise of private signals offers a good recommendation for actual players, given the observed distribution of actions. We also deduce subjective beliefs and compare them with objective probabilities.     

Fragility of information cascades: an experimental study using elicited beliefs

This paper examines the occurrence and fragility of information cascades in two laboratory experiments. One group of low informed participants sequentially guess which of two states has been randomly chosen. In a matched pairs design, another group of high informed participants make similar guesses after having observed the guesses of the low informed participants. In the second experiment, participants’ beliefs about the chosen state are elicited. In equilibrium, low informed players who observe an established pattern of identical guesses herd without regard to their private information whereas high informed players always guess according to their private information. Equilibrium behavior implies that information cascades emerge in the group of low informed participants, the belief based solely on cascade guesses is stationary, and information cascades are systematically broken by high informed participants endowed with private information contradicting the cascade guesses. Experimental results show that the behavior of low informed participants is qualitatively in line with the equilibrium prediction. Information cascades often emerge in our experiments. The tendency of low informed participants to engage in cascade behavior increases with the number of identical guesses. Our main finding is that information cascades are not fragile. The behavior of high informed participants differs markedly from the equilibrium prediction. Only one-third of laboratory cascades are broken by high informed participants endowed with private information contradicting the cascade guesses. The relative frequency of cascade breaks is 15% for the situations where five or more identical guesses are observed. Participants’ elicited beliefs are strongly consistent with their own behavior and show that, unlike in equilibrium, the more cascade guesses participants observe the more they believe in the state favored by those guesses.     

Is it my money or not? An experiment on risk aversion and the house-money effect

The house-money effect, understood as people’s tendency to be more daring with easily-gotten money, is a behavioral pattern that poses questions about the external validity of experiments in economics: to what extent do people behave in experiments like they would have in a real-life situation, given that they play with easily-gotten house money? We ran an economic experiment with 122 students to measure the house-money effect on their risk preferences. They received an amount of money with which they made risky decisions involving losses and gains; a randomly selected treatment group received the money 21 days in advance and a control group got it the day of the experiment. From a simple calculation we found that participants in the treatment group only spent on average approximately 35 % of their cash in advance. The data confirms the well documented results that men are more tolerant to risk than women, and that individuals in general are more risk tolerant towards losses than towards gains. With our preferred specification, we find a mean CRRA risk aversion coefficient of 0.34, with a standard deviation of 0.09. Furthermore, if subjects in the treatment group spent 35 % of the endowment their CRRA risk aversion coefficient is higher than that of the control group by approximately 0.3 standard deviations. We interpret this result as evidence of a small and indirect house money effect operating though the amount of the cash in advance that was actually spent. We conclude that the house money effect may play a small role in decisions under uncertainty, especially when involving losses. Our novel design, however, could be used for other domains of decision making both in the lab and for calibration of economic models used in micro and macroeconomics.     

Payoff dominance and risk dominance in the observable delay game: a note

We examine whether the payoff dominant sequential-move (Stackelberg) outcome is realized when timing is endogenized. We adopt the observable delay game formulated by Hamilton and Slutsky [Games Econ Behav 2(1):29–46, 1990]. We find that if one sequential-move outcome is payoff dominant, either (i) the outcome both players prefer is the unique equilibrium; or (ii) two sequential-move outcomes are equilibria and the one both players prefer is risk dominant. In other words, no conflict between payoff dominance and risk dominance in the observable delay game exists, in contrast to other games such as (non pure) coordination games. We also find that even if one of two sequential-move outcomes is the unique equilibrium outcome in the observable delay game, it does not imply that the equilibrium outcome is payoff dominant to the other sequential-move outcome.      

When less information is good enough: experiments with global stag hunt games

There is mixed evidence on whether subjects coordinate on the efficient equilibrium in experimental stag hunt games under complete information. A design that generates an anomalously high level of coordination, Rankin et al. (Games Econo Behav 32(2):315–337, 2000), varies payoffs each period in repeated play rather than holding them constant. These payoff “perturbations” are eerily similar to those used to motivate the theory of global games, except the theory operates under incomplete information. Interestingly, that equilibrium selection concept is known to coincide with risk dominance, rather than payoff dominance. Thus, in theory, a small change in experimental design should produce a different equilibrium outcome. We examine this prediction in two treatments. In one, we use public signals to match Rankin et al. (2000)’s design; in the other, we use private signals to match the canonical example of global games theory. We find little difference between treatments, in both cases, subject play approaches payoff dominance. Our literature review reveals this result may have more to do with the idiosyncrasies of our complete information framework than the superiority of payoff dominance as an equilibrium selection principle.     

Bubbles and Crises

In recent financial crises a bubble, in which asset prices rise, is followed by a collapse and widespread default. Bubbles are caused by agency relationships in the banking sector. Investors use money borrowed from banks to invest in risky assets, which are relatively attractive because investors can avoid losses in low payoff states by defaulting on the loan. This risk shifting leads investors to bid up the asset prices. Risk can originate in both the real and financial sectors. Financial fragility occurs when positive credit expansion is insufficient to prevent a crisis.     

Technology adoption in markets with network effects: Theory and experimental evidence

We examine a technology-adoption game with network effects in which coordination on either technology A or technology B constitutes a Nash equilibrium. Coordination on technology B is assumed to be payoff dominant. We define a technology’s critical mass as the minimal share of users, which is necessary to make the choice of this technology the best response for any remaining user. We show that the technology with the lower critical mass implies risk dominance and selection by the maximin criterion. We present experimental evidence that both payoff dominance and risk dominance explain participants’ choices in the technology-adoption game. The relative riskiness of a technology can be proxied using either technologies’ critical masses or stand-alone values absent any network effects.     

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.     

On the willingness to pay to reduce risks of small losses

While willingness to pay is a common concept to measure the benefit gained from a reduction in the probability of loss, it is still questionable how it is linked to risk aversion and risk elimination behaviors, and how it is affected by the presence of an exogenous source of risk. By focusing only on risks of small losses, this article sheds light on these three issues and provides new results on the determinants of the willingness to pay.      

A semi-parametric approach to estimating the operational risk and Expected Shortfall

In this article, we propose improvements to the peak-over-threshold (POT) method and apply this improved method for modelling US business operational losses and estimating operational risks (ORs). In the widely used traditional POT method, the generalized Pareto distribution (GPD) is fitted to severity losses, while an empirical distribution is fitted to small to medium losses. Then, the Expected Loss and the 99.9% operational value-at-risk (OpVaR) are estimated. Additionally, the Expected Shortfall (ES) – a coherent risk measure – is estimated in this article as an alternative to OpVaR. These risk measures constitute the levels of regulatory and economic capitals to cover risks. With the improved POT method, the risks can be estimated more accurately than with the traditional POT method. The results indicate that the OpVaR are much lower than the ES and that the larger the tail losses the greater the difference between these two risk measures. Our findings imply that the ES would provide higher levels of capitals to cover risks than would the OpVaR, particularly during crises, and they have implications for the efficient OR management and regulators.     

Past Experiences,Personality Traits,and Risk Aversion: Evidence from Individual Risk Attitudes during the COVID-19 Pandemic

Individuals’ risk attitudes play an important role in economic decision making and policy evaluation, particularly in the midst of unprecedented uncertainty caused by the COVID-19 pandemic. We adopt a multiple-price-list elicitation method with real money incentives to measure precisely individuals’ risk attitudes at different stake levels and the extent to which they are affected by personal and social shocks following the COVID-19 outbreak in China. We find that subjects who had previously experienced negative personal shocks are more risk-averse at medium and large stakes but more risk loving at very small stakes. For our sample, COVID-19 has no significant impact on risk attitudes, as it is more likely to be regarded as a social shock. The result indicates that the impact of COVID-19 on individual risk attitudes is not as influential as expected, unless the individual’s personal life is affected directly.