Risk attitudes, randomization to treatment, and self-selection into experiments

Randomization to treatment is fundamental to statistical control in the design of experiments. However randomization implies some uncertainty about treatment condition, and individuals differ in their preferences towards taking on risk. Since human subjects often volunteer for experiments or are allowed to drop out of the experiment at any time if they want to, it is possible that the sample observed in an experiment might be biased because of the risk of randomization. On the other hand, the widespread use of a guaranteed show-up fee that is non-stochastic may generate sample selection biases of the opposite direction, encouraging more risk averse samples into experiments. We directly test these hypotheses that risk attitudes play a role in sample selection. Our results suggest that randomization bias does affect the overall level of risk aversion in the sample we observe, but that it does not affect the demographic mix of risk attitudes in the sample. We show that the common use of non-stochastic show-up fees can generate samples that are more risk averse than would otherwise have been observed.     

Range convexity and ambiguity averse preferences

We show that range convexity of beliefs, a `technical' condition that appears naturally in axiomatizations of preferences in a Savage-like framework, imposes some unexpected restrictions when modelling ambiguity averse preferences. That is, when it is added to a mild condition, range convexity makes the preferences collapse to subjective expected utility as soon as they satisfy structural conditions that are typically used to characterize ambiguity aversion. Received: February 25, 2000; revised version: April 17, 2000     

A SMOOTH AMBIGUITY MODEL OF THE COMPETITIVE FIRM

This paper examines the optimal production decision of the competitive firm under price uncertainty when the firm's preferences exhibit smooth ambiguity aversion. Ambiguity is modeled by a second‐order probability distribution that captures the firm's uncertainty about which of the subjective beliefs govern the price risk. Ambiguity preferences are modeled by the (second‐order) expectation of a concave transformation of the (first‐order) expected utility of profit conditional on each plausible subjective distribution of the price risk. Within this framework, we derive necessary and sufficient conditions under which the ambiguity‐averse firm optimally produces less in response either to the introduction of ambiguity or to greater ambiguity aversion when ambiguity prevails. In the case that the price risk is binary, we show that ambiguity and greater ambiguity aversion always adversely affect the firm's production decision.     

The Determinants of Risk Aversion: The Role of Intergenerational Transmission

This article studies the relationship between risk attitudes and individual characteristics focusing on the intergenerational transmission of risk preferences. We use a dataset of a sample of Italian students which allows us to build different measures of risk aversion based, respectively, on a survey asking students about their willingness to invest in a risky asset and about their preferences for job security and on the results of an entry test using explicit penalty points in the case of incorrect answers. In line with the findings highlighted by the existing literature, we find that women are more risk averse than men, more patient subjects are more risk averse, while high‐ability students are less risk averse. As far as intergenerational transmission of preferences is concerned, it emerges that students whose fathers are entrepreneurs have a higher propensity to take risks, while students whose fathers are employed in the public sector are more risk averse. Only fathers matter with regards to their children's risk attitudes. These results are robust to different measures of risk aversion and to different specifications of our model.     

Culture in Preferences for Income Equality and Safety Nets

Economic and social policies vary across countries, reflecting their cultures and shaping them. People in some countries are more loss averse than in others. People in some countries express stronger preferences for income equality than do people in others, and some countries offer stronger safety nets than others do. The cultural dimension of uncertainty avoidance expresses the degree to which people in a country feel uncomfortable with uncertainty and the way a country deals with the fact that the future can never be known. The author finds that uncertainty avoidance is associated with loss aversion. People are more loss averse in the domains of both portfolios and jobs in countries where uncertainty avoidance is high. Moreover, people in countries where uncertainty avoidance is high express stronger preferences for income equality, and social spending in such countries is high. The cultural dimension of power distance expresses the degree to which the less powerful members of a society accept and expect that power is distributed unequally. The author finds that people in countries where power distance is high express weaker preference for income equality, and social spending in such countries is low.     

Does decision error decrease with risk aversion?

There is substantial evidence that risky decision-making involves a stochastic error process. The literature has adopted different approaches to address this issue, however, risk preferences are not uniquely identified by the most popular methods; decision error is not predicted to monotonically decrease with risk aversion. This paper reports the results of an experiment that elicits risk preferences to identify risk averse individuals and evaluates the frequency the stochastically dominant of two lotteries is chosen. Risk averse subjects exhibit a strong preference for dominant lotteries. More importantly, violations are consistent with stochastic decision error that decreases with risk aversion.     

The Impact of Regret on Exports

We examine optimal production and export decisions of a firm facing exchange rate uncertainty, where the firm's management is not only risk averse but also regret averse, i.e., is characterized by a utility function that includes disutility from having chosen ex post suboptimal alternatives. Experimental and empirical results support the view that managers tend to be regret averse. Under regret aversion a negative risk premium need not preclude the firm from exporting which would be the case if the firm were only risk averse. Exporting creates an implicit hedge against the possibility of regret when the realized spot exchange rate turns out to be high. The regret‐averse firm as such has a greater ex ante incentive to export than the purely risk averse firm. Finally, we use a two‐state example to illustrate that the firm optimally exports more (less) to the foreign country than in the case of pure risk aversion if the low (high) spot exchange rate is more likely to prevail. Regret aversion as such plays a crucial role in determining the firm's optimal allocation between domestic sales and foreign exports.     

Completing the State Space with Subjective States

We define an opportunity act as a mapping from an exogenously given objective state space to a set of lotteries over prizes, and consider preferences over opportunity acts. We allow the preferences to be possibly uncertainty averse. Our main theorem provides an axiomatization of the maxmin expected utility model. In the theorem we construct subjective states to complete the objective state space. As in E. Dekel et al. (Econometrica, in press), we obtain a unique subjective state space. We also allow for preference for flexibility in some of the subjective states and commitment in others. Journal of Economic Literature Classification Number: D81.     

Staying ahead and getting even: Risk attitudes of experienced poker players

Frequent online poker players with extensive experience calculating probabilities and expected values might be expected to behave as Expected Utility maximizers, in that small shocks to their wealth would not affect risk preferences (Rabin, 2000). By contrast, reference-dependent loss aversion (as in Prospect Theory) (Koszegi and Rabin, 2006, Kahneman and Tversky, 1979) predicts that risk aversion decreases as wealth moves away from the reference point in either direction. In terms of continuing to play, as well as a more aggressive playing style, we find strong evidence for the break-even effect, the increased pursuit of risk as a player is losing within a session. Players' behavior also appears consistent with existing evidence on reference-dependent labor supply, in their tendency to reduce effort and risk-taking in response to being ahead. Our findings provide evidence for reference-dependent behavior in a flexible, high-skilled setting, under conditions of well-understood monetary risk.     

Preference for safety under the Choquet model: in search of a characterization

Victor prefers safety more than Ursula if whenever Ursula prefers a constant to an uncertain act, so does Victor. This paradigm, whose expected utility (EU) version is Arrow and Pratt’s more risk aversion concept, will be studied in the Choquet expected utility (CEU) model. Necessary condition Pointwise inequality between a function of the utility functions and another of the capacities is necessary and sufficient for the preference by Victor of safety over a dichotomous act whenever such is the preference of Ursula. However, increased preference for safety versus dichotomous acts does not imply preference by Victor of safety over a general act whenever such is the preference of Ursula. A counterexample will be provided, via the casino theory of Dubins and Savage. Sufficient condition Separation of the two functions by some convex function is sufficient for Victor to prefer safety more than Ursula, over general acts. Furthermore, a condition on the capacities will be presented for simplicity seeking, the preference by Victor over any act for some dichotomous act that leaves Ursula indifferent. This condition is met in particular if Victor’s capacity is a convex function of Ursula’s capacity. For these cases, the pointwise inequality (necessary) condition is a characterization of greater preference for safety, extending the Arrow–Pratt notion from EU to CEU and rank-dependent utility (RDU). These inequalities preserve the flavor of the “more pessimism than greediness” characterization of monotone risk aversion by Chateauneuf, Cohen and Meilijson in the RDU model and its extension by Grant and Quiggin to CEU. Preferences between safety and dichotomous acts are at the core of the biseparable preferences model of Ghirardato and Marinacci.     

Monotone risk aversion

Summary. This paper defines decreasing absolute risk aversion in purely behavioral terms without any assumption of differentiability and shows that a strictly increasing and risk averse utility function with decreasing absolute risk aversion is necessarily differentiable with an absolutely continuous derivative. A risk averse utility function has decreasing absolute risk aversion if and only if it has a decreasing absolute risk aversion density, and if and only if the cumulative absolute risk aversion function is increasing and concave. This leads to a characterization of all such utility functions. Analogues of these results also hold for increasing absolute and for increasing and decreasing relative risk aversion.Received: 31 January 2003, Revised: 15 January 2004, JEL Classification Numbers: D81.The views, thoughts and opinions expressed in this paper are those of the author in his individual capacity and should not in any way be attributed to Morgan Stanley or to Lars Tyge Nielsen as a representative, officer, or employee of Morgan Stanley.     

Efficient egalitarian equivalent allocations over a single good

This paper studies efficient and egalitarian allocations over a single heterogeneous and infinitely divisible good. We prove the existence of such allocations using only measure-theoretic arguments. Under the additional assumption of complete information, we identify a sufficient condition on agents’ preferences that makes it possible to apply the Pazner–Schmeidler rule for uniquely selecting an efficient egalitarian equivalent allocation. Finally, we exhibit a simple procedure that implements the Pazner–Schmeidler selection in a subgame-perfect equilibrium. We thank Gabrielle Demange, William Thomson, two referees and seminar audiences at Boston, Palermo and Rochester University for their comments. Financial support from MIUR is acknowledged.     

Dynamic variational preferences

We introduce and axiomatize dynamic variational preferences, the dynamic version of the variational preferences we axiomatized in [F. Maccheroni, M. Marinacci, A. Rustichini, Ambiguity aversion, robustness, and the variational representation of preferences, Mimeo, 2004], which generalize the multiple priors preferences of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141-153], and include the Multiplier Preferences inspired by robust control and first used in macroeconomics by Hansen and Sargent (see [L.P. Hansen, T.J. Sargent, Robust control and model uncertainty, Amer. Econ. Rev. 91 (2001) 60-66]), as well as the classic Mean Variance Preferences of Markovitz and Tobin. We provide a condition that makes dynamic variational preferences time consistent, and their representation recursive. This gives them the analytical tractability needed in macroeconomic and financial applications. A corollary of our results is that Multiplier Preferences are time consistent, but Mean Variance Preferences are not.     

Attitudes toward uncertainty and randomization: an experimental study

Subjects are randomization-loving if they prefer random mixtures of two bets to each of the involved bets. Various approaches appeal to such preferences in order to explain uncertainty aversion. We examine the relationship between uncertainty and randomization attitude experimentally. Our data suggest that they are not negatively associated: most uncertainty-averse subjects are randomization-neutral rather than loving. Surprisingly, a non-negligible number of uncertainty-averse subjects even seems to dislike randomization.     

The effect of ambiguity aversion on reward scheme choice

We test the implications of ambiguity aversion in a principal–agent problem with multiple agents. Models of ambiguity aversion suggest that, under ambiguity, comparative compensation schemes may become more attractive than independent wage contracts. We test this by presenting agents with a choice between comparative reward schemes and independent contracts, which are designed such that under uncertainty about output distributions (that is, under ambiguity), ambiguity averse agents should typically prefer comparative reward schemes, independent of their degree of risk aversion. We indeed find that the share of agents who choose the comparative scheme is higher under ambiguity.     

Ambiguity,uncertainty aversion and equilibrium welfare

Summary. In order to analyse the effect of ambiguity and uncertainty aversion on equilibrium welfare, a two period, pure exchange one good economy is considered. Agents are Choquet-expected-utility maximizers with same convex capacity and strictly concave utility index. It is proven that equilibrium is indeterminate whenever several probabilities in the core of the capacity minimize the expected value of aggregate endowment and not all agents have same expected endowments under those probabilities. It is further shown that small changes in aggregate endowment may have drastic welfare implications. A more general model is considered in the case of no aggregate uncertainty: agents have a set of priors and are uncertainty averse as modelled by Gilboa-Schmeidler [1989]. In the case of complete markets, it is shown that assets have a spread of equilibrium prices similar to the spread of no-arbitrage prices compatible with absence of arbitrage in markets with imperfections.Received: 2 June 2000, Revised: 27 March 2003, JEL Classification Numbers: D46, D59,D60, G12.I have benefited from conversations with L. Epstein, F. Magnien and J. M. Tallon.     

Context matters

Eliciting the level of risk aversion of experimental subjects is of crucial concern to experimenters. In the literature there are a variety of methods used for such elicitation; the concern of the experiment reported in this paper is to compare them. The methods we investigate are the following: Holt–Laury price lists; pairwise choices, the Becker–DeGroot–Marschak method; allocation questions. Clearly their relative efficiency in measuring risk aversion depends upon the numbers of questions asked; but the method itself may well influence the estimated risk-aversion. While it is impossible to determine a ‘best’ method (as the truth is unknown) we can look at the differences between the different methods. We carried out an experiment in four parts, corresponding to the four different methods, with 96 subjects. In analysing the data our methodology involves fitting preference functionals; we use four, Expected Utility and Rank-Dependent Expected Utility, each combined with either a CRRA or a CARA utility function. Our results show that the inferred level of risk aversion is more sensitive to the elicitation method than to the assumed-true preference functional. Experimenters should worry most about context.     

RISK AVERSION AND FIELD OF STUDY CHOICE: THE ROLE OF INDIVIDUAL ABILITY

Does the choice of field of study depend on individual risk aversion? The direction of the relationship between individual risk attitudes and type of university degree chosen is potentially ambiguous. On the one hand, risk averse individuals may prefer degree courses which allow high returns in the labour market; on the other hand, if these degrees expose students to a higher probability of dropping out, those who are more risk averse may be induced to choose less challenging fields. Using data from a sample of students enrolled at a middle‐sized Italian public university in 2009, we find that, controlling for a large number of individual characteristics, more risk averse students are more likely to choose any other field (Humanities, Engineering, and Sciences) rather than Social Sciences. We interpret this result bearing in mind that some of these fields, such as Humanities, involve a reduction in the risk of dropping out, while others (such as Engineering and Sciences) involve a lower risk in the labour market. It also emerges that the effect of risk aversion on degree choice is related to student ability. Risk averse students characterized by high abilities tend to prefer Engineering, while the propensity of risk averse students to enrol in Humanities decreases when ability increases, suggesting that the attention paid to labour market risks and drop‐out risk varies according to student skills.     

Optimal sequential contract with a risk‐averse supplier

We study optimal contracts in environments where a risk‐averse supplier discovers cost information privately and gradually over time: the supplier is privately informed about its cost uncertainty at the time of contracting and discovers the realization of cost condition privately after contracting and before production. We show that both the buyer and the supplier prefer more cost uncertainty when the supplier is not very risk‐averse but less cost uncertainty when the supplier is sufficiently risk‐averse. However, the buyer always prefers to contract before the cost uncertainty resolves regardless of the supplier's degree of risk aversion. The nature of the optimal contract also depends on the supplier's risk preference. A separating contract is optimal when the supplier is not very risk‐averse; however, a pooling contract, which offers the same contract terms regardless of the cost uncertainty, can be optimal when the supplier becomes sufficiently risk‐averse. Moreover, the optimal production schedule is often characterized by “inflexible rules.”     

风险冲击对农户经济决策的影响与正规小额信贷的作用

本文基于行为与实验经济学理论与方法，通过对吉林省3 445个农户开展的实地实验，使用双重差分评估了风险冲击对农户经济偏好与决策的因果效应。研究发现，风险冲击会使农户更加厌恶风险，回避高风险—高回报的生产投资策略，并加大农户对跨期时间偏好不一致的程度，从而降低农户的跨期决策效率。传统的新古典微观经济学对理性人拥有稳定偏好的假设至少在冲击后短期内并不成立。正规小额信贷可得性能够调节风险冲击，表现在：缓解个体尤其是男性、中老年或低教育水平人口在风险冲击下的焦虑、压力和负面情绪，从而促进农户面对风险冲击时的风险承担行为；降低女性的风险厌恶概率；缓解农户跨期时间贴现偏好不一致的程度；缓解中老年或资产贫困人口的损失厌恶程度。