Ambiguity aversion and the propensities for self-insurance and self-protection

Two models of ambiguity preferences that permit comparative statics analysis of greater ambiguity aversion yield definite predictions concerning propensities for self-insurance and self-protection: The levels of both activities that are optimal for an ambiguity-averse decision maker are higher in the presence of ambiguity than in its absence, and demands for both activities increase with greater ambiguity aversion. The reason is that, at levels optimal for one decision maker, an increase in either activity results in a mean-preserving contraction in the distribution of expected utility in the presence of ambiguity, which is valuable to anyone with the same risk preferences who is more ambiguity averse.     

Recursive expected utility and the separation of attitudes towards risk and ambiguity: an experimental study

We use the multiple price list method and a recursive expected utility theory of smooth ambiguity to separate out attitude towards risk from that towards ambiguity. Based on this separation, we investigate if there are differences in agent behaviour under uncertainty over gain amounts vis-a-vis uncertainty over loss amounts. On an aggregate level, we find that (i) subjects are risk averse over gains and risk seeking over losses, displaying a “reflection effect” and (ii) they are ambiguity neutral over gains and are mildly ambiguity seeking over losses. Further analysis shows that on an individual level, and with respect to both risky and ambiguous prospects, there is limited incidence of a reflection effect where subjects are risk/ambiguity averse (seeking) in gains and seeking (averse) in losses, though this incidence is higher for ambiguous prospects. A very high proportion of such cases of reflection exhibit risk (ambiguity) aversion in gains and risk (ambiguity) seeking in losses, with the reverse effect being significantly present in the case of risk but almost absent in case of ambiguity. Our results suggest that reflection across gains and losses is not a stable individual characteristic, but depends upon whether the form of uncertainty is precise or ambiguous, since we rarely find an individual who exhibits reflection in both risky and ambiguous prospects. We also find that correlations between attitudes towards risk and ambiguity were domain dependent.      

Stability of risk preferences and the reflection effect of prospect theory

Are risk preferences stable over time? To address this question we elicit risk preferences from the same pool of subjects at two different moments in time. To interpret the results, we use a Fechner stochastic choice model in which the revealed preference of individuals is governed by some underlying preference, together with a random error. We take cumulative prospect theory as the underlying preference model (Kahneman and Tversky, Econometrica 47:263–292, 1979; Tversky and Kahneman, Journal of Risk and Uncertainty 5:297–323, 1992). We observe that the aggregate pattern of preferences is very similar in both sessions, and it matches the results reported in the literature. Most subjects are risk averse for gains, and risk seeking for losses. However, the subjects that jointly agree with the reflection effect of prospect theory are around 50%. The percentage of individuals that change their responses across sessions is quite high, 63%. Estimating the stochastic choice model we find that 72% of the subjects have an underlying preference which agrees with the reflection effect of prospect theory. The remaining 28% are mainly classified as risk averse for both gains and losses. The results reinforce the empirical validity of the reflection effect. Deviations from the reflection effect can be attributed to noise, as well as to the existence of a fraction of risk averse subjects.     

Measuring ambiguity attitude: (Extended) multiplier preferences for the American and the Dutch population

Empirical studies of ambiguity aversion often use measures that are not grounded in theory. This paper shows how a theoretically-founded measure of ambiguity aversion can be derived from Hansen and Sargent’s theory of multiplier preferences. Multiplier preferences are used in macroeconomics to capture model uncertainty. At the micro level, they have not been applied yet, because they do not permit ambiguity seeking, which is usually observed for a substantial proportion of subjects. We give a preference foundation for (extended) multiplier preferences accommodating both ambiguity aversion and ambiguity seeking and we propose a simple method to measure them using matching probabilities. We illustrate our method in two large representative samples (Dutch and American) and obtain the first micro estimates of multiplier preferences.     

Stake effects on ambiguity attitudes for gains and losses

We test the effect of stake size on ambiguity attitudes. Compared to a baseline condition, we find subjects to be more ambiguity seeking for small-probability gains and large-probability losses under high stakes. They are also more ambiguity averse for large-probability gains and small-probability losses. We trace these effects back to stake effects on decisions under risk (known probabilities) and uncertainty (unknown probabilities). For risk, we replicate previous findings. For uncertainty, we find an increase in probabilistic insensitivity under high stakes that is driven by increased uncertainty aversion for large-probability gains and for small-probability losses.     

Time preferences and risk aversion: Tests on domain differences

Understanding how individuals discount and evaluate the risks of environmental outcomes is a prime component in designing effective environmental policy. We use an incentivized experimental design to investigate whether subjects’ time preferences and risk aversion across the monetary and environmental domains differ. We find that subjects’ time preferences are not significantly different across the two domains. In contrast, subjects exhibit a higher degree of risk aversion in the environmental domain. Furthermore, we corroborate earlier results, documenting that women are more risk averse than men in the monetary domain, and show this finding to also hold in the environmental domain.     

Subjective beliefs and confidence when facts are forgotten

Forgetting can be a salient source of uncertainty for subjective beliefs, confidence, and ambiguity attitudes. To investigate this, we run several experiments where people bet on propositions (facts) that they cannot recall with certainty. We use betting preferences to infer subjects’ revealed beliefs and their revealed confidence in these beliefs. Forgetting is induced via interference tasks and time delays (up to one year). We observe a natural memory decay pattern where beliefs become less accurate and confidence is reduced as well. Moreover, we find a form of comparative ignorance where subjects are more ambiguity averse when they cannot recall the truth rather than never having learnt it. In a different vein, we identify an overconfidence pattern: on average, subjects overpay for bets on propositions that they believe in, but underpay for the opposite bets. We formulate a two-signal behavioral model of forgetting that generates all of these patterns. It suggests new testable hypotheses that are confirmed by our data.

     

Ambiguity and risk taking in organizations

Kunreuther, Meszaros, and Hogarth (1993) argue that insurers are risk averse and ambiguity averse, and that they use cognitive reference points and constraints in making pricing decisions. They further claim that insurer ambiguity may be a factor that has a role in market failure at the industry level. Arguably, ambiguity may be an important aspect of decision behavior. In this article, research on managerial risk taking is reviewed with a focus on the relationship between ambiguity and risk taking. In particular, the effects of the organizational and institutional context are highlighted. It is argued that the political aspects of insurer decision behavior should be considered as well. Implications for further study and understanding of decision making are discussed.     

Ambiguity attitudes and social interactions: An experimental investigation

This paper reports the results of experiments testing prevalence of non-neutral ambiguity attitudes and how these attitudes change as a result of interpersonal interactions. To address the first question we conducted experiments involving individual choice between betting on ambiguous and unambiguous events of the subject’s choice. We found that a large majority of subjects display ambiguity neutral attitudes, many others display ambiguity incoherent attitudes, and few subjects display either ambiguity-averse attitudes or ambiguity-seeking attitudes. To address the second question we designed a new experiment with a built-in incentive to persuade. We found that interpersonal interactions without incentives to persuade have no effect on behavior. However, when incentives were introduced, the ambiguity neutral subjects were better able to persuade ambiguity seeking and ambiguity incoherent subjects to adopt ambiguity neutral choice behavior and, to a lesser extent, also ambiguity averse subjects.     

Granny Versus Game Theorist: Ambiguity in Experimental Games

We report on an experiment in which subjects choose actions in strategic games with either strategic complements or substitutes against a granny, a game theorist or other subjects. The games are selected in order to test predictions on the comparative statics of equilibrium with respect to changes in strategic ambiguity. We find that subjects face higher ambiguity while playing against the granny than playing against the game theorist if we assume that subjects are ambiguity averse. Moreover, under the same assumption, subjects choose more secure actions in games more prone to ambiguity which is in line with the predictions.      

Ambiguity aversion in multi-armed bandit problems

In multi-armed bandit problems, information acquired from experimentation is valuable because it tells the agent whether to select a particular option again in the future. This article tests whether people undervalue this information because they are ambiguity averse, or have a distaste for uncertainty about the average quality of each alternative. It is shown that ambiguity averse agents have lower than optimal Gittins indexes, appearing to undervalue information from experimentation, but are willing to pay more than ambiguity neutral agents to learn the true mean of the payoff distribution, appearing to overvalue objectively given information. This prediction is tested with a laboratory experiment that elicits a Gittins index and a willingness to pay on six two-armed bandits. Consistent with the predictions of ambiguity aversion, the Gittins indexes are significantly lower than optimal and willingnesses to pay are significantly higher than optimal.     

Normalized measures of concavity and Ross’s strongly more risk averse order

The Arrow-Pratt (A-P) definitions of absolute and relative risk aversion dominate the discussion of risk aversion and defining “more risk averse”. Ross (Econometrica 49:621–663, 1981) notes, however, that being A-P more risk averse is not sufficient for addressing many important comparative static questions. Consequently he introduces “a new and stronger measure for comparing two agents’ attitudes towards risk…”. Ross does not provide a corresponding measure of risk aversion. This paper uses a normalized measure of concavity to characterize the Ross definition of strongly more risk averse on bounded intervals. Other properties and uses of these normalized measures of concavity are also presented.     

Ambiguity aversion under maximum-likelihood updating

Maximum-likelihood updating (MLU) is a well-known approach for extending static ambiguity sensitive preferences to dynamic set-ups. This paper develops an example in which MLU induces an ambiguity averse maxmin expected utility (MEU) decision-maker to (1) prefer a bet on an ambiguous over a risky urn and (2) be more willing to bet on the ambiguous urn compared to an (ambiguity neutral) subjective expected utility (SEU) decision-maker. This is challenging, since prior to observing (symmetric) draws from the urns, the MEU decision-maker (in line with the usual notion of ambiguity aversion) actually preferred the risky over the ambiguous bet and was less willing to bet on the ambiguous urn than the SEU decision-maker. The identified switch in betting preferences is not due to a violation of dynamic consistency or consequentialism. Rather, it results from MLU’s selection of extreme priors, causing a violation of the stability of set inclusion over the course of the updating process.     

School environment and risk preferences: Experimental evidence

Using a field experiment with high school students, we evaluate the development of risk preferences. Examining the impact of school characteristics on preference development reveals both peer and quality effects. For the peer effect, individuals in schools with a higher percentage of students on free or reduced lunches (hence a higher proportion of low-income peers with whom to interact) are significantly more risk averse. For the quality effect, individuals in schools with smaller class sizes and a higher percentage of educators with advanced degrees have higher, more moderate levels of risk aversion. We further discuss economic, cognitive and emotional development theories of risk preferences. Data show demographic-related patterns: girls are more risk averse on average, while taller and nonwhite individuals are more risk tolerant.     

A simplified axiomatic approach to ambiguity aversion

This paper takes the Anscombe–Aumann framework with horse and roulette lotteries, and applies the Savage axioms to the horse lotteries and the von Neumann–Morgenstern axioms to the roulette lotteries. The resulting representation of preferences yields a subjective probability measure over states and two utility functions, one governing risk attitudes and one governing ambiguity attitudes. The model is able to accommodate the Ellsberg paradox and preferences for reductions in ambiguity.     

Risk aversion and religion

We use a dataset for a demographically representative sample of the Dutch population that contains a revealed preference risk attitude measure, as well as detailed information about participants’ religious background, to study three issues. First, we find strong confirmatory evidence that more religious people, as measured by church membership or attendance, are more risk averse with regard to financial risks. Second, we obtain some evidence that Protestants are more risk averse than Catholics in such tasks. Third, our data suggest that the link between risk aversion and religion is driven by social aspects of church membership, rather than by religious beliefs themselves.     

Hard evidence and ambiguity aversion

This article shows that if an allocation rule can be implemented with unlimited information certification, then it can also be implemented with limited information certification if the designer can use ambiguous communication mechanisms, and if agents are averse to ambiguity in the sense of maxmin expected utility. The reverse implication is true if there is a single agent and a worst outcome.     

Preference Reversals and Induced Risk Preferences: Evidence for Noisy Maximization

We combine two research lines: preference reversal research (Lichtenstein and Slovic, 1971) and research on lottery-based risk preference induction (Roth and Malouf, 1979). Our results are informative for both research lines. We show that inducing risk preferences in preference reversal experiments has dramatic effects. First, while our subjects still display reversals, they do not display the usual pattern of predicted reversals suggested by the compatibility hypothesis. By inducing risk averse and risk loving preferences, we can dramatically reduce reversal rates and even produce the opposite pattern of reversals. Our results are consistent with the assumption that subjects maximize expected utility with error. This provides evidence that Camerer and Hogarth's (1999) framework for incentive effects can be extended to include the risk preference induction reward scheme.     

Measuring ambiguity preferences: A new ambiguity preference survey module

Journal of Risk and Uncertainty - Ambiguity preferences are important to explain human decision-making in many areas in economics and finance. To measure individual ambiguity preferences, the...     

On probabilities and loss aversion

This paper reviews the most common approaches that have been adopted to analyze and describe loss aversion under prospect theory. Subsequently, it is argued that loss aversion is a property of observable choice behavior and two new definitions of loss averse behavior are advocated. Under prospect theory, the new properties hold if the commonly used utility based measures of loss aversion are corrected by a probability based measure of loss aversion and their product exceeds 1. It is shown that prominent parametric families of weighting functions, while successful in accommodating empirical findings on probabilistic risk attitudes, may not fit well with the theoretical implications of the new loss averse behavior conditions.