Averting risk in the face of large losses: Bernoulli vs. Tversky and Kahneman

We experimentally question the assertion of Prospect Theory that people display risk attraction in choices involving high-probability losses. Indeed, our experimental participants tend to avoid fair risks for large (up to ? 90), high-probability (80%) losses. Our research hinges on a novel experimental method designed to alleviate the house-money bias that pervades experiments with real (not hypothetical) loses.Our results vindicate Daniel Bernoulli?s view that risk aversion is the dominant attitude,But, contrary to the Bernoulli-inspired canonical expected utility theory, we do find frequent risk attraction for small amounts of money at stake.In any event, we attempt neither to test expected utility versus nonexpected utility theories, nor to contribute to the important literature that estimates value and weighting functions. The question that we ask is more basic, namely: do people display risk aversion when facing large losses, or large gains? And, at the risk of oversimplifying, our answer is yes.

Multiple sclerosis decreases explicit counterfactual processing and risk taking in decision making.

INTRODUCTION: Deficits in decision making (DM) are commonly associated with prefrontal cortical damage, but may occur with multiple sclerosis (MS). There are no data concerning the impact of MS on tasks evaluating DM under explicit risk, where different emotional and cognitive components can be distinguished. METHODS: We assessed 72 relapsing-remitting MS (RRMS) patients with mild to moderate disease and 38 healthy controls in two DM tasks involving risk with explicit rules: (1) The Wheel of Fortune (WOF), which probes the anticipated affects of decisions outcomes on future choices; and (2) The Cambridge Gamble Task (CGT) which measures risk taking. Participants also underwent a neuropsychological and emotional assessment, and skin conductance responses (SCRs) were recorded. RESULTS: In the WOF, RRMS patients showed deficits in integrating positive counterfactual information (p<0.005) and greater risk aversion (p<0.001). They reported less negative affect than controls (disappointment: p = 0.007; regret: p = 0.01), although their implicit emotional reactions as measured by post-choice SCRs did not differ. In the CGT, RRMS patients differed from controls in quality of DM (p = 0.01) and deliberation time (p = 0.0002), the latter difference being correlated with attention scores. Such changes did not result in overall decreases in performance (total gains). CONCLUSIONS: The quality of DM under risk was modified by MS in both tasks. The reduction in the expression of disappointment coexisted with an increased risk aversion in the WOF and alexithymia features. These concomitant emotional alterations may have implications for better understanding the components of explicit DM and for the clinical support of MS patients.

Aversion Analysis

In this paper : a) the consumer’s problem is studied over two periods, the second one involving S states, and the consumer being endowed with S+1 incomes and having access to N financial assets; b) the consumer is then representable by a continuously differentiable system of demands, commodity demands, asset demands and desirabilities of incomes (the S+1 Lagrange multiplier of the S+1 constraints); c) the multipliers can be transformed into subjective Arrow prices; d) the effects of the various incomes on these Arrow prices decompose into a compensation effect (an Antonelli matrix) and a wealth effect; e) the Antonelli matrix has rank S-N, the dimension of incompleteness, if the consumer can financially adjust himself when facing income shocks; f) the matrix has rank S, if not; g) in the first case, the matrix represents a residual aversion; in the second case, a fundamental aversion; the difference between them is an aversion to illiquidity; this last relation corresponds to the Drèze-Modigliani decomposition (1972); h) the fundamental aversion decomposes also into an aversion to impatience and a risk aversion; i) the above decompositions span a third decomposition; if there exists a sure asset (to be defined, the usual definition being too specific), the fundamental aversion admits a three-component decomposition, an aversion to impatience, a residual aversion and an aversion to the illiquidity of risky assets; j) the formulas of the corresponding financial premiums are also presented.

A DSGE model with loss aversion in consumption and leisure: an explanation for business cycles asymmetries

In this chapter, an asymmetric DSGE model is built in order to account for asymmetries in business cycles. One of the most important contributions of this work is the construction of a general utility function which nests loss aversion, risk aversion and habits formation by means of a smooth transition function. The main idea behind this asymmetric utility function is that under recession the agents over-smooth consumption and leisure choices in order to prevent a huge deviation of them from the reference level of the utility; while under boom, the agents simply smooth consumption and leisure, but trying to be as far as possible from the reference level of utility. The simulations of this model by means of Perturbations Method show that it is possible to reproduce asymmetrical business cycles where recession (on shock) are stronger than booms and booms are more long-lasting than recession. One additional and unexpected result is a downward stickiness displayed by real wages. As a consequence of this, there is a more persistent fall in employment in recession than in boom. Thus, the model reproduces not only asymmetrical business cycles but also real stickiness and hysteresis.

Heterogeneity and the formation of risk - sharing coalitions

We offer a new explanation of partial risk sharing based on coalition formation and segmentation of society in a risky environment, without assuming limited commitment and imperfect information. Heterogenous individuals in a society freely choose with whom they will share risk. A partition belonging to the core of the membership game obtains. Perfect risk sharing does not necessarily arise. Focusing on mutual insurance rule and assuming that individuals only differ with respect to risk, we show that the core partition is homophily-based. The distribution of risk affects the number and size of these coalitions. Individuals may pay a lower risk premium in riskier societies. A higher heterogeneity in risk leads to a lower degree of risk sharing. We discuss how the endogenous partition of society into risk-sharing coalitions may shed light on empirical evidence on partial risk sharing. The case of heterogenous risk aversion leads to similar results.

Does uncertainty cause inertia in decision making? An experimental study of the role of regret aversion and indecisiveness

Previous research has shown that often there is clear inertia in individual decision making---that is, a tendency for decision makers to choose a status quo option. I conduct a laboratory experiment to investigate two potential determinants of inertia in uncertain environments: (i) regret aversion and (ii) ambiguity-driven indecisiveness. I use a between-subjects design with varying conditions to identify the effects of these two mechanisms on choice behavior. In each condition, participants choose between two simple real gambles, one of which is the status quo option. I find that inertia is quite large and that both mechanisms are equally important.

Risk, ambiguity, and diversification

Attitudes toward risk influence the decision to diversify among uncertain options. Yet, because in most situations the options are ambiguous, attitudes toward ambiguity may also play an important role. I conduct a laboratory experiment to investigate the effect of ambiguity on the decision to diversify. I find that diversification is more prevalent and more persistent under ambiguity than under risk. Moreover, excess diversification under ambiguity is driven by participants who stick with a status quo gamble when diversification among gambles is not feasible. This behavioral pattern cannot be accommodated by major theories of choice under ambiguity.

Bt cotton and production risk: Panel data evidence

The farm-level success of Bt-cotton in developing countries is well documented. However, the literature has only recently begun to recognise the importance of accounting for the effects of the technology on production risk, in addition to the mean effect estimated by previous studies. The risk effects of the technology are likely very important to smallholder farmers in the developing world due to their risk-aversion. We advance the emergent literature on Bt-cotton and production risk by using panel data methods to control for possible endogeneity of Bt-adoption. We estimate two models, the first a fixed-effects version of the Just and Pope model with additive individual and time effects, and the second a variation of the model in which inputs and variety choice are allowed to affect the variance of the time effect and its correlation with the idiosyncratic error. The models are applied to panel data on smallholder cotton production in India and South Africa. Our results suggest a risk-reducing effect of Bt-cotton in India, but an inconclusive picture in South Africa.

Accounting for the economic risk, caused by variation in disease severity, in fungicide dose decisions: exemplified for Mycosphaerella graminicola on winter wheat

A method is presented to calculate economic optimum fungicide doses accounting for the risk-aversion of growers responding to variability in disease severity between crops. Simple dose-response and disease-yield loss functions are used to estimate net disease-related costs (fungicide cost, plus disease-induced yield loss) as a function of dose and untreated severity. With fairly general assumptions about the shapes of the probability distribution of disease severity and the other functions involved, we show that a choice of fungicide dose which minimises net costs on average across seasons results in occasional large net costs caused by inadequate control in high disease seasons. This may be unacceptable to a grower with limited capital. A risk-averse grower can choose to reduce the size and frequency of such losses by applying a higher dose as insurance. For example, a grower may decide to accept ‘high loss’ years one year in ten or one year in twenty (i.e. specifying a proportion of years in which disease severity and net costs will be above a specified level). Our analysis shows that taking into account disease severity variation and risk-aversion will usually increase the dose applied by an economically rational grower. The analysis is illustrated with data on septoria tritici leaf blotch of wheat caused by Mycosphaerella graminicola. Observations from untreated field plots at sites across England over three years were used to estimate the probability distribution of disease severities at mid-grain filling. In the absence of a fully reliable disease forecasting scheme, reducing the frequency of ‘high loss’ years requires substantially higher doses to be applied to all crops. Disease resistant cultivars reduce both the optimal dose at all levels of risk and the disease-related costs at all doses.

The lottery-panel task for bi-dimensional parameter-free elicitation of risk attitudes

We propose first, a simple task for the eliciting attitudes toward risky choice, the SGG lottery-panel task, which consists in a series of lotteries constructed to compensate riskier options with higher risk-return trade-offs. Using Principal Component Analysis technique, we show that the SGG lottery-panel task is capable of capturing two dimensions of individual risky decision making i.e. subjects’ average risk taking and their sensitivity towards variations in risk-return. From the results of a large experimental dataset, we confirm that the task systematically captures a number of regularities such as: A tendency to risk averse behavior (only around 10% of choices are compatible with risk neutrality); An attraction to certain payoffs compared to low risk lotteries, compatible with over-(under-) weighting of small (large) probabilities predicted in PT and; Gender differences, i.e. males being consistently less risk averse than females but both genders being similarly responsive to the increases in risk-premium. Another interesting result is that in hypothetical choices most individuals increase their risk taking responding to the increase in return to risk, as predicted by PT, while across panels with real rewards we see even more changes, but opposite to the expected pattern of riskier choices for higher risk-returns. Therefore, we conclude from our data that an “economic anomaly” emerges in the real reward choices opposite to the hypothetical choices. These findings are in line with Camerer's (1995) view that although in many domains, paid subjects probably do exert extra mental effort which improves their performance, choice over money gambles is not likely to be a domain in which effort will improve adherence to rational axioms (p. 635). Finally, we demonstrate that both dimensions of risk attitudes, average risk taking and sensitivity towards variations in the return to risk, are desirable not only to describe behavior under risk but also to explain behavior in other contexts, as illustrated by an example. In the second study, we propose three additional treatments intended to elicit risk attitudes under high stakes and mixed outcome (gains and losses) lotteries. Using a dataset obtained from a hypothetical implementation of the tasks we show that the new treatments are able to capture both dimensions of risk attitudes. This new dataset allows us to describe several regularities, both at the aggregate and within-subjects level. We find that in every treatment over 70% of choices show some degree of risk aversion and only between 0.6% and 15.3% of individuals are consistently risk neutral within the same treatment. We also confirm the existence of gender differences in the degree of risk taking, that is, in all treatments females prefer safer lotteries compared to males. Regarding our second dimension of risk attitudes we observe, in all treatments, an increase in risk taking in response to risk premium increases. Treatment comparisons reveal other regularities, such as a lower degree of risk taking in large stake treatments compared to low stake treatments and a lower degree of risk taking when losses are incorporated into the large stake lotteries. Results that are compatible with previous findings in the literature, for stake size effects (e.g., Binswanger, 1980; Antoni Bosch-Domènech & Silvestre, 1999; Hogarth & Einhorn, 1990; Holt & Laury, 2002; Kachelmeier & Shehata, 1992; Kühberger et al., 1999; B. J. Weber & Chapman, 2005; Wik et al., 2007) and domain effect (e.g., Brooks and Zank, 2005, Schoemaker, 1990, Wik et al., 2007). Whereas for small stake treatments, we find that the effect of incorporating losses into the outcomes is not so clear. At the aggregate level an increase in risk taking is observed, but also more dispersion in the choices, whilst at the within-subjects level the effect weakens. Finally, regarding responses to risk premium, we find that compared to only gains treatments sensitivity is lower in the mixed lotteries treatments (SL and LL). In general sensitivity to risk-return is more affected by the domain than the stake size. After having described the properties of risk attitudes as captured by the SGG risk elicitation task and its three new versions, it is important to recall that the danger of using unidimensional descriptions of risk attitudes goes beyond the incompatibility with modern economic theories like PT, CPT etc., all of which call for tests with multiple degrees of freedom. Being faithful to this recommendation, the contribution of this essay is an empirically and endogenously determined bi-dimensional specification of risk attitudes, useful to describe behavior under uncertainty and to explain behavior in other contexts. Hopefully, this will contribute to create large datasets containing a multidimensional description of individual risk attitudes, while at the same time allowing for a robust context, compatible with present and even future more complex descriptions of human attitudes towards risk.

Responsibility effects in decision making under risk

We systematically explore decision situations in which a decision maker bears responsibility for somebody else's outcomes as well as for her own in situations of payoff equality. In the gain domain we confirm the intuition that being responsible for somebody else's payoffs increases risk aversion. This is however not attributable to a 'cautious shift' as often thought. Indeed, looking at risk attitudes in the loss domain, we find an increase in risk seeking under responsibility. This raises issues about the nature of various decision biases under risk, and to what extent changed behavior under responsibility may depend on a social norm of caution in situations of responsibility versus naive corrections from perceived biases. To further explore this issue, we designed a second experiment to explore risk-taking behavior for gain prospects offering very small or very large probabilities of winning. For large probabilities, we find increased risk aversion, thus confirming our earlier finding. For small probabilities however, we find an increase of risk seeking under conditions of responsibility. The latter finding thus discredits hypotheses of a social rule dictating caution under responsibility, and can be explained through flexible self-correction models predicting an accentuation of the fourfold pattern of risk attitudes predicted by prospect theory. An additional accountability mechanism does not change risk behavior, except for mixed prospects, in which it reduces loss aversion. This indicates that loss aversion is of a fundamentally different nature than probability weighting or utility curvature. Implications for debiasing are discussed.

The effect of accountability on loss aversion.

This paper investigates the effect of accountability-the expectation on the side of the decision maker of having to justify his/her decisions to somebody else-on loss aversion. Loss aversion is commonly thought to be the strongest component of risk aversion. Accountability is found to reduce the bias of loss aversion. This effect is explained by the higher cognitive effort induced by accountability, which triggers a rational check on emotional reactions at the base of loss aversion, leading to a reduction of the latter. Connections to dual-processing models are discussed.

Risk taking of executives under different incentive contracts: experimental evidence

Classic financial agency theory recommends compensation through stock options rather than shares to counteract excessive risk aversion in agents. In a setting where any kind of risk taking is suboptimal for shareholders, we show that excessive risk taking may occur for one of two reasons: risk preferences or incentives. Even when compensated through restricted company stock, experimental CEOs take large amounts of excessive risk. This contradicts classical financial theory, but can be explained through risk preferences that are not uniform over the probability and outcome spaces, and in particular, risk seeking for small probability gains and large probability losses. Compensation through options further increases risk taking as expected. We show that this effect is driven mainly by the personal asset position of the experimental CEO, thus having deleterious effects on company performance.

The trade-off between incentives and endogenous risk

Standard models of moral hazard predict a negative relationship between risk and incentives, but the empirical work has not confirmed this prediction. In this paper, we propose a model with adverse selection followed by moral hazard, where effort and the degree of risk aversion are private information of an agent who can control the mean and the variance of profits. For a given contract, more risk-averse agents suppIy more effort in risk reduction. If the marginal utility of incentives decreases with risk aversion, more risk-averse agents prefer lower-incentive contractsj thus, in the optimal contract, incentives are positively correlated with endogenous risk. In contrast, if risk aversion is high enough, the possibility of reduction in risk makes the marginal utility of incentives increasing in risk aversion and, in this case, risk and incentives are negatively related.

Evidence on the relationship between incentives and exogenous risk

Theoretical models on moral hazard provide competing predictions on the incentive-risk relationship. These predictions are derived under the assumptions of homogeneous agents and exogenous risk. However, the existing empirical evidence does not account for risk-aversion heterogeneity and risk endogeneity. This paper uses a well-built database on tenancy contracts to address these issues. Detailed information on cropping activities is used to measure the exogenous risk. Risk-aversion heterogeneity and other self-selection problems are addressed through a portfolio schedule and a subsample of farmers who simultaneously own and sharecrop different farms. This controlled exercise finds a direct relation between incentives and exogenous risk.