An index of loss aversion

To a considerable extent, risk aversion as it is commonly observed is caused by loss aversion. Several indexes of loss aversion have been proposed in the literature. The one proposed in this paper leads to a clear decomposition of risk attitude into three distinct components: basic utility, probability weighting, and loss aversion. The index is independent of the unit of payment. The main theorem shows how the indexes of different decision makers can be compared through observed choices.     

Inter-temporal choices with temporal reference dependence

I develop an intertemporal choice model for rational deviators whose preferences depend not only on their actual consumption but also on comparison to their beliefs about the optimal consumption. The standard decision maker is loss averse with respect to this belief-dependent reference point. When psychologically weighted loss aversion is low, a decision maker deviates from the standard intertemporal choice behavior and over-consumption, as well as the alternative possibility of under-consumption can be rationalized. When the decision maker has time-varying degrees of loss aversion, he re-optimizes the consumption plan through adjusted beliefs as subsequent selves realize that past decision for the present period is no longer optimal. In the dynamic model, I solve for consistent intertemporal optimization rules by which a dynamic deviator should meet rational intertemporal consistency at each point in time. Finally, I demonstrate that the dynamic reference dependent model can solve a puzzling feature in lifecycle consumption data.     

Production and insurance under regret aversion

This paper examines the behavior of a regret-averse producer facing revenue risk. To insure against the revenue risk, the producer can purchase a coinsurance contract with an endogenously chosen coinsurance rate. Regret-averse preferences are characterized by a utility function that includes disutility from having chosen ex-post suboptimal alternatives. We show that the regret-averse producer never fully insures against the revenue risk even though the coinsurance contract is actuarially fair. When the producer is sufficiently regret averse and the loss probability is high, we further show that the regret-averse producer chooses not to purchase the actuarially fair coinsurance contract. Even when purchasing the actuarially fair coinsurance contract is optimal, we derive sufficient conditions under which the regret-averse producer reduces the optimal output level as compared to that without the coinsurance contract. These results are distinct from those under pure risk aversion, thereby making the consideration of regret aversion crucial.     

“Fair go” for all? Wealth and Risk Aversion of Australian Households*

A mean‐variance framework is applied to Australian household financial portfolios in order to provide estimates of relative risk aversion in the economy. Controlling for various socio‐economic characteristics, we explore whether risk aversion heterogeneity is a function of wealth heterogeneity. In contrast to most studies, we find evidence of very high risk aversion amongst the majority of households of poor households but vastly lower risk aversion amongst the high percentiles in the wealth distribution. Applying a first differences model across three survey waves spanning 2002 to 2010, we find that risk tolerance increases significantly with wealth. Risk tolerance is positively associated with mortgage payments, but rental payments have no relationship. In addition, we found no evidence that holding a university education has any discernible impact on risk aversion. Lastly, we present some preliminary findings as to the impact of financial advice on observed risk aversion. Financial advice is found to accentuating risk aversion, particularly amongst the wealthiest households. The findings have potential implications for the distribution of wealth in Australia that has received renewed interest recently.     

Greater prudence and greater downside risk aversion

Variation in the degree of downside risk aversion across decision makers has implications for efficient risk sharing. However, except for small differences in risk preferences, there is no index, analogous to the Arrow-Pratt index of risk aversion, that depends only on local properties of the utility function and indicates the degree of aversion to downside risk. A measure that does depend only on local properties of the utility function u, the index of prudence p=−u^?/u^″, is related to downside risk aversion, which is indicated by a positive value for u^?. Although we show that the degree of prudence is not an accurate indicator of the degree of downside risk aversion, we nonetheless demonstrate that a uniform increase in prudence accompanied by a uniform increase (decrease) in risk aversion is sufficient to indicate greater downside risk aversion, provided prudence is greater (less) than three times the degree of risk aversion.     

Convex and decreasing absolute risk aversion is proper

Proper risk aversion, a pivotal concept in the study of behavioral conditions on utility functions, states that an undesirable risk can never be made desirable by the presence of an independent risk. It is well known that standard risk aversion is sufficient for this concept. We show in this short article that convex and decreasing absolute risk aversion is an alternative sufficient condition.     

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.     

Risk aversion and optimal reserve prices in first- and second-price auctions

We analyze the effects of buyer and seller risk aversion in first- and second-price auctions in the classic setting of symmetric and independent private values. We show that the seller's optimal reserve price decreases in his own risk aversion, and more so in the first-price auction. The reserve price also decreases in the buyers' risk aversion in the first-price auction. Thus, greater risk aversion increases ex post efficiency in both auctions - especially that of the first-price auction. At the interim stage, the first-price auction is preferred by all buyer types in a lower interval, as well as by the seller.     

Greater downside risk aversion in the large

In this paper, we advance a definition of greater downside risk aversion that applies to both large and small changes in risk preference, and thereby complements the results for small changes reported previously. We show that a downside risk-averse transformation of a utility function results in a function that is more downside risk averse in the same manner that a risk-averse transformation increases risk aversion. Our demonstration is conducted first by using the compensated approach introduced by Diamond and Stiglitz [P. Diamond, J. Stiglitz, Increases in risk and in risk aversion, J. Econ. Theory 8 (1974) 337-360] and then by using an adaptation of the risk premium approach taken by Pratt [J. Pratt, Risk aversion in the small and in the large, Econometrica 32 (1964) 122-136].     

A note on comparative downside risk aversion

We provide comparative global conditions for downside risk aversion, which are similar to the ones studied by Ross for risk aversion. We define a coefficient of downside risk aversion, and study its local properties.     

Loss Aversion and Individual Characteristics

Many studies have shown that loss aversion affects the valuation of non-market goods. Using stated choice data, this paper presents an empirical investigation of how individual-level loss aversion varies with observable personal characteristics and with the choice context. We investigate loss aversion with respect to travel time and money, and find significant loss aversion in both dimensions. The degree of loss aversion in the time dimension is larger than in the money dimension, and depends on age and education. Subjects tend to be more loss averse when the reference is well established.     

Invariant risk attitudes

Concepts of constant absolute risk aversion and constant relative risk aversion have proved useful in the analysis of choice under uncertainty, but are quite restrictive, particularly when they are imposed jointly. A generalization of constant risk aversion, referred to as invariant risk aversion is developed. Invariant risk aversion is closely related to the possibility of representing preferences over state-contingent income vectors in terms of two parameters, the mean and a linearly homogeneous, translation-invariant index of riskiness. The best-known index with such properties is the standard deviation. The properties of the capital asset pricing model, usually expressed in terms of the mean and standard deviation, may be extended to the case of general invariant preferences.     

A little fairness may induce a lot of redistribution in democracy

We use a model of self-centered inequality aversion suggested by Fehr and Schmidt (Quart. J. Econom. 114 (3) (1999) 817) to study voting on redistribution. We theoretically identify two classes of conditions when an empirically plausible amount of fairness preferences induces redistribution through referenda. We test the predictions of the adapted inequality aversion model in a simple redistribution experiment and find that it predicts voting outcomes far better than the standard model of voting assuming rationality and strict self-interest.     

Wealth inequality and dynamic stability

We explore the link between wealth inequality and stability in a two-sector neoclassical growth model with heterogeneous agents. We show that when the inverse of absolute risk aversion (or risk tolerance) is a strictly convex function, wealth inequality is a factor that favors instability. In the opposite case, inequality favors stability. Our characterization also shows that whenever absolute risk tolerance is linear, as when preferences exhibit hyperbolic absolute risk aversion (HARA), wealth heterogeneity is neutral.     

First-price sealed-bid auctions when bidders exhibit different attitudes toward risk

When bidders have different risk aversion levels, we determine in a first-price auction, the asymmetric equilibrium strategies. We analyze the impact of asymmetric risk aversion levels on bidders’ markups and on the expected revenue and allocative efficiency of the auction.     

Risk aversion,prudence and temperance: An experiment in gain and loss

We characterize the individual's attitude towards risk, prudence and temperance in the gain and loss domains. We analyze the links between the three features of preferences for a given domain and between domains for each feature of preferences. Consequently, the reflection effect, the mixed risk aversion and the risk apportionment, are key concepts of our study. We also display some determinants for risk aversion, prudence and temperance in each domain. To do this, we conducted a lab experiment with students eliciting risk aversion, prudence and temperance in the two domains, and collected information about each subject's characteristics.     

Winner's curse without overbidding

We report the results of a series of second-price auction experiments where each bidder's signal is given by a normally distributed value plus a normally distributed error. While bidders’ values differ in one treatment they are the same in another, which allows for a direct test of the “winner's curse” irrespective of confounding factors. Bidders may also fall prey to a “news curse” when they do not sufficiently take into account that signals and errors are correlated. We find that the effects of the winner's curse are mitigated by a news curse and loss or risk aversion.     

Regret aversion and opportunity dependence

This paper provides an axiomatic model of decision making under uncertainty in which the decision maker is driven by anticipated ex post regrets. Our model allows both regret aversion and likelihood judgement over states to coexist. Also, we characterize two special cases, minimax regret with multiple priors that generalizes Savage's minimax regret, and a smooth model of regret aversion.     

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.     

Efficient allocations under ambiguity

Important implications of the expected utility hypothesis and risk aversion are that if agents have the same probability belief, then consumption plans in every efficient allocation of resources under uncertainty are comonotone with the aggregate endowment, and if their beliefs are concordant, then the consumption plans are measurable with respect to the aggregate endowment. We study these two properties of efficient allocations for models of preferences that exhibit ambiguity aversion using the concept of conditional beliefs, which we introduce in this paper. We provide characterizations of such conditional beliefs for the standard models of preferences used in applications.