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Risk Aversion and Expected Utility Theory: A Calibration Theorem
TL;DR: Within the expected-utility framework, the only explanation for risk aversion is that the utility function for wealth is concave: a person has lower marginal utility for additional wealth when she is wealthy than when he is poor as discussed by the authors.
Abstract: Within the expected-utility framework, the only explanation for risk aversion is that the utility function for wealth is concave: A person has lower marginal utility for additional wealth when she is wealthy than when she is poor. This paper provides a theorem showing that expected-utility theory is an utterly implausible explanation for appreciable risk aversion over modest stakes: Within expected-utility theory, for any concave utility function, even very little risk aversion over modest stakes implies an absurd degree of risk aversion over large stakes. Illustrative calibrations are provided. June 2000
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TL;DR: In this paper, the authors discuss the discounted utility (DU) model, its historical development, underlying assumptions, and "anomalies" -the empirical regularities that are inconsistent with its theoretical predictions.
Abstract: This paper discusses the discounted utility (DU) model: its historical development, underlying assumptions, and "anomalies" - the empirical regularities that are inconsistent with its theoretical predictions. We then summarize the alternate theoretical formulations that have been advanced to address these anomalies. We also review three decades of empirical research on intertemporal choice, and discuss reasons for the spectacular variation in implicit discount rates across studies. Throughout the paper, we stress the importance of distinguishing time preference, per se, from many other considerations that also influence intertemporal choices.
5,242 citations
TL;DR: In this article, a menu of paired lottery choices is structured so that the crossover point to the high-risk lottery can be used to infer the degree of risk aversion, and a hybrid "power/expo" utility function with increasing relative and decreasing absolute risk aversion is presented.
Abstract: A menu of paired lottery choices is structured so that the crossover point to the high-risk lottery can be used to infer the degree of risk aversion With normal laboratory payoffs of several dollars, most subjects are risk averse and few are risk loving Scaling up all payoffs by factors of twenty, fifty, and ninety makes little difference when the high payoffs are hypothetical In contrast, subjects become sharply more risk averse when the high payoffs are actually paid in cash A hybrid "power/expo" utility function with increasing relative and decreasing absolute risk aversion nicely replicates the data patterns over this range of payoffs from several dollars to several hundred dollars
4,687 citations
TL;DR: This paper introduced a three-item Cognitive Reflection Test (CRT) as a simple measure of one type of cognitive ability, i.e., the ability or disposition to reflect on a question and resist reporting the first response that comes to mind.
Abstract: This paper introduces a three-item "Cognitive Reflection Test" (CRT) as a simple measure of one type of cognitive ability—the ability or disposition to reflect on a question and resist reporting the first response that comes to mind. The author will show that CRT scores are predictive of the types of choices that feature prominently in tests of decision-making theories, like expected utility theory and prospect theory. Indeed, the relation is sometimes so strong that the preferences themselves effectively function as expressions of cognitive ability—an empirical fact begging for a theoretical explanation. The author examines the relation between CRT scores and two important decision-making characteristics: time preference and risk preference. The CRT scores are then compared with other measures of cognitive ability or cognitive "style." The CRT scores exhibit considerable difference between men and women and the article explores how this relates to sex differences in time and risk preferences. The final section addresses the interpretation of correlations between cognitive abilities and decision-making characteristics.
3,902 citations
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TL;DR: In this paper, reference-dependent gain-loss utility is combined with standard economic consumption utility, and a consumer's willingness to pay for a good is endogenously determined by the market distribution of prices and how she expects to respond to these prices.
Abstract: We develop a model that fleshes out, extends, and modifies existing models of reference dependent preferences and loss aversion while accomodating most of the evidence motivating these models. Our approach makes reference-dependent theory more broadly applicable by avoiding some of the ways that prevailing models—if applied literally and without ancillary assumptions—make variously weak and incorrect predictions. Our model combines the reference-dependent gain-loss utility with standard economic “consumption utility†and clarifies the relationship between the two. Most importantly, we posit that a person’s reference point is her recent expectations about outcomes (rather than the status quo), and assume that behavior accords to a personal equilibrium: The person maximizes utility given her rational expectations about outcomes, where these expectations depend on her own anticipated behavior. We apply our theory to consumer behavior, and emphasize that a consumer’s willingness to pay for a good is endogenously determined by the market distribution of prices and how she expects to respond to these prices. Because a buyer’s willingness to buy depends on whether she anticipates buying the good, for a range of market prices there are multiple personal equilibria. This multiplicity disappears when the consumer is sufficiently uncertain about the price she will face. Because paying more than she anticipated induces a sense of loss in the buyer, the lower the prices at which she expects to buy the lower will be her willingness to pay. In some situations, a known stochastic decrease in prices can even lower the quantity demanded.
1,968 citations
TL;DR: In this article, the authors present experimental evidence in support of an additional factor: women may be less effective than men in competitive environments, even if they are able to perform similarly in non-competitive environments.
Abstract: Even though the provision of equal opportunities for men and women has been a priority in many countries, large gender differences prevail in competitive high-ranking positions. Suggested explanations include discrimination and differences in preferences and human capital. In this paper we present experimental evidence in support of an additional factor: women may be less effective than men in competitive environments, even if they are able to perform similarly in non-competitive environments. In a laboratory experiment we observe, as we increase the competitiveness of the environment, a significant increase in performance for men, but not for women. This results in a significant gender gap in performance in tournaments, while there is no gap when participants are paid according to piece rate. This effect is stronger when women have to compete against men than in single-sex competitive environments: this suggests that women may be able to perform in competitive environments per se.
1,943 citations
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TL;DR: In this paper, the authors present a critique of expected utility theory as a descriptive model of decision making under risk, and develop an alternative model, called prospect theory, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights.
Abstract: This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory. Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory. In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses. In addition, people generally discard components that are shared by all prospects under consideration. This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights. The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. Decision weights are generally lower than the corresponding probabilities, except in the range of low prob- abilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling. EXPECTED UTILITY THEORY has dominated the analysis of decision making under risk. It has been generally accepted as a normative model of rational choice (24), and widely applied as a descriptive model of economic behavior, e.g. (15, 4). Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory (47, 36), and that most people actually do, most of the time. The present paper describes several classes of choice problems in which preferences systematically violate the axioms of expected utility theory. In the light of these observations we argue that utility theory, as it is commonly interpreted and applied, is not an adequate descriptive model and we propose an alternative account of choice under risk. 2. CRITIQUE
35,067 citations
TL;DR: In this article, the authors present a reference-dependent theory of consumer choice, which explains such effects by a deformation of indifference curves about the reference point, in which losses and disadvantages have greater impact on preferences than gains and advantages.
Abstract: Much experimental evidence indicates that choice depends on the status quo or reference level: changes of reference point often lead to reversals of preference. We present a reference-dependent theory of consumer choice, which explains such effects by a deformation of indifference curves about the reference point. The central assumption of the theory is that losses and disadvantages have greater impact on preferences than gains and advantages. Implications of loss aversion for economic behavior are considered. The standard models of decision making assume that preferences do not depend on current assets. This assumption greatly simplifies the analysis of individual choice and the prediction of trades: indifference curves are drawn without reference to current holdings, and the Coase theorem asserts that, except for transaction costs, initial entitlements do not affect final allocations. The facts of the matter are more complex. There is substantial evidence that initial entitlements do matter and that the rate of exchange between goods can be quite different depending on which is acquired and which is given up, even in the absence of transaction costs or income effects. In accord with a psychological analysis of value, reference levels play a large role in determining preferences. In the present paper we review the evidence for this proposition and offer a theory that generalizes the standard model by introducing a reference state. The present analysis of riskless choice extends our treatment of choice under uncertainty [Kahneman and Tversky, 1979, 1984; Tversky and Kahneman, 1991], in which the outcomes of risky prospects are evaluated by a value function that has three essential characteristics. Reference dependence: the carriers of value are gains and losses defined relative to a reference point. Loss aversion: the function is steeper in the negative than in the positive domain; losses loom larger than corresponding gains. Diminishing sensitivity: the marginal value of both gains and losses decreases with their
5,864 citations
TL;DR: A wine-loving economist we know purchased some nice Bordeaux wines years ago at low prices as discussed by the authors, but would neither be willing to sell the wine at the auction price nor buy an additional bottle at that price.
Abstract: A wine-loving economist we know purchased some nice Bordeaux wines years ago at low prices. The wines have greatly appreciated in value, so that a bottle that cost only $10 when purchased would now fetch $200 at auction. This economist now drinks some of this wine occasionally, but would neither be willing to sell the wine at the auction price nor buy an additional bottle at that price. Thaler (1980) called this pattern—the fact that people often demand much more to give up an object than they would be willing to pay to acquire it—the endowment effect. The example also illustrates what Samuelson and Zeckhauser (1988) call a status quo bias, a preference for the current state that biases the economist against both buying and selling his wine. These anomalies are a manifestation of an asymmetry of value that Kahneman and Tversky (1984) call loss aversion—the disutility of giving up an object is greater that the utility associated with acquiring it. This column documents the evidence supporting endowment effects and status quo biases, and discusses their relation to loss aversion.
4,025 citations
TL;DR: Mehra and Prescott as mentioned in this paper proposed a new explanation based on two behavioral concepts: investors are assumed to be "loss averse" meaning that they are distinctly more sensitive to losses than to gains.
Abstract: The equity premium puzzle refers to the empirical fact that stocks have outperformed bonds over the last century by a surprisingly large margin. We offer a new explanation based on two behavioral concepts. First, investors are assumed to be "loss averse," meaning that they are distinctly more sensitive to losses than to gains. Second, even long-term investors are assumed to evaluate their portfolios frequently. We dub this combination "myopic loss aversion." Using simulations, we find that the size of the equity premium is consistent with the previously estimated parameters of prospect theory if investors evaluate their portfolios annually. There is an enormous discrepancy between the returns on stocks and fixed income securities. Since 1926 the annual real return on stocks has been about 7 percent, while the real return on treasury bills has been less than 1 percent. As demonstrated by Mehra and Prescott [1985], the combination of a high equity premium, a low risk-free rate, and smooth consumption is difficult to explain with plausible levels of investor risk aversion. Mehra and Prescott estimate that investors would have to have coefficients of relative risk aversion in excess of 30 to explain the historical equity premium, whereas previous estimates and theoretical arguments suggest that the actual figure is close to 1.0. We are left with a pair of questions: why is the equity premium so large, or why is anyone willing to hold bonds? The answer we propose in this paper is based on two concepts from the psychology of decision-making. The first concept is loss aversion. Loss aversion refers to the tendency for individuals to be more sensitive to reductions in their levels of well-being than to increases. The concept plays a central role in Kahneman and Tversky's [1979] descriptive theory of decision-making under
2,576 citations