Harstad and Selten (this forum) raise interesting questions about the relative promise of optimization models and bounded-rationality models in making progress in economics. This article builds from their analysis by indicating the potential for using neoclassical (broadly defined) optimization models to integrate insights from psychology on the limits to rationality into economics. I lay out an approach to making (imperfect and incremental) improvements over previous economic theory by incorporating greater realism while attempting to maintain the breadth of application, the precision of predictions, and the insights of neoclassical theory. I then discuss how many human limits to full rationality are, in fact, well understood in terms of optimization.

USING EXPECTED-UTILITY THEORY, economists model risk aversion as arising solely because the utility function over wealth is concave.This diminishing-marginal-utility-ofwealth theory of risk aversion is psychologically intuitive, and surely helps explain some of our aversion to large-scale risk: We dislike vast uncertainty in lifetime wealth because a dollar that helps us avoid poverty is more valuable than a dollar that helps us become very rich.Yet this theory also implies that people are approximately risk neutral when stakes are small.Arrow (1971, p. 100) shows that an expected-utility maximizer with a differentiable utility function will always want to take a sufficiently small stake in any positiveexpected-value bet.That is, expected-utility maximizers are (almost everywhere) arbitrarily close to risk neutral when stakes are arbitrarily small.While most economists understand this formal limit result, fewer appreciate that the approximate risk-neutrality prediction holds not just for negligible stakes, but for quite sizable and economically important stakes.Economists often invoke expected-utility theory to explain substantial (observed or posited) risk aversion over stakes where the theory actually predicts virtual risk neutrality.While not broadly appreciated, the inability of expected-utility theory to provide a plausible account of risk aversion over modest stakes has become oral tradition among some subsets of researchers, and has been illustrated in writing in a variety of different contexts using standard utility functions.2In this paper, I reinforce this previous research by presenting a theorem that calibrates a relationship between risk attitudes over small and large stakes.The theorem shows that, within the expected-utility model, anything but virtual risk neutrality over modest stakes implies manifestly unrealistic risk aversion over 1 Many people, including

This article proposes an approach to improving the psychological realism of economics while maintaining its conventional techniques and goals--formal theoretical and empirical analysis using tractable models, with a focus on prediction and estimation. Besides tolerating the imperfections that come with precision, models should aim for two crucial criteria: power and scope. The approach advocated is to develop portable extensions of existing models that embed preexisting theories as parameter values, while introducing the new psychological assumptions as alternative parameter values, and make the model portable by defining it in all cases where existing models make predictions.

We experimentally investigate the time-inconsistent taste for immediate gratification and future-preference misprediction. Across 7 weeks, 100 participants choose the number of unpleasant transcription tasks given various wages to complete immediately and at different future dates. Participants preferred 10–12% fewer tasks in the present compared to any future date, leading to an estimated $β $ of 0.83. Comparing predictions with actual immediate-work choices provides evidence against substantial sophistication, with estimates implying that participants understand no more than 24% of their present bias. Finally, we find evidence of “projection bias”: participants wished to complete 4–12% fewer tasks when decisions were elicited right after completing tasks rather than before.

When a Bayesian learns new information and changes her beliefs, she must on average become concomitantly more certain about the state of the world. Consequently, it is rare for a Bayesian to frequently shift beliefs substantially while remaining relatively uncertain, or, conversely, become very confident with relatively little belief movement. We formalize this intuition by developing specific measures of movement and uncertainty reduction given a Bayesian’s changing beliefs over time, showing that these measures are equal in expectation and creating consequent statistical tests for Bayesianess. We then show connections between these two core concepts and four common psychological biases, suggesting that the test might be particularly good at detecting these biases. We provide support for this conclusion by simulating the performance of our test and other martingale tests. Finally, we apply our test to data sets of individual, algorithmic, and market beliefs.

There is evidence that people do not fully take into account how other people's actions depend on these other people's information. This paper defines and applies a new equilibrium concept in games with private information, cursed equilibrium, which assumes that each player correctly predicts the distribution of other players' actions, but underestimates the degree to which these actions are correlated with other players' information. We apply the concept to common-values auctions, where cursed equilibrium captures the widely observed phenomenon of the winner's curse, and to bilateral trade, where cursedness predicts trade in adverse-selections settings for which conventional analysis predicts no trade. We also apply cursed equilibrium to voting and signalling models. We test a single-parameter variant of our model that embeds Bayesian Nash equilibrium as a special case and find that parameter values that correspond to cursedness fit a broad range of experimental datasets better than the parameter value that corresponds to Bayesian Nash equilibrium.

We develop a rational dynamic model in which people are loss averse over changes in beliefs about present and future consumption. Because changes in wealth are news about future consumption, preferences over money are reference-dependent. If news resonates more when about imminent consumption than when about future consumption, a decision maker might (to generate pleasant surprises) overconsume early relative to the optimal committed plan, increase immediate consumption following surprise wealth increases, and delay decreasing consumption following surprise losses. Since higher wealth mitigates the effect of bad news, people exhibit an unambiguous first-order precautionary-savings motive.

We use Kőszegi and Rabin's (2006) model of reference-dependent utility, and an extension of it that applies to decisions with delayed consequences, to study preferences over monetary risk. Because our theory equates the reference point with recent probabilistic beliefs about outcomes, it predicts specific ways in which the environment influences attitudes toward modest-scale risk. It replicates “classical” prospect theory—including the prediction of distaste for insuring losses—when exposure to risk is a surprise, but implies first-order risk aversion when a risk, and the possibility of insuring it, are anticipated. A prior expectation to take on risk decreases aversion to both the anticipated and additional risk. For large-scale risk, the model allows for standard “consumption utility” to dominate reference-dependent “gain-loss utility,” generating nearly identical risk aversion across situations.

Economics has always been concerned not only with describing or predicting economic behavior but also with understanding economic well-being. The traditional, official way economists (claimed to) have assessed well-being is from “revealed preference’’—observing what people choose under the maintained hypothesis of 100 percent rationality. For instance, when we teach millions of students each year the conditions under which interfering with free-market exchange will make people worse off, by interfering with satisfying their wants, we do so under the compelling assumption that people tend to make choices that rationally maximize their own well-being. While economists are humble about the fact that we are not in a privileged position to declare what goals society should pursue, welfare economics has provided guidance on the determinants of well-being according to this restrictive set of criteria. Although all of us also assess well-being in other ways, it is only recently that economists have begun to do so in a more focused way. A growing number of researchers have begun to study alternatives to the 100 percent rationality assumption, while other researchers have used sundry techniques to measure well-being directly. In this article, we explore some conceptual issues as to why and how one might use these new assumptions and approaches to supplement and modify the revealed-preference approach as it is conventionally conceived. We take the central question of welfare economics to be: how do different situations or economic environments affect people’s well-being? When doing so with sensible ancillary assumptions, inferring people’s well-being from their choices, based on the presumption that they are rationally pursuing their goals, is, in our view, the best scientific approach to research on well-being yet formulated. Our first goal in this

While present bias is an old idea, it only took hold in economics following David Laibson's (1994) dissertation. Over the past 20 years, research has led to a much better theoretical understanding of present bias, when and how to apply it, and which ancillary assumptions are appropriate in different contexts. Empirical analyses have demonstrated how present bias can improve our understanding of behavior in various economic field contexts. Nonetheless, there is still much to learn. In this paper, we give our assessment of some lessons learned, and to be learned.