Search

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.

Significance Frequent mass testing can slow a rapidly spreading infectious disease by quickly identifying and isolating infected individuals from the population. One proposed method to reduce the extremely high costs of this testing strategy is to employ pooled testing, in which samples are combined and tested together using one test, and the entire pool is cleared given a negative test result. This paper demonstrates that frequent pooled testing of individuals with correlated risk—even given large uncertainty about infection rates—is particularly efficient. We conclude that frequent pooled testing using natural groupings is a cost-effective way to suppress infection risk in a pandemic., Pooled testing increases efficiency by grouping individual samples and testing the combined sample, such that many individuals can be cleared with one negative test. This short paper demonstrates that pooled testing is particularly advantageous in the setting of pandemics, given repeated testing, rapid spread, and uncertain risk. Repeated testing mechanically lowers the infection probability at the time of the next test by removing positives from the population. This effect alone means that increasing frequency by x times only increases expected tests by around x. However, this calculation omits a further benefit of frequent testing: Removing infections from the population lowers intragroup transmission, which lowers infection probability and generates further efficiency. For this reason, increasing testing frequency can paradoxically reduce total testing cost. Our calculations are based on the assumption that infection rates are known, but predicting these rates is challenging in a fast-moving pandemic. However, given that frequent testing naturally suppresses the mean and variance of infection rates, we show that our results are very robust to uncertainty and misprediction. Finally, we note that efficiency further increases given natural sampling pools (e.g., workplaces, classrooms) that induce correlated risk via local transmission. We conclude that frequent pooled testing using natural groupings is a cost-effective way to provide consistent testing of a population to suppress infection risk in a pandemic.

Group testing increases efficiency by pooling patient specimens and clearing the entire group with one negative test. Optimal grouping strategy is well studied in one-off testing scenarios with reasonably well-known prevalence rates and no correlations in risk. We discuss how the strategy changes in a pandemic environment with repeated testing, rapid local infection spread, and highly uncertain risk. First, repeated testing mechanically lowers prevalence at the time of the next test. This increases testing efficiency, such that increasing frequency by x times only increases expected tests by around vx rather than x. However, this calculation omits a further benefit of frequent testing: infected people are quickly removed from the population, which lowers prevalence and generates further e?ciency. Accounting for this decline in intra-group spread, we show that increasing frequency can paradoxically reduce the total testing cost. Second, we show that group size and e?ciency increases with intra-group risk correlation, which is expected in natural test groupings based on proximity. Third, because optimal groupings depend on uncertain risk and correlation, we show how better estimates from machine learning can drive large efficiency gains. We conclude that frequent group testing, aided by machine learning, is a promising and inexpensive surveillance strategy.

We model two agents who wish to determine if their types match, but who also desire to reveal as little information as possible to non-matching types. For example, firms considering a merger must determine the merger's profitability, but would prefer to keep their information private if the deal fails. In the model, agents with different traits reveal information to a potential partner to determine if they share the same type, but face a penalty depending on the accuracy of their partner's posterior beliefs. With limited signaling, there is a universally-preferred dynamic communication protocol in which traits are sequentially revealed depending on the sensitivity of the trait. Interestingly, the rarity of an agent's traits plays no role due to the balance of opposing effects: although revealing a rare trait reveals more information immediately, it also screens more partners from later learning information about other traits.

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.

We model religious faith as a “demand for beliefs,” following the logic of the Pascalian wager. We show how standard experimental interventions linking financial consequences to falsifiable religious statements can elicit and characterize beliefs. We implemented this approach with members of a group that expected the “End of the World” to occur on May 21, 2011 by varying monetary prizes payable before and after May 21st. To our knowledge, this is the first incentivized elicitation of religious beliefs ever conducted. The results suggest that the members held extreme, sincere beliefs that were unresponsive to experimental manipulations in price.

How restrictive is the assumption of rational expectations in asset markets? We provide two contributions to address this question. First, we derive restrictions on the admissible variation in asset prices in a general class of rational-expectations equilibria. The challenge in this task is that asset prices reflect both beliefs and preferences. We gain traction by considering market-implied, or risk-neutral, probabilities of future outcomes, and we provide a mapping between the variation in these probabilities and the minimum curvature of utility — or, more generally, the slope of the stochastic discount factor — required to rationalize the marginal investor’s beliefs. Second, we implement these bounds empirically using S&P 500 index options. We find that very high utility curvature is required to rationalize the behavior of risk-neutral beliefs, and in some cases, no stochastic discount factor in the class we consider is capable of rationalizing these beliefs. This provides evidence of overreaction to new information relative to the rational benchmark. We show further that this overreaction is strongest for beliefs over prices at distant horizons, and that our findings cannot be explained by factors specific to the option market.

In this paper, we examine the eect of "choice fatigue"on decision making. We exploit a natural experiment in which voters face the same contest at dierent ballot positions due to dierences in the number of local issues on their ballot. Facing more decisions before a given contest signi…cantly increases the tendency to abstain or rely on decision shortcuts, such as voting for the status quo or the …rst listed candidate. We estimate that, without choice fatigue, abstentions would decrease by 8%, and 6% of the propositions in our dataset would have passed rather than failed.

This article theoretically and empirically analyses behaviour in penny auctions, a relatively new auction mechanism. As in the US dollars or war-of-attrition, players in penny auctions commit higher non-refundable costs as the auction continues and only win if all other players stop bidding. I first show that, in any equilibria that does not end immediately, players bid probabilistically such that the expected profit from every bid is zero. Then, using two large data sets covering 166,000 auctions, I calculate that average profit margins actually exceed 50%. To explain this deviation, I incorporate a sunk-cost fallacy into the theoretical model to generate a set of predictions about hazard rates and player behaviour, which I confirm empirically. While players do (slowly) learn to correct this bias and there are few obvious barriers to competition, activity in the market is rising and concentration remains relatively high.