This paper explores how Bayes-rational individuals learn sequentially from the discrete actions of others. Unlike earlier informational herding papers, we admit heterogeneous preferences. Not only may type-specific ‘herds’ eventually arise, but a new robust possibility emerges: confounded learning. Beliefs may converge to a limit point where history offers no decisive lessons for anyone, and each type's actions forever nontrivially split between two actions. To verify that our identified limit outcomes do arise, we exploit the Markov-martingale character of beliefs. Learning dynamics are stochastically stable near a fixed point in many Bayesian learning models like this one.

Abstract In the standard herding model, privately informed individuals sequentially see prior actions and then act. An identical action herd eventually starts and public beliefs tend to “cascade sets” where social learning stops. What behaviour is socially efficient when actions ignore informational externalities? We characterize the outcome that maximizes the discounted sum of utilities. Our four key findings are: (1) cascade sets shrink but do not vanish, and herding should occur but less readily as greater weight is attached to posterity. (2) An optimal mechanism rewards individuals mimicked by their successor. (3) Cascades cannot start after period one under a signal log-concavity condition. (4) Given this condition, efficient behaviour is contrarian, leaning against the myopically more popular actions in every period. We make two technical contributions: as value functions with learning are not smooth, we use monotone comparative statics under uncertainty to deduce optimal dynamic behaviour. We also adapt dynamic pivot mechanisms to Bayesian learning.

In an influential paper, David S. Scharfstein and Jeremy C. Stein (1990) modeled sequential investment by agents concerned about their reputation as good forecasters. Consider an agent who acts after observing the behavior of another ex ante identical agent. Scharfstein and Stein argue that reputational herding requires that better agents have more correlated signals conditionally on the state of the world. They claim that without correlation the second agent would have no incentive to attempt to manipulate the market inference about ability by imitating the behavior of the first agent. In this Note we show that in their model, correlation is not necessary for herding, other than in degenerate cases. Our clarification exploits a parallel with statistical herding, introduced by Abhijit V. Banerjee (1992) and Sushil Bikhchandani et al. (1992) (henceforth, BHW). BHW feature investors who maximize expected profits in a common-value environment and have access to conditionally independent private signals of bounded precision, while still observing the behavior of others. Eventually, the evidence accumulated from observing earlier decisions is sufficiently strong to swamp the private information of a single decision maker. Thereafter, everyone rationally copies the prevailing behavior. We notice that payoffs have a common-value nature in both the statistical and the reputational model. The observed behavior of other agents possibly affects the probability belief attached to different states of the world as well as the payoff conditional on each state. Herding arises from the interaction of these two channels affecting the expected payoff, be it physical or reputational. Positive differential conditional correlation of signals in the reputational model is tantamount to the introduction of positive payoff externalities in the statistical model. This reinforces the tendency to herd already present with independence. The fact that differential conditional correlation is not needed for herding is a clear strength of the reputational herding model. It is not necessary to assume common unpredictable components of returns at the individual level in order to rationalize the empirical findings that individual prediction errors of security analysts are correlated. After setting up Scharfstein and Stein’s model in Section I, we summarize their findings in Section II and provide a unified definition of herd behavior in Section III. Section IV contains our critique of their line of argument and clarifies the role of differential conditional correlation. In Section V we propose alternative robust scenarios where herding would indeed be driven by correlation. Section VI concludes.

This paper analyzes how asset prices in a binary market react to information when traders have heterogeneous prior beliefs. We show that the competitive equilibrium price underreacts to information when there is a bound to the amount of money traders are allowed to invest. Underreaction is more pronounced when prior beliefs are more heterogeneous. Even in the absence of exogenous bounds on the amount that traders can invest, prices underreact to information provided that traders become less risk averse as their wealth increases. In a dynamic setting, underreaction results in initial momentum and then reversal in the long run. (JEL D83, D84, G11, G12, G14)

Empirical analyses of parimutuel betting markets have documented that market probabilities of favorites (longshots) tend to underestimate (overestimate) the corresponding empirical probabilities. We argue that this favorite-longshot bias is consistent with bettors taking simultaneous positions on the basis of private information about the likelihood of different outcomes. The ex post realization of a high market probability indicates favorable information about the occurrence of an outcome—and the opposite is true for longshots. This explanation for the bias relies on the bettors' inability to incorporate the surprise revealed by the final odds. (JEL D81, D82, L83)

Are the highest sample realizations selected from a larger presample more or less informative than the same amount of random data? Developing multivariate accuracy for interval dominance ordered preferences, we show that sample selection always benefits (or always harms) a decision maker if the reverse hazard rate of the data distribution is log‐supermodular (or log‐submodular), as in location experiments with normal noise. We find nonpathological conditions under which the information contained in the winning bids of a symmetric auction decreases in the number of bidders. Exploiting extreme value theory, we quantify the limit amount of information revealed when the presample size (number of bidders) goes to infinity. In a model of equilibrium persuasion with costly information, we derive implications for the optimal design of selected experiments when selection is made by an examinee, a biased researcher, or contending sides with the peremptory challenge right to eliminate a number of jurors.

Abstract We construct and run an experiment to test the most basic choice effect predicted by salience theory. Subjects allocate wealth between a risky and a safe investment. While we vary an apparent payoff ratio to influence salience, treatments have economically equivalent consequences. Most other theories of behavior then predict zero effect. Our experimental findings are strongly consistent with the behavioral implication of a continuous version of salience theory. We provide a novel structural estimate on the strength of salience. In our setting, increasing the relative payoff contrast by 1% is equivalent to an increased odds ratio by about 0.4%.

The deterioration of economic performance in Sweden from about 1970 was to some extent result of a number of exogenous shocks and unnecessary policy mistakes. It was, however, also related to basic changes in economic and social system in Sweden in late 1960s and early 1970, when government spending, taxes, and regulations started to expand dramatically. It is also argued in paper that problematic political, economic, and social mechanisms had become embedded in long-term dynamics of system itself. These various experiences are background for recent reforms and retreats of the Swedish experiment.