Observations of financial anomalies have motivated new theories of the rational expectations ideal. The paper “Efficient markets and Bayes’ rule” by Alvaro Sandroni points out that there exist two types of agents participating in the market, the Behavioral and Bayes’ agents. Talking about Behavioral agents, today’s literature on behavioral finance suggests a relaxation of the strategy that agents form believes only based on laws of probability and rather rely on simpler heuristic rule. Behavioral agents do not process information according to Bayes’ rule and automatically suffer from cognitive biases when forming beliefs. On the other hand, literature approaching the strategy of agents who process information through the Bayes’ rule is coming to the conclusion that Bayes’ agents end up not having enough information to know the true data generating process. They have a disadvantage because they do not have adequate information about the structure of the economy holding the correct beliefs.
In the paper “Efficient markets and Bayes’ rule” a model gets introduced in which Bayesian and Behavioral agents exist simultaneously in a market and trade in a standard pricing model. Investigations have shown that in the long run Bayesian agents drive out Behavioral agents of the market. That is why the paper is concluding that prices in the market arise through the Bayesian paradigm.
Nonetheless, economists could not prove that agents using the Bayes’ rule were able to accumulate wealth at the expense of Behavioral agents, not using the standard laws of probability. According to the paper, there exists literature which demonstrates that Bayes’ agents with correct believes drive other Bayes’ agents with wrong beliefs out of the market. This acknowledgement only accounts for correct and incorrect beliefs though and does not have any linkage to the performance in the market with rational and probability based expectations.
Summing up, it is a very interesting question which information agents take into account if they participate in the market and how this has an impact on the price formation. Moreover, the different outcomes are worth an investigation. The paper goes into further detail in comparing the performance of agents using the Bayes’ rule with correct and incorrect information. Unfortunately, the paper does not come up with a conclusion about the different performance of Bayes using agents and rational expectation using agents. I would encourage to read the paper because it goes into further details and explains things that were briefly touched in my blog post for this week.