Limited higher order beliefs and the welfare effects of public information

In games with strategic complementarities, public information about the state of the world has a larger impact on equilibrium actions than private information of the same precision, because the former is more informative about the likely behavior of others. This may lead to welfare-reducing “overreactions” to public signals as shown by Morris and Shin (2002). Recent experiments on games with strategic complementarities show that subjects attach a lower weight to public signals than theoretically predicted. The purpose of this paper is to reconsider the welfare effects of public signals accounting for the weights observed in experiments.

Aggregate behavior observed in experiments on games with strategic complementarities can be explained by a cognitive hierarchy model where subjects employ limited levels of reasoning. They respond in a rational way to the non-strategic part of a game and they account for other players responding rationally, but they neglect that other players also account for others’ rationality. This paper analyzes the welfare effects of public information under such limited levels of reasoning.

In the model by Morris and Shin (2002) public information is always welfare improving if strategies are derived from such low reasoning levels. The optimal degree of publicity is decreasing in the levels of reasoning. For the observed average level of reasoning, full transparency is optimal, if public information is more precise than private information. If the policy maker has instruments that are perfect substitutes to private actions, the government should secretly respond to its information without disclosing or signaling it to the private sector independent of the degree of private agents’ rationality.

This paper takes experimental evidence back to theory and shows that the main result obtained by the theory under rational behavior breaks down if theory accounts for the bounded rationality observed in experiments.