The value of information with heterogeneous agents and partially revealing prices

This paper studies how the arrival of more precise information affects welfare in an economy with incomplete and differential information. We consider a single period, pure exchange economy with aggregate uncertainty in which agents show different attitudes towards risk: wealthy individuals are 'de facto' less risk averse than poor individuals. The first ones can then partially insure the last ones, allowing for mutual gains from trade. Agents ignore the actual probability distribution over the states. Instead, they learn from the market price and private signals, which in fact accounts for the presence of heterogeneous beliefs. In equilibrium, the dispersion in beliefs introduces an adverse effect: risk-taking agents are more pessimistic than the rest. This limits the possibilities to share risks and has a negative impact on welfare. The arrival of more precise information has therefore a double effect: it weakens the adverse effect on trade (as risk-taking agents become more optimistic, they offer more insurance) at the same time that it strengthens the Hirshleifer effect (agents are no longer able to insure against news that have already arrived). The first effect fosters and the second one discourages risk-sharing trades. The paper discusses in detail a case where the positive effect on trade offsets the negative effect. This lets us conclude that in an economy with partial information, agents' welfare may increase upon the receipt of more precise information. Even though the result looks intuitive, most of the previous literature has focused on the case with homogeneous beliefs. In such a framework, only the Hirshleifer effect is at work, and thus better information typically leads to a decrease in welfare