The Value of Information with an Endogenous Public Signal

Abstract

This paper analyses the equilibrium and welfare properties of an economy characterised by uncertainty and payoff externalities using a general model that nests several applications. Agents receive a private signal and an endogenous public signal, which is a noisy aggregate of individual actions and causes an information externality. Agents in equilibrium underweight private information for a larger payoff parameter region in relation to when public information is exogenous. In addition, the welfare planner gives a higher weight to private information when public information is endogenous rather than exogenous. The welfare effect of increasing the precision of the noise in the public signal has the same sign with endogenous or exogenous public information, but its magnitude differs. The social value of private information may be overturned in relation to when public information is exogenous: from positive to negative if agents in equilibrium coordinate more than is socially optimal with exogenous public information, and the opposite if they coordinate less.