Optimal and Robust Disclosure of Public Information
A policymaker discloses public information to interacting agents who also acquire costly private information. More precise public information reduces the precision and cost of acquired private information. Considering this effect, what disclosure rule should the policymaker adopt? We address this question under two alternative assumptions using a linear-quadratic-Gaussian game with arbitrary quadratic material welfare and convex information costs. First, the policymaker knows the cost of private information and adopts an optimal disclosure rule to maximize the expected welfare. Second, the policymaker is uncertain about the cost and adopts a robust disclosure rule to maximize the worst-case welfare. Depending on the elasticity of marginal cost, an optimal rule is qualitatively the same as in the case of either a linear information cost or exogenous private information. The worst-case welfare is strictly increasing if and only if full disclosure is optimal under some information costs, which provides a new rationale for central bank transparency.
Consider a policymaker (such as a central bank) who discloses public information to interacting agents (such as firms and consumers) who also acquire costly private information. The policymaker’s concern is social welfare, including the agents’ cost of information acquisition. When the policymaker provides more precise public information, the agents have less incentive to acquire private information, reducing its precision and cost. This effect of public information is referred to as the crowding-out effect (Colombo et al., 2014). Less private information can be harmful to welfare, but less information cost is beneficial; that is, the welfare implication of the crowding-out effect is unclear. Then, what disclosure rule should the policymaker adopt?