Optimal and Robust Disclosure of Public Information

Abstract: 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 that 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.