Incomplete Information and Informative Pricing: Theory and Application

This paper studies the information contained in the equilibrium aggregate price level of an economy where firms make output price decisions faced with incomplete information about economy-wide disturbances. It is shown that when heterogeneously informed firms are allowed to extract information from the equilibrium aggregate price, the ability of the aggregate price to be a sufficient statistics of the underlying aggregate disturbance depends on the degree of strategic complementarity in firms' pricing strategy. As the incentive to price similarly increases, aggregate price goes from a perfect to an imperfect signal of changes in the aggregate state of the economy. More generally, this paper contributes to the expanding literature on monetary business cycle and incomplete information initiated by Woodford (2003a) in three directions. First, it proposes a set of techniques in the frequency domain that allow for the explicit derivation of individual heterogeneous expectations in a log-linear framework while preserving the tractability of the equilibrium fixed point condition. Second, it develops and solves a stylized model where aggregate price plays a key informational role for imperfectly informed firms of the type advocated by Hayek. Finally, it presents an application to monetary policy in a setting with a simple feedback rule for the supply of money.