Optimal monetary policy with imperfect common knowledge

We study optimal nominal demand policy in an economy with monopolistic competition and flexible prices when firms have imperfect common knowledge about the shocks hitting the economy. Parametrizing firms' information imperfections by a (Shannon) capacity parameter that constrains the amount of information flowing to each firm, we study how policy that minimizes a quadratic objective in output and prices depends on this parameter. When price setting decisions of firms are strategic complements, for a large range of capacity values optimal policy nominally accommodates mark-up shocks in the short-run. This finding is robust to the policy maker observing shocks imperfectly or being uncertain about firms' capacity parameter. With persistent mark-up shocks accommodation may increase in the medium term, but decreases in the long-run thereby generating a hump-shaped price response and a slow reduction in output. Instead, when prices are strategic substitutes, policy tends to react restrictively to mark-up shocks. However, rational expectations equilibria may then not exist with small amounts of imperfect common knowledge.