Monetary discretion, pricing complementarity and dynamic multiple equilibria

In a plain-vanilla New Keynesian model with two-period staggered price-setting, discretionary monetary policy leads to multiple equilibria. Complementarity between the pricing decisions of forward-looking firms underlies the multiplicity, which is intrinsically dynamic in nature. At each point in time, the discretionary monetary authority optimally accommodates the level of predetermined prices when setting the money supply because it is concerned solely about real activity. Hence, if other firms set a high price in the current period, an individual firm will optimally choose a high price because it knows that the monetary authority next period will accommodate with a high money supply. Under commitment, the mechanism generating complementarity is absent: the monetary authority commits not to respond to future predetermined prices. Multiple equilibria also arise in other similar contexts where (i) a policymaker cannot commit, and (ii) forward-looking agents determine a state variable to which future policy responds.