State-dependent pricing and optimal monetary policy

This paper analyzes optimal monetary policy under precommitment in a state-dependent pricing (SDP) environment. Under SDP, monopolistically competitive firms are allowed to endogenously change the timing of price adjustments. I show that this endogenous timing of price adjustment alters the tradeoff and the cost of inflation variation faced by the monetary authority in comparison to the standard time-dependent pricing (TDP) assumption. In particular, it is desirable to let inflation vary more under SDP. Despite the change in the policy tradeoff, however, the optimal response under SDP to either a productivity shock or a government purchase shock under the timeless perspective (long-run) policy can still be characterized as an approximate price stability rule. In addition to a standard first-order approximation to the equilibrium solution, this paper also computes a second-order solution where the effect of state-dependence can play a central role. The policy response under SDP exhibits some degree of nonlinearity, especially in the presence of larger shocks and when the state of the economy is farther away from the steady state. Finally, this paper also studies the optimal policy start-up problem related to the cost of adopting the timeless perspective policy instead of the true Ramsey policy. The SDP assumption leads to different start-up dynamics compared to the dynamics under the TDP assumption in several interesting ways. In particular, the change in the policy tradeoff gives rise to much higher start-up inflation under SDP.