We reconsider the optimal central banker contract derived in Walsh (1995). We show that if the government's objective function places weight (value) on the cost of the contract, then the optimal inflation contract does not completely neutralize the inflation bias. That is, a fraction of the inflation bias emerges in the resulting inflation rate after the central banker's monetary policy decision. Furthermore, the more concerned the government is about the cost of the contract or the less selfish (more benevolent) is the central banker, the smaller is the share of the inflation bias eliminated by the contract. No matter how concerned the government is about the cost of the contract or how unselfish (benevolent) the central banker is, the contract always reduces the inflationary bias by at least half. Finally, a central banker contract written in terms of output (i.e., incorporating an output target) can completely eradicate the inflationary bias, regardless of concerns about contract costs.
Chortareas, Georgios E. and Miller, Stephen M., "Monetary Policy Delegation, Contract Costs, and Contract Targets" (2000). Economics Working Papers. 200001.