Inflation Targeting: What Inflation Rate to Target?

Although CPI inflation and PPI inflation are both readily observable, the latter has received much less attention in the design of optimal monetary policy, despite the apparent difference in the cyclical behaviors of the two price indices. This paper constructs a sticky-price DSGE model, in which final consumption goods are produced through two stages of processing, and thus a natural distinction between PPI and CPI arises. We derive a utility-based objective function for a benevolent central bank, and, under this objective, we characterize optimal monetary policy and compare the welfare implications of several simple interest rate rules. Under the optimal monetary policy, the central bank should care not only about variations in CPI inflation and output gap, but also about variations in PPI inflation and the gap of the real marginal cost in the intermediate good sector. In general, the central bank faces a tradeoff between stabilizing the gaps and the two measures of inflation and cannot attain the Pareto optimal allocation. Although implementing the optimal policy requires excessive information, a simple hybrid rule under which the short-term interest rate responds to CPI inflation and PPI inflation results in a welfare level close to the optimum, while simple rules that ignore PPI inflation result in significant welfare losses.