Estimating the Optimal Inflation Target from Trends in Relative Prices

We derive closed-form expressions for the optimal inflation target under Calvo and menu-cost frictions in a model featuring a product life cycle and multiple sources of heterogeneity across goods. We show that both frictions deliver the same optimal target and how it can be estimated from observed trends in relative prices. Using micro price data underlying the CPI in the United Kingdom, we document that relative prices fall over the product lifetime in most expenditure items. This causes the optimal inflation target to be positive, with our baseline estimate for the United Kingdom being equal to 2.6 percent in 2016. The optimal target has steadily increased over the prior two decades due to an acceleration in the rates of relative price decline over time. (JEL C51, D15, E31, L11)