Price Trends over the Product Life Cycle and the Optimal Inflation Target

We present a sticky price model featuring a product life cycle and rich amounts of heterogeneity that allow capturing salient features of micro price data. We analytically derive the optimal steady-state inflation rate and show how the optimal inflation target trades off price and mark-up distortions across different product categories. We then devise an empirical approach that permits identifying the optimal inflation target from relative price trends over the product life cycle. Using the micro Price data underlying the U.K. consumer price index, we show that the relative price of products decreases over the life cycle for almost all expenditure categories and that this causes positive inflation targets to be optimal. The optimal U.K. inflation target is estimated to range between 2.6% and 3.2% in the year 2016. The optimal target has steadily increased over the years 1996-2016. We explain how changes in relative price trends contributed to this increase.