Estimating the optimal inflation target from trends in relative prices

Using the official micro price data underlying the U.K. consumer price index, we document a new stylized fact for the life-cycle behavior of consumer prices: relative to a narrowly defined set of competing products, the price of individual products tends to fall over the product lifetime. We show that this data feature has important implications for the optimal in ation target. Constructing a sticky-price model featuring a product life cycle and heterogeneous relative-price trends, we derive closed-form expressions for the optimal in ation target under Calvo and menu-cost frictions. We show how the optimal target can be estimated from the observed trends in relative prices. For the U.K. economy, we find the optimal target to be equal to 2.6% in 2016. It has steadily increased over the period 1996 to 2016 due to changes in relative price trends over this period.