Inflation composition and monetary stabilization

Every inflation index is an aggregation rule. This paper asks when the aggregation that measures the cost of living is also the one that should guide monetary stabilization. A Consumer Price Index (CPI) measures purchasing power; a stabilization index should weight sectoral prices by what they reveal about states in which the policy rate has high marginal welfare value. In standard New-Keynesian models, the two indices coincide. We show that they diverge when the sectors generating price movements differ from the sectors through which interest rates move demand, income, and marginal costs. New euro-area data reveal such a mismatch. Discretionary sectors are the cyclical quantity margin and employ many hand-to-mouth workers, while necessity sectors account for much of inflation variation. After a contractionary monetary policy shock, discretionary consumption and employment adjust the most, but necessity prices respond more. We lay out a two-sector New-Keynesian model with non-homothetic demand and sectoral labour market heterogeneity that is consistent with these findings. Even with symmetric shocks and homogeneous nominal rigidities, optimal simple rules place nearly all weight on discretionary inflation, because reacting to necessity inflation uses the discretionary sector as the adjustment margin for price movements in sectors with little quantity traction. With stickier discretionary prices, as observed in the euro area, a discretionary inflation rule improves welfare further and closes about two thirds of the welfare gap between a CPI inflation rule and Ramsey policy. Under the empirical distribution of euro-area shocks, the gains come from lower sectoral inflation volatility rather than lower aggregate real volatility. Expenditure weights need not be stabilization weights.