The optimal rate of inflation with trending relative prices

The relative prices of different categories of consumption goods have been trending over time. Assuming they are exogenous with respect to monetary policy, these trends imply that monetary policy cannot stabilize the prices of all consumption categories. If prices are sticky, monetary policy then must trade off relative price distortions within different categories of consumption. Optimally, more weight should be placed on stabilizing goods and services prices that are less flexible. Calibrating a simple sticky price model to U.S. data, we find that slight deflation is optimal, even absent transactions frictions leading to a demand for money. Optimality of deflation derives from the fact that relative prices have been trending up for services, whose nominal prices seem to be less flexible.