How Costly is CPI Inflation Targeting: A Two Sector Model with No Labor Mobility

This paper studies the welfare costs of price rigidities in a closed economy without labor mobility. First, in a one-sector model, I find a significant welfare cost of price rigidities under a standard Taylor rule, especially when labor is immobile. In the one-sector model, strict CPI inflation targeting is able to eliminate the welfare cost of price rigidities, with or without labor mobility. Then, I develop a vertically integrated two-sector model with nominal and real rigidities where there is a natural distinction between the rates of inflation in the final and intermediate goods sectors. In the two-sector model, the real rigidities are introduced by assuming that labor is immobile across sectors and firms. In the model, labor immobility plays an allocative role and causes large fluctuations in hours of work. This, in turn, magnifies the welfare costs of nominal rigidities. I find that the welfare costs range from 1.62 percent to 2.33 percent of consumption per period for different degree of price rigidities under an estimated Taylor rule over the Volcker and Greenspan years. Taking the household welfare under optimal (Ramsey) monetary policy as a benchmark, I show that an optimal modified Taylor rule with two measures of inflation is able to bring welfare closer to the benchmark value and reduces the welfare costs substantially, even if labor mobility is restricted.