The hump-shaped behavior of inflation and a dynamic externality

We propose a general equilibrium model that explains the empirical evidence of the hump-shaped response of inflation to a monetary policy shock. The model replaces backward-looking indexation à la Christiano et al. [2005. Nominal rigidities and the dynamic effect of a shock to monetary policy. Journal of Political Economy 113(1), 1-45] with a dynamic externality into the production function of firms. The model, armed with sticky wages and variable capital utilization, has two offsetting effects on real marginal cost over the business cycle. First, increasing factor prices raise real marginal cost in response to an expansionary monetary policy shock in the intermediate run. Second, a dynamic externality reduces real marginal cost in the short run because it raises productivity in response to an increase in output following the shock. Overall, the resulting short-run decrease and intermediate-run increase in marginal cost replicate the hump-shaped behavior of inflation under purely forward-looking price and wage Phillips curves.