Navigating by falling stars: monetary policy with fiscally driven natural rates

We study a new type of monetary-fiscal interaction in a heterogeneous-agent New Keynesian model with a fiscal block. Due to household heterogeneity, the stock of public debt affects the natural interest rate, forcing the central bank to adapt its monetary policy rule to the fiscal stance to guarantee that inflation remains at its target. There is, however, a minimum level of debt below which the steady-state inflation deviates from its target due to the zero lower bound on nominal rates. We analyze the response to a debt-financed fiscal expansion and quantify the impact of different timings in the adaptation of the monetary policy rule, as well as the performance of alternative monetary policy rules that do not require an assessment of the natural rates. We validate our findings with a series of empirical estimates.