Stepping on a Rake: Replication and Diagnosis

Abstract

This paper replicates Sims (2011) “stepping on a rake” model. It derives the model, shows how to solve it, offers some extensions, and boils the paper down to its central ingredient. Sims’ article is important: it is a simple modern economic model that produces a temporary decline in inflation when the central bank persistently raises interest rates. Inflation then rises. The model’s essential feature is long term debt. When interest rates increase, the nominal market value of long-term government debt falls. If fiscal surpluses are unchanged, the price level must fall so that the real value of government debt matches the unchanged real present value of surpluses. The model offers a unified treatment of interest rate targets, quantitative easing and forward guidance that works even in a frictionless setup.