A note on equilibrium uniqueness in new Keynesian models and implications for the fiscal theory of the price level

This note clarifies some issues related to local determinacy and global equilibrium uniqueness in a class of New Keynesian models. The results are not new. They exist in various forms in different parts of the literature. I present them in a way that I have found useful to articulate some of the controversies surrounding the Fiscal Theory of the Price Level, transversality conditions and Ricardian equivalence. In models with Ricardian households such as the textbook RANK model, equilibrium uniqueness with active fiscal policy and passive monetary policy relies on the household transversality condition. In models with non-Ricardian households such as HANK, OLG and bonds-in-utility (BIU) models, the transversality condition is not required for uniqueness. As a result these models are not subject to many of the critiques laid on FTPL in RANK models. I illustrate this by showing that in the RANK-BIU model with active fiscal policy and passive monetary policy, boundedness of output and inflation is sufficient for a locally unique equilibrium and for global uniqueness when debt diverges. Ruling out isolated unstable periodic orbits in the bounded-debt case, which would complete the global uniqueness proof, is left to future work.