Existence and Uniqueness of Solutions to Dynamic Models with Occasionally Binding Constraints

Occasionally binding constraints (OBCs) like the zero lower bound (ZLB) can lead to multiple equilibria, and so to belief-driven recessions. To aid in finding policies that avoid this, we derive existence and uniqueness conditions for otherwise linear models with OBCs. Our main result gives necessary and sufficient conditions for such models to have a unique (“determinate”) perfect foresight solution returning to a given steady state, for any initial condition. While standard New Keynesian models have multiple perfect-foresight paths eventually escaping the ZLB, price level targeting restores uniqueness. We also derive equilibrium existence conditions under rational expectations for arbitrary non-linear models.

MPCs, MPEs, and Multipliers: A Trilemma for New Keynesian Models

We show that New Keynesian models with frictionless labor supply face a challenge: given standard parameters, they cannot simultaneously match plausible estimates of marginal propensities to consume (MPCs), marginal propensities to earn (MPEs), and fiscal multipliers. A HANK model with sticky wages provides a solution to this trilemma.

On global determinacy of New Keynesian models

New Keynesian models assume that inflation rate and output level are endogenous variables. However, given that firms are price setters and suppliers in the models, it is more reasonable to assume that, absent equilibrium coordination (or tatonnement) issues usually abstracted away, both variables actually are state variables determined by expectations in the past. This secures global equilibrium determinacy and a previously unavailable account of inflation rate for New Keynesian models. Furthermore, the principle of effective demand is implemented via the expectation channel.

TAX RULES TO PREVENT EXPECTATIONS-DRIVEN LIQUIDITY TRAPS

Multiple equilibria arise in standard New Keynesian models when the nominal interest rate is set according to the Taylor rule and constrained by a zero lower bound (ZLB). One of these equilibria is deflationary and referred to as an expectations-driven liquidity trap (ELT) as it arises because of the de-anchoring of inflation expectations. This study demonstrates that a simple tax rule responding to inflation can prevent a liquidity trap from arising without increasing government spending or debt. We analytically investigate the necessary and sufficient conditions to prevent an ELT and show that both the frequency and persistence of ELT episodes affect the extent to which the tax rule must respond to inflation. In brief, the higher the frequency or the longer the persistence of the ELT, the greater the response of the tax rate must be.