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.

MODELLING STATE-CONTINGENT FISCAL RULES IN THE UNITED KINGDOM

I assess a novel rule that was introduced in the UK in 2015. It gave the British government fiscal flexibility whenever GDP growth warranted it. This rule lasted just a year, but it had features worth exploring. I apply solution methods for models with occasionally-binding constraints to assess the demand stabilisation properties of state-contingent fiscal rules. First it is shown that fiscal flexibility can make recessions shallower. Second, it is suggested that GDP growth, rather than measures of the output gap, is a better indicator for triggering fiscal flexibility.