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 necessar...

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Bibliographic Details
Published in:The review of economics and statistics 2023-11, Vol.105 (6), p.1481-1499
Main Author: Holden, Tom D.
Format: Article
Language:English
Subjects:
Determinate
Dynamic models
Linear analysis
Nonlinear analysis
Price levels
Rational expectations
Uniqueness
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Summary: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 nonlinear models.
ISSN:0034-6535
1530-9142
DOI:10.1162/rest_a_01122