This paper presents an algorithm for simulating multiple equilibria in otherwise-linear dynamic models with occasionally-binding constraints. Our algorithm extends the guess-and-verify approach of Guerrieri and Iacoviello (2015) to detect and simulate multiple perfect foresight equilibria, and allows arbitrary “news shocks” up to a finite horizon. When there are multiple equilibria, we show how to compute expected paths using a “prior probabilities” approach and we provide an approach for running stochastic simulations with switching between equilibria on the simulated path. A policy application studies a New Keynesian model with a zero lower bound on nominal interest rates and multiple equilibria, including a “bad” solution based on self-fulfilling pessimistic expectations. A price-level targeting rule does not always eliminate the bad solution, but it shrinks the indeterminacy region substantially and improves stabilization and welfare relative to more conventional interest rate rules or forward guidance.
