This paper proposes a piecewise-linear Kalman filter (PKF) to estimate DSGE models with occasionally binding constraints. This method expands the set of models suitable for nonlinear estimation. It straightforwardly handles missing data, non-singularity (more shocks than observed time series),...

We estimate a workhorse dynamic stochastic general equilibrium (DSGE) model with an occasionally binding borrowing constraint. First, we propose a new specification of the occasionally binding constraint, where the transition between the unconstrained and constrained states is a stochastic...

We present the first necessary and sufficient conditions for there to be a unique perfect-foresight solution to an otherwise linear dynamic model with occasionally binding constraints, given a fixed terminal condition. We derive further results on the existence of a solution in the presence of...

We present the first necessary and sufficient conditions for the existence of a unique perfect-foresight solution, returning to a given steady-state, in an otherwise linear model with occasionally binding constraints. We derive further conditions on the existence of a solution in such models,...

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...