'This practical review assesses several approaches to solving medium- and large-scale dynamic stochastic general equilibrium (DSGE) models featuring occasionally binding constraints. In such models, global solution methods are not possible because of the curse of dimensionality. This causes the modeller to look elsewhere for methods that can handle the significant non-linearities and non-differentiable functions that inequality constraints represent. The paper discusses methods-including Newton-type solvers under perfect foresight, the piecewise linear algorithm (OccBin), regime-switching models (RISE) and the news shocks approach (DynareOBC) - and compares the results from a simple borrowing constraints model obtained using projection methods, providing example MATLAB code. The study focuses on the news shocks method, which I find produces higher accuracy than other methods and allows the modeller to study multiple equilibria and determinacy issues'--Abstract, page ii.

Structural macroeconometric analysis and new HANK-type models with extremely high dimensionality require fast and robust methods to efficiently deal with occasionally binding constraints (OBCs), especially since major developed economies have again hit the zero lower bound on nominal interest rates. This paper shows that a linear dynamic rational expectations system with OBCs, depending on the expected duration of the constraint, can be represented in closed form. Combined with a set of simple equilibrium conditions, this can be exploited to avoid matrix inversions and simulations at runtime for significant gains in computational speed. An efficient implementation is provided in Python programming language. Benchmarking results show that for medium-scale models with an OBC, more than 150,000 state vectors can be evaluated per second. This is an improvement of more than three orders of magnitude over existing alternatives. Even state evaluations of large HANK-type models with almost 1000 endogenous variables require only 0.1 ms.

We present an algorithm for estimating non-linear dynamic models, including those featuring occasionally binding constraints. The algorithm extends the Cubature Kalman Filter of Arasaratnam and Haykin (2009) with dynamic state space reduction, to give adequate speed in the presence of occasionally binding constraints, and to ensure that it can handle the large state spaces generated by pruned perturbation solutions to medium-scale DSGE models. We further extend the base algorithm to allow for alternative cubature procedures to improve the tracking of non-linearities. The algorithm relies on the solution method for models with occasionally binding constraints of Holden (2016b). We illustrate that the method can solve some of the identification problems that plague linearized DSGE models.

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