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 such terminal conditions. These results give determinacy conditions for models with occasionally binding constraints, much as Blanchard and Kahn (1980) did for linear models. In an application, we show that widely used New Keynesian models with endogenous states possess multiple perfect foresight equilibrium paths when there is a zero lower bound on nominal interest rates, even when agents believe that the central bank will eventually attain its long-run, positive inflation target. This illustrates that a credible long-run inflation target does not render the Taylor principle sufficient for determinacy in the presence of the zero lower bound. However, we show that price level targeting does restore determinacy providing agents believe that inflation will eventually be positive.

'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.

Standard New Keynesian (NK) models feature an optimal inflation target well below two percent, limited welfare losses from business cycle fluctuations and long-term monetary neutrality. We develop a NK framework with labour market frictions, endogenous productivity and downward wage rigidity (DWR) which challenges these results. The model features a non-vertical long-run Phillips curve between inflation and unemployment and a trade-off between price distortions and output hysteresis that change the welfare-maximizing inflation level. For a plausible set of parameters, the optimal inflation target is in excess of two percent, a target value commonly used across central banks. Deviations from the optimal target carry welfare costs multiple times higher than in traditional NK models. The main reason is that endogenous growth and DWR generate asymmetric and hysteresis effects on unemployment and output. Price level targeting or a Taylor-rule responding to the unemployment rate can handle better the asymmetric and hysteresis effects in our model and deliver significant welfare gains. Our results are robust to the inclusion of the effective lower bound on the monetary policy interest rate.