Optimal Policy with Occasionally Binding Constraints: Piecewise Linear Solution Methods

Abstract

This paper develops a piecewise linear toolkit for optimal policy analysis of linear rational expectations models, subject to occasionally binding constraints on (multiple) policy instruments and other variables. Optimal policy minimises a quadratic loss function under either commitment or discretion. The toolkit accounts for the presence of ‘anticipated disturbances’ to the model equations, allowing optimal policy analysis around scenarios or forecasts that are not produced using the model itself (for example, judgement-based forecasts such as those often produced by central banks). The flexibility and applicability of the toolkit to very large models is demonstrated in a variety of applications, including optimal policy experiments using a version of the Federal Reserve Board’s FRB/US model.