An efficient application of the extended path algorithm in Matlab with examples

Recent experience with interest rates hitting the effective lower bound and agents facing binding borrowing constraints has emphasised the importance of understanding the behaviour of an economy in which some variables may be restricted at times. The extended path algorithm is a commonly used and fairly general method for solving dynamic nonlinear models with rational expectations. This algorithm can be used for a wide range of cases, including for models with occasionally binding constraints, or for forecasting with models in which some variables must satisfy a certain path. In this paper I propose computational improvements to the algorithm that speed up the calculations via vectorisations of the Jacobian matrix and residual equations. I illustrate the advantages of the method with a number of policy relevant applications: conditional forecasting with both exactly identified and underidentified shocks, occasionally binding constraints on interest rates, anticipated shocks, calendar-based forward guidance, optimal monetary policy with a binding constraint and transition paths.