Solving rational expectations models: a practical approach using Scilab®

Abstract

This Handbook is about useful numerical methods for models commonly used in central banks. The linear general equilibrium model with rational expectations is a natural part of the central bank economist's toolkit. The appropriate modelling of monetary policy in these models is even more so. This Handbook aims to get people familiar with the methods and then to use them on their own problems by demonstrating exactly how to do it in as simple a way as possible.  The Handbook is structured so that the exercises and suggested variations should help the reader to both understand the techniques being used and the Scilab code itself. The Scilab code forms a useful library of routines than can be reused by economists wishing to investigate the properties of their models. The Handbook first introduces a basic New Keynesian (NK) model, briefly discussing each of the equations that comprise the system. Then is shows how to put the model into state space, how to solve the model for a given calibration, and present results for the model in terms of impulse responses and moments. The remainder of the Handbook builds on this by considering how to handle variations on this simple model, with modifications to the IS curve, the Phillips Curve, the policy rule and extending to an open economy. We also examine alternative forms of modelling monetary policy, in particular how to calculate optimal policies and to optimise the coefficients of a simple policy rule.DSGE; model solution; policy design;