Analytic Derivatives for Linear Rational Expectations Models

This paper sets out the analytic solution for the calculation of exact derivatives in linear rational expectations models with reference to the optimal simple rule problem. We argue that there are substantial computational advantages of using analytic derivatives and compare the likely computational costs of using approximate and exact derivatives when calculating optimal coefficients for simple feedback rules. A specific algorithm for finite time optimization is also outlined, which will reduce the computational time required and is simple to implement. We discuss modifications to allow for stochastic models.