The Linearisation and Optimal Control of Large Non-Linear Rational Expectations Models by Persistent Excitation

Abstract

Since the onset of the rational expectations revolution in macroeconomics some 30 or more years ago, a variety of techniques have evolved for the solution of rational expectations models. The first generation of methods were for linear models starting with the method of Blanchard and Kahn (1980). Because the models are large and usually non-linear, methods for solving (and optimising) such models have evolved in parallel (Holly and Zarrop, 1983; Finan and Tetlow, 1999; Fair, 2003). In contrast to recent methods that apply secon-order approximations (Schmitt-Grohe and Uribe, 2004; Sims, 2002b) in this paper we describe some computationally simple methods for linearising a non-linear model with rational expectations using persistent excitation. Each instrument, exogenous variable and expectational term is excited with a white noise process. Given superimposition, each input process is orthogonal so each equation can be estimated by OLS. Once the linear form is obtained and the time-consistent optimal feedback rule computed by dynamic programming, we apply the rational expectations solution of Anderson and Moore (1985) which is particularly suited when the leading structural matrix is singular. We apply the method to a nonlinear model of the UK Economy and report a series of impulse responses for output, inflation, the exchange rate and the short term interest rate.