RDP 2008-10: Solving Linear Rational Expectations Models with Predictable Structural Changes 1. Introduction

Methods for solving linear stochastic models with rational expectations, like Blanchard and Kahn (1980), Binder and Pesaran (1995), Uhlig (1995), Anderson (1997), Klein (2000) and Sims (2002), assume a time-invariant structure; the parameters that govern the behaviour of the system are taken to be constant. Although the rational expectations solution has recently been extended so as to allow some of the parameters to vary in accordance with an exogenous Markov process with given transition probabilities – see Davig and Leeper (2007) and Farmer, Waggoner and Zha (2007) – these methods do not handle credible announcements that entail future variations to the structural parameters.

The situations we have in mind are not merely theoretical curiosities, but rather real situations of practical importance. Take, for instance, the case of Chile with respect to announcements regarding inflation targets. For example, the first inflation target was announced in September 1990 for the 12 months of 1991; later, in September 1999, the central bank announced a point target for 2000 and also, starting in 2001, a stationary target range for the indefinite future.^[1] Other examples include the announcement of the introduction of the goods and services tax in Australia in 2000 and the recent announcement by the UK Government to lower the VAT only to increase it again after 13 months. To the extent that such announcements are credible, the behaviour of the economy in the period between the announcement of the policy and its implementation would be poorly captured using available solution methods.

As emphasised by Marschak (1953), in the case of a foreseen change in structure, the purely empirical projection of observed past regularities into the future cannot be used reliably in decision-making. To produce meaningful forecasts, knowledge of the past structure and of observed past regularities has to be supplemented by the way the structure is expected to change.

This paper establishes a rational expectations solution for linear stochastic models in the face of predictable structural variations. The next section reviews the time-invariant solution of Sims (2002) for linear rational expectations models upon which we build to develop the solution under anticipated structural variations. Section 3 states the problem formally and then develops the rational expectations solution under predictable structural and additive variations. Section 4 illustrates the solution with a set of numerical examples while Section 5 concludes.

Footnote

See Morandé and Schmidt-Hebbel (2000) [1]