Estimation and Solution of Models with Expectations and Structural Changes

Standard solution methods for linearised models with rational expectations take the structural parameters to be constant. These solutions are fundamental for likelihood-based estimation of such models. Regime changes, such as those associated with either changed rules for economic policy or changes in the technology of production, can generate large changes in the statistical properties of observable variables. In practice, the impact of structural change on estimation is often addressed by selecting a sub-sample of the data for which a time-invariant structure seems valid. In this paper we develop solutions for linearised models in the presence of structural changes using a variety of assumptions relating to agents' beliefs when forming expectations, and whether the structural changes are known in advance. The solutions can be put into state space form and the Kalman filter used for constructing the likelihood function. Structural changes and varying beliefs trigger movements in the reduced-form coefficients and hence model variables follow a time-varying coefficient VAR. We apply the techniques to two examples: a disinflation program and a transitory slowdown in trend growth.