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, institutional changes, or changes in the technology of production, can generate large changes in the statistical properties of observable variables. In practice, structural change is accounted for during estimation by selecting a sub-sample for which a time-invariant structure seems valid. In this paper we develop solutions for linearised models with structural changes under a variety of assumptions regarding agents’ beliefs about those structural changes. We put the solutions in state space form and use the Kalman filter to construct the likelihood function. We apply the techniques to three examples: an inflationary program, a disinflation program and a transitory slowdown in trend growth. ∗We thank Adam Cagliarini, Alex Heath, Gordon Menzies, James Morley and Michael Plumb for comments. †School of Economics, Australian School of Business, University of New South Wales. [email protected] ‡School of Economics, Faculty of Arts and Social Sciences, University of Sydney. [email protected]