Estimation and Solution of Models with Expectations and Structural Changes

Abstract

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

Approximating Time Varying Structural Models with Time Invariant Structures

“…Thus, to match the time varying coe¢ cient VAR evidence, it is necessary to consider variations in DSGE auxiliary parameters rather than variations in DSGE structural parameters. Kulish and Pagan (2014) have developed solution and estimation procedures for models with abrupt breaks and learning between the states. Their solution for the pre-break and post-break period is a constant coe¢ cient VAR, while for the learning period is a time varying coe¢ cient VAR.…”

“…Kulish and Pagan (2014) characterize the decision rules of a DSGE model when predictable structural breaks occur. Magnusson and Mavroedis (2014) and Huang (2014) examine how variations in the certain parameters may a¤ect the identi…cation of other structural parameters and the asymptotic theory of maximum likelihood estimators.…”

Estimating the Expected Duration of the Zero Lower Bound in DSGE Models with Forward Guidance

“…To solve for equilibria under forward guidance we use a special case of the solution developed by Kulish and Pagan [2012] for forward-looking models in the presence of possibly anticipated structural change. That solution has more general application than the context we are considering here, so we provide a simplified discussion to highlight some important features.…”

“…Our approach here is different. We build on Kulish and Pagan [2012] and construct the likelihood function for the case in which monetary policy switches at the zero lower bound from following a standard Taylor-type rule to forward guidance. We use the model of Ireland [2004] as a benchmark because it is the closest estimated specification to the simple type of New Keynesian model used in the theoretical literature on forward guidance.…”

Time-varying Cointegration and the UK Great Ratios

“…2 Galvão et al (2016) by contrast use methods similar to those employed in this paper. Finally, Kulish and Pagan (2017) consider some different assumptions about belief updating and explore various solution methods.…”