RDP 2012-08: Estimation and Solution of Models with Expectations and Structural Changes 5. Conclusion

In this paper we develop a solution for linear models in which agents use model-consistent expectations but their beliefs about the structure may or may not be consistent with the correct model of the economy, at least for a period of time. The solution in each case takes the form of a time-varying coefficient VAR. This can be put into a state space form and the Kalman filter can be used to construct the likelihood.

In the case of an anticipated structural change, standard estimation methods with observed past regularities would not be a reliable guide, unless the estimation is supplemented by some knowledge of the way the structure was expected to evolve. As we have shown through numerical examples, knowledge of any in-sample structural changes that have taken place can increase the number of observations which are usable and can therefore substantially improve the quality of estimation. Even credible announcements of structural changes that take place out-of-sample would serve to improve the estimates.