RDP 2008-10: Solving Linear Rational Expectations Models with Predictable Structural Changes 5. Conclusions

We have outlined a technique to solve linear rational expectations models in the face of anticipated changes to the parameters or exogenous variables. This solution has a number of important applications. Pre-announced changes to a policy rule can be examined using the techniques discussed in this paper. Variations in the response of monetary policy to the state of the economy, adjustments to the monetary policy objectives or anticipated deviations from a policy rule can all be analysed using the methods outlined in this paper. In more fully specified models, one can examine the consequences of shifting from one policy regime (such as monetary targeting) to another policy regime (inflation targeting). Of course, the method we propose also deals with other anticipated changes to the structure of an economy.

We have shown that the properties of the final structure are crucial for the way the system behaves between the time agents become aware of a forthcoming event and the time that the event occurs.

The results have implications for the application of policy rules. For example, if a policy-maker uses a monetary policy rule that does not satisfy the Taylor principle, then a unique rational expectations equilibrium typically does not exist. These rules are considered ‘bad’ as they lead to multiple equilibria. However, if the policy-maker makes a credible announcement that it will adopt a better rule, one that satisfies the Taylor principle, at some point in the future, then a unique equilibrium will exist for the economy – regardless of exactly when this will occur or how bad the policy rule is in the intervening period.

We have assumed that all announcements, for instance, of an impending policy change, are credible. Further research could extend these techniques to examine the effect of such announcements when credibility is less than perfect.