small subset of information available to the central bank, namely, inflation, the
output gap and, possibly, asset prices. On the other hand, optimal rules take
into account all state variables, shocks and the uncertainty in the economy,
namely, in our economy it takes into account the switching nature of asset
prices and therefore the probability of a crash. To obtain the results reported
below, we employed the methods proposed by (Svensson and Williams 2005),
assuming full information under commitment.2
We focus our analysis on output and real interest rate adjustment when the
asset price bubble bursts, namely, we compare the performance of Taylor-type
rules and optimal policy during and after a bubble episode. Simulations
seem to suggest that the optimal policy is more effective in containing the
bubble-induced expansion, producing a soft landing. Additionally, our results
suggest that real interest rates are less volatile under Taylor-type rules.
Our exposition is organised as follows. Section 2 presents the model and
discusses the monetary policy framework. Section 3 evaluates the performance
of the economy under Taylor-type rules and optimal policy. Section 4 concludes.
2 A model with Markov-switching asset prices
In a world where asset price movements simply reflect fundamentals, their only
role in monetary policy making is as a conveyer of information about the state
of the economy. However, there is evidence that asset prices are partly driven by
non-fundamental movements, that is, there are fads or bubbles — e.g., (Shiller
2000). In these periods, asset prices may induce inefficient decisions by firms
and consumers, and therefore destabilise the economy. This has been the main
argument for monetary policy to respond directly to asset prices — see, for
2(Alexandre, Baçào, and Driffill 2007) use those methods in the context of an
open-economy model.