period. However, the transition probabilities are known and exogenous. In
our computations we used the values 0.25, 0.50 and 0.75 for pii, though here
we only report results obtained with p11 = p22 = 0.5, which were found to be
representative. The other parameters in the model take the same values as in
(Dupor 2005, Table 1, page 738).
We focus our analysis on the comparison of the behaviour of the optimal
policy and of the Taylor rule. In the case of the Taylor rule, the interest
rate reacts to output and inflation with coefficients of 0.5 and 1.5, respectively
(Taylor 1993).
The solution of the model is obtained using the method proposed by (Svensson
and Williams 2005) for solving Markov-switching rational expectations models.
Appropriately for our purposes, these authors argue that their approach to
model uncertainty is consistent with Greenspan’s risk-management approach,
mentioned in the Introduction.
2.2 Taylor-type rules
Simple, or Taylor-type, rules have been widely discussed among academics in
monetary policy analysis. Several arguments have been used in its defense. On
one hand, it has been argued that simple rules perform nearly as well as optimal
rules (see, for example, (Rudebusch and Svensson 1999)). On the other hand, it
has been argued that simple rules are very robust to several types of uncertainty
(see, for example, (Levin, Wieland, and Williams 1999)). We therefore consider
a set of simple rules to see how they compare to the optimal policy rule and
how good they are in dealing with uncertainty concerning movements in asset
prices. The set of rules used in our computations are summarised in Table 2.
We consider the original Taylor rule (Taylor 1993), where the interest rate
reacts to output and inflation with coefficients of 0.5 and 1.5, respectively. As