do that using the optimal policy, described above, as a benchmark. We only
present the results for p11 = 0.5 and p22 = 0.5, as we did not find significant
differences in our computations for the other combinations of transition probabilities.
We start by computing the unconditional standard deviations of the variables
of the model, for the optimal policy and for Taylor-type rules. The results
are presented in Table 3. Except for the simple inflation-forecast based rule
(IFB), output and its components (consumption and investment) are much
more stable under Taylor-type rules than under the optimal policy. From the
results in Table 3, we would conclude that the Taylor rule is significantly more
effective at stabilising output, but not employment. In fact, output is much
more stable (around ten times) under a Taylor rule than under the optimal
policy. The performance of the simple inflation-forecast based rule, which, in
general, delivers the worst results in terms of volatility, improves significantly
when the interest rate reacts to expected output and to asset prices. These
results may be related with the findings of (Levin, Wieland, and Williams 2003)
that including an output gap term makes inflation-forecast based rules more
robust. The real interest rate is always much more stable when policymakers
follow Taylor-type rules than when they follow the optimal policy, which may
be a sign that the Taylor rules are not aggressive enough.
To analyse the adjustment process of output following the collapse of asset
prices, under Taylor-type rules and optimal policy, we investigate the dynamics
of the economy when a persistent non-fundamental shock hits the economy. We
do this evaluation by means of impulse-response functions, Figure 2 to 8, and
by analysing t-steps ahead standard deviations of output following a persistent
non-fundamental shock in asset prices, reported in Tables 4 and 5.
Concerning the impulse-response functions, except for the simple inflation-based
forecast rule, which seems to produce very unstable patterns, the results are
very similar for the whole set of simple Taylor-type rules considered in this
11