perception of the inflation target. Gradually, all variables return to their pre-shock levels.
5 Impulse response tradeoffs associated with different
learning rates
The estimated learning function in the time-varying target model implies very slow learning
about the target shift. In Figure 9, it takes 16 quarters for the perceived target to move
half way to the new target. To gain insight about the effects of improved credibility with
faster learning, the estimated learning parameter δ = 0.079 was increased by two standard
errors to 0.157 to simulate the implications of faster learning:
πP (t +1) =πP (t) - 0.157[rt - rte]+uP,t. (6)
Impulse responses were recalculated assuming all other aspects of the model would be
unaffected.7
Responses to the transitory policy shock show how faster learning can lead to excess
volatility in steady states. Here, a steady state corresponds to a policy regime with a
constant inflation target. With the inflation target unchanged, faster learning implies that
variables return to unchanged natural rates more quickly. However, as shown in Figure 11,
with faster learning, responses to a transitory policy shock are more volatile. The higher
volatility reflects that the immediate response of the perceived target to the transitory
policy shock is larger under faster learning.
With faster learning, the total real effects associated with transition to a new policy
regime are smaller. Figure 12 shows responses to a permanent target shock. The perceived
target adjusts halfway to the new target in 8 quarters and 3/4 of the way in 16 quarters—the
time it took to adjust halfway with the slower estimated learning parameter. Total real
effects can be measured as the integral between the impulse response of the output gap and
7This ceteris paribus is a simplifying assumption and may not hold in a general analysis containing a
model of endogenous learning.
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