Dynamic Macroeconomics

20.6 Monetary Policy Shocks and the Optimal Policy Rule
Up to now we have been assuming that the monetary policy rules can be
implemented without any policy errors. Yet there are two potential policy
errors that can creep into the implementation of monetary policy rules, and
will affect macroeconomic outcomes.
One is 
estimation errors
. If the central bank does not have full
information about the model of the economy, the natural rate of interest, the
natural rate of output (or unemployment), or even current macroeconomic
conditions, it will have to rely on estimates of these variables. Yet even the
best estimates will be characterized by estimation and prediction errors,
which will affect macroeconomic outcomes. Monetary policy rules must be
simple enough to be robust to such estimation errors, as an erroneous
assessment of the required policy action may destabilize rather than stabilize
the economy.
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The second is 
implementation errors
. Even an effectively designed
monetary policy rule may be subject to implementation errors, such as
delays, lags in the transmission mechanism of monetary policy, or other
human errors. Such errors will be equivalent to nominal shocks that affect
macroeconomic outcomes.
In what follows, we shall examine optimal monetary policy rules in the
presence of implementation errors of monetary policy. In the presence of
such errors, the optimal inflation rule in response to stochastic shocks is
given by

---

where is a white noise error in the implementation of the optimal inflation
rule 
(20.24)
. Thus, it can be seen as a nominal (monetary) shock.
The rational expectations solution of 
(20.38)
 is given by
Substituting 
(20.39)
 in 
(20.2)
, which determines deviations of output from its
natural rate, we get that fluctuations of output around its natural rate are
determined by
Optimal monetary policy is now third best. It cannot completely stabilize
both inflation and employment in response to productivity shocks, because it
operates through aggregate demand, and productivity shocks are supply
shocks. In addition, because of errors in the determination of the optimal
inflation rule, monetary policy shocks also affect fluctuations in both inflation
and output.
The same would apply to a Taylor rule, if that rule was subject to
implementation errors. Assume that instead of 
(20.31)
, the Taylor rule took
the form
where is a white noise error in the implementation of the optimal nominal
interest rate rule 
(20.31)
. This can be seen as a nominal (monetary) shock.
Inflation would then be
The rational expectations solution of 
(20.42)
 is given by
The inflation error in this case is 
ε
π
= −
γ
2
ε
i
.

---

As long as 
(20.36)
 is satisfied, the Taylor rule is equivalent to the optimal
(third-best) monetary policy rule 
(20.39)
. However, as with the optimal
inflation rule, in the case of monetary policy shocks, these nominal shocks
affect fluctuations of both inflation and real output.
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The analysis can be generalized to the version of the model with
endogenous unemployment persistence. In this case, not only will deviations
of inflation from target and unemployment from its natural rate be affected by
nominal and real shocks, even under the optimal monetary policy, but they
will also display endogenous persistence.
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