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.¹⁶

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.

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 = −γ₂εⁱ.

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.¹⁷

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.¹⁸

20.7