RDP 1999-10: The Implications of Uncertainty for Monetary Policy 6. Optimal Policy Acknowledging Parameter Uncertainty

In this section we present uncertainty-aware optimal policy computations for the model described in Section 3 and compare them with naive optimal policy responses. The uncertainty-aware optimal policy response computed from Equation (8) is estimated using one thousand different draws from the underlying parameter distribution. A large number of draws is required because of the large number of parameters.

When computing the naive optimal policy response, it is necessary to specify the parameter vector that the monetary authority interprets as being the ‘true’ parameter values. Usually this vector would contain the original parameter estimates. However, we compute the naive policy response using the average value of the parameter vector draws. This prevents differences between the two policy profiles being driven by the finite number of parameter draws, the average of which may not coincide exactly with the original parameter draw.

Beginning with a one percentage point shock to output, Figure 5(a) compares optimal policy responses using the model described in Section 3. The darker line represents optimal policy when parameter uncertainty is taken into account while the lighter line represents the naive optimal policy response.

Figure 5: Optimal Interest Rate Responses Ignoring and Acknowledging Parameter Uncertainty
Deviations from equilibrium, percentage points
Figure 5: Optimal Interest Rate Responses Ignoring and Acknowledging Parameter Uncertainty

The key feature of interest in Figure 5(a) is the larger initial policy response when uncertainty is taken into account. While later oscillations in the cash rate are similar in magnitude, the early response of the cash rate is somewhat larger when policy takes parameter uncertainty into account. The finding that policy should react more aggressively because of parameter uncertainty is specific to the output shock used to generate Figure 5(a). For example, the naive policy response is relatively more aggressive for a one percentage point shock to the real exchange rate, as shown in Figure 5(b). This suggests that the persistence of a real exchange rate shock is more precisely estimated than the persistence of an output shock relative to the estimated effectiveness of policy for each of these shocks. With less relative uncertainty about the persistence of a real exchange rate shock, the optimal policy response taking into account uncertainty is more conservative because it is dominated by uncertainty about policy effectiveness.

Figures 5(c) – 5(e) present the policy responses to shocks to import prices, consumer prices and unit labour costs respectively. In each case, the naive policy response is initially more conservative than the policy response which takes account of parameter uncertainty.

These three types of nominal shocks to the model confirm that conservatism is by no means the generic implication of parameter uncertainty. In our model, it appears that uncertainty about the effectiveness of the policy instrument is generally dominated by uncertainty about model persistence and this explains the more aggressive optimal policy response to most of the shocks which we examined.