We first consider the relationship between the optimal value of p and the preference for funds rate volatility implicitly imposed in drawing the frontiers. For each model, Figure 7 shows three frontiers with different restrictions on funds rate volatility. In each case the baseline E-frontier is shown as a solid line. Using frontier rules as a guide, the stabilization gains from increased funds rate volatility are evidently rather small. Table 5 shows typical values of the standard deviation of the level of the funds rate generated by the policies that underlie the frontiers shown in the figure. In each case, outcomes corresponding to the baseline E-frontier are given in the first two columns. Except for the MSR model, relaxing the constraint on funds rate volatility much beyond that implied by the E-frontier entails so much volatility of the level of the funds rate that the optimal policy rule would regularly dictate negative nominal interest rates in an environment of reasonably low steady-state nominal interest rates (steady state inflation plus real interest rate).

Qualitatively, all four models exhibit a pattern in which allowing higher interest volatility is associated with smaller values of p for the 3-parameter rules on the policy frontier. However, the quantitative results differ somewhat across models. In the FM model, the reduction inp is particularly pronounced: doubling the upper bound on SD(Ar) causes the range of values for p to drop from [0.85,0.95] to [0.75,0.92]. In the other three models, relaxing the funds rate volatility constraint leads to somewhat smaller reductions in the optimal value of p. In the FRB model, doubling SD(Ar) reduces the optimal value of p by about 0.07 on average, from a range of [0.96,1.02] to [0.93,0.96]. In TAYMCM and in MSR, doubling SD(Ar) only reduces the optimal value of p by about 0.03. Evidently, even with relatively high interest rate volatility, a high degree of interest rate smoothing is preferred in these models.

Volatility of Funds Rate Levels and Changes

Model | E Frontier | Alternative Frontier #1 | Alternative Frontier #2 | |||

SD(Ar) | SD(r) | SD(Ar) | SD(r) | SD(Ar) | SD(r) | |

FM | 1.0 | 5 | 2.0 | 7 | 3.0 | 9 |

MSR | 0.6 | 1.5 | 1.2 | 2.3 | 1.7 | 2.9 |

FRB | 1.2 | 4.5 | 2.4 | 7 | 3.7 | 9 |

TAYMCM | 2.6 | 6 | 5.1 | 9 | 7.7 | 11 |

We first consider the relationship between the optimal value of p and the preference for funds rate volatility implicitly imposed in drawing the frontiers. For each model, Figure 7 shows three frontiers with different restrictions on funds rate volatility. In each case the baseline E-frontier is shown as a solid line. Using frontier rules as a guide, the stabilization gains from increased funds rate volatility are evidently rather small. Table 5 shows typical values of the standard deviation of the level of the funds rate generated by the policies that underlie the frontiers shown in the figure. In each case, outcomes corresponding to the baseline E-frontier are given in the first two columns. Except for the MSR model, relaxing the