In this section, we focus in greater detail on the properties of 3-parameter rules of the form given in equation (4). This class of policy rules nests ‘level” rules such as those considered by Henderson and McKibbin (1993) and Taylor (1993), in which the lagged funds rate coefficient p = 0. We shall use the term ‘Interest rate smoothing” to refer to rules in which this coefficient is substantially larger than zero, as in partial adjustment rules.

Table 3 indicates the values of a, p, and p for six different rules in this class. Rules “A” and “B” are first-difference rules taken from the policy frontier of the FRB model. These rules correspond to values of X = 1/4 and X = 3/4, respectively (i.e., the weight on output volatility relative to inflation volatility) in the objective function given in equation (3). Rule “T” is the rule proposed by Taylor (1993a). Rule “T2” is a modified version of Taylorfc rule in which the coefficient on the output gap has been doubled. Rules “V” and “W” are optimal policy rules for the dynamic general equilibrium model analyzed by Rotemberg and Woodford (1997).

Table 4 Rule Comparison Table

Standard Deviations | |||||

Model | Rule | SD(y) | SD(n) | SD(r) | SD(Ar) |

FM | A | 3.78 | 1.85 | 8.89 | 1.97 |

В | 2.37 | 2.45 | 7.71 | 1.83 | |

T | 2.68 | 2.63 | 3.57 | 0.75 | |

T2 | 2.32 | 2.84 | 3.83 | 0.90 | |

V | 21.2 | 7.13 | 27.2 | 4.38 | |

w | 20.5 | 6.57 | 27.9 | 4.59 | |

MSR | A | 0.84 | 0.4 | 1.17 | 0.34 |

В | 0.58 | 0.53 | 1.33 | 0.48 | |

T | 0.99 | 0.7 | 1.01 | 0.3 | |

T2 | 0.87 | 0.73 | 1.19 | 0.5 | |

V | 1.95 | 0.41 | 1.31 | 0.19 | |

W | 1.88 | 0.38 | 1.3 | 0.19 | |

FRB | A | 2.12 | 1.46 | 4.34 | 1.22 |

В | 1.41 | 1.65 | 4.5 | 1.24 | |

T | 2.92 | 1.86 | 2.51 | 0.9 | |

T2 | 2.21 | 2.02 | 3.16 | 1.2 | |

V | 6.32 | 1.55 | 4.67 | 1.11 | |

W | 6.06 | 1.53 | 4.88 | 1.19 | |

TAYMCM | A | 2.33 | 1.73 | 4.78 | 1.71 |

В | 1.95 | 1.79 | 5.03 | 2.01 | |

T | 2.89 | 2.58 | 4 | 1.58 | |

T2 | 2.55 | 2.36 | 4.35 | 2.41 | |

V | 4.31 | 2.06 | 4.24 | 1.24 | |

w | 4.26 | 2.02 | 4.47 | 1.33 | |

U.S. Data (1980:1- 1995:2) | 2.4 | 2.1 | 3.7 | 1.3 |

Table 4 clearly shows that rules T and T2, in which the level of the funds rate responds to the output gap and inflation rate, are dominated by rules like A and B, where thefirst-difference of the funds rate responds to the output gap and inflation rate. Rules V and W exhibit very small responses to the output gap, and therefore also do relatively poorly at stabilizing output and inflation in the four models studied here. Even if policymakers only care about stabilizing inflation (i.e., X = 0), the output gap coefficient should be substantially larger than that of rules V and W, because the current output gap is an important leading indicator for the inflation rate.

In this section, we focus in greater detail on the properties of 3-parameter rules of the form given in equation (4). This class of policy rules nests ‘level” rules such as those considered by Henderson and McKibbin (1993) and Taylor (1993), in which the lagged funds rate coefficient p = 0. We shall use the term ‘Interest rate smoothing” to refer to rules in which this coefficient is substantially larger than zero, as in partial adjustment rules. Table 3 indicates the values of a, p, and p for six different rules in this class. Rules “A” and “B” are first-difference rules taken from the policy frontier of the FRB model. These rules correspond to values of X = 1/4 and