We consider a temporary ZLB episode, as in Werning (2011). Between times 0 and $T>0$, the natural rate of interest is negative. In response, the central bank maintains its policy rate at 0. After time $T$, the natural rate is positive again, and monetary policy returns to normal. This scenario is summarized in table 1A. We analyze the ZLB episode using the phase diagrams in figure 2.

Figure 2.

Table 1.

. | Timeline . | Natural Rate of Interest . | Monetary Policy . | Government Spending . |
---|---|---|---|---|

A. ZLB episode | ||||

ZLB | $t\u2208(0,T)$ | $rn<0$ | $i=0$ | – |

Normal times | $t>T$ | $rn>0$ | $i=rn+\varphi \pi $ | – |

B. ZLB episode with forward guidance | ||||

ZLB | $t\u2208(0,T)$ | $rn<0$ | $i=0$ | – |

Forward | $t\u2208(T,T+\Delta )$ | $rn>0$ | $i=0$ | – |

guidance | ||||

Normal times | $t>T+\Delta $ | $rn>0$ | $i=rn+\varphi \pi $ | – |

C. ZLB episode with government spending | ||||

ZLB | $t\u2208(0,T)$ | $rn<0$ | $i=0$ | $g>0$ |

Normal times | $t>T$ | $rn>0$ | $i=rn+\varphi \pi $ | $g=0$ |

. | Timeline . | Natural Rate of Interest . | Monetary Policy . | Government Spending . |
---|---|---|---|---|

A. ZLB episode | ||||

ZLB | $t\u2208(0,T)$ | $rn<0$ | $i=0$ | – |

Normal times | $t>T$ | $rn>0$ | $i=rn+\varphi \pi $ | – |

B. ZLB episode with forward guidance | ||||

ZLB | $t\u2208(0,T)$ | $rn<0$ | $i=0$ | – |

Forward | $t\u2208(T,T+\Delta )$ | $rn>0$ | $i=0$ | – |

guidance | ||||

Normal times | $t>T+\Delta $ | $rn>0$ | $i=rn+\varphi \pi $ | – |

C. ZLB episode with government spending | ||||

ZLB | $t\u2208(0,T)$ | $rn<0$ | $i=0$ | $g>0$ |

Normal times | $t>T$ | $rn>0$ | $i=rn+\varphi \pi $ | $g=0$ |

This table describes the three scenarios analyzed in section IV: the ZLB episode, in section IVA; the ZLB episode with forward guidance, in section IVB; and the ZLB episode with government spending, in section IVC. The parameter $T>0$ gives the duration of the ZLB episode; the parameter $\Delta >0$ gives the duration of forward guidance. We assume that monetary policy is active ($\varphi >1$) in normal times in the NK model; this assumption is required to ensure equilibrium determinacy (Taylor principle). In the WUNK model, monetary policy can be active or passive in normal times.

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