RDP 2011-02: Long-term Interest Rates, Risk Premia and Unconventional Monetary Policy 6. Announcements and Transitions
April 2011
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The analysis to this point assumes that the long-term interest rate rule has always been in operation. This is an unrealistic assumption for the types of policies we want to study. In practice, it is relevant to know how the economy would behave if the central bank announced a temporary deviation from a rule or the adoption of a different rule in the future. As Taylor (1993) stresses, the temporary deviation from a rule and the transition towards a new rule are relevant practical concerns despite having received little academic attention. It is therefore important to know how the economy would behave if, in the case of long-term interest rate rules, the implementation of the new policy is announced in advance, or if, in the case of announcements about the future path of the short rate, the deviation from an established policy is temporary. Next, we study the economy's response to a temporary deviation from a rule at the zero lower bound and to a transition from a Taylor rule to a long-term interest rate rule.
Standard solutions for linear rational expectations models cannot capture temporary deviations or transitions if the reversion to an abandoned rule or the implementation of the new rule is known in advance. These announcements represent a foreseen structural change; standard solutions presuppose a constant structure. Cagliarini and Kulish (2008), however, extend the rational expectations solution to handle foreseen structural changes.^{[16]} They show that if the structure to which an economy converges is consistent with a unique equilibrium, then so is the transition to it. So, if the policy rule to which an economy converges implies a unique equilibrium, the transition to that rule or a temporary deviation from that rule is also unique. At the zero lower bound, this result has an important implication. In general, a constant interest rate, by itself, generates indeterminacy. But if the central bank announces that it will keep the interest rate constant for a finite period and then revert to a rule that achieves a unique equilibrium, that path would be unique.
The zero lower bound
Figure 7 shows two simulations in which the short rate approaches the zero lower bound. Interest rates are in per cent, rather than percentage deviations from steady-state. There are no more shocks from period five on. The first simulation – the baseline – shows how the economy returns to steady state if the policy rule remains unchanged. The second simulation considers the consequences of announcing in period 5 that the short-term interest rate will be held at zero for 8 quarters after which the central bank reverts to the abandoned rule.^{[17]}
For the announcement to be stimulatory, the sequence of interest rates that is announced has to be lower than otherwise. If the interest rate would have been zero for 8 quarters regardless, the announcement would have no impact. The announcement matters precisely because it changes expectations about the future path of the short rate. The top panels show how the announcement of future lower short rates increases output and inflation relative to the baseline.
The middle right panel shows the response of the long-term nominal interest rate, R_{12,t}. The expectation that short-term rates will remain low for an extended period works, through the expectations hypothesis channel, to lower the long rate. Interestingly, the announcement also lowers the long rate through its impact on the risk premium. The reasoning lies in the response of the money supply. To implement a lower short-term nominal rate, the central bank has to expand the money supply, and in doing so, it increases liquidity and thereby decreases the premium required to hold long-term debt. Ugai (2006) argues that in Japan, a commitment to maintain zero interest rates is likely to impact on the risk premium between the short-term interest rate and the yield on long-term government bonds. In the model, this is true.
The transition to a new rule
If a central bank decides to adopt a long-term interest rate rule, an important consideration is how the economy reacts both to the change itself and to the announcement of the change.
Figure 8 shows a simulation in which the central bank announces that, in 4 quarters, it will use a rule for instead of the Taylor rule. At the same time, the central bank announces a more expansionary setting of the long-term interest rate rule (ρ_{R} = 0.75, ρ_{y} = 0.045, ρ_{π} = 0.49 and ρ_{µ} = 0.35). The economy starts away from steady-state after being hit with a technology shock. The announcement happens in period 6. Figure 8 shows the dynamics of key variables over the period. Relative to the response that would prevail if the Taylor rule were not abandoned, the policy rule calls for a lower real long-term interest rate. Consistent with this, through the term structure relation, the real short rate is also lower. Output and inflation, as a result, are both stronger than otherwise.
Footnotes
See Appendix C for details. [16]
We assume the announcement to be perfectly credible. For an analysis of imperfect credibility at the zero lower bound see Bodenstein, Hebden and Nunes (2010). [17]