Forward guidance with an escape clause: when half a promise is better than a full one

ABSTRACT

Using a three-equation New Keynesian model we find that incorporating an escape clause (EC) into forward guidance (FG) is welfare improving as it allows the monetary authority to avoid cases in which the cost of reduced flexibility is too high. The EC provides the central bank with another instrument (additional to the promised policy rate), the announced threshold. The greater the size of the recessionary shock the lower the optimal promised rate and the higher the optimal threshold (i.e. the higher the probability of delivering the promised rate). While FG with an EC is better than discretion for facing any zero-lower bound (ZLB) situation, unconditional FG performs better than discretion only in the most extreme $16\mathrm{\%}$ of ZLB events. Furthermore, even for very large recessionary shocks it is not optimal to make unconditional promises.

KEYWORDS:

• Forward guidance
• escape clause
• zero-lower bound
• central bank communication

JEL CLASSIFICATION:

• E47
• E52
• E58

Acknowledgements

We are grateful to Luis E. Basto, Petra M. Geraats and seminar participants at Banco de la Republica and at the EEA-ESEM 2014 Conference for their comments. The views expressed here are those of the authors and do not represent those of Banco de la Republica or Ministerio de Hacienda y Credito Publico.

ORCID

Julian A. Parra-Polania http://orcid.org/0000-0003-3344-5949

Notes

¹ Examples of this practice after the crisis can be seen in the communications of the Fed, since 2008, the Bank of Japan and the Bank of Canada, since 2009, and the Bank of England and the European Central Bank, since 2013.

² These names are related to two stories from the Greek mythology. The first one refers to the Oracle of Delphi, where Pythia the priestess used to foretold the future. The second refers to the story of Odysseus (Ulysses) who had his men tie him to the mast in order to escape from the temptation of the Sirens’ song.

³ In August 2013, during a press conference, the Governor of the Bank of England (BoE) declared that their guidance did not imply a change in the reaction function (Bank of England 2013b). Furthermore, in recent speeches the Deputy Governor for Monetary Policy of the BoE remarked that their intention was not to pre-commit to a ‘lower for longer’ policy (Bank of England 2013c) and one of the members of the Monetary Policy Committee attributed the interest rates’ rise to the fact that markets were expecting that the economy would reach 7% unemployment before it was originally expected and stated that ‘this is rather sooner than I think is likely’ (Bank of England 2013d). These type of statements seemed to communicate that the BoE was not changing its approach to the conduct of policy but had a more negative view on future economy than the market (totally in contradiction to the type of guidance that stimulates the economy).

⁴ Announcing the conditions that might lead to deviations from the promised rate is also known as ‘state-contingent’ guidance as opposed to ‘time-contingent’ guidance, in which the central bank sets a date after which the current policy stance may change. The Fed started providing time-contingent guidance but it currently provides ‘state-contingent’ guidance, as does the Bank of England (Bank of England 2013a). Previous literature has pointed out that time-contingent guidance may impose high costs on the central bank in terms of flexibility and, for the same reason, may be less credible and effective (Woodford 2012).

⁵ In order to have a terminal point a third period is assumed in which shocks and variables return to their long-run expected values.

⁶ Since there is no commitment and shocks are independently distributed over time $E_t{y}_{t+1}$, $E_t{\pi }_{t+1}=0$.

⁷ This is a simplification related to the fact that we reduce the analysis of the lower-bound problem to a two-period model. In a multiple or infinite period model one could take into account the possibility of facing the lower-bound situation for several periods before the economic recovery. In our two-period setup, we eliminate uncertainty about the moment in which recovery occurs (the shock in $t+1$ is certainly positive) but there is still uncertainty about its strength (the exact value of ${\epsilon }_{t+1}$ is unanticipated).

⁸ Note that $E_t{\pi }_{t+1}=\kappa E_t{y}_{t+1}$ and $E_t{y}_{t+1}=-\frac{1}{\delta }{\theta }_{t+1}F({\epsilon }_h)+{\int }_0^{{\epsilon }_h}{\epsilon }_{t+1}f({\epsilon }_{t+1})d{\epsilon }_{t+1},$ where $F(\cdot )$ corresponds to the cdf of ${\epsilon }_{t+1}$.

⁹ We use Matlab R2013b. The numerical solution is obtained by calculating Equation 8 for many different values of ${\theta }_{t+1}$ and ${\epsilon }_h$ (i.e. using a fine grid in the ranges $[-0.8\mathrm{\%},0\mathrm{\%}]$ and $[0,0.4]$, respectively). As explained below, we assume $f({\epsilon }_{t+1})$ is a truncated normal on ${\mathbb{R}}^{+}$. Then we find the minimum value of (8), and therefore the optimal values of ${\theta }_{t+1}$ and ${\epsilon }_h$. As an additional step, we verify that the obtained solution satisfies the FOCs of the problem (i.e. derivatives of (8) with respect to ${\theta }_{t+1}$ and ${\epsilon }_h$ must be zero).

¹⁰ Following the structure of the standard New Keynesian model, the parameter $\kappa$ is equal to $\left[\frac{(1-\omega )(1-\beta \omega )}{\omega }\right]\left[\frac{\delta +\phi }{1+\phi \mu }\right]$ and $\lambda =\frac{\kappa }{\mu },$ where $\omega (0.66),\mu (7.66)\mathrm{a}\mathrm{n}\mathrm{d}\phi (0.47)$ are underlying structural parameters representing, respectively, the probability that the firm cannot adjust its price (under Calvo pricing), the elasticity of substitution between goods and the elasticity of the real marginal cost with respect to the output level.

¹¹ This probability is taken from Fernandez-Villaverde et al. (2015). Gavin et al. (2013) estimate the probability of hitting the ZLB for different Taylor-type rules (they allow for variation of the weights on inflation and output) and find values between 1.5% and 8.4%.

The probability of hitting the ZLB is very sensitive to the combination of values set to $i_l,\delta$ and to ${\sigma }_{\epsilon ,t}$, such that a small change to one of these parameters may lead to an economy that virtually never hits the ZLB or, on the contrary, that is permanently experiencing such situation. For the values set to $\delta$ (0.16) and $i_l$ ($-5.2\mathrm{\%}$), the consistent value of ${\sigma }_{\epsilon ,t}$ is 0.2034.

¹² It can be verified that ${\bar{\epsilon }}_{t+1}=0.1623$ and ${\sigma }_{\epsilon ,t+1}=0.1226$.

¹³ Since $E_{t+1}{y}_{t+2}=E_{t+1}{\pi }_{t+2}=0$ (see footnote 5), $y_h=-(1/\delta ){\theta }_{t+1}+{\epsilon }_h$ and ${\pi }_h=\kappa y_h$. Note that we are only translating the optimal threshold in terms of observable variables in practice. The problem becomes more complex if the central bank chooses the optimal threshold in terms of an endogenous variable i.e. y or $\pi$ (rather than in terms of an exogenous shock) due to the fact that these variables are functions of the announced rate.

¹⁴ Strictly speaking, no promise is unconditional unless ${\epsilon }_h\to \mathrm{\infty }$; however, for practical purposes one could treat as ‘unconditional’ a promise that implies a fulfilment probability higher than $95\mathrm{\%}$.

¹⁵ We also allow for changes in $i_l$ in the range of $[-7\mathrm{\%},-3\mathrm{\%}]$. Since the results may become unreasonable when we change this parameter only (as explained in footnote 11), for each value we also recalibrate ${\sigma }_{\epsilon ,t}$ so as to make it consistent with a probability of ZLB equal to $5.5\mathrm{\%}$. We find that although an increase in the absolute value of $i_l$ (accompanied by a consistent change in ${\sigma }_{\epsilon ,t}$) increases both the absolute value of the promised rate and the announced threshold, it affects neither the relative promised rate (${\theta }_{t+1}/i_l$) nor the probability of delivering it ($F({\epsilon }_h)$). Furthermore, it does not affect $\mathrm{\Delta }L$ either.

¹⁶ For illustration purposes, we present some results for different values of $\omega$ and $\beta$ in Tables A1 and A2.