Hedging the zero bound with threshold-based forward guidance

Richard Harrison, Lena Boneva and Matt Waldron.

Following the Great Recession, many central banks cut their policy rates towards their lower bounds and turned to unconventional policy measures in a bid to revive their economies.   That was accompanied by an increasing use of `forward guidance’ about the future path of the policy rate.  In this post we summarise results from our ongoing research on `Threshold-Based Forward Guidance’, whereby the policymaker links their decision to raise the policy rate from the lower bound to outturns for particular macroeconomic variables.   We show that TBFG can improve welfare at the lower bound by increasing expected future inflation and, unlike forward guidance based purely on calendar time, by shrinking the variance of possible outcomes for inflation around the target.


One rationale for forward guidance (and the rationale in our paper) is to provide near-term stimulus through a commitment to hold the policy rate `lower for longer’ to reduce long-term real interest rates in order to stimulate economic activity and raise inflation.  This type of commitment policy at the lower bound was first proposed by Paul Krugman in his 1998 paper and has subsequently been advocated by some academics and policymakers in the guise of, for example, nominal GDP targeting or the temporary adoption of a price-level target.

All of these policies – including the forward guidance policy we study – have in common that they involve a promise to temporarily overshoot the inflation target in the future, thus reducing expected real interest rates and increasing aggregate demand today.  As a result, forward guidance of this sort is sometimes called `Odyssean’ because, just as Odysseus committed himself to ignoring the siren calls and staying on his ship by having himself bound to the mast, the policymaker is committing themselves to future policy actions that they may not wish to enact when the time comes.  Consequently, as noted by Nakata, some policymakers have cautioned against such policies because they seem sceptical of their ability to credibly commit to ‘time inconsistent’ actions. To take just one example, Cœuré argues that

“The promise of higher future inflation, if credible, induces private agents to substitute future for current consumption, hence providing additional stimulus today. […] The main challenge of such guidance is its inherent inconsistency over time and thus lack of credibility. When the time comes, the central bank may be tempted to deviate from its prior commitment.”

In our paper we study a form of `threshold-based’ forward guidance (TBFG), in which the policymaker’s commitment to hold the policy rate at the lower bound is state contingent.  The state-contingent commitment is designed to ensure that certain macroeconomic variables do not exceed pre-specified `threshold’ values in any state of the world in which the TBFG policy remains in effect.  As discussed below, our results suggest that this form of TBFG can be used as a temporary policy measure to improve outcomes at the lower bound, while limiting the extent to which the policymaker promises to behave in a time inconsistent manner.

While our analysis is clearly motivated by policies implemented by the FOMC and MPC, both of whom stated that policy rates would not be increased at least until (among other conditions) the unemployment rate fell below certain ‘threshold’ values, it falls well short of an evaluation of those real-world policies for two reasons.  First, we abstract from many of the details of those policies – e.g. consideration for financial stability concerns.  Second, the communications that accompanied those policies tended to emphasise their role in clarifying central bank behaviour rather than in providing stimulus.  With that in mind, our exercise could be regarded as an evaluation of `what if’ a central bank did try to use TBFG to impart stimulus at the lower bound.

A brief description of the exercise

Our model economy is a textbook New Keynesian model containing forward-looking IS and New Keynesian Phillips curves.  Expectations are rational.  We solve the model using global methods, allowing us to account for the skewed distributions of the output gap and inflation, particularly in the vicinity of the lower bound.

The baseline description of monetary policy is that it follows ‘optimal discretion’: it is set on a period-by-period basis to maximise the welfare of households without any commitment to future policy actions, which means that it is time consistent.

We then consider a situation in which a negative demand shock arrives that is sufficiently large to cause the policy rate to be constrained by the lower bound.  The shock creates a recession because monetary policy cannot be eased enough to offset the negative impulse to demand.  The resulting equilibrium distributions for inflation, the output gap and the policy rate represent our baseline case against which we compare the outcomes of alternative policies.

Our policy experiment starts in the period after the negative demand shock hits the economy.  We focus on whether outcomes can be improved relative to the baseline policy behaviour, while limiting the extent to which the policymaker promises to do something time inconsistent.  To do so, we must relax the baseline assumption that the policymaker cannot make promises.

Specifically, we assume that the policymaker is able to make a one-off, fully credible commitment that the policy rate will be held at the lower bound until a particular set of threshold conditions has been met.  In one set of experiments, we examine TBFG policies with thresholds defined in terms of the inflation rate.  In another set, we examine ‘calendar based’ forward guidance (CBFG) in which the policymaker promises to hold the policy rate at the lower bound until a pre-specified date.

Headline results

Figure 1 plots the distribution of inflation conditional on the large negative demand shock hitting the economy in period 0, for a selection of alternative policies.  Panel (a) shows the distribution of inflation for the baseline policy assumption of optimal discretion.   The lower bound on the policy rate induces a negative skew in the distributions of inflation and output because it cannot fall sufficiently to offset the negative shocks (assuming that the policymaker has no other tools available).  This effect was explored in another Bank Underground post by Alex Haberis, Riccardo Masolo and Kate Reinold.

Panel (b) shows that if the inflation threshold is set equal to the target (of zero), then the distribution of inflation outcomes is almost identical to the baseline case of optimal discretion.  That is because the policymaker is not promising to behave in a way that is very different from the optimal discretion case (panel (a)).  Inflation expectations are no higher and so there is no stimulus relative to that case.

Panel (c) shows that when the inflation threshold is set above the inflation target (at a value that turns out to maximise welfare in the experiment), the inflation distribution is narrowed dramatically.  The threshold-based guidance provides stimulus in ‘bad’ states of the world, substantially reducing the negative skew in the distribution.  But in ‘good’ states of the world, when positive demand shocks arrive, it is more likely that the threshold will be crossed with policy returning to the time consistent optimal discretion rule.  In those cases, the additional stimulus associated with the threshold is removed.

The contrast with calendar-based guidance in panel (d) is stark.  CBFG imparts stimulus regardless of the state of the economy.  While it offsets the negative skew by raising expectations sufficiently to reduce the impact of the zero bound constraint, it leads to worse outcomes in both good and bad states of the world because it provides too much stimulus in good states and insufficient stimulus in bad states.  As a result, the variance of the inflation distribution increases substantially.

Figure 1: Distributions of quarterly inflation for alternative policies given a large negative demand shock

(a) Optimal discretionf1a

(b) TBFG: inflation threshold = 0f1b

(c) TBFG: inflation threshold = 0.75

(d) CBFG (4 periods)

An important implication of this discussion (which we quantify in our paper) is that not only does appropriately calibrated TBFG (e.g., as in panel (c)) deliver better outcomes (averaging across different states of the world) than CBFG, it is also much less time inconsistent.


We have shown that TBFG can be used as a state-contingent lower-for-longer policy to impart stimulus when interest rates have become constrained by the lower bound.  The state-contingency of the promise is crucial.  Relative to forward guidance policies that only involve calendar time, TBFG performs much better because it builds in a commitment to provide additional stimulus should the economy turn out worse than expected and to remove stimulus should it turn out better.

Could central banks adopt TBFG as a stimulatory policy tool at the lower bound either now or in the future?  One advantage that TBFG has over other policies that have been proposed (like price level targeting) is that the thresholds can be specified in terms of variables that form part of existing remits (like inflation).  However, in order for TBFG to impart any stimulus it is necessary for policymakers to commit to overshooting their targets.  Such time inconsistent policies may never be perfectly credible, but perhaps small overshoots are a small price to pay for better overall outcomes.

Richard Harrison works at UCL as a visiting researcher on a secondment from the Bank’s Monetary Assessment and Strategy Division, Lena Boneva works in the Bank’s Conjunctural Assessments and Projections Division and Matt Waldron works in the Bank’s Monetary Assessment and Strategy Division.

If you want to get in touch, please email us at bankunderground@bankofengland.co.uk

Bank Underground is a blog for Bank of England staff to share views that challenge – or support – prevailing policy orthodoxies. The views expressed here are those of the authors, and are not necessarily those of the Bank of England, or its policy committees.