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Authorized for public release by the FOMC Secretariat on 1/12/2024
July 18, 2018
Monetary Policy Options at the Effective Lower Bound:
Assessing the Current Policy Toolkit1
Introduction and summary
This memo quantifies some of the risks stemming from the effective lower bound
(ELB) on the federal funds rate and assesses the efficacy of the Committee’s options,
within its current toolkit, to provide monetary policy accommodation in the event of a
recession. In the first part, we estimate the probability of ELB episodes and their
associated macroeconomic outcomes assuming that the federal funds rate is governed by
a simple policy rule. In the second part, we explore the extent to which the FOMC can
use threshold-based forward guidance and balance sheet policies of the kind used during
the previous recession to mitigate ELB risks and improve macroeconomic outcomes.
The policy options considered herein are consistent with the Committee’s Statement on
Longer-Run Goals and Monetary Policy Strategy; options that might require changes to
that statement are not in scope.
Our analysis is part of prudent planning: Familiarity with policy options and their
likely effects may facilitate judicious and prompt deployment if the economic outlook
were to deteriorate significantly. Moreover, our analysis is motivated by estimates of a
decline in the neutral rate of interest over the past decade: All else equal, a lower neutral
rate reduces the scope to cut the federal funds rate in response to economic downturns,
makes ELB episodes more likely to occur, makes them more severe when they do occur,
and raises the need for the use of unconventional policy tools. In addition, understanding
The authors of this memo are Hess Chung, Etienne Gagnon, Taisuke Nakata, Matthias Paustian, Bernd
Schlusche, James Trevino, Diego Vilán, and Wei Zheng from the Federal Reserve Board. The authors
benefited from the comments and suggestions of Michele Cavallo, James Clouse, Rochelle Edge, Eric
Engen, Chris Erceg, Jon Faust, Jane Ihrig, Michael Kiley, Thomas Laubach, David López-Salido, Trevor
Reeve, Robert Tetlow, David Wilcox, and Beth Anne Wilson. The authors also thank Sarah Baker, Robert
Chen, and Eric Till for their expert assistance.
1
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the capacity of the current toolkit to address ELB risks is a prerequisite for determining
whether alternative policy strategies and tools should, at some point, be adopted.
Our main findings are:
•
There is a material risk that the ELB will restrain policymakers’ ability to
support the economy in the future.
o Simulations using the FRB/US model suggest a roughly 10 to
25 percent probability that the federal funds rate will be
constrained by the ELB at some point between now and the end of
2022. That probability and the associated economic consequences
are sensitive to the baseline path of the federal funds rate and the
assumed volatility of economic shocks. Time-series (statistical)
models suggest probabilities of an ELB episode over that horizon
as high as around 35 percent.
o Over the next decade, the simulations imply a roughly 20 to 50
percent probability that the federal funds rate will be constrained
by the ELB at some point, with the per-period risk growing as the
economic momentum in the current economic projection wanes.
o These estimates of ELB risk are appreciably higher than assessed
by the staff in memos sent to the FOMC about a decade ago, when
participants discussed the choice of a numerical price objective and
the policy framework. 2
•
The current monetary policy toolkit can offset only to some extent the
effects of significant recessionary shocks.
o During a recession, the FOMC’s ability to contain the initial rise in
the unemployment rate and fall in inflation is limited because of
lags in the transmission of monetary policy actions.
For example, in March 2007, the staff’s assessment was that “the adverse effect from the zero lower
bound is modest for inflation objectives at or above 1½ percent, though we recognize that ‘modest’ in the
eye of one beholder may be either ‘de minimis’ or ‘significant’ in the eyes of others.” See Kiley,
Mauskopf, and Wilcox (2007), “Issues Pertaining to the Specification of a Numerical Price-Related
Objective for Monetary Policy,” memorandum to the FOMC, Division of Research and Statistics, March
12.
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o If a recession leaves the federal funds rate constrained by the ELB,
the unconventional policy tools examined in this memo can
strengthen somewhat the labor market recovery and help raise
inflation toward 2 percent over time.
▪
Credible announcements that policymakers intend to keep
the federal funds rate at the ELB until the labor market
improves, inflation moves close to target, or both, put
downward pressure on real long-term borrowing rates and
the exchange value of the dollar, boost asset prices, and
thus help stimulate economic activity.
▪
Large-scale asset purchases (LSAPs) similarly can help
support an economic recovery, notably by putting
downward pressure on the term premium components of
longer-term rates and easing financial conditions more
broadly.
▪
By contrast, resuming full reinvestment of principal
payments on the Federal Reserve’s security holdings or
implementing a maturity extension program (MEP)—two
measures that leave the size of the balance sheet
unchanged—would provide only limited additional policy
accommodation.
o Given that the transmission of monetary policies is subject to long
lags, policymakers should deploy such policies rapidly in the event
of an incipient recession.
o Overall, our analysis is consistent with the preponderance of
empirical studies suggesting that the forward guidance and balance
sheet policies deployed by the FOMC in the aftermath of the
global financial crisis lowered the unemployment rate and raised
inflation notably. However, there is considerable uncertainty
around empirical estimates—even studies that find notable effects
of balance sheet policies on Treasury yields can differ substantially
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in the transmission of such effects to broader financial conditions
and economic activity.3 Moreover, the efficacy of these policies in
our model is predicated on the FOMC making credible multi-year
commitments to maintain accommodative financial conditions as
well as on the public understanding those commitments and their
effects.
Part I: How likely is the policy rate to be constrained by the ELB in the
future? How severe would the consequences be?
Modeling approach
The federal funds rate could be constrained by the ELB in the future if adverse
shocks were to cause inflation and economic activity to deteriorate sufficiently. The
latest economic projections of FOMC participants are consistent with the federal funds
rate settling between 2¼ and 3½ percent over the longer run. This range is lower than the
cumulative rate cuts implemented by the FOMC in each of the past three recessions—
roughly 5 percentage points—and thus suggests a material risk that the federal funds rate
will be constrained by the ELB in the next economic downturn.
To estimate the frequency, duration, and severity of ELB episodes, we simulate
the FRB/US model using historical shocks of the kind and size experienced by the U.S.
economy over the past several decades.4 Our stochastic simulations start in the third
quarter of 2018 and extend several decades into the future. To establish a benchmark, we
abstract for the moment from active use of unconventional monetary policies, assuming
instead that the federal funds rate is set by a simple policy rule and that the term premium
The staff’s approach to estimating the effect of balance sheet policies on term premiums is described in
Ihrig and co-authors (2012), itself building on Li and Wei (2013). As described in the former paper, in the
main staff framework, these term premium effects transmit to macroeconomic variables via the
conventional channels linking the term structure of interest rates to economic activity and inflation.
Alternative structural models of balance sheet policies, featuring a distinctive transmission mechanism for
asset purchase programs, include Andrés and co-authors (2004), Gertler and Karadi (2011, 2013), D’Amico
and co-authors (2012), Chen and co-authors (2012), and Kiley (2014, 2018).
4
Our approach is similar to that employed by Reifschneider and Williams (2000), Williams (2009) and
Kiley and Roberts (2017), though, as we discuss later on, the details of our implementation differ along a
number of dimensions.
3
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effects (TPEs) of the Federal Reserve’s existing asset holdings gradually dissipate as
assumed under the staff’s baseline projection.5 We impose an ELB of 12.5 basis points, a
value equal to the mid-point of the lowest range for the federal fund rate implemented by
the FOMC during the global financial crisis. See Appendix I for a summary of our
modeling assumptions.
The risks of an ELB episode depend on a number of factors, three of which we
emphasize in our analysis:
•
The baseline economic projection. We simulate the FRB/US model
around an economic projection consistent with the medians of the June
2018 Summary of Economic Projections (SEP). For comparison, we also
report statistics based on simulations around the June 2018 Tealbook
baseline in Appendix II. The Tealbook baseline implies a higher path for
the federal funds rate in coming years—and thus lower ELB risk—than
the SEP-consistent baseline.
•
The conduct of monetary policy. We assume that the federal funds rate is
set according to either the inertial Taylor (1999) rule, which the staff uses
to construct the Tealbook baseline, or an “asymmetric” version of that rule
that calls for quicker cuts in the federal funds rate when the labor market is
deteriorating. The inertial Taylor (1999) rule is given by:
𝑅𝑡 = 0.85𝑅𝑡−1 + 0.15(𝑟 𝐿𝑅 + 𝜋𝑡 + 0.5(𝜋𝑡 − 2) + 𝑦𝑔𝑎𝑝𝑡 ),
where 𝑅𝑡 is the federal funds rate, 𝑟 𝐿𝑅 is the real federal funds rate in the
longer run, 𝜋𝑡 is four-quarter core PCE inflation, and 𝑦𝑔𝑎𝑝𝑡 is the output
gap. The asymmetric version of that rule includes an extra term that calls
for lowering the federal funds rate more rapidly than otherwise when the
In addition, we assume that the term premiums in the model are insensitive to movements in resource
slack. All else equal, assuming that term premiums fall when resource slack tightens would imply that
changes in the conduct of monetary policy have somewhat larger effects on real activity and inflation than
suggested by our model simulations. See Appendix VIII for a discussion of this assumption.
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unemployment rate is both rising and above the natural rate of
unemployment, which is 4½ percent in this baseline.6 We see the
asymmetric policy rule as more consistent with the speed at which the
Committee has cut policy rates in past economic downturns—and might
do so in the future—than the inertial Taylor (1999) rule.
•
The neutral level of the real federal funds rate in the longer run (rLR). The
value of rLR influences the level of the federal funds rate over time and,
hence, the typical room to cut before reaching the ELB. Because rLR is
unobserved and estimated with a high degree of uncertainty, we consider
values corresponding to the median, minimum, and maximum of longerrun estimates among SEP respondents.
Main results
Table 1 reports the probability that the ELB will bind at any point between now
and selected dates in the future. The simulations suggest only a modest probability of
returning to the ELB by the end of 2020 under the SEP-consistent baseline, at less than
5 percent. This low probability reflects, in large part, the current strength of the economy
and the time it takes for the economy to respond to shocks in the model. The ELB
probability is much higher in the longer run when the economic momentum present in the
first several years of the projection has dissipated and the underlying shocks have
transmitted fully to the economy.7 Another key factor for the low probabilities reported
in Table 1 is the assumed gradual rise of the federal funds rate to about 3½ percent over
the medium term, which leaves some room for policymakers to ease financial conditions
by lowering the federal funds rate without necessarily setting that rate back to the ELB.
Simulations around the June 2018 Tealbook baseline (reported in Appendix II) point to
The extra term in the asymmetric rule is −0.85(𝑈𝑡 − 𝑈𝑡−2 )𝕀{𝑈𝑡 − 𝑈𝑡−2 > 0}𝕀{𝑈𝑡 > 𝑈𝑡∗ }, where 𝑈𝑡 is the
unemployment rate in quarter t and 𝑈𝑡∗ is the natural rate of unemployment in that quarter. This extra term
is nonzero when the unemployment rate has been rising, on net, over the past two quarters, a condition that
seeks to avoid quick cuts in policy rates in response to idiosyncratic movements in 𝑈𝑡 . The further
requirement that 𝑈𝑡 > 𝑈𝑡∗ seeks to avoid triggering the asymmetry when the unemployment rate is
converging toward its natural level from below.
7
In fact, under the asymmetric rule, the per-period ELB probability in the longer run is about 15 percent;
see Table 4.
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even smaller ELB risk over the next few years than simulations under the SEP-consistent
baseline because the staff projection assumes a higher path for the federal funds rate and
thus greater room to cut before the ELB binds.
Table 1: Probability of an ELB episode between now and selected periods based on
stochastic simulations around June 2018 SEP-consistent baseline (in percent)
rLR = 0.88 (SEP median)
Inertial Taylor (1999) rule
Asymmetric rule
LR
r = 1.50 (SEP maximum)
Inertial Taylor (1999) rule
Asymmetric rule
rLR = 0.25 (SEP minimum)
Inertial Taylor (1999) rule
Asymmetric rule
Addendum
Survey of Primary Dealers
(Median, June 2018)
2020:Q4
2022:Q4
2027:Q4
2.7
4.2
10.6
18.8
28.8
42.1
2.4
3.6
8.2
14.6
23.0
34.4
3.3
5.7
14.7
24.7
36.8
50.9
20.0
n.a.
n.a.
Note: Staff calculations using 20,000 stochastic simulations of FRB/US model around the June
2018 SEP-consistent baseline, holding balance sheet policy constant.
Beyond 2020, the federal funds rate in the SEP-consistent baseline projection falls
from its peak of 3½ percent to its longer-run level of 2.88 percent. As a result of this
decline, policymakers are left with less scope to cut the federal funds rate in response to
adverse shocks before the ELB binds and thus they face greater ELB risk in each period.
Looking at the next 10 years or so, our simulations assign a 29 to 42 percent probability
that the ELB will bind at some point depending on the policy rule. On a per-period basis
(not shown in Table 1), the risk that the federal funds rate is constrained by the ELB rises
beyond 2020 as the economic momentum embedded in the economic projection
gradually wanes and as shocks and their effects cumulate. Estimates of the ELB risk at
long horizons are sensitive to a number of modeling assumptions. In Appendix III, we
compare our per-period ELB probabilities in the longer run to those found by Williams
(2009) and Kiley and Roberts (2017) in studies that also use the FRB/US model.
Overall, the probabilities reported in Table 1 are somewhat lower at all horizons
under the inertial Taylor (1999) rule than under its asymmetric version because the
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asymmetry leads, by design, to larger cumulative cuts in policy rates when the labor
market deteriorates. Of course, the fact that the ELB binds more frequently under the
asymmetric rule need not imply that macroeconomic outcomes under that rule are worse
than under the inertial Taylor (1999). To the contrary, as we discuss later, prompt policy
rate cuts early in economic downturns can help attenuate the effects of recessionary
shocks (although doing so improves outcomes only slightly in our model simulations).
Sensitivity to longer-run neutral rate assumptions
Moderate deviations from the SEP-baseline assumption about rLR have the
expected effect on ELB risk: Lower (higher) rLR values imply greater (lower) risk.
Quantitatively, moderate deviations from baseline rLR assumptions have modest effects
on the ELB risk over the next few years, in part because the assumed gradualism in the
conduct of monetary policy during normal times implies that changes in rLR feed into the
path of the federal funds rate only slowly.8 For example, as Table 1 shows, assuming a
path of the federal funds rate consistent with the lowest estimate of rLR among SEP
respondents (0.25 percent) is associated with a probability of returning to the ELB by the
end of 2022 of 25 percent under the asymmetric rule compared with a probability of
19 percent for the median estimate of rLR.9
Estimates from alternative models
Our conclusions about the frequency of ELB episodes are sensitive to the choice
of a model to perform the analysis. Table 2 reports ELB risk estimates from three timeseries models developed by Federal Reserve staff: Johannsen and Mertens (2016), Lubik
and Matthes (2015), and Del Negro and co-authors (2017).10 In contrast to the preceding
To obtain an economic projection under an alternative value of rLR, we simply replace the path of the
federal funds rate in the SEP-consistent baseline projection with the path that is prescribed by the
asymmetric rule with the alternative rLR value, keeping all other elements of the baseline projection
unchanged.
9
When we posit very low rLR values—say, negative 1.5 percent—and subject the model to shocks over
long horizons, we sometimes encounter “death spirals” by which the policy rate response to recessionary
shocks is constrained by the ELB to such an extent that the economy fails to recover after a recession. As a
result, output tends to drift below its potential level by an ever increasing margin over time, causing the
federal funds rate to be persistently stuck at the ELB. While such a low value is well below the range of
responses in the SEP, it is encompassed in the uncertainty bands of several empirical estimates at standard
levels of statistical significance.
10
We thank the authors of these papers for providing the results reported in Table 2.
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FRB/US simulations, the predictions from these models do not depend on a judgmental
economic projection. In these models, the federal funds rate responds symmetrically to
economic developments by construction and the degree of inertia in policy decisions is
estimated to be large. Importantly, these models take into account the uncertainty
attached to current estimates of rLR, as opposed to postulating a specific value. To
provide some idea of this uncertainty, we report in Table 2 each model’s median estimate
of rLR for the second quarter of 2018 along with the associated 68-percent uncertainty
range.
Table 2: rLR estimates and probability of ELB episode between now and period
shown from selected time-series models (in percent)
rLR estimate
68-percent
median uncertainty
range
probability of ELB episode
2020:Q4
2022:Q4
2027:Q4
Johannsen and Mertens
(2016)
Lubik and Matthes (2015)
0.7
[–0.2, 1.6]
13.5
22.2
35.3
1.0
[–0.6, 2.8]
10.8
18.1
29.3
Del Negro and co-authors
(2017)
1.3
[1.0, 1.7]
28.5
36.8
52.0
Sources: Authors of each study.
Compared with the FRB/US simulations, the three time-series models imply a
somewhat higher probability—between 22 and 37 percent—that the ELB will bind
between now and the end of 2022. This higher ELB risk reflects, in large part, the weight
that these models assign to the possibility that rLR is currently low and will be so in the
future. More generally, they suggest that occasional returns to the ELB will be a feature
of policymaking in the future: Over the next decade or so, the models predict a 29 to 52
percent probability of seeing at least one ELB episode, a range high enough that the
design of monetary strategies to deal with the ELB arguably warrants special attention.11
Yet another approach to extracting estimates of ELB risk is to simulate dynamic stochastic general
equilibrium (DSGE) models. In many such models, the probability of observing an ELB episode is very
sensitive to the rule governing the federal funds rate. For example, Kiley and Roberts (2017) demonstrate
11
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Macroeconomic outcomes associated with ELB episodes
ELB episodes could be a source for concern even when infrequent if they are
associated with large economic losses. Conversely, ELB episodes need not have large
economic consequences if the constraint binds only for short periods or if economic
conditions would have called for setting the “notional” federal funds rate (that is, the rate
prescribed by the policy rule in the absence of the ELB) only modestly below the ELB.
To assess the negative effects on economic conditions that are attributable to the ELB,
Table 3 compares outcomes for the unemployment rate and inflation when policy rates
are constrained by the ELB (labeled “With ELB”) to the counterfactual outcomes that
would be observed in its absence (labeled “No ELB”).12 The simulations are computed
under the assumption that policymakers use the asymmetric policy rule to set the federal
funds rate. For comparability, the statistics are computed, for each combination of a
period shown and rLR value, using only the observations for which the ELB binds in that
period under the “With ELB” policy.
that a standard DSGE model implies very high ELB risk under traditional Taylor-type rules whereas more
efficient strategies imply very low ELB risk. The sensitivity of results to the precise form of the interest
rate rule arises, in part, because aggregate demand and inflation are more responsive to monetary policy
than in the FRB/US model and can thus be stabilized through rules that adjust the expected path of shortterm interest rates relatively modestly, but in a manner that is targeted to offset aggregate demand
shortfalls. With regard to ELB risk over the next decade, the DSGE model of Del Negro and co-authors
(2017) implies that the probability of being at the ELB at some point between now and 2020, 2022, and
2027 is 47 percent, 60 percent, and 72 percent, respectively, under the same inertial Taylor rule used in the
FRB/US simulations. These probabilities are high, in part, because the authors estimate a volatile
economic environment. Moreover, the model calls for a relatively low path for the policy rate in coming
years to offset the effects of persistently high risk and liquidity premiums.
12
The simulations without imposing the ELB should not be interpreted as suggesting that it is possible, in
practice, to set policy rates much below zero or that the monetary transmission mechanism would be the
same under negative policy rates. Rather, the simulations provide benchmarks for the shortfall in monetary
policy accommodation due to the ELB and the likely effects of that shortfall on macroeconomic outcomes.
Staff analysis suggests that, in the FRB/US model, being able to set interest rates about 50 basis points
below the ELB assumed in the simulations for this memo would improve macroeconomic outcomes only
modestly. See Hess Chung and Edward Herbst (2016), “Unconventional Policy Responses to a Recession,”
memorandum to the FOMC, Division of Research and Statistics and Division of Monetary Affairs, March
4. See also Sriya Anbil, Courtney Demartini, Laura Lipscomb, Patrick E. McCabe, Marcelo Rezende,
Heather A. Wiggins, John P. McGowan, and Patricia Zobel (2016), “Considerations for Implementation of
Negative Policy Rates in the United States,” memorandum to the FOMC, Federal Reserve Board and
FRBNY, March 4.
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Table 3: Macroeconomic outcomes conditional on being in an ELB episode in period
shown (in percent)
2020:Q4
Ut
median
rLR = 0.875
(SEP median)
With ELB
No ELB
LR
r = 1.50
(SEP max.)
With ELB
No ELB
LR
r = 0.25
(SEP min.)
With ELB
No ELB
2027:Q4
2022:Q4
πt
Ut
95th
95th
median
highest
lowest
median
πt
Ut
95th
95th
median
highest
lowest
median
πt
95th
95th
median
highest
lowest
6.9
6.4
8.0
7.3
0.8
1.0
0.1
0.4
6.5
5.9
8.8
7.8
1.0
1.2
-0.4
0.1
6.6
5.9
9.7
8.1
0.7 -1.4
1.0 -0.2
7.0
6.5
7.9
7.4
0.8
1.0
0.2
0.4
6.7
6.2
8.8
7.9
0.9
1.1
-0.3
0.0
6.9
6.2
9.6
8.3
0.7 -1.2
0.9 -0.2
6.7
6.1
8.1
7.3
0.8
1.1
0.0
0.4
6.2
5.7
8.9
7.6
1.0
1.3
-0.5
0.2
6.4
5.7
9.9
7.9
0.8 -1.8
1.1 -0.1
Notes: Staff calculations using 20,000 stochastic simulations of the FRB/US model around the
June 2018 SEP-consistent baseline and under the assumption that policymakers follow the asymmetric
policy rule. For comparability, simulations in which we impose the ELB (labeled “With ELB”) and in
which we do not (labeled “No ELB”) are performed using identical sequences of economic shocks. For
each combination of a period and rLR value, all statistics are computed using the subset of observations for
which the ELB binds under the “With ELB” simulations.
Overall, Table 3 shows that policymakers’ inability to lower the federal funds rate
below the ELB is associated with a weaker economy than would exist otherwise. For
example, the median unemployment rate across all simulations in which the ELB binds in
the final quarter of 2020 is roughly ½ percentage point higher than would have been
observed had the ELB not been a constraint on policy. For inflation, the median reading
conditional on being at the ELB in 2020:Q4 is a couple tenths of a percentage point lower
than otherwise. We find roughly similar differences in median constrained and
unconstrained outcomes when we look at ELB events later in the simulation period or
when we look at moderately higher or lower values of rLR.13
Because the sets of ELB observations reported in the table are specific to each period and value of rLR,
comparisons of statistics across rLR assumptions and periods should be made with caution. For example,
for a given sequence of shocks, low values of rLR are typically associated with a greater deterioration in
macroeconomic outcomes at the ELB than high values of rLR. However, given our sampling procedure,
there exists a countervailing selection effect by which ELB episodes under relatively high values of rLR tend
to be associated with the sampling of shocks from the most severe historical recessions.
13
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The disruptive effects of the ELB are more readily apparent when we look at tail
events for which the constraint is binding more strongly. Again conditional on being at
the ELB in 2020:Q4, the 95th highest percentile of the unemployment rate is
¾ percentage point higher than in the absence of the ELB whereas the 95th lowest
percentile of inflation is 0.3 percentage point lower than in the absence of the constraint;
these differences are somewhat larger than the corresponding differences for the medians.
Moreover, the differences between constrained and unconstrained outcomes grow in
magnitude as we consider ELB events at later horizons because the accumulation of
economic shocks leads to more dispersed outcomes, including several for which the ELB
is a significant constraint on policy. For example, for a value of rLR equal to the SEP
median, the difference between constrained and unconstrained outcomes in 2027:Q4 is
1.6 percentage points for the 95th highest percentile of the unemployment rate and
1.2 percentage points for 95th lowest percentile of inflation.14
The above simulations are conditioned on model parameters and economic shocks
that are estimated on macroeconomic data over the last five decades or so. Of course, in
the future, the structure of the economy and the distribution of economic shocks may
differ. For example, the experience in Japan over the past few decades suggests that ELB
episodes could be more frequent and longer lasting—particularly if inflation expectations
were to drift downwards substantially. Overall, the significant difference between
outcomes when we impose the ELB and when we do not is revealing of the shortfall in
policy accommodation due to the ELB constraint and motivates our consideration below
of unconventional policy tools.
Part II: To what extent can the use of forward guidance and balance sheet
policies help provide additional policy accommodation at the ELB?
We next explore how two kinds of unconventional policies used by the FOMC in
response to the global financial crisis—threshold-based forward guidance about the
Model estimates of the severity of the economic disruptions induced by the ELB are sensitive to a
number of modeling assumptions, including the conduct of fiscal policy, the monetary policy strategy, and
expectation formation. See Appendix III for a related discussion of how these factors affect long-run ELB
risk in the simulations.
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federal funds rate and balance sheet policies—might help stabilize the economy
following adverse shocks. We first illustrate the macroeconomic effects of such policies
in a stylized recession scenario in which the ELB binds for an extended period.15 We
next perform stochastic simulations of the FRB/US model to assess the overall
improvement in macroeconomic outcomes and mitigation of tail risks provided by
unconventional policy tools.
II.A Unconventional policies in a recession scenario
Description of our recession scenario
Our recession scenario is similar in severity to the 2008–2009 recession: Starting
in the third quarter of 2018 (the first quarter in the simulation), a sequence of adverse
spending shocks lifts the unemployment rate to 10 percent at its peak and lowers inflation
to an annual rate of ¾ percent at the trough.16 We assume that policymakers set the
federal funds rate according to the asymmetric policy rule, subject to the ELB, and that
balance sheet policy is completely passive; that is, full reinvestment of principal
payments on the Federal Reserve’s security holdings is not resumed. Instead, only
principal payments on Treasury securities in excess of $30 billion per month and on
agency securities in excess of $20 billion per month are reinvested, while the rest is
redeemed, until the size of the balance sheet is normalized.17 These assumptions are
made for simplicity and to establish a benchmark for assessing the effects of alternative
monetary policies later on. As shown in Figure 1, economic conditions in this scenario
deteriorate sufficiently that the ELB binds for nearly five years. In the absence of the
ELB constraint, the asymmetric rule would have called for lowering the federal funds rate
to -8 percent, which, when implemented in the model, takes off 1½ percentage points
This approach is similar to that in Reifschneider (2016), Yellen (2016), and Chung and Herbst (2016).
The deterioration in macroeconomic outcomes in our recession scenario is also similar to that in the
“severely adverse scenario” featured in the Federal Reserve’s 2018 supervisory stress tests.
17
Whereas the amount of maturing Treasury securities and agency debt are known, at least in the near term,
principal payments on agency MBS in our simulations depend on the evolution of the economic outlook.
Our cap structure is a simplified version of the one currently in place for principal payments on SOMA
securities, as detailed in the addendum to the FOMC’s Policy Normalization Principles and Plans released
on June 14, 2017.
15
16
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from the peak in the unemployment rate. Hence, the ELB materially constrains
policymakers’ ability to stabilize the economy in this scenario.
In the FRB/US model, the more rapid cuts in the federal funds rate prescribed by
the asymmetric rule in response to the recession do little, by themselves, to improve
economic conditions. As seen in the inset box of Figure 1, under the asymmetric rule,
policymakers lower the federal funds rate to the ELB two quarters earlier than under the
inertial Taylor (1999) rule, and subsequently implement the same paths for the policy
rate. Under the assumption maintained in the simulations that price setters, wage setters,
and financial market participants perfectly understand the policy rule in place, the
difference in policy stance during the first few quarters of the simulation makes virtually
no difference for the real longer-term interest rates that influence economic activity in the
model.18 As a result, the unemployment rate and inflation outcomes are almost identical
between the asymmetric rule and the inertial Taylor (1999) rule. This result is a reminder
that it is the entire expected path of policy—rather than only the prevailing policy
settings—that influences economic conditions in the model. With that in mind, we next
turn to policy strategies that seek to influence policy expectations over extended
horizons.
In practice, a failure of the FOMC to cut policy rates as swiftly as expected by the public in response to
an incipient recession might lead the public to question policymakers’ resolve and, in turn, erode
confidence and aggravate the economic situation. More generally, the adoption of a particular policy
strategy by the FOMC—including recourse to threshold-based forward guidance and balance sheet
policies—might well entail periods during which the public learns the policy strategy and its
macroeconomic implications. We abstract from such consideration in our analysis.
18
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Figure 1: Recession scenario under baseline policy rule with and without ELB
Notes: We constructed the recession scenario in the FRB/US model around the SEP-consistent
baseline projection using a sequence of negative spending shocks starting in the third quarter of 2018, the
first quarter in the simulation. We assumed that the federal funds rate is determined by the asymmetric
policy rule without thresholds and that the balance sheet is passive.
Threshold-based forward guidance
In models like FRB/US, in which some or all agents are forward looking, central
bank communications about the future path of monetary policy can stimulate economic
activity and inflation by lowering expectations of the path of short-term interest rates,
which helps, in turn, ease overall financial conditions.19 We explore the effects of
For empirical assessments of the financial market effects of past FOMC communications, as well as for
discussions and illustrations of the related transmission channels of central bank communications to
19
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explicit forward guidance about the future path of the policy rate in the form of credible
announcements that policymakers will keep the federal funds rate at the ELB at least until
some specific improvement in economic conditions has been achieved; thereafter, the
policy rate is guided by the asymmetric rule.20 Similar to the forward guidance
implemented by the FOMC in December 2012, the forward guidance assumed here takes
the form of thresholds for the unemployment rate and inflation. To the extent that the
thresholds delay liftoff from the ELB, the forward guidance in our simulations is a
commitment to a more accommodative path for the federal funds rate in the future than
under the asymmetric rule. In practice, policymakers can also use forward guidance to
clarify the intended path of monetary policy or might issue forward guidance about the
speed at which they intend to raise the federal funds rate after departure from the ELB;
our analysis abstracts from these aspects.21
Effects on macroeconomic outcomes
Figure 2 shows simulation results for three unemployment rate thresholds:
5.5 percent, 4.5 percent, and 3.5 percent. These thresholds are, respectively, 1 percentage
point above, equal to, and 1 percentage point below the natural rate of unemployment in
the SEP-consistent baseline. The setting of an unemployment rate threshold above the
natural rate—as the FOMC did in 2012—can be motivated on the basis that Taylor-type
policy rules typically call for removing accommodation before the unemployment rate
and inflation have returned to their longer-run values. Alternatively, such a threshold
may reflect policymakers’ concern about inadvertently choosing too low a threshold in
light of uncertainty about the value of the natural rate. Moreover, when policymakers
value a gradual approach to policy normalization, raising the federal funds rate from the
economic activity and inflation, see, notably Campbell and co-authors (2012), Woodford (2012), Engen,
Laubach, and Reifschneider (2015), and Campbell and co-authors (2016).
20
For simplicity, we also assume that the TPEs are held at their levels under the baseline recession
scenario.
21
Clarifying the intended path of monetary policy was a central motivation for the issuance of thresholdbased forward guidance by the FOMC in response to the global financial crisis. Such motivation is
difficult to capture in our model because there is no disagreement among agents about the future course of
monetary policy. Moreover, the assumptions that price setters, wage setters, and financial market
participants form model-consistent expectations and understand policymakers’ intended course of policy
curtail the possibility that monetary policy communications would be misunderstood.
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Figure 2: Forward guidance with unemployment rate thresholds in a recession
scenario
Note: We constructed the recession scenario in the FRB/US model by subjecting the SEPconsistent baseline to a sequence of negative spending shocks starting in the third quarter of 2018, the first
quarter in the simulation. We assumed that the federal funds rate is determined by the asymmetric policy
rule without thresholds and that the balance sheet is passive.
ELB early does not necessarily conflict with the maintaining of an accommodative stance
of monetary policy in subsequent years. That said, given the severity of the recession
scenario considered here, policymakers might judge it desirable to provide even more
policy accommodation by setting an unemployment rate threshold at or below the natural
rate. We combine our unemployment rate thresholds with an “escape clause” that allows
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liftoff from the ELB when inflation rises above 2.5 percent. 22 This clause turns out not to
be invoked in this recession scenario but is invoked occasionally in the stochastic
simulations performed later. 23
Forward guidance in the form of an unemployment rate threshold of 5.5 percent
has no effect on the simulation results because, in our recession scenario, the
unemployment rate is already below 5.5 percent by the time the asymmetric rule
prescribes raising the federal funds rate above the ELB.24 A threshold of 4.5 percent
delays liftoff by three quarters and results in a path for the real 10-year Treasury yield
that is only slightly lower than under the asymmetric rule through 2025, so that the
unemployment rate and inflation paths are little changed. A threshold of 3.5 percent is
more consequential: Compared with the asymmetric rule, it delays liftoff by more than
three years and lowers the real 10-year Treasury yield about ½ percentage point, on
average, through 2025. Given the lags in the monetary transmission mechanism, the
3.5 percent threshold shaves off only 0.2 percentage point from the peak in the
unemployment rate. Later in the scenario, the extra monetary stimulus gains traction and
the unemployment rate bottoms out at 3½ percent, about ½ percentage point less than
under the asymmetric rule. Inflation under this threshold policy is ¼ to ½ percentage
point higher than otherwise. This more accommodative monetary policy lifts inflation
toward 2 percent immediately in the simulations because of our assumption that price and
We specify the escape clause in terms of realized rather than projected inflation, in contrast with the
FOMC’s December 2012 forward guidance that policymakers would maintain policy rates at the ELB at
least until “inflation between one and two years ahead [was] projected to be no more than a half percentage
point above the Committee’s 2 percent longer-run goal.” Because the simulations shown in Figure 2 are
conducted under perfect foresight, we could have achieved the same liftoff dates and macroeconomic
outcomes using threshold specified in terms of projected values. In a dynamic environment, the use of
projected values for inflation might help policymakers communicate that they would see through transitory
influences.
23
These results depend on the model specification and could be different in alternative models. For
example, Chung, Herbst, and Kiley (2015) use DSGE models and report sizable and persistent
overshooting of inflation following threshold policies for the unemployment rate that are less
accommodative than the more aggressive strategies we consider; this result points to the possibility that
inflation risks associated with these strategies could be greater than suggested by simulations of the
FRB/US model.
24
In an uncertain environment, a 5.5 percent unemployment rate threshold would clarify that the Federal
Reserve stands ready to provide more accommodation than under the asymmetric rule in the event that the
labor market deteriorates. Because our simulations assume perfect foresight, this potential benefit is not
captured in the results shown in Figure 2.
22
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wage setters are forward looking: In short, the specification of a binding unemployment
rate threshold leads to the anticipation of less resource slack over the medium term than
in the absence of the threshold, which, in turn, results in the setting of higher prices and
wages in the near term.25
In this recession scenario, the return of inflation to the 2 percent goal lags the
return of the unemployment rate to its natural level, as appears to be the case in the U.S.
recovery from the global financial crisis. Even under our most aggressive unemployment
rate threshold, inflation runs well below the FOMC’s goal for nearly a decade, a situation
that could pose a serious risk to longer-run inflation expectations. For this reason, it is
natural to consider forward guidance formulations that delay departure from the ELB at
least until policymakers have achieved meaningful progress in returning inflation to
2 percent. In Figure 3, we consider three inflation thresholds: 1¾ percent, 2 percent, and
2¼ percent. These thresholds delay liftoff from the ELB by between three and five years
relative to the asymmetric rule with no threshold. After liftoff from the ELB, the path for
the federal funds rate is steeper for a time under the inflation thresholds than without
them because future policymakers respond to higher inflation and tighter resource
utilization. In particular, under the most aggressive threshold of 2¼ percent, the path for
the real 10-year Treasury yield is, on average, about ¾ percentage point lower than under
the asymmetric rule over the first seven years of the scenario. Under this policy, the
decline in inflation is greatly attenuated; inflation bottoms out at 1½ percent and runs
slightly above the inflation target starting in 2025.26 By comparison, under the less
aggressive thresholds of 2 percent and 1¾ percent, the return of inflation to 2 percent is
delayed until 2027 and 2030, respectively.
Whether policymakers would see the improvements in macroeconomic outcomes during the recession
and recovery phase as worthy of a more pronounced undershooting of the natural rate of unemployment
and, possibly, inflation running above 2 percent for a time depends on policymakers’ preferences over
outcomes. In Appendix V, we provide some simple metrics to compare the extent of deviations from
longer-run values in our recession scenario and of how unconventional policies can attenuate or amplify
these deviations.
26
The inflation overshooting and the unemployment rate undershooting are key features of optimal
commitment policy in New Keynesian DSGE models. See, for example, Eggertsson and Woodford (2003).
25
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Figure 3: Forward guidance with inflation thresholds in a recession scenario
Note: We constructed the recession scenario in the FRB/US model by subjecting the SEPconsistent baseline to a sequence of negative spending shocks starting in the third quarter of 2018, the first
quarter in the simulation. We assumed that the federal funds rate is determined by the asymmetric policy
rule without thresholds and that the balance sheet is passive.
Key lessons and caveats
Our analysis suggests that threshold-based forward guidance only modestly limits
the deterioration of labor market conditions during a severe recession because of the long
lags in the transmission of monetary policy. The thresholds can have somewhat larger
beneficial effects during the subsequent economic recovery but the gains are obtained
through commitments to keep policy more accommodative than otherwise for many years
into the future. Because the return of inflation to the 2 percent objective lags the closing
of the unemployment gap in our recession scenario, we find that a commitment to remain
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at the ELB until labor market slack is absorbed leaves inflation running well below
2 percent for many years. In fact, given the flatness of the short-run Phillips curve in the
FRB/US model, achieving the inflation thresholds requires running the economy hot for
an extended period of time. In that respect, forward guidance formulations that delay
departure from the ELB until inflation has returned to, or exceeded, 2 percent are most
successful in preventing inflation from running persistently below the FOMC’s goal for
an extended period, though this results hinges in part on the behavior of inflation in the
model.
The results are subject to at least four important caveats. First, the potency of
forward guidance might depend crucially on the formation of expectations. In our
simulations, we assume that some agents fully understand the forward guidance and
dynamics of the model whereas other agents form expectations through simple
projections of current and past variables without regard to the forward guidance. To
some readers, these assumptions might suggest that we are underestimating the effects of
forward guidance: In the FRB/US model, limitations in the forward-looking behavior of
households and businesses contribute to creating long lags in the transmission of shocks,
so that threshold-based forward guidance has little effect on the unemployment rate in the
first couple years after its issuance. In other macroeconomic models, agents are more
forward looking and the transmission lags are accordingly shorter.27 By contrast, other
readers might argue that the assumption that price setters, wage setters, and financial
market participants form model-consistent expectations is too strong, leading us to
overstate the effectiveness of the forward guidance and, in particular, the initial boost to
inflation expectations.
Second, the potency of threshold-based forward guidance to improve economic
outcomes rests on policymakers’ ability to make credible commitments to keep the
federal funds rate lower than otherwise at distant horizons. Under such commitments,
Appendix IV presents a simulation of the recession scenario and threshold-based forward guidance in a
variant of the DSGE model of Del Negro, Giannoni, and Schorfheide (2015) in which households discount
future interest rates when making spending decisions similar to what is assumed in the FRB/US model.
The effects of forward guidance on inflation and output are somewhat larger than in our FRB/US
simulations.
27
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economic conditions might eventually improve to such an extent that future policymakers
would prefer ex post to implement a tighter monetary policy than the one originally
communicated (that is, the policy commitments entailed by the forward guidance may not
be “time consistent”). For example, in Figure 3, the improvement in economic conditions
achieved under inflation thresholds of 2 percent or more is associated with promises to
keep the federal funds rate at the ELB even as the unemployment rate falls well below its
longer-run level and inflation is on its way to modestly overshoot 2 percent for several
years. When faced with the prospect of an overheating economy, future policymakers
may well judge that they are “falling behind the curve” and opt to drop the policy
commitment. In practice, policymakers would have to weigh various benefits, costs, and
risks in deciding whether to depart from an announced forward guidance. Notably,
policymakers might worry that the public would react negatively to such a departure,
causing a loss of reputation that would make recourse to forward guidance less effective
in future recessions. Appendix VI explores some of the prospective costs and benefits of
deviating from the forward guidance. To the extent that the public anticipates such timeinconsistent behavior, the provision of forward guidance could lack credibility and
economic conditions could fail to improve as a result. The recent Japanese experience
provides a note of caution on the effectiveness of forward guidance in the form of
inflation thresholds in some circumstances.28
A third caveat is that the potency of forward guidance hinges on the public’s
understanding of the implications of a strategy to keep policy rates low for an extended
period. The adoption of a particular policy strategy by the FOMC—including recourse to
threshold-based guidance in response to economic downturns—might well entail periods
during which the public learns about the policy strategy and its macroeconomic
implications. The market reaction to the FOMC’s adoption of calendar-based forward
In 2013, the Bank of Japan (BOJ) announced a 2 percent inflation target along with a substantial openended asset purchase program aimed to achieve that objective. Longer-run inflation expectations moved up
sharply around the time of the announcement but partly retraced these gains subsequently. In September
2016, the BOJ––in conjunction with the introduction of a target for the 10-year yield on the Japanese
government bond––committed to expand the monetary base until inflation exceeds 2 percent and stays
above that target in a stable manner. To date, these measures have not succeeded in lifting longer-run
inflation expectations to the new target and inflation has continued to run well below 2 percent.
28
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guidance in August 2011 is encouraging in that respect because the announcement led to
immediate, sizeable adjustments in federal funds rate expectations.29 That said, policy
commitments beyond a few years or involving complex conditionality on economic
outcomes might be more difficult for the public to process. For example, it could be
challenging for policymakers to communicate to the public that they would see through a
breach of an inflation threshold due to transitory factors.
Finally, our analysis focuses on a relatively small number of transmission
channels that are well modeled using standard macroeconomic theory. However, forward
guidance and other unconventional policies might operate through other channels. For
example, during the global financial crisis, the FOMC’s policy actions might have
boosted confidence to a greater extent than in the past. Therefore, the limited effects that
we find might understate the benefits of forward guidance in some situations.
Balance sheet policies
Next, we analyze the effects of four balance sheet policies in the recession
scenario and compare their macroeconomic outcomes to those achieved under the passive
balance sheet policy used to construct the recession scenario. In these simulations, we
solve jointly the FRB/US model and a detailed model of the Federal Reserve’s balance
sheet and of its effects on financial conditions and macroeconomic outcomes.30 The four
balance sheet policies are assumed to affect macroeconomic conditions through their
influence on the term premiums embodied in longer-term interest rates.
Description of balance sheet policies
All four balance sheets policies that we consider are initiated as soon as the ELB
binds, a fact known by the model’s price setters, wages setters, and financial market
participants at the onset of the simulations. Under the “reinvestment-only” policy, the
In August 2011, the FOMC stated its anticipation “that economic conditions—including low rates of
resource utilization and a subdued outlook for inflation over the medium run—[were] likely to warrant
exceptionally low levels for the federal funds rate at least through mid-2013.” Market expectations of the
federal funds rate over that period and beyond fell immediately upon the announcement.
30
For background on the integrated model, its solution, and its applications, see the forthcoming FEDS
note by Hess Chung, Cynthia Doniger, Cristina Fuentes-Albero, Bernd Schlusche, and Wei Zheng
“Simulating the Macroeconomic Effects of Unconventional Monetary Policy.”
29
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Federal Reserve resumes full reinvestment of principal payments on its SOMA security
holdings as soon as the federal funds rate reaches the ELB. Under the “MEP” policy, the
Federal Reserve extends the average duration of its SOMA security holdings while
keeping the size of its SOMA portfolio unchanged. Under our “LSAP” and “LSAP +
inflation threshold” policies, the Federal Reserve increases the size of its SOMA holdings
through purchases of longer-term Treasury securities. Compared with the passive policy
used to construct the recession scenario, all four balance sheet policies result in the
Federal Reserve reducing the total duration risk faced by private investors in the model,
which, in turn, puts downward pressure on term premiums and longer-term borrowing
rates, thereby supporting economic activity. We implement the four policies as follows:
•
Reinvestment-only. We assume that principal payments from the Federal
Reserve's holdings of Treasury securities are fully reinvested into Treasury
securities and, similarly, principal payments from agency debt and agency
mortgage-backed securities (MBS) are fully reinvested into agency MBS
until either the unemployment rate drops below 5½ percent, inflation rises
above 1¾ percent, or the asymmetric rule prescribes raising the federal
funds rate from the ELB.31 Thereafter, only principal payments on
Treasury securities in excess of $30 billion per month and on agency
securities in excess of $20 billion per month are reinvested until the size of
the balance sheet is normalized.
•
MEP. We posit that the Federal Reserve purchases $55 billion of
Treasury securities with remaining maturities between six and 30 years
each month for 12 months.32 These purchases are funded through the sale
or redemption of equal amounts of Treasury securities with remaining
maturities between zero and three years. Principal payments on SOMA
For a discussion of the effects of reinvestment policies, see Hess Chung, Cynthia Doniger, Cristina
Fuentes-Albero, David López-Salido, and Bernd Schlusche (2017), “The Macroeconomic Effects of State
Contingent Ending of Reinvestment,” memorandum to the FOMC, March 3.
32
The total size of the program ($660 billion) and its length (one year) roughly match those of the Federal
Reserve’s 2011–2012 MEP. Moreover, the total size is similar to the Federal Reserve’s current holdings of
Treasury securities with a remaining maturity of three years or less.
31
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holdings are reinvested under the same conditions as under the
reinvestment-only policy.
•
LSAP. The program consists of purchases of $85 billion per month in
longer-term Treasury securities—the same monthly combined amount of
Treasury securities and MBS purchased under the third LSAP program
launched by the Federal Reserve in October 2012—until either the federal
funds rate lifts off from the ELB, the unemployment rate drops below
5½ percent, or inflation rises above 1¾ percent.33 Principal payments on
SOMA securities are fully reinvested during the LSAP program as well as
for a period of 12 months after its conclusion. Subsequently, only
principal payments on Treasury securities in excess of $30 billion per
month and on agency securities in excess of $20 billion are reinvested
until the size of the balance sheet is normalized.
•
LSAP + inflation threshold. Under this policy, asset purchases continue
until a 2 percent inflation threshold is achieved. Similarly, we assume that
liftoff from the ELB is delayed at least until the 2 percent inflation
threshold is satisfied. Therefore, under this policy, the federal funds rate
and balance sheet policies do not work at cross purposes. We retain the
same reinvestment policy as under the LSAP policy.
Effects on the Federal Reserve’s balance sheet and macroeconomic outcomes
The top-left and top-right panels of Figure 4 show the total assets held by the
Federal Reserve and the TPEs on the 10-year Treasury yield, respectively, for each
balance sheet policy. While under the passive policy the balance sheet continues to
normalize during the recession, policymakers under the reinvestment-only and MEP
policies keep the size of the balance sheet constant at around $4 trillion starting in early
2019, when they lower the federal funds rate to the ELB. As a result of the larger balance
This monthly amount is for illustrative purposes and might be different from the amount that the Open
Market Desk at the Federal Reserve Bank of New York may suggest as feasible at the time of
implementation.
33
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Figure 4: Balance sheet policies in a recession scenario
Note: The results are obtained by solving the FRB/US and balance sheet models jointly so that, for
each balance sheet policy, the macroeconomic outcomes, balance sheet holdings, and term premium effects
are mutually consistent. The results are conditioned on the assumption that price and wage setters, as well
as financial market participants, have perfect foresight of the recession scenario and balance sheet policies.
The “LSAP + inflation threshold” policy maintains policy rates at the ELB and continues asset purchases
until inflation reaches 2 percent.
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sheet compared with the passive balance sheet policy, the reinvestment-only policy
achieves somewhat more negative TPEs. In turn, the more negative TPEs under the
reinvestment-only policy imply a slight improvement in macroeconomic outcomes.
TPEs under the MEP policy are marginally more negative than under the reinvestmentonly policy, owing to a modest lengthening in the average duration of the SOMA
portfolio.34 Macroeconomic outcomes are nearly the same as under the reinvestmentonly policy.
Under the LSAP policy, policymakers boost the size of the balance sheet to nearly
$8 trillion (about 33 percent of GDP) in 2023. For reference, the Federal Reserve’s
actual balance sheet size peaked at about $4.5 trillion in 2015 (roughly 25 percent of
GDP). The expansion of the balance sheet under the LSAP policy exerts notable
downward pressure on term premiums in the model: The 10-year TPE is over 100 basis
points more negative, on average, over the next several years under the LSAP policy than
under the reinvestment-only and MEP policies.35 As a result of more accommodative
financial conditions, the unemployment rate path declines faster over the medium term,
reaching its natural rate four quarters earlier than under the passive policy. For the same
reason, the inflation path is about ½ percentage point higher than under the passive policy
at the trough. Because of the overall stronger economic outlook, the federal funds rate
departs from the ELB three quarters sooner than under the passive policy.
While the LSAP policy improves macroeconomic outcomes, it is still associated
with inflation running well below the FOMC’s 2 percent objective through much of the
next decade, an outcome policymakers might judge inconsistent with their mandate. For
this reason, in Figure 4, we report outcomes under a more aggressive LSAP policy by
The largest feasible size of an MEP depends on the Federal Reserve’s holdings of shorter-term Treasury
securities. In the future, the FOMC could, in principle, conduct more potent MEP programs than the one
shown here if it were to maintain permanently larger holdings of shorter-term securities.
35
Under the LSAP policy, the 10-year (nominal) Treasury yield initially declines below ½ percent and
stays below 1 percent for two years. Although our modeling assumptions imply that the marginal effects of
LSAPs are roughly invariant to the level of Treasury yields, it could be that LSAPs have diminishing
potency when nominal Treasury yields are near zero and terms premiums are already low. The experience
of the Bank of Japan with rapid balance sheet expansion and low longer-term rates and term premiums
seems to corroborate this view.
34
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which policymakers continue asset purchases until core inflation reaches 2 percent. This
threshold delays departure from the ELB until 2025, after which date the federal funds
rate rises to contain a mild overheating of the economy. Asset purchases throughout the
seven years during which the ELB binds boost the size of the Federal Reserve’s balance
sheet to over $10 trillion (about 38 percent of GDP). The balance sheet expansion pushes
the path of the TPE on 10-year Treasury yields about 60 basis points lower, on average,
relative to the corresponding path under the LSAP policy over the period shown.36
Compared with the other policies analyzed here, this more aggressive LSAP policy
succeeds in bringing inflation close to 2 percent in coming years, an outcome achieved by
eventually lowering the unemployment rate to around 3 percent, a level last seen in the
1950s.
Key lessons and caveats
Overall, none of the balance sheet policies considered herein meaningfully
contains the sharp rise in the unemployment rate brought on by the recession, a result that
arises even though we have assumed that price setters, wage setters, and financial market
participants in the model fully understand and anticipate the implementation of those
policies at the onset of the recession. This finding reflects the feature that, similar to
movements in the federal funds rate, changes in the size and composition of the Federal
Reserve’s balance sheet affect economic activity with a lag in the model. More
encouragingly, we find that LSAP policies do hasten the labor market recovery and lift
the path of inflation somewhat. By contrast, our simulations suggest that policymakers
could improve macroeconomic outcomes only marginally through an MEP or by
resuming full reinvestment of principal payments on SOMA securities.
Our balance sheet simulations are subject to several caveats, of which we
highlight three. First, the macroeconomic effects and channels of transmission of balance
Under the “LSAP + inflation threshold” policy, the 10-year (nominal) Treasury yield initially declines to
¼ percent and stays below 1 percent for three years. Thus, the caveat noted in the previous footnote
applies.
36
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sheet policies are subject to considerable uncertainty.37 A number of papers have found
that measures of Treasury debt supply are helpful for capturing the dynamics of the yield
curve and event studies of asset purchase program announcements have demonstrated
that news about these programs can leave a noticeable imprint on financial markets, at
least in the very short run.38 However, the literature features some papers supporting
long-lasting effects while others suggest quite rapid attenuation. 39 Moreover, regarding
macroeconomic effects, our assumption that balance sheet policy affects the economy
through conventional yield curve channels is only one possibility. A number of
alternative transmission channels have been proposed, and these could have different
implications for the effectiveness of purchase programs. For example, the market
segmentation that permits Treasury supply to affect yields may also limit the sensitivity
of aggregate spending to changes in term premiums, as compared to changes in the
federal funds rate that would have an equivalent effect on long-term interest rates.40
Similarly, balance sheet policies may interact with the state of the financial sector: effects
could be larger if financial stress is intense, while very low long-term interest rates could
negatively affect bank profitability, attenuating these effects. 41
For a review of the macroeconomic effects and transmission channels of balance sheet policies, see
Deborah Leonard, David López-Salido, and Fabio Natalucci (2016), “Balance Sheet Considerations for the
Federal Reserve’s Long-Run Framework,” memorandum to the FOMC, Federal Reserve System, October
14.
38
Work supporting the relevance of Treasury debt supply includes Bernanke and co-authors (2004), Engen
and Hubbard (2005), Krishnamurthy and Vissing-Jorgensen (2012), Laubach (2009), Hamilton and Wu
(2012) and Li and Wei (2013). Early event studies of the Federal Reserve’s asset purchase programs
include Gagnon and co-authors (2011) and Krishnamurthy and Vissing-Jorgensen (2011). While much of
the literature attributes balance sheet effects to term premium movements, it is possible that these programs
also operate by affecting expectations about the future conduct of policy regarding the federal funds rate
(the “signaling channel”). For example, Christensen and Rudebusch (2012) and Woodford (2012) find an
important signaling channel for the United States.
39
Using data on LSAP purchases at the CUSIP level, D’Amico and King (2013) find substantial and
persistent effects from purchases. Wright (2011) and Greenlaw and co-authors (2018) report very transient
effects from LSAPs. By contrast, Swanson (2017) argues that the appearance of transient LSAP effects is
highly dependent on the behavior of yields following the QE1 announcement and, if that event is excluded,
LSAP effects appear durable.
40
The models of Chen and co-authors (2012) and Kiley (2014) both have this feature.
41
The effectiveness of U.S. balance sheet policy in the Gertler and Karadi (2013) paper depends on a
constraint limiting the lending ability of financial intermediaries; LSAPs would have larger effects when
this constraint is more tightly binding. Brunnermeier and Koby (2017) provide a model in which the
negative effects of low long-term interest rates on bank profitability may make such policies contractionary
beyond a certain minimum rate.
37
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Second, the accommodation provided through LSAPs under the most aggressive
policies is achieved by pushing the size of the balance to levels that have never been
experienced in the United States; such large increases in the balance sheet may entail
costs and risks that are not captured by our analysis. 42 Third, balance sheet policies, like
threshold-based forward guidance, entail multi-year commitments by policymakers so
that the efficacy of those policies might hinge on their credibility and on expectation
formation. That said, the FOMC’s policy decisions to date to reduce the size of the
balance sheet in a gradual and predictable manner would likely enhance the public’s
confidence in such commitments in the future.
II.B Unconventional policies in stochastic simulations
We next investigate how a policy strategy involving systematic recourse to either
threshold-based forward guidance or balance sheet policies during ELB episodes might
limit the duration and severity of these episodes going forward, and, more generally,
improve macroeconomic outcomes and mitigate macroeconomic risk over time. Doing
so requires the performance of stochastic simulations in which we specify a monetary
policy strategy that encompasses both conventional and unconventional tools.
Threshold-based forward guidance
We first conduct stochastic simulations for each of the six policy strategies
considered earlier that entail setting the federal funds rate according to the asymmetric
policy rule in normal times and, whenever the ELB binds, delaying normalization of the
stance of policy at least until some pre-announced unemployment rate or inflation
threshold has been satisfied. The simulations abstract from balance sheet policies and are
conducted under the assumptions that policymakers credibly commit to following a
particular policy strategy forever and that price setters, wage setters, and financial market
participants immediately and correctly understand the implications of this commitment
That said, a number of foreign central banks have increased the size of their balance sheets relative to
their GDP to higher levels than the Federal Reserve in response to the global financial crisis, in particular
the European Central Bank (about 40 percent of GDP), the Bank of England (almost 30 percent of GDP),
the Bank of Japan (nearly 100 percent of GDP), and the Swiss National Bank (about 110 percent of GDP).
Overall, staff sees these interventions as having had positive effects, though the extent of policy
accommodation achieved is uncertain.
42
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for interest rates and the macroeconomy. The simulations extend many decades into the
future in order to derive the distributions of macroeconomic outcomes in the longer run
that are associated with each policy rule.
Table 4 summarizes our key findings. The first two columns report the
probability that in any given period the ELB is binding and the mean duration of ELB
episodes over the longer run for the asymmetric rule with no forward guidance and for
each of the six strategies with threshold-based forward guidance. The subsequent four
columns report statistics on the distribution of unemployment rate and inflation
outcomes. For comparability, the latter statistics are computed over the set of periods
during which the asymmetric rule without thresholds is constrained by the ELB and use
the same shock sequences.43
Consistent with the findings for our illustrative recession scenario, we find that
setting a relatively high threshold for the unemployment rate under the asymmetric rule
alters the path of policy little, if at all, compared with the same policy rule without such a
threshold. By contrast, policy strategies that entail commitments to keep the federal
funds rate at the ELB at least until either the unemployment rate has fallen below its
longer-run level (“Ut < 3½ percent”) or inflation has risen back to or modestly exceeded
its longer-run value (“πt > 2 percent” or “πt > 2¼ percent”) deliver moderately better
outcomes over time. In particular, these rules are shown to achieve, on average,
unemployment rates and inflation rates that are between ¼ to ½ percentage point lower
and higher, respectively, than the outcomes under the asymmetric rule for periods during
which the ELB binds under that latter rule. The simulations also point to some
commensurate reduction in the severity of tail events. For example, the 95th percentile
highest unemployment rate and 95th percentile lowest inflation readings during periods
Table 4 also reports statistics under the inertial Taylor (1999) rule. In contrast with our earlier finding
that the asymmetric and inertial Taylor (1999) rules achieve nearly identical outcomes in a baseline
recession scenario, we find that the asymmetric rule leads to modestly lower unemployment rates and
higher inflation rates in ELB episodes in stochastic simulations. The reason for this difference is that, in a
stochastic environment, sequences of shocks lifting the unemployment rate above the natural rate, even by
small amounts, occasionally call for extra easing relative to the inertial Taylor (1999) rule, making the
asymmetric rule relatively more accommodative on average.
43
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when the ELB binds under the asymmetric rule fall ¼ percentage point and rise
½ percentage point respectively. The range of gains is admittedly modest.44
Table 4: Longer-run ELB risks and macroeconomic outcomes under thresholdbased forward guidance
ELB episodes
Asymmetric rule (AR)
AR + unemployment
rate threshold
Ut < 5½ percent
Ut < 4½ percent
Ut < 3½ percent
AR + inflation
threshold
πt > 1¾ percent
πt > 2 percent
πt > 2¼ percent
Addendum
Inertial Taylor
(1999) rule
Per-period
Mean
probability
duration
(in percent) (in quarters)
Ut
median
πt
95th
highest
median
95th
lowest
15.0
7.8
6.5
8.8
1.0
-0.4
16.5
19.0
17.8
9.1
11.4
7.4
6.5
6.4
6.2
8.8
8.8
8.5
1.0
1.0
1.4
-0.4
-0.4
0.1
19.2
19.5
19.8
10.5
9.8
9.3
6.3
6.3
6.2
8.7
8.6
8.6
1.2
1.3
1.4
-0.1
0.0
0.1
13.5
10.5
6.8
9.5
0.9
-0.7
Note: For comparability, the statistics in the last four columns are calculated using periods in
which the ELB is binding under the asymmetric rule without threshold.
In our simulations, a policy of keeping the federal funds rate at the ELB until
some unemployment rate or inflation threshold is met is associated with a greater fraction
of periods spent at the ELB than in the absence of thresholds. However, policies that
entail relatively large amounts of accommodation might improve outcomes to such an
extent that they are associated with shorter ELB episodes, on average, than policies with
relatively small amount of extra accommodation. For example, the setting of an
unemployment rate threshold equal to the natural rate lengthens the average duration of
ELB episodes from 15 to 19 quarters compared with the asymmetric rule without the
For reference, we show in Appendix VII the longer-run distributions of unemployment rates and inflation
rates at the ELB under the asymmetric rule and a forward guidance policy in the form of an inflation
threshold.
44
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threshold. However, lowering the unemployment rate threshold to 3½ percent then
reduces the average duration by one quarter. This phenomenon illustrates the stabilizing
effects of a strong forward guidance strategy in the model. This stabilization hinges on
the assumed credibility of the forward guidance and the forward-looking nature of agents
in the model.
Balance sheet policies
In this section, we analyze the performance of the LSAP policy relative to the
passive policy benchmark in stochastic simulations around the SEP-consistent baseline.
The outcomes are generated using the integrated FRB/US and balance sheet models
under the assumption that the federal funds rate follows the prescriptions of the
asymmetric rule. Because the two balance sheet policies differ principally when the
policy rate reaches the ELB, we restrict our focus to outcomes around ELB episodes.45
To this end, we begin by identifying the simulations for which the ELB binds under the
passive policy in the final quarter of each year through 2022. For each such simulation,
we then compute the outcomes under the LSAP policy for the same underlying shocks.
By following this approach, we are able to attribute differences in outcomes exclusively
to differences in balance sheet policies.
Figure 5 presents the median and interquartile range of macroeconomic outcomes
and balance sheet sizes. As shown in the top-left panel, under the passive policy, the
balance sheet size decreases over time as policymakers in the simulations are assumed to
continue with their balance sheet normalization program even as the ELB binds.
Moreover, the distribution of balance sheet sizes exhibits negligible variability, as
evidenced by the interquartile range being almost indistinguishable from the median. 46
By contrast, under the LSAP policy, the distribution of balance sheet sizes is much more
Because price setters, wage setters, and financial market participants in the model understand
policymakers’ strategy, they may anticipate the ELB constraint to bind and LSAPs to be conducted in the
future if the incoming shocks have led them to expect a significant deterioration in economic conditions. In
such a case, the anticipation of balance sheet actions would exert downward pressure on longer-term
interest rates even before the ELB is reached and LSAPs are launched, leading to a difference in outcomes
under the two policies.
46
Variability in balance sheet size is possible in our stochastic simulations under a passive policy because
of the possibility that declines in interest rates affect MBS prepayments.
45
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Figure 5: Outcomes in stochastic simulations with balance sheet policies conditional
on a binding ELB
Note: The markers and the intervals show the median and the interquartile range, respectively, of
the distribution of macroeconomic outcomes under each policy. For comparability, the distributions are
calculated for the same sequences of shocks for which the ELB binds under the passive balance sheet
policy in the final quarter of each period shown. The statistics are computed through stochastic simulations
around the SEP-consistent baseline projection.
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dispersed and stretches much higher than under the passive policy. The interquartile
range widens progressively through 2022 as economic shocks accumulate. As the topright panel shows, the larger balance sheet sizes under the LSAP policy imply median
TPEs that are much more negative than those under the passive policy and, hence, real
longer-term interest rates (the middle-right panel) that are notably lower.
The additional stimulus under the LSAP policy leads to a somewhat improved
distribution of macroeconomic outcomes. By the end of 2020, the median unemployment
rate associated with being at the ELB in that quarter is 6.7 percent as compared to
7.0 percent under the asymmetric rule with the passive balance sheet policy; the
interquartile range shifts down by a similar amount. Also, at the end of 2020, the median
inflation rate conditional on a binding ELB in that quarter is 1 percent under the LSAP
policy as compared to 0.8 percent under the passive balance sheet policy.
On the surface, these modest differences seem to suggest that the LSAP policy
has only small effects. Such a conclusion needs to be qualified, however, because, as we
noted earlier, the transmission of unconventional monetary policies in the FRB/US model
occurs with substantial lags. The distributions of economic outcomes in Figure 5
comprise primarily observations for which the effects of LSAPs have yet to transmit to
the economy. For this reason, we examine in Figure 6 the distributions of
macroeconomic outcomes conditional on the number of quarters that have elapsed since
the beginning of ELB episodes. 47 Because of the lags in monetary policy transmission,
the median differences in unemployment rates and inflation between the LSAP policy
and the passive policy are initially small but eventually grow in significance: After
12 quarters, the median difference in unemployment rates is almost -70 basis points and
the median difference in inflation reaches nearly 40 basis points. In short, the LSAP
policy leads to a significant improvement in macroeconomic outcomes over time relative
to the passive policy. And because it takes time for the effects to build, our simulations
Specifically, we identify sequences of shocks that cause the ELB to bind in 2019 and 2020 under the
passive balance sheet policy. For each ELB episode, we then compute the difference between outcomes
under the LSAP policy and the passive policy at a given number of quarters from the start of the episode,
whether the episode is continuing or not. Finally, we pool all such differences to construct the distribution
of effects induced by the LSAP policy.
47
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Figure 6: Distribution of macroeconomic effects of LSAP policy conditional on the
number of quarters elapsed since reaching the ELB
Note: The red line and the shaded region show the median difference and the interquartile range
of differences, respectively, in macroeconomic outcomes between the LSAP policy and passive balance
sheet policy. For comparability, the differences are measured for the same periods and sequences of shocks
for which the ELB binds under the passive balance sheet policy. The statistics are reported from the first
quarter in the ELB episode up to 12 quarters out whether the ELB continues to bind or not.
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suggest that policymakers may find it beneficial to deploy LSAPs rapidly when faced
with an incipient recession.
As noted earlier, our estimates of the macroeconomic effects of balance sheet
policies are subject to much uncertainty, as is the importance of various transmission
channels. One such potential channel is the response of term premiums to economic
activity. In our simulations, we have assumed that the modestly negative correlation
between economic activity and excess returns on bonds in the data does not reflect an
endogenous countercyclical component in term premiums. In Appendix VIII, we show
that balance sheet policies are more potent when we posit that term premiums are
countercyclical.
Balance sheet risks
A possible risk stemming from LSAP policies is the “ratcheting-up” effect: In an
environment with frequent and prolonged ELB episodes, either because asset purchases
continue for an extended time in a lengthy ELB episode or because new LSAP programs
are initiated before past programs have had time to unwind, the size of the balance sheet
may drift up over time to very high levels. A related concern is that the Federal Reserve
could end up holding a large share of outstanding government securities, a situation that
might hinder market functioning. Our model simulations suggest that these concerns are
unlikely to materialize for at least the next several years. In particular, as shown in the
top-left panel of Figure 5, the size of the Federal Reserve’s balance sheet exceeds
$5 trillion by 2022 in roughly 25 percent of the simulations that entail a return to the ELB
under the passive policy. A balance sheet of that size would be equivalent to about
25 percent of GDP, a ratio comparable to the peak observed during the global financial
crisis. So far, none of the asset purchase programs have been associated with undue
disruptions to market functioning. Figure 7 shows that, under all of our simulations,
including those draws that call for large expansions of the balance sheet, the share of
outstanding federal debt held by the Federal Reserve over the 2018–2022 period stays at
moderate levels.48 In part, these modest levels are attributable to the fact that, during
48
For reference, the Federal Reserve currently holds a little less than 14 percent of federal debt outstanding.
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severe downturns, Treasury debt issuance rises sharply, creating room for the Federal
Reserve to expand its balance sheet through purchases of government securities without
necessarily crowding out private investors.
Figure 7: Distributions of Treasury holdings in stochastic simulations
Note: Frequency counts for the Federal Reserve’s Treasury holdings as a share of the outstanding
federal debt are obtained via stochastic simulations in the FRB/US model around the SEP-consistent
baseline over a four-year horizon. The frequency counts shown here condition on being at the ELB under
the passive policy. The statistic for each simulation corresponds to the maximum value of the share
between the third quarter of 2018 and the final quarter of 2022.
Due to the computational complexities of our augmented FRB/US–balance sheet
model, it is difficult to assess balance sheet risks over long horizons. 49 Obviously,
Using an alternative approach, which allows for the performance of stochastic simulations over long
horizons, Kiley (2018) provides an encouraging assessment of the ratcheting-up risk. Under a proactive
49
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estimates of the distribution of the balance sheet size over long horizons are highly
uncertain and are likely sensitive to assumptions about the conduct of monetary policy
going forward—including the assumption about the longer-run level of reserve balances,
the frequency and depth of recessions, the equilibrium level of policy rates, and various
other modeling factors that affect ELB risk. 50
Concluding remarks
Our analysis indicates that there is a significant risk that conventional interest rate
policy will be constrained by the ELB in future recessions. Unconventional policies of
the sort used by the FOMC during the last recession can help diminish the severity of
ELB episodes. In particular, although threshold-based forward guidance and balance
sheet polices have only a small effect in our simulations in limiting the rise in the
unemployment rate during a recession, if credible, they can be modestly effective in
speeding up the subsequent labor market recovery and return of inflation to 2 percent.
LSAP policy, he finds that policymakers would conduct asset purchases roughly 7 percent of the time and
that the Federal Reserve’s total asset holdings due to ongoing and past LSAP programs—that is, the size of
the balance sheet relative to its steady state—would be less than $3.2 trillion (measured in constant 2015
dollars) about 95 percent of the time; for comparison, a $3.2 trillion expansion of the balance sheet is
roughly on the order of the expansion observed in response to the global financial crisis.
50
For example, Cavallo and co-authors (2018) assess the implications of alternative assumptions about the
Federal Reserve’s longer-run balance sheet size for both remittances to the U.S. Treasury and broader fiscal
outcomes. The authors find that for sufficiently large longer-run balance sheet sizes, the probability of
negative net earnings and of recording a deferred asset increases substantially as the policy rate along the
economic recovery is expected to rise after the termination of an asset purchase program.
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Appendix I: Key modeling assumptions
Unless otherwise noted, we perform our simulations using the linearized version
of the FRB/US model under the following set of assumptions:
•
The baseline economic projection comes from the public FRB/US data
base that is consistent with the median responses of FOMC participants in
the June 2018 Summary of Economic Projections.
o To construct this baseline projection, we interpolated annual SEP
information to a quarterly frequency and assumed that, beyond
2020 (the final year reported in the June 2018 SEP), the economy
transitions to the longer-run values in a smooth and monotonic
way. We also posited economic relationships to project variables
not covered in the SEP. For example, we assume an Okun’s law
relationship to recover an output gap from the deviation of the
median SEP unemployment rate from the median SEP estimate of
its longer-run value.
o The projection is consistent with longer-run values of the
unemployment rate and inflation of 4½ percent and 2 percent,
respectively.
•
Unless specified otherwise in the text, the federal funds rate in our
simulations is set according to an asymmetric version of the inertial Taylor
(1999) rule that staff uses to construct the Tealbook baseline.
o The inertial Taylor (1999) rule is given by 𝑅𝑡 = 0.85𝑅𝑡−1 +
0.15(𝑟𝐿𝑅 + 𝜋𝑡 + 0.5(𝜋𝑡 − 2) + 𝑦𝑔𝑎𝑝𝑡 ), where 𝑅𝑡 is the federal
funds rate, 𝑟 𝐿𝑅 is the real federal funds rate in the longer run, 𝜋𝑡 is
four-quarter core PCE inflation, and 𝑦𝑔𝑎𝑝𝑡 is the output gap.
o The asymmetric version of that rule includes an extra term,
−0.85(𝑈𝑡 − 𝑈𝑡−2 )𝕀{𝑈𝑡 − 𝑈𝑡−2 > 0}𝕀{𝑈𝑡 > 𝑈𝑡∗ }, that calls for
lowering the federal funds rate more rapidly than otherwise when
the unemployment rate, 𝑈𝑡 , is both rising and above the natural
rate of unemployment , 𝑈𝑡∗ .
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o We impose an ELB of 12.5 basis points, a value equal to the midpoint of the lowest range for the federal fund rate implemented by
the FOMC during the global financial crisis.
•
We specify the model equations as follows:
o We assume that price setters, wage setters, and financial market
participants form model-consistent expectations; all other agents
project future variables using small systems of equations and
historical data.
o We assume that the term premiums in the model do not respond to
resource slack. See Appendix VIII for a discussion.
o When running stochastic simulations over many decades, as we do
for the threshold-based forward guidance simulations in Part II.B,
we assume that fiscal policy is twice as responsive to the output
gap as in the standard version of FRB/US. This alternative
assumptions helps ensure that simulations produce stable solutions
over long horizons. See Appendix III for a discussion of that
assumption.
•
We perform stochastic simulations of the model using an approach similar
to that implemented in the Risks and Uncertainty section of Tealbook A to
derive uncertainty bands around the staff projection.
o We sample from the model’s equation residuals from the 1969–
2016 period.
o To ensure consistency with the frequency and severity of historical
economic downturns, we sample recessions with the same
probability as in the data and, when a recession occurs, we draw
the entire sequence of equation residuals associated with one of the
historical recessions.
o We scale down mark-up shocks to lower their variance by half,
which helps limit occurrences of ELB episodes driven by falls in
inflation unrelated to developments in real economic activity. This
change is motivated by our judgment that historical innovations to
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inflation were more volatile than innovations to inflation going
forward because the FOMC lacked an explicit inflation objective
over most of the sample period.
o For Part I of this memo, we perform stochastic simulations using
20,000 draws in order to have reasonably small sampling
uncertainty for tail event statistics.
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Appendix II: ELB risk and outcomes under the Tealbook baseline
Table A1 reports the probability that the ELB will bind at some point between
now and various future periods based on stochastic simulations of the model around the
June 2018 Tealbook baseline (as opposed to the SEP-consistent baseline shown in the
main text). The simulations suggest only a modest probability of returning to the ELB
between now and the end of 2022 whether one uses the inertial Taylor (1999) rule or its
asymmetric version. These probabilities are smaller than those shown in Table 1 for the
SEP-consistent baseline, a difference that primarily reflects the larger rise in the federal
funds rate projected by the staff in coming years than in the path of median SEP
responses. These probabilities are also well below those assigned by market participants
over the next few years, as reported in the Desk’s Survey of Primary Dealers. As was the
case with the SEP-consistent baseline, moderate departures from the assumed baseline
value of rLR have only a limited incidence on ELB risk in the simulations.
Table A1: Probability of ELB episode between now and period shown based on
stochastic simulations around June 2018 Tealbook baseline
rLR = 0.50 (staff assumption)
Baseline rule
Asymmetric rule
rLR = 1.00 (staff assumption + 0.50)
Baseline rule
Asymmetric rule
LR
r = 0.00 (staff assumption − 0.50)
Baseline rule
Asymmetric rule
Addendum
Survey of Primary Dealers
(Median, June 2018)
2020:Q4
2022:Q4
2027:Q4
1.9
3.1
5.6
8.5
23.1
32.6
1.6
3.0
4.8
7.7
19.5
28.1
2.1
3.3
6.3
9.7
27.6
38.0
20.0
n.a.
n.a.
Note: Staff calculations using 20,000 stochastic simulations of FRB/US model.
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Appendix III: Comparison of longer-run ELB risk in studies using the
FRB/US model
This appendix illustrates the sensitivity of ELB risk estimates to a number of key
modeling assumptions. We focus on the per-period probability that the federal funds rate
is constrained by the ELB over the long run, which allows us to compare our findings
more directly to earlier studies in the literature. Because shocks take time to diffuse in
the FRB/US model, this longer-run focus also allows us to look more broadly at the range
of macroeconomic outcomes likely to be experienced over time.
As shown in Table A2, the probability of being at the ELB at any point in time
over the long run is 13.5 percent and 15.0 percent for the inertial Taylor (1999) rule and
the asymmetric version of that rule, respectively. 51 The ELB episodes under these
policies last, on average, between 8 and 11 quarters. The per-period probabilities are
similar to those reported by Williams (2009), when he assumes that rLR equals 1 percent
and that the shocks to the model are drawn from the 1968–2002 period (these
assumptions are the most similar to ours among the various parameter values and sample
periods considered in Williams (2009)). By contrast, Kiley and Roberts (2017) report
per-period probabilities between 30 and 40 percent, depending on the monetary policy
rule, for a comparable value of rLR and shocks drawn from the 1960–2007 period.
Gust and co-authors (2017) estimate a DSGE model imposing that the ELB is only occasionally binding.
Their estimates of the per-period ELB probability are disperse across stochastic simulations but in a similar
range as ours: About 15 percent of their stochastic simulations have a probability of being at the ELB more
than 10 percent of the time and about 3 percent of the draws have a probability of being there more than
17 percent of the time. In addition, these authors show that the distribution for the duration of an ELB spell
is skewed to the right and also has a long right tail.
51
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Table A2: ELB risk in the longer run in the FRB/US model
r
(in percent)
Per-period
probability
(in percent)
This memo
Inertial Taylor (1999) rule
Asymmetric rule
…+ passive fiscal policy
…+ full model-consistent expectations
Mean
duration
(in
quarters)
0.88
0.88
0.88
0.88
13.5
15.0
24.0
39.6
10.5
7.8
12.2
25.8
Williams (2009)
Taylor (1993) rule
1.00
13
n.a.
Kiley and Roberts (2017)
Estimated rule
Non-inertial Taylor (1999) rule
1.00
1.00
31.7
38.3
9.2
9.8
LR
Note: The baseline economic projection, model parameters, and simulation parameters differ
across studies; see each study for a description.
Although these studies all use the FRB/US model, they differ in several key
assumptions. With regard to behavior at the ELB, the most important such assumptions
govern how common are episodes with explosive dynamics when the ELB binds for a
sufficiently long duration. 52 These dynamics are widely regarded as implausible and
users of the FRB/US model typically offset them when running long-horizon stochastic
simulations.53 Much of the differences between our simulations and the others presented
in Table A2 stem from different strategies for dealing with these pathologies. We
highlight two key differences.
•
Fiscal policy: Our long-run simulations are conducted under fiscal
assumptions such that only extremely long ELB episodes may lead to
explosive dynamics. These assumptions help keep the volatility of
In particular, as demonstrated by Carlstrom, Fuerst, and Paustian (2015), in many New Keynesian
models with sticky prices, such as FRB/US, there is a certain length of time at the ELB such that, as one
nears this horizon, the stimulus provided by positive shocks to aggregate demand grows very rapidly, only
to become sharply contractionary once this horizon has been passed. Simulations in the vicinity of this
horizon will tend to feature explosive dynamics in which the output gap diverges without bound.
53
For example, Williams (2009) and Kiley and Roberts (2017) assume that economic slumps are eventually
reversed by the implementation of an emergency fiscal package.
52
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macroeconomic outcomes in a range that we see as plausible but they may
not provide an accurate depiction of fiscal policy in all adverse situations.
When we assume less stabilization from fiscal policy, the per-period
probability under the asymmetric policy rule steps up to 24 percent (see
entry labeled “… + passive fiscal policy”).54
•
Expectations formation: In our simulations, price setters, wage setters,
and financial market participants form model-consistent expectations
whereas other agents, in particular households, form expectations using
small systems of equations that rely solely on past economic outcomes.
When, in addition to assuming a more passive fiscal policy, we assume
that all agents form model-consistent expectations, we find that the perperiod ELB probability jumps to a level similar to that reported in Kiley
and Roberts (2017). The modeling of expectations matters to such a
degree because the time horizon for explosive amplification under fully
model-consistent expectations is much shorter than under our setting. The
risk of unbounded divergence is especially heightened when the model
lacks a stabilizing fiscal policy.
Finally, although the choice between the inertial Taylor (1999) rule and its
asymmetric version has only a small effect on long-run ELB risk in our simulations, the
monetary policy strategy assumptions can nonetheless matter much for longer-run ELB
risk. For example, Kiley and Roberts (2017) attribute much of the gap in their
assessment of ELB risks and that of Williams (2009) to an assumption in the latter paper
that leads to additional accommodation when the economy deteriorates.55
Our results labeled “…+ passive fiscal policy” and “…+full model-consistent expectations” also undo the
toning down of the volatility of the markup shocks in the model, which has only a small effect on longerrun ELB risk.
55
In Williams (2009), the intercept of the policy rule falls in a persistent manner when economic conditions
deteriorate. The anticipation of more accommodative monetary policy, in turn, helps strengthen the
economic outlook and limit the occurrence and duration of ELB episodes. In this memo as well as in Kiley
and Roberts (2017), the intercept of policy rules is fixed. Moreover, Williams (2009) allows for a shorter
maximum length of ELB episodes than Kiley and Roberts (2017), which the latter authors argue account
for much of the remaining difference in ELB risk.
54
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In sum, our discussion illustrates the sensitivity of ELB risk assessment to the
assumptions under which the model simulations are conducted, even holding large
aspects of the model constant. In particular, the extent of ELB risk seems particularly
sensitive to assumptions that limit the amount of policy stabilization by monetary and
fiscal authorities, or that makes agents in the model more prone to becoming pessimistic
about economic outcomes.
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Appendix IV: Forward Guidance in a DSGE model
Figure A1: Forward guidance in a DSGE model with discounting
Note: Simulations of forward guidance strategies in a variant of the model of Del Negro,
Giannoni, and Schorfheide (2015), in which consumers discount future interest rates at a rate of 5 percent
per quarter. The simulations is constructed around the same baseline as in the recession scenario in the
FRB/US model in Part II of this memo.
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Appendix V: Monetary policy and the tradeoffs in macroeconomic outcomes
over time
When faced with severe shocks, policymakers can limit the deterioration in
economic outcomes and hasten the economic recovery by pursuing accommodative
policies that, eventually, may lead to a tight labor market and inflation running above
2 percent. Table A3 illustrates the tradeoffs in macroeconomic outcomes over time for
each of the unconventional policies that we considered in our recession scenario. For the
unemployment rate, we report the cumulative difference from the natural rate,
distinguishing between the initial period when the unemployment rate overshoots the
natural rate and the subsequent period when the unemployment rate undershoots the
natural rate. Similarly, for inflation, we report the cumulative difference from 2 percent,
distinguishing between the initial period when inflation undershoots that goal and the
subsequent period (if present) when inflation overshoots that goal. The calculations are
performed over the simulation periods shown in Figures 2, 3, and 4, which run from the
third quarter of 2018 through the second quarter of 2033. The statistics are expressed in
percentage points per year equivalents. For example, under the asymmetric rule, inflation
undershoots 2 percent over the entire period shown by an equivalent of 9.8 percentagepoint-years, meaning that the cumulative undershooting of inflation over the period
shown is equivalent to inflation undershooting the inflation goal by 9.8 percentage points
for one year.
Overall, Table A3 shows that greater policy accommodation, as expected, leads to
a reduction in the overshooting of the natural rate of unemployment and in the
undershooting of the inflation objective during the recession and ensuing economic
recovery. However, greater policy accommodation subsequently comes at the cost of a
more pronounced undershoot of the natural rate of unemployment under all policies and,
in some cases, with a modest inflation overshoot of 2 percent. To decide which policy is
most appropriate in response to the recession, policymakers would need to weigh the
improvement in macroeconomic outcomes early on against the possible deterioration in
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macroeconomic outcomes later on. 56 The loss policymakers attach to various outcomes
may well differ from the simple cumulative sums reported in Table A3. For example,
policymakers might attach greater importance to improving the worse outcomes or might
put greater weight on economic developments in the near term than several years out.
Table A3: Cumulative overshoots and undershoots of longer-run values in a
recession scenario under unconventional policies
Ut
πt
overshoot
(in p.p.-year)
undershoot
(in p.p.-year)
Asymmetric rule (AR)
15.3
1.5
0
9.8
AR + threshold-based
forward guidance
Ut < 5½ percent
Ut < 4½ percent
Ut < 3½ percent
πt > 1¾ percent
πt > 2 percent
πt > 2¼ percent
15.3
15.1
13.8
13.9
13.4
13.0
1.5
1.7
4.3
4.2
5.5
7.2
0
0
0.1
0
0.6
1.7
9.8
9.4
5.0
5.1
3.5
2.0
15.3
14.3
14.2
12.1
1.5
1.8
1.8
3.3
0
0
0
0
9.8
8.6
8.6
5.3
11.2
7.8
2.0
0.9
AR + balance sheet
policies
Passive
Reinvestment only
MEP
LSAP
LSAP + inflation
threshold
overshoot
undershoot
(in p.p.-year) (in p.p.-year)
Note: The table shows, for each policy considered, the cumulative difference from either the
natural rate of unemployment or the 2 percent inflation goal under the recession scenario. Separate
statistics are computed for the periods of undershooting and overshooting. The statistics are computed over
the 2018:Q3–2033:Q2 period.
In addition to specifying their preferences over outcomes, policymakers would likely take account of
other elements, such as risk management and communication considerations.
56
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Appendix VI: Reputational concerns and forward guidance
In our discussion of forward guidance under a recession scenario, we noted that
threshold policies that entail promises to overheat the economy in the future may not be
time consistent: Eventually, economic conditions might improve to such an extent that
policymakers would prefer to abandon their forward guidance in favor of a tighter stance
of policy to contain the projected undershoot of the natural rate of unemployment and its
accompanying inflationary pressures. Although departing from announced forward
guidance might bring some immediate benefits, policymakers might worry that doing so
entails a loss of credibility that could diminish the potency of central bank
communications in future downturns.
In this appendix, we quantitatively explore reputational concerns under the
assumption that policymakers face an uncertain future around the recession baseline, set
the federal funds rate in normal times according to the asymmetric rule, and seek to
implement forward guidance in the form of a 2¼ percent inflation threshold whenever the
ELB is binding. We further posit that policymakers’ preferences are captured by a
simple loss function that penalizes unemployment rate realizations above the natural rate
and inflation deviations—positive and negative—from the FOMC’s 2 percent goal. 57
Finally, we assume that policymakers’ forward guidance is initially fully credible and
that any departure from an announced forward guidance prevents policymakers from
issuing forward guidance for a fixed number of periods; thereafter, their forward
guidance is again fully credible until another departure occurs. The latter assumptions
capture, in a simple manner, the loss of credibility due to broken policy promises.58
We measure the net benefit of deviating from the forward guidance as the
difference in expected discounted losses between a policy that departs from the forward
guidance and a policy that abides by it. The net benefit can be decomposed into the short
Formally, we assume that policymakers’ preferences are given by a discounted sum of the squared
excesses in the unemployment rate and squared deviations of inflation from 2 percent, ∑𝑇𝝉=𝟎 𝛽𝜏 ((𝑈𝑡 −
𝑃𝐶𝐸
𝑈 ∗ )2 𝕀{𝑈𝑡 > 𝑈 ∗ } + (𝜋𝑡+𝜏
− 2)2 ), where 𝛽 = 0.99 and 𝑇 is large. This loss function could capture the
preferences of policymakers who do not regard unemployment rate realizations below the natural rate as
undesirable unless these realizations are accompanied by inflation readings above 2 percent.
58
For formal analysis of the role of reputation for monetary policymaking in a liquidity trap, see Nakata
(2015, 2018) and Walsh (2018).
57
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run gain from reneging from a promise and the long run cost of not being able use
forward guidance in a future recession. When this difference is positive, policymakers
judge it advantageous to abandon the guidance and, conversely, prefer to follow through
with the guidance when this difference is negative.
The first line of Table A4 shows the net benefit of deviating from an inflation
threshold of 2¼ percent in the absence of economic uncertainty in our baseline recession
scenario. The net benefit is measured in 2026—as policymakers contemplate a lengthy
overheating period—under the assumption that deviating from the announced policy
forever prevents recourse to forward guidance. The net benefit is positive in that period,
meaning that policymakers unambiguously prefer to abandon the forward guidance. As
Table A3 shows, this net benefit is equivalent to preventing inflation from exceeding
2 percent by 0.4 percentage point for three years. Because there is no uncertainty in the
baseline recession scenario, losing the ability to issue forward guidance in the future
entails no cost in terms of economic stabilization because the economy never faces the
ELB again.
The remaining rows of Table A4 show the net benefit when the evolution of the
economy is uncertain, so that a loss of credibility limits policymakers’ ability to stabilize
economic activity through forward guidance in future ELB episodes. We consider three
durations for policymakers’ inability to use forward guidance after a departure: 5 years,
10 years, and 20 years. The net benefit is calculated as the expected difference in losses
over the duration under consideration between the asymmetric rule with and without
forward guidance, starting from the model’s steady state. The net benefit is negative for
all three durations considered, suggesting that preserving the credibility of future forward
guidance improves outcomes in future downturns to such an extent that policymakers
today are better off implementing the announced guidance, even if it implies overheating
the economy for a time, rather than deviate and face more severe ELB episodes in the
future. The table also suggests that the greater the loss in credibility (as measured by the
duration without recourse to forward guidance), the less inclined policymakers would be
to deviate from their past communications.
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This type of cost-benefit analysis is subject to various caveats, including our
assumption about policymakers’ preferences over macroeconomic outcomes. However,
our simulations suggests that, once reputational concerns are taken into account, carrying
through with an announced forward guidance offers benefits in terms of better economic
stabilization over the longer run: Those benefits may more than outweigh the near-term
gains from abandoning the forward guidance.
Table A4: Net benefit of abandoning the forward guidance in a recession scenario
1.4
Equivalent three-year
inflation deviation
(in percentage point)
0.4
-1.4
-5.3
-12.8
-0.4
-0.7
-1.1
Net benefit
Recession scenario (no uncertainty)
Extended simulations (with uncertainty)
5-year loss of credibility
10-year loss of credibility
20-year loss of credibility
Note: “Net benefit” statistics are calculated as the difference in the present discounted loss
between versions of the asymmetric rule without and with a 2¼ percent inflation threshold. The assumed
loss function penalizes unemployment rate realizations above the natural rate and inflation deviations—
positive and negative—from 2 percent. “Equivalent three-year inflation deviation” statistics are calculated
as the percentage-point deviations of inflation from 2 percent that, if maintained for three years, would
result in present discounted losses equivalent to the (absolute) net benefit, holding future inflation and the
unemployment rate at their long-run levels.
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Appendix VII: Macroeconomic outcomes in the longer run under thresholdbased forward guidance
Figure A2: Distribution of longer-run macroeconomic outcomes under thresholdbased forward guidance
Note: The left and right panels show a distribution of unemployment rate outcomes and inflation
outcomes, respectively, in stochastic simulations around a steady-state baseline and conditional on being in
an ELB episode. The blue histograms show distributions for the asymmetric rule without threshold-based
forward guidance, whereas the orange histograms show the distributions when the asymmetric rule is
complemented with credible forward guidance that the ELB will bind at least until inflation exceeds
2¼ percent. For comparability, both sets of histograms are calculated using the subset of periods for which
the ELB binds under the asymmetric rule without threshold-based forward guidance.
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Appendix VIII: Macroeconomic effects of LSAPs under countercyclical term
premiums
In the data, simple correlations suggest that the term premiums are mildly
countercyclical, though the economic reasons for such countercyclicality and the possible
connections to monetary policy are debated. In our simulations, we have assumed for
simplicity that term premiums do not respond to the business cycle. If, instead, we were
to assume an endogenous countercyclical component in term premiums consistent with
the idea that risk premiums in general tend to rise amid poor economic conditions, our
simulated monetary policy effects would be larger, both for conventional interest rate
policy and for balance sheet policy. We isolate this effect for the LSAP policy in Figure
A3, which, like Figure 5, focuses on distributions of the unemployment rate and inflation
outcomes when the ELB binds in each period shown. The first two intervals in each year
are the same as previously reported in Figure 5: They are the interquartile range of the
distributions assuming acyclical term premiums for the LSAP and passive balance sheet
policies. The next two intervals are the corresponding interquartile ranges when we
instead assume term premiums that are as countercyclical as in the data.
When the term premiums incorporate a countercyclical element, all else equal,
cyclical movements in the unemployment rate and inflation are amplified. For example,
a strengthening in the economy brings about a reduction in term premiums, which
supports additional economic strength. This mechanism also means that monetary policy
can be more effective at macroeconomic stabilization. On net, our simulations indicate
that the economy tends to be more volatile, as evidenced by the increased dispersion in
unemployment rate and inflation outcomes under both the passive policy and the LSAP
policy.
Under the passive policy, for inflation, the bulk of the interquartile range with
countercyclical term premiums is below the median outcomes for the same policy with
acyclical term premiums. For the unemployment rate, the medians are similar between
the simulations with and without endogenous term premiums. However, with the greater
dispersion, the 75th percentile of the unemployment rate distribution with countercyclical
term premiums is well above the corresponding percentile with acyclical term premiums.
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Figure A3: Effect of assumptions about the cyclicality of term premiums on balance
sheet policy outcomes
Note: The markers and the intervals show the median and the interquartile range, respectively, of
the distribution of macroeconomic outcomes under each policy. For comparability, the distributions are
calculated for the same sequences of shocks for which the ELB binds under the passive balance sheet
policy in the final quarter of each period shown. The statistics are computed through stochastic simulations
around the SEP-consistent baseline projection. The red dot and green square show the medians of the
distribution assuming acyclical term premiums, under the passive and LSAP policies, respectively. The red
star and green triangle show the medians assuming endogenous term premiums, again under the passive
policy and the LSAP policy, respectively.
If we compare the difference between the macroeconomic outcomes under the
LSAP policy and the passive policy, the differences are typically larger when the term
premiums are countercyclical than when they are acyclical:
•
With countercyclical term premiums, by the end of 2022, the median
unemployment rate under the LSAP policy is 36 basis points lower than it
is under the passive policy; by contrast, with acyclical term premiums, the
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median unemployment rate under the LSAP policy is only 25 basis points
lower than under the passive policy.
•
Moreover, with countercyclical term premiums, the LSAP policy is more
successful in limiting extreme outcomes. For example, when term
premiums are countercyclical, the 75th percentile of the unemployment
rate under the passive policy is somewhat above 7¾ percent, but is close
to 7¼ percent under the LSAP policy. When term premiums are instead
assumed to be acyclical, the 75th percentile of the unemployment rate
under the passive policy is 7.4 percent, whereas that percentile of the
distribution under the LSAP policy is around 7.2 percent—a much smaller
difference than we show when term premiums are countercyclical.
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@FedFRASER