Forward Guidance and Asset Prices
Yıldız Akkaya∗

Refet S. Gürkaynak†
Burçin Kısacıkoğlu‡
Jonathan H. Wright§
April 21, 2015

Abstract
This paper examines the effects of forward guidance at the zero lower boundon the term structure of interest rates in a shadow-rate macro-finance term
structure model. The effects on the yield curve are found to depend on thetype of forward guidance and on the current level of the shadow rate. The morenegative the shadow rate, and so the further away liftoff is, the less effective isforward guidance. Forward guidance affects both the expected path of future
short rates, but also term premia. Our model allows us to estimate these effects
separately. We also conduct an event-study in which we break out FOMC
announcements into surprises concerning the future path of the funds rate, anduncertainty around that path, and then estimate the impacts of each on equity
and currency markets.

∗

Department of Economics, Bilkent University, 06800 Ankara, Turkey. yakkaya@bilkent.edu.tr.
Department of Economics, Bilkent University, 06800 Ankara, Turkey and CEPR.
refet@bilkent.edu.tr.
‡
Department of Economics, Johns Hopkins University, Baltimore MD 21218. bkisaci1@jhu.edu.
§
Department of Economics, Johns Hopkins University, Baltimore MD 21218. wrightj@jhu.edu.
†

1Introduction

Forward guidance about the path of future short-term interest rates arose as animportant policy tool for many central banks when the zero lower bound (ZLB)
became binding in the Great Recession. The original perspective on forward guidance(Eggertsson and Woodford, 2003) involves a central bank making a commitment to
low future spot rates, thereby reducing longer term interest rates via the expectations
hypothesis. Indeed, the Federal Reserve influenced expectations of future rates anduncertainty around those expectations via their statements well before the GreatRecession, especially from 2003 to 2005. But forward guidance became much more
important at the ZLB. After reaching the ZLB in December 2008, the FOMC firstused rather vague forward guidance, as they had done from 2003 to 2005. The
FOMC stated that exceptionally low interest rates were likely to be appropriate for an“extended period”. Then in August 2011 it transitioned to “calendar-based” forward
guidance in which it stated that liftoff was not expected until at least mid-2013. In
December 2012, it switched to “ threshold-based” forward guidance, in which theconditions for liftoff were that the unemployment rate hit 6.5 percent, or that theforecast of inflation reach 2.5 percent. As the unemployment rate has fallen below
6.5 percent, the FOMC has reverted to vaguer forward guidance. See Campbell etal. (2012) and Filardo and Hoffmann (2014) for more detailed accounts of forward
guidance.
Forward guidance has similarly been an important element of the ZLB toolkitof the Bank of England and the Bank of Japan. The European Central Bank was
reluctant to adopt forward guidance1 , but has now come to use it as well.
The theoretical mechanism by which forward guidance circumvents the ZLB is
1

Former president Trichet stated that the ECB would never pre-commit.

1

by constraining monetary policy to be easier than it other would be in the future,
overcoming a time-consistency problem (Kydland and Prescott, 1977). It is essentiallya commitment to be the opposite of the conservative central banker of Rogoff (1985):
it is a promise that monetary policy will be more accommodative than the central
bank would ex-post desire (Eggertsson and Woodford, 2003; Woodford, 2012). Thereis a tension between the theory and practice of forward guidance. At the ZLB,
central banks would like to see easier financial conditions, but central banks havenever said that they are constraining their own future actions, and saying so would
be politically difficult. Without tying the central bank’s hands, forward guidance canonly work if private sector agents misunderstand the central bank’s reaction function,or if the central bank has a different view of future macroeconomic conditions andcan furthermore persuade private sector agents that its forecast is superior2 . Whilethese circumstances could arise, such forward guidance can only be a solution to the
problem of the ZLB under very particular conditions and only to a limited extent.
Indeed, while convincing the private sector that the economic outlook is weak might
persuade investors that rate hikes are far off, it seems a rather counterproductive
strategy to promote an economic recovery. In practice, we suspect that central banks
fervently hope that forward guidance is interpreted as a commitment, while at thesame time protesting that it is nothing of the sort.
This paper is an empirical analysis of forward guidance in the context of the US.
Unlike Eggertsson and Woodford (2003), we note that forward guidance does nothave to operate via the expectations hypothesis alone: it can also increase or reduce
term premia. Forward guidance seems likely to remain important after liftoff fromthe ZLB. We would like to study the effectiveness of forward guidance at and away2

Campbell et al. (2012) refer to forward guidance that resolves the time-consistency problem as
Odyssean and forward guidance that communicates information about the economic outlook as
Delphic.

2

from the ZLB and understand the mechanisms through which it affects long-term
interest rates and other asset prices.
We approach the empirical analysis of forward guidance by estimating a macrofinance term structure model which is standard, except that it incorporates the ZLB
and a shadow short term interest rate, as proposed by Black (1995). The shocks havea structural interpretation. The shadow short rate is set via a Taylor rule and cango negative, but the actual short rate is the maximum of the shadow short rate andthe lower bound. We model forward guidance as anticipated monetary policy shocks
as in Laseen and Svensson (2011) and Del Negro et al. (2012). We use our model toestimate how different types of forward guidance can affect both the expected pathof policy and term premia. The effects of forward guidance can depend on how far
the shadow rate is below zero—the more negative is the shadow rate, the less effectmost forms of forward guidance will have. The intuition is simple: if investors do not
expect liftoff for some time, then a credible commitment to keep interest rates at the
ZLB for some time doesn’t change much.
As a supplementary empirical exercise, we use an event study methodology thatexamines both the effects of surprises about the future path of policy and surprises
about the level of monetary policy uncertainty on asset prices.
The plan for the remainder of this paper is as follows. Our term structure modeland the resulting estimates of the effects of forward guidance are given in section 2.
Section 3 contains the event study analysis, and section 4 concludes.

3

2

Effects of forward guidance in a term structuremodel

Our main approach in this paper involves estimating a macro-finance term structure
model, incorporating the ZLB. In our model, the shadow short rate follows a Taylor
rule:
st = ρ0 + ρ1 ut + ρ2 πt + ft

(1)

where ut is the unemployment rate, πt is inflation (core PCE, year-over-year) and ft
is a monetary policy surprise. The actual short rate is:(2)

rt = max(st , r)where r is the zero lower bound (which need not necessarily be exactly zero). The
state vector is Xt = (ut , πt , ft )0 , which follows a VAR(1) under the physical (P)measure:Xt = µ + ΦXt−1 + Σεt(3)where the structural shocks εt are iid(0,1), φ11 φ12 φ13 



Φ=
 φ21 φ22 φ23 


0
0 φ33
and



(4)



0 
 Σ11 0



Σ=
0
Σ
0
22




0
0 Σ33

4

(5)

This means that ft does not respond to any other elements of the state. The monetary
policy shock is the last element of εt . Exactly the same model applies under the riskneutral (Q) measure except that under this measure the state vector instead follows
the process:
Xt = µQ + ΦQ Xt−1 + Σεt(6)where µQ and ΦQ are unrestricted. This is like the model in Ang et al. (2011), exceptthat it does not allow for time-variation in ρ1 and ρ2 , but does instead incorporate
the ZLB constraint. Ignoring the ZLB, the model implies that bond yields are affine
functions of Xt , that are available in closed form. Treating observed yields as being
measured with error, the model can then easily be estimated via the Kalman filter.
But once one takes account of the ZLB, bond prices do not exist in closed form.
Instead, we can note that the price of an n-period zero-coupon bond is:Pt (n) = EtQ (exp(−Σn−1
i=0 rt+i ))(7)

and we compute this by simulation, taking draws of Xt from equation (6) and thenworking out the implied path of short-rates using equations (1) and (2).
Our yield data consist of 1 and 6 month T-Bill yields and 1-5 year zero coupon
yields.

The 1 month T-Bill yield was treated as the short rate. Our estimation

strategy follows Bauer and Rudebusch (2013). We first estimated the model given byequations (1)-(5) using monthly data from January 1990 to December 2007. Over
this period, we neglected the zero lower bound (ZLB). We estimated ρ0 , ρ1 and ρ2
by OLS, hence recovered Xt and estimated µ, Φ and Σ. Finally, treating each yieldother than the 1 month yield as being measured with error with standard deviation
σi , we estimated µQ , ΦQ and the σi s by maximum likelihood.

5

Table 1 shows the estimated standard deviation of the yield measurement error.
The measurement error ranges from 40 to 100 basis points. This measurement error
could surely be reduced by adding in a latent factor, but that would make macroeconomic interpretation harder.
Next, we held these parameters fixed, and used the unscented Kalman filter (Julier
and Uhlmann, 1997) to extract smoothed estimates of the state over the period since
January 2008, using simulations to price bonds at the ZLB, as described above. We
set the effective lower bound, r, to 10 basis points per annum3 .
The implied shadow rate is ρ̂0 + ρ̂1 ut + ρ̂2 πt + fˆt where ρ̂0 , ρ̂1 and ρ̂2 are estimatesof ρ0 , ρ1 and ρ2 and fˆt is the smoothed estimate of ft . Note that at the ZLB, ft is notobservable even conditional on the parameters. The implied shadow rate is shown in
Figure 1. In effect, the term structure model is inferring the shadow rate from theyield curve—the further out the term structure interest rates are close to zero, themore negative is the shadow rate. So the shadow rate is effectively a measure of how
far out Fed communications have pushed the expected time of liftoff. Figure 1 also
shows the shadow rate implied by the Taylor rule in the absence of any monetary
policy surprise, ρ̂0 + ρ̂1 ut + ρ̂2 πt .
In early 2008, the ZLB was not yet binding. The shadow rate was the actual
rate4 . Moreover, the actual shadow rate was below the Taylor rule shadow rate.
In late 2008 and early 2009, the Taylor rule shadow rate fell sharply below zero,
whereas the shadow rate declined a bit less. By late 2009, the shadow rate was a
bit above the Taylor rule shadow rate. But then in 2011, the shadow Taylor rule3

For institutional reasons, the Federal Reserve never tried to drive short rates all the way to zero,and instead targeted a federal funds rate in the range 0-25 basis points.
4
Recall that the short-rate considered here is the one-month T-Bill yield. The one-month T-Bill yieldis typically slightly below the federal funds rate, because the federal funds rate is an uncollateralizedinterbank rate with some credit risk, and also because Treasury Bills have some tax advantages.
The gap widens out at times of financial stress. Early in 2008, one-month T-Bill rates were quite
a bit below the federal funds rate.

6

started climbing back to zero, while the shadow rate stayed around -4 percent until
2013. Mechanically, this is because the ZLB became binding further out the term
structure, a point demonstrated by Bauer and Rudebusch (2013) and Swanson andWilliams (2014). Substantively, this is the effect of forward guidance. By mid-2012,
the shadow rate Taylor rule was calling for short rates around zero, but the Fed had
signalled that lift-off was quite some time off, keeping longer-term yields down. The
model interprets this as a shadow rate that is still negative because of a negativevalue of ft .
At the end of the sample, in December 2013, we can study the effects of a few
counterfactual forward guidance experiments. Each of these is interpreted as announcing monetary policy shocks (shocks to future ft s). It is important to rememberthat there was already considerable forward guidance in place in December 2013,
as represented in the model by the fact that the shadow rate was around 250 basis
points below the shadow rate Taylor rule. Our counterfactual experiments involvethe incremental effects of additional forward guidance as follows:
1. Volatility forward guidance. For the next two years, there will be no shocks toft (Σ33 = 0).
2. Shocks to the shadow rate. A sequence of monetary policy shocks will lower
the shadow rate st by 1 percent for 2 years.
3. Unconditional commitment. A sequence of monetary policy shocks are promised
such that the short rate will be kept at the ZLB for two years.
4. Conditional commitment. A sequence of monetary policy shocks are promised
such that the short rate will be kept at zero until the first time that the unem-

7

ployment rate hits 5.5 percent.5
These policies all involve modeling forward guidance as anticipated monetary policy
shocks as in Laseen and Svensson (2011) and Del Negro et al. (2012)6 . The forward
guidance is assumed to be perfectly credible in each case. Agents learn about thesefuture shocks today, and the yield curve consequently jumps. In each case, after 2
years (or when the unemployment rate hits 5.5 percent for case 4), normal shocks
resume. Importantly, this doesn’t mean that the level of short rates immediately
jumps back to where it would have been in the absence of any forward guidance—
under policies 2-4 one would expect monetary policy to be more accommodative forsometime after normal shocks resume than it would have been in the absence ofany forward guidance, because of persistence in monetary policy. Any one of thesepolicies should lower near-term uncertainty about future rates. Indeed, as the FOMC
sharpened its forward guidance from 2010 to 2012, uncertainty about future shortterm US interest rates, as measured from interest rate options, fell sharply, especiallyon days of monetary policy announcements (Bauer, 2012). At the same time, interest
rates became unresponsive to macroeconomic news further out the term structure(Swanson and Williams, 2014).
The four panels of Figure 2 show the model estimates of the effects of each of thesefour policies on the yield curve in December 2013. Each panel shows the difference
between model-implied yields with one of these policies and model-implied yields
without any of these policies. Results are shown both under the Q and P measures.
5

Note that this does not correspond to the numerical threshold for unemployment in forward guidance given by the FOMC—that threshold was 6.5 percent. By December 2013, the unemployment
rate was 6.7 percent, and so a 6.5 percent threshold was moot. But in that month, the FOMC
stated that the funds rate would stay at zero “well past the time that the unemployment rate
declines below 6-1/2 percent.” Minneapolis Fed President Narayana Kocherlakota proposed a 5.5
percent threshold for liftoff.
6
Laseen and Svensson (2011) and Del Negro et al. (2012) were considering DSGE models, not anaffine term structure model as in the present paper.

8

The results under the Q measure show the effects on actual yields. The results under
the P measure can be interpreted as showing the effects on average expected future
short rates over different horizons. The difference between the two is the effect on
the term premium.
Volatility forward guidance lowers expected future rates. This arises because of
the ZLB. In the absence of forward guidance, a large enough positive shock to theshadow rate would raise expected short rates, whereas a negative shock to the shadow
rate cannot do anything to short rates. Removing shocks consequently lowers the expected path of policy. But, as can be seen in Figure 2, volatility forward guidance also
operates through reducing term premia. Volatility forward guidance can lower yields
by up to 25 basis points, with the peak effect occurring at the 2-3 year maturity.
Akkaya (2014) considers a DSGE model of stochastic monetary policy uncertainty
and shows, via a third order perturbation solution, that forward guidance affects realvariables as much through reducing monetary policy uncertainty as through reducing
the level of interest rates. There the mechanism works via consumers’ risk aversion
and precautionary savings. Filardo and Hoffmann (2014) suggest that forward guidance might lower term premia via reducing uncertainty, and our results are consistent
with their conjecture. Volatility forward guidance may be politically appealing because it doesn’t involve a change in the mean reaction function. At the same time,it does not directly map into any of the forms of forward guidance that the Fed orother central banks have employed.
A shock to the shadow rate is also a rather vague form of forward guidance, thatcan be interpreted as simply setting a higher bar for liftoff than would be impliedby direct application of the Taylor rule (equation (1)). This policy lowers expected
future short rates, but actually raises term premia. On net, longer-term bond yields
drop slightly under this policy. A possible economic intuition for the increase in9

term premia is that more accommodative monetary policy increases the inflation risk
premium.
Unconditional commitment corresponds to calendar-based forward guidance, although no central bank has issued such guidance without some kind of escape clause.
The effects on short-term yields are limited, because the shadow rate starts out too
far below zero for it to matter. But yields with maturities from about two to five years
drop by about 50 basis points. Conditional commitment corresponds to thresholdbased forward guidance. This has a smaller effects on the yield curve than unconditional commitment, but the effect is still sizeable. With both policies 3 and 4, average
expected future short rates decline by more than yields, as the forward guidance policy
causes term premia to rise.
We also consider the effects of applying the same four policies in December 2012.
As can be seen in Figure 1, in December 2012, the shadow rate was a good bit lower
than it was a year later. That in turn alters the effects of the forward guidance.
The four panels of Figure 3 show the model-implied effects of each of these policies
in December 2012. The volatility forward guidance, shock to the shadow rate, andunconditional commitment all have effects in the same direction, but of smaller magnitude, than in December 2013 (Figure 2). Intuitively, this is because the further the
shadow rate is below zero, the less impact monetary policy shocks over the next twoyear are going to have. On the other hand, the conditional commitment has about
the same effect on longer term yields in December 2012 as it does in December 2013,
though the effects on shorter term yields are smaller in December 2012. Intuitively,
this is because conditional commitment will affect the expected future policy path atsome horizon no matter what the level of the shadow rate, though the more negativeis the shadow rate, the more delayed the effect on the policy path will be. In thispaper, we assume all policies to be perfectly credible. But in practice, of course, the10

further out commitment is tying the hands of a central bank, the less credible it islikely to be.
Finally, we consider the effects of applying the first two types of forward guidance:
volatility forward guidance and forward guidance concerning shocks to the shadow
rate in December 2007, before the ZLB applied. The effects of these shocks dependvery little on the state vector once short rates are above zero, and so we can think ofthese as impulse responses at any time when the ZLB is far from binding. Away fromthe ZLB, commitment to keep rates at zero is of course not a meaningful experiment,
which is why we consider only the first two types of forward guidance. The results areshown in Figure 4. The volatility forward guidance has no effect. This is because awayfrom the ZLB, eliminating shocks is as likely to raise as to lower the expected pathof future short rates. Away from the ZLB, shocks to the shadow rate are effectively
shocks to the short rate and they consequently have a much larger effect on the yield
curve than we found for shocks to the shadow rate in Figures 2 and 3.

3

Event-study analysis of monetary policy shocks
at the ZLB

As noted above, forward guidance may jointly reduce both the expected path of futuremonetary policy and uncertainty around this path. In this section, we use an eventstudy methodology to examine the separate effects on equity and currency marketsof news about the path of future monetary policy and news about the uncertainty
surrounding that path.
It has long been understood that monetary policy announcements are complicatedand contain much more information than just the decision about the target federal

11funds rate. Before the ZLB era, Gürkaynak et al. (2005) considered two measures of
the information content of a monetary policy announcement—the “target surprise”
and the “path surprise”. The target surprise is the unexpected component of thedecision about the target federal funds rate; the path surprise is the orthogonalized
jump in four-quarter ahead interest rate futures, reflecting the content of the Fed’s
statement.

In this paper, we propose updating this methodology to the ZLB pe-

riod. There are no longer shocks to the federal funds target—no FOMC meeting
since December 2008 has made any change to the target funds rate, nor did investors
assign any probability to funds rate changes. But there were path surprises, which
we define as the change on FOMC announcement days in the eighth eurodollar futures contract7 . And, we add a new element of monetary policy announcements—the“uncertainty surprise”. This can be measured from the change in options-implied
volatility on the eighth eurodollar futures contract on the day of the monetary policy
announcement, orthogonalized with respect to the path surprise. The orthogonalization is important because at the ZLB, a downward shift in the expected path of policy
will mechanically lower interest rate uncertainty. We use the event-study methodology to estimate the effects of each of path and uncertainty shocks on stock prices.
This is a model-free way of assessing the separate impacts of changes in the expected
path of monetary policy, and changes in uncertainty about that path. The event
study regression isyt = β1 P atht + β2 U ncertaintyt + εt(8)where yt is the change in an asset price on the day of a monetary policy announcement, and P atht and U ncertaintyt represent the path surprise and orthogonalized
7

The eighth contract is a bet on interest rates about two years ahead. Nearer term futures contracts
are less sensitive to incremental forward guidance because for much of the ZLB period, nearer-term
expectations were already stuck near zero (Swanson and Williams, 2014).

12

uncertainty surprise, both as defined above.
The results are shown in Table 2 for three assets: S&P returns and the dollar
exchange rates viz-a-viz the euro and yen (both defined as dollars per unit foreign
currency). These asset returns are important, because the stock market wealth channel and exchange rate channel are two important ways in which unconventional monetary policy can be hoped to support economic activity. The regression is run overthe period from January 2009 to March 2014, a period with a total of 42 FOMC
announcements. The sample size is fairly small, but there were a number of sizeable
surprises over this period. The path and uncertainty surprises are both estimated tohave a negative effect on stock prices. This means that the equity market is boosted
by both a lower futures-implied path and by less interest rate uncertainty. However,
the effect of the path surprise is only statistically significant at the 10 percent level,
whereas the effect of the uncertainty surprise is statistically significant at the 1 percent level. Uncertainty shocks seem to have a separate (and more strongly identified)effect on equity markets. On the other hand, the path surprise is estimated to havea negative effect on the euro and yen exchange rates (a lower futures-implied path
implies a weaker dollar) which is significant at the 5 percent level, but uncertainty surprises are not estimated to have any significant effects on currency returns. We do notshow the effects of path and uncertainty surprises on long-term interest rates—pathsurprises have a significant positive effect on long-term interest rates while uncertainty surprises do not, but this is almost by construction, since the path surprise isa measure of the change in the slope of the yield curve. It should also be borne inmind that our path and uncertainty surprises reflect news both about future policy
expectations/uncertainty and about bond risk premia. The event study approach
does not allow these to be separated out.

13

4Conclusions

We have examined forward guidance in a macro-finance shadow rate term structure
model. We find that it affects yields both via changing the expected future path ofpolicy and via changing term premia, although these two effects may go in opposite
directions. We have evaluated the effects of different types of forward guidance.
Most forms of forward guidance are more effective if the shadow rate is close tozero than if it is substantially negative, but of course a central bank is most likely
to be uncomfortable about an additional commitment to accommodative monetary
policy when liftoff is near. In other words, forward guidance is most effective when
liftoff is near precisely because it constrains the central bank to make a commitmentthat it may well regret ex-post.

We also considered an event study analysis of

the effects of monetary policy shocks at the ZLB. We split the monetary policy
news into orthogonal path and uncertainty surprises. We find that monetary policy
announcements that reduce interest rate uncertainty significantly boost the stock
market.

14

Table 1: Measurement Error in Yields
Maturity Standard Deviation (percent per annum)
6 months
0.42
1 year
0.42
2 year0.80
3 year
0.57
4 year
0.68
5 years
0.98
Note: This table shows the maximum likelihood estimates of the yield fitting error standard deviation(in percent per annum) over the pre-ZLB sample (January 1990-December 2007). By construction,
the one month yield always fits perfectly.

Table 2: Event Study Results
S&P
Euro
Yen
∗
∗∗
Path Surprise
-3.33
-3.38
-2.96∗∗(1.87)(1.70) (1.41)∗∗∗
Uncertainty Surprise -25.37
0.09
1.51
(5.77)(7.37) (5.16)
Note: This table shows the estimates from the estimation of equation (7). The path surprise is definedas the change in the eighth eurodollar futures contract on the days of FOMC announcements, andthe uncertainty surprise is defined as the orthogonalized change in the implied volatility from options
on this contract. The surprises are both measured in percentage points; stock and currency returns
are measured as 100 times log daily changes. Heteroskedasticity-robust standard errors are given inparentheses. One, two and three asterisks denote statistical significance at the 10, 5 and 1 percent
levels, respectively. The sample period is all FOMC meetings from January 2009 to March 2014,
inclusive, for a total of 42 observations.

15

Figure 1: Shadow short-term interest rates January 2008-December 2013

5
Estimated Shadow Rate
Taylor Rule Shadow Rate

4
3

Percent Per Annum

2
1
0
-1
-2
-3
-4
-5
2008

2009

2010

2011

2012

2013

2014

Note: This figure shows the estimate of the shadow rate: ρ̂0 + ρ̂1 ut + ρ̂2 πt + fˆt and the Taylor rule
shadow rate: ρ̂0 + ρ̂1 ut + ρ̂2 πt , in the model given by equations (1)-(5), estimated as described in the
text.

16

Figure 2: Effects of Counterfactuals on the Yield Curve: December 2013

Volatility Shock

Shock to shadow rate0

Percent-0.2-0.4
Q-measureP-measure

-0.6
-0.8
-1

Unconditional Commitment

Conditional Commitment

0

Percent

-0.2
-0.4
-0.6
-0.8
-1
0

1

2
3
4
Maturity (Years)

5

0

1

2
3
4
Maturity (Years)

5

Note: This figure plots the estimated effects of counterfactual policies 1-4, described in the text, on theterm structure of interest rates under the P and Q measures. Results under the Q measure correspondto the predicted effects on yields; results under the P measure correspond to the predicted effect on
expected future average short rates. These calculations assume that the state vector is initially as
estimated in December 2013.

17

Figure 3: Effects of Counterfactuals on the Yield Curve: December 2012

Volatility Shock

Shock to shadow rate0

Percent-0.2-0.4
Q-measureP-measure

-0.6
-0.8
-1

Unconditional Commitment

Conditional Commitment

0

Percent

-0.2
-0.4
-0.6
-0.8
-1
0

1

2
3
4
Maturity (Years)

5

0

1

2
3
4
Maturity (Years)

5

Note: As for Figure 2, except that these calculations assume that the state vector is initially as estimatedin December 2012.

18

Figure 4: Effects of Counterfactuals on the Yield Curve: December 2007

Volatility Shock0
Q-measureP-measure

Percent

-0.2
-0.4
-0.6
-0.8
-1
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

3.5

4

4.5

5

Shock to shadow rate0

Percent

-0.2
-0.4
-0.6
-0.8
-1
0

0.5

1

1.5

2
2.5
3
Maturity (Years)

Note: As for Figure 2, except that these calculations assume that the state vector is initially at its value
in December 2007. Results are only shown for counterfactual policies 1 and 2. Impulse responses arevery similar if the state vector is set to its value at any time when the ZLB is far from binding.

19

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