Rethinking the Power of
Forward Guidance:
Lessons from Japan
Keynote Speech by Mark Gertler
In the spring of 2013 the Bank of Japan introduced a state-of-the-art
monetary policy which included among other things inflation targeting
and aggressive use of forward guidance. In contrast to the predictionsof conventional macroeconomic theory, these policies have had only very
limited success in reflating the economy. I argue that the disconnect between the Japanese experience and existing theory can be traced to theforward guidance puzzle (FGP). As recent literature suggests, the essenceof the FGP is that existing models predict implausibly strong eﬀects of expected future interest rate changes on the economy, with the strength ofthe eﬀect increasing with the expected horizon of the interest rate change.
Accordingly, in this lecture I sketch a model meant to capture the challenge of reflation in Japan. As in recent literature I attempt to mute thepower of forward guidance by stepping outside of rational expectations.
In particular, I introduce a hybrid adaptive/rational expectations belief
mechanism. Most relevant to the Japanese experience is that individuals
have adaptive expectations about trend inflation, which is consistent withthe evidence. As Kuroda (2016) emphasizes, for an economy without ahistory of inflation being anchored by a target, individuals need direct
evidence that the central bank is capable of moving inflation to target.
Keywords: Forward guidance; Inflation targeting; Hybrid adaptive/rational expectations
JEL Classification: E31, E52, D84

Henry and Lucy Moses Professor of Economics, New York University and National Bureau of
Economic Research (E-mail: mark.gertler@nyu.edu).....................................................................................................................
Prepared for the annual IMES conference at the Bank of Japan in May 2017. Thanks to both
Diego Anzoaetgui and Joseba Martinez for great research assistance. The views expressed inthis text are those of the author and do not necessarily reflect the oﬃcial views of the Bank ofJapan.

MONETARY AND ECONOMIC STUDIES / NOVEMBER 2017
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39

I. Introduction
Recent events in the global economy have forced a reevaluation of much of what weknow in macroeconomics. Chief among the challenges is accounting for the sustained
low inflation and economic weakness in Japan. It is no longer possible to blame thestagnation in Japan on mismanagement of monetary policy. Since the spring of 2013,
through the introduction of Quantitative and Qualitative Monetary Easing (QQE), theBank of Japan has implemented what many view as a state-of-the-art policy program.
Sustained low inflation and economic weakness has been of course a recent global
phenomenon. The 2008/9 financial crisis plunged the advanced economies of the world
into a liquidity trap. The central banks of these economies, further, have been largely
unable to reflate their way out. The general problem, though, has been more severe forJapan. It has lasted much longer, beginning with the financial crisis of the late 1980s.
Further, unlike countries such as the U.S., inflation expectations have not been tightly
anchored by an inflation target.
From a scientific perspective, it is not easy to explain the diﬃculties that central
banks have had moving their respective economies out of a liquidity trap. The standard
models predict that central banks can eﬀectively stimulate an economy in a liquidity
trap by managing expectations of future policy. Of course, the central bank’s promises
about future policy must be seen as credible. If not, “forward guidance” will not be effective. However, I will argue it is unlikely that imperfect credibility alone can accountfor the slow recovery from a liquidity trap. It may not even be the most significant
factor. Indeed, I illustrate with an example below why the commitment problem may
not be particularly severe.
Instead I will argue that an important aspect of the disconnect between existingmodels and the slow global reflation is related to what is now popularly known as theforward guidance puzzle (FGP). The essence of the FGP is that the existing models predict implausibly strong eﬀects of expected future interest rate changes on the economy.
Somewhat perversely, as McKay, Nakamura and Steinsson (2016) and Del Negro, Giannoni and Patterson (2012) emphasize, the strength of the eﬀect increases with the
expected horizon of the interest rate change.
It has become clear thanks to a rapidly burgeoning literature that the FGP is tied tothe assumption of rational expectations. Accordingly, eﬀorts to address the FGP have
involved stepping outside the rational expectations hypothesis as a means to introduce
some form of eﬀective myopia. For example, Gabaix (2016) and García-Schmidt andWoodford (2015) take a behavioral approach. Angeletos and Lian (2016) introduce
incomplete information along with higher order beliefs. Farhi and Werning (2017)combine a behavioral approach with financial market frictions.
In this lecture I take the opportunity to be speculative by sketching a model meant
to capture the challenge of reflation in Japan. My approach is not meant to be a final
word, just a road map. As in recent literature I attempt to mute the power of forward
guidance by stepping outside of rational expectations.
What I oﬀer is less theoretically elegant than in the literature, but has the virtueof being simple and perhaps easier to connect to data, particularly survey data on
expectations. In particular I introduce a hybrid adaptive/rational expectations belief

40 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2017

Rethinking the Power of Forward Guidance: Lessons from Japanmechanism. Individuals have adaptive expectations about macro aggregates (e.g., output and inflation) which is consistent with the survey evidence (see e.g., Coibion and
Gorodnichenko [2012]). At the same time they make rational forecasts of policy in therespect that they understood the policy rule and are receptive to central bank communication.1 As I will argue, this approach is consistent with the evidence that central bankcommunication indeed aﬀects market interest rates (e.g., Evans et al. [2012]).
Most relevant to the Japanese experience is that individuals have adaptive expectations about trend inflation. Unlike the restrictions in standard models, individuals do
not simply accept the central bank’s desired inflation target as the relevant measure oftrend inflation. As Kuroda (2016) emphasizes, for an economy without a history of
inflation being anchored by a target, individuals need direct evidence that the central
bank is capable of moving inflation to target. That is they have to see it to believe it. It
is not so much that they do not trust the central bank’s intentions. Rather they need tobe convinced that the central bank can indeed deliver on its promises.

II. Some Evidence on Expectations
To motivate the use of an adaptive mechanism for beliefs about macro aggregates, I
first present some evidence on survey forecasts versus actual data. I start with U.S.
data. Following Coibion and Gorodnichenko (2012), I compare the median forecast
from the Survey of Professional Forecasters (SPF) to the realized value of a variable.
Figure 1 plots the median quarterly SPF forecast of core CPI inflation versus therealized value over the sample 2007Q2 to 2017Q1. There are three points to note: First,
the forecast errors appear highly serially correlated. Second, actual inflation tends tolead the movement of expected inflation. Note for example the drop in inflation during
the recession and then the increase in mid 2010, each time with expectations lagging
behind. Third, after dipping below two percent for several years following the GreatRecession, expectations return to this level for the duration of the sample. The first two
points appear consistent with an adaptive mechanism. The third suggests that the twopercent inflation target may have had a role in helping anchor expectations.
Figure 2 plots the median SPF forecast of real output growth versus the realized
value. As with inflation, the forecast errors appear highly serially correlated, withvariation in output growth leading the movement in the forecast. Again the evidence isconsistent with an adaptive mechanism.
Next I turn to long horizon inflation expectations. Figure 3 plots the median SPF
forecast of headline CPI inflation ten years ahead versus actual CPI inflation over the
sample 1979Q4 to 2016Q4. For the early years, the Blue Chip forecast stands in for the
SPF forecast. It is useful to divide the sample in half. From 1979Q4 to the late 1990s
the ten year inflation forecast drifts steadily downward from roughly eight percent to
two percent. Actual inflation tends to lead the long horizon forecast downward suggesting an adaptive mechanism. Beginning in the late 1990s the ten year forecast stays
roughly anchored just above two percent. While the Federal Reserve did not introduce................................
1. In Farhi and Werning (2017) individuals similarly respond “rationally” to forward guidance. In their framework
individuals use level k learning to form beliefs about the real sector. There is some similarity between level klearning and adaptive expectations in that near term behavior plays an important role in beliefs about the future.

41

Figure 1 Core CPI Inflation and Quarter-Ahead SPF Forecast: US Quarterly Data

Sources: The Federal Reserve Bank of Philadelphia; U.S. Bureau of Labor Statistics.

Figure 2 Real GDP Growth and Quarter-Ahead SPF Forecast: US Quarterly Data

Sources: The Federal Reserve Bank of Philadelphia; U.S. Bureau of Labor Statistics.

a formal inflation target until after the Great Recession, it arguably implemented an
implicit target of two percent. At the time members of the FOMC began to define twopercent inflation as price stability and this practice continued until the implementation

42 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2017

Rethinking the Power of Forward Guidance: Lessons from Japan

Figure 3 Annual Headline CPI and Expected Rate for Next 10 Years (SPF+Blue Chip):
US Data

Sources: The Federal Reserve Bank of Philadelphia; Blue Chip Economic Indicators; U.S. Bureau of
Economic Analysis.

of a formal target. The long experience with the two percent target (including the period of implicit targeting) undoubtedly helped anchor beliefs in the face of volatile CPI
inflation during and after the Great Recession.
Finally, I turn to Japanese data. Figure 4 plots survey expectations of CPI inflation six to ten years out against actual inflation excluding fresh food over the sample 1989Q1 to 2017Q1. Early in the sample, long horizon inflation expectations areroughly three percent. As the Japanese economy experiences a sequence of recessions,inflation steadily drops, turning to deflation at the turn of the century. Long horizon expectations follow behind, suggesting an adaptive mechanism, similar to what occurredin the early part of the U.S. sample (see Figure 3).
Behavior in the latter part of the sample, however, is diﬀerent from the U.S. Whilein the U.S. long horizon inflation expectations were roughly at the two percent target,they hovered at one percent on the eve of the ascension of the Abe government to powerin early 2013. At this point the stimulus beginning in 2013Q2 from the introduction
by the Bank of Japan of QQE pushed inflation up, leading to a slow upward driftof expected inflation. Though the BOJ introduced a two percent target, expectations
did not jump immediately to this level. Instead, inflation expectations slowly followed
actual inflation upward. Unfortunately, a recession and weakening of commodity prices
reduced inflation sharply, inducing a downward drift in inflation, despite the aggressive
BOJ policies. Without a history of anchored expectations, the inflation target did notseem to curtail the downward movement in expected inflation.

43

Figure 4 Inflation and Expected Rate for Next 10 Years: Japanese Data

Sources: Consensus Economics Inc., Consensus Forecasts; Ministry of Internal Affairs and Communications of Japan.

III. The Forward Guidance Puzzle: Inspecting the Mechanism
In this section I review the simple New Keynesian model with rational expectations,which serves as the basis for the macroeconomic models used for forecasting and policy evaluation at central banks. I illustrate the power of forward guidance within thisframework. I then do several policy experiments to illustrate how the strength of forward guidance suggests escaping a liquidity trap may not be so diﬃcult. This sets thestage for the next section where I dampen the power of forward guidance by introducing a form of hybrid adaptive/rational expectations.
A. New Keynesian Model with Trend Inflation
Consider the canonical New Keynesian model with consumption goods only. The one
variation is that I allow for trend inflation, which individuals perceive as obeying arandom walk. To keep the algebra as simple as possible, I assume that prices areindexed to trend inflation. Finally, the source of exogenous variation is a demand
disturbance in the form of a shock to the household discount factor βt .
Let yt be the log of the output gap; it the net nominal interest rate; rt∗ the natural(flexible price equilibrium) rate of interest, πt the rate of inflation from t − 1 to t andπt trend inflation. As is standard, we can then express the model in terms of threeequations in three unknowns: yt , πt and it (see e.g., Clarida, Galí and Gertler [1999],
Galí [2015]):
IS curve
yt = E t yt+1 − σ(it − E t πt+1 − rt∗ ) .

44 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2017(1)

Rethinking the Power of Forward Guidance: Lessons from Japan

Phillips curve
πt = λyt + βE t πt+1 + (1 − β)πt .

(2)

it = max{rt∗ + πt + φπ (πt − πt ) + φy yt , 0} ,(3)Policy rulewith φπ > 1; φy > 0.
Equation (1) relates the current output gap positively to expected future output gap
and inversely to the gap between the real rate of interest it − E t πt+1 and the natural rate
rt∗ . The parameter σ is the household’s intertemporal elasticity of substitution. In thissimple model rt∗ = − log βt .
Equation (2) relates inflation to the output gap plus a trend term equal to a convex
combination of expected inflation next period and trend inflation. The parameter β isthe steady state household discount factor. The slope of the Phillips curve λ depends
inversely on the degree of price rigidity (measured by the probability a firm does notchange price in a period) as well as the elasticity of marginal cost with respect to output.
Finally equation (3) is a simple Taylor rule that has the nominal rate equal to anintercept plus adjustment for deviations of inflation and the output gap from their respective targets. The intercept is the sum of the natural rate and trend inflation. Since
the central bank controls trend inflation, the latter must correspond to its inflation target. In addition we impose a zero lower bound constraint. (Later I briefly discuss
negative rates.)
B. Rational Expectations and the Power of Forward Guidance
To see the power of forward guidance, we solve the model under rational expectations:yt = E t∞∗−σ(it+ j − πt+1+ j − rt+
j) .

(4)

j=0

πt = E t∞

β j λyt+ j + πt .

(5)

j=0

Output gap depends inversely on the sum of current and expected future interest gaps
while inflation depends on a discounted sum of expected output gaps plus an additive
term equal to trend inflation.
We can now see how the eﬀect of E t it+ j on yt is increasing in j. First note thatthe direct eﬀect of E t it+ j on yt (from equation (4)) is the same for all j. In otherwords, there is no discounting of interest rate changes expected to come in the future.
As pointed out by Angeletos and Lian (2016) and others, the absence of discounting
reflects general equilibrium eﬀects in conjunction with rational expectations. In partial
equilibrium, individuals discount the eﬀects of future interest rate changes. Under
rational expectations they take into account the eﬀect of the future interest rate change
on future aggregate activity and in turn on their future earnings. In this simple model,

45

taking into account the general equilibrium eﬀect exactly undoes the discounting of
future interest rate changes.
In addition to the direct eﬀect of E t it+ j on yt that is independent of j, there is anindirect eﬀect due to the impact on expected inflation that works to magnify the overall
impact. In particular, the direct eﬀect of an increase in E t it+ j is to reduce yt . The indirect
eﬀect then works as follows. The increase in E t it+ j reduces E t yt+k from k = 1 to j. Thisin turn has the eﬀect of reducing the path of inflation over this interval, thus raising thepath of real rates. The magnified increase in the path of the real rate amplifies the
reduction in yt . Since this indirect eﬀect is clearly increasing in the horizon j, so too is
the overall impact of an increase in E t it+ j on yt .
It is also worth emphasizing that there is a significant eﬀect of the inflation target on
the path of inflation. Under rational expectations, a (credible) increase in the inflation
target leads to an immediate one-for-one increase in inflation.
It is now straightforward to illustrate how the power of forward guidance facilitates
managing a liquidity trap. When the sum of the natural rate and trend inflation isnegative, i.e., rt∗ + πt < 0, the zero lower bound on it binds. Now suppose that there is a∗negative demand shock (increase in βt ) that leads to rt+
j + πt+ j < 0 from j = 0 to k − 1and ≥ 0 after. Given that the central bank reduces it to zero over the period where thezero lower bound is binding, we can express the IS curve as:yt = E t

k−1

j=0

∗
σ(πt+1+ j + rt+j ) + Et∞∗−σ(it+ j − πt+1+ j − rt+
j) .

(6)

j=k

Equation (5) continues to characterize inflation.
Even with a binding zero lower bound, the model suggests two immediate ways
to stimulate the economy in a liquidity trap by managing expectations. First, keep thenominal rate “lower for longer.” Commit to keep nominal rates suﬃciently low so thatthe interest rate gap is negative for a period after the economy emerges from the liquidity trap. Given the power of forward guidance, the model suggests that this tool shouldbe eﬀective. Of course it requires that the central bank can commit to pursuing an inflationary policy for a period after the economy is free of the liquidity trap. However,as I demonstrate shortly, the commitment problem may not be especially challenging
since only modest levels of inflation overshooting may be required.
The second tool is to raise the inflation target. The simple model suggests thatan increase in the target should have an immediate eﬀect on inflation and should thus
stimulate the economy by reducing real rates. One might debate whether raising thetarget above two percent for a country like the U.S. might be credible. However, forJapan, going to a two percent target should not impose any kind of credibility problem.
C. Numerical Illustration
To illustrate the eﬀectiveness of forward guidance under rational expectations, we consider several numerical experiments. To perform the experiments, we use the following
parameter values: We set the intertemporal elasticity of substitution σ equal to unity(i.e., log utility) and the quarterly steady state discount factor β equal to 0.99. We fix
the slope λ on the output gap in the Phillips curve equal to 0.04 which is within the

46 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2017

Rethinking the Power of Forward Guidance: Lessons from Japan

Figure 5 Forward Guidance under Rational Expectations

range of estimates in the literature. We set the feedback coeﬃcients in the policy rule
φπ and φy equal to 1.5 and 0.5, respectively. Finally, we assume that steady state trend
inflation initially is zero.
We then suppose that the model economy is subject to a demand shock that puts
it into a liquidity trap. Suppose, outside the steady state the log of discount factor
obeys a first order autoregressive process, with an autoregressive coeﬃcient equal to0.9. We then consider a negative shock that pushes the natural rate of interest below
zero for roughly two years. (Again, the natural rate of interest in this simple model
equals minus the log of the discount factor.) Since trend inflation is zero, the economy
is in a liquidity trap with a binding zero lower bound on the nominal interest rate overthis period.
We now consider three policy responses to the liquidity trap. The first is to do
nothing: wait until the economy is out of the liquidity trap and then have policy revert
to the Taylor rule. The second two involve management of expectations in an attempt
to stimulate the economy while it is still in the liquidity trap. One is to keep rates“lower for longer” by waiting to raise rates until four quarters after the economy is outof the liquidity trap. The other is to raise the inflation target.
Figure 5 analyzes the case where the central bank responds to the liquidity trap by47

keeping rates lower for longer. As a benchmark, the dashed line in each panel reports
the case where the central bank does nothing. In this case the economy experiences alarge recession: Output gap falls four percentage points while inflation drops one anda half percentage points. The lower bound on the nominal rate prevents the central
bank from stimulating the economy in the absence of managing expectations of future
policy.
The solid line reflects the case where the central bank promises to keep the nominal
rate at zero for four quarters after the liquidity trap. Due to the promise of lower rates
in the future, the recession becomes mild and brief as the output gap becomes positive
after several quarters. Inflation no longer falls: It now increases modestly.
It is true that a potential commitment problem emerges. After the economy leaves
the liquidity trap (i.e., when the natural rate turns positive after quarter seven) inflation
overshoots its target, a consequence of the central bank having to carry out the stimulus
it promised earlier. However, the degree of overshooting is relatively modest. Once outof the liquidity trap inflation is less than a half a percent above target for less than ayear. This degree of overshooting of the inflation target is well within the norm, forexample, of what the Federal Reserve has done in the past twenty years. There is thus
reason to believe that a central bank pursuing this kind of policy is likely to be seen as
credible by the private sector.
Figure 6 portrays the impact of the central bank raising the inflation target one
hundred basis points. Under rational expectations, individuals’ expectations of trend
inflation immediately increase by the same amount. In turn, holding constant the output
gap, inflation increases one hundred basis points. The net eﬀect is a reduction in realinterest rates which stimulates the economy. As the solid line shows, relative to thecase where the central bank is passive, the stimulus provided from raising the inflation
target increases both output gap and inflation. Note that inflation moves quickly to the
new target.
Overall, under rational expectations, forward guidance, i.e., managing expectationsof the future path of policy, provides an eﬀective means of stimulating the economy,
and implausibly so as many would argue.

IV. A Hybrid Adaptive / Rational Expectations Alternative
In order to dampen the power of forward guidance, I next consider an alternative belief
mechanism. The basic idea is as follows. Individuals make rational partial equilibrium decisions, but they’re uncertain about how the partial equilibrium feeds into thegeneral equilibrium. In the context of the simple New Keynesian model with consumption goods only, individuals make optimal consumption/saving decisions given
their respective beliefs about discounted earnings. While individuals understand how
their earnings may be correlated with aggregate output, they are unable to calculate
the general equilibrium determination of its expected path. This leads them to use a
mixture of adaptive and rational beliefs.
The adaptive part works as follows. Individuals use an adaptive mechanism forbeliefs about the future output gap and trend inflation. Given they understand how

48 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2017

Rethinking the Power of Forward Guidance: Lessons from Japan

Figure 6 +100 bp Inflation Target Increase under Rational Expectations

their own earnings are correlated with the output gap they can use this forecast to
project their respective future income. We also allow them to understand the partial
equilibrium relation for inflation, i.e., the New Keynesian Phillips curve (equation (2)).
Given their forecasts of the output gap and trend inflation, they can then compute a
forecast of inflation as I describe below.
The rational part then works as follows. Through experience, individuals understand the central bank policy rule given by equation (3). (Again, they are good atpartial equilibrium but not general equilibrium). They also view as credible central
bank guidance about the policy instrument path. In this respect, the calculation about
the path of the policy instrument is rational. One caveat: while they understand the
Taylor rule, they use the adaptive mechanism to form beliefs about the deviations ofinflation and the output gap from target. At the same time, they accept central bankguidance about deviations from the traditional rule. It’s just they just can’t make thecalculation of the general equilibrium eﬀect of the policy on the economy.

49

A. The Model with Hybrid Beliefs
Accordingly, suppose the private sector forecast of the output gap is given by the following adaptive mechanism:
t yt+1 = γ(yt − E
t−1 yt ) + ρEt−1 yt ,E(7)

t denotes expectations under our hybrid mechanism. Under beliefs given by
where Et−1 yt )equation (7), the updated forecast depends positively on the forecast error (yt − Eand the lagged forecast E t−1 yt . The lagged forecast is weighted by ρ < 1 to take into
account that the output gap is stationary and that individuals recognize this. In the end,
the output gap forecast depends on a geometrically distributed lag of current and pastvalues, where the weights sum to a number between zero and unity.
In turn, beliefs about trend inflation are given by the following adaptive mechanism:
t πt = δ(πt − E
t−1 πt−1 ) + E
t−1 πt−1 .
E(8)Individuals update their forecast based on the forecast error. They treat trend inflation
as non-stationary: Accordingly the weight on the lagged forecast is unity. As a result,the forecast of trend inflation is a geometrically distributed lag of past inflation where
the weights sum to unity. Given the forecasts of the output gap and trend inflation andt yt+1 , it is then possible to combine with the Phillips curve (2) tot yt+1+i = ρi E
given E
construct a forecast of inflation, as follows:t πt+1 =E

λ t πt .
E t yt+1 + E
1 − βρ

(9)

Let πcbt be the central bank’s inflation target and ft+ j be the projected deviation of
the interest rate from the policy rule due to forward guidance. Then the forecast of theinterest rate is given as follows:cbcb∗t it+ j = max{Et [rt+E
j + πt + φπ (πt+ j − πt ) + φy yt+ j − ft+ j ], 0} .

(10)

We assume individuals know the form of the policy rule. They use the adaptive
forecasts of πt and yt to construct measures of deviations of inflation and output gap
from target. But at the same time, they view as credible central bank pronouncements
about the inflation target as well as central bank guidance about the future path ofinterest rates. Put diﬀerently, in computing the expected path of the interest rate, they
accept the central bank’s pronouncements about πcb
t and ft+ j . In this regard, central
bank communication about the path of future policy (through both πcb
t and ft+ j ) will
indeed aﬀect the expected path of rates.
Under “hybrid” expectations, the complete model is then given by the following
three equations:
IS curve
t yt+1 + E
tyt = χ E∞∗
β j [−σ(it+ j − πt+1+ j − rt+j )] .

j=0

50 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2017(11)

Rethinking the Power of Forward Guidance: Lessons from Japan

Phillips curve
πt = λ(yt +β t πt .
E t yt+1 ) + E
1 − βρ

(12)

Policy rulecb
it = max{rt∗ + πcb
t + φπ (πt − πt ) + φy yt − ft , 0} ,

(13)

1−β
with χ = 1−ρβ
< 1 and where the forecasts of yt , πt , πt and it are given by equations (7),(8), (9) and (10), respectively.
Relative to the case of rational expectations, the power of forward guidance ismuted in the model with hybrid beliefs. Note first that in the aggregate demand relation given by equation (11), the eﬀect of future interest rates is discounted by β j ,unlike what occurs under rational expectations. Second, given that forecasts of inflation are adaptive, the movement in expected inflation is muted, which dampens theeﬀect of an expected future nominal rate change on the path of real rates. In contrast to
the case of rational expectations, there is no large multiplier eﬀect on real rates arisingfrom movement in expected inflation.

B. Numerical Experiments with Hybrid Beliefs
We now repeat the policy experiments we performed with the model under rational
expectations. For the adaptive rule for output gap, we suppose that the updating parameter γ is given by 0.125 and the serial correlation parameter ρ is given by 0.95. Thiscalibration suggests that individuals use a geometrically distributed lag of roughly two
years of past data to forecast the output gap. We suppose much slower adjustment ofbeliefs about trend inflation: δ is given by 0.5. In this instance individuals eﬀectively
use more than ten years of lagged data.2
As earlier, we consider a demand shock that the pushes the economy into a liquidity
trap for roughly seven quarters. Also as before, we first consider the eﬀect of the central
bank promising to keep the nominal rate at zero for a year after the economy leaves theliquidity trap. Figure 7 illustrates the results. Once again, the dashed line is the casewith no forward guidance, while the solid line reflects the case with forward guidance,
though this time with hybrid expectations as opposed to rational expectations.
Overall, the policy response has a much weaker eﬀect on output gap and inflation
than under rational expectations. In the latter case, the policy virtually eliminated theoutput gap and pushed inflation modestly above target. Under hybrid expectations theimpact is more modest. The policy is stimulative since individuals recognize that theliftoﬀ of nominal rates from zero will be delayed. However, the output gap decline
is only about one percent less than the case of no policy response. Similarly, inflation
dips before returning to target. The weak response of economic activity to the stimulus,of course, is the product of how the hybrid belief mechanism dampens the power offorward guidance.
................................
2. Though it is beyond the scope of this paper, one way to discipline the learning parameters would be to matchthe serial correlation in the forecast errors from the survey data.

51

Figure 7 Forward Guidance under Hybrid Expectations

Next we consider raising the inflation target by one hundred basis points. Under
rational expectations, there is an immediate jump in beliefs about trend inflation. With
adaptive expectations about trend inflation, individuals have to see it to believe it. As
Figure 8 illustrates, relative to the case of rational expectations, there is a much slower
increase in inflation, mainly due to the slow adjustment of expectations of trend inflation. The policy does provide some stimulus, though. Raising the inflation target
implies that everything else equal, the path of future interest rates will be lower (giventhat the feedback coeﬃcient on inflation, φπ exceeds unity). The reduction in expected
future interest rates then stimulates current spending. Thus, even though individuals
have adaptive expectations about output gap and inflation, they do respond to central
bank eﬀorts to stimulate by managing expectations.
We next explore how transitory factors can aﬀect the central bank’s ability toachieve the inflation target. The motive is to understand how the recession and commodity deflation during 2014/15 frustrated the BOJ’s eﬀort to reflate the economy. We
accordingly modify the model to introduce a cost shock ut that obeys the following firstorder process:ut = ρu ut−1 + t ,where the error termt is i.i.d.

with mean zero. The cost shock aﬀects the Phillips

52 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2017

Rethinking the Power of Forward Guidance: Lessons from Japan

Figure 8 +100 bp Inflation Target Increase under Hybrid Expectations

curve as follows:t
πt = E∞t πt .
β j [λyt+ j + κut+ j ] + E

(14)

β 
t πt + κ ut .
E t yt+1 ) + E
1 − βρ
1 − ρu(15)

j=0

πt = λ(yt +I now repeat the experiment of Figure 8. The economy is hit by a demand shockthat moves it into a liquidity trap. The central bank responds by raising the inflation
target by one hundred basis points. This time, however, while in the liquidity trap,
the economy also experiences a reduction in costs (i.e., a drop in ut ) which reduces
inflation. Given adaptive beliefs about trend inflation, the cost shock leads a decline
in the long horizon forecast of inflation, similar to what happened in Japan (Figure 9).
Interestingly, the shock also induces a decline in output gap: The reduction in inflation
expectations raises the real interest rate, reducing demand.
Overall, the model captures how bad luck due to recession and commodity pricedeflation can frustrate the central bank’s eﬀorts to reflate, as occurred recently in Japan.
At the same time, good luck could do just the opposite. For example, if the global economy picks up, then commodity prices and inflation may increase, helping economic
activity and inflation in Japan move back to target.

53

Figure 9 +100 bp Inf. Target and Cost Declines under Hybrid Expectations

V. Connection to QQE
I now discuss briefly how the analysis relates to QQE. There were four key aspects to
the April 2013 plan. The first was to set an inflation target of 2%. The second wasto commit to a sustained rise in the monetary base by expanding asset purchases. The
third was to purchase long term bonds. The fourth, which was introduce more recently,
was to implement negative interest rates.
I would argue that the first two policies correspond to what I analyzed in the simulations. Raising the inflation target corresponds exactly to one of the policy experiments
I considered. Given that increasing the monetary base pushes short rates down, thepromise of sustained monetary base expansion, in turn, is in eﬀect a promise to keep
short rates low after the economy has recovered from the liquidity trap. In this respect
it corresponds to the policy of keeping rates “lower for longer.”
The second two policies, long-term bond purchases and negative interest rates, areappealing in light of the muted power of forward guidance. In particular, the analysis suggests that, changes in credit costs today, everything else equal, are going tohave a greater eﬀect than projected reductions in costs way into the future. Long-termbond purchases reduce current costs by reducing term premia. Negative interest rates
obviously reduce credit costs today directly as well.
Overall, both of the policies make sense in light of the muted power of forward

54 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2017

Rethinking the Power of Forward Guidance: Lessons from Japan

guidance. But it’s also the case that there’s limits to how much one can use each tool
to reduce credit costs. Bond purchase can only push down the term premium so much.
Otherwise, private speculators will start issuing long-term bonds and going long inshort term assets. The government could also start issuing long-term bonds. There’s
also a limit to how much one make rates negative because individuals and institutions
will go into cash.

VI. Concluding Remarks
As the Japanese experience makes clear, the process of reflation from a liquidity trap
can take much longer than most existing macroeconomic models suggest. This canbe true even with textbook state-of-the-art monetary policy. This phenomenon is a loteasier to understand once we step outside of pure rational expectations. Accordingly,
this paper develops a hybrid adaptive/rational mechanism for formation of beliefs anduses the approach to illustrate the challenges of a central bank in trying to reflate bymanaging beliefs about future policy. A key lesson from the Japan experience is thatabsent a history of inflation being anchored by a target, individuals need to see someinflation in order to believe that more is coming.
Creating inflation in turn is certainly going to involve skill on the part of the central
bank. But, it is also going to involve luck. Despite the best eﬀorts of a central bank,global factors that moderate inflation may frustrate eﬀorts to reflate. So what is the best
course of action? Continue aggressive monetary policy and hope for some luck. Somecooperation from fiscal policy of the kind that Ben Bernanke discussed earlier in theconference may also help (Bernanke [2017]).

APPENDIX: DERIVATION OF THE IS CURVE UNDER HYBRID EXPECTATIONS
The baseline framework is a textbook NK model with consumption goods only. Output
is linear in labor. Discount factor shocks are the only source of variation. A representative household chooses consumption/saving and labor supply to maximize expecteddiscount utility. Period utility is separable in consumption and labor supply. Period
utility from consumption is logarithmic.
Let ct be the log deviation of consumption from steady state and vt be the log deviation of household wealth, including human wealth and asset wealth. Note that since(i) utility is logarithmic, (ii) there are only discount factor shocks and (iii) consumption equals output and output equals labor, the flexible price equilibrium values of bothconsumption, employment and output are constant. Hence ct is also the log deviationof consumption from its natural value.
Combining the loglinearized first order conditions from the household consumption/saving problem with the loglinearized budget constraint yields the following relationship for consumption demand:
ct = vt .

(16)

55

∞

∗
vt = E t{(1 − β)β j yt+ j − β1+ j (it+ j − E t πt+1+ j − rt+j )} .

(17)

j=0

In keeping with the permanent income hypothesis, consumption varies proportionately
with wealth. Wealth in turn is the expected discounted sum of income, where yt+i is thesum of labor income and profits from monopolistically competitive firms.
As the literature emphasizes, discounting of the future disappears in the rational
expectations general equilibrium. To see, express vt recursively:
vt = (1 − β)yt + βE t vt+1 − β(it − E t πt+1 − rt∗ ) .

(18)

Given ct = yt , it follows that yt = νt and E t yt+1 = E t vt+1 . Accordingly we can write
yt = (1 − β)yt + βE t yt+1 − β(it − E t πt+1 − rt∗ ) .

(19)

Rearranging then yields the familiar New Keynesian IS curve:
yt = E t yt+1 − (it − E t πt+1 − rt∗ ) .

(20)

Observe that discounting of the future disappears after the general equilibrium withrational expectations is imposed.
To see how discounting remains under hybrid beliefs, first note that aggregate demand can be expressed as:
tyt = E∞∗{(1 − β)β j yt+ j − β1+ j (it+ j − E t πt+1+ j − rt+j )} ,(21)

j=0

t is the expectation operator under hybrid beliefs and has the following propwhere E
erties for forecasts of output gap:
t yt = yt ,E(22)

t−1 yt ) + ρEt−1 yt ,t yt+1 = γ(yt − EEi
t yt+1 .
t yt+1+i = ρ E
ECombining (21) and (22) then yields
tyt = E∞∗{(1 − β)(βρ) j yt+1 − β j (it+ j − E t πt+1+ j − rt+j )} ,(23)

j=0

which can be rearranged to obtain the IS curve under hybrid beliefs:
t yt+1 + E
tyt = χ E∞∗
β j [−σ(it+ j − πt+1+ j − rt+j )] ,

j=0
1−β. Under the hybrid mechanism, accordingly, discounting remains.
with χ = 1−ρβ56 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2017(24)

Rethinking the Power of Forward Guidance: Lessons from Japan

References
Angeletos, George-Marios, and Chen Lian, “Forward Guidance without Common Knowledge,”
mimeo, 2016.
Bernanke, Ben S., “The Mayekawa Lecture: Some Reflections on Japanese Monetary Policy,” Monetary and Economic Studies, 35, Institute for Monetary and Economic Studies, Bank of Japan,
2017, pp. 23–38 (this issue).
Clarida, Richard, Jordi Galí, and Mark Gertler, “The Science of Monetary Policy: A New Keynesian
Perspective,” Journal of Economic Literature, 37(4), 1999, pp.1661–1707.
Coibion, Olivier, and Yuriy Gorodnichenko, “What Can Survey Forecasts Tell Us about Information
Rigidities?” Journal of Political Economy, 120(1), 2012, pp. 116–159.
Del Negro, Marco, Marc Giannoni, and Christina Patterson, “The Forward Guidance Puzzle,” Staﬀ
Reports, 574, Federal Reserve Bank of New York, 2012.
Evans, Charles L., Jonas D.M. Fisher, Alejandro Justiniano, and Jeﬀrey R. Campbell, “Macroeconomic Eﬀects of FOMC Forward Guidance,” Brookings Papers on Economic Activity, Spring,
2012, pp. 1–80.
Farhi, Emmanuel, and Iván Werning, “Monetary Policy, Bounded Rationality, and Incomplete Markets,” mimeo, 2017.
Gabaix, Xavier, “A Behavioral New Keynesian Model,” NBER Working Paper No. 22954, National
Bureau of Economic Research, 2016.
Galí, Jordi, Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian
Framework and Its Applications, 2nd Edition, Princeton University Press, 2015.
García-Schmidt, Mariana, and Michael Woodford, “Are Low Interest Rates Deflationary? A Paradoxof Perfect-Foresight Analysis,” mimeo, 2015.
Kuroda, Haruhiko, “Re-Anchoring Inflation Expectations via ‘Quantitative and Qualitative Monetary
Easing with a Negative Interest Rate’,” remarks at the Economic Policy Symposium held by
the Federal Reserve Bank of Kansas City on August 27, 2016.
McKay, Alisdair, Emi Nakamura, and Jón Steinsson, “The Power of Forward Guidance Revisited,”
American Economic Review, 106(10), 2016, pp. 3133–3158.

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