Mitigating the forward guidance puzzle : inattention, credibility, finite planning horizons and learning.
Date: 2020-07-01
Institutions: European Central Bank
Subjects: economic cycle, economic model, interest, monetary policy, simulation

Oliver de Groot, Falk Mazelis 

Working Paper Series 

Mitigating the forward  
guidance puzzle:  
inattention, credibility, finite planning 
horizons and learning 

No 2426 / June 2020 

Disclaimer: This paper should not be reported as representing the views of the European Central Bank 
(ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB. 

 
 
 
Abstract

This paper develops a simple, consistent methodology for generating empirically realistic

forward guidance simulations using existing macroeconomic models by modifying expecta-

tions about policy announcements. The main advantage of our method lies in the exact

preservation of all other shock transmissions. We describe four scenarios regarding how

agents incorporate information about future interest rate announcements: “inattention”,

“credibility”, “ﬁnite planning horizon”, and “learning”. The methodology consists of de-

scribing a single loading matrix that augments the equilibrium decision rules and can be

applied to any standard DSGE, including large-scale policy-institution models. Finally, we

provide conditions under which the forward guidance puzzle is resolved.

Keywords: Monetary policy, Expectations, Unconventional Policy

JEL Classiﬁcations: C63, E32, E52

ECB Working Paper Series No 2426 / June 20201Non-technical Summary

Since the 2007-08 global ﬁnancial crisis, central banks across the developed world have struggled

with weak aggregate demand and short-term nominal interest rates at historically low levels.

In the face of these challenges, central banks have started to make increased use of interest

rate forward guidance – that is, announcements to keep future short-term nominal interest

rates lower for longer than expected by economic agents. Standard macroeconomic models

predict unrealistically powerful eﬀects of forward guidance announcements – a problem called

the Forward Guidance Puzzle.

This paper provides a practical and discreet methodology for generating empirically realistic

forward guidance experiments in otherwise standard macroeconomic models. We propose four

scenarios to dampen the Forward Guidance Puzzle: “inattention”, “credibility”, “ﬁnite planning

horizon”, and “learning”.

The method relies on a transparent modiﬁcation of agents’ forecasts of the monetary policy “news

states”, which is recorded in a single lower-triangular matrix. This modiﬁcation guarantees that

the solution to the model is not changed in any other way, therefore keeping the transmission of

all other shocks exactly the same as in the non-modiﬁed case. This is especially beneﬁcial in case

of large-scale policy-institution models that exhibit shock transmissions which have undergone

signiﬁcant vetting.

We explore four lower-triangular matrices (henceforth, scenarios) that embody the above four

scenarios. These scenarios (loosely) coincide with several of the more rigorous resolutions of

the forward guidance puzzle in the literature using small-scale models. Inattention is when a

fraction of agents are inattentive to central bank announcements about the future. Credibility is

when a decaying fraction of agents believe promises of the central bank further out in the future.

Finite planning horizon is when agents dismiss all announcements past a certain horizon. Finally,

learning is when a small fraction of agents initially incorporate forward guidance announcements

in their expectations, but as the horizon at which announcements are made increases, a growing

fraction begin to incorporate the forward guidance announcements into their expectations.

ECB Working Paper Series No 2426 / June 20202The modiﬁcations are presented in a simple small-scale model that captures the problem of

the Forward Guidance Puzzle under full attention. The scenarios are able to dampen the FG

Puzzle under various parameterisations. An extended medium-scale model, which includes a

modiﬁcation that is informed by empirical evidence, resolves the FG Puzzle. This model does not

exhibit the counterintuitive reversals pointed out by Carlstrom et al. (2015), where the increase

of a peg by one quarter switches the eﬀects from highly expansionary to highly contractionary.

ECB Working Paper Series No 2426 / June 202031 Introduction

Since the 2007-08 global ﬁnancial crisis, central banks across the developed world have struggled

with weak aggregate demand and short-term nominal interest rates stuck at historically low lev-

els. In the face of these challenges, central banks have used forward guidance—that is, announce-

ments to keep future short-term nominal interest rates lower-for-longer in the future. Standard

DSGE models predict unrealistically powerful eﬀects of forward guidance announcements—a

problem ﬁrst articulated by Del Negro et al. (2012) as the forward guidance puzzle.

Many insightful and elegant resolutions to the puzzle have since been proposed. However, many

of them are not able to provide quantitative policy advice. This is because they fall into one of

two general problems. Problem 1: The proposed resolution requires a substantial reworking of

the microfounded building blocks of the existing model. For example, Del Negro et al. (2012)’s

proposed resolution is an overlapping generations (OLG) structure, thus doing away with the

inﬁnitely-lived representative agent. In so doing, however, the modeler needs to take a stance

on ﬁscal policy, since the model also becomes non-Ricardian as a consequence of the OLG

assumption. Problem 2: The proposed resolution requires non-linear solution techniques. For

example, McKay et al. (2016) propose modeling heterogeneous households with uninsurable

income risk. Solving the model non-linearly, however, constrains the scope of the model to be

small-scale. Other resolutions, like sticky information al a Kiley (2016), substantially change

the transmission of standard monetary policy and all other shocks. After all, with an inertial

Taylor rule, the power of an unanticipated monetary policy shock is also largely the result of

agents beliefs that rates will return to normal only gradually. Sticky information discounts how

forward looking agents are, thus, not only dampening forward guidance, but dampening the

eﬀectiveness of monetary policy in general.

Faced with these challenges, we propose a practical and discreet methodology for generating

empirically realistic forward guidance experiments using existing models. Realistic, because the

method can be easily calibrated to the growing number of empirical studies of the power of

forward guidance. Practical, because, it is an addition to any standard (linearized) structural

model, and discreet because it does not alter the predictions of the model to other standard

shocks.1 Our implicit assumption, therefore, is that a policy institution’s current model is the

1On request, a Dynare add-on to replicate the results in this paper will be provided by the authors.

ECB Working Paper Series No 2426 / June 20204best model for simulating standard monetary policy, aggregate demand, technology shocks etc.,

because it has been rigorously estimated and its out-of-sample properties rigorously tested. And

so, we do not want to alter this. The only dimension along which we want to alter the predictions

of the model is the dimension that these models do poorly on—forward guidance.

Our method relies on modifying agents’ forecasts of the monetary policy “news states” (that

is, the exogenous state variables that carry the announcement from about the future to the

present). This modiﬁcation is recorded in a single lower-triangular matrix, thus providing full

transparency and control over how the simulation is conducted. We explore four lower-triangular

matrices (henceforth, scenarios) that we call “inattention”, “credibility”, “ﬁnite planning hori-

zon”, “learning”. These labels (loosely) coincide with several of the more rigorous resolutions

of the forward guidance puzzle in the literature using small-scale models. Inattention is when a

fraction 1 − α of agents are inattentive to central bank announcements about the future. Credi-

bility is when a decaying fraction of agents believe promises of the central bank further out in the

future. That is, a fraction α believe promises about the next quarter, α2 believe promises about

2-quarters ahead, and so on. Finite planning horizon is when agents dismiss all announcements

past horizon N . Finally, learning is when a small fraction of agents initially incorporate forward

guidance announcements in their expectations, but as the horizon at which announcements are

made increases, a growing fraction begin to incorporate the forward guidance announcements

into their expectations. We parameterize this learning process with a 2-parameter logistic func-

tion (that controls initial beliefs and the speed of learning, respectively).

The rest of the paper proceeds as follows. Section 2 describes the methodology. Section 3

provides illustrative results from a small model, including conditions under which the forward

guidance puzzle is resolved. Section 4 provides results from the Smets and Wouters (2007)

model. Section 5 concludes.

ECB Working Paper Series No 2426 / June 202052 Methodology

2.1 Setup

The model we are interested can be represented in the following form

˜Ayt = BE∗

t yt+1 + Cyt−1 + Dit + Eut,

it = F yt + Gmt,

mt = M mt−1 + N εt,

ut, εt ∼ iid (0, 1) ,

(1)

(2)

(3)

where (1) is the non-policy block of equilibrium conditions, (2) is the monetary policy reaction

function, and (3) governs the evolution of forward guidance promises (the “news states”). The

rest of the notation is as follows: yt is an η × 1 vector of endogenous state variables, it is the

nominal short-term interest rate (the policy instrument of the central bank), ut is an ηu × 1

vector of shocks, and εt is a T × 1 vector of anticipated monetary policy shocks, where T is the
maximum horizon at which the central bank makes promises.2 ˜A, B, C, D, E, F , G, M , and

N are coeﬃcient matrices of appropriate dimension. E∗

t (·) is an expectations operator, with the
∗ denoting that the expectations are not necessarily full-information rational expectations with

respect to the news states, (3).

The key vector of interest for us is mt which keeps track of the evolution of anticipated monetary

policy shocks. It has the following form

mt ≡ [[m00t, . . . , m0T t] , [m11t, . . . , m1T t] , . . . , [mT −1T −1t, mT −1T t] , [mT T t]](cid:48) ,

(4)

with dimensions T × 1, where T ≡ (T + 2) (T + 1) /2. The notation works as follows: m00t

is the standard unanticipated monetary policy shock. m11t, in contrast, is the announcement

of a policy shock that will occur one-period ahead. m01t is the arrival of the shock that was

announced one-period ahead, and so on. Thus, m00t = ε0t and m11t = ε1t are iid shocks, while

2In principle, T can be arbitrarily large. For expositional purposes we restrict ourselves to announcements up

to T = 12 quarters ahead.

ECB Working Paper Series No 2426 / June 20206m01t = m11t−1. Generalizing this gives the structure of G, M , and N as follows

(cid:20)

=

G
1×T

1
1×(T +1)

0
1×(T +1)T /2

(cid:21)

,

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0
1×(T +1)

0

0

0

0
...

0

0

0

I
T ×T

0

0

0

0

0

0

0

0

I
(T −1)×(T −1)

0

0

0

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

· · ·

. . .

0

0

0

0
...

0

1
1×1

· · ·

0

M
T×T

=

, N
T×T

=

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1

0 0 · · ·

0 0

0
T ×1

0

0
(T −1)×1
...

0

0
1×1

0

0 0

1 0

0 0

0 0

0 0

0 0

0 0

0 0
...

1 0

0 0

. . .

0 0 · · ·

0 1

(5)

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

.

(6)

Note that only the variables m0nt for n = 1, . . . , T enter the monetary policy reaction function.

These are when the previously announced promises are actually implemented. Note also that M

and N are both sparse matrices. In M , the 1s capture the transmission of future announcements

to the present. In N , the 1s relate the mnnt variables for n = 1, . . . , T to the appropriate shock,

εnt.

2.2 Expectations formation

Agents in the model need to form expectations of the evolution of the forward guidance states. In

particular, they need to evaluate E∗

t mt+1. The full-information, rational expectations solution
forecast is given by Etmt+1 = M mt. Instead, we assume that the agents form the following

forecasts

E∗

t mt+1 = (Z ◦ M ) mt,

(7)

where Z is also of dimension T × T and ◦ denotes element-by-element multiplication. Since

this is an element-by-element operation, only (T + 1) T /2 will be nonzero, corresponding to the

ECB Working Paper Series No 2426 / June 20207location of the 1s in M . Thus, we use the following compact notation, denoted Z, which maps

into the sparse matrix Z. In particular, the Z notation is given by

Z =

z11

z12
...
z1T

z22
...
z2T

. . .

· · · zT T

(8)

and maps into Z as follows

0 · · ·

0

0

· · ·

· · ·

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Z =

0 · · ·
...
...
0 · · ·

0 · · ·

0 · · ·
...
...
0 · · ·
...

0 · · ·

0 · · ·

0 · · ·

0

0
...

0

0

· · ·

z12

. . .

0 z11
...
...
0

0
...
0

· · ·

0

z1T

0

0
...
...
0

0

0

0

0

0
...
...
0

0

0

0

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

0

0
...
...
0

0

0

0

0

0
...
...
0

0

0
...
0

0

0

0

· · ·

· · ·

· · ·

· · ·

z22

0

· · ·

· · ·

z23

· · ·

· · ·

· · ·

. . .

· · ·

0

0
...
...
0

0

0
...

0

· · ·

0

z2T

. . .

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

0

0

0

zT T

· · ·

0

0

0
...
...
0

0

0
...
...
0
...

0

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

.

(9)

In the non-modiﬁed case, all elements of Z are 1. At the other extreme, when all elements

of Z = 0, agents react to all forward guidance announcements as if they were unanticipated

shocks when they arrive. We are interested in four intermediate scenarios we call “inattention”,

“credibility”, “ﬁnite planning horizon” and “learning”, as follows:

Scenario I (Inattention): Under inattention, a fraction 1 − α of agents are inattentive

ECB Working Paper Series No 2426 / June 20208to forward guidance announcements of the central bank, with α ∈ [0, 1]. In this case

ZI =

α

α α
...
...
α α · · · α

. . .

(10)

Scenario II (Credibility): Under credibility, a decaying fraction of agents believe for-

ward guidance announcements at further horizons.

In particular, a fraction α ∈ [0, 1]

believe announcements 1-quarter ahead, a fraction α2 believe announcments 2-quarters

ahead etc. In this case

ZII =

α

α α2
...
...
α α2

. . .

· · · αT

(11)

Scenario III (Finite planning horizon): Under a ﬁnite planning horizon, all agents

dismiss announcements that are more than N periods ahead. Columns 1 to N of Z will

contains 1s and the rest will contain 0s. For example, if agents dismiss all announcements

more than 1-quarter ahead (N = 1), we get

ZIII =

1

1 0
...
...
1 0 · · · 0

. . .

(12)

Scenario IV (Learning): Under learning, a large fraction of agents initially dismiss

forward guidance announcements, but this fraction falls as time passes and the central

ECB Working Paper Series No 2426 / June 20209bank is able to show its commitment to its promises.

ZIV =

1
1+e−β1(1−β2)
1
1+e−β1(2−β2)

...

1
1+e−β1(T −β2)

1
1+e−β1(1−β2)

...
· · ·

. . .

1
1+e−β1(1−β2)

(13)

The learning scenario is parameterized by a 2-parameter logistic function where β1 controls

the speed of learning, while β2 controls the initial beliefs.

Notice that in scenarios I-III, the elements of the same column of Z contain the same loading. In

contrast, in scenario IV, the diagonals contain the same loadings. Finally, note that all elements

of Z are bounded by the [0, 1] interval.

If all elements of Z are equal to 1, then we get the

standard full-information rational expectations solution. If instead all element of Z are equal to

0 then every announcement arrives as if it were a completely unanticipated shock. Thus, all our

simulation results will be bounded between these two extreme outcomes.

2.3 Solving the model

Except for the assumption we make regarding the forecasting of mt+1, the method for solving the
equilibrium decision rules is standard.3 However, the loading coeﬃcients on mt in the equilibrium

decision rules take a particular form that is of interest for understanding the forward guidance

puzzle and its potential resolution.

First, we postulate the minimum state variable decision rule as

yt = Hyyt−1 + Hmt + Huut,

(14)

where Hy, H, and Hu are the unknown loading coeﬃcients that we wish to solve for. The matrix

of loading coeﬃcients of mt is denoted by H and has the following form

H
η×T

≡ [H00:T , H11:T , . . . , HT T :T ] ,

(15)

3See Sims (2002); Uhlig (1998).

ECB Working Paper Series No 2426 / June 202010where Hjj:T has dimensions η × (1 + T − j). That is, in a single endogenous variable model,

H00:T contains [h00, h01, . . . , h0T ] and H01:T contains [h11, h12, . . . , h1T ], etc. Substituting the

postulated decision rule into the equilibrium conditions, (1), gives

A (Hyyt−1 + Hmt + Huut) = BHy (Hyyt−1 + Hmt + Huut) + BHE∗

t (mt+1)

+ Cyt−1 + DGmt + Eut,

where A ≡ ˜A − DF . Substituting for our forecasting rule, (7), gives

A (Hyyt−1 + Hmt + Huut) = BHy (Hyyt−1 + Hmt + Huut) + BH (Z ◦ M ) mt

+ Cyt−1 + DGmt + Eut.

This equation imposes a set of identifying restrictions that allow us to solve for the unknown

loading coeﬃcients, Hy, H, and Hu. In particular, Hy and Hu solve

AHy = BH 2

y + C,

AHu = BHyHu + E,

(16)

(17)

respectively. The ﬁrst implicitly deﬁnes Hy as the solution of a matrix-quadratic system of

equations. The second is a linear-matrix system and solves Hu, given Hy. Notice though that

neither of these two sets of loading coeﬃcients are dependent on Z. In that sense, the response

of the model to the non-policy shocks, ut, are completely unaﬀected by our assumption about

how agents forecast the propagation of forward guidance announcements.

Proposition 1 The decision rule loading coeﬃcients, Hy and Hu, (and thus the behavior of the

model to non-policy shocks) are independent of Z (our assumptions regarding agents reactions

to forward guidance announcements).

We are interested in H, which solves

(A − BHy) H = BH (Z ◦ M ) + DG.

(18)

Given the form of G and Z ◦ M (see (5), (6), and (9)), we can solve this in a block-recursive

ECB Working Paper Series No 2426 / June 202011manner. First, to solve for the loading coeﬃcients on m00:T t ≡ [m00t, . . . , m0T t], the above

equation simpliﬁes

giving

AH00:T = BHyH00:T + D × ones

,
1×(T +1)

H00:T = (A − BHy)−1 D × ones
.
1×(T +1)

(19)

(20)

Note that the (i, j)th element of H00:T − is the response of the ith variable in yt to a change in
m0jt and that the value of the (i, j)th and the (i, k)th element are equal for all j, k = 0, ..., T .

Next, it follows that

Hjj:T = (A − BHy)−1 BHj−1j:T × diag

(cid:32)

(cid:33)

[zjj, · · · , zjT ]
1×(T +1−j)

for all

j = 1, . . . , T.

(21)

Thus, H11:T is a function of H01:T , and H22:T is a function of H12:T etc. For Scenario I, II, and

III, zjj = · · · = zjT , which means that the elements of each row of Hjj:T are identical. That is,

the marginal eﬀect of a policy shock is the same independent of when the shock was announced.

Since the above notation is rather cumbersome, consider a simple example with η = 1 and T = 3.

In this case, (18) becomes

(a − bhy)

(cid:48)
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h00

h01

h02

h11

h12

h22

= b

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(cid:48) 

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h00

h01

h02

h11

h12

h22

0 0 0

0

0 0 0 z11

0 0 0

0 0 0

0 0 0

0 0 0

0

0

0

0

0

0

z12

0

0

0

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0

0

0

0

z22

0

+ d [1, 1, 1, 0, 0, 0] .

where the lower case a, b, d and hy denote that the coeﬃcient matrices are scalars in this simple

example. Rearranging, this can be written as

(a − bhy) [[h00, h01, h02] , [h11, h12] , h22] = [[0, 0, 0] , b [z11h01, z12h02] , bz22h12] + [d [1, 1, 1] , [0, 0] , 0] ,

ECB Working Paper Series No 2426 / June 202012or, in recursive form as follows

[h00, h01, h02] =

[h11, h12] =

h22 =

d
(a − bhy)
b
(a − bhy)
b
(a − bhy)

[1, 1, 1] ,

[z01h01, z02h02] ,

z12h12.

2.4 Dampening the eﬀects of forward guidance

The recursive form in the previous section means that we do not need to resolve the original

model. Rather, let us deﬁne H ∗ as the H when all elements of Z are set to 1. That is, the

decision rule coeﬃcients absent any of the modiﬁcations that we apply in this paper. It is then

possible to write the new augmented H as follows

H = ones
η×1

× Z∗
1×T

× H ∗,

(22)

where Z∗ takes the following form

Z∗ ≡ (cid:2)[z∗

00, . . . , z∗

0T ] , [z∗

11, . . . , z∗

1T ] , . . . , (cid:2)z∗

T −1T −1, z∗

T −1T

or, using the compact triangular-form notation, Z∗, as follows

Z∗ =

z∗
00
z∗
01
z∗
02
...
z∗
0T

z∗
11
z∗
12
...
z∗
1T

z∗
22
...
z∗
2T

. . .

· · · z∗

T T

(cid:3) , [z∗

T T ](cid:3)(cid:48) ,

(23)

(24)

Notice that (24) is larger than Z, with an additional ﬁrst column. The elements in the ﬁrst

column are generically always equal to 1. The relation between the elements of Z and Z∗ are

ECB Working Paper Series No 2426 / June 202013given as follows

Z∗ =

(1)

(1)

(1)
...
(1)

(z11)

(z12)
...
(z1T )

(z12z22)
...
(z1T z2T )

. . .

· · ·

(z1T × · · · × zT T )

(25)

From this we can understand how assumptions about Z impact the decision rule loading coeﬃ-

cients, H.

Scenario I: Under the inattention scenario, all elements of ZI equal α, which translates
into (Z∗)I as follows

(Z∗)I =

1

1 α

1 α α2
...
...
...
1 α α2

. . .

· · · αT

(26)

Thus, even though a ﬁxed fraction of agents are inattentive to the forward guidance an-

nouncements, the loading coeﬃcients on news states far out in the future are discounted

at a higher rate than near news states.

Scenario II: Consequently, under the credibility scenario, the dampening of loading co-

eﬃcients on news states far out in the future is even more rapid. In particular,

(Z∗)II =

1

1 α

1 α α3
...
...
...
1 α α3

. . .

· · · α(T +1)T /2

(27)

For scenario III (planning horizon), the elements of Z∗ simply reﬂects Z with elements either

ECB Working Paper Series No 2426 / June 202014zero or one. For scenario IV (learning), the loadings in Z∗ are growing as you move South, but

shrinking as you move South-East and East through the triangle.

3 Results

We ﬁrst demonstrate the methodology from Section 2 in a benchmark model before proceeding

to a medium- and large-scale new-Keynesian model.

3.1 Benchmark model

In this section we consider a simple model consisting of only an IS equation (with habits in

consumption) and a Taylor rule responding to the output gap, with inﬂation ﬁxed at zero.

Thus, (1) and (2) are as follows

xt = (1 − ω) E∗

t xt+1 + ωxt−1 − it,

it = φxt +

T
(cid:88)

j=0

m0jt,

(28)

(29)

where xt is the output gap. Table 1 summarizes the parameterization of the model.

Table 1: Parameterization

Parameters

ω

φ

Values

0.5

1.5

Table 2 summarizes and Figure 1 depicts graphically the parameterization of Z that we will use in

the experiments below. In Scenario I we consider the two extreme calibrations (full-attention and

full-inattention, Case 1 and Case 3, respectively) in addition to an intermediate case in which half

of all agents are attentive to forward guidance announcements. In Scenario II, the intermediate

case is one in which the agents that believe the forward guidance announcement decay at a rate

of 0.5. Scenario III considers the possibility that agents dismiss all announcements above an

horizon of 1 and 2 quarters, respectively. Finally, scenario IV presents a situation in which the

ECB Working Paper Series No 2426 / June 202015initial beliefs about forward guidance are close to zero, but grow as the peg is maintained over

time. With the blue line (β = (10, 5)) agents almost completely dismiss forward guidance for

the ﬁrst 5-periods before learning to be almost fully attentive to them thereafter. The red line

(β = (1, 5)) is one in which agents learn more steadily, incorporating 50% of forward guidance

announcements by period 5 are almost full attentive by period 10. In contrast, the yellow line

(β = (1, 10)) is one in which the learning process is much slower.

Table 2: Z parameters

Scenario Parameters Case 1 Case 2 Case 3

I

II

III

IV

α

α

N

1

1

2

0.5

0.5

1

0

0

0

(β1, β2)

(10, 5)

(1, 5)

(1, 10)

Figure 2 shows the response of the output gap xt to a 1 ppt unanticipated monetary policy

tightening at horizons 0 to 10. The top row shows the full-attention responses while the bottom

row shows the case where agents pay zero attention to forward guidance announcements. Notice

that the responses look near identical. For the 10 period-ahead shock, the initial response is

essentially zero and the peak response is approximately -0.4%, for both α = 0 and α = 1. The

only diﬀerence comes in the few quarters leading up to the announced shock. In the full attention

model, xt already begins to fall, albeit by a modest amount (0.08% in quarter 9), while in the

full inattention model, there is not response.

Figure 3 shows the responses to pegging the interest rate 400 basis points below the steady

state for 1 to 10 quarters(which corresponds to a peg close to the zero lower bound in case of a

nominal steady state interest rate of 4%). In each case, the steady state interest rate is 4%. In

this case, the diﬀerence in responses between the three values of α (1, 0.5, and 0) is stark. In

particular, with full-attention, the peak response of the output gap xt to a 10 quarter peg is 32%,

while under full-inattention, it is only 2.3%. Thus, the responses to individual unanticipated

responses as in Figure 2 can be misleading with regards to predicting the eﬀect of an interest

rate peg.

ECB Working Paper Series No 2426 / June 202016Figure 1: Visual representation of Z

0246800.51=1=0.5=00246800.51=1=0.5=00246800.511=10, 2=51=1, 2=51=1, 2=100200000.51N=2N=1N=0ECB Working Paper Series No 2426 / June 202017Figure 2: Scenario I (Inattention): Anticipated MP shock IRFs

051015-0.4-0.20051015-0.500.5051015-0.4-0.20051015-0.500.5051015-0.4-0.20051015-0.500.5ECB Working Paper Series No 2426 / June 202018For the “Credibility” scenario (II), the IRFs and the responses to the ZLB scenarios are very

similar to the “Inattention” scenarios (shown in Appendix Figure A.1). This is because it is the

response of xt, one-quarter before an announced shock that is the key to determining the power

of forward guidance.

Figure 3: Scenario I (Inattention): ZLB simulations

Figure 4 plots simulations using the “Planning horizon” scenario (III). When N = 2, agents

are fully attentive to announcements 2-quarters ahead but completely dismiss announcements

further in the future. Remarkably, this assumption generates responses that are of the same

order of magnitude as the full-attention model. In particular, a 10-quarter ZLB announcement

generates a peak output gap of 24% despite the fact that agents dismiss all announcements apart

from those being realized in the next two periods.

Finally, Figure 5 presents the “Learning” scenario (IV). In the top row, it takes approximately

5-periods of ZLB for agents to become convinced of the central bank’s credibility. In period 5

05101502040051015010200510150505101505100510150240510150510ECB Working Paper Series No 2426 / June 202019Figure 4: Scenario III (Planning horizon): ZLB simulations

051015024051015051005101501020051015010200510150204005101501020ECB Working Paper Series No 2426 / June 202020there is a large jump in the fraction of agents that deem the policy credible. Thus, the response

of xt begins modestly but accelerates after quarter 5.

In contrast, in the middle row (with

(β1, β2) = (1, 5) the learning process in more constant.

Figure 5: Scenario IV (Learning): ZLB simulations

3.2 Resolving the forward guidance puzzle

It is instructive to provide a formal deﬁnition of the forward guidance puzzle and what constitutes

a resolution of the puzzle. We thus provide the following deﬁnitions, where H denotes the length

of the interest rate peg.

Deﬁnition 2 (Forward guidance puzzle:) The forward guidance puzzle exists in a model if

limH→∞ max (xt) = +∞.

051015024051015051005101505100510150510051015051005101501020ECB Working Paper Series No 2426 / June 202021Deﬁnition 3 (Resolution of the forward guidance puzzle:) The forward guidance puzzle

is resolved in a model if limH→∞ max (xt) = ¯x, where ¯x is ﬁnite.

A corollary of this deﬁnition of the forward guidance puzzle is that the marginal beneﬁt of an

additional period pegged far out in the future remains strictly positive. A resolution of the

forward guidance puzzle is one in which this marginal beneﬁt of an additional period pegged

approaches zero as the forward guidance horizon tends to inﬁnity.

The deﬁnitions are put into action in Figure 6.

In the full attention model (α = 1), the

initial response of xt (top-left panel) grows linearly while the maximum response (bottom-left

panel) grows explosively. When α < 1, the marginal contribution to the initial xt response of

an additional period pegged (top-right panel) is decaying and approaches zero, monotonically

related to α. For α = 0.9 the maximal xt response (bottom-left panel) is initially convex before

turning concave. That is, the marginal beneﬁt of increasing the announcement from 2-quarters to

3-quarters is greater than extending the announcement from 1-quarter to 2-quarters. However,

the marginal beneﬁt of increasing from 7-quarters to 8-quarters is lower. Thus, we observe a

hump shaped pattern in the green line of the bottom-right panel. In general, when α < 1, the

maximal output-gap curve changes from convex to concave, with the turning point increasing

in α.

Figure 7 shows the same plots for the “Planning horizon” scenario (III). It again demonstrates

that when agents are attentive to only 2-quarter-ahead announcements, then the responses are

very close to the full-attention (N → ∞ or equivalently α = 1) experiment.

4 Extended model

The benchmark model in the previous section provided useful intuition.

In this section, we

demonstrate the results of this method in the Smets and Wouters (2007) model. We calibrate the

model to the empirical evidence from ˚Ahl (2017), shown in Appendix Figure A.2. In particular,

we use the “Credibility” scenario (II) and derive α = 0.7.

Figure 8 shows the ZLB experiments in the Smets and Wouters model. The middle panel shows

ECB Working Paper Series No 2426 / June 202022Figure 6: Marginal contribution of an additional ZLB period (Scenario I)

24681001020304024681003691224681001.534.5624681000.30.60.91.2ECB Working Paper Series No 2426 / June 202023Figure 7: Marginal contribution of an additional ZLB period (Scenario III)

24681001020304024681003691224681001.534.5624681000.30.60.91.2ECB Working Paper Series No 2426 / June 202024the responses uses our preferred calibration of α = 0.7. This signiﬁcantly dampens the eﬀect of

forward guidance relative to the full-attention model (in the top row).

Figure 8: Interest rate pegs in Smets & Wouters (Scenario II)

Figure 9 shows the eﬀect of the peg at diﬀerent horizons on the initial and maximal output

gap and the marginal contribution is more informative. With α = 1, we observe the asymp-

totes documented by Carlstrom et al. (2015): for a small change in the length of the interest

rate peg from 8 to 9 periods, the eﬀects of the peg switch from highly expansionary to highly

contractionary. The eﬀect reverses yet again when we keep the peg for an additional quarter.

With α = 0.9, the marginal contribution of an additional period continues to grow exponentially.

However, for our preferred calibration of α = 0.7, marginal contribution to the initial output

gap response is clearly falling (top-right panel). The marginal eﬀect of the maximal output gap

response appears to peak with the announcement of a 5 quarter peg (bottom-right) panel. The

asymptotes observed in the full attention model are absent in any of the dampened scenarios.

0510152001020051015200510051015200510051015200510051015200240510152005ECB Working Paper Series No 2426 / June 202025Figure 9: Marginal contribution of an additional ZLB period in the Smets & Wouters model
(Scenario II)

24681012012345246810120123452468101201234524681012012345ECB Working Paper Series No 2426 / June 2020265 Conclusion

This paper provides a practical and discreet methodology for generating empirically realistic

forward guidance experiments. We propose four scenarios to dampen the Forward Guidance

Puzzle: “inattention”, “credibility”, “ﬁnite planning horizon”, and “learning”.

The method relies on a transparent modiﬁcation of agents’ forecasts of the monetary policy “news

states”, which is recorded in a single lower-triangular matrix. This modiﬁcation guarantees that

the solution to the model is not changed in any other way, therefore keeping the transmission of

all other shocks exactly the same as in the non-modiﬁed case. This is especially beneﬁcial in case

of large-scale policy-institution models that exhibit shock transmissions which have undergone

signiﬁcant vetting.

The modiﬁcations are presented in a simple small-scale model that captures the problem of

the Forward Guidance Puzzle under full attention. The scenarios are able to dampen the FG

Puzzle under various parameterisations. An extended medium-scale model, which includes a

modiﬁcation that is informed by empirical evidence, resolves the FG Puzzle. This model does not

exhibit the counterintuitive reversals pointed out by Carlstrom et al. (2015), where the increase

of a peg by one quarter switches the eﬀects from highly expansionary to highly contractionary.

ECB Working Paper Series No 2426 / June 202027References

˚Ahl, M. (2017): “How big is the toolbox of a central banker? Managing expectations with
policy-rate  forecasts:  Evidence  from  Sweden,”  Sveriges  Riksbank  Working  Paper  Series.

Carlstrom,  C.  T.,  T.  S.  Fuerst,  and  M.  Paustian  (2015):  “Inﬂation  and  output  in  New

Keynesian  models  with  a  transient  interest  rate  peg,”  Journal  of  Monetary  Economics,  76, 

230–243.

Del  Negro,  M.,  M.  P.  Giannoni,  and  C.  Patterson  (2012):  “The  forward  guidance

puzzle,”  Federal  Reserve  Bank  of  New  York  Staff  Reports.

Kiley,  M.  T.  (2016):  “Policy  paradoxes  in  the  New  Keynesian  model,”  Review  of  Economic

Dynamics,  21,  1–15.

McKay,  A.,  E.  Nakamura,  and  J.  Steinsson  (2016):  “The  power  of  forward  guidance

revisited,”  The  American  Economic  Review,  106,  3133–3158.

Sims, C. A. (2002):  “Solving Linear Rational Expectations Models,” Computational Economics,

20,  1–20.

Smets,  F.  and  R.  Wouters (2007):  “Shocks and frictions in US business cycles:  A Bayesian

DSGE  approach,”  American  economic  review,  97,  586–606.

Uhlig,  H.  (1998):  “A  Toolkit  for  Analysing  Nonlinear  Dynamic  Stochastic  Models  Easily,”  .

ECB Working Paper Series No 2426 / June 202028A Further derivations

Figure A.1: Scenario II (Credibility): ZLB simulations

0510150240510150510051015050510150510051015051005101501020ECB Working Paper Series No 2426 / June 202029Figure A.2: Empirical evidence on α from ˚Ahl (2017)

1234567891011-0.100.10.20.30.40.50.60.70.8ECB Working Paper Series No 2426 / June 202030Acknowledgements 

We thank Kai Christoffel, Günter Coenen, Carlos Montes-Galdon, Roberto Motto and Mathias Trabandt for comments and discussions 
that improved the paper. Disclaimer: The views in this paper are those of the authors and do not necessarily reflect the views of the 
European Central Bank. 

Oliver de Groot 
University of Liverpool Management School, Liverpool, United Kingdom; email: oliverdegroot@gmail.com 

Falk Mazelis 
European Central Bank, Frankfurt am Main, Germany; email: falk.mazelis@ecb.europa.eu 

© European Central Bank, 2020 

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This paper can be downloaded without charge from www.ecb.europa.eu, from the Social Science Research Network electronic library or 
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