The Limits of Forward Guidance\Taper Tantrum" episode 2 Lack of credibility: The central bank does...

$: The Limits of Forward Guidance\Taper Tantrum" episode 2 Lack of credibility: The central bank does not know its future intentions. Unforeseen events: the failure of LTCM in September$
The Limits of Forward Guidance

Jeffrey Campbell (FRB Chicago & Tilburg)

Filippo Ferroni (FRB Chicago)

Jonas Fisher (FRB Chicago)

Leonardo Melosi (FRB Chicago, EUI & CEPR)

Bank of Finland and CEPR ConferenceOctober 2019

The views in this paper are solely the responsibility of the authors and should not be interpretedas reflecting the views of the the Federal Reserve Bank of Chicago or any other personassociated with the Federal Reserve System.

BoF-CEPR 2019 page 1 of 35

Introduction

Outline

1 Introduction

2 Example

3 Communication, Model and Estimation

4 The dynamic effects of forward guidance

5 FWG puzzle

6 Role of Noise


Introduction

How effective is forward guidance?

• The central bank is commonly assumed to have perfect control over privateexpectations about policy actions

• This assumption gives rise to implausible implications

• Source of “forward guidance puzzle” (Del Negro et al., 2015)• This has sparked a voluminous literature

• We investigate the plausibility of this assumption


Introduction

Communications are central

• We develop a modeling framework in which the central bank communicatesimperfectly with markets

• The central bank sends noisy signals to agents about its future intentions(deviations from the rule)

• Noise reflects two key challenges in communication

1 Lack of clarity: The words used by the central bank may confuse the public.Bond markets overreacted to remarks by Bernanke in May 2013 leading to the“Taper Tantrum” episode

2 Lack of credibility: The central bank does not know its future intentions.Unforeseen events: the failure of LTCM in September 1998, the onset of the firstGulf War in August 1990, etc.


Introduction

What we do

• Embed imperfect communication into an empirical DSGE model

• Estimate the model using a large data set including market’s expected future FFR

• We use the model to address the following questions

1 Has the Fed communicated clearly and credibly?

2 If not, what are the consequences of failures in communication?


Introduction

Main findings

1 The Fed’s ability to move expected rates at long horizons is limited

2 Imperfect communications influence the propagation of shocks

Effects of forward guidance are delayed

3 ‘Forward guidance puzzle’ is substantially limited.

The difficulties inherent in communicating complicated decisions about the future path of

interest rates may be too great for FWG to be the powerful tool predicted by standard NK

models.

4 Unintended communications spur sizable macroeconomic volatility.

Role of noise in the recent episodes of FWG communication.


Introduction

Related literature

• Forward guidance puzzle

• Del Negro et al. (2015); McKay, Nakamura and Steinsson (2015); Gabaix (2016);Fahri and Werning (2017); Angeletos and Lian (2018); Kaplan, Moll, and Violante(2018); and Hagedorn et al. (2019) among others

• Importance of communications

• Woodford (2013); Eusepi and Preston (2010); Andrade, Gaballo, Mengus andMojon (2018)

• Empirical models quantifying effects of FG

• Campbell, et al (2017); Bianchi and Melosi (2017); Nakamura and Steinson (2018);Campbell, et al (2012)

• How should central bank’s communicate?

• Morris and Shin (2002); Angeletos and Pavan (2007); Melosi (2016)

• High frequency reduced form literature

• Kuttner (2001); Gurkaynak, Sack and Swanson (2005); Campbell, et al (2012)


Example

Outline

1 Introduction

2 Example



5 FWG puzzle

6 Role of Noise


Example

Heuristic Example

• Assume that the CB follows this rule

Rt = gt(Rt−1, πgapt , y gap

t ) + θt ,

• The rule and the arguments of the rule (and their evolution beyond time t) arewell understood by everybody.

• θt deviations from the rule at time t; at time t, when Rt is observed, θt is known.

• Assume that at time t the central bank announces the deviation from the rule forthe next period, t + 1.


Example

News Representation

• In the News Representation, we have

θt = ε0t + ε1

t−1 εjt ∼ (0, 1) i .i .d .

implying that σ2θ ≡ E(θ2

t ) = 2

• In the news world, the time t information set is

Ωnt = ε0

t , ε1t

• The expectation about the future deviation conditional on Ωnt are given by

θt ≡ E(θt+1|Ωnt ) = E(θt+1|ε0

t , ε1t ) = ε1

t


Example

Signal Representation• In the Signal Representation, Agents receive a (noisy) signal about the future

deviation

st = θt+1 + vt vt ∼ (0, σ2v )

θt+1 ∼ (0, σ2θ)

• In the signal world, the time t information set is

Ωst = st , θt

• The expectation about the future deviation conditional on Ωst are given by

θt ≡ E(θt+1|Ωst ) = E(θt+1|st , θt) =

= E(θt+1) +cov(θt+1, st)

var(st)[st − E(θt+1)] =

=σ2θ

σ2θ + σ2

vst = κst (1)

where the second line derives from the projection theorem. κ (Kalman gain):extent to which agents believe the CB announcement


Example

New/Noise representation

• For a given news representation, there exists an observationally equivalent signalrepresentation, Chahrour and Jurado (2018 AER).

• In this example, this occurs when σν = σθ = 2More details

• Signal and news worlds generate the same I and II moments in terms ofobservables;

• however, they are not quite equivalent in terms of policy implications.


Example

Impulse responses

• How do expectations about the future deviation respond to news (∂ε1t )?

• in the news world (if agents’ info set is Ωnt = ε0

t , ε1t),

∂θt∂ε1

t

= 1

• in the signal world (if agents’ info set is Ωst = st , θt),

∂θt∂ε1

t

=∂θt∂st× ∂st∂θt+1

× ∂θt+1

∂ε1t

= κ× 1× 1 = 1/2

• Expectations about future deviations respond less in the signal representation

• When σ0 → 0 in the news, σν → 0 and κ→ 1 in the signal rep.


Communication, Model and Estimation

Outline

1 Introduction

2 Example



5 FWG puzzle

6 Role of Noise



Central bank communications

• Forward guidance: communicating to private sector about future policy deviationsθt+h, h = 0, 1, 2, . . . ,H

• Communication at date t: (H + 1)× 1 vector of noisy signals st = [sht ] about thefuture deviations

st = θt + vt

where θt = [θt+h]: mean zero, serially correlated up to H lags andvt = [vh

t ] ∼ IID N (0,Ξv ).

• Agents use the signals and the Kalman filter to update their beliefs about thefuture policy deviations θt

Etθt = Et−1θt + κ · (st − Et−1θt)

whereκ = Ξθ [Ξθ + Ξv ]−1



The CEE-SW-esque model

• Representative household with preferences for consumption (habit), leisure, andgovernment bonds

• Monopolistic competition in product and labor markets with Calvo-style wage andprice adjustment

• “I-dot” investment adjustment costs, variable capacity utilization

• Balanced growth from neutral and investment-specific technical change

• Monetary policy rule, communications and learning

• “Government” spending financed with lump-sum taxes, bonds in zero net supply

• Eight non-monetary structural shocks: discount rate, liquidity preferences, twotechnologies, marginal efficiency of investment, “government” spending, wage andprice markups



Signal/news representations

• Models with noise shocks have unique observationally equivalent newsrepresentation (Chahrour and Jurado AER 2018)

• The news representation is easier to solve and estimate than our model

• We estimate the news representation and map the estimated parameters to thoseof our model

• Instead of signals agents receive news εhR,t at each t about policy deviations thatwill materialize at t + h, h = 0, 1, . . . ,H

lnRt = gt(Rt−1, πgapt , y gap

t ) +H∑j=0

εjR,t−j︸︷︷︸θt

• This is how we map one to the other. Mapping



Measurements

∆ lnQobst = f

(ct , ct−1, it , it−1, gt , ωt , π

g,obst

);

∆ lnC obst = z∗ + ∆ct + zt ;

∆ ln I obst = z∗ + ω∗ + ∆ıt + zt + ωt ;

logHobst = Ht ;

πi,obst = ω∗ + ωt + ui

t ;

Robst = R∗ + Rt ;

R j,obst = R∗ + Et Rt+j , j = 1, 2, . . . ,H;

πl,j,obst = π∗ + πl,j

∗ +β l,j

l

l∑i=1

Et πt+i + ul,j,πt , j = 1, 2, l = 1, 40;

πj,obst = π∗ + πj

∗ + βπ,j πt + γπ,jπd,obst + uj,p

t , j = 1, 2, 3;

∆ lnw j,obst = z∗ + w j

∗ + βw,j (wt − wt−1 + zt) + uj,wt , j = 1, 2;

πd,obst = πd

∗ + β1,1πd,obst−1 + β1,2π

d,obst−2 + ud

t ;

πg,obst = πg

∗ + β2,1πg,obst−1 + β2,2π

g,obst−2 + ug

t .



Estimation strategy

• We estimate the log-linearized model’s news representation

• Calibrate neoclassical growth model parameters• Bayesian estimation for remaining parameters

• Estimate using 1993q1-2008q3 sample

• Unanticipated and permanent changes in 2008q4

• Steady state changes: decline in growth and risk free rates• Forward guidance changes: from H = 4 to H = 10• π∗t = π∗

• Hold parameters fixed in 2008q4-2016q4 sample except re-estimate FG, somemeasurement parameters


The dynamic effects of forward guidance

Outline

1 Introduction

2 Example



5 FWG puzzle

6 Role of Noise



Dynamic response to forward guidance shock

• Forward guidance shock: affects all signals at t excluding the current one. details

• The central bank announces a vector of signals in period t,

• signals comprise its actual policy deviations from period t + 1 through period t + H• signals are accurate (contain no noise)

• We assume that

• The announcement comes when the economy is at steady state• No more signals communicated after period t + H• No more deviations carried out after period t + H⇒ the economy starts converging back to steady state in t + H + 1

• Consider two cases

1 Perfect communication ⇔ Kalman gain = identity matrix2 Imperfect communication ⇔ Estimated Kalman gain = the estimated one



Evolution of beliefs about θt (2nd Sample)

0 5 100

0.51

Time t

0 5 100

0.51

Time t+1

0 5 100

0.51

Time t+2

0 5 100

0.51

Time t+3

0 5 100

0.51

Time t+4

0 5 100

0.51

Time t+5

0 5 100

0.51

Time t+6

0 5 100

0.51

Time t+7

0 5 100

0.51

Time t+8

0 5 100

0.51

Time t+9

0 5 100

0.51

Time t+10

0 5 100

0.51

Time t+11



Response of hours to FG shock (2nd Sample)

0 2 4 6 8 10 12 14 16 18 20

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2


FWG puzzle

Outline

1 Introduction

2 Example



5 FWG puzzle

6 Role of Noise


FWG puzzle

Imperfect communications and FWG puzzle

2017Q1 2017Q3 2018Q1 2018Q3 2019Q1 2019Q30

0.5

1

1.5

2

2.5

3FFR path

2017Q1 2017Q3 2018Q1 2018Q3 2019Q1 2019Q30

1

2

3

4

5

6Output Growth


Role of Noise

Outline

1 Introduction

2 Example



5 FWG puzzle

6 Role of Noise


Role of Noise

Role of noise and historical episodes

Figure: Contribution of identified noise to six-quarter ahead expected funds rate.


Role of Noise

Conclusion

• Develop an empirical model to study central bank communication

• Imperfect communication limits the Fed’s ability to affect beliefs

⇒ challenges the empirical relevance of the forward guidance puzzle

• While imperfect, FG pulls forward the effects of policy

⇒ forward guidance still a valuable stabilization tool

• Unintended communications spur sizable macroeconomic volatility

⇒ there are clear benefits to investing in better communications

⇒ helps explain why central bankers are so wary of talking in public


Role of Noise

Appendix


Role of Noise

Innovation Representation

• There always exists the innovation process such as

θt+1 = E(θt+1|Ωst ) + wt+1 = θt + wt+1 wt ∼ (0, σ2

w ) (2)

which is observationally equivalent to the signal representation, (Anderson andMoore, 1979, ch 9).

• Match variances E(θ2t+1) = E(θt

2) + E(w 2

t+1). This occurs when

σ2w = κσ2

v

• Combining the latter with (1) and (2), we obtain

θt = κst−1 + wt wt ∼ (0, κσ2v )


Role of Noise

News/Signal Equivalence

• Signal [θt = wt + κst−1] and news [θt = ε0t + ε1

t−1] representations coincide when

ε0t = wt

ε1t = κst

• Since they are i.i.d. zero mean normal random variables, we need to matchvariances only, i.e.

1 = κσ2v

1 = κ2(σ2θ + σ2

v )

which occurs when σ2θ = σ2

v .

• So, when σ2θ = σ2

v = 2 news and signal representations are observationallyequivalent.

back


Role of Noise

Mapping the news representation to our model

• Let εR,t = [ε0R,t , ε

1R,t , . . . ε

HR,t ]′ where E(εR,t) = 0 and E(εR,tε

′R,t) = Σε (not

necessarily diagonal)

• Factor structure as in HF literature, e.g. GSS(2005). In matrix notation, we have

εR,t = αf αt + βf βt + ψηt

• Deviations form the rule can be written as

θt =

θtθt+1

...θt+H

= JHεR,t+H + · · ·+ J1εR,t+1 + εR,t + J ′1εR,t−1 + · · ·+ J ′HεR,t−H

where Jk is a (H + 1)× (H + 1) matrix of zeros with ones on the kth lowerdiagonal; J0 coincides with the identity matrix.


Role of Noise

Mapping the news representation to our model

• In the news world,Etθt − Et−1θt = εR,t

• In the signal world,Etθt − Et−1θt = κ · (st − Et−1θt)

• Combining the two, we have

εR,t = κ · (θt + vt − Et−1θt)

• ‘Squaring’ and taking expectations

Σε = κ (Ξθ + Ξv )κ′

where Ξθ = E(θt − Et−1θt)(θt − Et−1θt)′ = JHΣεJ

′H + · · ·+ J1ΣεJ

′1 + Σε

• Which implies

Σν =(

Ξ−1θ ΣεΞ−1

θ

)−1

− Ξθ

back


Role of Noise

Define a forward guidance shock

• Write the signal equation as follows:

st = θt + vt = Φut ,

where ut ∼ N (0, I) is a (H + 1)× 1 random vector of shocks

• Forward guidance shock: affects all signals at t excluding the current one

• Exploit Cholesky factorization of the matrix

Et−1

(s ts′t

)= Et−1

(Φutu

′tΦ′) = Ξθ + Ξν .

• FG shock corresponds to the second column of the lower triangular matrixobtained from the factorization back


Role of Noise

Evolution of FFR and its expectations

2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 20220

0.5

1

1.5

2

2.5

3

3.5

4

Ann

ual R

ate

Second Sample FFR: 2008Q4-2019Q2


The Limits of Forward Guidance\Taper Tantrum" episode 2 Lack of credibility: The central bank does...

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