Macroeconomic Effects of MonetaryPolicy Forward Guidance

Jeffrey Campbell Charles EvansJonas Fisher Alejandro Justiniano

FRB Chicago

National Bank of BelgiumNovember 25, 2012

Views expressed are solely those of the authors. They do notrepresent those of the Federal Reserve Bank of Chicago, the

Federal Reserve System, or its Board of Governors.

What is Forward Guidance?

I Forward guidance (FG) : Monetary authorities’ views aboutthe economic outlook and state of future policy.

I FOMC: use of implicit or explicit FG since at leastmid-1990s; hallmark of US monetary policy since onset ofthe financial crisis

A Taxonomy

I Delphic forward guidance: forecasts future macroeconomicperformance and likely actions based on Fed’s informationset

I Odyssean Forward Guidance: commitment to futuredeviations from “normal policy”

What is Forward Guidance?

I Forward guidance (FG) : Monetary authorities’ views aboutthe economic outlook and state of future policy.

I FOMC: use of implicit or explicit FG since at leastmid-1990s; hallmark of US monetary policy since onset ofthe financial crisis

A Taxonomy

I Delphic forward guidance: forecasts future macroeconomicperformance and likely policy actions based on Fed’sinformation set

I Odyssean Forward Guidance: commitment to futuredeviations from “normal policy”

Examples of Forward Guidance

I Early 2000 direct signals of policy inclinations replacedwith language describing "balance of risks”

I August 2003: “. . . the Committee believes that policyaccommodation can be maintained for a considerableperiod”

I January 2004: “the Committee believes that it can bepatient in removing its policy accommodation”

I May 2004: “policy accommodation can be removed at apace that is likely to be measured”

I December 2005: “further policy firming may be needed”I December 2008: policy rates will be low for "an extended

period"I October 2012: "exceptionally low levels for the federal

funds rate are likely to be warranted through mid-2015"

Analysis of Forward Guidance

I Monetary policy: management of private expectationscrucial for better macroeconomic outcomes

I Woodford (2003)I Rudebusch and Williams (2008 ), Laseen and Svensson

(2011)I ZLB: Krugman (1998), Eggertson and Woodford (2003)

I Empirical work: high frequency identification of policysurprises

I Kohn and Sack (2003)I Effects on other assets: Bernanke, Rainhart and Sack

(2004), Gurkaynak, Sack and Swanson (GSS, 2005)

Our Analysis

Empirical analysis of FG

1. Event studyI Extension of GSS factor analysis with high frequency data,

pre and post crisis

2. Rule-based measurement of FGI Introduce FG in interest rate ruleI Estimate reduced-form system of policy rules

3. Inference with medium-scale DSGEI Introduce factor structure an extended interest rate rule with

FGI CFJ (2012)

Our Analysis

Empirical analysis of FG

1. Event studyI Extension of GSS factor analysis with high frequency data,

pre and post crisis

2. Rule-based measurement of FGI Introduce FG in interest rate ruleI Estimate reduced-form system of policy rules

3. Inference with medium-scale DSGEI Introduce factor structure an extended interest rate rule with

FGI CFJ (2012)

Our Analysis

Empirical analysis of FG

1. Event studyI Extension of GSS factor analysis with high frequency data,

pre and post crisis

2. Rule-based measurement of FGI Introduce FG in interest rate ruleI Estimate reduced-form system of policy rules

3. Inference with medium-scale DSGEI Introduce factor structure an extended interest rate rule with

FGI CFJ (2012)

Our Analysis

Empirical analysis of FG

1. Event studyI Extension of GSS factor analysis with high frequency data,

pre and post crisis

2. Rule-based measurement of FGI Introduce FG in interest rate ruleI Estimate reduced-form system of policy rules

3. Inference with medium-scale DSGEI Introduce factor structure in extended interest rate rule with

FGI Details in CFJ (2012)

Outline

1. Introduction

2. An interest rule with FG

3. DSGE-based measurement of FG

4. Rule-based measurement of FG

5. Conclusion

An Interest Rate Rule with Forward Guidance

I Consider

rt = ρ1rt−1 +ρ2rt−2 +(1− ρ1 − ρ2)(φππt + φy yt

)+

M∑j=0

νt−j,j .

(1)

I πt and yt : inflation and activity gap

Systematic component of policy or "normal policy"

r st = ρ1rt−1 + ρ2rt−2 + (1− ρ1 − ρ2)

(φππt + φy yt

)Deviations from systematic component

I M + 1 shocks or signals, νt−j,j for j = 0,1, . . . ,M.

An Interest Rate Rule with Forward Guidance (cont.)

νt ,0

I Conventional monetary policy disturbance, unanticipatedI Temporary deviation from systematic component, i.e. from

"normal policy" prescription

νt−j,j for j = 1,2, . . . ,M

I Forward Guidance Shocks:signals on future path ofinterest rates

I νt−j,j revealed in quarter t − j , applies to the rule at(t − j) + j = t

I Anticipated future deviations from “normal policy”

An Interest Rate Rule with Forward Guidance (cont.)

νt ,0

I Conventional monetary policy disturbance, unanticipatedI Temporary deviation from systematic component, i.e. from

"normal policy" prescription

νt−j,j for j = 1,2, . . . ,M

I Forward Guidance Shocks: signals on future path ofinterest rates

I νt−j,j revealed in quarter t − j , applies to the rule at(t − j) + j = t

I Anticipated future deviations from “normal policy”

An Interest Rate Rule with Forward Guidance (cont.)

I Signals revealed at t ~νt :

~νt ≡ (νt ,0, νt ,1, . . . , νt ,M)

I ~νt : news in period t

I Cross-sectional correlation: E [~νt~ν′t ] non-diagonal

I Important implications for transmission (later)

I No time series correlation: E [~νt~ν′t−s] = 0 for s 6= 0

I νt−j,j and νt−s,s apply to rule at t , revealed at differentpoints in time

An Interest Rate Rule with Forward Guidance (cont.)

I Signals revealed at t ~νt :

~νt ≡ (νt ,0, νt ,1, . . . , νt ,M)

I ~νt : news in period t

I Cross-sectional correlation: E [~νt~ν′t ] non-diagonal

I Important implications for transmission (later)

I No time series correlation: E [~νt~ν′t−s] = 0 for s 6= 0

I νt−j,j and νt−s,s apply to rule at t , revealed at differentpoints in time

An Interest Rate Rule with Forward Guidance (cont.)

I Signals revealed at t ~νt :

~νt ≡ (νt ,0, νt ,1, . . . , νt ,M)

I ~νt : news in period t

I Cross-sectional correlation: E [~νt~ν′t ] non-diagonal

I Important implications for transmission (later)

I No time series correlation: E [~νt~ν′t−s] = 0 for s 6= 0

I νt−j,j and νt−s,s apply to rule at t , revealed at differentpoints in time

An Interest Rate Rule with Forward Guidance

rt = ρ1rt−1 + ρ2rt−2 + (1− ρ1 − ρ2)(φππt + φy yt

)+

M∑j=0

νt−j,j

NotationI Let M = 4

I Forecast xt , a quarter t random variable.

I x jt ≡ E[xt |It−j ] ≡ Et−j [xt ].

I Expectation revision: x j−1t − x j

t ≡ Et−j+1[xt ]− Et−j [xt ]

An Interest Rate Rule with Forward Guidance

rt = ρ1rt−1 + ρ2rt−2 + (1− ρ1 − ρ2)(φππt + φy yt

)+

M∑j=0

νt−j,j

NotationI Let M = 4

I Forecast xt , a quarter t random variable, e.g. rt , πt , yt

I x jt ≡ E[xt |It−j ] ≡ Et−j [xt ].

I Expectation revision: x j−1t − x j

t ≡ Et−j+1[xt ]− Et−j [xt ]

An Interest Rate Rule with Forward Guidance

rt = ρ1rt−1 + ρ2rt−2 + (1− ρ1 − ρ2)(φππt + φy yt

)+

M∑j=0

νt−j,j

NotationI Let M = 4

I Forecast xt , a quarter t random variable, e.g. rt , πt , yt

I x jt ≡ E[xt |It−j ] ≡ Et−j [xt ].

I Expectation revision: x j−1t − x j

t ≡ Et−j+1[xt ]− Et−j [xt ]

Recovering the Forward Guidance Shocks

I Difference expectations at two adjacent dates, j and j − 1 ,for 0 ≤ j < M:

r j−1t − r j

t =ρ1

(r j−2t−1 − r j−1

t−1

)+ ρ2

(r j−3t−2 − r j−2

t−2

)+ (1− ρ1 − ρ2)

(φπ

(πj−1

t − πjt

)+ φy

(y j−1

t − y jt

))+ νt−j,j .

I νt−j,j : change in expected interest rate at t accounting forrevisions during quarter t − j in the expected systematiccomponent of policy

I If 1) correctly capture policymakers’ behavior and 2)revisions, and 3) rule stable then νt−j,j can be interpretedas Odyssean FG

Recovering the Forward Guidance Shocks

I Difference expectations at two adjacent dates, j and j − 1 ,for 0 ≤ j < M:

r j−1t − r j

t =ρ1

(r j−2t−1 − r j−1

t−1

)+ ρ2

(r j−3t−2 − r j−2

t−2

)+ (1− ρ1 − ρ2)

(φπ

(πj−1

t − πjt

)+ φy

(y j−1

t − y jt

))+ νt−j,j .

I νt−j,j : change in expected interest rate at t accounting forrevisions during quarter t − j in the expected systematiccomponent of policy

I If correctly capture policymakers’ behavior and revisions,and rule stable then νt−j,j can be interpreted as OdysseanFG

Two Approaches to Inference

1. Rule-based measurement

I Survey data Et [rt+j ],Et [yt+j ],Et [πt+j ] for j = 1, ...,Mcontrols for revisions in private expectations of systematiccomponent

I Lack structural model to trace effects of policy expectationson activity and inflation

2. Empirical DSGEI Capture feedback effectsI Data on Et [rt+j ] and long-run inflation only (for now)

Two Approaches to Inference

1. Rule-based measurement

I Survey data Et [rt+j ],Et [yt+j ],Et [πt+j ] for j = 1, ...,Mcontrols for revisions in private expectations of systematiccomponent

I Lack structural model to trace effects of policy expectationson activity and inflation

2. Empirical DSGEI Capture feedback effectsI Data on E [rt+j |t ] and long-run inflation only (for now)

Outline

1. Introduction

2. An interest rule with FG

3. DSGE-based measurement of FG

4. Rule-based measurement of FG

5. Conclusion

The Model

I Builds on CEE (2005) and SW (2007)

I Distinguishing features:

1. Interest rate rule

2. Stochastic trend in ISTS, JPT (2011)

3. Financial accelerator mechanism, Gilchrist et. al (2011)

4. Multiple prices with factor structure, differentiate betweenconsumer prices and GDP deflator

Interest rate rule

rt = ρr rt−1 + (1− ρr )(φππt + φy yt

)+

4∑j=0

νt−j,j ,

πt =14

2∑j=−1

Et πt+j − π∗t ,

I Time-varying inflation anchor π∗t , highly persistent

Interest rate rule (cont.)

rt = ρr rt−1 + (1− ρr )(φππt + φy yt

)+

4∑j=0

νt−j,j ,

I Output gap: 4Q average of model-based filtered GDP

yt =14

2∑j=−1

Et xt+j .

I Follow Curdia et al. (2011), xt model-based approximationto HP filter

I Smoothing parameter λ estimated

Structure on Forward Guidance

~νt ≡ (νt ,0, νt ,1, . . . , νt ,M)

I E [~νt~ν′t ] = Ω

I Literature on News: Ω diagonal

I Here, non-diagonal

I Limit number of parameters estimated by imposing factorstructure

Structure on Forward Guidance

νt ,j = Aj f Tt + Bj f P

t + ut ,j .

I Factors f Tt and f P

t ; idiosyncratic disturbances ut ,j i.i.d.

I Identifying restriction: hierarchical structureA0 = 1,B0 = 0,B1 = 1

νt ,0 = 1f Tt + ut ,0

νt ,1 = A1f Tt + 1f P

t + ut ,1

νt ,2 = A2f Tt + B2f P

t + ut ,1

... = ...

νt ,M = AM f Tt + BM f P

t + ut ,M

Structure on Forward Guidance

νt ,j = Aj f Tt + Bj f P

t + ut ,j .

I Factors f Tt and f P

t ; idiosyncratic disturbances ut ,j i.i.d.

I Identifying restriction: hierarchical structureA0 = 1,B0 = 0,B1 = 1

νt ,0 = 1f Tt + ut ,0

νt ,1 = A1f Tt + 1f P

t + ut ,1

νt ,2 = A2f Tt + B2f P

t + ut ,1

... = ...

νt ,M = AM f Tt + BM f P

t + ut ,M

Structure on Forward Guidance

νt ,j = Aj f Tt + Bj f P

t + ut ,j .

I Factors f Tt and f P

t ; idiosyncratic disturbances ut ,j i.i.d.

I Identifying restriction: hierarchical structureA0 = 1,B0 = 0,B1 = 1

I f Tt Target factor: affects current rate, direct and indirecteffects on future rates

I f Pt Path factor: no effects on current rate, direct effectsthrough loadings Bj j = 1, ...,4 and indirect effects troughAR dynamics.

I Estimate loadings and std. devs. σfT , σfP and σfj

Structure on Forward Guidance

νt ,j = Aj f Tt + Bj f P

t + ut ,j .

I Factors f Tt and f P

t ; idiosyncratic disturbances ut ,j i.i.d.

I Identifying restriction: hierarchical structureA0 = 1,B0 = 0,B1 = 1

I f Tt Target factor: affects current rate, direct and indirecteffects on future rates

I f Pt Path factor: no effects on current rate, direct effectsthrough loadings Bj j = 1, ...,4 and indirect effects troughAR dynamics.

I Estimate loadings and std. devs. σfT , σfP and σj

(Partial) Dataset and Identification

DataI Federal Fund’s Futures and Eurodollar deposits for

E [rt+j |t ] j = 1, ..,4

I Survey of Professional Forecasters E [πt+40|t ]

IdentificationI Target Factor: moves current rate (possibly more than

future rates)

I Path factor and inflation anchor: move expected future ffrmore than current rates

I Inflation anchor: moves expected inflation more than Pathfactor

(Partial) Dataset and Identification

DataI Federal Fund’s Futures and Eurodollar deposits for

E [rt+j |t ] j = 1, ..,4

I Survey of Professional Forecasters E [πt+40|t ]

IdentificationI Target Factor: moves current rate (possibly more than

future rates)

I Path factor and inflation anchor: move expected future ffrmore than current rates

I Inflation anchor: moves expected inflation more than Pathfactor

Comments

I Challenging to use data on E [yt+j |t ], or short-horizonE [πt+j |t ]

I News about which shocks?

I Identification of Odyssean vs. Delphic FG: requiresassuming model-based expectations correctly capturechanges in outlook

(More) data: 1989q2 to 2007q2

I Nominal per capita GDP, Investment and Consumptiongrowth

I Level of per capita hours (NFBS)I Nominal compensation per hour (NFBS)I GDP deflator, consumption and investment deflators, core

PCE, core CPII 10-year ahead average expected inflation (SPF)I Interest rate spread ( composite of high yield and ABS less

TB )I Ratio of private credit to GDPI Federal funds rateI Expectations of federal funds rate 1 to 4 qtrs hence

8 Non-policy Shocks

I DemandI Discount (Euler Equation)I G + NX + ∆Inv (Resource Constraint )I Spread (External Finance Premium of FA )I Net worth (Evolution of Net Worth )

I SupplyI Neutral technologyI Investment-specific technologyI Price markupsI Labor disutility ARMA(1,1)(Equivalent Wage Markup )

Monetary Policy Parameter Estimates

Parameter Description Modeρπ Inflation anchor persistence 0.99ρR Inflation rate smoothing 0.85φp Inflation gap response 1.35φy Output gap response 0.10σπ Inflation anchor std. dev. 0.008σf1 Target Factor std. dev. 0.04σf2 Path Factor std. dev. 0.06A1 Lead 1 1.25A2 Lead 2 0.69A3 Lead 3 0.42A4 Lead 4 -0.21B1 Lead 1 0.80B2 Lead 2 1.00B3 Lead 3 0.92B4 Lead 4 0.43

Other Parameter Estimates

Parameter Description Mode

α Capital Share 0.17δ Depreciation rate 0.03ιp Indexation Prices 0.08ιw Indexation Wages 0.28H Habit 0.89ν Inverse Frisch elasticity 2.17κp Price Phillip’s curve slope 0.002κw Wage Phillip’s curve slope 0.005χ Utilization elasticity 4.80S Investment adjustment elasticity 7.84B/N Steady state borrowing to net worth ratio 1.11FKN Steady state spread 0.69τ Net worth elasticity 0.003ζ Entrepreneur survival prob 0.91

IRF Path Factor

0 4 7 110

0.1

0.2

0.3

0.4

Federal Funds Rate

0 4 7 11−0.35

−0.3

−0.25

−0.2

−0.15

GDP (level)

0 4 7 11−0.16

−0.14

−0.12

−0.1

−0.08

−0.06Consumption (level)

0 4 7 11−1.2

−1

−0.8

−0.6

Investment (level)

0 4 7 11−0.35

−0.3

−0.25

−0.2

−0.15

Hours

Forward Guidance Factor

0 4 7 11

−0.025

−0.02

−0.015

−0.01PCE Core

I 1 std. dev., annualized

Responses to Idiosyncratic Signals

ξt ,j = Aj f Tt + Bj f P

t + ut ,j .

I Anticipation effects: future tightening implies decline inoutput gap and inflation until tightening realizes

I Systematic component of policy: loosening today, policyreversal later

I Similar to News literature: anticipated shocks notcorrelated in cross-section

Responses to Idiosyncratic Signal

0 4 7 11

0

0.05

0.1

0.15

Federal Funds Rate

0 4 7 11

−0.1

−0.08

−0.06

−0.04

GDP (level)

0 4 7 11

−0.05

−0.04

−0.03

−0.02

Consumption (level)

0 4 7 11−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

Investment (level)

0 4 7 11

−0.1

−0.08

−0.06

−0.04Hours

Idiosyncratic Component of Signal 4Q Ahead

0 4 7 11−10

−8

−6

−4

x 10−3 PCE Core

Forward Guidance and Business Cycle

I Variance shares explained over frequency bandcorresponding to [6,32] quarters

Shocks’ Business Cycle Contributions

Variables Target Factor Path Factor Inflation DriftGDP 0.03 0.09 0Cons. 0.01 0.02 0Invest. 0.02 0.05 0Hours 0.04 0.09 0PCE Core 0 0.01 0.12FFR 0.27 0.42 0.01FFR Expected 4 Q 0.12 0.35 0.02

Variable Discount Spread Neutral PMarkGDP 0.31 0.37 0.11 0Cons. 0.72 0.13 0.08 0Invest. 0 0.88 0.02 0Hours 0.32 0.4 0.09 0PCE Core 0.05 0.09 0 0.58FFR 0.08 0.11 0.02 0.02

Factors

1990 1992 1994 1996 1998 2000 2002 2004 2006

−0.1

−0.05

0

0.05

0.1Target Factor

1990 1992 1994 1996 1998 2000 2002 2004 2006

−0.1

−0.05

0

0.05

0.1

Path Factor

Historical Effects of Forward Guidance

I 1994-1995: sharp tightening and quick reversal end of1994, beginning of 1995

I 2002-2004: rates considerably lower than prescribed byrule

Decomposition of Shocks’ Contribution to FFR

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q2

2

4

6

8

Data

Annua

lized

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q2

2

1

0

1Demand

Annua

lized

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q22

1.5

1

Supply

Annua

lized

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q22

1

0

1

FG

Annua

lized

Federal Funds Rate

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q2

1

0

1

2

3

Other Policy

Annua

lized

Decomposition of Shocks’ Contribution to GDP

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q2

20246

Data

Annua

lized

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q2

5

0

5Demand

Annua

lized

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q22

1

0

1

2

Supply

Annua

lized

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q2

1

0

1

FG

Annua

lized

GDP (per capita)

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q2

0.50

0.51

1.5

Other Policy

Annua

lized

Decomposition of Shocks’ Contribution to Inflation

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q2

2

3

4

5

Data

Annua

lized

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q2

1.21

0.80.60.40.2

Demand

Annua

lized

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q2

2

1

0

Supply

Annua

lized

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q2

0.05

0

0.05

0.1

0.15FG

Annua

lized

PCE Core

1989Q2 1991Q2 1993Q2 1995Q2 1997Q2 1999Q2 2001Q2 2003Q2 2005Q2 2007Q2

1

1.5

2

Other Policy

Annua

lized

Extension

I Path factor for model forecasts conditional on zero lowerbound (ZLB)

I Extended analysis to 10q of FFR expected data since2008Q1

I Break in rule parameters in 2008Q1

I Estimate new and additional loadings, volatilities

Results

I ZLB binding since 2008q4I Systematic policy component⇒ E [rt+j |t ] < 0 for at least

one j

I Path factor significant boost to output and inflation

Outline

1. Introduction

2. An interest rule with FG

3. Rule-based measurement of FG

4. Analysis of inferred FG

5. Conclusion

An Interest Rate Rule with Forward Guidance

rt = ρ1rt−1 +ρ2rt−2 +(1− ρ1 − ρ2)(φππt + φy yt

)+

M∑j=0

νt−j,j . (2)

Information Flow

t − j t − j + 1 · · · t t + 1

x jt

νt−j,j x j−1t · · · x0

t νt ,0

xt is realized.

x−1t

I Forecast xt , a quarter t random variable.I x j

t ≡ E[xt |It−j ] ≡ Et−j [xt ].I It−j is measured at the start of t − j .

I Agents learn νt−j,j during t − j .I Nowcast x0

t ≡ E[xt |It−j , νt−j,j , νt−j+1,j−1, . . . , νt−1,1].I Backcast x−1

t ≡ E[xt |It−j , νt−j,j , νt−j+1,j−1, . . . , νt−1,1, νt ,0]

Information Flow

t − j t − j + 1 · · · t t + 1

x jt νt−j,j

x j−1t · · · x0

t νt ,0

xt is realized.

x−1t

I Forecast xt , a quarter t random variable.I x j

t ≡ E[xt |It−j ] ≡ Et−j [xt ].I It−j is measured at the start of t − j .I Agents learn νt−j,j during t − j .

I Nowcast x0t ≡ E[xt |It−j , νt−j,j , νt−j+1,j−1, . . . , νt−1,1].

I Backcast x−1t ≡ E[xt |It−j , νt−j,j , νt−j+1,j−1, . . . , νt−1,1, νt ,0]

Information Flow

t − j t − j + 1 · · · t t + 1

x jt νt−j,j x j−1

t

· · · x0t νt ,0

xt is realized.

x−1t

I Forecast xt , a quarter t random variable.I x j

t ≡ E[xt |It−j ] ≡ Et−j [xt ].I It−j is measured at the start of t − j .I Agents learn νt−j,j during t − j .

I Nowcast x0t ≡ E[xt |It−j , νt−j,j , νt−j+1,j−1, . . . , νt−1,1].

I Backcast x−1t ≡ E[xt |It−j , νt−j,j , νt−j+1,j−1, . . . , νt−1,1, νt ,0]

Information Flow

t − j t − j + 1 · · · t t + 1

x jt νt−j,j x j−1

t · · ·

x0t νt ,0

xt is realized.

x−1t

I Forecast xt , a quarter t random variable.I x j

t ≡ E[xt |It−j ] ≡ Et−j [xt ].I It−j is measured at the start of t − j .I Agents learn νt−j,j during t − j .

I Nowcast x0t ≡ E[xt |It−j , νt−j,j , νt−j+1,j−1, . . . , νt−1,1].

I Backcast x−1t ≡ E[xt |It−j , νt−j,j , νt−j+1,j−1, . . . , νt−1,1, νt ,0]

Information Flow

t − j t − j + 1 · · · t t + 1

x jt νt−j,j x j−1

t · · · x0t

νt ,0

xt is realized.

x−1t

I Forecast xt , a quarter t random variable.I x j

t ≡ E[xt |It−j ] ≡ Et−j [xt ].I It−j is measured at the start of t − j .I Agents learn νt−j,j during t − j .I Nowcast x0

t ≡ E[xt |It−j , νt−j,j , νt−j+1,j−1, . . . , νt−1,1].

I Backcast x−1t ≡ E[xt |It−j , νt−j,j , νt−j+1,j−1, . . . , νt−1,1, νt ,0]

Information Flow

t − j t − j + 1 · · · t t + 1

x jt νt−j,j x j−1

t · · · x0t νt ,0

xt is realized.

x−1t

I Forecast xt , a quarter t random variable.I x j

t ≡ E[xt |It−j ] ≡ Et−j [xt ].I It−j is measured at the start of t − j .I Agents learn νt−j,j during t − j .I Nowcast x0

t ≡ E[xt |It−j , νt−j,j , νt−j+1,j−1, . . . , νt−1,1].

I Backcast x−1t ≡ E[xt |It−j , νt−j,j , νt−j+1,j−1, . . . , νt−1,1, νt ,0]

Information Flow

t − j t − j + 1 · · · t t + 1

x jt νt−j,j x j−1

t · · · x0t νt ,0

xt is realized.

x−1t

I Forecast xt , a quarter t random variable.I x j

t ≡ E[xt |It−j ] ≡ Et−j [xt ].I It−j is measured at the start of t − j .I Agents learn νt−j,j during t − j .I Nowcast x0

t ≡ E[xt |It−j , νt−j,j , νt−j+1,j−1, . . . , νt−1,1].I Backcast x−1

t ≡ E[xt |It−j , νt−j,j , νt−j+1,j−1, . . . , νt−1,1, νt ,0]

DataI For j = 0, . . . ,M − 1 with M = 4I r j

t Fed Funds Futures and Eurodollar contractsI Blue Chip data on CPI Inflation, unemployment rate and

medium-run unemployment to construct

yt = ut =13

1∑j=−1

(uj−1

t+j − umrt

)

πt =13

1∑j=−1

πj−1t+j

I umrt :average unemployment expected over the next 7-11

years.

System GMM

I System for [rt , r0t , r

1t , r

2t , r

3t ]

Expected interest with info set at j

r jt = ρ1r j−1

t−1 +ρ2r j−2t−2 +(1− ρ1 − ρ2)

(φππ

jt + φy y j

t

)+[

4∑s=j+1

νt−s,s]

I Estimate for j = 0,1,2,3 and realized data

System GMM

I System for [rt , r0t , r

1t , r

2t , r

3t ]

E [gt (γ)⊗ Zt ] = 0. (3)

I γ = (ρ1, ρ2, φπ, φy )

I gt (·) returns the vector (νt ,0, νt−1,1, . . . , νt−4,4)

I Zt = (u4t , π

4t , r

2t−2, r

3t−1)

I instruments: info set at beginning of t − 4

Estimates

Sample: 1996Q1-2007Q2

rt =− 0.05(0.02)

+ 1.60(0.02)

× rt−1 − 0.66(0.02)

× rt−2

− (1− 0.94)× 1.10(0.28)

ut + (1− 0.94)× 2.32(0.18)

πt

+4∑

j=0

νt−j,j

I Inferred ~νt :~ν ≡ (νt ,0, νt ,1, νt ,2, νt ,3, νt ,4)

Deviations from the Interest Rate Rule

Table: 8: Summary Statistics

Standard Deviations(in basis points)

νt ,0 νt ,1 νt ,2 νt ,3 νt ,412 20 13 11 9

Correlations

νt ,0 νt ,1 νt ,2 νt ,3 νt ,4ξt ,0 1.00ξt ,1 0.02 1.00ξt ,2 -0.05 0.22 1.00ξt ,3 -0.32 0.03 -0.17 1.00ξt ,4 -0.32 -0.26 -0.22 0.16 1.00

Forward Guidance Component

1996q1 2001q1 2007q2-90.00

0.00

55.00

Interest Rate Rule's ResidualResidual's Anticipated Component

Residual is∑4

j=0 νt−j,j ; Anticipated drops νt ,0

80 percent of deviations from policy rule anticipated 1 to 4 Q inadvance

Analyze deviations from the Interest Rate Rule

1. Factor analysis and propagation through rule (skip)

2. Effects on asset prices

3. Effects on revisions to expectations of activity and inflation

2. Effects of Forward Guidance on Asset PricesRegress quarterly changes in asset prices (eoq to eoq) on ~νt

νt ,0 νt ,1 νt ,2 νt ,3 νt ,4 R2

2-Year Note 1.08∗∗∗ 1.98∗∗∗ 1.56∗∗∗ 0.70∗ 0.89∗ 0.77(0.37) (0.22) (0.33) (0.42) (0.50)

5-Year Note 0.61∗ 1.83∗∗∗ 1.91∗∗∗ 1.43∗∗∗ 1.25∗∗ 0.78(0.36) (0.21) (0.32) (0.40) (0.49)

10-Year Note 0.38 1.48∗∗∗ 1.60∗∗∗ 1.41∗∗∗ 1.29∗∗∗ 0.70(0.37) (0.22) (0.33) (0.42) (0.50)

Aaa CB 0.19 0.65∗∗∗ 0.75∗∗ 0.86∗∗ 0.17 0.33(0.38) (0.23) (0.34) (0.43) (0.52)

Baa CB 0.13 0.69∗∗∗ 0.71∗∗ 1.00∗∗∗ 0.37 0.42(0.33) (0.20) (0.30) (0.38) (0.45)

Stderr in parenthesis; ∗, ∗∗ and ∗∗∗ significance at 10, 5 and 1 percent

1 bp. increase in FG 1 Q ahead moves notes by 2 bp.

3. Forward Guidance and Expectation Revisions

νt ,0 νt ,1 νt ,2 νt ,3 νt ,4 R2

u0t+1 − u1

t+1 -0.34 -0.30∗∗ -0.05 -0.27 0.54 0.27(0.24) (0.14) (0.22) (0.27) (0.33)

u1t+2 − u2

t+2 -0.46∗ -0.47∗∗∗ -0.02 -0.20 0.30 0.34(0.24) (0.14) (0.22) (0.27) (0.33)

u2t+3 − u3

t+3 -0.31 -0.47∗∗∗ -0.00 -0.07 0.26 0.34(0.22) (0.13) (0.20) (0.25) (0.30)

π0t+1 − π

1t+1 -0.18 0.17 0.05 -0.44 0.07 0.10

(0.24) (0.14) (0.21) (0.27) (0.33)π1

t+2 − π2t+2 -0.05 0.15 0.11 0.35 -0.02 0.10

(0.22) (0.13) (0.20) (0.25) (0.30)π2

t+3 − π3t+3 -0.25 0.18∗ -0.07 0.09 -0.04 0.14

(0.18) (0.10) (0.16) (0.20) (0.24)

3. Forward Guidance and Expectation Revisions(cont.)

I Anticipated policy tightening associated with lowerunemployment, higher inflation

I Contrary to expected signs if Odyssean

Interpretation 1: Delphic, revealing information about a strongeroutlook

Interpretation 2: Fed responds briskly to recent news on activityto not fall "behind the curve"

rt = ρ1rt−1 + ρ2rt−2 + (1− ρ1 − ρ2)(φππt + φuut

)+

η(

ut − uLt

)+

M∑j=0

νt−j,j

Conclusions

DSGE-Based Measurement of Forward Guidance

I Introduce into a rich DSGE convenient structure(statistically and economically) to identify FG shocks

I Findings:I FG accounts for half of business cycle variation in the ffr

I FG explains 9% of output fluctuations at business cyclefrequencies, but much more in certain episodes, which arebroadly consistent with historical record

Conclusions (cont.)

Rule-Based Measurement of Forward Guidance

I 80 percent of deviations from systematic component ofpolicy anticipated

I Significant effects on asset prices

I Wrong sign on revisions to expected unemployment (andinflation )

I Likely due to Delphic components unaccounted for

Pending

I DSGE Model:I More expectations data, e.g. short-run inflation and output

I Interplay between inflation drift and policy expectations?

I Bridge results from DSGE and rules

I Can we identify Odyssean vs. Delphic?

Additional Slides

Appendix: History of Forward Guidance

I 1983 to 1999: FOMC voted on future policy tilt, but info.made public after the following meeting.

I In February 1994 first statement of policy moveI In May 1999 first included language on future stance of

policy: “the Committee . . . adopted a directive that is tiltedtoward the possibility of a firming in the stance of monetarypolicy.”

I Language would change as FOMC sought to maintaintransparency without confusing markets and adjusted toevolving policy environment. But FG a fixture of statementlanguage going forward.

Appendix: Gurkaynak, Sack and Swanson (2005)

I Expectations of future ffr changes with new info. on futureeconomic activity.

I Study ffr rate futures in short windows surrounding releaseof FOMC statements

I July 1991 through December 2004: FOMC statements hadsignificant affects on ffr futures and Treasury yields.

I Decompose changes in asset prices into “target” and“path” factors, latter is FG

I 75 to 90 percent of the explainable variation in five- andten-year Treasury yields is due to the path factor

1. Factor Analysis

~νt = B × ft + et

Table: 9: Factor Model Parameter Estimates

νt ,0 νt ,1 νt ,2 νt ,3 νt ,4B −5 −6 −4 3 7

I "Tilt" in policy: accommodation rapidly withdrawn

I Compare propagation of ft and ξt ,0 through estimatedpolicy rule

I Note: misses feedback with inflation and activity

Responses to Factor and Standard Policy Shocks

0 1 2 3 4 5 6 7 8 9-25

-20

-15

-10

-5

0

Quarters Since Initial Impulse

Bas

is P

oint

s

Factor ImpulseStandard Contemporaneous Impulse

Policy acceleration — quick accommodation that is rapidlywithdrawn.