understanding and influencing the yield curve at the zero lower … · 2020. 2. 26. ·...

Understanding and Influencing the YieldCurve at the Zero Lower Bound

Glenn D. Rudebusch

Federal Reserve Bank of San Francisco

October 25, 2014Macroeconomic Measurement, Theory, Prediction, and Policy:

A Colloquium Honoring the Legacy of Lawrence R. KleinUniversity of Pennsylvania

My comments do not necessarily represent the views of others in the Federal Reserve.

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Understanding and influencing the yield curveat the ZLB

Understanding the yield curve

1. What do financial economists do at the ZLB?

Develop new term structure models

Influencing the yield curve

2. What do central bankers do at the ZLB?

Worry!

Consider unconventional tools and strategies

2 / 40

Short-term rates at ZLB in many countries

0

3

6

9

12

15

90 92 94 96 98 00 02 04 06 08 10 12

US

UK

Germany/ECB

Japan

Source: OECD, Federal Reserve Board

Percent

3 / 40

So far: Almost 6 years at ZLB in U.S.!

Year

Per

cent

1985 1990 1995 2000 2005 2010

02

46

810

12 10y T−yield2y T−yield3m T−bill rate

4 / 40

1. What do financial economists do at the ZLB?

Problem: Standard Gaussian term structure models do notrestrict interest rates to be nonnegative.

Term structure models that do respect ZLB:

I Shadow-rate term structure models

I Stochastic-volatility models with square-root processes

I Gaussian quadratic models

I AR gamma zero process of Monfort, Pegoraro, Renne,Roussellet (2014)

Literature has focused on shadow-rate models:

I Issues include tractability, whether ZLB is reflecting orabsorbing barrier, and familiarity away from ZLB.

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Shadow-rate dynamic term structure models

Standard affine Gaussian DTSM

I Short rate: rt = δ0 + δ′1Xt

I VAR for Xt under risk-neutral (Q) and real-world (P)

I Risk adjustment links cross section to time series

Shadow-rate DTSM based on Black (1995)

I Shadow rate: st = δ0 + δ′1Xt

I Short rate: rt = max(0, st) or rt = max(rmin, st)

Bond prices and yields

I ymt = m−1∑m−1

i=0 EPt rt+i + YTPmt

I Affine model: yields and term premia are linear functions of Xt

I Shadow-rate model is non-linear with no analytical solution

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Some related literature

Japan

I Gorovoi and Linetsky (2004). Ueono et al. (2006), Ichiue andUeno (2007)

I Kim and Singleton (2012). Christensen and Rudebusch(2014), Monfront et al (2014)

United States

I Bomfim (2003), Hamilton and Wu (2011)

I Krippner (2013), Xia and Wu (2013), Christensen andRudebusch (2013), Andreasen and Meldrum (2013, Kim andPriebsch (2013), Christensen, Lopez, and Rudebusch (2014)

Euro Area

I Renne(2014)

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Christensen and Rudebusch (JFinEc 2014):Estimate 1-, 2-, 3-factor shadow-rate models

1996 2000 2004 2008 2012

01

23

45

Rat

e in

per

cent

10−year yield 4−year yield 1−year yield 6−month yield

Japanese Government Bond Yields—weekly frequency

8 / 40

Fit of Standard and Shadow-Rate Models (RMSE)

RMSE, all yields(in b.p.)

One-factor modelsaffine: V(1) 34.4shadow: B-V(1) 32.7Two-factor models

affine: AFNS(2) 12.2shadow: B-AFNS(2) 10.3Three-factor modelsaffine: AFNS(3) 9.7shadow: B-AFNS(3) 7.0

Shadow-rate models have somewhat closer fit.

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Fitted Yield Curves: Two- and Three-Factor Models

0 2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

Time to maturity in years

Rat

e in

per

cent

AFNS(2) model B−AFNS(2) model Observed yields

0 2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

Time to maturity in yearsR

ate

in p

erce

nt

AFNS(3) model B−AFNS(3) model Observed yields

I On July 1, 2005, gain from shadow-rate implementation forthe two-factor model, less for the three-factor model.

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Why Use a Shadow-Rate Model?Zero Probability of Negative Future Short Rates

1995 2000 2005 2010

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babi

lity

AFNS(3) model

Affine model produces significant probability that short ratewill be negative three months ahead.

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Why use a shadow-rate model?Volatility compression for intermediate yields

1995 2000 2005 2010

020

4060

8010

0

Rat

e in

bas

is p

oint

s

1995 2000 2005 2010

020

4060

8010

0

Rat

e in

bas

is p

oint

s

Correlation = 72.4%

AFNS(3) model B−AFNS(3) model Three−month realized volatility of two−year yield

Near ZLB, volatility of two-year yield is also near zero.Shadow-rate model can replicate this correlation.

12 / 40

Bauer and Rudebusch (2014):Shadow-rate model with U.S. data

Advantages of shadow-rate models at ZLB:

Better cross-sectional fit

I Shadow-rate models fit the yield curve better

Avoid violations of ZLB by affine models

I Forward curves and short-rate expectations dip below zero

I Probability of negative future rates while mean positive

Greater forecast accuracy

I Shadow-rate models forecast better out of sample

I Macroeconomic information improves performance

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Shadow-rate model gives more accurate forecastsOut-of sample RMSEs (in basis points). Forecasts of 3-monthT-bill rate 12 months ahead, Dec. 2008 to June 2011

Model RMSEYields-only

affine (2,0) 32.3shadow (2,0) 17.8

affine (3,0) 22.3shadow (3,0) 14.3

Macro-finance

affine (1,2) 103.5shadow (1,2) 10.9

affine (2,2) 49.6shadow (2,2) 10.4

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Why are macro variables helpful at the ZLB?Unemployment rate can help pin down shadow rate:

-6

-4

-2

0

2

4

6

8

10

1985 1990 1995 2000 2005 2010

Percent

Unemployment gap

3m T-bill rate

-2.7

-5.8

-2.2

-5.3

-4.5

-4.9

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Unconventional tools and strategies:

Mitigate effects of ZLB

Try to ease financial conditions—e.g., lower long-term yields

I Conduct quantitative easing (QE)

I Provide forward guidance about future policy

I Conduct credit easing

Avoid future episodes at ZLB

I Reconsider the level of the inflation target

I Put greater emphasis on avoiding financial crises

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ZLB was sizable constraint on U.S. monetary policy

-8

-6

-4

-2

0

2

4

6

8

10

12

88 90 92 94 96 98 00 02 04 06 08 10 12 14

Quarterly average Federal Funds Rate

Percent

Fed's Target Rate

Target Rule = 2.1 + 1.5 x Inflation - 2.0 x Unemployment gap (Unemployment Gap = Unemployment rate - CBO NAIRU)

Simple estimated policy rule recommendation

Monetary policy shortfall

17 / 40


Unconventional tools and strategies:

Mitigate effects of ZLB

Try to ease financial conditions—e.g., lower long-term yields

I Conduct quantitative easing (QE) (A)

I Provide forward guidance about future policy (B)

I Conduct credit easing

Avoid future episodes at ZLB

I Reconsider the level of the inflation target

I Put greater emphasis on avoiding financial crises (C)

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A. Central banks purchase assets (QE)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

2007 2008 2009 2010 2011 2012 2013 2014

Source: Federal Reserve Board; short-term Treasuries have a maturity of 3 years or less

Federal Reserve Assets $, Trillions

Short-term Treasuries

Liquidity programs and other assets

GSE securities

9/24

Long-term Treasuries

QE1 QE2 MEP QE3

19 / 40

Long-term bond yields fall on QE announcement

0

0.5

1

1.5

2

2.5

3

3.5

0 12 24 36 48 60 72 84 96 108 120

Treasury Bond Yields

Bond Maturity (in months)

Percent

Before Announcement (March 17, 2009)

After Announcement (March 18,2009)

Treasury bond yields fall after March 18th FOMC announcement of $300 billion future purchases of Treasury securities.

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How did QE Work?

Chairman Bernanke (2010) saw portfolio balance channel:

“Purchases work primarily through the so-called portfoliobalance channel [...] Different financial assets are notperfect substitutes in investors’ portfolios, so thatchanges in the net supply of an asset available toinvestors affect its yield and those of broadly similarassets.”

But LSAPs also may have provided news about

I a longer period of near-zero policy rate and slower liftoff

I lower risks around a little-changed policy path

I higher medium-term inflation and lower real rates

I improved prospects for real activity (esp. lower tail)

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Bauer-Rudebusch (IJCB, 2014)Signaling vs. portfolio balance channels for QE

How did QE affect long-term Treasury yields?

I Yield decomposition:

ynt = n−1n−1∑i=0

Etrt+i + TPnt

I Signaling Channel: Announcements of asset purchases signallower future policy rates to market participants, so QEreduces expectations component of Treasury yields.

I Portfolio Balance Channel: Changes in supply have priceeffects because of imperfect substitutability. Reduction insupply lowers term premium component of Treasury yields.

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Changes in expected policy path during QE1

0 20 40 60 80 120

−15

0−

100

−50

0

months forward

basi

s po

ints

Unrestr. risk prices (URP)

forward ratesexpectationsconf. int.

0 20 40 60 80 120

−15

0−

100

−50

0

months forward

Restr. risk prices (RRP)

23 / 40

Christensen-Rudebusch (EJ, 2012)Support signaling channel in U.S.

0 2 4 6 8 10

−10

0−

80−

60−

40−

200


Net

cha

nge

in b

asis

poi

nts

Instantaneous forward rate Forecasted future spot rate Instantaneous forward term premium

I Policy expectations declined the most at the two- tothree-year horizon as one would expect from a signaling effect.

24 / 40

Christensen-Rudebusch (EJ, 2012)Support portfolio balance channel in U.K.

0 2 4 6 8 10

−80

−60

−40

−20

020

40


Net

cha

nge

in b

asis

poi

nts

Instantaneous forward rate Forecasted future spot rate Instantaneous forward term premium

I Term premiums declined at all horizons, but the most in thethree- to ten-year maturity range.

25 / 40

Will QE be part of the new normal?

Event studies suggest QE did effect yield curve

I But did effects persist?

I Did changes in yields pass through to private rates?

I Did changes in asset prices alter aggregate demand?

Potential costs:

I Loss of monetary/fiscal credibility (and pi*)

I Capital losses to central bank

I Financial instability

I Impaired securities market functioning

I Increased difficulty of managing monetary policy

Analysis needed to integrate QE into DTSM

26 / 40

Christensen-Lopez-Rudebusch (2014):Probability-Based Stress Test of Fed

1990 1995 2000 2005 2010 2015 2020

020

4060

8010

012

0

Bill

ions

of d

olla

rs

Realized remittances to the Treasury 1990−2007 trend of remittances 2008−2020 trend projection of remittances Median, 2014−2020 projections 90% confidence band, 2014−2020 projections

27 / 40

B. Central bank guidance on future policy

Modern central banking stresses importance of guidingexpectations about future monetary policy actions.

I Monetary policy is process of shaping or managing yield curve.

How can central banks best guide private expectations of futuremonetary policy actions?

I Old answer: Actions speak louder than words

I New answer: Talk, talk, talk, plus forecasts

Rudebusch, Glenn, and John C. Williams, 2008, “Revealing theSecrets of the Temple: The Value of Publishing Central BankInterest Rate Projections.” in Asset Prices and Monetary Policy.

28 / 40

Narrative forward guidance by Federal Reserve

Aug. 2003 - June 2006

accommodation can be “maintained for a considerable period,” or“removed at a pace that is likely to be measured,”

March 2009“economic conditions are likely to warrant exceptionally low levelsof the federal funds rate for an extended period.”

August 2011

“economic conditions...are likely to warrant exceptionally low levelsfor the federal funds rate at least through mid-2013.”

December 2012

the “low range for the federal funds rate will be appropriate atleast as long as the unemployment rate remains above 6.5%...”

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Quantitative forward guidance by Fed

30 / 40

Probability density of future short rate

Distribution under Q-measure, on December 31, 2012, four-yearhorizon, model MZ(2)

−6 −4 −2 0 2 4 6

0.00

0.05

0.10

0.15

Percent

Den

sity

mode mean

density shadow ratedensity short rate

31 / 40

Liftoff estimate based on forward rates

Forward rates (EQt rt+h) on December 31, 2012, for model MZ(2)

0 10 20 30 40 50 60

−2

−1

01

23

Horizon

Per

cent

forward rates

32 / 40

Liftoff estimate based on modal pathBauer and Rudebusch (2013): Forward rates (EQt rt+h), shadowforward rates (EQt st+h), and modal path, December 31, 2012

0 10 20 30 40 50 60

−2

−1

01

23

Horizon

Per

cent

forward ratesshadow forward ratesmodal path

33 / 40

Estimated horizon (in months) until policy liftoff

Year

Mon

ths

2008 2009 2010 2011 2012 2013 2014

010

2030

4050

60 based on forward curvebased on modal path

34 / 40

Assessing effectiveness of forward guidance

Merits of clear forward policy guidance

I Greater policy effectiveness through greater transparency

Potential pitfalls of forward policy guidance

I Misinterpretation of conditionality of policy guidance”... tendency for the public to infer more of a commitment tofollowing the implied path than would be appropriate for goodpolicy.” Kohn (2008)

I Incorrect inference about the meaning of the policy guidance(Rudebusch and Williams, 2008)

I Reduction in incentives for the collection of private-sectorinformation. (Morris and Shin)

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C. Policy actions to avoid financial crises

Should monetary policy take a more active role and try tooffset financial imbalances (e.g. deflate an asset pricebubble)?

To do so, three questions must be addressed:

I Can an asset price bubble be identified?

I Will the bubble cause significant macro problems?

I Is monetary policy a good tool to deflate bubble? (Alternativewould be macroprudential policy)

see Rudebusch, Glenn D., 2005, ”Monetary Policy and Asset PriceBubbles,” FRBSF Economic Letter.

36 / 40

Equity prices in 1999-2000

0

100

200

300

400

500

600

700

800

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

January 3, 2005 = 100

US Stock Market IndicesIndex

S&P 500

NASDAQ

37 / 40

House price bubble?

0.5

0.75

1

1.25

1.5

1.75

1970 1975 1980 1985 1990 1995 2000 2005 2010

U.S. National Case-Shiller Index divided by Owner's Equivalent Rent

Ratio of House Prices to Rent

Average 1970-2000

2014Q1

38 / 40

Was there a 2004-06 bond yield “conundrum”?

RW Model Residuals for 10-Year Yield

40-50 bp conundrum

-60

-40

-20

0

20

40

60

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

basi

s po

ints

Rudebusch, Glenn D., Eric Swanson, and Tao Wu, 2006, ”TheBond Yield ‘Conundrum’ from a Macro-Finance Perspective,”Monetary and Economic Studies 24, 83-128.

39 / 40

Lessons for everyone at the ZLB

Probability of ZLB seems higher than many judged

I This has implications for modeling the yield curve

I Possible implications for inflation target

Central Bank affects whole yield curve

I Recommends macro-finance term structure approach

I Should unconventional policies become conventional?

I Financial stability may be emphasized as goal for policy

Credit risk for sovereign debt.

I Government fiscal issues effect yield curve

I “flight to quality” adjustments as well

40 / 40

understanding and influencing the yield curve at the zero lower … · 2020. 2. 26. ·...

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