Inflation Expectations Spillovers between the United States and Euro Area

In�ation Expectations Spillovers between the

United States and Euro Area

Aleksei Net²unajev

Lars Winkelmann

School of Business and Economics

Freie Universität Berlin

CRC 649 "Economic Risk"

Introduction 1-1

In�ation expectations and monetary policy

� Anchoring of in�ation expectations → macro stability.

Bom�n and Rudebusch (2000), Orphanides and Williams (2005)

� FED press release December 12, 2012:"... the Committee [...] anticipates that the federal funds rate willbe appropriate at least as long as [...]

I in�ation between one and two years ahead is projected to beno more than a half percentage point above the Committee's 2percent longer-run goal,

I and longer-term in�ation expectations continue to be wellanchored."

In�ation Expectations spillover

Introduction 1-1

In�ation expectations and monetary policy

� Anchoring of in�ation expectations → macro stability.

Bom�n and Rudebusch (2000), Orphanides and Williams (2005)

� FED press release December 12, 2012:"... the Committee [...] anticipates that the federal funds rate willbe appropriate at least as long as [...]

I in�ation between one and two years ahead is projected to beno more than a half percentage point above the Committee's 2percent longer-run goal,

I and longer-term in�ation expectations continue to be wellanchored."


Introduction 1-2

Empirical literature on in�ation expectations

� Anchoring criteria: Long run expectations are ...

I ... insensitive to macroeconomic news. Gürkaynak et al. (2010)I ... uncorrelated with shorter term expectations. Jochmann et

al. (2010), Gefang et al. (2011), Lemke, Strohsal (2013)

∆πe

t(long) = α0 + α1∆πe

t(short) + ut

→ cross countries spillovers are neglected!

� However: Evidence about a global in�ation factor. Ciccarelli,

Mojonit (2010), Mumtaz, Surico (2012), Bataa et al. (2013)


Introduction 1-2





∆πe


t(short) + ut





Introduction 1-2





∆πe


t(short) + ut





Introduction 1-3

This paper

Extension of the conventional pass through model.

� Focus on in�ation expectations spillovers between US and EA.

� Study structural in�ation expectations shocks.

� Allow for time-varying spillovers. Diebold, Yilmaz (2009)

Model: Markov switching SVAR.

Lanne, Lütkepohl, Maciejowska (2010), Lütkepohl, Net²unajev (2013).

� Identi�cation through heteroscedasticity.

� Test over identifying restrictions. Avoid "ad hoc" restrictions.


Introduction 1-3

This paper

Extension of the conventional pass through model.

� Focus on in�ation expectations spillovers between US and EA.

� Study structural in�ation expectations shocks.

� Allow for time-varying spillovers. Diebold, Yilmaz (2009)

Model: Markov switching SVAR.

Lanne, Lütkepohl, Maciejowska (2010), Lütkepohl, Net²unajev (2013).

� Identi�cation through heteroscedasticity.

� Test over identifying restrictions. Avoid "ad hoc" restrictions.


Introduction 1-4

Outline

1. Introduction X2. Data: Break even in�ation rates

3. Methodology: The MS- SVAR model

4. Results: In�ation expectations spillovers

5. Conclusion


Data: Break even in�ation rates 2-1

US and EA data

Measure of in�ation expectations: Break even in�ation (BEI)

Fisher (1930), Christensen et al. (2010), Joyce et al. (2010)

BEIt(τ) ≡

nominal yield︷︸︸︷yNt (τ) −

real yield︷︸︸︷yRt (τ) =

expectations︷︸︸︷πet (τ) +

risk premium︷︸︸︷φt(τ)

� Weekly data from 2004 -2011 (372 obs.).

� BEIt(τ): One year (implied) forward with τ = 5, 10.

� φt : VIX volatility index.

Söderlind (2011) and Christensen and Gillan (2012)



Figure 1: Weekly 5- and 10-year BEI rates

2004 2005 2006 2007 2008 2009 2010 2011

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

BEI (US 5Y)BEI (EA 5Y)

2004 2005 2006 2007 2008 2009 2010 20111.5

2

2.5

3

3.5

4

BEI (US 10Y)

BEI (EA 10Y)



Figure 2: Weekly VIX and V-STOXX

2004 2005 2006 2007 2008 2009 2010 201110

20

30

40

50

60

70

80

VIXVSTOXX

� Correlation VIX � V-STOXX: 0.98.

� US and EA BEI rates are a�ected by the common

Risk premium shocks.


Methodology: The MS- SVAR model 3-1

Markov Switching Structural VAR

Lanne, Lütkepohl, Maciejowska (2010)

K = 5- dimensional VAR(p)

Yt = ν + A1Yt−1 + · · ·+ ApYt−p + Ut ,

� Orthogonal structural shocks: εt = B−1Ut or Ut = Bεt .

� Ut follows a Markov process with states st = 1, 2, ..,M:

Ut |st ∼ N(0,Σst ), Σst = BΛstB′, and Λ1 = IK .

� If volatility changes of structural shocks are pairwise distinct,

B can be uniquely determined without any restrictions.



Model selection

Table 1: MS-VAR model selectionTable 1: Markov switching- VAR model selection.

Model logLT AIC SC

VAR(3) without MS 783.79 -1377.59 -1006.07MS(2)-VAR(3) 1163.39 -2106.78 -1676.59MS(3)-VAR(3) 1252.51 -2255.03 -1766.18∗MS(4)-VAR(3) 1290.15 -2300.30∗ -1752.78Notes: LT is the value of the likelihood function, AIC = −2 logLT +2×no of free parameters, SC = −2 logLT +log T×no of free parameters.Full sample Jan. 2004 - Jan. 2011 (T = 372 obs.).

representation, see further discussion in Appendix X. Note that a likelihood ratio testwith the corresponding MS(3)-SVAR(3) does not reject the hypothesis of a state-invariantmatrix B. This provides first evidence in favor of the model specification with a statedependent covariance matrix but time-invariant impulse responses.11

The estimated smoothed state probabilities for three Markov states are illustrated inFigure 2. State 1 is the lowest volatility regime and State 3 the highest volatility regime.It can be seen that the first part of the sample until 2007 is mainly associated with State1, while State 2 and 3 dominate the second part of the sample. The period since 2007is well known to coincide with the global financial crisis, the global recession and theEuropean sovereign debt crisis. We label State 1 as a "non-crisis" state and State 2 and3 as "crisis" states. Since crisis times include periods of relaxation, occasionally State 1also materializes from 2007 onwards. State 3 captures the timing of key events like thefailure of the home loan mortgage corporation Fannie Mae and Freddie Mac (July 2008),the investment banks Bear Stearns (March 2008) and Lehman Brothers (September 2008)as well as the downgrading of Greek government debt to junk bond status (April 2010).For that reason State 3 is also referred to as an "outbreak" or "intensification" state.

Given the indications in favor of the reduced form MS(3)-VAR(3) model, we estimate itsstructural counterpart with three volatility regimes and three lags. Although the systemis (statistically) identified by distinct changes in the variances of the structural shocks,Lanne et al. (2010) show that the estimated elements of the matrix B may not correspondto the ordering of the variables in Yt and may be subject to changes in sign. To pick theright label for a given structural shock, we impose zero restrictions on elements in B. Sincethe structural model is already identified, each restriction on B becomes over-identifying.11We also checked whether the assumption about time-invariant impulse responses is too strong. For thatpurpose we have estimated a reduced form VAR(3) where all coefficients (including the constant and thecoefficients of lagged variables) are allowed to switch across states. Impulse responses of reduced formshocks are compared across states.

9



Markov states

Figure 3: State probabilities MS(3)-VAR(3).Figure 2: State probabilities of unrestricted MS(3)-VAR(3) model.

2004 2005 2006 2007 2008 2009 2010 20110

0.5

1

State 1

2004 2005 2006 2007 2008 2009 2010 20110

0.5

1

State 2

2004 2005 2006 2007 2008 2009 2010 20110

0.5

1

State 3

Notes: The states are characterized by three different volatility regimes. State 1 the lowest,State 3 the highest volatility.

Figure 3: Impulse responses to US and EA 5 year inflation-expectations-shocks.

0 5 10 15 20−0.5

0

0.5

1

1.5

US

sho

ck

BEI (US 5Y)

0 5 10 15 20−0.1

0

0.1

0.2

0.3BEI (EA 5Y)

0 5 10 15 20−0.5

0

0.5

1BEI (US 10Y)

0 5 10 15 20−0.2

0

0.2

0.4

0.6BEI (EA 10Y)

0 5 10 15 20−5

0

5

10

15

20VIX

0 5 10 15 20−0.2

0

0.2

0.4

0.6

EA

sho

ck

0 5 10 15 200

0.2

0.4

0.6

0.8

1

0 5 10 15 20−0.2

0

0.2

0.4

0.6

0 5 10 15 20−0.6

−0.4

−0.2

0

0.2

0.4

0 5 10 15 200

5

10

15

Notes: MS(3)-VAR(3) impulse responses of BEI rates to a one unit structural shock (label:inflation-expectations-shock) with 95% confidence bands. Full sample period (374 obs.).

13

� Volatility increasing in states.

� Labeling: 1 "non-crisis", 2 "crisis", 3 "outbreak".



Identi�cation I

Table 2: LR-Tests of pairwise variancesTable 3: Tests for Equality of variances across states.

H0 LR statistic p-value

λ21 = λ22, λ31 = λ32 5.46 0.06λ21 = λ23, λ31 = λ33 10.25 0.00λ21 = λ24, λ31 = λ34 4.23 0.12λ21 = λ25, λ31 = λ35 7.84 0.01λ22 = λ23, λ32 = λ33 10.27 0.00λ22 = λ24, λ32 = λ34 7.73 0.02λ22 = λ25, λ32 = λ35 4.13 0.13λ23 = λ24, λ33 = λ34 4.99 0.08λ23 = λ25, λ33 = λ35 10.29 0.00λ24 = λ25, λ34 = λ35 4.23 0.12Notes: Tests for Equality of λijs of MS(3)-VAR(3). Modelwith State-invariant and unrestricted B.

Table 4: Contemporaneous transmission (Tests of zero restrictions on B).

No. H0 LR df p-value

R0 state-invariant B 9.98 10 0.44R1 R0 + 10Y shocks exogenous 4.60 4 0.33R2 R1 + 5Y US shocks no effect on EA 6.63 6 0.36R3 R1 + 5Y EA shocks no effect on US 8.44 6 0.21R4 R3 + R2 + 5Y&10Y no effect on risk 19.71 12 0.00Note: MS(3)-VAR(3) model. H1 of R1-R4: state-invariant B, H1 of R0: fully unre-stricted. LR = 2(logLT − logLrT ), where LrT denotes the maximum likelihood under H0and LT denotes the maximum likelihood for the model under H1. T = 372 obs.

Table 5: Inflation expectations spillovers.

US 10Y EA 10Y

State 1 2 3 1 2 3

επe(US 5Y) 18.2 28.3 34.7 2.9 3.1 3.7

επe(EA 5Y) 3.3 7.1 5.6 5.7 8.8 8.5

επe(US 10Y) 64.5 45.1 44.2 3.6 1.8 2.2

επe(EA 10Y) 14.0 19.4 15.5 87.8 86.3 84.6

Note: Percentage of risk adjusted BEI variance explained by thestructural inflation expectations shocks (επe) in states 1 (lowestvolatility) to state 3 (highest volatility). Calculated from forecasterror variance decomposition at 100 weeks horizon.

12

� i) distinct variances, ii) state invariant B (p-value 0.44)

=> the MS(3)-SVAR(3) is (statistically) identi�ed.



Identi�cation I

Table 2: LR-Tests of pairwise variancesTable 3: Tests for Equality of variances across states.







US 10Y EA 10Y

State 1 2 3 1 2 3

επe(US 5Y) 18.2 28.3 34.7 2.9 3.1 3.7

επe(EA 5Y) 3.3 7.1 5.6 5.7 8.8 8.5

επe(US 10Y) 64.5 45.1 44.2 3.6 1.8 2.2

επe(EA 10Y) 14.0 19.4 15.5 87.8 86.3 84.6


12

� i) distinct variances, ii) state invariant B (p-value 0.44)

=> the MS(3)-SVAR(3) is (statistically) identi�ed.



Identi�cation II

Assumptions proposed by the literature:

1. Long horizon BEI rates are exogenous. Jochmann et al. (2010)

2. Spillovers across countries are neglected.Gürkaynak et al. (2010)

3. No immediate responses of BEI risk premia to in�ation

expectations shocks. Beechey et al. (2011)

B =

b11 0 0 0 b150 b22 0 0 b25b31 0 b33 b34 b350 b42 b43 b44 b350 0 0 0 b55

, εt =

επe(US 5Y)t

επe(EA 5Y)t

επe(US 10Y)t

επe(EA 10Y)t

ε Riskt



Identi�cation II

Assumptions proposed by the literature:

1. Long horizon BEI rates are exogenous. Jochmann et al. (2010)

2. Spillovers across countries are neglected.Gürkaynak et al. (2010)

3. No immediate responses of BEI risk premia to in�ation

expectations shocks. Beechey et al. (2011)

B =

b11 0 0 0 b150 b22 0 0 b25b31 0 b33 b34 b350 b42 b43 b44 b350 0 0 0 b55

, εt =

επe(US 5Y)t

επe(EA 5Y)t

επe(US 10Y)t

επe(EA 10Y)t

ε Riskt



Testing

Table 3: Testing of identifying restrictions.Table 2: Contemporaneous transmissions (Tests of zero restrictions on B).


R1 10Y IE shocks no effect on 5Y BEI 4.60 4 0.33R2 R1 + 5Y IE shocks no effect on foreign BEI 11.67 8 0.17R3 R2 + 5Y&10Y IE shocks no effect on VIX 19.71 12 0.00Note: Likelihood ratio tests are based on the MS(3)-SVAR(3) model. H1 of all tests:state-invariant B. LR = 2(logLT − logLrT ), where LrT denotes the maximum likelihoodunder H0 and LT denotes the maximum likelihood for the model under H1. T = 372obs.

• Restriction 4: Immediate responses of BEI risk premia to inflation expectation shocksare zero (e.g. Beechey et al., 2011). Inflation expectations shocks originating atthe medium (5Y) and long (10Y) horizon have no instantaneous effect on the VIX.

HR40 : b51 = b52 = b53 = b54 = 0

Table 2 shows the LR- test statistics and corresponding p-values for each of the four re-strictions. The tested restrictions R1 to R4 include the previous restrictions if supportedby the data. The test results lead us to impose Restriction 1, 2 and 3 but to reject Re-striction 4. Not rejecting Restriction 2 and 3 suggests that contemporaneous spillovers ofinflation expectation shocks on the mean of US and EA BEI rates are not systematicallydifferent from zero. Since adjustments in risk premia can not be set to zero (rejection ofR4), conclusions about adjustments in US and EA inflation expectations are not straight-forward.

In the following we present the impulse responses and variance decomposition of the MS(3)-SVAR(3) with Restrictions 1 to 3 imposed. In particular the variance decomposition allowsus to address the role of the risk premium and to derive spillovers of the structural shockson US and EA inflation expectations across the three Markov regimes.

4.2 Inflation expectations spillovers

The primary focus of the present paper is to study inflation expectation spillovers acrossthe US and EA. Since it is usually the long expectation horizon that is of main interest inempirical studies and monetary policy practice (e.g. regarding the anchoring of inflationexpectations), we concentrate our discussion of the empirical results on two perspectives.First, how do the US and EA 5 year inflation expectation shocks pass through to themean of 10 years US and EA BEI rates? Second, how much of the variance of 10 year USand EA inflation expectations can be explained by foreign structural inflation expectation

11


Results: In�ation expectations spillovers 4-1

Impulse responses

Figure 4: Transmission of structural shocks.

0 10 20−0.5

00.5

11.5

BE

I (U

S 5

Y)

US 5Y shock

0 10 20−0.5

0

0.5EA 5Y shock

0 10 20−0.5

0

0.5US 10Y shock

0 10 20−0.5

0

0.5EA 10Y shock

0 10 20−0.04

−0.02

0Risk shock

0 10 20−0.5

0

0.5

BE

I (E

A 5

Y)

0 10 200

0.51

1.5

0 10 20−0.5

0

0.5

0 10 20−0.5

0

0.5

0 10 20−0.04−0.02

00.02

0 10 20−1

0

1

BE

I(U

S 1

0Y)

0 10 20−0.5

0

0.5

0 10 20−0.5

00.5

11.5

0 10 20−1

0

1

0 10 20−0.04−0.02

00.02

0 10 20−0.5

0

0.5

BE

I(E

A 1

0Y)

0 10 20−0.5

0

0.5

0 10 20−0.5

0

0.5

0 10 200

0.51

1.5

0 10 20−0.02−0.01

00.01

0 10 20−10

01020

VIX

0 10 200

10

20

0 10 20−5

05

10

0 10 20−10

01020

0 10 20−0.5

00.5

11.5



Variance spilloversFigure 5: Variance decomposition.

US

EA

Risk

US US

EAEA

RiskRisk

State 1 State 2 State 3

BEI(US 10Y)

EA10Y

USRisk

EA EA

Risk

US

EA

Risk

USBEI(EA 10Y)

� Changes in risk are dominating.

Up to 30% of variance is explained by the risk premium shock!In�ation Expectations spillover


Risk adjusted spillovers

Table 4: In�ation expectations spillovers.

Table 3: Tests for Equality of variances across states.







US 10Y EA 10Y

State 1 2 3 1 2 3

επe(US 5Y) 18.2 28.3 34.7 2.9 3.1 3.7

επe(EA 5Y) 3.3 7.1 5.6 5.7 8.8 8.5

επe(US 10Y) 64.5 45.1 44.2 3.6 1.8 2.2

επe(EA 10Y) 14.0 19.4 15.5 87.8 86.3 84.6


12

� Spillovers EA → US: 17.3%, 10ppt increase in crisis state.

� Spillovers US → EA: 6.5% rather stable across states.

� Weaker anchoring during crisis times.


Conclusion 5-1

Conclusion

Main results about spillovers:

� Cross country spillovers increase during crisis times.

� US expectations stronger a�ected than EA expectations.

� Elevated market uncertainty reduces the anchoring of in�ation

expectations.

Policy conclusion:

� Results speak in favor of ...

I discussion and advice between policy makers about appropriatepolicy measures.

I coordinated policy actions at an international level.


Economy & Finance

Inflation Expectations Spillovers between the United States and Euro Area