10 .mail 2019 toimus Eesti Pangas avatud seminar, kus Cardiffi ülikooli majandusprofessor Konstantinos Theodoridis tutvustas uurimust teemal „Understanding International Long-Term Interest Rate Comovement“. Uurimuses tuleb Suurbritannia majanduse näitel jutuks seos Ameerika Ühendriikide intressimäärade ja väikeste avatud riikide intressimäärade dünaamika vahel.

1. Understanding International Long-Term Interest Rate
Comovement
Michael Chin
Norges Bank Investment Management
Ferre De Graeve
KU Leuven
Thomai Filippeli
Queen Mary University of London
Konstantinos Theodoridis
Cardiff University
Eesti Pank, Tallinn
May 10, 2019

2. Figure: Long-Term Interest Rate Comovement (Wright (2011) data)
72Jan 77Jan 82Jan 87Jan 92Jan 97Jan 02Jan 07Jan
2
4
6
8
10
12
14
Australia
Canada
Germany
Japan
New zealand
Norway
Sweden
Switzerland
UK
US

3. Table: Long-Term Interest Rate Comovement
Correlation with US 10 year rate
Australia 0.93
Canada 0.97
Switzerland 0.84
Germany 0.74
Japan 0.89
Norway 0.63
New Zealand 0.89
Sweden 0.85
United Kingdom 0.93
Average 0.85
Notes: Calculations based on Wright (2011) data.

4. Modern Macro (Stylised Model)
ˆyt − hˆyt−1 = Et ˆyt+1 − hˆyt − σC (1 − h) (ˆrt − Et ˆπt+1)
ˆyt − hˆyt−1 = −σC (1 − h) [Σ∞
i=0Et ˆrt+i − Σ∞
i=0Et ˆπt+1+i ] (1)
ˆπt − κˆπt−1 = β (Et ˆπt+1 − κˆπt) + ξˆyt (2)
ˆrt = ρˆrt−1 + (1 − ρ) (γπ ˆπt + γˆyt) (3)
ˆrL
t =
1
L
ΣL
i=0Et ˆrt+i + tpt (4)

5. Policy Question
On August 2013 the Bank of England launched a forward guidance unconventional
policy program: flattening the expected path of policy rates aiming to reduce long-term
interest rates, in view of ultimately boosting demand and closing the output gap
Economists and policy makers expressed concerns about the ability of the UK
Monetary Policy Committee (MPC) to ‘decouple’ the long end of the UK yield curve
from the US long-term interest rate given they are so highly correlated (0.93)
More generally, if monetary policy is transmitted via long-term interest rate, how
domestic central banks can pursue their own policies?

6. Existing Literature & Proposed Interpretations
Term structure reduced-form models (Diebold et al. (2008), Dahlquist and Hasseltoft
(2013) and Jotikasthira et al. (2015))
Term premia being correlated internationally, an observation which is supported by the
finance literature (Wright (2011) and Dahlquist and Hasseltoft (2013))

7. What We Do
We augment a standard small open-economy model with imperfectly substitutable
government bonds and time-varying term premia
We ensure the estimated model:
fits the real economy and financial data remarkably well
replicates important data moments
delivers term-premium estimates that are comparable with those obtained from
term-structure models
We use the estimated model to talk:
US long-term interest rate
identify what causes the strong co-movement between the long-end of the UK and US
yield curve

8. Preview of the Results: I
We confirm the findings of Del Negro et al. (2017) and Krishnamurthy and
Vissing-Jorgensen (2012), the Savings Glut shock in the model contributes about
90bps (on average) to the fall of the US long-term interest rate post 2000
The US inflation target shock contributes about 90 bps (on average), however, this
number is driven by the Great Recession; post 2008Q4 this estimate increases to 170
bps (on average)
The Savings Glut shock has only a small (and an opposite relative to US) contribution
to UK asset. This is consistent with the Safe Asset literature that wants US to be the
only safe asset provider

9. Preview of the Results: II
Term premia cross-country correlation has a high frequency effect that disappears afet
a year and hence cannot explain the strong co-movement between US and UK
long-term government yields
The US inflation target is the one that explains both the strong correlation and
variability of the UK long-term asset
The cause of comovement is the central bank of the small open economy
accommodating foreign inflation trends, rather than systematically curbing them
Small open economies may find themselves much more affected by changes in the US
inflation trends than the US itself

10. Policy Trilemma
The Policy Trilemma (Obstfeld and Taylor (2003)) suggests that domestic monetary
authorities can pursue their own inflation policies in a perfect capital mobility word as
long as the exchange rate is flexible
We illustrate here that this statements is not true when there are shocks that move
long-term inflation expectations persistently
In this environment if the FED decides to increase its inflation target, the BoE has two
options:
1. either to accommodate this foreign policy change
2. or cause a recession to decouple domestic long-term inflation form the US one

11. Financial Intermediaries: I
Balance Sheet Equation:
bh
κ,t =
bS
κ,t
εbS
t
+
pL,tbL
κ,t
εbL
t
+
qt tp∗
L,tbL,∗
κ,t
εbL
t
Profit Function
ξκ,t = bh
κ,t +
rS
t−1
πc
t
bS
κ,t−1 +
rL
t
πc
t
pL,tbL
κ,t−1 +
rL,∗
t
πc,∗
t
p∗
L,tbL,∗
κ,t−1
revenues
−
bS
κ,t
εbS
t
−
pL,tbL
κ,t
ε
¯bL
t
−
qt p∗
L,tbL,∗
κ,t
ε
¯bL
t
−
rh
t−1
πc
t
bh
κ,t−1 −
x
2
[lqκ,t−1 − ϑlqt−2 − (1 − ϑ) lq]2 Zt−1
πc
t
expenditures

12. Financial Intermediaries: II
Household Interest Rate
ˆrh
t = ˆrS
t + ˜x lqt − ϑlqt−1 + ˆεbS
t
Long-Term Interest Rate
ˆrL
t = (1 − βκ)
∞
i=0
(βκ)i
Et ˆrS
t+i
Policy Rate Expectations (PEt )
+ (1 − βκ)
∞
i=0
(βκ)i
EtˆεbS
t+i − EtˆεbL
t+i
Risk Premium (RPt )
+
(1 − βκ) ˜x (1 + δ)
δ
∞
i=0
(βκ)i
Et lqt+i − ϑlqt+i−1
Liquidity Premium (LPt )

13. Financial Intermediaries: III
Long Term Interest Rate
ˆrL,∗
t = PE
∗
t + RP
∗
t + LP
∗
t
Term Premium (TP
∗
t )
UIP
Et∆ˆqt+1 = ˆrS
t − Etπc
t+1 − ˆrS,∗
t − Etπc,∗
t+1
Real Interest Rate Differentials
+
˜x (1 + δ)
δ
lqt − ϑlqt−1 + ˆεbS
t − ˆε
¯bL
t −
˜x∗
(1 + δ∗
)
δ∗ lq
∗
t − ϑlq
∗
t−1 + ˆεbS,∗
t − ˆε
¯bL,∗
t
Endogenous UIP Deviations
ˆqt = RR
Diff
t + TP
Diff
t

14. Fit of the Model
76Q1 86Q1 96Q1 06Q1 15Q4
-4
-2
0
2
4
6
8
UK GDP Growth
76Q1 86Q1 96Q1 06Q1 15Q4
-2
0
2
4
UK Wage Growth
76Q1 86Q1 96Q1 06Q1 15Q4
5
10
15
20
UK Inflation
76Q1 86Q1 96Q1 06Q1 15Q4
-5
0
5
10
15
20
25
UK Import Inflation
76Q1 86Q1 96Q1 06Q1 15Q4
10
15
20
Real Exchange Rate
76Q1 86Q1 96Q1 06Q1 15Q4
10
12
14
16
18
20
22
UK Policy Rate
76Q1 86Q1 96Q1 06Q1 15Q4
0
10
20
30
40
50
60
UK 10-year yield
76Q1 86Q1 96Q1 06Q1 15Q4
-2
0
2
4
6
8
US GDP Growth
76Q1 86Q1 96Q1 06Q1 15Q4
0
2
4
6
US Wage Growth
76Q1 86Q1 96Q1 06Q1 15Q4
6
8
10
12
US Inflation
76Q1 86Q1 96Q1 06Q1 15Q4
10
15
20
US Policy Rate
76Q1 86Q1 96Q1 06Q1 15Q4
10
12
14
16
18
20
US 10-year yield

15. Moments
Mnemonic Data Mode 5th
95th
ρrL,rL,∗ 0.93 0.93 0.93 0.94
ρrS ,rL 0.90 0.89 0.89 0.90
ρrS ,rS,∗ 0.84 0.79 0.79 0.80
ρy,y∗ 0.65 0.65 0.64 0.66
ρπ,π∗ 0.85 0.83 0.83 0.84
ρc,c∗ 0.62 0.61 0.60 0.62
σrS 4.50 4.67 4.62 4.72
σrL 3.63 3.48 3.43 3.53
σ∗
rS 4.02 3.56 3.50 3.62
σ∗
rL 3.12 2.68 2.61 2.73
σy 2.19 2.15 2.08 2.22
σy∗ 2.09 2.12 2.03 2.18
σπ 4.07 4.69 4.64 4.74
σ∗
π 2.04 3.00 2.95 3.05
σq 11.22 11.36 11.28 11.43

16. Term Premium Estimates (US, UK)
76Q4 82Q1 87Q3 93Q1 98Q3 04Q1 09Q3 15Q1
-3
-2
-1
0
1
2
3
98Q3 01Q2 04Q1 06Q4 09Q3 12Q2 15Q1
-1
-0.5
0
0.5
1
1.5

17. Reduced versus Structural Analysis
ˆrS,∗
t = λW ,L
rS,∗ LW
t + λUS,L
rS,∗ LUS
t + rS,∗
t
ˆrL,∗
t = λW ,L
rL,∗ LW
t + λW ,S
rL,∗ SW
t + λUS,L
rL,∗ LUS
t + λUS,S
rL,∗ SUS
t + rL,∗
t
ˆr5L,∗
t = λW ,L
r5L,∗ LW
t + λW ,S
r5L,∗ SW
t + λUS,L
r5L,∗ LUS
t + λUS,S
r5L,∗ SUS
t + r5L,∗
t
ˆrS
t = λW ,L
rS LW
t + λUK,L
rS LUK
t + rS
t
ˆrL
t = λW ,L
rL LW
t + λW ,S
rL SW
t + λUK,L
rL LUK
t + λUK,S
rL SUK
t + rL
t
ˆr5L
t = λW ,L
r5L LW
t + λW ,S
r5L SW
t + λUK,L
r5L LUS
t + λUK,S
r5L SUS
t + r5L
t
LW
t = φW
L,LLW
t−1 + φW
L,S SW
t−1 + σW
L vLW
t
SW
t = φW
S,LLW
t−1 + φW
S,S SW
t−1 + σW
S vSW
t
LUS
t = φLW
LUS LW
t−1 + φSW
LUS SW
t−1 + φLUS
LUS LUS
t−1 + φSUS
LUS SUS
t−1 + σUS
L vLUS
t
SUS
t = φLW
SUS LW
t−1 + φSW
SUS SW
t−1 + φLUS
SUS LUS
t−1 + φSUS
SUS SUS
t−1 + σUS
S vLUS
t
LUK
t = φLW
LUK LW
t−1 + φSW
LUK SW
t−1 + φLUS
LUK LUK
t−1 + φSUS
LUK SUK
t−1 + σUK
L vLUK
t
SUK
t = φLW
SUK LW
t−1 + φSW
SUK SW
t−1 + φLUS
SUK LUK
t−1 + φSUS
SUK SUK
t−1 + σUK
S vLUK
t

18. Reduced versus Structural Analysis (continued)
Variables Simulations
Data Median 5th
95th
World US UK World US UK World US UK World US
US 3 month 66.35 33.65 0.00 42.69 57.31 0.00 10.68 9.90 0.00 90.10 89.32
US 5 year 84.49 15.51 0.00 65.72 34.28 0.00 19.63 2.00 0.00 98.00 80.37
US 10 year 90.42 9.58 0.00 76.28 23.72 0.00 29.27 1.77 0.00 98.23 70.73
UK 3 month 85.94 0.00 14.06 78.05 0.00 21.95 21.25 0.00 1.09 98.91 0.00 7
UK 5 year 98.99 0.00 1.01 83.32 0.00 16.68 16.34 0.00 1.04 98.96 0.00 8
UK 10 year 99.27 0.00 0.73 91.21 0.00 8.79 17.60 0.00 0.56 99.44 0.00 8

19. Table: Decomposing Comovement via the DSGE Model
ρ rL
, rL∗
σ rL∗
σ rL
Data 0.93 3.12 3.63
US Productivity 0.98 0.12 0.13
US Monetary policy 0.67 0.16 0.06
US LT debt risk premium -0.32 1.16 0.25
US ST debt risk premium 0.84 0.15 0.06
US Wage markup -0.06 0.10 0.02
US Price markup 0.92 0.02 0.01
US Inflation target 1.00 1.41 2.33
Notes: The table suppresses UK shocks since these cannot generate variance in the US due to
the small open economy nature of the UK in the model. In other words, conditional on UK shocks
σ(rL∗) = ρ(rL, rL∗) = 0. In the σ(rL) -column the contributions do not sum to the total data
variance because of the additional variance caused by UK-specific shocks (not reported).

20. Figure: US Inflation Target Shock
5 10 15
2
4
6
8
10-3GDP US
5 10 15
0.08
0.1
0.12
CPI Inflation US
5 10 15
-20
-10
0
10-3Real rate US
5 10 15
0.09
0.1
0.11
0.12
Policy rate US
5 10 15
0.106
0.108
0.11
Long rate US
5 10 15
0.06
0.08
0.1
0.12
GDP UK
5 10 15
0.3
0.4
0.5
0.6
CPI Inflation UK
5 10 15
-0.4
-0.2
0
Real rate UK
5 10 15
0.1
0.15
0.2
0.25
Policy rate UK
5 10 15
0.12
0.13
0.14
Long rate UK
5 10 15
0.26
0.28
0.3
0.32
Domestic inflation UK
5 10 15
0.5
1
1.5
2
2.5
Import inflation UK
5 10 15
0.6
0.8
1
1.2
Real exchange rate

21. Intuition
RER Definition
∆qt = ∆st + π∗
t − πt
Perfect Capital Mobility
lim
t→∞
∆qt = 0
UIP
Et∆st+1 = rS
t − rS,∗
t =⇒ rS
− π = rS,∗
− π∗
UK and US Policy Reaction Functions
rS
= φππ
rS,∗
= φ∗
ππ∗
Long Run Inflation Expectations Relation
π =
φ∗
π − 1
φπ − 1
π

22. Figure: US Inflation Target Shock Under Counterfactual Calibrations
5 10 15
-4
-2
0
2
4
6
8
10
-3 GDP US
5 10 15
0.04
0.06
0.08
0.1
0.12
CPI Inflation US
5 10 15
-20
-15
-10
-5
0
5
10
-3Real rate US
5 10 15
0.02
0.04
0.06
0.08
0.1
0.12
Policy rate US
5 10 15
0.02
0.04
0.06
0.08
0.1
Long rate US
5 10 15
-10
-5
0
10
-3 GDP UK
5 10 15
0
0.01
0.02
0.03
0.04
CPI Inflation UK
5 10 15
-0.01
0
0.01
0.02
0.03
0.04
Real rate UK
5 10 15
0
0.01
0.02
0.03
0.04
Policy rate UK
5 10 15
-12
-10
-8
-6
-4
-2
10
-3Long rate UK
5 10 15
-2
0
2
4
10
-3Domestic inflation UK
5 10 15
0
0.05
0.1
0.15
0.2
0.25
Import inflation UK
5 10 15
0.02
0.04
0.06
0.08
0.1
0.12
Real exchange rate
High CB response
Low persistence

23. Table: The Effect of US Long-Term Inflation Expectations on US and UK Inflation
Coefficient on US LT expectations (ˆβ)
Regression: i = US i = UK
πi
t = c + βEt(πUS
t+40) + εt 1.13 1.75
(28.86) (12.70)
πi
t = c + β∆Et(πUS
t+40) + εt 1.44 2.73
(1.51) (1.49)
πi
t = c + ρπi
t−1 + βEt(πUS
t+40) + εt -0.04 0.15
(-1.25) (2.30)
πi
t = c + ρπi
t−1 + β∆Et(πUS
t+40) + εt 0.32 1.01
(2.64) (2.33)
Notes: t-stats in parenthesis. Long-term inflation expectations from Federal Reserve Board.
Sample: 1975Q1-2015Q4.

24. Figure: BVAR
10 20 30 40
0
0.05
0.1
0.15
0.2
0.25
0.3
Uhlig
10 20 30 40
0
0.1
0.2
0.3
0.4
10 20 30 40
0
0.2
0.4
0.6
0.8
10 20 30 40
-0.1
0
0.1
0.2
0.3
US Long Term
Inflation
Expectations
10 20 30 40
0
0.05
0.1
0.15
Choleski
US Inflation
10 20 30 40
0
0.05
0.1
0.15
UK Inflation
10 20 30 40
0
0.1
0.2
0.3
0.4
0.5
Differences
10 20 30 40
-0.1
0
0.1
0.2
0.3
0.4
Notes: IRF from a BVAR on (Et (πUS
t+40), πUS
t , πUK
t ) under two different identification schemes. Choleski: shock to Et (πUS
t+40) with Et (πUS
t+40) ordered first. Uhlig:
shock that maximizes FEVD of Et (πUS
t+40) at horizon t to t + 40. Solid line: median response. Shaded area: 16th-84th percentile bands. IRFs in the fourth column
measure the response of πUK
t+h − πUS
t+h. Sample: 1975Q1-2015Q4.

25. US Long Term Interest Rates Post 2000
98Q1 00Q1 02Q1 04Q1 06Q1 08Q1 10Q1 12Q1 14Q1 15Q4
-4
-3
-2
-1
0
1
Savings Glut
Financial
Supply
UK Policy
Inlfation Target

26. UK Long Term Interest Rates Post 2000
98Q1 00Q1 02Q1 04Q1 06Q1 08Q1 10Q1 12Q1 14Q1 15Q4
-4
-3
-2
-1
0
1
Savings Glut
Financial
Supply
UK Policy
US Policy
US Inlfation Target

27. Co-Movement: Savings Glut Shock
2 6 10
0.4
0.6
0.8
1
1.2
Savings Glut
2 6 10
0.04
0.06
0.08
US GDP
2 6 10
0.005
0.01
0.015
0.02
0.025
US Wages
2 6 10
0.011
0.012
0.013
0.014
0.015
US Inflation
2 6 10
0
0.02
0.04
0.06
0.08
US Policy Rate
2 6 10
-1
-0.8
-0.6
-0.4
US Long Rate
2 6 10
-1
-0.8
-0.6
-0.4
US Term Premium
2 6 10
0
0.1
0.2
UK GDP
2 6 10
0.3
0.4
0.5
0.6
UK Wages
2 6 10
-0.4
-0.2
0
UK Inlfation
2 6 10
-0.2
0
0.2
UK Policy Rate
2 6 10
-0.02
0
0.02
0.04
0.06
UK Long Rate
2 6 10
-0.26
-0.25
-0.24
UK Term Premium
2 6 10
-6
-4
-2
Real Exchange Rate
2 6 10
0.06
0.08
0.1
Domestic Inflation
2 6 10
-3
-2
-1
0
Imported Inflation
2 6 10
1
2
3
4
Exports
2 6 10
3
4
5
6
7
Imports
2 6 10
-2.4
-2.2
-2
-1.8
-1.6
Net Trade
2 6 10
0
0.2
0.4
Export Prices

28. UIP Reversal
1 2 3 4 5 6 7 8 9 10 11 12
0
2
4
6
8
10
No-Stationary US Inflation Target Shock (autocorrelation equal to 0.999)
Real Interest Rate Differential
Term Premium Diferential
1 2 3 4 5 6 7 8 9 10 11 12
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Stationary US Inflation Target Shock (autocorrelation equal to 0.99)

29. Conclusion
We develop a small open economy micro-founded model to explain the stylised fact
that domestic long-term interest co-move more strongly with US long than domestic
short-term interest rates
The model fits the data remarkably well and its predictions are consistent with the
literature
The strong co-movement between US and UK long-term government yields is induced
by US inflation target shocks and perfect capital mobility
Our analysis has direct implications about the Policy Trilemma

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Del Negro, M., D. Giannone, M. Giannoni, and A. Tambalotti (2017): “Safety, Liquidity, and the Natural Rate of Interest,” Brookings Conference on
Economic Activity: Spring 2017, Brookings Institution Press, 235–294.
Diebold, F. X., C. Li, and V. Z. Yue (2008): “Global yield curve dynamics and interactions: A dynamic Nelson-Siegel approach,” Journal of Econometrics, 146,
351–363.
Jotikasthira, C., A. Le, and C. Lundblad (2015): “Why do term structures in different currencies co-move?” Journal of Financial Economics, 115, 58 – 83.
Krishnamurthy, A. and A. Vissing-Jorgensen (2012): “The Aggregate Demand for Treasury Debt,” Journal of Political Economy, 120, 233–267.
Obstfeld, M. and A. M. Taylor (2003): “Globalization and Capital Markets,” in Globalization in Historical Perspective, National Bureau of Economic Research, Inc,
NBER Chapters, 121–188.
Wright, J. H. (2011): “Term Premia and Inflation Uncertainty: Empirical Evidence from an International Panel Dataset,” American Economic Review, 101, 1514–34.