INTERNATIONAL LINKAGES AND THE

CHANGING NATURE OF INTERNATIONAL

BUSINESS CYCLES

Wataru Miyamoto Thuy Lan NguyenUniversity of Hong Kong SF Fed & Santa Clara University

CBMMW – Norges BankOctober 8, 2020

The views are of the authors and not of the SF Fed or the Federal Reserve System

1

INTERNATIONAL LINKAGES

I Change in total trade shares: Increase in openness in mostcountriesI (Exports+Imports) over VA in manufacturing increased

from 80% in 1970 to nearly 250% in 2007 at median.

1970 1975 1980 1985 1990 1995 2000 2005

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Exp

orts

and

Impo

rts

over

Val

ue A

dded

Trade Openness for Each Sector

ManufacturingNon-Manufacturing

2

INTERNATIONAL LINKAGES

I Change in trade partnersI Example: US trades more with China and Mexico than with

Japan in 2007

1970 1975 1980 1985 1990 1995 2000 2005

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Sha

re o

f Sec

tor

VAUSA Manufacturing Trade Partners

CanadaChinaJapanMexico

3

CHANGING NATURE OF BUSINESS CYCLES

1980 1985 1990 1995 2000

0.6

0.7

0.8

0.9

1

Median Volatilities

OutputConsumptionInvestment

I The median 10-year rolling over standard deviations of theHP-filtered output, consumption and investment in 23 countriesbetween 1970 and 2007.

4

OUR PAPERI Question: To what extent does change in international

input-output linkages affect business cycles in differentcountries?

I Approach: Build a 24-country 2-sector augmented IRBCmodelI Match with World IO table changes from 1970–2007I Decompose total effects of World IO table changes into

several channelsI Answer:

I Changes in international input-output linkages explain15% of drop in output volatilities at median in the baselineI Compare to about 40% in the data

I The effects are heterogeneous across countriesI International linkages tend to stabilize domestic volatilities

but more risk from foreign shocksI Estimates depend on degrees and mechanism of

transmission in the model5

RELATIONSHIP BETWEEN INTERNATIONAL

LINKAGES AND OUTPUT VOLATILITY

I 2 country 2 sector model: Canada and the USI Varies trade shares in manufacturing sector

0 0.5 1(Export+Import)/VA: Country 1

0

1

2

3

SD

of V

A: C

ount

ry 1

Baseline

TotalDomestic ShockForeign Shock

0 0.5 1(Export+Import)/VA: Country 1

0

1

2

3

4

SD

of V

A: C

ount

ry 1

Larger Foreign Shocks

6

WORLD IO CHANGES & CHANGING

VOLATILITIES

1980 1990 2000

0.6

0.7

0.8

0.9

1

Total

Model: Median25-7510-90Data: Median

1980 1990 2000

0.6

0.7

0.8

0.9

1

International Linkage

1980 1990 2000

0.6

0.7

0.8

0.9

1

Sector Size

7

WORLD IO CHANGES & CHANGING OUTPUT

VOLATILITIES: HETEROGENEITYAll countries Relative Sizes

1980 1990 2000

0.7

0.8

0.9

1Canada

TotalInternational LinkageSector Size

1980 1990 2000

0.7

0.8

0.9

1US

1980 1990 2000

0.85

0.9

0.95

1

1.05Mexico

8

MULTIPLIERS OVER TIMEω(year) based on entire World IO Table change

1970 1980 1990 20000

0.1

0.2

0.3

US

1970 1980 1990 20000

0.02

0.04

0.06

0.08China

Median25-7510-90

1970 1980 1990 20000

0.05

0.1

0.15Japan

1970 1980 1990 20000

0.1

0.2

0.3

Germany

9

FULL PRESENTATION

10

RELATED LITERATURE

I Accounting volatility changes using network structureI Foerster et al. (2011), Moro (2012), Carvalho and Gabaix (2013),

Atalay (2017)

I Trade, Diversification, and VolatilitiesI di Giovanni and Levchenko (2009), Caselli et al. (2017)

I International Business Cycle ComovementI BKK (1992), Kose and Yi (2002), Burstein et al. (2008), Johnson

(2013), Davis and Huang (2011), Liao and Santacreu (2015), Nosalet al. (2015), Miyamoto and Nguyen (2017), de Soyres (2018)

I Role of intermediate good tradeI Burstein et al. (2008), di Giovanni and Levchenko (2010), Bems et

al. (2015)

11

MODEL OVERVIEW

I 24-country, 2-sector augmented International RealBusiness Cycle ModelI To capture the input-output linkages within and across

countries and generate endogenous transmission of shocksacross countries

I Additional FeaturesI Intermediate goods trade across countries and sectorsI Variable capacity utilizationI Variable markup generated by firms’ entry and exitI Investment adjustment cost

12

PRODUCTION OVERVIEW

(C,I)

Manufacturing/Nonmanufacturing

Local Industry l ∈ (0, 1)

Firms N

(C,I)

Manufacturing/Nonmanufacturing

Local Industry l ∈ (0, 1)

Firms N

13

FINAL AND INTERMEDIATE GOODS

PRODUCTION

I Final good firms produce consumption goods:

C (i) =

[S

∑s=1

(ωCF (s, i))1

γF (fC (s, i))γF−1

γF

sectoral final composite good

] γFγF−1

fC (s, i) =

[I

∑j=1

(ωCf ((j, s) , i)

) 1γf (f ((j, s) , i))

γf−1γf

shipment from country j to i

] γfγf−1

I Similar for Investment I(i) and Intermediate goods M(i)

14

RAW OUTPUT PRODUCTION

Firms have market power, modeled by firms’ entry and exit(Jaimovich and Floetotto (2008 JME))Variable markup: depending on states of business cycles, highin slumps and low in boomsI Each local industry has a limited number of firmsI Local output L (i, s|l) where l ∈ [0, 1]

L (i, s|l) = Nf (i, s|l)−1

γL−1

[ Nf

∑k=1

q (i, s|l, f )γL−1

γL

] γLγL−1

I Raw sector output is given by:

Q (i, s) =[∫ 1

0L (i, s|l)

γQ−1γQ dl

] γQγQ−1

15

RAW OUTPUT PRODUCTION

I Production technology for each firm f :

q (i, s|l, f ) =

ωq (i, s)1

γq(

A (i, s)K (i, s|l, f )α H (i, s|l, f )1−α) γq−1

γq

+(1−ωq (i, s)

) 1γq (M (i, s|l, f ))

γq−1γq

γq

γq−1

−φ (i, s)

I Productivity process:

ln At (i, s) = ρA ln At−1 (i, s) + eAt (i, s)

16

HOUSEHOLDS

max E0

∞

∑t=0

βtU(C(i), H(i))

subject to budget constraint:

Ct(i) + pIt(i)It(i) + Etεt(i)rt,t+1Bt+1(i) ≤

Wt(i)Ht(i) + Rkt (i) (ut(i)Kt(i)) + εt(i)Bt(i)

Capital accumulation:

Kt+1(i) ≤ (1− δ(ut(i)))Kt(i) + It(i)(

1− S(

It(i)It−1(i)

))

17

RESOURCE CONSTRAINTS

n (i)Q (i, s) =I

∑j=1

n (j) [fC ((i, s) , j) + fI ((i, s) , j)]

+I

∑j=1

S

∑k=1

n (j)m ((i, s) , (j, k))

where n(i) is the size of country i.

Additionally, ∑Ss=1 H(i, s) = H(i) and ∑S

s=1 K(i, s) = u(i)K(i)

18

SHOCK TRANSMISSION: TWO-COUNTRY

TWO-SECTOR MODEL

0 2 4 6 80

1

2

VA

Country 1Country 2

0 2 4 6 80

0.5

1

1.5Consumption

0 2 4 6 80

2

4

Investment

0 2 4 6 80

0.5

1

Hours

0 2 4 6 80

1

2

3

VA Sector 1

0 2 4 6 80

0.5

1

1.5

2VA Sector 2

19

RELATIONSHIP BETWEEN INTERNATIONAL

LINKAGES AND OUTPUT VOLATILITY

I 2 country 2 sector model: Canada and the USI Varies trade shares in manufacturing sector

0 0.5 1(Export+Import)/VA: Country 1

0

1

2

3

SD

of V

A: C

ount

ry 1

Baseline

TotalDomestic ShockForeign Shock

0 0.5 1(Export+Import)/VA: Country 1

0

1

2

3

4

SD

of V

A: C

ount

ry 1

Larger Foreign Shocks

20

MODEL MECHANISM: WHY VOLATILITY

STABILIZED

Domestic positive productivity shockI Supply side: domestic firms try to use more intermediate

inputsI More openness⇒ need foreign intermediate inputs which

is not supplied more as no change in foreign productivity⇒ constrain production relative to closed economy case

I Demand side: foreign households/firms try to importdomestic goodsI More openness⇒more dependent on foreign demand⇒ foreign demand does not increase much as foreigneconomy is not directly impacted by productivity shock⇒ constrain demand for domestic goods relative to closedeconomy case

21

RELATIONSHIP BETWEEN RELATIVE SECTOR

SIZE AND OUTPUT VOLATILITY

2 2.5 3 3.5 4Size of Sector2/Sector1

2

2.1

2.2

2.3

2.4

2.5

2.6SD of VA: Country 1

22

CALIBRATION: DATA

I Data for 23 countries between 1970 and 2007I Australia, Austria, Belgium, Brazil, Canada, China,

Germany, Denmark, Spain, Finland, France, UK, Greece,India, Ireland, Italy, Japan, Korea, Mexico, Netherland,Portugal, Sweden, USA

I Several data sources:I NBER–UN and CEPII detailed bilateral trade dataI World IO table from Johnson and Noguera (2016)I OECD quarterly data on output, consumption, investmentI World Bank WDI national account dataI UN data for gross and value added data

23

CALIBRATION

Common parameters:

Parameter Valueβ 0.96 Discount factorα 0.36 Labor share parameterδ 0.1 Depreciation rateσ 2 Inverse of IESν 1 Inverse of Frisch labor supplyκ 0.1 Wealth effect parameterδ′′uδ′u

u 0.05 Inverse utilization elasticityγF 1 ES between sectoral goodsγf 1 ES between home and foreign goodsεmarkup 0.12 Elasticity of markups 0.1 Investment adjustment costρA 0 Shock persistence

24

CALIBRATION

Calibrate productivity shock standard deviations

I Let ω be the vector of steady state parameters that includeall share and size parameters in IO table

I Calibrate ω: Average of World IO table (1984–1993)I Midpoint of the sampleI Average to eliminate the effects of business cycles

I Match the standard deviations of sectoral value added ineach country

σdataVA(i, s) = σmodelVA(i, s)

25

MODEL FIT

Data Model

Standard deviationsOutput 1.3 1.5Consumption 1.2 1.0Investment 3.8 3.3Manufacturing real value added 2.7 2.7Non-manufacturing real value added 1.4 1.4

AutocorrelationOutput 0.32 0.26Consumption 0.35 0.23Investment 0.39 0.47Manufacturing real value added 0.25 0.12Non-manufacturing real value added 0.32 0.3

Notes: The second moments reported in both the model and the data are taken as median across countries using HPfiltered data between 1971 and 2007.

26

DECOMPOSITION: WORLD IO TABLE

TABLE: General World IO table

CA CA US US CA US GOs1 s2 s1 s2 final final

CA s1 M11 M12 M13 M14 F11 F12 Q1

CA s2 M21 M22 M23 M24 F21 F22 Q2

US s1 M31 M32 M33 M34 F31 F32 Q3

US s2 M41 M42 M43 M44 F41 F42 Q4

VA V1 V2 V3 V4

GO Q1 Q2 Q3 Q4

Notes: M is IS× IS, V is IS× 1, Q is IS× 1 and F is IS× I.

27

EXPERIMENT 1: WORLD IO TABLE CHANGE

I Fix shock processes

I We solve the model corresponding to each year

I Denote ω(year) to be the steady state for each year

I Calibrate ω(year) using 11-year rolling mean WIOT andsolve modelI Mean of WIOT 1985-1995→ ω(1990)→ σY

1990I Mean of WIOT 1986-1996→ ω(1991)→ σY

1991I Mean of WIOT 1987-1997→ ω(1992)→ σY

1992I σY

1992 − σY1990 is the effect of World IO changes between 1990

and 1992

28

DECOMPOSITION

I Total effects include several changes such as changes in1. international input-output linkages

2. relative sector sizes

3. relative country sizes

4. domestic input-output linkages

5. value added shares in production

I Goal is to isolate the effects of these changes.

I Focus on (1) and (2)

29

EXPERIMENT 2: INTERNATIONAL LINKAGESGoal: Isolate changes due to openness from others such assectoral compositions of inputs and sector sizes

I Construct hypothetical W̃IOT at each year TI Use information in both T and T− 1I In W̃IOT, only international dimension changes based on

WIOT at T

I Calibrate ω(year) using W̃IOT and solve modelI Actual WIOT 1990→ ω(1990)→ σY

1990

I Hypothetical W̃IOT 1991→ ω(1991)→ σ̃Y1991

I σ̃Y1991 − σY

1990 is the effect of international linkage changesbetween 1990 and 1991

I Accumulate the effects over time30

EXPERIMENT 2: INTERNATIONAL LINKAGES

Construction of W̃IOT

CA CA US US CA US GOs1 s2 s1 s2 final final

CA s1 m11 m12 m13 m14 f11 f12 Q1

CA s2 m21 m22 m23 m24 f21 f22 Q2

US s1 m31 m32 m33 m34 f31 f32 Q3

US s2 m41 m42 m43 m44 f41 f42 Q4

VA v1 v2 v3 v4

GO Q1 Q2 Q3 Q4

where technical coefficients mij =MijQj

and fij =FijQi

and vi =ViQi

I Keep shares of VA in GOI Keep m11 + m31

I Change m11/m31, recover M’sI Calculate F = GO−M, change f11/f21

31

EXPERIMENT 3: RELATIVE SECTORAL SIZE

Goal: Isolate changes due to sector size from others such assectoral compositions of inputs, country sizes

I Construct hypothetical W̃IOT at each year TI Use information in both T and T− 1I In W̃IOT, only relative sector sizes based on WIOT at T

I Calibrate ω(year) using W̃IOT and solve modelI Actual WIOT 1990→ ω(1990)→ σY

1990

I Hypothetical W̃IOT 1991→ ω(1991)→ σ̃Y1991

I σ̃Y1991 − σY

1990 is the effect of international linkage changesbetween 1990 and 1991

I Accumulate the effects over time32

EXPERIMENT 3: RELATIVE SECTORAL SIZE

Construction of W̃IOTCA CA US US CA US GOs1 s2 s1 s2 final final

CA s1 m11 m12 m13 m14 f11 f12 Q1

CA s2 m21 m22 m23 m24 f21 f22 Q2

US s1 m31 m32 m33 m34 f31 f32 Q3

US s2 m41 m42 m43 m44 f41 f42 Q4

VA v1 v2 v3 v4

GO Q1 Q2 Q3 Q4

where technical coefficients mij =MijQj

and fij =FijQi

and vi =ViQi

I Change Q1/Q2

I Calculate F = GO−M, keep f11/f21

33

WORLD IO CHANGES & CHANGING

VOLATILITIES

1980 1990 2000

0.6

0.7

0.8

0.9

1

Total

Model: Median25-7510-90Data: Median

1980 1990 2000

0.6

0.7

0.8

0.9

1

International Linkage

1980 1990 2000

0.6

0.7

0.8

0.9

1

Sector Size

34

WORLD IO CHANGES & CHANGING OUTPUT

VOLATILITIES: HETEROGENEITYAll countries Relative Sizes

1980 1990 2000

0.7

0.8

0.9

1Canada

TotalInternational LinkageSector Size

1980 1990 2000

0.7

0.8

0.9

1US

1980 1990 2000

0.85

0.9

0.95

1

1.05Mexico

35

INTERNATIONAL LINKAGE CHANGES’ EFFECTS

ON VOLATILITY

-0.8 -0.6 -0.4 -0.2 0International linkages change 1970--2007

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Tot

al tr

ade

shar

e in

VA

cha

nge

1970

--20

07

AUS

AUT

BEL

BRA

CAN

CHN

DEUDNKESP

FIN

FRA

GBR

GRCIND

IRL

ITA

JPN

KOR

MEXNLD

PRT

SWE

USA

36

RELATIVE SECTOR SIZE CHANGES’ EFFECTS ON

VOLATILITY

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2Sector size effects

-0.15

-0.1

-0.05

0

0.05

0.1

Cha

nges

in m

anuf

actu

ring

shar

e in

VA

AUSAUT

BEL

BRA

CAN

CHN

DEU

DNK

ESP

FIN

FRA

GBR

GRC

IND

IRL

ITAJPN

KOR

MEX

NLD

PRTSWE

USA

37

OTHER VARIABLES

1980 1990 2000

0.6

0.7

0.8

0.9

1C : Total

1980 1990 2000

0.6

0.7

0.8

0.9

1C : International Linkage

1980 1990 2000

0.6

0.7

0.8

0.9

1C : Sector Size

1980 1990 2000

0.6

0.7

0.8

0.9

1

I : Total

1980 1990 2000

0.6

0.7

0.8

0.9

1

I : International Linkage

1980 1990 2000

0.6

0.7

0.8

0.9

1

I : Sector Size

Median25-7510-90

38

INSPECTING MECHANISM

1980 1990 2000

0.8

0.85

0.9

0.95

1Baseline

1980 1990 2000

0.85

0.9

0.95

1RBC

1980 1990 2000

0.8

0.85

0.9

0.95

1Low Elasticity

1980 1990 2000

0.9

1

1.1

Correlated Shock

1980 1990 2000

0.8

0.9

1Confidence Shock

BaselineRobustnessBaseline 25-75Robustness 25-75

39

POTENTIAL RISK: CROSS-COUNTRY VALUE

ADDED MULTIPLIERS

I How much do shocks in one country affect other countriesover time?I Our model can predict foreign shocks can be more

important over time

I Model provides decomposition but depends on calibratedfixed standard deviations of shocksI Decomposition exercise is about the long runI A rare large shock in foreign country as in Great Recession

can increase observed volatility with more linkagesI Even when theoretical long run volatility declines

I We next isolate the effects of a unit GDP shock in onecountry to other countries over time

40

POTENTIAL RISK: CROSS-COUNTRY VALUE

ADDED MULTIPLIERS

I Define Cross-country value added multipliers

MHUS =

∑Hh=1

∂VAX,h∂AUS,1

∑Hh=1

∂VAUS,h∂AUS,1

(1)

with X as other countries in the sampleI Over H years, if US output goes up by 1%, Country X’s

output goes up by M%I Account for only degree of transmission of shocks across

countries over time

41

MULTIPLIERS OVER TIMEω(year) based on entire World IO Table change

1970 1980 1990 20000

0.1

0.2

0.3

US

1970 1980 1990 20000

0.02

0.04

0.06

0.08China

Median25-7510-90

1970 1980 1990 20000

0.05

0.1

0.15Japan

1970 1980 1990 20000

0.1

0.2

0.3

Germany

42

CONCLUSION

I Our model implies that international linkages explain asizable change in aggregate volatilitiesI Magnitude depends on the mechanism and transmission

channels

I Increase in potential risk of global recession

43

EXTRA SLIDES

44

RELATIVE SECTOR SIZES

Back

1970 1975 1980 1985 1990 1995 2000 2005

0.25

0.3

0.35

0.4

GO Shares of Manufacturing Sector

MedianCanadaUSMexico25-75% percentile

45

Back

1980 2000

0.9

0.95

1AUS

1980 2000

0.8

0.9

1AUT

1980 2000

0.8

0.9

1BEL

1980 2000

0.8

1BRA

1980 2000

0.8

0.9

1CAN

1980 2000

0.5

1CHN

1980 2000

0.70.80.9

DEU

1980 2000

0.9

1DNK

1980 2000

0.8

0.9

1ESP

1980 20000.8

0.9

1FIN

1980 20000.9

0.95

1FRA

1980 20000.850.9

0.95

GBR

1980 2000

0.9

0.95

1GRC

1980 2000

0.9

1IND

1980 2000

0.8

1

IRL

1980 2000

0.8

0.9

1ITA

1980 2000

0.70.80.9

JPN

1980 2000

0.80.9

1

KOR

1980 2000

0.850.9

0.951

MEX

1980 20000.9

0.95

1NLD

1980 20000.8

0.9

1PRT

1980 2000

0.8

0.9

1SWE

1980 20000.8

0.9

1USA

TotalInternational LinkageSector Size

46