Exploring the Macroeconomic Interdependence of East
Asian Countries: A GVAR Approach ∗Tomoo Inoue†

Tuan Khai Vu‡

October 10, 2023
Abstract
Over the past few decades, with rapid economic growth, East Asia has also experienced deepening economic integration with active intraregional economic activities suchas trade and investments. This development has contributed to the complex and possibly
time-varying macroeconomic interdependence of countries in the region. To understandthis interdependence more fully, this study aims to employ the Global Vector Autoregressive (GVAR) model. This model is useful because it can comprehensively capture
the interdependence of domestic macroeconomies in the region and quantitatively describe the impact of shocks that occur in East Asian countries on the macroeconomies
of other countries. By incorporating changes in trade relations over time, the model cancapture the temporal evolution of shock propagation through supply chains. Furthermore, the idea of connectedness measures, developed by Diebold and Yilmaz (2009),
will be applied to quantify changes in the interdependence of East Asian countries overthe past 40 years.

Keywords: Business cycle; Connectedness; Global Vector Autoregression; Trade Linkage
JEL Classiﬁcation Numbers: C32, C53, F62∗ We would like to thank Koki Tanaka at Seikei University for his research assistantship.

† Faculty of Economics, Seikei University. 3-3-1 Kichijoji Kita-machi, Musashino, Tokyo 180-8633, Japan.

Email: inoue@econ.seikei.ac.jp.

‡ Faculty of Economics, Hosei University. 4342 Aihara-machi, Machida-shi, Tokyo 194-0298, Japan. Email:vu.tuankhai@hosei.ac.jp.

1 Introduction
In recent years, there has been an increase in economic interdependence between countries.
This can be attributed to various factors, such as the expansion of trade integration, thecreation of global supply chains, the growth of international ﬁnancial markets, and the implementation of coordinated ﬁscal and monetary policies by national governments and central
banks. As a result, numerous empirical studies have examined the connection between international business cycles, including noteworthy works from authors such as Duval et al. (2016),
Di Giovanni et al. (2017), Davis (2014), and Chiquiar and Ramos-Francia (2005). Various
empirical analysis methods have been employed, such as the pairwise correlation of GDPs by
Backus et al. (1995) and Baxter (1995), and the dynamic latent factor models proposed by
Kose et al. (2003). In recent years, the measure of connectedness proposed by Diebold andYılmaz (2015) has also become a powerful analytical method.
This study presents a novel analytical approach that builds upon Diebold and Yılmaz (2015),
an inﬂuential contribution to the ﬁeld. Our approach combines the GVAR model suggested
by Pesaran et al. (2004) with the connectedness measure proposed by Diebold and Yılmaz
(2014) to derive a new index from at least three viewpoints.
Our methodology has the advantage of expanding the number of countries that can be analyzed. With the growth of numerous emerging economies and the intricate blend of economies
in close geographic proximity, it is advantageous to widen the analysis scope. To examine
the connection between business cycles among the G7 countries (excluding Canada), Diebold
and Yılmaz (2015) estimated the six-variable VAR model using monthly industrial production
indices for the six nations, and computed a connectedness. However, the curse of dimensionality prevents the application of their approach when the sample size in the time dimension
is limited (as data are only available quarterly) or when the sample size in the cross-sectional
dimension is extensive (with an increasing number of countries). To address this issue, thisstudy utilizes a GVAR model.*1 。

*1 SeeBinderand
Sooﬁ-Siavash(2017)
fora
combined
analysisofDieboldYilmaz’s connectedness index and the GVAR model;
Their paper is available athttps://drive.google.com/ﬁle/d/16NAw89kPCD4XbLoSImHTz8veKMnqG1IA/view

2

The second feature involves quantifying business cycle linkages and determining the directionof impact between diﬀerent levels of units. While the FEVD has been commonly used inprevious GVAR-related studies, the application of connectedness measures by Diebold andYılmaz (2014) provides insight into unexplored interrelationships.
The third objective is introducing a novel approach to computing time-varying connectedness measures. To create a time-varying measure of connectedness, Diebold and Yılmaz (2014)
uses rolling-sample estimation. While this approach is preferable for maintaining objectivity
in the analysis*2 , it proves ineﬀective when dealing with a large number of sample countries
and only quarterly data is available, resulting in a small sample size in the time direction
as in this study. Thus, this study employs a time-varying weighted formulation, one of the
GVAR’s features. Speciﬁcally, we include changes in trade dependence. This formulation has
been extensively utilized in other GVAR empirical applications. Moreover, this speciﬁcation
is suitable for this study since several previous studies have indicated that the intensity of the
trade connection in business cycle synchronization is linked to the synchronization between
domestic and foreign GDP (Frankel and Rose (1998), Inklaar et al. (2008), and Rana et al.
(2012)).
As an example of this innovative approach, we investigate the economic interdependencein East Asia. The rationale for examining this region is that, as noted by Vu (2015), it
distinguishes from the Latin American and African regions in that intra-regional trade andinvestment are thriving and, furthermore, the economies of each country are ﬁrmly connected
through production relationships of intermediate goods. Therefore, this study is considered an
exceptional case study for the analytical method proposed. Additionally, economic relations
among East Asian countries have experienced signiﬁcant transformations over the past four
decades. In the 1980s, following the Plaza Accord, economic interdependence deepened, andsupply chains were established via the overseas expansion of Japanese ﬁrms. Around 2000,
the prominence of the Chinese economy grew, further transforming economic relations within
the region. Therefore, analyzing the East Asian economies is an appropriate case study for*2 As a reason for using rolling-sample estimation, they wrote ”Our goal was always the empirical descriptionof connectedness and its evolution, “getting the facts straight” with minimal assumptions.” See Diebold
and Yilmaz (2023).

3

the proposed analytical approach.
In the following, Section 2 explains how to construct the connectedness measures from the
GVAR model. Section 3 describes the data. In particular, changes in the interrelationships oftrade networks are important, and we provide a descriptive statistical overview of this point.
Section 4 presents the estimation results and the various connectedness measures calculated,
and Section 5 summarizes the results.

2 Connectedness Measures and GVAR Model
This section ﬁrst presents the deﬁnitions of the various connectedness measures and thenexplains how to calculate the FEVD, which is essential information for their calculation.

2.1 Measures of Connectedness
Table 1 is a conceptual representation of the connectedness table in Diebold and Yılmaz (2014).
The central part of this table consists of H-step-ahead forecast error variance decompositionH
matrix DH = [dHij ] computed from the VAR model and others. By dij , we denote the fractionof variable i’s H-step-ahead forecast error variance due to shocks in variable j. In addition,
the connectedness table extends DH with the rightmost column containing the row sums, thebottom row containing the column sums, and the bottom right element containing the grandmean in all cases of i ̸= j.
Based on this information, Diebold and Yılmaz (2014) deﬁnes several connectedness measures, broadly categorized, that capture the connectedness of individuals to individuals, individuals to the rest of the whole, and connectedness as a whole. Below, we review the deﬁnitions
in turn.
The ﬁrst indicator expresses the connectedness between country i and country j and is themost basic connectedness measure. The “(gross) pairwise directional connectedness” fromcountry j to country i is deﬁned as
H
Ci←j
= dH
ij

(1)

H
H
In general, Ci←j
̸= Cj←i, so there are N 2 − N pairwise directional connectedness. Then, fromH
H
the asymmetry Ci←j
̸= Cj←i, we use these to deﬁne “net pairwise directional connectedness”

4Table 1: Connectedness Table Schematic

x1
x2
..
.

x1
dH
11
dH
21
..
.

x2
dH
12
dH
22
..
.

···
···
···
..
.

xN
dH
1N
dH
2N
..
.

From Others to i
H
C1←G
H
C2←G
..
.

xN
To Others from j

dH
N1
H
CG←1

dH
N2
H
CG←2

···
···

dH
NN
H
CG←N

H
CN
←G
H
CG

Notes: Authors’ modiﬁcation based on Table 1 in Diebold and Yilmaz (2014). dH
ij denotes the fraction ofvariable i’s H-step-ahead forecast error variable due to shocks inP
variable j. Hence,
H-step-ahead total
P the H
H
= 100·( j∈G,j̸=i dH
directional connectedness from others to i is given by Ci←Gij )/( j∈G dij ), and the H-stepPP
H
H
ahead total directional connectedness to other from j is given by CG←j
= 100 · ( i∈G,i̸=j dH
ij )/( i∈G dij ).

as follows
H
H
H
Cij
= Cj←i− Ci←j(2)

In this study, this measure shows the net eﬀect of shocks occurring in each of the two speciﬁccountries on the GDP forecast errors of the other country.
The second measure is the connectedness between country j and other countries. We now
deﬁne “total directional connectedness from others to i” as follows.
P
Hj∈G,j̸=i dij
HCi←G= 100 · PHj∈G dij(3)This can be calculated for each country, so there are N possible values. Then, as an inverse
relationship, the “total directional connectedness to others from j” isP
Hi∈G,i̸=j dij
HCG←j = 100 · P
Hi∈G dij(4)This also exists in N ways. Based on these two types of connectedness measures, we deﬁne“net total directional connectedness” of i as follows:
H
H
H
Ci,G
= CG←i− Ci←G(5)This indicator shows whether, on a net basis, i countries have more impact on other countries
or receive more impact from other countries.
The third indicator is the “total connectedness” of the entire sample. It is the sum of theoﬀ-diagonal elements of DH divided by the sum of all elements of DH .
P
Hi,j∈G,i̸=j dij
H
CG = 100 · P
Hi,j∈G dij
5

(6)This paper proposes two new indicators. These are indicators that capture connectivity
within a region.*3 The ﬁrst is the connectedness of country i to the other countries in a group.
This is a similar indicator to total directional connectedness but diﬀers in that the countries
that make up the others are the others in the group, not the whole of the others. The purpose
here is to measure the possibility that the connectedness of country i to the whole is diﬀerent
from that of a particular group of countries when looking at the connectedness of country ito the rest of the group.
We ﬁrst deﬁne “total directional connectedness from others in group R to i” as:P
Hj∈R,j̸=i dij
HPCi←R = 100 ·Hj∈R dij(7)

This can be calculated for each country in group R. Similarly, “total directional connectedness
to others in group R from j” can be deﬁned. Using these, we deﬁne “net pairwise within-group
R directional connectedness” as
H
H
H
Ci,R
= CR←i− Ci←R.

(8)

The second new indicator is the total connectedness within group R, which is the sum of
the non-diagonal elements of DH in group R divided by the sum of all elements of DH also
in group R.
P

Hi,j∈R,i̸=j dij
PHi,j∈R dijH
CR
= 100 ·

(9)In the following, we use these indicators to analyze connectedness among East Asian countries.

2.2 Speciﬁcation of GVAR Model
The GVAR model comprises VARX* models estimated individually for each economy. These
VARX* models are essentially VAR models that contain distinct exogenous variables (alsoknown as star variables, denoted by ∗), where X stands for the exogenous variable. An
explanation of the star variables is provided below.
In this initial study, we assume the domestic variables to comprise only real GDP. In contrast, a typical empirical analysis within the GVAR framework assumes a VARX* model*3 This is similar to the way the 150 bank connections were analyzed by Demirer et al. (2018), which

aggregated the D matrix by country to provide an overview of the relationship.

6

consisting of approximately ﬁve domestic variables and an equivalent number of foreign variables for each of over 30 economies. A more recent and common approach is to include aninternational commodity market model in the system. The formulation used in this study
is ARX instead of VARX, strictly speaking. However, for future expandability purposes, weshall refer to it as GVAR and further elaborate on it below.*4 。
The present ARX* model represents the dynamic behavior of GDP xit in the economy ofcountry ixit = ai0 + ai1 t + ϕi1 xi,t−1 + ϕi2 xi,t−2 + λi0 x∗it + λi1 x∗i,t−1 + ψi0 ωt + ψi1 ωt−1 + uit(10)

where ai0 , ai1 , ϕi1 , ϕi2 , λi0 , λi1 , ψi0 , ψi1 represents the regression coeﬃcients. The variable t
denotes the time trend, x∗it denotes the foreign GDP, ωt represents the crude oil price, and uit
is the error term. Now deﬁne the following for i = 1, . . . , N .
Θi = {ai0 , ai1 , ϕi1 , ϕi2 , λi0 , λi1 , ψi0 , ψi1 },E(u2it ) = σu2 i

In VAR models, which are frequently employed in empirical analyses of macroeconomic policy,
the model is typically formulated solely with the domestic macroeconomic variable xit or withthe addition of the oil price as a foreign factor. In contrast, the GVAR is distinguished by
the incorporation of the star variable x∗it , enabling the examination of how domestic shocks
spread to foreign countries or aﬀect domestic macroeconomic variables due to shocks fromother countries. Given the economic susceptibility of small open economies like East Asian
nations, accounting for ﬂuctuations originating abroad in the domestic economy is imperative.
As such, the GVAR serves as an eﬀective analytical framework for examining the region’s
economies.
Next, we also consider the ARX* model to explain the behavior of the oil price ωtωt = µ0 + µ1 t + ϕ1 ωt−1 + ϕ2 ωt−2 + λ1 x̃t−1 + ηt .

(11)Here, ωt represents the oil price, and the coeﬃcients of the VAR are denoted by µ0 , µ1 , ϕ1 ,and λ1 , while ηt signiﬁes the error vector. Additionally, x̃t−1 serves as a feedback variable for*4 In this section, we assume that the lags of home GDP extend up to two periods, while the lags of foreign

GDP and oil prices extend up to one period. This simpliﬁes the explanation; however, it is important
to note that selecting the appropriate lag order is also a crucial aspect of estimation.

7

capturing exogenous factors that might impact commodity price changes. As in the country
models, the following is deﬁned here.
Θdu = {µ0 , µ1 , ϕ1 , ϕ2 , λ1 },E(ηt2 ) = ση2 .

The GVAR model includes a feedback variable, x̃t . This variable allows for the considerationof global economic ﬂuctuations on international commodity markets, using world GDP basedon the GDP of the country analyzed. Endogenous treatment of oil prices in the domestic
model is feasible for large open economies such as the US economy by including oil prices.
However, the oil price is primarily an externally determined factor for small open economies
such as those in East Asia. In this regard, the initial generation of GVAR models considered
the oil price an endogenous variable in the US economic model, while in the VAR models ofother small open economies, it was deemed exogenous. However, when examining the potential
for rapid expansion of the Chinese economy during the analysis period and its eﬀect on global
commodity prices, such as oil prices, it is uncertain whether treating commodity prices as
an endogenous variable solely in the US model is valid. Therefore, in the second-generation
GVAR model, the international market block, encompassing crude oil prices, is depicted by anindependent VAR model. A variable designating global factors is further included to renderinternational commodity prices an endogenous variable in the system’s entirety.

2.3 Derivation of Generalized FEVDIn the following, GFEVD is derived from Eq.(10) and Eq.(11). Initially, a variable vector zit
including home GDP xit and foreign GDP x∗it for country i is deﬁned.
 
xit
zit =
x∗it
Furthermore, the ARX* model for country i described in Eq.(10) can be expressed in thefollowing manner.
Gi0 zit = ai0 + ai1 t + Gi1 zi,t−1 + Gi2 zi,t−2 + ψi0 ωt + ψi1 ωt−1 + uit(12)

where Gi0 = (1, −λi0 ), Gi1 = (ϕi1 , λi1 ), and Gi2 = (ϕi2 , λi2 ).
Then, two identities between zit , x̃t , and xt = (x1t , . . . , xN t )′ is established by means of the
f outlined in Section 3.
link matrix Wi and W
f t
zit = Wi xt , x̃t = Wx
8

(13)

Then, Eq.(12) is rewritten as
Gi0 Wi xt = ai0 + ai1 t + Gi1 Wi xt−1 + Gi2 Wi xt−2 + ψi0 ωt + ψi1 ωt−1 + uit ,So, if we stack up the ARX models for N countries, we obtain
G0 xt = a0 + a1 t + G1 xt−1 + G2 xt−2 + Ψ0 ωt + Ψ1 ωt−1 + ut .

(14)

where the corresponding relevant coeﬃcient matrices are deﬁned below.








a1j
G1j W1ψ1ju1t
 , Ψj =  :  , ut =  :  .
:aj =  :  , Gj = aN j
GN j WNψN j
uN t
The ARX* model for oil prices can also be reformulated through the use of a link matrix.
f t−1 + ηt .
ωt = µ0 + µ1 t + ϕ1 ωt−1 + ϕ2 ωt−2 + λ1 Wx(15)Next, we deﬁne variable vector yt as:
yt =

 
xt
.
ωt

With this, the global model combining Eq.(15) and Eq.(14) can be formulated as follows.
H0 yt = h0 + h1 t + H1 yt−1 + H2 yt−2 + ζt
where


G0
H0 =
0


 
 

G1
−Ψ0
a0
a1
, h0 =, h1 =, H1 =
f
1
µ0
µ1
λ1 W



Ψ1
G2
, H2 =
0
ϕ1

(16)


 
0
ut
, ζt =.
ϕ2ηtNote that we assume the covariance matrix of ζt to be diagonal. We then multiply both sidesof Eq.(16) by H−1
0 from the left to derive the ﬁrst-order autoregressive expression for yt .
−1
−1
−1
−1
yt = H−1
0 h0 + H0 h1 t + H0 H1 yt−1 + H0 H2 yt−2 + H0 ζt= c0 + c1 t + C1 yt−1 + C2 yt−2 + ϵt .

(17)

The moving average expression corresponding to Eq.(17) is
yt = dt +∞X

Bs ϵt−s = dt + B0 ϵt + B1 ϵt−1 + B2 ϵt−2 + · · · .

(18)

s=0

where dt is the deterministic components, and the coeﬃcient matrices B are recursively deﬁnedasC1 Bs−1 + C2 Bs−2
Bs = I09

s = 1, 2, . . .
.
s=0
s<0

Therefore, for instance, the coeﬃcient of impulse response H terms ahead to a shock to ζt canbe calculated using the formula Bh H−1
0 .
Lastly, the Generalised FEVD is calculated as follows.
PH(σjj )−1 h=0 (e′i Bh (H0 )−1 Σζ ej )2H
dij = PH′−1 Σ ((H )−1 )′ (B )′ eζ0hi
h=0 ei Bh (H0 )(19)This shows us how much a shock occurring in the j-th variable aﬀects the H-step-ahead
forecast error variance of the i-th variable. ei is the selection vector whose ith element is 1(s)

and the rest are 0, and σjj is the variance of the disturbance term in the jth expression (or(s)

the jth diagonal element of Σζ ). Note that in GFEVD, the shocks are not orthogonalized,
so the sum of the relative variance contribution (RVC) of the forecast error variance is notnecessarily equal to 1. Therefore, the following standardization is used.
dgijg˜
dij = PNg
j=1 dij(20)

In the following, GFEVD is denoted by dij to simplify notation, but all connectedness measuresin this study are calculated using the standardized value D̃H = [d˜Hij ].

3 DataIn this study, real GDP by country (log-transformed values) and oil prices (also logtransformed values) from the Mohaddes and Raissi (2020) data set are used in the analysis.*5 Speciﬁcally, 10 countries from East Asia and the Paciﬁc region: Australia (AUS), China(CHN), Indonesia (IDN), Japan (JPN), Korea (KOR), Malaysia (MYS), New Zealand (NZL),
Philippines (PHL), Singapore (SGP), Thailand (THA); 13 countries from Europe and Central
Asia region: Austria (AUT), Belgium (BEL), Finland (FIN), France (FRA), Germany (DEU),
Italy (ITA), Netherlands (NLD), Norway (NOR), Spain (ESP), Sweden (SWE), Switzerland(CHE), Turkey (TUR), United Kingdom (GBR); ﬁve countries from the Latin American region: Argentina (ARG), Brazil (BRA), Chile (CHL), Mexico (MEX), Peru (PER); 2 countries
from North American region: Canada (CAN), United States (USA). The other three countries*5 Mohaddes,

K. and M. Raissi (2020). Compilation, Revision and Updating of the Global VAR(GVAR) Database, 1979Q2-2019Q4. University of Cambridge: Judge Business School (mimeo).
https://www.mohaddes.org/gvar. The data set covers the period from the fourth quarter of 1979 to
the fourth quarter of 2019. In addition to the data used in this paper, the data set also includes thelong-term interest rate, stock prices, and the bilateral exchange rate against the dollar.

10are: Saudi Arabia (SAU) in the Middle East and North Africa region; India (IND) in SouthAsia; and South Africa (ZAF) in Sub-Saharan Africa. Total number of countries is 33.
The foreign GDP x∗it was calculated using the matrix Wi , which depicts the relations
between countries. This matrix was derived from the annual trade ﬂow data provided by
Mohaddes and Raissi (2020).*6 Based on annual trade ﬂow data, the linkage coeﬃcient wij
between countries i and j is calculated as follows.
Trade volume between country i and country j
wij = PN
k=1 Trade volume between country i and country k(21)

where trade volume is the sum of annual exports and imports between the two countries. For
example, foreign GDP for Japan is deﬁned in the following way.
x∗jpn,t =33
X

wjpn,j xj,t(22)

j=1,j̸=jpn

By the way, it is widely acknowledged that China’s economy has experienced signiﬁcant
growth over the last 30 years, resulting in substantial alterations in its economic partnerships
with neighboring countries, speciﬁcally those in East Asia. Figure 1 displays individual countries’ linkage coeﬃcients and GDP at four selected time points from the sample period, namely,
1985, 1995, 2005, and 2015. The circle’s center depicts the USA, while the circles on the circumference represent 32 sample countries excluding the USA. Each circle’s size corresponds to
the respective economy’s size, while the arrows indicate the inﬂuencing relationships. Arrows
with lower than 20.5 percent linkage coeﬃcient values have been disregarded to emphasize themore critical relationships.
From Figure 1, it is evident that the trade relationship, which is measured by the linkage
coeﬃcient as deﬁned in Eq.(21), has been dynamically evolving over time. To account forthese changes, Wi in Eq.(13) is altered to be time-varying. This is done to accurately capture
the modiﬁcations occurring in the trade relationship over time. The linkage coeﬃcient iscomputed based on the previous year’s trade volume. In accordance with this, the weighted
coeﬃcient of foreign GDP changes annually and the GFEVD, as deﬁned in Eq.(C.3), also
*6 Values for the three most recent years were updated using rates of change calculated from annual export

and import values (in U.S. dollars) obtained from the latest Direction of Trade Statistics (DOTS).
Because the interest of this study is real economic interrelationships rather than ﬁnancial ones, andbecause of the availability of data, trade volume data were employed. Another approach is to use capital
investment and asset portfolio data.

11

Fig. 1: Trade networks
Note: See Table A.1 in Appendix for country codes. The circles on the circumference indicate the size of theeconomy based on real GDP, and arrows are marked if the relevance calculated from trade ﬂows is 20.5% or
more, while the thickness of the arrows indicates the strength of the relevance.

ﬂuctuates to reﬂect diverse evaluation points in time. Thus, measures of connectedness will
also vary over time.
et in the oil price model is a weighted average of each country’s
Finally, the feedback variable xflog-transformed GDP value. The weights to determine the average (represented by the W
matrix in Eq.(13)) were calculated using the share obtained from the 2014-2016 average of
nominal GDP in PPP (in current international $) for each respective country, as reported by

12the World Bank’s WDI. This variable serves as a proxy for global business cycle ﬂuctuations
and covers aspects of oil demand. Examining crude oil supply factors is also valuable for priceﬂuctuations, but this study does not include them.

4 Results
4.1 Estimation of GVAR Model
Estimation is conducted on a model-by-model basis, following the standard VAR model. The
number of lags for home and foreign variables included in the model is set at p = 4 and q = 4,
respectively. In the case of the oil price model, the number of lags is also set at four periods
for both the own and feedback variables.
When multiple countries are analyzed simultaneously, the presence of outliers can cause thesystem to become unstable and divergent. The sample period encompasses the Asian currency
crisis, the substantial devaluation of currencies in Thailand and other Asian nations during
1997-1998, and the worldwide ﬁnancial crisis between 2007-2008. Other local shocks include
the Severe Acute Respiratory Syndrome (SARS) in China from approximately November 2002
to the ﬁrst half of 2003, the Great East Japan Earthquake in Japan in March 2011, and thesigniﬁcant ﬂooding in Thailand in the latter half of the same year. These events not only
impacted domestic economic activities in each country but also aﬀected supply chains. The
concern lies in the impact of these events not just on domestic economic activities in eachcountry but also on the economies of other countries connected through supply chains andother means.
Normally, historical data should be employed to identify outliers. However, due to the vast
number of countries covered, statistical criteria were used to identify outliers, and we assigned
dummy variables to manage them. Speciﬁcally, if the maximum absolute value of the residuals
did not fall within three standard deviations of the error variance, dummy variables wereallocated to the residuals of the ARX* model computed for each country. This procedure was
performed iteratively until all anomalies were identiﬁed for each country. The same approach
was followed for the model of crude oil prices.

13

4.2 Various Measures of Business Cycle Connectedness
The connectedness measures presented in this study are computed using generalized forecast
error variance decomposition for the next 12 quarters (three years). Estimated tables depicting
connectedness in 1985, 1995, 2005, and 2015 are presented in the Appendix.
Let us begin by examining the Own eﬀect, represented by the diagonal element in theConnectedness Table. Table 2 presents the eﬀect of each country in 10-year intervals from1985. The eight countries with low own eﬀects (1/4 of the total sample) are highlighted forclarity. The table reveals that several European countries have low own eﬀects, which is acomprehensible phenomenon owing to their near economic relations. The inﬂuence of the
USA also extends to Canada. Notably, the East Asian region is not among the countries
highlighted. Peru and Brazil in South America have experienced a noteworthy diminution ofhome-country eﬀects from 1985 to 2015 (i.e., they have become more vulnerable to foreigninﬂuences). Meanwhile, the value of China, Indonesia, and South Korea in East Asia has
increased, albeit only slightly. On the contrary, the Philippines and Japan have experienced
a decrease of approximately 9 and 5 percent, respectively.
4.2.1 Total Connectedness
Now, we shall assess connectivity. Firstly, let us examine the overall connectivity. Please refer
to Figure 2, highlighting the Total Connectedness for all 33 countries considered. The Total
Connectedness value decreased from 18% in 1981 to around 15% in 1985. It remained around
15% until approximately 2000, after which it increased and attained over 22% in 2019. For
reference, excluding China, the calculation of total connectedness demonstrated a long-term
decline over the analyzed period. This implies that the increase in global connectedness could
be attributed to the Chinese economy.
Next, let us examine the total connectedness of sub-groups, with the ﬁrst group beingclassiﬁed based on geographical location. The left panel of Figure3 illustrates the following
three regions: (1) East Asia & Paciﬁc, (2) North America, Latin America & Caribbean, and(3) Europe & Central Asia. The regional variations are evident from Figure 3: whilst Europe& Central Asia has the highest level over the period, it shows a decreasing trend with an

14

Table 2: Own eﬀect: 1985, 1995, 2005, and 2015
Note: Each year, the eight countries with small home country eﬀect values (corresponding to 1/4 of the total
sample) are highlighted.

Fig. 2: Total ConnectednessPP
H = 100 · (HHNote: Total Connectedness is calculated as CGi,j∈G,i̸=j dij )/( i,j∈G dij ). This calculation
excludes the part related to oil prices. The forecasting horizon, H, is set to 12.

amplitude of 20-year cycles. In contrast, North America, Latin America & the Caribbean,
and East Asia & the Paciﬁc display lower absolute levels, although the magnitude of East
Asia & the Paciﬁc has exhibited a consistent increase since 2000.
How about another grouping: the G7, BRICs, Next 11*7 , ASEAN and ASEAN+3? The*7 The Next Eleven are the eleven countries - Bangladesh, Egypt, Indonesia, Iran, Mexico, Nigeria, Pakistan,15

Fig. 3: Total Connectedness within Diﬀerent GroupsPP
H = 100·(
H
H
Note: Within-region total connectedness is calculated as CR
i,j∈R,i̸=j dij )/( i,j∈R dij ). The ﬁgureon the left depicts diﬀerent geographic regions, whilst the ﬁgure on the right shows various groups, including
G7, BRICS, ASEAN, and Next-11. The forecasting horizon, H, is set to 12.

G7 group peaked in the mid-1980s and experienced a gradual decline until the end of thesample period, ultimately reaching the same level as the other groups. Conversely, the BRICS
group displayed a considerable increase starting in 2000, which aligns with the growth of theChinese economy. On the other hand, the level of total connectedness observed in the Next-11
remains notably low, despite an upward trend that began around 1985. Turning to Asia, theconnectedness of the ASEAN countries encompasses the Asian currency crisis in the middleof the sample period. However, no signiﬁcant changes were observed during this time, andthe level has remained stable. Conversely, ASEAN+3, incorporating China, Japan and Korea
alongside ASEAN, displayed a considerable decline during the Asian currency crisis, followed
by a consistent upward trend.
4.2.2 Total Directional Connectedness
Let us focus on East Asian nations and examine their directional connectedness of businesscycles across countries within and beyond the region.
Figure 4 displays the directional connectedness between the 10 East Asian countries in thedataset and the other 32 countries. The graph illustrates the changes over time in terms ofHH“connectedness to others (CG←i)”, “connectedness from others (Ci←G)”, and “net connect-

edness to others (CiH )”. Here denoted by the acronym G for Global, meaning the whole

the Philippines, South Korea, Turkey, and Vietnam

16

H
H
Fig. 4: Directional Connectedness: CG←i
, Ci←G, and CiH

Note: The forecasting horizon, H, is set to 12.

world.
Only three countries (Japan, China and Singapore) displayed positive values for net connectedness across the sample period. This implies that these three countries were net transmittersof business cycle shocks. During the mid-1980s to mid-1990s, Figure 4, column 3 indicatesthat Japan was responsible for net connectedness. During this period, Japan’s gross connectedness with other countries reached approximately 40%, while the connectedness received by
Japan from other nations was around 15%, resulting in a net connectedness of up to 25%
from Japan. Japan’s net connectedness started to decline from mid-1995. Contrarily, China’s

17

Fig. 5: Directional Connectedness within the East Asian and Paciﬁc Region
Note: The forecasting horizon, H, is set to 12.

inﬂuence grew rapidly, reaching 60% by around 2010.
What happens if we limit the measurement of directional connectedness to East Asian
countries? Based on the data, there is no signiﬁcant alteration in the trends observed inJapan and China. However, a few countries show noteworthy variations. Korea, New Zealand,
and Thailand are net recipients of business cycle shocks, as net connectedness is negative
throughout the sample period. Nonetheless, Figure 4 indicates a tendency for the negativevalue to reduce towards the latter half of the period, while Figure 5 shows a tendency toincrease. This trend may indicate a growing inﬂuence of the economies of these three countries

18Fig. 6: China’s Pairwise Directional Connectedness within East Asian and Paciﬁc
Note: The forecasting horizon, H, is set to 12.

by the East Asian region.
4.2.3 Pairwise Directional Connectedness
Finally, let us examine the interrelationships among East Asian nations. As this study’s
primary focus is on the waning impact of the Japanese economy and the growing inﬂuenceof the Chinese economy, let us consider China, Japan, and Korea’s relationship with other
Asian states. Figure 6 shows the pairwise directional connectedness of China, Figure 7 shows
the pairwise directional connectedness of Japan, and Figure 8 shows the pairwise directional
connectedness of South Korea.
Figure 6 shows that China has been the net transmitter of business cycle shock for East
Asian countries since 2000. According to the latest assessment, Malaysia has more than 20

19

Fig. 7: Japan’s Pairwise Directional Connectedness within East Asian and Paciﬁc
Note: The forecasting horizon, H, is set to 12.

percent of the inﬂuence from China; Japan, the Philippines, and Thailand have about 10
percent, followed by Singapore and South Korea.
In contrast, Figure 7, which shows the inﬂuence of Japan, shows that its role as a transmitterof business cycle shocks is gradually diminishing. It has been a net recipient of China since
2000. However, except for Korea, the other countries remain net transmitters, although theirinﬂuence has diminished.
Korea’s role is more complex: Figure 8 shows that it is mostly a net recipient for China andJapan over the period. However, it is a net transmitter for Australia, Malaysia, New Zealand,
the Philippines, and Thailand, and its role for Indonesia and Singapore varies from period toperiod.

20

Fig. 8: Korea’s Pairwise Directional Connectedness within East Asian and Paciﬁc
Note: The forecasting horizon, H, is set to 12.

Finally, it is essential to mention the relationship between trade relations and connectedness measures. The time-varying connectedness measure proposed in this study is due to using
time-varying trade weights for the foreign variables in the GVAR. What is the relationshipbetween the GVAR and the trade weights, which is the most important information in calculating the connectedness measure? In Figure 9, the variable on the vertical axis is the (gross)pairwise directional connectedness from country j to country i, and the horizontal axis is thetrade ratio for the country in question. For example, in the second column, the vertical vari12
able is the inﬂuence of China on country i (Ci←CHN), and the horizontal variable is the traderatio of country i with China in the previous year. A noticeable quadratic correlation exists
between the two variables in the second column of Figure 9. However, for other nations, the21Fig. 9: Pairwise directional connectedness vs trade ratio of the East Asian and Paciﬁc Countries
Note: The variable on the vertical axis is the (gross) pairwise directional connectedness from country j tocountry i, and the horizontal axis is the trade ratio for the country in question. The forecasting horizon, H,
is set to 12.

correlation is frequently uncertain. This phenomenon veriﬁes that the connectedness metricis linked to the trade ratio but doesn’t solely rely on information concerning the trade ratio.

5 Conclusion
Over the past few decades, with rapid economic growth, East Asia has also experienced deepening economic integration with active intraregional economic activities such as trade andinvestments. This development has contributed to the complex and possibly time-varying
macroeconomic interdependence of countries in the region.
To understand this interdependence more fully, we present a novel analytical approach thatbuilds upon Diebold and Yılmaz (2015) as a novel contribution to the ﬁeld. Our approachcombines the GVAR model suggested by Pesaran et al. (2004) with the connectedness measure22

proposed by Diebold and Yılmaz (2014) to derive a new index which is used to analyze thebusiness cycle shock transmission.
Using quarterly GDP and oil price data for 33 countries from 1979 to 2019, we analyzed thegrowing interdependence of business cycles and dependencies between regions and countries
in East Asia from various perspectives. Notably, the study employed the GVAR model toinvestigate the ﬂow of stock transmissions, yielding intriguing ﬁndings.
One of the remaining concerns is to ensure the results’ robustness from varying viewpoints.
For this analysis, the forecasting period of the GFEVD was ﬁxed at 12 quarters, and otherperiods were not investigated. It may also be necessary to consider the formulation of the
GVAR model since it can be converted to a diﬀerenced VAR or a cointegrating VAR. The
impact of the change in the formulation on the results must be analyzed. These issues will be
the subject of future work.

23

References
Backus, D. K., Kehoe, P. J., and Kydland, F. E. (1995). International business cycles: Theory and evidence, in thomas f. cooley (ed.) frontiers of business cycle research. Princeton
University Press, Princeton, pages 331–357.
Baxter, M. (1995). International trade and business cycles. Handbook of International Economics, 3:1801–1864.
Chiquiar, D. and Ramos-Francia, M. (2005). Trade and business-cycle synchronization: Evidence from mexican and us manufacturing industries. The North American Journal of
Economics and Finance, 16(2):187–216.
Davis, J. S. (2014). Financial integration and international business cycle co-movement. Journal of Monetary Economics, 64:99–111.
Demirer, M., Diebold, F. X., Liu, L., and Yilmaz, K. (2018). Estimating global bank network
connectedness. Journal of Applied Econometrics, 33(1):1–15.
Di Giovanni, J., Levchenko, A. A., and Mejean, I. (2017). Large ﬁrms and international
business cycle comovement. American Economic Review, 107(5):598–602.
Diebold, F. X. and Yılmaz, K. (2014). On the network topology of variance decompositions:
Measuring the connectedness of ﬁnancial ﬁrms. Journal of Econometrics, 182(1):119–134.
Diebold, F. X. and Yılmaz, K. (2015). Measuring the Dynamics of Global Business Cycle
Connectedness. In Koopman, S. and Shephard, N., editors, Unobserved Components andTime Series Econometrics: Essays in Honor of Andrew C. Harvey, pages 45–70. Oxford
University Press.
Diebold, F. X. and Yilmaz, K. (2023). On the past, present, and future of the diebold–yilmaz
approach to dynamic network connectedness. Journal of Econometrics, 234:115–120.
Duval, R., Li, N., Saraf, R., and Seneviratne, D. (2016). Value-added trade and business cycle
synchronization. Journal of International Economics, 99:251–262.
Frankel, J. A. and Rose, A. K. (1998). The endogenity of the optimum currency area criteria.
The Economic Journal, 108(449):1009–1025.
Inklaar, R., Jong-A-Pin, R., and De Haan, J. (2008). Trade and business cycle synchronization24

in oecd countries―a re-examination. European Economic Review, 52(4):646–666.
Kose, M. A., Otrok, C., and Whiteman, C. H. (2003). International business cycles: World,
region, and country-speciﬁc factors. American Economic Review, 93(4):1216–1239.
Mohaddes, K. and Raissi, M. (2020). Compilation, revision and updating of the global VAR(GVAR) database, 1979Q2-2019Q4.
Pesaran, M. H., Schuermann, T., and Weiner, S. M. (2004). Modeling regional interdependencies using a global error-correcting macroeconomic model. Journal of Business & Economic
Statistics, 22(2):129–162.
Rana, P. B., Cheng, T., and Chia, W.-M. (2012). Trade intensity and business cycle synchronization: East asia versus europe. Journal of Asian Economics, 23(6):701–706.
Vu, T. K. (2015). Exchange rate regimes and the sources of real exchange rate ﬂuctuations:
Evidence from East Asia. Meisei University Discussion Paper Series No.31.

25

Appendix

26

A List of Countries
iso3
ARG
AUS
AUT
BEL
BRA
CAN
CHN
CHL
FIN
FRA
DEU
IND
IDN
ITA
JPN
KOR
MYS
MEX
NLD
NOR
NZL
PER
PHL
ZAF
SAU
SGP
ESP
SWE
CHE
THA
TUR
GBR
USA

Code
213
193
122
124
223
156
160
228
172
132
134
534
536
136
158
542
548
273
138
142
196
293
566
199
456
576
184
144
146
578
186
112
110

Country
Argentina
Australia
Austria
BelgiumBrazilCanadaChina
Chile
FinlandFranceGermany
India
Indonesia
Italy
Japan
Korea
Malaysia
MexicoNetherlands
NorwayNew Zealand
Peru
Philippines
South Africa
Saudi Arabia
Singapore
Spain
SwedenSwitzerland
ThailandTurkeyUnited Kingdom
United States

RegionLatin America & Caribbean
East Asia & Paciﬁc
Europe & Central Asia
Europe & Central Asia
Latin America & Caribbean
North America
East Asia & Paciﬁc
Latin America & Caribbean
Europe & Central Asia
Europe & Central Asia
Europe & Central Asia
South Asia
East Asia & Paciﬁc
Europe & Central Asia
East Asia & Paciﬁc
East Asia & Paciﬁc
East Asia & Paciﬁc
Latin America & Caribbean
Europe & Central Asia
Europe & Central Asia
East Asia & Paciﬁc
Latin America & Caribbean
East Asia & Paciﬁc
Sub-Saharan Africa
Middle East & North Africa
East Asia & Paciﬁc
Europe & Central Asia
Europe & Central Asia
Europe & Central Asia
East Asia & Paciﬁc
Europe & Central Asia
Europe & Central Asia
North America

G7

OECD

ASEAN

N-11

X

X

X
X
X
X

X

X
X

X
X
X
X

X
X

X
X
X

X
X

X
X
X
X
X

X

X
X
X
X
X
X
X

X
X
X

X

Table A.1: ISO3 Country codes, Country names, Geographical Regions, and Associations of Countries

B Connectedness Tables
Tables B.2, B.3, B.4, and B.5 are the connectedness tables as of 1985, 1995, 2005, 2015,
respectively. Cells with a value greater than 0.005 are highlighted because of the small fontsize. The diagonal cells in the table are highlighted because they are their own eﬀect, so
it is obvious that their values are larger than the other cells. We can also see that for all
countries, the impact of oil price shocks is relatively non-negligible compared to shocks fromother countries.

27

Table B.2: Connectedness Table: 1985
Note: Cells with a value greater than 0.005 are highlighted.

28

Table B.3: Connectedness Table: 1995
Note: Cells with a value greater than 0.005 are highlighted.

29

Table B.4: Connectedness Table: 2005
Note: Cells with a value greater than 0.005 are highlighted.

30

Table B.5: Connectedness Table: 2015
Note: Cells with a value greater than 0.005 are highlighted.

31

C Calculation Procedure of Generalized FEVD
Forecast Error Variance Decomposition (FEVD) was calculated in the following way.
1. The data are used to estimate the coeﬃcient matrix Θ̂i of the country-speciﬁc VARX
2model and the variance of the error term σ̂i2 (i = 1, . . . , N ), and the Θ̂du and σ̂duare estimated. The diagonal matrices are assumed for the covariance matrix of the
disturbance vector of Eq.(16).
 
ut
ζt =
ηt
It seems safe to assume no correlation for the error terms among the VARXs for eachcountry since the foreign variables are included at the same time as the explained
variable. On the other hand, it is not clear from the formulation whether the error
terms between the country models and the international market model at the same time
are uncorrelated or not. However, when N → ∞, ωt can function as a proxy variable
for a common factor that cannot be directly observed and can be approximated by x∗ ,so we judged that assuming uncorrelation would pose few problems.
2. Next, the error variance σi2 is generated for each i = 1, . . . , N separately using theinverse Wishart distribution and the coeﬃcient matrix is generated based on the normal
distribution
N vec(Θ̂i ), σ̂i2 ⊗ (X′i Xi )−1

subject to this covariance matrix and the data matrix, Xi , for each VARX. The error
variance and regression coeﬃcient matrices are generated in a similar manner for theoil price model.
2(s)3. Using the generated σi2(s)and σdu , construct the covariance matrix:

 2(s)
σ1

0

 
 .
2(s)
2(s)
2(s)
(s)
Σζ = diag σ1 , . . . , σN , σdu = 
 ..

 0
0
(s)

Bj

(s)

(j = 1, 2, . . . ) are calculated from Θi
32

0
2(s)

σ2
..
.

0
0
(s)

···
···
..
.

0
0
..
.

···
···

2(s)
σN

and Θdu as follows.

0

0
0
..
.









0 

2(s)

σdu

(C.1)

（a）First, using
(s)

Θi

(s)

(s)

(s)

(s)

(s)

(s)

(s)

(s)

(s)

(s)

(s)

(s)

(s)

= {ai0 , ai1 , ϕi1 , ϕi2 , λi0 , λi1 , ψi0 , ψi1 }(s)

Θdu = {µ0 , µ1 , ϕ1 , ϕ2 , λ1 },construct
(s)

(s)

(s)

(s)

(s)

(s)

Gi0 = (1, −λi0 ), Gi1 = (ϕi1 , λi1 ), Gi2 = (ϕi2 , λi2 ).
Then, from these vectors and the trade weight matrix, W, we construct(s)
G1j W1(s):Gj = 
.
(s)
GN j WN(s)(s)

Then, construct H0 and H1 .

(s)
H0 =

(s)

(s)

−Ψ0
1

G0
0

(s)


,

(s)

G1
(s) f
λ1 W

(s)
H1 =

(s)

!

Ψ1
(s)
ϕ1

,

(s)
H2 =

(s)

G2
0

!
0
(s)
ϕ2

(s)

（b）Next, construct C1and C2 as follows.

C1 = (H0 )−1 H1 ,
(s)

(s)

(s)

(j = 1, 2, . . . ).*8（c）Lastly, construct Bj(s)

C2 = (H0 )−1 H2
(s)

(s)

 (s) (s)(s) (s)
C1 Bj−1 + C2 Bj−2(s)
Bj = I0(s)

j = 1, 2, . . .
j=0
j<0

4. Generalized FEVD is calculated as:
PH
(s)
(s)
(s)
(s)
(σjj )−1 h=0 (e′i Bh (H0 )−1 Σζ ej )2H
dij = PH(s) −1 (s)
(s)
(s)
′ (s)
Σζ ((H0 )−1 )′ (Bh )′ ei
h=0 ei Bh (H0 )(C.3)

This shows us how much a shock occurring in the j-th variable aﬀects the H-stepahead forecast error variance of the i-th variable. ei is the selection vector whose ith(s)element is 1 and the rest are 0, and σjj is the variance of the disturbance term in(s)

the jth expression (or the jth diagonal element of Σζ ). Note that in GFEVD, the*8 The eigenvalue of Eq.(17) can be obtained from the following companion form

 
C1
yt
=
I
yt−1



C1
0

33



  
ϵ
yt−1
+ t .
0
yt−2

(C.2)

shocks are not orthogonalized, so the sum of the relative variance contribution (RVC)of the forecast error variance is not necessarily equal to 1. Therefore, the following
standardization is used.
dH
ij
d˜H
=
P
ij
N

H
j=1 dij(C.4)

H
The connectedness measures calculated in this paper are based on d˜Hij , not dij .

5. Repeat steps 2. through 4. a suﬃcient number of times. In this study, it was repeated
1,000 times.

34