Journal of Banking and Finance 76 (2017) 150174 [618455]

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Journal of Banking and Finance 76 (2017) 150174 [618455]

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Journal of Banking and Finance 76 (2017) 150–174
Contents lists available at ScienceDirect
Journal of Banking and Finance
journal homepage: www.elsevier.com/locate/jbf
Which market integration measure? /p82
M. Billio a , ∗, M. Donadelli b , A. Paradiso a , M. Riedel b
a Ca’Foscari University of Venice, Department of Economics, Cannaregio 873, 30121, Venice, Italy
b Research Center SAFE, Goethe University Frankfurt, Theodor-W.-Adorno-Platz 3 60323, Frankfurt am Main, Germany
a r t i c l e i n f o
Article history:
Received 10 September 2015
Accepted 2 December 2016
Available online 7 December 2016
JEL classiﬁcation:
F15
F44
G15
Keywords:
Equity market integration
Dynamic correlation
Principal components
International diversiﬁcation beneﬁts a b s t r a c t
This paper compares the dynamics of the ﬁnancial integration process as described by different empiri-
cal approaches. To this end, a wide range of measures accounting for several dimensions of integration
is employed. In addition, we evaluate the performance of each measure by relying on an established
international ﬁnance result, i.e., increasing ﬁnancial integration leads to declining international portfolio di-
versiﬁcation beneﬁts . Using monthly equity market data for three different country groups (i.e., developed
markets, emerging markets, developed plus emerging markets) and a dynamic indicator of international
portfolio diversiﬁcation beneﬁts, we ﬁnd that ( i ) all measures give rise to a very similar long-run integra-
tion pattern; ( ii ) the standard correlation explains variations in diversiﬁcation beneﬁts as well or better
than more sophisticated measures. These ﬁndings are robust to a battery of robustness checks.
©2 0 1 6 Elsevier B.V. All rights reserved.
1. Introduction
International ﬁnancial markets have become increasingly in-
tegrated over the last 30 years. An increasing degree of ﬁnancial
integration across countries and regions provides both advantages
and disadvantages. On the one side, a relatively high level of in-
tegration (i.e., complete international ﬁnancial markets) increases
risk-sharing opportunities by allowing for larger insurance beneﬁts
and more eﬃcient consumption smoothing (see, among others,
Jappelli and Pistaferri, 2011; Suzuki, 2014 ). In this respect, ﬁnan-
cial integration may generate both short- and long-run welfare
beneﬁts ( Colacito and Croce, 2010; Yu, 2015 ). On the other side,
the increasing level of global ﬁnancial integration induces strong
positive cross-country equity return correlations. As a result,
the beneﬁts from international portfolio diversiﬁcation decrease
( Goetzmann et al., 2005; Christoffersen et al., 2012; Donadelli
and Paradiso, 2014 ). Moreover, increasing ﬁnancial integration and
frictionless international capital markets tend to affect countries’
speciﬁc policy targets. Blanchard et al. (2010) , for instance, argue
that the current international ﬁnancial markets environment may
undermine domestic policies’ effectiveness.
/p82 An earlier version of this paper circulated under the title “Measuring Financial
Integration: Lessons from the Correlation. ”
∗Corresponding author.
E-mail addresses: [anonimizat] (M. Billio), [anonimizat]
(M. Donadelli), antonio.paradiso@unive.it (A. Paradiso), riedel@safe.uni-frankfurt.de
(M. Riedel). Financial integration has thus received an enormous amount of
attention, much of it devoted to measuring it. Both, policymakers
and investors need an instrument that is able to measure inte-
gration and its evolution over time. A key challenge consists in
ﬁnding an integration measure that balances the trade-off between
computational complexity and measurement accuracy. As there
are many possible measures of ﬁnancial integration, it is natural to
ask whether they all provide similar results in terms of integration
levels and patterns, and whether some might be more preferred
to others.
The objective of this study is to compare the ﬁnancial integra-
tion patterns that are generated using different empirical method-
ologies. A large body of literature proposes novel integration mea-
sures, while another employs existing measures to capture either
regional or global ﬁnancial integration. To our knowledge, there
exists no study that attempts to compare and rank all these mea-
sures. Our contribution is therefore twofold. First, we examine the
degree of heterogeneity in the information provided by different
measures over time. Loosely speaking, we ask whether these mea-
sures provide similar equity market integration patterns. Second,
we relate the integration patterns reproduced by different mea-
sures with ﬁnancial integration-driven phenomena. More precisely,
we examine the relationship between integration patterns and a
dynamic international diversiﬁcation beneﬁts indicator introduced
by Christoffersen et al. (2011, 2012) . This allows us to quantitatively
evaluate the ability of each integration measure in explaining de
facto integration.
http://dx.doi.org/10.1016/j.jbankﬁn.2016.12.002
0378-4266/© 2016 Elsevier B.V. All rights reserved.

M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174 151
Table 1
Financial integration measures: existing studies and measures’ characteristics.
Measure Studies on ﬁnancial integration Dynamic Comov. Heterosk. Stochastic
Bias (Vol.) Interdep.
PANEL A:
SC Goetzmann et al. (20 05) ; Quinn and Voth (20 08) X
¯R 2 Pukthuanthong and Roll (2009) ; Yu et al. (2010) X X
1 stPC Volosovych (2011) ; Volosovych (2013) X X
Corr. (ASI) Ball and Torous (2006) X X
Forbes-Rigobon Corr. Connolly et al. (2007) X X
DCC-GARCH Chiang et al. (2007) ; Wang and Moore (2008) ; Egert and Kocenda (2011) X X
BEKK-GARCH Caporale and Spagnolo (2011) ; Bekiros (2013) X X
Cond. Beta Choudhry and Jayasekera (2013) ; Jayasinghe et al. (2014) X X
PANEL B:
¯R 2 (ASI) This paper X X X
1 stPC (ASI) This paper X X X
Forbes-Rigobon Corr. This paper X X ∗
Notes : Panel A lists the methodologies (and their respective technical features) employed by the international ﬁnance literature to measure equity market integration over
time. Panel B reports newly introduced measures. ∗The volatility-adjustment is introduced by relying on the set of relevant political and ﬁnancial events indicated in the US
and EU economic policy uncertainty indexes (see Baker et al., 2015 ).
To account for all possible dimensions of integration, a rela-
tively large number of existing indicators is considered. Table 1
(Panel A) presents a list of main measures proposed by the lit-
erature over the last ten years – and employed in this study –
along with their properties. Being largely accepted that integra-
tion is a dynamic concept, we consider exclusively methodologies
that allow us to capture the evolution of the degree of equity mar-
ket integration over time. Our simplest measure of integration is
the standard correlation (henceforth SC ). Since the SC has been
largely criticized as measure of integration (see, among others,
Bekaert et al., 2009; Pukthuanthong and Roll, 2009; Volosovych,
2011 ), two recently introduced robust PCA-based measures are
used: ( i ) the percentage of variance explained by the ﬁrst princi-
pal component used by Volosovych (2011) , henceforth 1 stPC , and
( ii ) the multi-factor cross-country average adjusted R-square pro-
posed by Pukthuanthong and Roll (2009) , henceforth ¯R 2 . To ac-
count for stochastic interdependence (i.e., the linkage between
the correlation and stock return volatilities might be stochas-
tic and varying over time), the methodology of Ball and Torous
(2006) is also considered. In addition, we rely on a battery of
widely used heteroskedasticity-adjusted measures. Speciﬁcally, we
employ ( i ) the volatility-adjusted correlation introduced by Forbes
and Rigobon (2002) ; ( ii ) the BEKK-GARCH model along the lines of
Engle and Kroner (1995) ; ( iii ) the dynamic conditional correlation
model (DCC-GARCH) proposed by Engle and Sheppard (2001) and
Engle (2002) ; and ( iv ) a conditional time-varying beta. Improve-
ments with respect to existing studies are also carried out (see
Table 1 , Panel B). The volatility-adjustment in the SC is introduced
by relying on the key events embedded in the US and EU economic
policy uncertainty indexes proposed by Baker et al. (2015) . This al-
lows us to account for multiple changes in volatility, which corre-
spond to major political and ﬁnancial market events. 1 For robust-
ness, the ¯R 2 and 1 stPC are re-computed by accounting for stochas-
tic interdependence. In other words, in both PCA-based measures
the sample correlation is substituted with the correlation obtained
via Ball and Torous (2006) ’s procedure. This helps capturing inte-
gration during non-tranquil and tranquil times ( Ball and Torous,
2006 ). Based on the ongoing debate on whether or not the SC rep-
resents a robust measure of integration ( Carrieri et al., 2007; Puk-
thuanthong and Roll, 2009; Volosovych, 2011 ), this study uses the
latter as a benchmark indicator of ﬁnancial integration.
To ensure that our analysis is general and does not strictly de-
pend on the chosen sample, we implement all the measures listed
1 This differs from Forbes and Rigobon (2002) who focus on a single shift in the
variance level. in Table 1 by using data for three groups of countries: ( i ) de-
veloped markets (DMs); ( ii ) emerging markets (EMs) and ( iii ) de-
veloped plus emerging markets (ALL). While the ﬁrst two groups
consist of countries displaying similar characteristics in terms of
volatility patterns and average returns, the third group includes
economies with a large variety of sizes, degrees of openness, and
ﬁnancial market characteristics. We stress that this classiﬁcation
allows us to examine the evolution of equity market integration in
DMs and EMs as well as global equity market integration. There-
fore, we bridge the literature focusing exclusively on regional in-
tegration ( Yu et al., 2010; Bekaert et al., 2011; Volosovych, 2011;
Donadelli and Paradiso, 2014 ) and those studies examining global
equity market integration dynamics ( Carrieri et al., 2007; Puk-
thuanthong and Roll, 2009 ).
A natural question one might ask is then the following: how
can we evaluate the effectiveness of these measures in capturing
de facto ﬁnancial integration? To some extent ﬁnancial integration
is an abstract concept and measuring it realistically is challenging.
From a quantitative point of view, it is therefore diﬃcult to state
that one measure is better than another. At present, the interna-
tional ﬁnance literature does not provide any quantitative assess-
ments on existing measures’ ability in capturing real ﬁnancial in-
tegration dynamics. With this study, we also aim to ﬁll this gap.
A suggestion on how to build a ranking scheme allowing us to
quantitatively compare integration indicators’ performances comes
from an established international ﬁnance literature result: to a rise
in global market integration corresponds a drop in international port-
folio diversiﬁcation beneﬁts (see, among many others, Longin and
Solnik, 1995; Errunza et al., 1999; Driessen and Laeven, 2007;
Bekaert et al., 2009; Christoffersen et al., 2012 ). While many stud-
ies simply argue that the increasing comovement between interna-
tional equity market returns may lead to decreasing diversiﬁcation
beneﬁts, only one study proposes a dynamic international diver-
siﬁcation beneﬁts metric. Christoffersen et al. (2011, 2012) build a
dynamic volatility-based conditional diversiﬁcation beneﬁts mea-
sure (henceforth V −CDB ) for three country groups. We base our
ranking procedure on their measure as follows. First, following
Christoffersen et al. (2011) ; 2012 ), we compute an indicator of dy-
namic diversiﬁcation beneﬁts for each country group. Second, via
standard empirical analyses, we examine whether there is a link
between the integration pattern generated by the proposed mea-
sures and diversiﬁcation beneﬁts. Speciﬁcally, we ask whether one
measure explains better than another variations in international
portfolio diversiﬁcation beneﬁts (i.e., de facto integration).
Our main results are as follows. First, we observe that the
SC , 1 stPC and ¯R 2 give rise to almost identical equity market

152 M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174
integration patterns. Second, heteroskedasticity-adjusted measures
tend to produce more volatile integration patterns. Still, over the
long-run they give rise to very similar ﬁnancial integration trends.
It turns out that the long-run equity market integration patterns
extracted using different statistical methods do not show qual-
itatively relevant differences. Third, the SC , on average, explains
movements in international diversiﬁcation beneﬁts as well as, if
not better than, more sophisticated measures (i.e., PCA-based and
heteroskedasticity-adjusted measures). We stress that our main
ﬁndings survive a battery of robustness checks.
The remainder of this paper is organized as follows.
Section 2 reviews the literature on ﬁnancial integration mea-
sures. Sections 3 and 4 describe the methodologies and data,
respectively. Section 5 compares the ﬁnancial integration patterns
that are generated using different methodologies. Section 6 em-
ploys a novel and simple approach to evaluate the ability of
the proposed measures in explaining movements in de facto
integration. Section 7 provides additional discussions on the ad-
vantages and disadvantages of the employed integration measures.
Section 8 concludes.
2. Related literature: a focus on ﬁnancial integration measures
Broadly speaking, the existing ﬁnancial integration indicators
can be classiﬁed in three categories: ( i ) price-based indicators;
( ii ) quantity-based indicators; and ( iii ) regulatory (or institutional)
measures. Generally, four criteria are used to evaluate the useful-
ness of the above indicators ( Adam et al., 2002 ): ( i ) data availabil-
ity; ( ii ) reliability of the data on which the indicators are based;
( iii ) economic meaning of the indicators and ( iv ) the ease of build-
ing and updating the indicators. Based on these criteria, price-
based indicators – classiﬁed also as direct measures of integra-
tion –h a v e attracted more attention than quantity-based indica-
tors (i.e., stock or ﬂow data-based measures), as they satisfy the
above conditions. Since price-based indicators invoke the law of
one price, they also have a clear-cut interpretation, which is of-
ten lacking for those quantity-based indicators relying on ﬂow data
( Volosovych, 2011 ). For these reasons, several studies have focused
on the comovement between asset prices (see, among many oth-
ers, Kim et al., 2006; Carrieri et al., 2007; Bekaert et al., 2009 ).
Hence, although ﬁnancial integration encompasses many different
aspects of complex linkages across various ﬁnancial markets, our
study follows this strand of the international ﬁnance literature and
relies on international equity prices convergence.
From a methodological point of view, the empirical literature
has proposed different measurement frameworks relying on price-
based indicators: Vector Auto-Regression (VAR) models ( Khalid and
Kawai, 2003; Elyasiani and Wanli, 2008; Jayasuriya, 2011 ), standard
cross-country correlation ( Watson, 1980; Meric and Meric, 1989;
Goetzmann et al., 2005 ), cointegration and error-correction models
( Laopodis, 2011; Gupta and Guidi, 2012 ), GARCH models ( Kim et al.,
20 06; Carrieri et al., 20 07; Wang and Moore, 20 08; Egert and Ko-
cenda, 2011 ), asset pricing models ( Nellis, 1982; Mauro et al., 2002;
de Jong and de Roon, 2005; Barr and Priestley, 2004; Abad et al.,
2010; Volosovych, 2011; Donadelli and Paradiso, 2014 ), and com-
mon component approach ( Carrieri et al., 2007; Pukthuanthong
and Roll, 2009; Yu et al., 2010 ). VAR-based studies make use of im-
pulse response analysis to investigate the effects of contagion and
the degree of interdependence, whereas cointegration-based stud-
ies aim to assess the presence of a long-run equilibrium among
cross-country ﬁnancial variables, such as stock or bond prices. As-
set pricing models usually rely on a standard CAPM framework and
assume that the excess return of a country is generated by global
factors (with a coeﬃcient ξ) and idiosyncratic factors (with a co-
eﬃcient 1- ξ). In this setting, the parameter ξis meant to capture
equity market segmentation (see, among others, Barr and Priest- ley, 2004 ). Cointegration methods, VAR and asset pricing models
tend to have major drawbacks. For instance, cointegration and VAR
models are not able to produce a numerical measure of ﬁnan-
cial integration. 2 Moreover, cointegration methods have been crit-
icized for being static approaches and unable to capture the dy-
namic evolution of a process ( Kearney and Lucey, 2004; Kim et al.,
2006; Wang and Moore, 2008 ). For these reasons, cointegration-
and VAR-based metrics do not ﬁt the agenda of this paper.
The SC , a conventional measure of comovement, can be eas-
ily implemented and has a straightforward interpretation. To sum-
marize comovement in a group of markets, the usual practice is
to compute the average of the correlation coeﬃcients estimated
for each country-pair ( Mauro et al., 2002; Quinn and Voth, 2008 ).
Some studies employ SC over different sub-periods ( Goetzmann
et al., 2005; Quinn and Voth, 2008 ). Traditionally, however, the SC
implicitly assumes that the relationship between assets does not
change over time. Hence, it does not track down the dynamics
of the relationship between volatilities. To monitor movements in
the volatility across equity markets, dynamic conditional correla-
tion models are generally used ( Wang and Moore, 2008; Egert and
Kocenda, 2011 ). However, two issues arise from the use of these
models: ( i ) Longin and Solnik (2001) show that correlation is not
related to market volatility per sé but it is mainly affected by the
market trend; correlation seems to rise only when asset prices fall
(bear markets) and not when they are expected to rise (bull mar-
kets); ( ii ) Forbes and Rigobon (2002) argue that conditional corre-
lation is subject to a volatility bias; the coeﬃcient would increase
in periods of high volatility (during crises or shocks) and, as a con-
sequence, may lead to a wrong conclusion that there is a conta-
gion effect during a crisis. Therefore, there is no general consen-
sus on how one should account for conditional heteroskedasticity
( Volosovych, 2013 ).
Even if the SC and other correlation-based metrics are still
widely used as integration measures, they have been subject to
severe criticism. For instance, Bekaert et al. (2009) conclude that
“Correlations are an important ingredient in the analysis of in-
ternational diversiﬁcation beneﬁts and international ﬁnancial mar-
ket integration. Of course, correlations are not a perfect measure
of either concept ”( p . 2612). In line with Carrieri et al. (2007) ;
Pukthuanthong and Roll (2009) write: “The simple correlation be-
tween broad ﬁnancial market index returns from two countries can
be a poor measure of their economic integration ”( p . 231). Simi-
larly, Volosovych (2011) : “…a conventional measure of comovement,
the coeﬃcient of correlation, has limited applicability as a mea-
sure of economic integration ”( p . 1560). Based on these arguments,
Pukthuanthong and Roll (2009) and Volosovych (2011) propose
two PCA-based integration measures, which, as they argue, are
more robust than the SC . Pukthuanthong and Roll (2009) introduce
a novel measure based on the explanatory power of a multi-factor
model. In their setting, the ﬁrst ten principal components, which
explain close to 90% of the cross-sectional variation in country re-
turns, are employed as global factors. The ¯R 2 is then computed in
each calendar year for each country. The cross-country average ¯R 2
represents then their alternative integration measure. In the spirit
of Nellis (1982) and Mauro et al. (2002) , Volosovych (2011) , in-
stead, uses the proportion of total variation in individual returns
explained by the ﬁrst principal component to measure the degree
of ﬁnancial integration. 3 He focuses on the bond market of 15 in-
2 In a cointegrating framework, an error correction representation contains only
information on the speed of adjustment to long-run equilibrium but not on the
level of integration.
3 Mauro et al. (2002) ﬁnd that the ﬁrst principal component explains a large
proportion of variation of sovereign bond spreads for a group of emerging mar-
ket countries from 1877 to 1913 and an even larger proportion in the 1990s. Earlier,
Nellis (1982) used PCA to compare interest rate comovement among industrialized

M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174 153
dustrialized economies from 1875 to 2009 and computes the inte-
gration dynamics using a rolling window of 156 months. Of course,
PCA-based measures may also raise some concerns. For example,
among others, the PCA is usually subject to a trade-off between
the covariance and the correlation matrix used to derive the com-
ponents. In the correlation matrix, the variables are standardized.
The goal of this simple transformation is to give to all variables
an equal weight, even if they exhibit huge variance differences. In
general, such transformation is not required when variables have
the same unit. To be sure that high changes in the variance will
not dominate the principal components, this transformation is of-
ten accounted for. Of course, this may represent a non-negligible
drawback. Therefore, by using the covariance matrix there can be
the risk that variables with high variance will inﬂuence the overall
analysis.
Apparently, there is no general consensus on how to prop-
erly measure ﬁnancial integration. From this literature review, two
main issues remain open: ( i ) Is there heterogeneity in the set of
information provided by all these measures over the long-run? ( ii )
Do all these measures really capture movements in integration-
driven phenomena (e.g., international diversiﬁcation beneﬁts)? We
attempt to address these issues in Sections 5 and 6 .
3. Measuring ﬁnancial integration
This section describes the methodologies employed to build
the integration measures aimed at capturing regional and global
equity market integration dynamics. Speciﬁcally, we present in
detail all the measures listed in Table 1 . Section 3.1 intro-
duces the SC . In Section 3.2 , we present the two recently de-
veloped PCA-based measures (i.e., ¯R 2 and 1 stPC ). In the spirit
of Ball and Torous (2006) , Section 3.3 introduces the concept
of stochastic interdependence and applies it to the SC , ¯R 2 and
1 stPC . Finally, Section 3.4 focuses on well-known and widely used
heteroskedasticity-adjusted measures (i.e., Forbes-Rigobon, DCC-
GARCH, BEKK-GARCH, Conditional Beta).
3.1. The dynamic SC
The SC is one of the most widespread proxies for measuring
international markets comovement and thus ﬁnancial integration
( Kearney and Lucey, 2004 ). 4 Additionally, it is very easy to com-
pute and has a straightforward interpretation. Following standard
practices, we focus on bilateral correlations. This avoids the choice
of a benchmark market. Bilateral correlations are estimated using
a rolling window of 60 months. 5 Our dynamic SC is then deﬁned
as the cross-country average correlation, i.e., the average of upper
or lower triangular elements in the correlation matrix estimated in
each window.
3.2. Adding robustness
3.2.1. The ¯R 2
Pukthuanthong and Roll (2009) argue that the correlation co-
eﬃcient may represent an unsuitable measure of integration and
countries before and after the move to a ﬂoating exchange rate regime in the early
1970s.
4 Examples of studies using simple correlation include Panton et al. (1976) and
Hilliard (1979) .
5 The rolling window length over which correlations are computed can affect the
outcome. The window should be wide enough to leave suﬃcient observations to
compute precise correlation coeﬃcients but short enough in order to avoid smooth-
ing out important medium-term changes in integration. In general, the optimal win-
dow size cannot be determined analytically but has to be determined from the out-
set. We ﬁx the rolling window size at 60 months such that it approximates the
length of a full business cycle. In any case, our results are robust to varying win-
dow lengths (see Appendix A, Fig. A.1 ). show that two countries being perfectly integrated might not dis-
play perfect correlation between their returns. As an alternative,
they propose a measure based on the explanatory power of a
multi-factor linear model. This approach does not rely on any par-
ticular asset pricing model but merely requires globally common
factors that can be interpreted as non-traded risk factors driving
global ﬁnancial markets. The global factors f are obtained from ap-
plying the PCA to international equity returns:
f i,t = v i, 1 r 1 ,t + v i, 2 r 2 ,t + . . . v i,C r C,t , (1)
where r c, t is the country c ’s market return at time t and v ij is the
j th element of i th PC, also called scoring coeﬃcient or loading. The
ﬁrst K < C global factors serve then as explanatory variables in a
multi-factor regression for all C country index returns. Formally,
r c,t = βc, 0 + βc, 1 f 1 ,t + ···+ βc,K f K,t + /epsilon1n,t , c ∈ { 1 , . . . , C} , (2)
where βc, k measures country c ’s exposure to k th global factor. The
cross-country average of the ¯R 2 s obtained from the above regres-
sions serves as a robust measure of ﬁnancial integration. 6
We acknowledge that our estimation procedure slightly de-
viates from the original approach. Pukthuanthong and Roll
(2009) use daily returns and estimate the eigenvectors for each
calendar year separately and apply them to returns in the follow-
ing calendar year. In doing so, they produce out-of-sample global
factors that are then used as explanatory variables in the regres-
sions. The number of global factors is chosen such that they ex-
plain close to 90% of the total volatility in the covariance ma-
trix. Differently, we estimate the cross-country average ¯R 2 using a
rolling window of 60 months. Additionally, the correlation matrix
instead of the covariance matrix of country returns is used. 7 To be
homogeneous, we decide to employ K = 3 in-sample global factors
in each window and for each country group. On average, the ﬁrst
3 PCs explain around 70% of total returns variation. 8
3.2.2. The 1 stPC
Volosovych (2011) proposes an alternative PCA-based measure.
He argues that the proportion of total variation in individual eq-
uity returns explained by the 1 stPC – dynamically extracted using a
rolling window approach –c a n be employed to capture de facto in-
tegration (see also Nellis, 1982; Mauro et al., 2002 ). This approach
has several advantages: ( i ) it accounts for several dimensions of
integration including comovement and segmentation; ( ii ) it is ro-
bust to the presence of outliers or heavy-tailed distributions and
the choice of a reference country; and ( iii ) it has a clear theory-
based interpretation.
The estimation procedure is straightforward. The initial steps
correspond to the ones needed for computing the ¯R 2 . What is
different here is that instead of performing a PCA-based regres-
sion, Volosovych (2011) assumes that the variation explained by
6 The ¯R 2 as a potential measure of integration has been used also by Yu et al.
(2010) . However, their common component approach differs from the one devel-
oped by Pukthuanthong and Roll (2009) in several dimensions. First, the ¯R 2 is ob-
tained using a 3-year rolling OLS estimation. Second, the employed factors are not
represented by principal components (i.e., artiﬁcial risk factors) but by four traded
factors (i.e., currency returns, excess equity returns, dividend yields and forward
premia).
7 The correlation matrix is used to account for large variations across country re-
turns’ variances. In doing this, we avoid the dominance of a single PC. Note that the
use of the covariance matrix gives rise to similar cross-country average ¯R 2 dynamics
(see Appendix A, Fig. A.2 ).
8 In particular, the ﬁrst 3 PCs capture up to 80% of returns variation among DMs
over the period 2005–2015 and around 70% of return variation among EMs and ALL
during the mid-90s. Of course, the percentage of volatility in the correlation matrix
explained by the 3 PCs is increasing over time for each country group. Note that
using more or less factors still provides a similar pattern of growing integration
(see also Pukthuanthong and Roll, 2009 ). In particular, with more (less) factors the
¯R 2 s are slightly higher (lower).

154 M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174
the 1 stPC can serve as a measure of ﬁnancial integration. Formally,
Variation explained by 1 stP C = λ1 /summationtext C
i =1 λi , (3)
where λi is the eigenvalue of i th PC. The intuition behind this ap-
proach is that ﬁnancial market integration can be captured by the
proportion of countries’ returns explained by an unobserved factor.
We stress that the measures proposed by Pukthuanthong and Roll
(2009) and Volosovych (2011) are very similar. In particular, under
certain assumptions, these two approaches yield identical results
(see, Jong and Kotz, 1999 ). In Appendix B , we illustrate this by us-
ing a “two country-one PC example”.
3.3. Accounting for stochastic interdependence
3.3.1. The SC (ASI)
Existing empirical studies document a positive linkage between
correlation and volatility ( King et al., 1994; Ramchand and Susmel,
1998; Morana and Beltratti, 2008 ). Longin and Solnik (1995) , for
instance, provide evidence of instability in the correlation patterns
characterizing international stock markets. They observe that the
volatility and correlation increased in correspondence of the Octo-
ber 1987 stock market crash. Particularly, the correlation remained
on a relatively high level afterwards, while volatility reverted to
pre-crash levels. Forbes and Rigobon (2002) argue that changes in
market volatility can bias the correlation coeﬃcient and introduce
a correction term in order to obtain its unconditional counterpart.
They employ the newly obtained cross-market correlations to test
for contagion effects during stock market crises. Contagion is as-
sumed to take place only if market interdependence (i.e., strong
linkages that exist in all states of the world) exhibits a signiﬁcant
change during a crisis. While the authors’ analysis is character-
ized by a constant covariance structure in returns, Ball and Torous
(2006) take into account the time-varying and stochastic nature of
covariances. In the following, we present the latter approach while
the former is employed further below.
Similarly to Forbes and Rigobon (2002) , Ball and Torous
(2006) argue that using the correlation coeﬃcient for measuring
the comovement of stock markets might yield potentially biased
results. In order to account for this problem, the authors introduce
a linear state-space model in which they explicitly differentiate be-
tween measured variables and their population counterparts. We
follow this approach and use this model:
y t = αt + /epsilon1t , v ar(/epsilon1t ) = H, (4)
αt = T αt−1 + ηt , v ar(ηt ) = Q, (5)
where y t = { log σ2
i,t , log σ2
j,t , z i,j,t } is the observation vector of log
variances and Fisher transform z i,j = 1
2 log 1+ ρij
1 −ρij of the sample cor-
relation ρij , for countries i and j . The measurement Eq. (4) links y t
with its population counterpart αt . The measurement errors /epsilon1t are
assumed to be identically and independently distributed with non-
diagonal covariance matrix H . The transition Eq. (5) models the
stochastic evolution of αt with transition matrix T and residual er-
ror terms ηt with covariance matrix Q . We assume non-diagonality
in H and Q . The former speciﬁcation allows measurement errors to
be correlated. The latter takes into account the stochastic interde-
pendence between markets.
Following Ball and Torous (2006) , the covariance matrices H
and Q as well as the transition matrix T are estimated by apply-
ing the Kalman ﬁlter in combination with the EM Algorithm. 9 The
9 The estimation methodology goes along the lines described in the Appendix of
Ball and Torous (2006) . First, we ﬁt univariate linear state space models for each population correlation is then obtained by computing the inverse
of the Fisher transform using Broyden’s Method. Our estimation
procedure differs from the one originally proposed by Ball and
Torous (2006) in several aspects. The authors measure volatilities
and correlations by dividing the whole time series sample of daily
returns into sequential non-overlapping intervals. The countries’
return volatilities and the respective bilateral return correlations
are assumed to be constant within each interval but are allowed to
vary across the resultant intervals. Differently, we estimate volatil-
ities and correlations using monthly returns with overlapping in-
tervals of length 60 months (i.e., rolling windows). Within each
window, the moments are assumed to be constant but allowed to
vary across the rolling windows. 10 The cross-country average of the
rolling population correlation serves us as a new measure of ﬁnan-
cial market integration that accounts for cross-market stochastic
interdependence (ASI).
3.3.2. The ¯R 2 (ASI) and 1 stPC (ASI)
The estimation of ¯R 2 and 1 stPC relies on the PCA which, in turn,
uses the return correlation matrix as input. Using the above esti-
mation results, we are able to re-calculate the two measures in or-
der to accommodate stochastic interdependence between markets.
In practice, we substitute the sample correlations (i.e., measured
correlations) by their population counterparts. This is repeated for
each rolling window while all other calculation steps remain un-
affected. We ref er to these adjusted measures as: the ¯R 2 (ASI) and
the 1 stPC (ASI).
3.4. Accounting for heteroskedasticity
3.4.1. Forbes–Rigobon
When studying contagion in ﬁnancial markets, Forbes and
Rigobon (2002) ﬁnd larger cross-country correlation when com-
mon volatility is high. They argue that correlations are biased by
heteroskedasticity. In particular, volatilities rise during crises lead-
ing to an artiﬁcial upward-bias in correlations. In order to correct
for the bias, the authors propose a volatility-adjusted correlation
coeﬃcient which takes the following form:
ρF R
t = ρt /radicalbig
1 + δt [1 −(ρt ) 2 ] , (6)
where ρt is the Pearson correlation, and δt is the increase in the
variance of the returns in a pre-speciﬁed time-interval relative to
the period with the minimum variance.
Our estimation procedure goes as follows. As for the SC , we ﬁx
the rolling window at 60 months and compute the average volatil-
ity across all countries. Within each rolling window, we obtain the
variance correction δusing 24 month intervals. Finally, we correct
the cross-country average correlation using δand plot the resulting
volatility-corrected correlation ρFR .
In line with the original argument of Forbes and Rigobon
(2002) , we account for this volatility adjustment only in the pres-
ence of major international ﬁnancial and political events. To this
end, we rely on the US and EU economic policy uncertainty indices
developed by Baker et al. (2015) and consider the following events:
Second Oil Price Shock (July 1979–April 1980); 1980s US Reces-
sion (July 1981–November 1982); Black Monday (October 1987–
November 1987); 1st Gulf War (August 1990–February 1991); Japan
of the three series. Using the estimated coeﬃcients, we run the EM algorithm with
150 iterations in the multivariate case. Then, the EM estimates are used as starting
values in the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. We also employ
the Choleski factorization of H and Q to ensure positive deﬁniteness.
10 In our view, this can be interpreted as a low-frequency long-run mean esti-
mation of volatilities and correlations across a cycle. For robustness, we also apply
the original approach using 5 month non-overlapping intervals. The resulting equity
market integration dynamics are very similar and are available upon request.

M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174 155
Stock Price Crisis (January 1992–January 1993); Asian and Rus-
sian Crises (July 1997–March 1999); 9/11 (August 2001–November
2001); Invasion of Iraq (March 2003–May 2003); Great Recession
(December 20 07–June 20 09); EU Sovereign Debt Crisis (July 2011–
December 2011); Greek Default Risk (January 2015–August 2015);
Stock Market Crash in China (July 2015–September 2015).
3.4.2. BEKK
An alternative approach to measuring the extent of market in-
tegration in terms of volatility is the application of the multi-
variate Baba–Engle–Kraft–Kroner (BEKK) model proposed by Engle
and Kroner (1995) . For stationary return series, ARMA models can
be employed to model the mean while GARCH models can be
used to capture the time-varying volatilities of each return series.
In the following, we assume that the conditional mean of coun-
try i ’s return r i, t follows an ARMA(1,1) process, 11 (i.e., r i,t = μi +
φi r i,t−1 + θi e i,t−1 + e i,t ). The error vector e t is conditionally nor-
mal with mean zero and time-varying variance-covariance matrix
H t = [ h ij,t ] . The BEKK-GARCH(1,1) model assumes that the covari-
ance matrix can be decomposed as
H t = C C /prime + A /prime e t−1 e /prime
t−1 A + G /prime H t−1 G, (7)
where C, A and G are N ×N parameter matrices and C is upper
triangular. Note that the conditional variances ( h ii, t ) and the con-
ditional covariances ( h ij, t ) depend on lagged values of conditional
variances ( h ii,t−1 ) and the conditional covariances ( h ij,t−1 ), as well
as on lagged values of squared errors of both series and the cross-
products of the errors. This feature distinguishes the BEKK-GARCH
model from the univariate GARCH model ( Horvath and Petrovski,
2013 ). By employing a bivariate BEKK-GARCH(1,1) model speciﬁca-
tion, we estimate time-varying variances and covariances pairwise
between local market returns and then compute the conditional
correlations.
3.4.3. DCC-GARCH
The DCC-GARCH proposed by Engle and Sheppard (2001) and
Engle (2002) , is another model for examining correlation dynam-
ics among assets. It belongs to the family of multivariate GARCH
models and represents an extension of the Constant Conditional
Correlations model (CCC) proposed by Bollerslev (1990) . The DCC
approach calculates the current correlation between variables as
a function of past realizations of volatility within the variables as
well as the correlations between the variables. The model is de-
signed to allow for two stage estimation, where in the ﬁrst stage
univariate GARCH models are estimated for each residual series. In
the second stage, residuals, transformed by their standard devia-
tion estimated during the ﬁrst stage, are used to estimate the pa-
rameters of the dynamic correlation. Analogous to the BEKK model,
DCC requires standardized residuals from the mean-variance spec-
iﬁcation of each return series. Again, we employ an ARMA(1,1)
speciﬁcation with a conditionally normal error e t with mean zero
and a variance-covariance matrix that is decomposable into time-
varying correlations and standard deviations. Further, we assume
that the variances follow a GARCH(1,1). Then, the DCC correlation
speciﬁcation is given as
R t = diag { Q t } −1 / 2 Q t diag { Q t } −1 / 2 , (8)
where Q t = [ q ij,t ] is a symmetric positive deﬁnite variance-
covariance matrix of the GARCH residuals. As for the standard
correlation, this GARCH-based indicator of ﬁnancial integration is
computed by averaging all the dynamic conditional country-pair
correlations.
11 The estimation was also conducted using the BIC criterion to determine optimal
p and q for an ARMA(p,q) process. The results do not yield any qualitative improve-
ment and are included in the robustness section (see Appendix A, Fig. A.3 ) 3.4.4. Conditional time-varying beta
Previous literature suggests to employ the beta, as measured in
the CAPM, in order to gauge the extent of market integration (see,
among others, Koedijk et al., 2002 ; De Santis and Gérard, 1998) . In
the following, we model the expected returns on each local equity
market as a function of its conditional covariance with the returns
on the global market portfolio. We decide to apply the following
conditional one-factor model
E t−1 [ r i,t ] = Cov t−1 (r i,t , r m,t )
V ar t−1 (r m,t ) E t−1 [ r m,t ] , (9)
where r i and r m represent the local equity and the global mar-
ket, respectively. Application of this model requires the speciﬁca-
tion and estimation of the conditional variances. However, asset-
pricing theories do not specify how the conditional second mo-
ments should be modeled. Given the vast literature documenting
that equities exhibit volatility clustering and leptokurtosis, and due
to the estimation advantages of a simple GARCH framework, as
pointed out by De Santis and Gérard (1998) , we decide to em-
ploy a bivariate version of BEKK-GARCH(1,1) model. We estimate
the conditional sensitivities of local equity market index returns
to changes in the global portfolio for each country separately. The
MSCI World Index is used as a proxy for the global market port-
folio. The cross-country averaged Conditional Beta serves then as
proxy for equity market integration.
4. Data
Our sample consists of data representing three groups of coun-
tries: ( i ) DMs; ( ii ) EMs and ( iii ) ALL. Speciﬁcally, we use monthly
Total Return Indices (i.e., reinvested dividends are included) from
Level 1 (i.e., Market) of Datastream Global Equity Indices (DGEI)
for the following countries 12
• DMs: Australia, Austria, Belgium, Canada, Denmark, France, Ger-
many, Hong Kong, Ireland, Italy, Japan, Netherlands, Singapore,
Switzerland, United Kingdom and United States (16 countries);
• EMs: Chile, India, Indonesia, Korea, Malaysia, Mexico, Philip-
pines, South Africa, Taiwan, Thailand and Turkey (11 countries);
• ALL: 16 DMs + 11 EMs (27 countries).
DMs and EMs data run from January 1973 to January 2016 and
from May 1990 to January 2016, respectively. We use monthly data
in line with existing studies focusing on time-varying market inte-
gration (see, among others, Barr and Priestley, 2004; de Jong and
de Roon, 2005; Carrieri et al., 2007; Yu et al., 2010; Volosovych,
2011 ). Note also that monthly data, instead of daily data, are
employed to avoid a set of common high-frequency data issues:
( i ) presence of zero returns; ( iii ) non-synchronicity and ( ii ) ex-
cess noise (in particular, in the case of the EMs data). 13 Coun-
try equity market returns are computed from TRI as follows, r c,t =
[(T RI c,t /T RI c,t−1 ) −1] , where TRI c, t is the return index of country c
at time t . 14
We stress that our sample is homogeneous. First, the set of
countries belonging to each group does not change over time.
Second, differently from other studies, we use exclusively TRIs
12 Note that DGEI have been widely used by the international ﬁnance literature
(see, for instance, Baca et al., 20 0 0; Brooks and Negro, 2004; Donadelli and Par-
adiso, 2014 ).
13 In this respect, Pukthuanthong and Roll (2009) write: “There are reasons (thin
trading and other microstructure effects) to think that longer return intervals might be
better even though the number of observations would be reduced ”( p . 230). See also
Bekaert et al. (2009) on this issue.
14 Note that the use of different stock market indexes (i.e., OECD Share Price In-
dexes, Morgan Stanley Capital International (MSCI) Total Return Indices) does not
alter the paper’s main results.

156 M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174
Fig. 1. Financial and trade market openness. Notes : this ﬁgure reports the evolution of the total trade (sum of import and exports as a % of GDP), foreign direct investment
(FDI, net inﬂows, as % of GDP) and stocks traded (market value, as % of GDP) in DMs and EMs (excluding Taiwan). The dashed lines represent linear trends. Data are annual
and run from 1974 (or later) to 2012. Source: World Development Indicators (World Bank).
that are, of course, preferable. Let us remark that our coun-
try classiﬁcation allows to examine integration dynamics in both
developed and emerging markets as well as global market integra-
tion. 15 To account for all possible sources of comovement between
international equity returns – including changes in cross-country
currency variations –o u r TRIs are denominated in local currency
(see Volosovych, 2011 ). Finally, note that the period covered in this
study ( i ) is characterized by an increasing degree of ﬁnancial and
trade market openness (see Fig. 1 ) and ( ii ) includes relevant in-
ternational economic and political events (e.g., II Oil Price Shock
in July 1979; Black Monday in October 1987; 1st Gulf War in De-
cember 1990; Russian ﬁnancial crisis in August 1998; China WTO
entry in October 20 0 0; 9/11 terrorist attacks in September 2001;
Lehman Chapter 11 in September 2008; EU sovereign debt crisis,
among others).
5. Comparing ﬁnancial integration measures
Fig. 2 (Panel A) depicts the equity market integration patterns
generated by the SC , 1 stPC and ¯R 2 for the three country groups.
15 A similar classiﬁcation can be found in Christoffersen et al. (2012) . Our results suggest that the basic SC and the two recently in-
troduced PCA-based measures give rise to almost identical equity
market integration dynamics. In the dynamics depicted in Fig. 2 ,
the only noteworthy difference between the SC and the two PCA-
based measures is that the ¯R 2 tends to suggest a relatively high
level of integration. More speciﬁcally, for each country group the
¯R 2 is always above 0.5. Differently, the SC and 1 stPC range from
a minimum of 0.20 (mid-90s in EMs) to a maximum of 0.85 (sub-
prime crisis period in DMs). In other words, we observe only differ-
ences in the magnitude of the degree of integration while the in-
tegration trends are almost indistinguishable. We remark that the
similarity between the 1 stPC and ¯R 2 should not come as a surprise.
By construction, as mentioned in Section 3.2 , the percentage of
variance explained by the ﬁrst component and the cross-country
average regression R-square yield identical results. We show this
empirically (see Table B.1 ) and theoretically in Appendix B .
Let us remark that the methodology employed to compute the
dynamic ¯R 2 slightly differs from the one used in Pukthuanthong
and Roll (2009) . As a robustness check, we recompute this alter-
native measure by following the empirical strategy described in
Section 7 of Pukthuanthong and Roll (2009) . The original ¯R 2 is
plotted in Fig. A.4 along with ( i ) the dynamic SC – estimated as

M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174 157
Fig. 2. Integration dynamics: correlation vs. robust measures. Notes : this ﬁgure reports the equity market integration dynamics generated by the SC (dashed black line),
¯R 2 (light gray line) and 1 stPC (dark gray line) for DMs, EMs and ALL. In Panel B, the SC , ¯R 2 and 1 stPC account for stochastic interdependence (ASI) using the model proposed
by Ball and Torous (2006) . All measures are computed using a rolling window of 60 months. DMs data run from January 1973 to January 2016. EMs data run from May 1990
to January 2016. Source: DGEI.
described in Section 3.1 – and ( ii ) Yearly Correlation (i.e., cross-
country average correlation estimated during each calendar year
using daily returns). We observe almost the same pattern of grow-
ing integration over time for each country group. As in Fig. 2 , the
¯R 2 is –o n average – higher than the Yearly Correlation. 16 An ex-
ception is EMs where, over the period 1995–2007, the ¯R 2 and the
Yearly Correlation almost overlap ( Fig. A.4 , middle panel). 17 Once
again, the long-run integration patterns reproduced by the SC and
¯R 2 are almost identical.
The stochastic interdependence adjustment – implemented by
relying on the Ball and Torous (2006) methodology –d o e s not al-
ter much our main results (see Fig. 2 , Panel B). What we observe
are changes in the degree of integration estimated by the three
different measures. As expected, the magnitude of these changes
16 This result is not surprising. In our opinion, this result is partially driven by
the fact that the selected PCs explain a relatively large fraction of returns’ variation.
Pukthuanthong and Roll (2009) draw similar conclusions. In particular, the patterns
generated by the mean ¯R 2 and the mean correlation coeﬃcient are very similar. As
in our case, we can observe relevant differences only in the magnitude but not in
the trend Figs. 4 and 6 in Pukthuanthong and Roll (2009) ), regardless of the chosen
cohort. Of course, the use of a lower number of PCs has the only effect of reducing
such magnitude-gap.
17 This is at odds with the results presented in Pukthuanthong and Roll (2009) .
However, they focus on global equity market integration. At the regional level, and
in particular among EMs only, the idiosyncratic component may play an important
role regardless of the number of PCs used in each regression. tends to be stronger during crisis-periods. In practice, in the pres-
ence of crises the stochastic interdependence adjustment lowers
our metrics. This is more evident in EMs. In this respect, stochastic
interdependence can be interpreted as a Forbes-Rigobon volatility
adjustment. Still, over the long-run ASI-adjusted measures, the SC
and PCA-based measures deliver very similar integration dynamics.
Fig. 3 depicts integration dynamics for DMs, EMs and ALL
generated by employing heteroskedasticity-adjusted measures (i.e.,
Forbes-Rigobon correlation, DCC-GARCH, BEKK, Conditional Beta).
Even if adjusted for volatility, the underlying integration trend of
all these indicators seems to be similar to the integration patterns
depicted in Fig. 2 ( Fig. 3 , Panel A). 18 This shows up more clearly
once we plot the trend –e x t r a c t e d via a standard Hodrick-Prescott
ﬁlter –o f all these heteroskedasticity-adjusted integration indica-
tors ( Fig. 3 , Panel B). In general, integration seems to follow an
increasing trend, although with some differences among country-
groups. Precisely, we observe an increase in the trend from the
mid-1990s and a drop in the post-Lehman period. This supports
the stylized facts reported in Fig. 1 showing a drop in interna-
tional trade among countries in the aftermath of the 20 07–20 09
subprime crisis.
18 An exception is the Conditional Beta. This result conﬁrms that the cross-country
beta dynamics heavily depends on the choice of the factor.

158 M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174
Fig. 3. Integration dynamics: heteroskedasticity-adjusted measures. Notes : this ﬁgure depicts the equity market integration patterns generated by heteroskedasticity-
adjusted measures along with the dynamic SC (dashed black line) for DMs, EMs and ALL. The Forbes–Rigobon correlation is computed using a rolling window of 60 months.
DCC-GARCH and BEKK-GARCH are the average bilateral correlation coeﬃcients obtained from applying an ARMA(1,1)-DCC-GARCH and ARMA(1,1)-BEKK-GARCH model, re-
spectively. Conditional Beta is the cross-country average coeﬃcient estimated from Eq. (9) . Panel B reports the trend of the equity market integration patterns displayed in
Panel A. Trends are obtained via a standard Hodrick-Prescott ﬁlter (with λ= 14 , 400 ). DMs data run from January 1973 to January 2016. EMs data run from May 1990 to
January 2016. Source: DGEI.
From Figs. 2 and 3 we can draw the following conclusions. First,
the use of both sets of measures does not generate relevant long-
run differences in the equity market integration process. This holds
across different country-groups. Second, even if the trend is simi-
lar, by accounting for volatility a higher degree of heterogeneity
among indicators emerges. This is because volatility-adjusted mea-
sures, which explicitly capture periods of higher uncertainty, tend
to be more volatile than the measures plotted in Fig. 2 .
Taken together, the results depicted in Figs. 2 and 3 suggest the
presence of a common equity market integration trend. As afore-
mentioned, all the proposed measures suggest that after slowing
down during the crisis-period at the end of the1990s and the be-
ginning of 20 0 0s the equity market integration picked up again in
the period 20 04–20 08 and ﬂattened (or slightly decreased) in the
aftermath of the Lehman brothers’ collapse. A battery of robustness
checks conﬁrms that the SC and all the other alternative measures
give rise to a similar equity market integration trend. All the inte-
gration trends obtained from our robustness exercises are reported
in Appendix A ( Figs. A .1 –A .3 ). 19
19 In particular, our results are robust to: ( i ) different window-lengths ( Fig. A.1 ,
Panel A (36 windows) and Panel B (96 windows)); ( ii ) the use of a different number
of PCs in computing Volosovych (2011) ’s measure ( Fig. A.2 , Panel A); ( iii ) using the
covariance matrix in performing the PCA ( Fig. A.2 ), Panel A; ( iv ) the exclusion of However, the detected common trend, may not be suﬃcient to
implement effective investment strategies and policies. Therefore,
it may be worthwhile to provide a quantitative assessment of the
measures’ effectiveness in capturing de facto ﬁnancial integration
over time. We attempt to address this issue in the next section.
6. Ranking ﬁnancial integration measures
The debate on whether all these existing measures really cap-
ture de facto integration is still open. In this section we aim to eval-
uate the ability of each measure in capturing integration dynamics
by relying on an established international ﬁnance result: increasing
ﬁnancial integration leads to declining international portfolio diversi-
ﬁcation beneﬁts (see, among many others, Longin and Solnik, 1995;
Errunza et al., 1999; Driessen and Laeven, 2007; Bekaert et al.,
2009; Christoffersen et al., 2012; Donadelli and Paradiso, 2014 ). We
therefore examine whether one measure captures better than an-
other movements in international diversiﬁcation beneﬁts. 20
country c equity return in the data matrix employed for computing the PCs serving
as regressors in Eq. (2) ( Fig. A.2 , Panel C); ( v ) using asymmetric speciﬁcations in the
GARCH models ( Fig. A.3 , Panel B).
20 We thank two anonymous referees for asking questions that elicited the infor-
mation in this section.

M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174 159
Fig. 4. Conditional diversiﬁcation beneﬁts. Notes : this ﬁgure reports the dynamics of the volatility-based conditional diversiﬁcation beneﬁts measure for DMs, EMs and
ALL. In each country group, V −CDB is computed from monthly country TRIs using a rolling window of 60 months. /Sigma1t in Eq. (10) is estimated using historical returns. The
dashed line represents the linear trend. DMs data run from January 1973 to January 2016. EMs data run from May 1990 to January 2016. Source: DGEI.
6.1. Measuring international portfolio diversiﬁcation beneﬁts
A dynamic measure of international portfolio diversiﬁcation
beneﬁts is computed following the methodology described in
Christoffersen et al. (2011, 2012) . The dynamic measure relies on
the concept that correlations are time-varying. As a consequence,
diversiﬁcation beneﬁts also change over time. Let us deﬁne ﬁrst
portfolio volatility
σP,t ≡/radicalbig
w /prime /Sigma1t w . Note that the covariance matrix /Sigma1t can be decomposed as
/Sigma1t = D t /Xi1t D t ,
where D t is a matrix with standard deviations σi, t on the diagonal
and zero elsewhere, and /Xi1t has ones on the diagonal and correla-
tions off the diagonal. Consider then the extreme case of zero di-
versiﬁcation beneﬁts. This implies a correlation matrix /Xi1of ones.
In this scenario, portfolio volatility reads:
¯σP,t ≡/radicalbig
ω /prime
t D t J N×N D t ω t = ω /prime
t σt ,

160 M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174
Table 2
Integration indexes vs. diversiﬁcation beneﬁts: average correlation.
DMs EMs ALL
Panel A: SC and robust measures
SC −0.665 ∗∗∗−0.725 ∗∗∗−0.685 ∗∗∗
¯R 2 −0.586 ∗∗∗−0.635 ∗∗∗−0.640 ∗∗∗
1 stPC −0.637 ∗∗∗−0.721 ∗∗∗−0.661 ∗∗∗
Panel B: ASI-adjusted measures
SC (ASI) −0.666 ∗∗∗−0.638 ∗∗∗−0.686 ∗∗∗
¯R 2 (ASI) −0.604 ∗∗∗−0.693 ∗∗∗−0.633 ∗∗∗
1 stPC (ASI) −0.554 ∗∗∗−0.568 ∗∗∗−0.642 ∗∗∗
Panel C: heteroskedasticity-adjusted measures
Forbes–Rigobon −0.026 −0.060 −0.009
BEKK −0.529 ∗∗∗−0.703 ∗∗∗−0.576 ∗∗∗
DCC 0 .595 ∗∗∗0 .700 ∗∗∗−0.565 ∗∗∗
Cond. Beta −0.380 ∗∗∗0 .480 ∗∗∗−0.356 ∗∗∗
Notes : This table reports the average correlation between international diversiﬁ-
cation beneﬁts and integration dynamics depicted in Figs. 2 and 3 for DMs, EMs,
and ALL. In Panel B (for SC (ASI)), the dynamic international diversiﬁcation beneﬁts
measure is computed by adjusting /Sigma1t in Eq. (10) for stochastic interdependence. In
Panel C, the dynamic international diversiﬁcation beneﬁts measure is computed by
adjusting /Sigma1t in Eq. (10) for heteroskedasticity. All variables are expressed in log-
differences. DMs data run from February 1978 to January 2016, EMs and ALL run
from May 1995 to January 2016. Signiﬁcance of t -tests for the correlation coeﬃcient
at the 10%, 5% and 1% levels is denoted by ∗, ∗∗and ∗∗∗.
where J N ×N is a N ×N matrix of ones, σt is the vector of indi-
vidual volatilities at time t . The opposite extreme case would lead
to a scenario in which each pair of asset returns exhibit perfect
negative correlation (i.e., −1). In this case one would be able to
ﬁnd then a portfolio with zero volatility. Using the above portfolio
volatility upper and lower bounds, the volatility-based conditional
diversiﬁcation beneﬁt is given by:
V −CDB t = ¯σP,t −σP,t
¯σP,t = 1 −/radicalbig
ω /prime
t /Sigma1t ω t
(ω /prime
t σt ) . (10)
where, for the time being, /Sigma1t is estimated using historical equity
market returns. In order to obtain our diversiﬁcation beneﬁts mea-
sure, the portfolio weights ω t must be deﬁned. In this respect,
two approaches can be followed. First, one can select directly the
weights that maximize diversiﬁcation beneﬁts (see Choueifaty and
Coignard, 2008 ). Alternatively, one could construct the minimum
variance portfolio in each period and compute diversiﬁcation ben-
eﬁts associated to the minimum variance portfolio weights. Given
the vector of individual volatilities σt and the covariance matrix
/Sigma1t at time t , we decide to employ minimum variance portfolio
weights ω t for constructing the international diversiﬁcation ben-
eﬁts measure. In addition, it is assumed that the weights sum to
one and are non-negative.
The dynamics of the V −CDB for DMs, EMs and ALL is de-
picted in Fig. 4 . Not surprisingly, for each country group we ob-
serve decreasing diversiﬁcation beneﬁts. This result is in line with
Christoffersen et al. (2011) ; 2012 ) and suggests the presence of a
negative relationship between equity market integration and diver-
siﬁcation beneﬁts.
6.2. Financial integration vs. diversiﬁcation beneﬁts
To examine the relationship between international portfolio
diversiﬁcation beneﬁts and equity market integration, we em-
ploy two basic empirical strategies. First, we compute the aver-
age correlation between each of the integration measures plotted
in Figs. 2 and 3 and the international diversiﬁcation beneﬁts mea-
sure (see Table 2 ). Second, we regress diversiﬁcation beneﬁts on
each equity market integration measure and a number of control
variables (see Tables 3 –5 ). Speciﬁcally, we control ﬁrst for the de-
gree of trade openness (speciﬁcation (2)) and subsequently for the
level of macroeconomic policy uncertainty and bad economic times (speciﬁcation (3)). Needless to mention, all these factors are asso-
ciated with the ﬁnancial integration process. On the one hand, this
set of additional macro-economic variables is included to ensure
that our market integration coeﬃcients are statistically robust. On
the other hand, we do so to purge the market integration coeﬃ-
cient in our regressions from the movements in international trade,
economic uncertainty, and bad times (i.e., recessions). 21 Loosely
speaking, the proposed validation approach allows us to iden-
tify those integration measures that ( i ) exhibit a relatively strong
(and statistically signiﬁcant) negative relationship with diversiﬁca-
tion beneﬁts and ( ii ) capture variations in international diversiﬁca-
tion beneﬁts rather well. To ensure that our empirical results are
not sensitive to the use of the covariance matrix /Sigma1t – estimated
from raw historical equity returns –o u r measure of international
portfolio diversiﬁcation beneﬁts is re-computed by accounting for
the same heteroskedasticity structure of the employed correlation-
based integration measures. 22 In practice, we use four different
approaches to compute /Sigma1t : ( i ) historical returns (as assumed
in Eq. (10) ); ( ii ) ASI; ( iii ) DCC-GARCH; ( iv ) BEKK. We therefore
obtain three additional “heteroskedasticity-adjusted diversiﬁcation
beneﬁts measures”: V −CDB ASI , V −CDB DCC , V −CDB BEKK . Correla-
tion coeﬃcients ( Table 2 ) and regression estimates ( Tables 3 –5 )
are therefore produced using the diversiﬁcation beneﬁts measures
compatible with the same volatility adjustment applied to the in-
tegration measure. 23
Entries in Table 2 show that the SC is highly correlated with the
conditional international diversiﬁcation beneﬁts measure. Speciﬁ-
cally, the correlation between the SC and diversiﬁcation beneﬁts
is highest (second highest) for EMs (DMs and ALL). Additionally,
it is highly statistically signiﬁcant. Estimates from the regression
analyses in Tables 3–5 corroborate this result. Firstly, we observe
that, with the exception of the Forbes–Rigobon volatility-adjusted
measure, all integration indicators exhibit a negative and statisti-
cally signiﬁcant market integration coeﬃcient. This, conﬁrms that
an increase in the degree of equity market integration lowers in-
ternational portfolio diversiﬁcation beneﬁts. Secondly, entries in
Tables 3–5 show that the SC explains –o n average –a relatively
high percentage of V −CDB variation. In more detail, the SC ex-
hibits the highest adjusted R-square statistic for the country group
ALL ( Table 5 ). For DMs ( Table 3 ) and EMs ( Table 4 ), the perfor-
mance of the SC is in line with that one of more sophisticated
integration measures (i.e., PCA-based and volatility-adjusted mea-
sures). 24
We acknowledge that the computed ﬁnancial integration and
conditional diversiﬁcation beneﬁts indexes have measurement er-
rors and thus may give rise to weak OLS estimates. To ensure that
21 Our variable selection is motivated by the work of Volosovych (2011, 2013) . A
similar set of control variables is employed by Kirchner et al. (2010) to examine the
transmission mechanism of ﬁscal policies in the EU over time.
22 We thank an anonymous reviewer for pointing this out.
23 We relate ( i ) V −CDB with SC ; ( ii ) V −CDB ASI with SC (ASI); ( iii ) V −CDB DCC with
DC C −GARC H; and ( iv ) V −C DB BEKK with BEKK, FR , and Cond.Beta . Note that the use
of /Sigma1t corrected for the same international events used to compute the Forbes-
Rigobon correlation will lead to artiﬁcial estimates. For this reason, we relate the
Forbes-Rigobon volatility-adjusted correlation with V −CDB BEKK . We stress that us-
ing V −CDB DCC yields similar results.
24 We apply the same empirical strategies to examine whether the recent seg-
mentation index developed by Bekaert et al. (2011) performs as well as the pro-
posed integration indexes. Note that in this case equity market segmentation and
V −CDB should move in the same direction (i.e., V −CDB rise as segmentation in-
creases). Segmentation indexes, computed along the lines of Bekaert et al. (2011) ,
are plotted in Fig. C.1 . Additional details on the segmentation index and its abil-
ity in capturing de facto integration are reported in Appendix C . The results show
that this index is not able to explain the dynamics of international diversiﬁcation
beneﬁts (see Tables C.1 and C.2 ). In particular, we ﬁnd ( i ) a counterfactual negative
correlation coeﬃcient between the segmentation index and our measure of inter-
national diversiﬁcation beneﬁts, and ( ii ) a counterfactual negative (and statistically
insigniﬁcant) market segmentation coeﬃcient.

M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174 161
Table 3
Financial integration vs. diversiﬁcation beneﬁts: DMs .
Panel A: Standard measures Robust measures
SC ¯R 2 1 stPC
(1) (2) (3) (1) (2) (3) (1) (2) (3)
Integration index. −0.937 −0.935 −0.998 −1.955 −1.948 −2.044 −1.192 −1.189 −1.316
(0 .251) ∗∗∗(0 .250) ∗∗∗(0 .360) ∗∗∗(0 .474) ∗∗∗(0 .472) ∗∗∗(0 .637) ∗∗∗(0 .309) ∗∗∗(0 .309) ∗∗∗(0 .453) ∗∗∗
[0 .304] ∗∗∗[0 .309] ∗∗∗[0 .557] ∗[0 .589] ∗∗∗[0 .588] ∗∗∗[0 .974] ∗∗[0 .385] ∗∗∗[0 .378] ∗∗∗[0 .671] ∗∗
TO −0.020 −0.249 −0.031 −0.389 −0.036 −0.260
(0 .612) (0 .725) (0 .600) (0 .741) (0 .610) (0 .710)
[0 .692] [0 .912] [0 .707] [0 .924] [0 .699] [0 .912]
EPU −0.005 −0.007 −0.005
(0 .014) (0 .014) (0 .014)
[0 .014] [0 .014] [0 .013]
RI 0 .003 0 .003 0 .004
(0 .011) (0 .067) (0 .011)
[0 .010] [0 .064] [0 .010]
OLS
Adj-R2 0 .234 0 .232 0 .224 0 .204 0 .201 0 .196 0 .226 0 .224 0 .230
Avg Adj-R2 0 .230 0 .200 0 .227
GMM
Pseudo Adj-R2 0 .234 0 .232 0 .220 0 .207 0 .205 0 .195 0 .227 0 .224 0 .228
Avg Pseudo Adj R2 0 .229 0 .202 0 .226
SI-adjusted measures
Panel B: SC (ASI) ¯R 2 (ASI) 1 stPC (ASI)
(1) (2) (3) (1) (2) (3) (1) (2) (3)
Integration index. −0.497 −0.495 −0.563 −1.044 −1.041 −1.161 −1.771 −1.765 −2.590
(0 .158) ∗∗∗(0 .158) ∗∗∗(0 .253) ∗∗(0 .245) ∗∗∗(0 .244) ∗∗∗(0 .380) ∗∗∗(0 .473) ∗∗∗(0 .477) ∗∗∗(0 .582) ∗∗∗
[0 .218] ∗∗[0 .220] ∗∗[0 .458] [0 .303] ∗∗∗[0 .300] ∗∗∗[0 .638] ∗[0 .467] ∗∗∗[0 .470] ∗∗∗[0 .595] ∗∗∗
TO −0.456 −0.559 −0.034 −0.346 −0.351 −0.421
(1 .315) (1 .409) (0 .640) (0 .775) (0 .659) (0 .587)
[1 .746] [2 .115] [0 .715] [0 .931] [0 .762] [0 .943]
EPU 0 .0 0 0 −0.007 0 .006
(0 .026) (0 .014) (0 .015)
[0 .024] [0 .014] [0 .013]
RI 0 .003 0 .004 0 .003
(0 .024) (0 .012) (0 .008)
[0 .018] [0 .010] [0 .009]
OLS
Adj-R2 0 .097 0 .094 0 .091 0 .176 0 .174 0 .170 0 .217 0 .214 0 .319
Avg Adj-R2 0 .092 0 .173 0 .250
GMM
Pseudo Adj-R2 0 .100 0 .097 0 .092 0 .178 0 .176 0 .171 0 .263 0 .259 0 .343
Avg Pseudo Adj R2 0 .096 0 .175 0 .288
Panel C Heteroskedasticity-Adjusted Measures
Forbes-Rigobon BEKK DCC-GARCH Cond. Beta
(1) (2) (3) (1) (2) (3) (1) (2) (3) (1) (2) (3)
Integration index. −0.016 0 .008 0 .047 −0.100 −0.100 −0.109 −0.175 −0.174 −0.182 −0.063 −0.063 −0.062
(0 .093) (0 .090) (0 .132) (0 .019) ∗∗∗(0 .018) ∗∗∗(0 .026) ∗∗∗(0 .053) ∗∗∗(0 .052) ∗∗∗(0 .069) ∗∗∗(0 .012) ∗∗∗(0 .012) ∗∗∗(0 .014) ∗∗∗
[0 .095] [0 .095] [0 .138] [0 .016] ∗∗∗[0 .016] ∗∗∗[0 .023] ∗∗∗[0 .059] ∗∗∗[0 .058] ∗∗∗[0 .091] ∗∗[0 .013] ∗∗∗[0 .013] ∗∗∗[0 .016] ∗∗∗
TO 0 .701 −0.214 0 .049 −0.028 0 .044 −0.023 0 .103 0 .016
(2 .660) (2 .590) (0 .186) (0 .198) (0 .180) (0 .194) (0 .205) (0 .215)
[3 .346] [4 .046] [0 .317] [0 .387] [0 .314] [0 .382] [0 .346] [0 .411]
EPU −0.011 −0.0 0 0 −0.0 0 0 −0.0 0 0
(0 .018) (0 .001) (0 .001) (0 .002)
[0 .021] [0 .002] [0 .002] [0 .002]
RI −0.016 −0.002 −0.002 −0.002
(0 .014) (0 .001) (0 .001) (0 .001)
[0 .015] [0 .001] [0 .001] [0 .001]
OLS
Adj-R2 0 .0 0 0 0 .0 0 0 0 .0 0 0 0 .259 0 .258 0 .253 0 .223 0 .222 0 .208 0 .115 0 .115 0 .100
Avg Adj-R2 0 .0 0 0 0 .257 0 .218 0 .110
GMM
Pseudo Adj-R2 0 .0 0 0 0 .0 0 0 0 .0 0 0 0 .258 0 .257 0 .250 0 .215 0 .215 0 .202 0 .099 0 .098 0 .094
Avg Pseudo Adj R2 0 .0 0 0 0 .255 0 .211 0 .097
Notes : We regress dynamic international diversiﬁcation beneﬁts on each of the integration measures (for DMs ) depicted in Figs. 2 and 3 . Control variables: trade openness
( TO ), economic policy uncertainty ( EPU ) and recession indicator ( RI ). T O := (Exports + Imports ) /GDP(Country: OECD Total, Units: US Dollar, millions, 2010; Frequency: Quar-
terly; Source: OECD). EPU := Economic Policy Uncertainty Index for United States (Units: Index; Frequency: Monthly [average of daily ﬁgures]; Source: Baker et al. (2015) ).
RI := OECD based Recession Indicators for the United States from the Peak through the Trough (Units: +1 or 0; Source: Federal Reserve Bank of St. Louis). Monthly TO
ﬁgures are obtained using the Chow-Lin interpolation method ( Chow and Lin, 1971 ). In Panel B (for SC (ASI)), the dynamic international diversiﬁcation beneﬁts measure
is computed by adjusting /Sigma1t for stochastic interdependence. In Panel C, the dynamic international diversiﬁcation beneﬁts measure is computed by adjusting /Sigma1t for het-
eroskedasticity. All variables are expressed in log-differences except for EPU , which is expressed in log-levels. A constant is included. (1) = benchmark regression model
(Sample: 1978M2-2016M1). (2) = regression model 2 (Sample: 1978M2-2015M9). (3) = regression model 3 (Sample: 1985M2-2014M6). Newey-West (HAC) standard errors
are reported in parentheses. Bootstrapped standard errors (with 10,0 0 0 replications) are reported in square brackets. Pseudo Adj-R2 is the adjusted R-squared calculated
in GMM regressions. Pseudo Adj-R2 = 1 −{ 1 −[ cor r (V −CDB t , /hatwidest V −CDB t )] 2 } /parenleftbign −1
n −p /parenrightbig
, where /hatwidest V −CDB t is the ﬁtted value of V −CDB t , p is the number of explanatory variables
and n is the sample size. Employed instruments: lagged values of V −CDB and regressors (from t −1 to t −5 ). All GMM estimations pass the standard tests of instrument
validity. Signiﬁcance at the 10%, 5% and 1% levels is denoted by ∗, ∗∗and ∗∗∗.

162 M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174
Table 4
Financial integration vs. diversiﬁcation beneﬁts: EMs .
Panel A: Standard measures Robust measures
SC ¯R 2 1 stPC
(1) (2) (3) (1) (2) (3) (1) (2) (3)
Integration index −1.099 −1.080 −1.055 −2.488 −2.442 −2.395 −1.488 −1.461 −1.433
(0 .173) ∗∗∗(0 .165) ∗∗∗(0 .175) ∗∗∗(0 .431) ∗∗∗(0 .397) ∗∗∗(0 .418) ∗∗∗(0 .230) ∗∗∗(0 .216) ∗∗∗(0 .230) ∗∗∗
[0 .169] ∗∗∗[0 .158] ∗∗∗[0 .162] ∗∗∗[0 .422] ∗∗∗[0 .388] ∗∗∗[0 .404] ∗∗∗[0 .225] ∗∗∗[0 .210] ∗∗∗[0 .218] ∗∗∗
TO 1 .391 1 .128 1 .421 1 .151 ∗1 .309 1 .079 ∗
(0 .621) ∗∗(0 .623) ∗(0 .605) ∗∗(0 .606) (0 .578) ∗∗(0 .605)
[0 .933] [0 .967] [0 .955] [0 .993] [0 .900] [0 .936]
EPU 0 .004 0 .006 0 .005
(0 .005) (0 .005) (0 .005)
[0 .006] [0 .006] [0 .006]
RI −0.012 −0.014 −0.012
(0 .004) ∗∗∗(0 .005) ∗∗∗(0 .005) ∗∗
[0 .006] ∗[0 .007] ∗∗[0 .006] ∗
OLS
Adj-R2 0 .490 0 .503 0 .491 0 .419 0 .433 0 .426 0 .507 0 .518 0 .507
Avg Adj-R2 0 .495 0 .426 0 .511
GMM
Pseudo Adj-R2 0 .501 0 .510 0 .490 0 .433 0 .439 0 .415 0 .522 0 .528 0 .508
Avg Pseudo Adj-R2 0 .500 0 .429 0 .520
Panel B: ASI-adjusted measures
SC (ASI) ¯R 2 (ASI) 1 stPC (ASI)
(1) (2) (3) (1) (2) (3) (1) (2) (3)
Integration index −1.751 −1.714 −1.677 −1.576 −1.539 −1.504 −1.822 −1.807 −1.824
(0 .350) ∗∗∗(0 .341) ∗∗∗(0 .363) ∗∗∗(0 .352) ∗∗∗(0 .337) ∗∗∗(0 .330) ∗∗∗(0 .433) ∗∗∗(0 .407) ∗∗∗(0 .397) ∗∗∗
[0 .337] ∗∗∗[0 .313] ∗∗∗[0 .324] ∗∗∗[0 .334] ∗∗∗[0 .317] ∗∗∗[0 .311] ∗∗∗[0 .435] ∗∗∗[0 .408] ∗∗∗[0 .406] ∗∗∗
TO 2 .946 2 .588 1 .161 ∗0 .704 1 .190 0 .4 4 4
(1 .223) ∗∗(1 .244) ∗∗(0 .705) (0 .600) (0 .728) (0 .559)
[1 .484] [2 .035] [0 .972] [0 .967] [0 .895] [0 .902]
EPU 0 .009 0 .004 0 .002
(0 .011) (0 .005) (0 .006)
[0 .012] [0 .006] [0 .007]
RI −0.020 −0.016 −0.022
(0 .008) ∗∗(0 .006) ∗∗∗(0 .006) ∗∗∗
[0 .011] ∗[0 .007] ∗∗[0 .007] ∗∗∗
OLS
Adj-R2 0 .406 0 .422 0 .408 0 .400 0 .406 0 .404 0 .337 0 .356 0 .378
Avg Adj-R2 0 .412 0 .403 0 .357
GMM
Pseudo Adj-R2 0 .416 0 .431 0 .409 0 .475 0 .480 0 .449 0 .380 0 .401 0 .409
Avg Pseudo Adj-R2 0 .419 0 .468 0 .397
Panel C: Heteroskedasticity-Adjusted Measures
Forbes-Rigobon BEKK DCC-GARCH Cond. Beta
(1) (2) (3) (1) (2) (3) (1) (2) (3) (1) (2) (3)
Integration index −0.124 −0.133 −0.137 −0.113 −0.113 −0.114 −0.272 −0.272 −0.282 −0.075 −0.076 −0.081
(0 .069) ∗(0 .070) ∗(0 .068) ∗∗(0 .034) ∗∗∗(0 .034) ∗∗∗(0 .036) ∗∗∗(0 .084) ∗∗∗(0 .084) ∗∗∗(0 .088) ∗∗∗(0 .020) ∗∗∗(0 .021) ∗∗∗(0 .023) ∗∗∗
[0 .080] [0 .084] [0 .089] [0 .030] ∗∗∗[0 .028] ∗∗∗[0 .028] ∗∗∗[0 .076] ∗∗∗[0 .071] ∗∗∗[0 .075] ∗∗∗[0 .019] ∗∗∗[0 .019] ∗∗∗[0 .020] ∗∗∗
TO 2 .080 1 .032 0 .051 −0.051 0 .016 −0.048 0 .215 0 .084
(2 .405) (1 .892) (0 .148) (0 .128) (0 .124) (0 .119) (0 .231) (0 .187)
[5 .167] [4 .946] [0 .390] [0 .366] [0 .339] [0 .323] [0 .490] [0 .455]
EPU −0.003 −0.001 −0.0 0 0 −0.0 0 0
(0 .015) (0 .001) (0 .001) (0 .002)
[0 .020] [0 .002] [0 .001] [0 .002]
RI −0.024 −0.002 −0.001 −0.003
(0 .016) (0 .0 0 0) ∗∗(0 .0 0 0) ∗(0 .001) ∗∗
[0 .014] ∗[0 .0 0 0] ∗∗[0 .001] [0 .001] ∗∗
OLS
Adj-R2 0 .009 0 .011 0 .007 0 .349 0 .346 0 .345 0 .403 0 .400 0 .406 0 .134 0 .137 0 .143
Avg Adj-R2 0 .009 0 .347 0 .403 0 .138
GMM
Pseudo Adj-R2 0 .005 0 .008 0 .003 0 .349 0 .345 0 .341 0 .402 0 .399 0 .400 0 .135 0 .133 0 .132
Avg Pseudo Adj-R2 0 .005 0 .345 0 .400 0 .133
Notes : We regress dynamic conditional diversiﬁcation beneﬁts on each of the integration measures (for EMs ) depicted in Figs. 2 and 3 . Control variables: trade openness ( TO ),
economic policy uncertainty ( EPU ) and recession indicator ( RI ). T O := (Exports + Imports ) /GDP(Country: OECD Total, Units: US Dollar, millions, 2010; Frequency: Quarterly;
Source: OECD). EPU := Economic Policy Uncertainty Index for United States (Units: Index; Frequency: Monthly [average of daily ﬁgures]; Source: Baker et al. (2015) ). RI :=
OECD based Recession Indicators for the United States from the Peak through the Trough (Units: +1 or 0; Source: Federal Reserve Bank of St. Louis). Monthly TO ﬁgures are
obtained using the Chow-Lin interpolation method ( Chow and Lin, 1971 ). In Panel B (for SC (ASI)), the dynamic international diversiﬁcation beneﬁts measure is computed
by adjusting /Sigma1t for stochastic interdependence. In Panel C, the dynamic international diversiﬁcation beneﬁts measure is computed by adjusting /Sigma1t for heteroskedasticity.
All variables are expressed in log-differences except for EPU , which is expressed in log-levels. A constant is included. (1) = benchmark regression model (Sample: 1995M5-
2016M1). (2) = regression model 2 (Sample: 1995M5-2015M9). (3) = regression model 3 (Sample: 1995M5-2014M6). Newey-West (HAC) standard errors are reported in
parentheses. Bootstrapped standard errors (with 10,0 0 0 replications) are reported in square brackets. Pseudo Adj-R2 is the adjusted R-squared calculated in GMM regressions.
Pseudo Adj-R2 = 1 −{ 1 −[ cor r (V −CDB t , /hatwidest V −CDB t )] 2 } /parenleftbign −1
n −p /parenrightbig
, where /hatwidest V −CDB t is the ﬁtted value of V −CDB t , p is the number of explanatory variables and n is the sample
size. Employed instruments: lagged values of V −CDB and regressors (from t −1 to t −5 ). All GMM estimations pass the standard tests of instrument validity. Signiﬁcance
at the 10%, 5% and 1% levels is denoted by ∗, ∗∗and ∗∗∗.

M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174 163
Table 5
Financial integration vs. diversiﬁcation beneﬁts: ALL
Panel A: Standard measures Robust measures
SC ¯R 2 1 stPC
(1) (2) (3) (1) (2) (3) (1) (2) (3)
Integration index −1.361 −1.360 −1.370 −2.479 −2.486 −2.495 −1.575 −1.573 −1.587
(0 .138) ∗∗∗(0 .140) ∗∗∗(0 .136) ∗∗∗(0 .307) ∗∗∗(0 .305) ∗∗∗(0 .305) ∗∗∗(0 .172) ∗∗∗(0 .170) ∗∗∗(0 .176) ∗∗∗
[0 .134] ∗∗∗[0 .135] ∗∗∗[0 .136] ∗∗∗[0 .298] ∗∗∗[0 .290] ∗∗∗[0 .303] ∗∗∗[0 .171] ∗∗∗[0 .171] ∗∗∗[0 .175] ∗∗∗
TO −0.721 −1.084 −0.853 −1.142 −0.697 −1.062
(0 .393) ∗(0 .485) ∗∗(0 .416) ∗∗(0 .513) ∗∗(0 .411) ∗(0 .525) ∗∗
[0 .464] [0 .580] ∗[0 .500] ∗[0 .628] ∗[0 .482] [0 .591] ∗
EPU −0.012 0 .0 0 0 −0.001
(0 .006) (0 .006) (0 .006)
[0 .006] [0 .007] [0 .007]
RI −0.009 −0.008 −0.009
(0 .006) (0 .006) (0 .006)
[0 .007] [0 .007] [0 .007]
OLS
Adj-R2 0 .498 0 .501 0 .500 0 .442 0 .447 0 .440 0 .465 0 .468 0 .466
Avg Adj-R2 0 .500 0 .443 0 .466
GMM
Pseudo Adj-R2 0 .502 0 .519 0 .502 0 .442 0 .446 0 .438 0 .471 0 .473 0 .468
Avg Pseudo Adj-R2 0 .508 0 .442 0 .471
Panel B: ASI_adjusted measures
SC (ASI) ¯R 2 (ASI) 1 stPC (ASI)
(1) (2) (3) (1) (2) (3) (1) (2) (3)
Integration index −1.266 −1.270 −1.300 −2.184 −2.191 −2.200 −1.308 −1.315 −1.341
(0 .247) ∗∗∗(0 .252) ∗∗∗(0 .221) ∗∗∗(0 .268) ∗∗∗(0 .265) ∗∗∗(0 .290) ∗∗∗(0 .216) ∗∗∗(0 .216) ∗∗∗(0 .204) ∗∗∗
[0 .192] ∗∗∗[0 .191] ∗∗∗[0 .191] ∗∗∗[0 .269] ∗∗∗[0 .266] ∗∗∗[0 .271] ∗∗∗[0 .176] ∗∗∗[0 .176] ∗∗∗[0 .178] ∗∗∗
TO −1.167 −2.260 −0.881 −1.252 −0.840 −1.492
(0 .518) ∗∗(0 .877) ∗∗(0 .441) ∗∗(0 .620) ∗∗(0 .411) ∗∗(0 .613) ∗∗
[0 .741] [0 .906] [0 .496] ∗[0 .655] ∗[0 .509] [0 .654] ∗∗
EPU −0.001 0 .001 0 .0 0 0
(0 .009) (0 .007) (0 .006)
[0 .010] [0 .008] [0 .007]
RI −0.028 −0.011 −0.017
(0 .012) ∗∗(0 .008) (0 .008) ∗∗
[0 .011] ∗∗[0 .008] [0 .008] ∗∗
OLS
Adj-R2 0 .408 0 .411 0 .424 0 .424 0 .429 0 .426 0 .414 0 .418 0 .427
Avg Adj-R2 0 .453 0 .426 0 .419
GMM
Pseudo Adj-R2 0 .473 0 .479 0 .476 0 .425 0 .427 0 .420 0 .451 0 .457 0 .454
Avg Pseudo Adj-R2 0 .476 0 .424 0 .454
Panel C Heteroskedasticity-Adjusted Measures
Forbes-Rigobon BEKK DCC-GARCH Cond. Beta
(1) (2) (3) (1) (2) (3) (1) (2) (3) (1) (2) (3)
Integration index −0.050 −0.056 −0.062 −0.073 −0.072 −0.075 −0.164 −0.163 −0.173 −0.069 −0.069 −0.072
(0 .033) (0 .034) (0 .033) ∗(0 .011) ∗∗∗(0 .011) ∗∗∗(0 .011) ∗∗∗(0 .031) ∗∗∗(0 .032) ∗∗∗(0 .033) ∗∗∗(0 .015) ∗∗∗(0 .015) ∗∗∗(0 .016) ∗∗∗
[0 .040] [0 .044] [0 .049] [0 .012] ∗∗∗[0 .012] ∗∗∗[0 .012] ∗∗∗[0 .031] ∗∗∗[0 .031] ∗∗∗[0 .034] ∗∗∗[0 .019] ∗∗∗[0 .019] ∗∗∗[0 .021] ∗∗∗
TO 1 .0 0 0 0 .385 0 .0135 −0.011 0 .021 0 .002 0 .119 0 .057
(1 .147) (1 .102) (0 .079) (0 .088) (0 .078) (0 .090) (0 .117) (0 .116)
[1 .618] [1 .549] [0 .114] [0 .110] [0 .114] [0 .112] [0 .157] [0 .151]
EPU −0.006 −0.0 0 0 −0.0 0 0 −0.001
(0 .012) (0 .001) (0 .001) (0 .001)
[0 .012] [0 .001] [0 .001] [0 .001]
RI −0.007 −0.0 0 0 −0.0 0 0 −0.001
(0 .010) (0 .001) (0 .001) (0 .001)
[0 .010] [0 .001] [0 .001] [0 .001]
OLS
Adj-R2 0 .003 0 .004 0 .0 0 0 0 .408 0 .403 0 .404 0 .371 0 .365 0 .370 0 .164 0 .174 0 .170
Avg Adj-R2 0 .002 0 .405 0 .369 0 .169
GMM
Pseudo Adj-R2 0 .003 0 .0 0 0 0 .0 0 0 0 .407 0 .403 0 .408 0 .370 0 .366 0 .375 0 .166 0 .153 0 .157
Avg Pseudo Adj-R2 0 .0 0 0 0 .406 0 .37 0 .159
Notes : We regress dynamic international diversiﬁcation beneﬁts on each of the integration measures (for ALL ) depicted in Figs. 2 and 3 . Control variables: trade openness ( TO ),
economic policy uncertainty ( EPU ) and recession indicator ( RI ). T O := (Exports + Imports ) /GDP(Country: OECD Total, Units: US Dollar, millions, 2010; Frequency: Quarterly;
Source: OECD). EPU := Economic Policy Uncertainty Index for United States (Units: Index; Frequency: Monthly [average of daily ﬁgures]; Source: Baker et al. (2015) ). RI :=
OECD based Recession Indicators for the United States from the Peak through the Trough (Units: +1 or 0; Source: Federal Reserve Bank of St. Louis). Monthly TO ﬁgures are
obtained using the Chow-Lin interpolation method ( Chow and Lin, 1971 ). In Panel B (for SC (ASI)), the dynamic international diversiﬁcation beneﬁts measure is computed
by adjusting /Sigma1t for stochastic interdependence. In Panel C, the dynamic international diversiﬁcation beneﬁts measure is computed by adjusting /Sigma1t for heteroskedasticity.
All variables are expressed in log-differences except for EPU , which is expressed in log-levels. A constant is included. (1) = benchmark regression model (Sample: 1995M5-
2016M1). (2) = regression model 2 (Sample: 1995M5-2015M9). (3) = regression model 3 (Sample: 1995M5-2014M6). Newey-West (HAC) standard errors are reported in
parentheses. Bootstrapped standard errors (with 10,0 0 0 replications) are reported in square brackets. Pseudo Adj-R2 is the adjusted R-squared calculated in GMM regressions.
Pseudo Adj-R2 = 1 −{ 1 −[ cor r (V −CDB t , /hatwidest V −CDB t )] 2 } /parenleftbign −1
n −p /parenrightbig
, where /hatwidest V −CDB t is the ﬁtted value of V −CDB t , p is the number of explanatory variables and n is the sample
size. Employed instruments: lagged values of V −CDB and regressors (from t −1 to t −5 ). All GMM estimations pass the standard tests of instrument validity. Signiﬁcance
at the 10%, 5% and 1% levels is denoted by ∗, ∗∗and ∗∗∗.

164 M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174
our estimates are robust enough, we conduct a simulation exercise
to examine whether such errors are quantitatively relevant. Over-
all, results from this test show that the measurement errors em-
bedded in the computed integration indexes and conditional diver-
siﬁcation measures do not undermine our estimates. Details on the
employed methodology, simulation results and data measurement
errors are reported in Appendix D .
To evaluate the performance of our regression models, the
pseudo adjusted R-square statistic obtained from GMM estimations
is also used. 25 The SC exhibits –o n average –t h e highest pseudo
adjusted R-square. Therefore, GMM estimates conﬁrm our main
ﬁndings suggesting that the SC represents a good candidate to cap-
ture de facto integration. Note also that bootstrapped standard er-
rors –r e p o r t e d in square brackets –d o not alter the signiﬁcance
of the market integration coeﬃcients. 26
We stress that these results hold over time. This is conﬁrmed
by the dynamic regression adjusted R-square plotted in Fig. E.1 of
Appendix E . For the sake of brevity, results are reported for the
country group ALL only. Results for the country groups DMs and
EMs are qualitatively similar and are available upon request. Our
rolling estimates show that the percentage of variation in inter-
national diversiﬁcation beneﬁts explained by the SC and the two
robust PCA-based measures ( ¯R 2 and 1 stPC ) is very similar over
time ( Fig. E.1 , Panel A). This holds for the SI-adjusted ¯R 2 and 1 stPC
( Fig. E.1 , Panel B). Differently, heteroskedasticity-adjusted measures
tend to explain a lower percentage of diversiﬁcation beneﬁts vari-
ation ( Fig. E.1 , Panel C). This performance gap is – on average –
larger after the second half of 20 0 0s.
To shed further robustness on our main results, we adopt the
general-to-speciﬁc ( Gets ) variable selection approach described in
Hendry and Krolzig (20 03) ; 20 05 ) and Krolzig (20 08) . Speciﬁ-
cally, we apply this approach to a regression where the dependent
variable represents a synthesis of all diversiﬁcation beneﬁts mea-
sures (i.e., the ﬁrst PC extracted from the four different reproduced
dynamic diversiﬁcation beneﬁts measures, V −CDB ∗) and the ex-
planatory variables are represented by all the computed integra-
tion indicators. After having speciﬁed a general unrestricted model
including all the potential candidate variables able to explain a
target variable ( V −CDB ∗), the algorithm implements a multi-path
search aimed at eliminating all the “irrelevant variables”. The ad-
vantage of using this procedure is that it is able to handle high
collinearity among regressors ( Hendry and Krolzig, 2005 ). The re-
sults obtained from this procedure –r e p o r t e d in Appendix E (see
Table E.1 ) – conﬁrm that SC is the most signiﬁcant variable in ex-
plaining diversiﬁcation beneﬁts’ dynamics. Its coeﬃcient is highly
statistically signiﬁcant and, as expected, negative. As suggested by
Fig. E.2 , this holds across the full sample. Speciﬁcally, we observe
that the Gets procedure always selects as “best” integration mea-
sure the SC . The attached market integration coeﬃcient is always
25 As pointed out by Carroll et al. (2011) , GMM estimations may be useful in the
presence of error measurements. However, under the instrumental variable (IV)
variable approach the R-square statistic is not robust. Therefore, we calculate a
pseudo adjusted R-square statistic that uses the square correlation between the de-
pendent variable (i.e., international diversiﬁcation beneﬁts measure) and the ﬁtted
value of the dependent variable.
26 If only V −CDB (or a synthetic V −CDB capturing all the different diversiﬁcation
beneﬁts measures deﬁned in footnote 23) is used in our validation exercise, similar
correlation coeﬃcients and regression estimates are obtained. For space consider-
ations, all the results for these robustness experiments are not reported but are
available upon request. negative and highly signiﬁcant. 27
7. SC Vs. alternative measures: additional discussions
The results reported in the previous sections suggest that the
SC does not fail to capture regional and global equity market inte-
gration. Actually, we observe that the SC can act as a substitute for
the two recently introduced PCA-based integration measures (i.e.,
¯R 2 and 1 stPC ) and a number of widely used heteroskedasticity-
adjusted indicators (i.e., Forbes-Rigobon correlation, DCC-GARCH,
BEKK, Cond. Beta).
Our ﬁndings do not imply that SC represents the best and
most robust measure. All measures, of course, have their strengths
and weaknesses. Volatility- and heteroskedasticity-adjusted indica-
tors, for instance, tend to provide highly volatile integration pat-
terns. However, they do relatively well in capturing periods of high
uncertainty (e.g., ﬁnancial crises). Thus, for short-run analyses, it
might be more appropriate to employ heteroskedasticity-adjusted
measures. Nevertheless, this departs from the goal of measuring
long-run equity market integration trends.
As most correlation-based measures, 28 the two PCA-based mea-
sures have an upper bound of one. This suggests that as they ap-
proach one full equity market integration is detected. In addition,
similarly to the SC , Forbes-Rigobon correlation, DCC-GARCH and
BEKK do not rely on the choice of a benchmark country. Note also
that the ¯R 2 and 1 stPC , as all the correlation-based measures, rep-
resent price-based measures. As discussed in Section 2 , this im-
plies their reliance on historic price data, which tend to be avail-
able for a larger variety of countries, regions and industries, and
have a better quality than data on international capital ﬂows gen-
erally used to construct quantity-based measures (see Obstfeld and
Taylor, 2004 ).
PCA-based indicators may also have a clear theory-based inter-
pretation. In this respect, Volosovych (2011, 2013) argues that the
ﬁrst principal component extracted from a data matrix composed
by countries’ long-term bond yields serves as a proxy for the world
interest rate. Similarly, Pukthuanthong and Roll (2009) point out
that the ﬁrst 10 PCs extracted from a data matrix composed by
countries’ equity returns may proxy the 10 largest industries. Re-
gardless the debate of the existence of a world interest rate, it is
unclear to what extent these interpretations can be generalized.
The ﬁrst component extracted from countries’ equity returns may
or may not be regarded as the word equity return and the choice
of the number of countries is at the discretion of the researcher.
For instance, Volosovych (2011) extracts the ﬁrst component from
27 As a ﬁnal robustness check, we propose an alternative validation exercise. This
relies on the empirical regularities suggesting that increasing integration improves
trade and ﬁnancial openness (see Fig. 1 ). Financial integration lowers the cost of
capital, raises cross-country investment opportunities, and provides a more eﬃ-
cient international allocation of capital. This, of course, facilitates FDI. In practice,
we regress FDI on the reproduced integration patterns. To some extent this addi-
tional exercise ensures that our main ﬁndings do not rely on the choice of priced-
based indicators as unique integration-driven phenomena. Estimation results are re-
ported in Appendix F . Entries in Table F.1 corroborate our main ﬁnding. The SC cap-
tures movements in international investments better than the 1 stPC , ¯R 2 and het-
eroskedasticity adjusted measures. For brevity’s sake, we report in Table F.1 only
the results for the country group ALL. For DMs and EMs, results are very similar
and are available upon request.
28 An exception is the conditional beta, which is not bounded. For this reason,
it does not provide a clear-cut interpretation about the degree of equity market
integration.

M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174 165
only 11 countries, whereas including more countries might be
more appropriate for his interpretation. Also, Pukthuanthong and
Roll (2009) ’s choice of the number of PCs to be used as global fac-
tors in countries’ regressions is somehow arbitrary. Furthermore,
differently from standard asset pricing model, the ¯R 2 relies on non-
traded risk factors (i.e., artiﬁcial factors) while global macro-factors
or traded ﬁnancial risk factors are ignored. Admittedly, both PCA-
based measures rely on subjective choices.
The theoretical justiﬁcations provided to build the ¯R 2 and 1 stPC
are comprehensible. On the one hand, from a theoretical point
of view, it is true that two countries can exhibit simultaneously
a low correlation but a high ¯R 2 . On the other hand, however, as
global goods and ﬁnancial markets openness rises, returns tend to
be driven by similar global factors. It is, thus, very likely that a
number of global factors (and in particular principal components
extracted from a data matrix composed by international countries’
returns) will comove with most countries’ returns in a similar way,
both qualitatively and quantitatively (as suggested by our empirical
ﬁndings).
What emerges from our analysis is simply that the widely
used heteroskedasticity-adjusted, the two recently introduced ro-
bust measures of integration, and the SC give rise to a very sim-
ilar long-run equity market integration trend. Put differently, all
these measures tend to provide similar information on the regional
and global equity market integration processes. Further, we ob-
serve that the SC explains –o n average –v a r i a t i o n s in integration-
driven phenomena better than all the other proposed measures. If
a Gets reduction procedure is employed, then the SC results to be
the best candidate to explain movements in diversiﬁcation beneﬁts
(see Appendix E ).
The question one may pose is then the following: why should
we use alternative and more sophisticated measures if the SC pro-
vides very similar information on the shape of the integration pro-
cess? Differences in the set of information provided by different
measures become negligible in particular over the long-run and if
a relatively large number of countries is employed in the analy-
sis. Our view here is that the SC and all the other proposed mea-
sures capture somehow cross-country equity market returns’ co-
movement. The SC , of course, serves this purpose quite well. In ad-
dition, as opposed to all the other measures, it requires low com-
putational effort.
There is a number of directions in which this work could be
fruitfully extended. First, novel measures that do not rely on co-
movement should be developed. In this respect, recent methodolo-
gies – based on Granger-causality –e m p l o y e d to capture systemic
risk might be used as a benchmark (see Billio et al., 2012 ). Second,
theory-based validation schemes to rank different integration mea-
sures should be taken into account in future research. Finally, our
empirical analysis could be extended to other asset classes (e.g.,
bonds, commodities).
8. Concluding remarks
Changes in the degree of integration among international eq-
uity markets affect the decisions of policymakers, investors and
households. Therefore, measuring ﬁnancial integration and under- standing its evolution over time is of general interest. As there
are many possible measures of ﬁnancial integration, it is natural
to ask whether they all provide similar information. To this end,
we compare and evaluate the ﬁnancial integration patterns pro-
duced by a battery of different indicators. In particular, to account
for all possible dimensions of integration, we rely on: ( i ) the SC ;
( ii ) two PCA-based measures and ( iii ) several heteroskedasticity-
adjusted measures. Three novel indicators are also introduced: ( i )
a volatility-adjusted measure relying on main international ﬁnan-
cial and political crisis episodes and ( ii ) two PCA-based measures
adjusted for stochastic interdependence. Moreover, to ensure that
our results are robust with respect to the chosen sample, integra-
tion is investigated for three different country groups: DMs, EMs
and ALL (i.e., a group of economies with a large variety of sizes
and degrees of openness). Results, for all country-groups, suggest
that all measures exhibit a very similar long-run equity market in-
tegration trend. Speciﬁcally, we observe that ( i ) the SC and the two
PCA-based measures give rise to nearly identical equity market in-
tegration dynamics and ( ii ) heteroskedasticity-adjusted measures,
due to the presence of crises, tend to produce more volatile pat-
terns. Taken together, the reproduced dynamics suggest that the
SC and all the other proposed measures provide similar informa-
tion about the integration process.
To evaluate the performance of the proposed indicators in cap-
turing de facto integration, we link each of the produced integra-
tion patterns with a dynamic measure of international diversiﬁca-
tion beneﬁts. Our statistical results suggest that the SC performs as
well or better than more sophisticated measures (i.e., ¯R 2 , 1 stPC and
volatility-adjusted measures). It turns out that the dynamic SC cap-
tures de facto integration rather well. Said differently, if one aims
to understand the shape of the equity market integration process
over the long-run and is restricted by mathematical complexity or
computational power, then he is well advised to use the SC .
Acknowledgments
We thank for helpful comments on earlier versions Guglielmo
Maria Caporale, Roberto Casarin, Alessio Ciarlone, Fulvio Corsi, Giu-
liano Curatola, Daniele Massacci, Faek Menla Ali, Renatas Kizys,
Saten Kumar, Loriana Pelizzon, Christian Schlag, participants of
the 11th BMRC-DEMS Conference on Macro and Financial Eco-
nomics/Econometrics and 39th AMASES Annual Meeting. We also
thank two anonymous referees for their comments which sub-
stantially improved the paper. We gratefully acknowledge ﬁnancial
support from the project SYRTO, funded by the European Union
under the 7th Framework Programme (FP7-SSH/2007-2013 Grant
Agreement No. 320270) and the project MISURA, funded by the
Italian MIUR. Donadelli and Riedel also gratefully acknowledge ﬁ-
nancial support from the Research Center SAFE, funded by the
State of Hessen initiative for research LOEWE. The authors alone
are responsible for the views expressed in the paper and for any
errors that may remain.
Appendix A. Robustness checks

166 M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174
Fig. A.1. Equity market integration patterns: robustness checks. Notes : this ﬁgure reports the equity market integration dynamics generated by the SC (dashed black line),
¯R 2 (light gray line) and 1 stPC (dark gray line) for DMs, EMs and ALL. All measures are estimated using a rolling window of 36 months (Panel A) and 96 months (Panel B).
DMs data run from January 1973 to January 2016. EMs data run from May 1990 to January 2016. Source: DGEI.
Fig. A.2. Equity market integration dynamics: robustness checks. Notes : this ﬁgure reports the equity market integration dynamics generated by the SC (dashed black
line), ¯R 2 (light gray line) and 1 stPC (dark gray line) for DMs, EMs and ALL. Panel A depicts the variation explained by the 1st and 2nd PCs . The remaining two measures are
not modiﬁed. In Panel B the ¯R 2 and 1 stPC are obtained by employing the covariance matrix instead of the correlation matrix of returns in the PCA. In Panel C the ¯R 2 are
computed by excluding country c return in the data matrix employed for computing the PCs serving as regressors in Eq. (2) . DMs data run from January 1973 to January
2016. EMs data run from May 1990 to January 2016. Source: DGEI.

M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174 167
Fig. A.3. Equity market integration patterns: robustness checks. Notes : this ﬁgure depicts the equity market integration patterns generated by heteroskedasticity-adjusted
measures along with the SC (dashed black lines) for DMs, EMs and ALL. In Panel A the measures DCC-GARCH, BEKK-GARCH and Conditional Beta are calculated using the
BIC criterion to determine the optimal p and q in ARMA(p,q) and the Forbes-Rigobon Correlation is estimated using a one-year variance correction δ. Panel B depicts ADCC-
GARCH, ABEKK-GARCH and Conditional Beta assuming an asymmetric volatility model. DMs data run from January 1973 to January 2016. EMs data run from May 1990 to
January 2016. Source: DGEI.

168 M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174
Fig. A.4. Equity market integration: unconditional correlation vs. an alternative measure. Notes : this ﬁgure reports the equity market integration pattern generated by ( i )
the SC estimated as described in Section 3 using monthly data (dashed black line); ( ii ) the yearly correlation (light gray line) and ( iii ) the Pukthuanthong and Roll (2009) ’s
alternative measure (dark gray line). For each country, a correlation is computed with at least 50 daily returns during each calendar year. The yearly correlation is estimated
for each pair of countries during each calendar year using daily returns. The correlations are averaged across countries within each group. The ¯R 2
PR is estimated following the
empirical strategy described in Section 7 of Pukthuanthong and Roll (2009) using daily country returns. The number of global factors is chosen such that they account for
90% of total volatility in the covariance matrix. The proxies for global factors are the ﬁrst six, eight and ten principal components for DMs, EMs and ALL, respectively. DMs
data run from 1/2/1973 to 2/15/2016. EMs data run from 31/5/1990 to 2/15/2016. Source: DGEI.
Appendix B. The R-square vs. The 1st PC: additional insights
B1. Empirical evidence
B2. A two country-one PC example
The following example illustrates that ¯R 2 and 14st PC give rise
to almost identical results. The following calculations are based
on the procedure presented in Section 3.2 . For simplicity, assume
C = 2 and K = 1 . That is, we have two countries with one global
factor driving the individual returns r i , i = 1 , 2 . r i = (r i 1 , . . . , r iT ) /prime being a vector of past T returns for country i . The correlation ma-
trix between the countries is given by
P = /parenleftBigg 1 ρ
ρ1 /parenrightBigg
(B.1)
with eigenvalues λ1 = 1 + ρ, λ2 = 1 −ρ, and corresponding eigen-
vectors v 1 = (1 , 1) /prime , v 2 = (1 , −1) /prime . Assume that ρ< 0. Then, the
proportion of variance explained by the ﬁrst principal component
is given by
prop. of var. explained by 1 stP C = λ1
λ1 + λ2 = 1
2 (1 + ρ) , (B.2)

M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174 169
Table B.1
Additional evidence: ¯R 2 vs. 1 stPC .
(%) var explained by Mean Mean
x ﬁrst x PCs ¯R 2 R 2
Panel (A): DMs
1 53 .74% 53 .65% 53 .74%
2 60 .95% 60 .79% 60 .95%
3 65 .81% 65 .61% 65 .81%
Panel (B): EMs
1 42 .68% 42 .50% 42 .68%
2 52 .13% 51 .82% 52 .13%
3 60 .08% 59 .69% 60 .08%
Panel (C): ALL
1 50 .92% 50 .76% 50 .92%
2 58 .68% 58 .41% 58 .68%
3 62 .54% 62 .17% 62 .54%
Notes : This table illustrates the relation between 1 stPC and ¯R 2 . Variance explained
by ﬁrst x PCs (column 2) is obtained from PCA using the correlation matrix of coun-
try index returns. ¯R 2 (column 3) and R 2 (column 4) are obtained from regression Eq.
(2) . DMs data run from January 1973 to January 2016. EMs data run from May 1990
to January 2016. Source: DGEI.
where ρ= r /prime
1 r 2 / /radicalbig
(r /prime
1 r 1 )(r /prime
2 r 2 ) . Following Eq. (1) , the corresponding
global factor is deﬁned as f 1 = r 1 + r 2 . Regressing returns r i on f 1
according to Eq. (2) yields
R 2
i = r /prime
i f 1 (f /prime
1 f 1 ) −1 f /prime
1 r i
r /prime
i r i . (B.3)
Substituting f 1 and rearranging the above equation gives R 2
i =
1
2 (1 + r /prime
1 r 2 /radicalBig
(r /prime
1 r 1 )(r /prime
2 r 2 ) ) . This simple illustration conﬁrms that the cross-
country average R-square measures exactly the same information
as the proportion of variance explained by 1 stPC in Eq. (B.2) . Please
note that in general, for C > 2, R 2
i /negationslash = R 2
j . However, its cross-country
average still corresponds to the proportion of variance explained
explained by the ﬁrst PC, as shown in Jong and Kotz (1999) and
illustrated in Table B.1 . Given that the adjusted R-square is repre-
sented by the R-square corrected for the number of predictors, the
difference between the variance explained by x components and
the mean adjusted ¯R 2 is very small (see columns 2 and 3).
Appendix C. Additional check: segmentation index
In this section we examine whether there is a strong and sta-
tistically signiﬁcant relationship between international diversiﬁca-
tion beneﬁts and a recently introduced valuation-based measure of
segmentation. To this end we compute a segmentation index ( SI )
along the lines of Bekaert et al. (2011) . For robustness, we com-
pute two variants of the SI . The ﬁrst one makes use of country
equity index returns whereas the other relies on sectoral index re-
turns. Both variants –a s opposed to Bekaert et al. (2011) –e m p l o y s
aggregate data. Speciﬁcally, our country- and sector-based SI s (i.e.,
SI C and SI I ) are computed by using TRIs from Level 1 and Level 2
of DGEI, respectively. SI C and SI I are depicted in Fig. C.1 . Not sur-
prisingly, segmentation is decreasing over time. Therefore, a pos-
Table C.1
Segmentation index vs. V-CDB: average correlation.
DMs EMs ALL
SI C −0.069 −0.228 ∗∗∗−0.123 ∗
SI I −0.115 ∗∗−0.145 ∗∗−0.167 ∗∗∗
Notes : This table presents the average correlation, based on 5-year rolling windows,
between diversiﬁcation beneﬁts (i.e., V −CDB H ) and integration measures depicted
in Fig. C.1 for DMs, EMs, and ALL. DMs data run from February 1978 to January
2016, EMs and ALL run from May 1995 to January 2016. Signiﬁcance of t -tests for
the correlation coeﬃcient at the 10%, 5% and 1% levels is denoted by ∗, ∗∗and ∗∗∗. Table C.2
Market segmentation vs. diversiﬁcation beneﬁts.
Panel A : DMs SI C SI I
(1) (2) (3) (1) (2) (3)
Segmentation −0.064 −0.066 −0.074 −0.136 −0.139 −0.147
index (0 .050) (0 .050) (0 .057) (0 .063) ∗∗(0 .063) ∗∗(0 .069) ∗∗
[0 .059] [0 .060] [0 .066] [0 .081] ∗[0 .081] ∗[0 .087] ∗
TO 0 .083 −0.517 0 .153 −0.383
(0 .734) (1 .022) (0 .734) (1 .003)
[0 .793] [1 .058] [0 .824] [1 .068]
EPU −0.011 −0.009
(0 .016) (0 .016)
[0 .015] [0 .015]
RI 0 .003 0 .004
(0 .014) (0 .014)
[0 .011] [0 .011]
Adj-R2 0 .003 0 .0 0 0 0 .0 0 0 0 .011 0 .009 0 .007
Avg Adj-R2 0 .001 0 .009
Panel B : EMs SI C SI I
(1) (2) (3) (1) (2) (3)
Segmentation −0.184 −0.195 −0.190 −0.092 −0.101 −0.101
index (0 .107) ∗(0 .101) ∗(0 .101) ∗(0 .068) (0 .065) (0 .067)
[0 .098] ∗[0 .092] ∗∗[0 .094] ∗∗[0 .066] [0 .065] [0 .066]
TO 2 .132 1 .581 ∗2 .072 1 .365
(1 .007) ∗∗(0 .913) (1 .116) ∗(0 .966)
[1 .303] ∗[1 .347] [1 .388] [1 .357]
EPU −0.005 −0.007
(0 .009) (0 .009)
[0 .010] [0 .101]
RI −0.011 −0.013
(0 .007) (0 .007) ∗
[0 .008] [0 .008]
Adj-R2 0 .048 0 .079 0 .086 0 .017 0 .045 0 .054
Avg Adj-R2 0 .071 0 .039
Panel C : ALL SI C SI I
(1) (2) (3) (1) (2) (3)
Segmentation −0.072 −0.074 −0.071 −0.131 −0.139 −0.134
index (0 .046) (0 .046) (0 .049) (0 .070) ∗(0 .070) ∗∗(0 .072) ∗
[0 .044] ∗[0 .045] [0 .047] [0 .067] ∗[0 .068] ∗∗[0 .068] ∗
TO −0.192 −0.964 −0.207 −0.890
(0 .614) (0 .906) (0 .600) (0 .894)
[0 .672] [0 .097] [0 .672] [0 .941]
EPU −0.015 −0.014
(0 .011) (0 .011)
[0 .012] [0 .011]
RI −0.007 −0.006
(0 .011) (0 .011)
[0 .010] [0 .010]
Adj-R2 0 .011 0 .008 0 .013 0 .024 0 .024 0 .027
Avg Adj-R2 0 .011 0 .025
Notes : We regress diversiﬁcation beneﬁts on the segmentation indexes SI C and SI I
(for DMs, EMs and ALL) depicted in Fig. C.1 on and a bunch of control variables:
trade openness ( TO ), economic policy uncertainty ( EPU ) and recession indicator
( RI ). T O := (Exports + Imports ) /GDP(Country: OECD Total, Units: US Dollar, millions,
2010; Frequency: Quarterly; Source: OECD). EPU := Economic Policy Uncertainty In-
dex for United States (Units: Index; Frequency: Monthly [average of daily ﬁgures];
Source: Baker et al. (2015) ). RI := OECD based Recession Indicators for the United
States from the Peak through the Trough (Units: +1 or 0; Source: Federal Reserve
Bank of St. Louis). Monthly TO ﬁgures are obtained using the Chow-Lin interpo-
lation method ( Chow and Lin, 1971 ). All variables are expressed in log-differences
except for EPU , which is expressed in log-level. A constant is included. DMs : (1) =
benchmark regression model (Sample: 1978M2-2016M1). (2) = regression model 2
(Sample: 1978M2-2015M9). (3) = regression model 3 (Sample: 1985M2-2014M6).
EMs & ALL : (1) = benchmark regression model (Sample: 1995M5-2016M1). (2) =
regression model 2 (Sample: 1995M5-2015M9). (3) = regression model 3 (Sam-
ple: 1995M5-2014M6). Newey-West (HAC) standard errors are reported in parenthe-
ses. Bootstrapped standard errors (with 10,0 0 0 replications) are reported in square
brackets. Signiﬁcance at the 10%, 5% and 1% levels is denoted by ∗, ∗∗and ∗∗∗.

170 M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174
Fig. C.1. Equity market segmentation index: a valuation-based measure. Notes : this ﬁgure reports the simpliﬁed ( SI C , light grey line) and the original ( SI I , dark grey line)
segmentation index as proposed by Bekaert et al. (2011) . SI I depicts the cross-country average of individual equity market segmentations. The segmentation for each country
is the value-weighted sum of the absolute differences between local and global industry’s earnings yields. Industries were added to the calculation at the time they became
available in the database. SI c depicts the equal-weighted cross-country average of absolute differences between local country’s and global earnings yields. For SI I calculation,
monthly equity industry portfolio data using Level 2 ICB classiﬁcation were employed (i.e., BMATR, CNSMG, CNSMS, FINAN, HLTHC, INDUS, OILGS, TECNO, TELCM, and UTILS).
For SI C , total market indices were used (TOTMK). The global market is the world index (WD). DMs data run from January 1973 to January 2016. EMs data run from May 1990
to January 2016. Source: DGEI.
itive relationship between diversiﬁcation beneﬁts and segmenta-
tion should be observed (i.e., diversiﬁcation beneﬁts decrease as
equity markets segmentation decreases). Counterfactually, we ob-
serve a negative relationship between the diversiﬁcation beneﬁts
measure and our segmentation indexes. This is conﬁrmed by both
average correlations (see Table C.1 ) and regression coeﬃcients (see
Table C.2 ). Appendix D. On the measurement error
To quantify the effects of the presence of measurement errors
in our empirical estimates we ﬁrst rely on a simulation exercise.
In the spirit of McAvoy (1998) , we model the “true” ﬁnancial in-
tegration measure ( x ∗
t ) and conditional diversiﬁcation beneﬁts ( y ∗
t )

M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174 171
Table D.1
On the measurement error: simulated results with errors in the dependent variable and regressor.
StN s Case 1 Case 2 Case 3 Case 4
σe
σξ, ση
σξσe
σξ= ση
σξ= 0.125 σe
σξ= ση
σξ= 0.375 σe
σξ= ση
σξ= 0.625 σe
σξ= ση
σξ= 0.800
Mean SD Mean SD Mean SD Mean SD
True Adj R-square 0 .322 0 .050 0 .320 0 .052 0 .320 0 .051 0 .319 0 .049
Adj R-square (OLS) 0 .316 0 .050 0 .264 0 .051 0 .196 0 .048 0 .150 0 .042
Pseudo Adj R-square (GMM) 0 .316 0 .048 0 .291 0 .052 0 .251 0 .046 0 .217 0 .046
Notes : Adj R-square estimates based upon simulated data according to the system (D.1). True Adj. R-square is the observed R-square that one obtain from estimating Eq.
( d .2). Adj R-square is obtained estimating the Eq. (D.2) , whereas Pseudo Adj R-square is computed estimating the (D.2) via GMM and using four lagged values of y t and x t
as instruments. The pseudo adjusted R-square is deﬁned as described in Tables 3 –5 . Parameter values: ω = 0 . 5 ; α= 0 , β= −0 . 6 ; γ= 0 . 5 . Sample size is equal to 250 and
number of replications is 10 0 0.
as latent variables. We simulate the following system: ⎧
⎪ ⎨
⎪ ⎩ y t = ωy ∗
t + e t (d. 1)
y ∗
t = α+ βx ∗
t + ξt (d. 2)
x t = x ∗
t + ηt (d. 3)
x ∗
t = γx ∗
t−1 + νt (d. 4) (D.1)
where y t and x t are the observed variables, and e t and ηt capture
measurement errors. y ∗
t and x ∗
t are the unobserved true variables,
whereas ξt and νt are disturbance terms. For parsimony, all error
terms e t , ξt , ηt and νt are assumed to be normally distributed, mu-
tually independent, white noise processes.
In Table D.1 we present a simulation exercise for the system
( d .1)–( d .4) assuming the following parameter values: ω = 0 . 5 ; α=
0 , β= −0 . 6 ; γ= 0 . 5 . Based on different signal-to-noise ratio ( StN )
values, we study four scenarios: ( i ) low measurement error ( StN
= 0.125); ( ii ) medium measurement error ( StN = 0.375); ( iii ) high
measurement error ( StN = 0.6); and ( iv ) very high measurement
error ( StN = 0.8). In each scenario the adjusted R-square obtained
estimating the “true” Eq. ( d .2) is compared with the R-square ob-
tained estimating the following noise version of ( d .2):
y t = θ0 + θ1 x t + ε t (D.2)
A GMM version of Eq. (D.2) –w h e r e four lagged values for the
dependent and independent variables are used as instruments –
is also estimated. As discussed in Section 6.2 GMM estimations are
carried out to account for the presence of measurement errors (see
also Carroll et al., 2011 ). We remark that the standard R-square
statistic is not robust under IV estimates. Therefore, as goodness
of ﬁt in our GMM estimations a pseudo-adjusted R-square is com-
puted. Our results clearly suggest that when the StN s are lower
than 0.6, the GMM pseudo adjusted R-square and the true adjusted
R-square are very close. Differently, the OLS estimated adjusted R-
square and the true adjusted R-square are very close only in the
presence of a very low StN (see Table D.1 ).
How large are then the measurement errors in our dataset?
To address this issue we follow McAvoy (1998) and Cunningham
et al. (2012) and estimate a state-space model of the system in Eq.
(D.1) using a Kalman ﬁlter. Results are reported in Table D.2 . For
the sake of brevity we report estimates only for the best perform-
ing measures (i.e., SC, R 2 , 1 stPC, SC (ASI), R 2 (ASI), 1 stPC (ASI), as
suggested by estimates in Tables 3–5 ). Estimates suggest that only
in one case (i.e., SC (ASI) for EMs) the StN is larger than 0.6. In
all the other cases, the StN is far below 0.6. Taken together, the
numbers presented in this section show that measurement errors
do not lead to biased adjusted R-square statistics. In particular, if
GMM estimates are carried out the effect of the measurement er-
ror is negligible. Table D.2
State-space model estimation of the system (D.1).
DMs EMs ALL
SC 0 .230 0 .463 0 .375
SC (ASI) 0 .416 0 .673 0 .381
¯R 2 0 .120 0 .205 0 .190
¯R 2 (ASI) 0 .169 0 .267 0 .209
1 stPC 0 .297 0 .325 0 .317
1 stPC (ASI) 0 .213 0 .234 0 .256
Notes: The signal-to-noise ratio is estimated using the maximum likelihood ap-
proach with a Newton–Raphson optimization process.
Appendix E. Financial integration vs. diversiﬁcation beneﬁts:
additional insights
Table E.1
Explaining international diversiﬁcation beneﬁts (ALL).
Dependent variable: V −CDB ∗
Gets selection γj := SC Adj. Pseudo
procedure R-squared Adj-R2 (GMM)
−2.289
(0 .243) ∗∗∗
[0 .239] ∗∗∗
0 .486
0 .497
Notes : This table reports the results of the Gets reduction procedure applied to the
following regression model:
V −CDB ∗
t = α+γj 10 /summationdisplay
j=1 II j,t +/epsilon1t
where V −CDB ∗
t denotes international diversiﬁcation beneﬁts and II j, t (with j =
1 , . . . , 10 ) represent the ten integration measures plotted in Figs. 2 and 3 , i.e., SC ,
¯R 2 , 1 stPC, SC (ASI), ¯R 2 (ASI), 1 stPC (ASI), FR, DCC-GARCH, BEKK, COND. BETA. Sign
restrictions (i.e., γj ≤0) in the model search are imposed following Krolzig (2008) .
All variables are expressed in log-differences. Newey-West (HAC) standard errors
are reported in parentheses. Bootstrapped standard errors (with 10,0 0 0 replications)
are reported in square brackets. Pseudo Adj-R2 is the adjusted R-squared calculated
in GMM regressions. Pseudo Adj-R2 = 1 −{ 1 −[ cor r (V −CDB ∗
t , /hatwidest V −CDB ∗
t )] 2 } /parenleftbign −1
n −p /parenrightbig
,
where /hatwidest V −CDB ∗
t is the ﬁtted value of V −CDB ∗
t , p is the number of explanatory vari-
ables and n is the sample size. Employed instruments: lagged values of V −CDB ∗
and regressors (from t −1 to t −5 ). V −CDB ∗
t here is calculated as the ﬁrst princi-
pal component of all the previously deﬁned diversiﬁcation beneﬁts measures (i.e.,
V −CDB, V −CDB ASI , V −CDB BEKK , V −CDB DCC ). GMM estimation passes the stan-
dard tests of instrument validity. Sample: 1995M5-20016:M1. Signiﬁcance at the
10%, 5% and 1% levels is denoted by ∗, ∗∗and ∗∗∗.

172 M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174
Fig. E.1. Financial integration vs. diversiﬁcation beneﬁts: rolling regressions (ALL). Notes : this ﬁgure reports the dynamics of the percentage of variation in international
diversiﬁcation beneﬁts explained by the SC (solid black line) and all the other integration measures. The dynamic regression Adj. R-square of the benchmark model (1) –
estimated in Table 5 –i s computed using a rolling window of 60 months. A constant is included. All integration measures are computed as described in Section 3 .
Fig. E.2. Explaining international diversiﬁcation beneﬁts (ALL): the SC coeﬃcient dynamics. Notes : this ﬁgure reports the dynamics of the SC coeﬃcient estimated in
Table E.1 . The SC coeﬃcient is estimated using a rolling window of 60 months. Dashed lines identify conﬁdence intervals at 95%. Sample: 1995M5-20016:M1.

M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174 173
Appendix F. Financial integration vs. FDI global share
Table F.1
Integration indexes vs. FDI global share (ALL).
Panel A: Standard measures Robust measures SI-adjusted measures
SC ¯R 2 1 stPC SC ( ASI ) ¯R 2 ( ASI ) 1 stPC ( ASI )
Integration index ( −1) 0 .243 0 .411 0 .294 0 .189 0 .343 0 .234
(0 .067) ∗∗∗(0 .130) ∗∗∗(0 .086) ∗∗∗(0 .061) ∗∗∗(0 .096) ∗∗∗(0 .085) ∗∗∗
[0 .071] ∗∗∗[0 .126] ∗∗∗[0 .087] ∗∗∗[0 .062] ∗∗∗[0 .125] ∗∗∗[0 .085] ∗∗∗
Integration index ( −2) 0 .231 0 .368 0 .257 0 .162 0 .341 0 .191
(0 .089) ∗∗(0 .151) ∗∗(0 .100) ∗∗(0 .067) ∗∗(0 .160) ∗∗(0 .092) ∗∗
[0 .093] ∗∗[0 .158] ∗∗[0 .108] ∗∗[0 .078] ∗∗[0 .164] ∗∗[0 .105] ∗
Integration index ( −5) −0.105 −0.187 −0.130 −0.075 −0.154 −0.109
(0 .046) ∗∗(0 .099) ∗(0 .053) ∗∗(0 .021) ∗∗∗(0 .069) ∗∗(0 .029) ∗∗∗
[0 .052] ∗∗[0 .106] ∗[0 .064] ∗∗[0 .031] ∗∗[0 .084] ∗[0 .046] ∗∗
Adj-R2 0 .300 0 .259 0 .301 0 .296 0 .248 0 .251
Pseudo Adj-R2 (GMM) 0 .281 0 .190 0 .265 0 .191 0 .150 0 .086
Panel B Heteroskedasticity-adjusted measures
Forbes-Rigobon BEKK DCC-GARCH Cond. Beta
Integration index ( −1) 0 .102 0 .247 0 .126
(0 .048) ∗∗(0 .119) ∗∗(0 .044) ∗∗∗
[0 .050] ∗∗[0 .117] ∗∗[0 .050] ∗∗
Integration index ( −2) 0 .135 0 .303 0 .122
(0 .049) ∗∗∗(0 .115) ∗∗(0 .038) ∗∗∗
[0 .039] ∗∗∗[0 .095] ∗∗∗[0 .036] ∗∗∗
Integration index ( −3) −0.030 0 .089 0 .167 0 .069
(0 .012) ∗∗(0 .031) ∗∗∗(0 .059) ∗∗∗(0 .030) ∗∗
[0 .013] ∗∗[0 .037] ∗∗[0 .082] ∗∗[0 .039] ∗
Integration index ( −4) −0.027 0 .101 0 .161 0 .119
(0 .012) ∗∗(0 .031) ∗∗∗(0 .064) ∗∗(0 .035) ∗∗∗
[0 .014] ∗[0 .033] ∗∗∗[0 .079] ∗∗[0 .040] ∗∗∗
Integration index ( −5) −0.042
(0 .013) ∗∗∗
[0 .015] ∗∗∗
Adj-R2 0 .045 0 .259 0 .259 0 .178
Pseudo Adj-R2 (GMM) 0 .009 0 .204 0 .199 0 .122
Notes : We regress a measure of FDI global share (i.e., a global indicator of capital mobility among countries) on each of the integration measures depicted in Figs. 2 and 3 .
The optimal number of lags for each equation is selected using the Gets procedure described in Hendry and Krolzig (20 03) ; 20 05 ). Results are reported for the country group
ALL only. The global FDI share is obtained as a GDP-weighted average of cross-country FDI shares. FDI share at country level is deﬁned as the sum of inward and outward
FDI stocks divided by GDP. FDI share data are retrieved from UNCTAD . Data are available at annual frequency and are converted in quarterly using the Chow-Lin interpolation
method ( Chow and Lin, 1971 ). Quarterly ﬁnancial integration measures are obtained as averages of monthly ﬁgures. All variables are expressed in log-differences. A constant
is included in the regressions. Newey-West (HAC) standard errors are reported in parentheses. Bootstrapped standard errors (with 10,0 0 0 replications) are reported in square
brackets. Pseudo Adj-R2 is the adjusted R-squared calculated in GMM regressions. Pseudo Adj-R2 = 1 −{ 1 −[ cor r (F DI t , /hatwidest F DI t )] 2 } /parenleftbign −1
n −p /parenrightbig
, where /hatwidest F DI t is the ﬁtted value of FDI t ,
p is the number of explanatory variables and n is the sample size. Employed instruments: lagged FDI (from t −1 to t −4 ) and lagged integration index (from t −6 to t −8 ).
GMM estimation passes the standard tests of instrument validity. Sample: 1996Q1-2014Q4. Signiﬁcance at the 10%, 5%, and 1% levels is denoted by ∗, ∗∗, and ∗∗∗.
References
Abad, P. , Chuliá, H. , Gómez-Puig, M. , 2010. EMU and European government bond
market integration. J. Bank. Finance 34, 2851–2860 .
Adam, K. , Jappelli, T. , Menichini, A. , Padula, M. , Pagano, M. , 2002. Analyse, compare,
and apply alternative indicators and monitoring methodologies to measure the
evolution of capital market integration in the European Union. Univ. Salerno
Stud. Econ. Finance (CSEF) .
Baca, S.P. , Garbe, B.L. , Weiss, R.A. , 20 0 0. The rise of sector effects in major equity
markets. Financ. Anal. J. 56 (5), 34–40 .
Baker, S.R. , Bloom, N. , Davis, S.J. , 2015. Measuring economic policy uncertainty.
NBER Working Paper, 21633 .
Ball, C.A. , Torous, W.N. , 2006. Contagion in the presence of stochastic interdepen-
dence. Mimeo .
Barr, D. , Priestley, R. ,2 0 0 4 . Expected returns, risk and the integration of interna-
tional bond markets. J. Int. Money Finance 23, 71–97 .
Bekaert, G. , Harvey, C.R. , Lundblad, C.T. , Siegel, S. , 2011. What segments equity mar-
kets? Rev. Financ. Stud. 24, 3847–3890 .
Bekaert, G. , Hodrick, R. , Zhang, X. , 2009. International stock return comovements. J.
Finance 64, 2591–2626 .
Bekiros, S.D. , 2013. Contagion, decoupling and the spillover effects of the us ﬁnan-
cial crisis: evidence from the BRIC markets. Int. Rev. Financ. Anal. 33, 58–69 .
Billio, M. , Getmansky, M. , Lo, A.W. , Pelizzon, L. , 2012. Econometric measures of con-
nectedness and systemic risk in the ﬁnance and insurance sectors. J. Financ.
Econ. 104 (3), 535–559 . Blanchard, O. , Dell’Ariccia, G. , Mauro, P. , 2010. Rethinking macroeconomic policy. J.
Money Credit Bank. 42, 199–215 .
Bollerslev, T. , 1990. Modelling the coherence in short run nominal exchange rates:
a multivariate generalized ARCH model. Rev. Econ. Stat. 72, 498–505 .
Brooks, R. , Negro, M.D. , 2004. The rise in comovement across national stock mar-
kets: market integration or IT bubble? J. Empirical Finance 11, 659–680 .
Caporale, G.M. , Spagnolo, N. , 2011. Stock market integration between three CEECs,
Russia, and the UK. Rev. Int. Econ. 19, 158–169 .
Carrieri, F. , Errunza, V. , Hogan, K. , 2007. Characterizing world market integration
through time. J. Financ. Quant. Anal. 42, 915–940 .
Carroll, C.D. , Otsuka, M. , Slacalek, J. , 2011. How large are housing and ﬁnancial
wealth effects? a new approach. J. Money Credit Bank. 43 (1), 55–79 .
Chiang, T.C. , Jeon, B.N. , H, L. , 2007. Dynamic correlation analysis of ﬁnancial conta-
gion: evidence from asian markets. J. Int. Money Finance 26, 1206–1228 .
Choudhry, T. , Jayasekera, R. , 2013. Level of eﬃciency in the UK equity market: em-
pirical study of the effects of the global ﬁnancial crisis. Rev. Quant. Finance Acc.
44, 213–242 .
Choueifaty, Y. , Coignard, Y. , 2008. Toward maximum diversiﬁcation. J. Portfolio Man-
age. 35 (1), 40–51 .
Chow, G.C. , Lin, A.L. , 1971. Best linear unbiased interpolation, distribution, and ex-
trapolation of time series by related series. Rev. Financ. Stud. 53 (4), 372–375 .
Christoffersen, P. , Errunza, V. , Kris, J. , Langlois, H. ,2 0 1 1 . Is the potential for interna-
tional diversiﬁcation disappearing? Working Paper .

174 M. Billio et al. / Journal of Banking and Finance 76 (2017) 150–174
Christoffersen, P. , Errunza, V. , Kris, J. , Langlois, H. , 2012. Is the potential for inter-
national diversiﬁcation disappearing? a dynamic copula approach. Rev. Financ.
Stud. 25, 3711–3751 .
Colacito, R. , Croce, M.M. , 2010. The short- and long-run beneﬁts of ﬁnancial inte-
gration. Am. Econ. Rev. 100, 527–531 .
Connolly, R.A. , Stivers, C. , Sunc, L. , 2007. Commonality in the time-variation of stock-
-stock and stock-bond return comovements. J. Financ. Markets 10, 192–218 .
Cunningham, A. , Eklund, J. , Jeffery, C. , Kapetanios, G. , Labhard, V. , 2012. A state space
approach to extracting the signal from uncertain data. J. Bus. Econ. Stat. 30 (2),
173–180 .
De Santis, G. , Gérard, B. , 1998. How big is the premium for currency risk? J. Financ.
Econ. 49 (3), 375–412 .
Donadelli, M. , Paradiso, A. , 2014. Is there heterogeneity in ﬁnancial integration dy-
namics? evidence from country and industry emerging market equity indexes.
J. Int. Financ. Markets Inst. Money 32, 184–218 .
Driessen, J. , Laeven, L. , 2007. International portfolio diversiﬁcation beneﬁts: cross–
country evidence from a local perspective. J. Bank. Financ 31 (6), 1693–1712 .
Egert, B. , Kocenda, E. , 2011. Time-varying synchronization of European stock mar-
kets. Empir. Econ. 40 (2), 393–407 .
Elyasiani, E. , Wanli, Z. , 2008. International interdependence of an emerging market:
the case of Iran. Appl. Econ. 40, 395–412 .
Engle, R.F. , 2002. Dynamic conditional correlation: a simple class of multivariate
generalized autoregressive conditional heteroscedasticity models. J. Bus. Econ.
Stat. 20, 339–350 .
Engle, R.F. , Kroner, K.F. , 1995. Multivariate simultaneous generalized ARCH. Econ.
Theory 11, 122–150 .
Engle, R.F. , Sheppard, K. , 2001. Long-term global market correlations. NBER Working
Paper, 8554 .
Errunza, V. , Hogan, K. , Hung, M.-W. , 1999. Can the gains from international diversi-
ﬁcation be achieved without trading abroad? J. Finance 54 (6), 2075–2107 .
Forbes, K.J. , Rigobon, R. ,2 0 0 2 . No contagion, only interdependence: measuring stock
market comovements. J. Finance 57 (5), 2223–2261 .
Goetzmann, W. , Li, L. , Rouwenhorst, G. , 2005. Long-term global market correlations.
J. Bus. 71, 1–38 .
Gupta, R., Guidi, F., 2012. Cointegration relationship and time varying co-movements
among Indian and Asian developed stock markets. Int. Rev. Financ. Anal. 21 (0),
10–22. http://dx.doi.org/10.1016/j.irfa.2011.09.001 .
Hendry, D.F. , Krolzig, H.-M. ,2 0 0 3 . New developments in automatic general-to-spe-
ciﬁc modelling. Econ. Philos. Econ. 379–419 .
Hendry, D.F. , Krolzig, H.-M. , 2005. The properties of automatic gets modelling. Econ.
J. 115 (502), C32–C61 .
Hilliard, J.E., 1979. The relationship between equity indices on world exchanges. J.
Finance 34 (1), 103–114. doi: 10.1111/j.1540-6261.1979.tb02074.x .
Horvath, R. , Petrovski, D. , 2013. International stock market integration: central and
south eastern europe compared. Econ. Syst. 37, 81–91 .
Jappelli, T. , Pistaferri, L. , 2011. Financial integration and consumption smoothing.
Econ. J. 121, 678–706 .
Jayasinghe, P. , Tsui, A.K. , Zhang, Z. , 2014. New estimates of time-varying currency
betas: a trivariate BEKK approach. Econ. Model. 42, 128–139 .
Jayasuriya, S.A. , 2011. Stock market correlations between china and its emerging
market neighbors. Emerging Markets Rev. 12, 418–431 .
de Jong, F. , de Roon, F.A. , 2005. Time varying market integration and expected re-
turns in emerging markets. J. Financ. Econ. 78, 583–613 .
Jong, J.-C. , Kotz, S. , 1999. On a relation between principal components and regres-
sion analysis. Am. Stat. 53 (4), 349–351 .
Kearney, C. , Lucey, B.M. , 2004. International equity market integration: theory, evi-
dence and implications. Int. Rev. Financ. Anal. 13, 571–583 .
Khalid, A.M., Kawai, M., 2003. Was ﬁnancial market contagion the source of eco-
nomic crisis in Asia? evidence using a multivariate VAR model. J. Asian Econ.
14 (1), 131–156. http://dx.doi.org/10.1016/S1049-0 078(02)0 0243-9 . Kim, S.-J. , Moshirian, F. , Wu, E. , 2006. Evolution of international stock and bond
market integration: inﬂuence of the european monetary union. J. Bank. Finance
30, 1507–1534 .
King, M. , Sentana, E. , Wadhwani, S. , 1994. Volatility and links between national
stock markets. Econometrica 62 (4), 901–933 .
Kirchner, M. , Cimadomo, J. , Hauptmeier, S. , 2010. Transmission of government
spending shocks in the euro area: time variation and driving force. ECB Working
Paper, 1219 .
Koedijk, K.G., Kool, C.J., Schotman, P.C., van Dijk, M.A., 2002. The cost of capi-
tal in international ﬁnancial markets: local or global? J. Int. Money Finance
21 (6), 905–929 . International Financial Integration. http://dx.doi.org/10.1016/
S0261-5606(02)0 0 028-1
Krolzig, H. , 2008. Gets model selection with sign restrictions. Technical Report.
Working paper, University of Kent, Canterbury. Presented at the ESEM .
Laopodis, N.T., 2011. Equity prices and macroeconomic fundamentals: international
evidence. J. Int. Financ. Markets Inst. Money 21 (2), 247–276. http://dx.doi.org/
10.1016/j.intﬁn.2010.10.006 .
Longin, F. , Solnik, B. , 1995. Is the correlation in international equity returns con-
stant: 1960–1990? J. Int. Money Finance 14, 3–26 .
Longin, F. , Solnik, B. ,2 0 0 1 . Extreme correlation of international equity markets. J.
Finance 56 (2), 649–676 .
Mauro, P. , Sussman, N. , Yafeh, Y. , 2002. Emerging markets spreads: then versus now.
Q. J. Econ. 115, 695–733 .
McAvoy, G.E. , 1998. Measurement models for time series analysis: estimating dy-
namic linear errors-in-variables models. Political Anal. 7 (1), 165–186 .
Meric, I., Meric, G., 1989. Potential gains from international portfolio diversiﬁca-
tion and inter-temporal stability and seasonality in international stock mar-
ket relationships. J. Bank. Financ 13 (45), 627–640. http://dx.doi.org/10.1016/
0378- 4266(89)90034- 4 .
Morana, C. , Beltratti, A. , 2008. Comovements in international stock markets. J. Int.
Financ. Markets Inst. Money 18 (1), 31–45 .
Nellis, J. , 1982. A principal components analysis of international ﬁnancial integration
under ﬁxed and ﬂoating exchange rate regimes. Appl. Econ. 14, 339–354 .
Obstfeld, M. , Taylor, A. , 2004. Global Capital Markets: Integration, Crisis, and
Growth.. Cambridge University Press, New York/Cambridge .
Panton, D.B. , Lessig, V.P. , Joy, O.M. , 1976. Comovement of international equity mar-
kets: a taxonomic approach. J. Financ. Quant. Anal. 11 (3), 415–432 .
Pukthuanthong, K. , Roll, R. , 2009. Global market integration: an alternative measure
and its application. J. Financ. Econ. 94, 214–232 .
Quinn, D.P. , Voth, H.-J. , 2008. A century of global equity market correlations. Am.
Econ. Rev. 98 (2), 535–540 .
Ramchand, L., Susmel, R., 1998. Volatility and cross correlation across major
stock markets. J. Empirical Finance 5 (4), 397–416. http://dx.doi.org/10.1016/
S0927-5398(98)0 0 0 03-6 .
Suzuki, Y. , 2014. Financial integration and consumption risk sharing and smoothing.
Int. Rev. Econ. Finance 29, 585–598 .
Volosovych, V. , 2011. Measuring ﬁnancial market integration over the long run: is
there a U-shape? J. Int. Money Finance 30, 1535–1561 .
Volosovych, V. , 2013. Learning about ﬁnancial market integration from principal
components analysis. CESifo Econ. Stud. 59, 360–391 .
Wang, P. , Moore, T. , 2008. Stock market integration for the transition economies:
time-varying conditional correlation approach. Manchester Sch. 7, 116–133 .
Watson, J. , 1980. The stationarity of inter-country correlation coeﬃcients: A note. J.
Bus. Finance Acc. 7, 297–303 .
Yu, C. , 2015. Evaluating international ﬁnancial integration in a center-periphery
economy. J. Int. Econ. 95 . 129–14
Yu, I.-W. , Fung, K.-P. , Tam, C.-S. , 2010. Assessing ﬁnancial market integration in Asia
– equity markets. J. Bank. Finance 34, 2874–2885 .

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