Responses to Reviewer #1:
Dear reviewer:
Thank you for your comments on our manuscript. Those comments are valuable and very
helpful for revising and improving our paper. We have studied the comments carefully
and have made corrections which we hope to meet with approval finally.
Below we address each issue the reviewers raised and describe corresponding changes
in the revised manuscript. For ease of reference, changes were made by using blue
text in the revised manuscript. Reviewers’ comments are repeated in full using italics,
while our responses are typed in standard.
1.General Comment: Please see my detailed comments in your PDF manuscript as attached.
Response: Thank you for your valuable time and efforts in this review process, and
thanks for your excellent comments that could improve the quality of our manuscript.
Following you detailed comments in PDF manuscript, we significantly improved the quality
of this manuscript based on your constructive comments. Here we submitted a new version,
which has been further revised according to your suggestions. In summary, major modifications
include:
First, we have carefully rewritten the abstract according to the research objectives,
research methods, data, and the framework of the main findings
Second, in the first introduction part, we introduced BRI in a more concise way, restated
the research questions in this paper, and expounded the research content more accurately.
Third, in the second part of related literature, we reorganized relevant literature,
made some improvements in the measurement of business cycle synchronization, the
research on the structural characteristic of the BCSN, and summarized the shortcomings
of existing research and the contribution of this paper
Fourth, in the third part of research methods and data description, we mainly improved
the description of complex network analysis methods, especially the construction process
of BCSN, and added the calculation formula of structural characteristic indicators.
Fifth, in the fourth part of the overall characteristics analysis, we deleted the
redundant results of weighted clustering coefficient (WCC), added measuring results
and the analysis before and after the inception of the BRI, redrew the diagram of
network subgroup structure with VOSviewer software, and elaborated overall structural
characteristics of the BCSN from the network structure evolution and network subgroup
structure.
Sixth, in the part of individual characteristics analysis, we deleted the redundant
node strength (NS) results, improved the interpretation of the measurement results
before and after the inception of the BRI, and illustrated the individual structural
characteristics of the BCSN from node centrality and coreness degree.
Seventh, in the conclusion and discussion part, we rerefined the research conclusions,
deleted the original policy recommendations, and added the discussion on future research
prospects.
Eighth, we tried our best to correct punctuation marks, misspellings, grammar, references
and other details in the paper, and deleted the “speculative” statements, in order
to improve the quality of this paper and meet relevant requirements.
2.Major comments
Comment 1: Recalling the inception of the BRI in 2013, data analysis should be made.
Response 1: Thanks for your constructive comments. Following your suggestions, we
had added the data analysis to recalling the inception of the BRI. The detailed revision
is shown on pages 1-2 and below:
The BRI comprises of over 50 different economies, which cover 80% of globe population
and its the estimated cost is over $21.1 trillion US dollars (Klinger 2019). Since
the BRI was proposed in 2013, major achievements have been made in infrastructure
construction, international trade, cross-border investment and sustainable growth.
One World Bank report[ For a more details of the achievements of the BRI, please refer
to the World Bank report Belt and Road Economics: Opportunities and Risks of Transport
Communities, https://www.worldbank.org/en/topic/regional-integration/publication/belt-and-road-economics-opportunities-and-risks-of-transport-corridors.] noted that BRI is expected to increase real income by 1.2-3.4% in BRI economies
and 0.7%-2.9% globally, with investments that could lift more than 7.6 million people
out of extreme poverty. In particular, BRI transport projects have significantly reduced
trade costs, which are expected to increase trade in BRI economies by 2.8% to 9.7%,
increase in world trade by 1.7% to 6.2%, and total foreign direct investment in BRI
economies by 4.97% (World Bank, 2019).
Comment 2: Remove redundant description of the BRI.
Response 2: Thanks for your point. Following your suggestions and detailed comments
in PDF manuscript, we had removed redundant description of the BRI in the second paragraph
of the first page. The detailed revision is shown on pages 1-2 and below:
The BRI was initiated by the Chinese president Xi Jinping in 2013, and it was completely
introduced during the visit of Kazakhstan and Indonesia. In the background of the
history of China's ancient overland and maritime Silk Road, the BRI consists of the
Silk Road Economic Belt and the 21st Century Maritime Silk Road, geographically crossing
Asia, Europe and Africa. The BRI comprises of over 50 different economies, which cover
80% of globe population and its the estimated cost is over $21.1 trillion US dollars
(Klinger 2019). Since the BRI was proposed in 2013, major achievements have been made
in infrastructure construction, international trade, cross-border investment and sustainable
growth. One World Bank report[ For a more details of the achievements of the BRI,
please refer to the World Bank report Belt and Road Economics: Opportunities and
Risks of Transport Communities, https://www.worldbank.org/en/topic/regional-integration/publication/belt-and-road-economics-opportunities-and-risks-of-transport-corridors.] noted that BRI is expected to increase real income by 1.2-3.4% in BRI economies
and 0.7%-2.9% globally, with investments that could lift more than 7.6 million people
out of extreme poverty. In particular, BRI transport projects have significantly reduced
trade costs, which are expected to increase trade in BRI economies by 2.8% to 9.7%,
increase in world trade by 1.7% to 6.2%, and total foreign direct investment in BRI
economies by 4.97% (World Bank, 2019). The BRI has strengthened cooperation in trade,
investment, infrastructure construction, institutional and cultural exchange among
Asia, Europe and Africa, and formed a new economic network (Anwar et al., 2021). It
aims to build a community of shared future for mankind, and it is an important platform
for international multilateral cooperation and regional integration cooperation. Ultimately,
it will make the world economy and society more open, inclusive, balanced and benefit-sharing.[
More details about the BRI could check the website of Belt and Road Portal, https://eng.yidaiyilu.gov.cn/index.htm. ] However, there are still significant political, cultural, social, economic and
institutional differences among the BRI economies, especially in terms of economic
growth and their policies.[ Such differences are not only between China and BRI economies,
but also within BRI economies. Thus, these transnational differences are a collection
of differences between many parties. ]
Comment 3: Check several typos. Change “BRI economics” to “BRI economies”.
Response 3: We appreciated this important reminder, and Thanks for spotting this typo.
Following your suggestions, we changed “BRI economics” to “BRI economies” in this
paper, and carefully checked the similar misspellings.
Comment 4: Implication should be rewritten.
Response 4: Thanks for your excellent comments that could improve the quality of our
manuscript. Following your suggestions and detailed comments in PDF manuscript, we
had rewritten the implication. Based on your comments, we make the following amendments:
First, we changed the title of the last part of the paper (page 22) from “Conclusion”
to “Conclusion and Discussion”. Second, we summarized the conclusions of this paper
and discussed the structural characteristics of BCSN before and after the inception
of the BRI. Third, this paper only revealed the structural characteristics of BCSN
of BRI economies and did not make regression test on the driving factors of the BCSN,
so this paper could not make corresponding policy suggestions.
So, we deleted the policy implications in the introduction part and the policy recommendations
in the last paragraph (page 26), and added the discussion of future research directions.
The related revision is shown on pages 22-24 and below:
With the support of instantaneous quasi-correlation and complex network analysis method,
this article empirically analyzed the Topological characteristics of BCSN of BRI economies
from 2000 to 2019. The main research conclusions are as follows:
First, in the sample period, the business cycle synchronization linkage of BRI economies
is still relative weak, the network density and network efficiency has decreased after
the inception of the BRI.
Second, the BCSN of BRI economies always show a large clustering coefficient and a
short average path length, which presents a typical structural characteristic of “small
world”. Meanwhile, the clustering degree of output synchronization linkage of BRI
economies is weakened after the inception of the BRI.
Third, on the whole, the BCSN of BRI economies does not have the characteristic of
gradual evolution. But since the inception of the BRI，the evolution of the BCSN of
BRI economies shows a self-stability characteristic.
Fourth, the BCSN structure is composed of four subgroups. The synchronization linkage
level inside subgroups is obviously higher than the one outside subgroups. After the
inception of the BRI, the BCSN structure of BRI economies mainly consist of two-way
spillover subgroup and broker subgroup.
Fifth, the individual characteristics of the BRI economies are obviously different,
the relative influence of a country in the network does not fully show its hub role. After
the inception of the BRI, the function of China and other important nodes, such as
Southeast Asia, Central Asia and CEE, has been enhanced. From the perspective of different
regions, East Asia plays a relatively big role in the network, CEE and Central Asia
take the most prominent mediating effect.
Sixth, China's EC and coreness level have increased and ranked top during the sample
period, but its CC level is still low. After the inception of the BRI, China's relative
influence in the entire network has increased significantly, but does not show much
mediating effect.
Combined with instantaneous quasi-correlation and complex network analysis method,
this paper reveals the structural characteristics of the BCSN of BRI economies from
the overall and individual aspects. It should be noted that there are still some deficiencies in
this paper, which need to be improved by follow-up research. Specifically, future
research can be improved from the following three aspects. First of all, besides the
instantaneous quasi-correlation method, other methods can be used to measure the business
cycle synchronization, such as Markov switching model, dynamic correlation coefficient
method, GARCH Model, concordance index and difference method, to ensure the robustness
of empirical results. In addition, combined with cutting-edge complex network analysis
methods, it is considered to make a weighted business cycle synchronization matrix,
and further investigate the characteristics of the BCSN of BRI economies such as robustness
and vulnerability, so as to enrich the existing research. Finally, Multiple Regression
Quadratic Assignment Procedure (MRQAP) could be used to empirically study the driving
factors of the structure evolution of the BCSN of BRI economies, which may provide
some policy suggestions for strengthening the business cycle synchronization linkage
of BRI economies.
[References]
Anwar M. A., S. Nasreen, and A. K. Tiwari. Forestation, Renewable Energy and Environmental
Quality: Empirical Evidence From Belt and Road Initiative Economies[J]. Journal of
Environmental Management, 2021, 291(8):112684-112683.
Klinger J. Environment, Development, and Security Politics in the Production of Belt
and Road Spaces[J]. Territory Politics Governance, 2019,8(5):657-675.
World Bank. Belt and Road Economics: Opportunities and Risks of Transport Corridors[R].
Washington, DC: World Bank. 2019.
Responses to Reviewer #2:
Dear reviewer:
Thank you for your comments on our manuscript. Those comments are valuable and very
helpful for revising and improving our paper. We have studied the comments carefully
and have made corrections which we hope to meet with approval finally.
Below we address each issue the reviewers raised and describe corresponding changes
in the revised manuscript. For ease of reference, changes were made by using blue
text in the revised manuscript. Reviewers’ comments are repeated in full using italics,
while our responses are typed in standard.
1.General Comment: The paper is interesting, its structure is correct, and the topic
is clearly a hot one. Results are fine unless not surprising. However, from my point
of view, the following main issues make its publication not recommended at its current
state.
Response: Thank you for your valuable time and efforts in this review process, and
Thanks for your excellent comments that could improve the quality of our manuscript.
We significantly improved the quality of this manuscript based on your constructive
comments. Here we submitted a new version, which has been further revised according
to your suggestions. In summary, major modifications include:
First, in the first introduction part, we introduced BRI in a more concise way, restated
the research questions in this paper, and expounded the research content more accurately.
Second, in the second part of related literature, we reorganized relevant literature,
made some improvements in the measurement of business cycle synchronization, the
research on the structural characteristic of the BCSN, and summarized the shortcomings
of existing research and the contribution of this paper.
Third, in the third part of research methods and data description, we mainly improved
the description of complex network analysis methods, especially the construction process
of BCSN, and added the calculation formula of structural characteristic indicators.
Fourth, in the fourth part of the overall characteristics analysis, we deleted the
redundant results of weighted clustering coefficient (WCC), added measuring results
and the analysis before and after the inception of the BRI, redrew the diagram of
network subgroup structure with VOSviewer software, and elaborated overall structural
characteristics of the BCSN from the network structure evolution and network subgroup
structure.
Fifth, in the part of individual characteristics analysis, we deleted the redundant
node strength (NS) results, improved the interpretation of the measurement results
before and after the inception of the BRI, and illustrated the individual structural
characteristics of the BCSN from node centrality and coreness degree.
Sixth, in the conclusion and discussion part, we refined the research conclusions,
deleted the original policy recommendations, and added the discussion on future research
prospects.
Seventh, we tried our best to correct punctuation marks, misspellings, grammar, references
and other details in the paper, and deleted the “speculative” statements, in order
to improve the quality of this paper and meet relevant requirements.
2.Major comments
Comment 1: Introduction is extremely long and not very informative. At the end of
it, we still do not know what the “BRI” is (who is financing the initiative, what
for, what the achievements are, what kind of projects have been implemented, and so
on)
Response 1: Thanks for your constructive comments that could improve the quality of
our manuscript. Following your suggestions, we have simplified and adjusted the content
of the introduction. To be specific, first of all, we have rewritten the introduction
of BRI to highlight the origin, coverage, achievements, goals and challenges of BRI.
Secondly, based on the current challenges BRI is facing, this paper introduces relevant
research on business cycle synchronization, and reveals its key issues. Then, in order
to reveal the complex interdependence among economies, we introduce the complex network
analysis method and its application in analyzing the business cycle synchronization
linkage. Finally, taking BRI economies as the research object, we elaborate the problems
to be solved in this paper and introduce specific research methods.
For more detailed modifications, please refer to the introduction part (page 1-4).
More detialed introduction about BRI could refer to the website of Belt and Road Portal
(https://eng.yidaiyilu.gov.cn/index.htm). In addition, in order to facilitate reviewer's understanding, we make a separate
summary here.
About the origin of BRI, based on the history of China's ancient Silk Road, Chinese
President Xi Jinping proposed the Silk Road Economic Belt and the 21st Century Maritime
Silk Road during his visit to Kazakhstan and Indonesia in 2013, thus forming the whole
Belt and Road Initiative. As the initiator and leader of BRI, China hoped to strengthen
economic cooperation among BRI economies through this initiative and jointly realize
sustainable economic and social development.
About the coverage of BRI, the Belt and Road is composed of more than 50 different
economies, covering 80% of the global population with an economic scale of over 21
trillion US dollars (Klinger, 2019). BRI is an effort to create jointly-built trade
routes that emulate the ancient Silk Road and promote regional cooperation in Asia,
Europe, and Africa.
About the development achievements of BRI, it has strengthened cooperation in trade,
investment, infrastructure construction, institutional and cultural exchange among
Asia, Europe and Africa, and formed a new economic network (Anwar et al., 2021). Since
the inception of the BRI in 2013,a lot of achievements in infrastructure development,
international trade, cross-border investment and sustainable growth have been made. One
World Bank report[ For a more details of the achievements of the BRI, please refer
to the World Bank report Belt and Road Economics: Opportunities and Risks of Transport
Communities, https://www.worldbank.org/en/topic/regional- integration/publication/belt-and-road-economics-opportunities-and-risks-of-transport-corridors. ] noted that BRI is expected to increase real income by 1.2-3.4% in BRI economies
and 0.7%-2.9% globally, with investments that could lift more than 7.6 million people
out of extreme poverty. In particular, BRI transport projects have significantly reduced
trade costs, which are expected to increase trade in BRI economies by 2.8% to 9.7%,
increase in world trade by 1.7% to 6.2%, and total foreign direct investment in BRI
economies by 4.97%(World Bank, 2019). Based on policy coordination, facilities connectivity,
unimpeded trade, financial integration and people-to-people bond, some great achievements
have been made since the inception of the BRI in 2013. For policy coordination, at
presen, China has signed more than 200 agreements on BRI cooperation with 149 countries
and 32 international organizations, and successfully hosted two BRI Forums for international
cooperation. For facilities connectivity, infrastructure construction cooperation
between China and BRI economies in railways, ports, aviation, energy and communications
has strengthened the infrastructure quality of BRI member states. For unimpeded trade,
trade and investment among BRI economies have grown considerably, and BRI members
have actively participated in the China International Import Expo. For financial integration,
the Silk Road Fund and the Asian Infrastructure Investment Bank were set to provide
reliable financial support for BRI construction projects. For people-to-people bond,
China and BRI economies have deepened cooperation in cultural exchanges, scientific
and technological innovation, and conducted a series of humanitarian assistance in
medical care, poverty alleviation and food supply.
About development goals of BRI, it aims to build a community of shared future, and
it is an important platform for international multilateral cooperation and regional
integration cooperation. Ultimately, it will make the world economy and society more
open, inclusive, balanced and benefit-sharing.[ More details about the BRI could check
the website of Belt and Road Portal,https://eng.yidaiyilu.gov.cn/index.htm.]
About the challenge BRI is facing, there are still significant political, cultural,
social, economic and institutional differences among the BRI economies, especially
in terms of economic growth and their policies[ Such differences are not only between
China and BRI economies, but also within BRI economies. Thus, these transnational
differences are a collection of differences between many parties. ]. Just because
of the difference in economic base and growth, it poses certain challenges to promote
BRI development.
Comment 2: The paper, from my point of view, is very poorly written and difficult
to understand. There are plenty of examples, I will show just a couple of them:
• Page 8, “With the continuous advancement of economic globalization and international
division of labor, the correlation trend of output periodicity and economic scale
among countries presents a certain nonlinear and multi-threaded complex relationship,
and then forms an interactive BCSN in space”
• Page 9, “are regarded as nodes in this paper, and the quasi-correlation coefficients
between the actual economic scales of economics are regarded as the connecting edges
between nodes”
Response 2: Thanks for your excellent comments, and we appreciated this important
reminder. Following your suggestions, we tried our best to improve the English expression
and grammar in this paper in order to meet the relevant requirements as far as possible.
As the example sentence on page 8 you mentioned, after careful consideration, we have
deleted it directly. According to Antonakakis et al.(2015) and Papadimitriou et al.(2016),
we constructed BCSN directly using complex network analysis methods without additional
explanation.
As you mentioned on page 9, after careful analysis, we have changed the sentence as:
“According to complex network theory and graph theory, BRI economies are regarded
as nodes, and the business cycle synchronization (i.e. the value of instantaneous
quasi-correlation) between economies are regarded as edges between nodes.”
Comment 3: Figures throughout the paper are plotted in an extremely low quality and
they are no informative.
Response 3: Thanks for your excellent point. Following your suggestions, we had deleted
the original figures, and redrew it by VOSviewer software. The new figures are shown
on pages 16 and below:
Fig. 1. Network Subgroups during 2000-2013.
Source: Drawn by the authors from VOSviewer software.
Fig. 2. Network Subgroups during 2014-2019.
Source: Drawn by the authors from VOSviewer software.
Comment 4: The paper shows an important number of “speculative” statements, especially
when it comes to policy advice.
For instance, page 13, the authors claim: “It is worth noting that in 2019, network
density and efficiency saw a significant decline, which was mainly caused by the unilateral
trade protectionism and continuous trade frictions among western countries led by
the US in recent years, which worsened the previous positive global economic and trade
environment”. However, the authors do not analyse the variables affecting output synchronicity
and consequently they cannot state such connection.
In page 4 the authors claim that their paper will provide policy inspiration to enhance
economic synchronicity among BRI countries, however this is not possible with the
analysis the authors provide.
Response 4: Thanks for your constructive comments. It should be noted that the purpose
of this study is to reveal the structural characteristics of the BCSN, and the driving
factors of BCSN are not further investigated through regression test. Therefore, this
paper is indeed unable to explain the results of BCSN structural characteristics,
let alone make corresponding policy suggestions based on the existing results. In
view of this, as you mentioned, we have deleted the “speculative” statements on page
4 and page 13 mentioned by experts, and re-examined and revised the “speculative”
statements in the part of introduction, structural characteristics analysis and policy
suggestions in the paper.
In addition, it is worth noting that we have changed the title of the last part of
the paper (page 22) from “Conclusion” to “Conclusion and Discussion”. And then, we
summarized the conclusions of this paper and discussed the structural characteristics
of BCSN before and after the inception of the BRI. In the end, we deleted the policy
recommendations in the last paragraph (page 23-24), and added the discussion of future
research directions.
The related revision is shown on pages 22-24 and below:
With the support of instantaneous quasi-correlation and complex network analysis method,
this article empirically analyzed the Topological characteristics of BCSN of BRI economies
from 2000 to 2019. The main research conclusions are as follows:
First, in the sample period, the business cycle synchronization linkage of BRI economies
is still relative weak, the network density and network efficiency has decreased after
the inception of the BRI.
Second, the BCSN of BRI economies always show a large clustering coefficient and a
short average path length, which presents a typical structural characteristic of “small
world”. Meanwhile, the clustering degree of output synchronization linkage of BRI
economies is weakened after the inception of the BRI.
Third, on the whole, the BCSN of BRI economies does not have the characteristic of
gradual evolution. But since the inception of the BRI，the evolution of the BCSN of
BRI economies shows a self-stability characteristic.
Fourth, the BCSN structure is composed of four subgroups. The synchronization linkage
level inside subgroups is obviously higher than the one outside subgroups. After the
inception of the BRI, the BCSN structure of BRI economies mainly consist of two-way
spillover subgroup and broker subgroup.
Fifth, the individual characteristics of the BRI economies are obviously different,
the relative influence of a country in the network does not fully show its hub role. After
the inception of the BRI, the function of China and other important nodes, such as
Southeast Asia, Central Asia and CEE, has been enhanced. From the perspective of different
regions, East Asia plays a relatively big role in the network, CEE and Central Asia
take the most prominent mediating effect.
Sixth, China's EC and coreness level have increased and ranked top during the sample
period, but its CC level is still low. After the inception of the BRI, China's relative
influence in the entire network has increased significantly,but does not show much
mediating effect.
Combined with instantaneous quasi-correlation and complex network analysis method,
this paper reveals the structural characteristics of the BCSN of BRI economies from
the overall and individual aspects. It should be noted that there are still some deficiencies in
this paper, which need to be improved by follow-up research. Specifically, future
research can be improved from the following three aspects. First of all, besides the
instantaneous quasi-correlation method, other methods can be used to measure the business
cycle synchronization, such as Markov switching model, dynamic correlation coefficient
method, GARCH Model, concordance index and difference method, to ensure the robustness
of empirical results. In addition, combined with cutting-edge complex network analysis
methods, it is considered to make a weighted business cycle synchronization matrix,
and further investigate the characteristics of the BCSN of BRI economies such as robustness
and vulnerability, so as to enrich the existing research. Finally, Multiple Regression
Quadratic Assignment Procedure (MRQAP) could be used to empirically study the driving
factors of the structure evolution of the BCSN of BRI economies, which may provide
some policy suggestions for strengthening the business cycle synchronization linkage
of BRI economies.
Comment 5: References regarding network analysis applied to synchronization is quite
poor. The authors just cite 3 or 4 papers dealing with this issue but many more can
be found and should be referenced in the paper. In the same line, the authors have
not deeply revised the economic literature on business cycle synchronization.
Response 5: Thanks for your excellent comments that could improve the quality of our
manuscript. Following your suggestions, after carefully re-reading and sorting out
relevant literature, literature closely related to this paper mainly fall into the
following two categories: One is the measurement research on the international business
cycle synchronization (literature from economics view), the other is the related research
on the BCSN (literature about network analysis ). Therefore, we readjusted and improved
the related literature part, adding not only the economic literature on the measurement
of business cycle synchronization, but also the literature on the structural characteristics
of the BCSN. Specific modifications can be found in the related literature part on
pages 5-8 in the paper.
In order to facilitate the review by reviewers, we presented the revised related literature
part as:
The literature closely related to this paper mainly includes the following two categories:
one is the measurement and research on the international business cycle synchronization;
the other is on the BCSN.
The measurement and research on international business cycle synchronization mainly
includes static method and dynamic method. For the static methods, existing studies
mainly adopt simple correlation coefficient method (Giovanni and Levchenko, 2010; Papadimitriou
et al., 2014) and dynamic factor model (Del Negro and Otrok, 2008; Kose et al., 2012).
It should be noted that although the static method can intuitively judge the level
of the synchronization, it cannot reveal the dynamic characteristics of the business
cycle synchronization. Therefore, the follow-up measurement research has gradually
shifted from the traditional static methods to the dynamic methods. For dynamic methods,
existing studies mainly focus on Markov Regime Switching Model (Hamilton and Owyang,
2012; Leiva,Leon, 2014; Ductor and Leva-Leon, 2016), GARCH model (Savva et al., 2010;
Antonakakis,2012), Concordance Index (Harding and Pagan, 2006; Cerqueira and Martins,
2009; Cerqueira, 2013), Difference Method (Kalemli-Ozcan et al., 2013; Pyun and An,
2016) and instantaneous quasi-correlation method (Abiad et al., 2013; Duval et al.,
2016). In addition, some scholars used the Method of Hodrick-Prescott (HP) filter
to de-trend the original output data series and further calculate the business cycle
synchronization (Ng, 2010; Huang and Zhu, 2015). However, Hamilton (2018) believes
that HP filtering method introduces unreal dynamic linkages that are not based on
original data, and its results are affected by the size of smoothing parameter, so
it cannot truly reflect the level of business cycle synchronization. Compared with
other dynamic methods, the instantaneous quasi-correlation method is more efficient
and could carry out dynamic calculation and analysis, which avoids problems caused
by artificial parameter setting and distortion of original data. Therefore, it has
been widely used in practical calculation and analysis (Abiad et al., 2013; Yao and
Tang, 2020).
As for the research on the BCSN, the existing research is mainly conducted from the
perspective of network analysis. Diebold and Yilmaz(2013) investigated the linkages
between actual outputs of G7 countries from 1962 to 2010 by network analysis, and
found that the indicator of connectedness(density) could measure the pairwise output
fluctuation linkages between different countries. At the same time, global connectedness
will change as the business cycle changes. Gomez et al.(2013) adopted correlation
coefficient matrix and network analysis method to systematically investigate the co-movement
of business cycles synchronization in various countries since 1950, and believed that
the dynamic changes of interdependence among countries was mainly driven by the co-movement
of regional economic growth rather than co-movement of world economy. Caraiani (2013)
found that compared with the Granger causality method, using correlation coefficients
to construct a directed business cycle synchronization network can reflect the relative
influence of countries in the world economy more reasonably , and further empirical
findings showed that the United States finally occupies the core position of the business
cycle synchronization network of G7 and OECD. Papadimitriou et al. (2014) used Pearson
correlation coefficient and minimum dominating set to make an empirical study on the
BCSN structure of 22 EU sample member states, and found that after the adoption of
the common currency euro, the output of member states had a higher correlation, and
the BCSN density of EU was increasing. Xi et al. (2014) constructed the BCSN of G7
based on the pairwise Maximum Entropy Model, and found that the network presented
a clustering hierarchy and nearly accounted for almost half of the entire structure
of the interactions within the G7 system. Antonakakis et al. (2015) used sign concordance
index and threshold-minimum dominating set method to investigate topological characteristcs
of BCSN among 27 countries during 1875-2013 and find that there are obvious differences
in node degree of different countries in different periods. Gomez et al. (2017) used
correlation coefficient and minimum spanning tree technique to construct the BCSN
of EU, analyzed the business synchronization linkages and accessibility among member
states, and found that there was no obvious core-periphery structure inside the network.
Ductor and Leva-Leon (2016) adopted the social network analysis method and the indicator
of betweenness centrality to evaluate the relative influence of various countries
for global BCSN. It is found that a country's is more influential in the network tends
to increase when the economy is in recession, but becomes less influential when the
economy is expanding. With Pearson correlation coefficient, rolling window, threshold-minimum
dominating set and other methods, Papadimitriou et al. (2016) selected some indicators
such as the total number of peripheries, network density, the number of dominant and
isolated nodes and node degree to empirically investigate the topological characteristics
of European BCSN during 1986-2011. Matesanz and Ortega(2016) used similarity index
and Minimum Spanning Tree technique (MST) to construct the European BCSN from 1950
to 2013. Based on the dynamic network analysis, the correlations and connectivity
of the network increased significantly in 2009. In addition, differences in window
size, filtering method and similarity measure also affect the characteristics of the
BCSN. With the help of correlation coefficient index used by Cerqueira (2013), Belke
et al. (2017) investigated the the business cycle synchronization of the European
Monetary Union, focusing on the core-periphery mode of the business cycle within the
Union after the economic crisis. Leiva-Leon (2017) established American inter-state
BCSN by Markov Regime Switching framework and investigated the its evolution model
with indicators of MDS (multidimensional scaling) and closeness centrality. It is
found that the network has an obvious core-periphery structure. Sebestyén and Iloskics
(2020) employed the pairwise Granger causality between national outputs to construct
the global shock contagion network, and found that it has a relative long path length
and stronger transmission, and the degree distribution tends to be asymmetric.
For the research on the BSCN of BRI economies, Huang and Yao (2018) used CM (Cerqueira
& Martins) synchronization index to measure the business cycle synchronization between
China and BRI economies and find that it shows a certain “decoupling” trend, and there
are obvious differences in different stages and different development aspects. Cui
et al. (2020) used dynamic correlation coefficient to calculate and found that China
and Southeast and Central Asian countries, as well as Mongolia, Nepal, Pakistan, Sri
Lanka and other countries have a high business cycle synchronization level. Du et
al. (2020) found that the BRI strengthened the business cycle synchronization linkages
between China and ASEAN countries, while the network density and clustering coefficient
also increased to some extent.
Comment 6: I do not understand Table 1. In it the Networks density measure is provided.
This measure is shown for different years. However, if I am correct, the edges of
the network represent correlation degree while nodes represent countries. Therefore,
what is the meaning of this measure for year 2000, which is the first year of analysis?
Or the same measure for 2019? This is not clear to me.
Response 6: Thanks for your point. As you proposed, we used the quasi-correlation
degree and nodes to represent the periphery of the network and the BRI economies respectively.
In the complex network analysis part of this paper, we gave the meaning of the structural
characteristics indicators, and then calculate the results of the annual network structural
characteristics. At this point, we intended to show the results of overall structural
characteristics on the BCSN of BRI economies in some years in Table 1, including density
(DS), network efficiency (NE), clustering coefficient (CC), average distance (AD)
and other indicators. Before explaining this problem, we have added the formula and
definition of each indicator for your understanding.
In this paper, density (DS) describes the degree of business cycle synchronization
between the BRI economies. For better understanding, we added its formula as ，where
represents the actual number of effective linkages in the BCSN in year . represents
the nodes in the network (). It should be noted that the DS is calculated by annual
unweighted and undirected BCSN based on a symmetric Instantaneous Quasi-correlation
matrix. At this time, for the BCSN in year , the actual number of effective linkages
in the network equals to the actual effective business cycle synchronization linkages,
while in theory, the maximum linkage number equals to =53*52=2756. Furthermore, when
the instantaneous quasi-correlation between two economies is greater than the average
among all economies, it is indicated that the business cycle synchronization linkages
between the two economies is actually effective, and it will be recorded as an actual
effective linkage number. Since the output growth and growth rate of BRI economies
vary significantly every year, the size of the instantaneous quasi-correlation among
economies will also change, leading to changes in the actual number of effective linkages
in the network. Meanwhile, the constant number of nodes in the network is 53, so theoretically
the maximum linkage number does not change.
To sum up, no matter in 2000, 2019 or any other year, DS is calculated in the same
way with the same meaning, that is, the ratio of the actual effective number of linkages
in the network to the theoretical maximum number of linkages in year t .
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https://orcid.org/0000-0002-8770-8583
