A. Theoretical Implications

1. Varied effects. Theoretical models have different implications about how global integration should affect volatility of output and other macroeconomic aggregates. The same is true for co-movement of different macro variables. We review the literature on each of these separately.

Volatility and Synchronization of Output in Theory

2. Context matters. There is no consistent theoretical prediction across different models about how trade and financial linkages affect output volatility (Hirata, Kose, and Otrok, 2012). The effects of trade and financial integration depend, in different models, on the level of development, the nature of shocks, and the pattern of specialization.

3. Trade integration. International trade linkages generate both demand and supply-side spillovers across countries, which can increase the degree of business cycle co-movement. For example, on the demand side, an investment or consumption boom in one country can generate increased demand for imports, boosting economies abroad. On the supply side, a positive shock to output in tradable goods leads to lower prices; hence, imported inputs for other countries become cheaper.

4. Impact of specialization. Both classical and “new” trade theories imply that increased trade linkages lead to increased specialization. How does increased specialization affect the degree of co-movement? The answer depends on the nature of specialization (intra- vs. inter-industry) and the types of shocks (common vs. country-specific). If stronger trade linkages are associated with increased inter-industry specialization across countries, then the impact of increased trade depends on the nature of shocks. If industry-specific shocks are more important in driving business cycles, then co-movement is expected to decrease (Krugman, 1993). If common shocks, which might be associated with changes in demand and/or supply conditions, are more dominant than industry-specific shocks, then this would lead to a higher degree of business cycle co-movement (Frankel and Rose, 1998).

5. Financial integration. The effects of financial integration on cross-country correlations of output growth are also ambiguous in theory. Financial integration could reduce cross-country output correlations by stimulating specialization of production through the reallocation of capital in a manner consistent with countries’ comparative advantage. However, financial linkages could result in a higher degree of business cycle synchronization by generating large demand-side effects as the changes in equity prices affect the dynamics of wealth. Furthermore, contagion effects that are transmitted through financial linkages could also result in heightened cross-country spillovers of macroeconomic fluctuations (Claessens and Forbes, 2001).

6. Diversification and risk sharing. Financial integration allows relatively capital-poor emerging market economies (EMs) and other developing economies (ODEs) to diversify away from their narrow production bases, thereby reducing their output volatility. At a more advanced stage of development, however, trade and financial flows could allow for enhanced specialization (Imbs and Wacziarg, 2003). This could make advanced countries and EMs more vulnerable to industry-specific shocks and thereby could lead to higher output volatility (see Kalemli-Ozcan, Sorensen, and Yosha, 2003). That leaves open the question of whether financial integration promotes better risk sharing across countries, which we discuss next.

Consumption Risk-Sharing in Theory

7. Consumption smoothing. Basic theory has the strong prediction that, because financial integration should help countries diversify away country-specific shocks, it should result in more stable consumption patterns and stronger co-movement of consumption growth across countries. Since consumers and, by extension, economies are risk-averse, basic theoretical models predict that consumers should desire to use international financial markets to insure against income risk, thereby smoothing the effects of temporary idiosyncratic fluctuations in income on consumption. In particular, if output fluctuations are not perfectly correlated across countries, in a world with complete markets trade in financial assets can be used to delink national consumption levels from the country-specific components of output fluctuations. In turn, this should make consumption growth less volatile relative to income growth. And from a cross-country and time series perspective, increasing financial linkages should lead to lower and declining relative volatility of consumption growth (Lewis, 1999).

8. Model-specific features matter. While the benefits of international risk-sharing could be quite large, the magnitudes do depend on various model-specific features. In particular, the welfare gains in these models depend on the volatility of output shocks, the rate of relative risk aversion, the risk-adjusted growth rate and the risk free interest rate . These benefits are expected to be greater for EMs and ODEs as they are intrinsically subject to higher volatility because their production structures are less diversified than those of advanced economies. Recent research suggests that EMs and ODEs can indeed reap large benefits from international risk-sharing arrangements (Prasad et al., 2003).

B. Empirical Evidence

We organize our review of the empirical literature in parallel with our survey of the theoretical literature.

Business Cycle Synchronization

9. Impact of integration. Recent empirical studies are in general unable to provide a concrete explanation for the impact of stronger global linkages on the co-movement of business cycles. Some of these empirical studies employ cross-country or cross-region panel regressions to assess the role of global linkages on the co-movement properties of business cycles in advanced countries (Kose and Yi, 2006). While Imbs (2004) finds that the extent of financial linkages, sectoral similarity, and the volume of intra-industry trade all have a positive impact on business cycle correlations, Baxter and Kouparitsas (2005) document that international trade is the most important transmission channel for business cycle fluctuations. The results of Kose, Prasad, and Terrones (2003b) suggest that both trade and financial linkages have a positive impact on cross-country output and consumption correlations.

10. Diverse conclusions. Empirical studies do not provide a definite answer on how co-movement varies in response to changes in the volume of trade and financial flows. Findings on the temporal evolution of business cycle synchronization in response to increases in financial integration are diverse. Differences in country coverage, sample periods, aggregation methods used to create country groups, and econometric methods employed seem to contribute to these varying conclusions. Some studies find evidence of declining output correlations among advanced economies over the last three decades (Heathcote and Perri, 2004; Stock and Watson, 2003).

11. Stronger links. However, other studies document that business cycle linkages have become stronger over time. Kose, Otrok, and Whiteman (2008), employing a Bayesian dynamic factor model, find that for advanced countries business cycle correlations on average have risen since 1960. Using a longer sample of annual data (1880-2008), Bordo and Helbling (2011) also document that the degree of synchronization among advanced countries has increased over time. The evidence for a European business cycle and increasing business cycle co-movement in the EU area has also been mixed. For instance, Artis, Krolzig, and Toro (2004) find evidence of a European business cycle while Canova, Ciccarelli, and Ortega (2007) argue that, since the 1990s, there is no evidence of a specific European cycle (Hirata, Kose, and Otrok, 2011).

12. AMs and EMs. There has been a recent debate about the temporal evolution of the degree of synchronization of business cycles in advanced economies and emerging market countries. This debate focuses on the ability of EMs, especially emerging countries in the Asia-Pacific region, to decouple from a potential slowdown in the United States (Helbling et al., 2007; Kose and Prasad, 2010). Although there are many studies analyzing the decoupling potential of emerging economies using various methodologies, their results have not been conclusive so far.

13. The case against decoupling. Some studies employ simple correlations to make a case against the decoupling potential of emerging markets. For example, Flood and Rose (2009) use GDP data for 64 countries over the period 1974-2007. After de-trending these series using various filters, they analyze rolling-window correlations across advanced countries and developing economies and conclude that, while the average level of cross-correlations changes over time, there is no strong evidence that these correlations have become statistically significantly lower in the later parts of their sample. In a related study, Walti (2009) reports that the extent of co-movement of cycles across advanced countries and EMs has not changed much since the early 1980s.

14. The case for decoupling. Other studies provide evidence supporting the possibility of decoupling of business cycles in emerging markets from those in advanced countries. For example, Kose, Otrok, and Prasad (2012) examine the sources of macroeconomic fluctuations in the advanced and emerging market countries using dynamic factor models and the series of output, consumption, and investment for the 1960-2008 period. Their findings indicate that there has been a substantial convergence of business cycles among advanced economies and among emerging markets over time, but there has also been a concomitant divergence of business cycles between these two groups of countries. Mumtaz, Simonelli, and Surico (2011) also employ a dynamic factor model and report findings confirming the decoupling of business cycles using data for a group of 36 countries over a 75-year period. Other studies also provide support for the decoupling hypothesis (Dooley and Hutchison, 2009; Rossi, 2009; Fidrmuc and Korhonen, 2010).

Volatility of Output and Consumption

15. No systematic empirical relationship. Existing evidence, using a variety of regression models with different country samples and time periods, reports no systematic empirical relationship between the intensity of trade and financial linkages and output volatility. Some studies report that the ratio of consumption growth volatility to income growth volatility actually increased during the recent period of globalization for emerging market economies (Kose, Prasad, and Terrones, 2003b). Importantly, they find that the volatility of consumption rose (perhaps because of crises experienced by some of these economies) by more than income volatility did. This result runs counter to the theoretical prediction that financial integration allows countries to share income risk and smooth consumption. These authors also report that increasing financial integration is associated with rising relative volatility of consumption, albeit only up to a threshold. Beyond a certain level of financial integration, an increase in integration actually reduces the relative volatility of consumption.

16. Ambiguous evidence. Other studies, such as Bekaert, Harvey, and Lundblad (2006), find that, following equity market liberalizations, there is an outright decline in consumption volatility. Using both micro and macro datasets, Kalemli-Ozcan, Sorenson, and Volosovych (2010) examine the links between “deep” financial integration, a concept based on the idea of foreign ownership, and

business cycle volatility. They report that there is a positive association between foreign ownership and the volatility of a firm’s various outcomes, a result that extends to aggregate data as well. Differences across these studies could arise from variations in the definitions of financial integration, the measures of consumption volatility, data samples, and methodologies. Nevertheless, the evidence so far is ambiguous.

17. EMs. Why have financial flows been associated with an increase in the relative volatility of consumption in emerging market economies? One explanation is that positive productivity and output growth shocks in these countries led to consumption booms that were willingly financed by international investors. These consumption booms were accentuated by the domestic financial liberalization that many of these countries undertook at the same time that they opened up to international financial flows, thereby loosening financing constraints at both the individual and national levels. When negative shocks hit these economies, however, they rapidly lost access to international financial markets, depressing consumption. Consistent with this, a growing literature suggests that the procyclical nature of capital flows explains the adverse impact of international financial integration on consumption volatility in these economies. One manifestation of this procyclicality is the phenomenon of “sudden stops” of capital inflows (Calvo and Reinhart, 1999).

Consumption and Income Risk-Sharing

18. International consumption risk sharing. There is a rich empirical literature directly studying various dimensions of international consumption risk sharing, also in response to changes in financial integration. This literature may be divided into three categories.

• The first category includes studies focusing on the patterns of international correlations to determine the degree of consumption risk sharing (Kose, Prasad, and Terrones, 2003a, 2009; Ambler, Cardia, and Zimmermann, 2004). The results of these studies indicate that the theoretical predictions regarding perfect risk sharing do not have much empirical support for three reasons (Backus, Kehoe, and Kydland, 1992). First, empirical studies indicate that the correlations between the consumption paths of various countries are relatively low. Second, consumption correlations are lower than those of output. Third, correlations between consumption and domestic output are generally higher than those between consumption and world output.

• The second category tests more formally the hypothesis of perfect risk sharing with the help of regression models. In addition to the basic stylized facts reviewed above, researchers have employed more rigorous methods to test the risk sharing implications of models with financial integration. These tests generally use some versions of reduced form solutions (or first order conditions) of models and focus on the links between various measures of domestic consumption and world consumption (Cochrane, 1991; and Mace, 1991). For example, Lewis (1996) finds that the hypothesis of risk sharing is rejected for countries with few or limited capital controls. Relative to these countries, the correlations between domestic consumption and output are higher for countries with more restrictions, which suggests less risk sharing by countries in the latter group.

• The third category of studies employs various regression models to measure the extent of risk-sharing and the impact of financial flows on the degree of risk sharing. For example, Sorenson, Yosha, Wu, and Zhu (2007) analyze the relationship between home bias and international risk sharing. They document that the extent of international risk sharing has risen during the late 1990s, while home bias in debt and equity holdings has declined in advanced countries.

19. Modest degree of international risk sharing. However, Kose, Prasad, and Terrones (2009), using a variety of empirical techniques, conclude that there is at best a modest degree of international risk sharing, and certainly nowhere near the levels predicted by theory. In addition, only advanced countries have attained better risk sharing outcomes during the recent period of globalization, with developing countries, by and large, shut out of this benefit. Even EMs, which have witnessed large increases in cross-border capital flows, have seen little change in their ability to share risk (Giannone and Reichlin, 2006; Moser, Pointner, and Scharler, 2004). The composition of flows appears to be an important factor behind the modest degree of risk sharing in EMs, as portfolio debt—the dominant form of capital inflows to these economies—does not seem to be conducive to risk sharing.

20. Inconclusive findings. Although the implications of financial integration for business cycle volatility and co-movement have substantial implications for stability and welfare, the existing theoretical studies and empirical evidence are thus far inconclusive on this issue. In particular, financial integration does not always reduce the amplitude of business and financial cycles, and may actually increase it. While risk-sharing benefits of integration are apparent in theory, it is hard to find conclusive empirical evidence in support of these benefits. Why is it so difficult to obtain sharp results about the implications of financial integration for volatility and co-movement? One potential reason could be the changes in the nature of shocks as cross-border linkages become more intensive, which we discuss next.

C. Changing Nature of Shocks and Linkages

21. Integration and shocks. Increased integration could also affect the dynamics of co-movement by changing the nature and frequency of shocks.

• First, stronger trade and financial linkages may necessitate and lead to a higher degree of policy coordination which, in turn, raises the correlations between shocks associated with nation-specific fiscal and/or monetary policies. This could have a positive impact on the degree of business cycle synchronization (Darvas, Rose, and Szapary, 2005; Flood and Rose, 2009).

• Second, shocks pertaining to changes in productivity could become more correlated, if rising trade and financial integration leads to an increase in knowledge and productivity spillovers across countries (Kose, Prasad, and Terrones, 2009). More financially integrated economies are able to attract relatively large foreign direct investment flows, which have the potential to generate productivity spillovers.

• Third, increased financial integration and developments in communication technologies lead to faster dissemination of news shocks in financial markets. This could have a positive impact on the degree of business cycle synchronization if, for example, good news about the future of the domestic economy would increase domestic consumption through its impact on wealth, and if consumers in other countries, who hold stocks in the domestic country, raise demand for goods in their countries.

A. Introduction

1. An economic, not geographic, map. This note utilizes multidimensional scaling to construct a business cycle synchronicity map. A business cycle synchronicity map is a visual representation of real GDP growth correlations among a group of countries. Countries whose business cycles are more correlated (synchronous) will be located closer to each other on the map and less correlated countries will be located further away. Thus, economic relations, rather than geographic distance, determine countries’ proximity to each other.

2. Advantages. The non-metric multidimensional scaling (MDS) is an example of an ordination technique, a class of statistical methods designed to order objects such that similar objects are ordered closer to each other. Other examples of ordination techniques include principal components analysis and correspondence analysis. Some previous examples of the use of MDS include Mar-Molinero and Serrano-Cinca (2001) to model bank failure, and, most relevant for the purposes of this note, Camacho et al. (2006) to study the existence of the European business cycle. One advantage of the MDS methodology is that it requires limited assumptions on the underlying data, which makes the analysis reasonably robust to alternative assumptions. The method aims to provide a visualization for a set of high-dimensional data by giving each data point a location in a two or three-dimensional map.

B. Methodology

3. Growth correlations. We use the correlation of annual GDP growth rates as a measure of synchronicity of business cycles. The MDS algorithm begins by constructing an N by N distance matrix, where N is the number of countries in the analysis. To obtain a global picture, the analysis here focuses on two country groups: the largest 100 and 140 economies (see Figures 1 and 2). This matrix contains dissimilarity measures, i.e., measures of how dissimilar are the business cycles between two countries. We define the dissimilarity measure as one minus the correlation coefficient of two series of real GDP growth, over the sample period 1995-2010.²

4. Projecting to 2-D. The MDS algorithm optimally reduces the N-by-N synchronicity matrix into an N-by-2 matrix of coordinates such that the relative distances between them most accurately represent the relative synchronicity of business cycles. We choose a two-dimensional representation because it is easiest to interpret visually. Starting from an initial (possibly random) arrangement of the countries, the algorithm then regresses the actual dissimilarities on the distances in the two-dimensional map and minimizes the sum of squared differences between dissimilarities and the distances predicted by the regression (known as stress). The ideal solution would yield a regression with a perfect fit that is a two-dimensional map, which accurately represents the distances of the original matrix of dissimilarities. In practice, the ideal solution is not obtainable, but one can characterize the goodness of the approximation using the stress number. The MDS algorithm can be easily implemented using Matlab’s Statistics Toolbox or other statistical software.

C. Results and Policy Implications

5. Clusters of correlated economies. Global business cycle synchronicity maps reveal interesting intra and inter-regional clusters. Figures 1 and 2 show, respectively, business cycle synchronicity maps for the 100 and 140 largest economies. The results are also robust to an alternative method of representing dissimilarities between countries known as t-Distributed Stochastic Neighbor Embedding. A few interesting observations arise from the analysis:

• Advanced economies. The core advanced economies (AE), EU countries, the U.S., the U.K., and Canada, form a tight cluster. While Ireland and Portugal are situated close to the advanced economy core, Greece is further away from its euro area neighbors than some non-euro area countries. This illustrates the persistently asynchronous business cycles among certain euro area members despite common exchange rate and monetary policy. Such tensions between policy actions and macroeconomic fundamentals as shown for the case of Greece could serve as useful warning signal in Fund surveillance.

  

  

  Synchronized Output Map: Advanced Economies

  (Multidimensional scaling of GDP growth correlations, 1995-2010)

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  Synchronized Output Map: Advanced Economies

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  Synchronized Output Map: Advanced Economies

  (Multidimensional scaling of GDP growth correlations, 1995-2010)

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• East Asia. Separately, East Asian supply chain countries (Hong Kong SAR, Philippines, Malaysia, Taiwan, Province of China, Korea, Singapore, Vietnam, and Japan) are situated between China and the AE core, but they themselves do not form a tight cluster like the AE core. This illustrates that surveillance needs to take into account a variety of countries as possible sources of growth shocks, while at the same time convergence among Asian emerging markets is not nearly as significant as among the advanced economies.

• Latin American EMs. It is notable that most of the large Latin American EMs (except Mexico) are situated closer to the Asian EM cluster than to the AE core. This possibly reflects increased importance of commodity trade with China, the precise composition and extent of which may merit further exploration. It also sheds light on the stylized facts on AE and EM business cycle synchronicity as outlined in Note I. While AE business cycle synchronization has been close, EMs’ cycles have been somewhat less synchronized than AEs, although more synchronized with each other. This could be for a variety of factors, as discussed in Note I.

  

  

  Synchronized Output Map: Emerging Markets

  (Multidimensional scaling of GDP growth correlations, 1995-2010)

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  Synchronized Output Map: Emerging Markets

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  Synchronized Output Map: Emerging Markets

  (Multidimensional scaling of GDP growth correlations, 1995-2010)

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• Commodity exporters. For the oil producers, there is some weak clustering around Saudi Arabia. However, the majority of oil producers are fairly scattered around the AE and Asian/Latin American cluster. This highlights two interesting observations. First, while most of the oil producing countries face similar terms of trade shocks and have a common exchange rate policy that is pegged to the U.S. dollar, the map illustrates their business cycles are not that similar, suggesting another instance of tension between policy and fundamentals to be further explored in surveillance. Second, we also see that most of the oil producers are situated closer to the large Asian EMs (China and India) than the AE core, suggesting the former’s increasing importance as a source of demand.

  

  

  Synchronized Output Map: Oil Producers

  (Multidimensional scaling of GDP growth correlations, 1995-2010)

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  Synchronized Output Map: Oil Producers

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  Synchronized Output Map: Oil Producers

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• Low income countries (LICs). Finally, there is no observable clustering among LICs, which reflects the importance of idiosyncratic shocks (political cycle and weather pattern, etc.) to these countries business cycles.

D. An Application to Common Currency Areas

6. Euro Area. Since euro adoption, business cycles within the Euro Area (EA) have become largely synchronized, around a core comprising Germany, France, Italy, and some northern European countries (see Figure 3, upper panels). However, peripheral countries such as Greece, Ireland, Portugal, and Spain have remained located well outside that EA core in terms of business cycle synchronicity and unit labor cost convergence. Recent entrants into the European Union have also moved closer to the Euro Area, reflecting increased trading ties.

• Structural fissures through the EA core. Despite largely convergent macroeconomic policies, close trade and financial links, structural fissures run right through the EA core. On some measures, such as unit labor costs, France and Italy are far removed from Germany (see Figure 3, lower LHS panel). On current account balances, Germany forms one group with Austria and the Netherlands, while Belgium, Italy, and France join Greece, Ireland, Portugal, and Spain to form another (see Figure 3, lower RHS panel). The split in current account dynamics reflects the divergence in the countries’ national saving-investment balance and this reveals deeper structural differences among core EA countries.

7. West and Central African Monetary Union. The synchronicity map of West and Central African Monetary Union (which also have a fixed exchange rate between each other) shows that West African Monetary Union is slightly more homogeneous (see Figure 4). Note that the map is centered on the World real GDP series to analyze not only how close the countries are relative to each other, but also how they relate to the world business cycle. It is notable how the Central African Monetary Union splits up into two sub-clusters which are relatively distant from each other. Such patterns may merit further exploration in surveillance activities, as they call attention to possibly divergent macroeconomic outcomes against the backdrop of a common exchange rate policy.

8. Eastern Caribbean Union. The synchronicity map for Eastern Caribbean Union shows that the correlations between the member countries have increased considerably in the last 5 years, presumably due to the economic crisis (see Figure 5). In the earlier map in particular, there again seem to be two sub-clusters rather than one. Surveillance can further delve into the implications of such patterns, including the roles of natural disasters, fiscal space, and differences in income.

Map of Business Cycle Synchronicity Using Multi-Dimensional Scaling (MDS) (1995-2010) ^1/

(Red dots denote G20 countries)

Citation: Policy Papers 2012, 016; 10.5089/9781498340823.007.A001

^1/ Countries that are located closer together on the map have a higher degree of synchronization. Some country names have been shortened to improve readability of the chart.

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Map of Business Cycle Synchronicity Using Multi-Dimensional Scaling (MDS) (1995-2010) ^1/

(Red dots denote G20 countries)

Citation: Policy Papers 2012, 016; 10.5089/9781498340823.007.A001

^1/ Countries that are located closer together on the map have a higher degree of synchronization. Some country names have been shortened to improve readability of the chart.

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Map of Business Cycle Synchronicity Using Multi-Dimensional Scaling (MDS) (1995-2010) ^1/

(Red dots denote G20 countries)

Citation: Policy Papers 2012, 016; 10.5089/9781498340823.007.A001

^1/ Countries that are located closer together on the map have a higher degree of synchronization. Some country names have been shortened to improve readability of the chart.

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Map of Business Cycle Synchronicity Using MDS for 140 Countries (1995-2010) ^1/

(Red dots denote G20 countries)

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^1/ Countries that are located closer together on the map have a higher degree of synchronization.

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Map of Business Cycle Synchronicity Using MDS for 140 Countries (1995-2010) ^1/

(Red dots denote G20 countries)

Citation: Policy Papers 2012, 016; 10.5089/9781498340823.007.A001

^1/ Countries that are located closer together on the map have a higher degree of synchronization.

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Map of Business Cycle Synchronicity Using MDS for 140 Countries (1995-2010) ^1/

(Red dots denote G20 countries)

Citation: Policy Papers 2012, 016; 10.5089/9781498340823.007.A001

^1/ Countries that are located closer together on the map have a higher degree of synchronization.

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European Business Cycles Synchronization and Macro-imbalances

Since the adoption of the Euro, European business cycles have moved closer centered around Germany, while peripheralcountries remained outside the EA core.

Citation: Policy Papers 2012, 016; 10.5089/9781498340823.007.A001

Source: WEO and Staff calculations.1/ The synchronization maps are computed based on the MDS method, where countries that are located closer together on the map have a higher degree of synchronization.

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European Business Cycles Synchronization and Macro-imbalances

Since the adoption of the Euro, European business cycles have moved closer centered around Germany, while peripheralcountries remained outside the EA core.

Citation: Policy Papers 2012, 016; 10.5089/9781498340823.007.A001

Source: WEO and Staff calculations.1/ The synchronization maps are computed based on the MDS method, where countries that are located closer together on the map have a higher degree of synchronization.

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European Business Cycles Synchronization and Macro-imbalances

Since the adoption of the Euro, European business cycles have moved closer centered around Germany, while peripheralcountries remained outside the EA core.

Citation: Policy Papers 2012, 016; 10.5089/9781498340823.007.A001

Source: WEO and Staff calculations.1/ The synchronization maps are computed based on the MDS method, where countries that are located closer together on the map have a higher degree of synchronization.

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West (blue) and Central African Monetary (red) Union

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West (blue) and Central African Monetary (red) Union

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West (blue) and Central African Monetary (red) Union

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Eastern Carribbean Currency Union

Citation: Policy Papers 2012, 016; 10.5089/9781498340823.007.A001

Sources: WEO; and Fund staff calculations.

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Eastern Carribbean Currency Union

Citation: Policy Papers 2012, 016; 10.5089/9781498340823.007.A001

Sources: WEO; and Fund staff calculations.

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Eastern Carribbean Currency Union

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Sources: WEO; and Fund staff calculations.

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A. Motivation

1. A systemic perspective. Analyzing the cross-border propagation of shocks and of the systemic impact of policies is complex. While bilateral trade and financial connections are comprehensible, formally analyzing the chain of relations—direct and indirect—across a large number of countries is virtually intractable. There is a dimensionality problem related to the density of country-to-country relationships (across sectors, types of goods, and assets, etc.). Production chains and financial markets are deeply intertwined; as such, aggregation without double counting, or inappropriately specifying traditional models so as to avoid over or under estimation becomes daunting. Hence, traditional models have tended to simplify by studying the problem from the lens of a single country unit against the rest of the world or an aggregated basket of partners. They have rarely focused on understanding the structure of the flows between countries as a whole, the role of particular countries or flows in amplifying or dampening shocks, and most importantly how policies in certain countries can propagate and become systemic.

2. Framework. Network analysis, or graph theory—in particular centrality and cluster analysis—provides a theoretic framework which can help shed light on the complexity arising when trade and financial flows are viewed in the context of an aggregate network. Graph theory allows us to construct and analyze networks where any number of vertices are joined by edges. The edges between any two vertices can be directed (i.e., explicitly denoting a flow from one vertex to another) or weighted (i.e., reflecting some value relative to other edges). Taking trade and financial flows as networks, each country is a vertex (v), and the flow of any type of goods, service, or financial contract from one country to another constitutes an edge (e) which can be treated as either directed or weighted. Moreover, graph theory allows us to construct and analyze multigraphs, i.e. where more than one edge joins the same two vertices (multiple trade and financial links).

3. Structure of the note. The remainder of this note is organized as follows. Section B below briefly explains how we have built a network of aggregated trade and financial flows. Section C then develops the first steps in understanding the structure of the network, and shows the need for cluster analysis. Section D further develops the concept of clusters and explains the importance of appropriately choosing the identification technique, as well as our chosen methodology. Section E presents the results and explains the implications of a cluster analysis driven understanding of the aggregated trade and financial flows network. Section F presents some potential applications of cluster analysis to Fund surveillance.

B. A Network of Global Trade and Financial Flows

Building Blocks and Graph Construction

4. Data. We begin by constructing a series of n × n matrices (A) each respectively containing bilateral relationships for aggregate trade flows, consolidated and locational cross-border banking exposures (as collected by the Bank for International Settlements), as well as cross-border portfolio and direct investment exposures (from the Fund’s Coordinated Portfolio Investment Survey and Coordinated Direct Investment Survey, respectively). All data are taken at end-2009. The i and j entries in each respective A matrix reflect the raw values corresponding to the bilateral interaction between every two countries. In the case of trade, A contains the sum of exports and imports recorded bilaterally (hence A_ij = A_ji), while elsewhere the values reflect the gross claims of one country on another (hence A_ij ≠ A_ji). A contains 0 values on the diagonal (as internal trade and financial flows are not considered in our analysis).

5. Transforming the data. The entries of each A matrix are subsequently transformed into (wj) which represents the weight of the trade or financial flow between i and j in all flows out of i to the rest of the world. In cases where wij ≠ wji and neither one is zero, the weights are averaged to take the relative importance of the link for both countries. The upper triangular part of each matrix is taken to reflect the weighted edges between each two countries. The respectively weighted A matrices are then concatenated into a two dimensional array, wherein each entry represents the non-zero elements of the weighted A matrices. Finally, as the concatenated array will contain multiple edges between most country pairings, we coalesce the repeated edges by taking their geometric average. This results in a structure G = (V,E) where G is a connected and weighted graph consisting of a vertex (country) set V={d_{1, ...,} d_V}, and an edge set E ⊂ V × V (representing the weight of aggregated flows between countries) such that each edge {i,j} corresponds to a set of two adjacent vertices d₁, d₂ in V, and a wij.

The Structure of an Aggregated Trade and Financial Flows Graph

6. A dense center. As expected, the network representing trade and financial flows displays a high density of interactions. However, the distribution of edges between vertices does not seem to be uniform across the entire network. In particular, there seem to be a very dense set of relationships occurring at the center of the network, which peter-out as we travel toward the periphery. Moreover, there are some peripheral vertices which are linked to other peripheral vertices directly (see Figure 1 below).

Global Trade and Financial Flows Graph

Citation: Policy Papers 2012, 016; 10.5089/9781498340823.007.A001

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Global Trade and Financial Flows Graph

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Global Trade and Financial Flows Graph

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7. Architecture and function. Global trade and financial relationships are in large part associated with economic activity undertaken between, and through, countries at the “core” (red vertices in Figure 1). Moreover, this suggests that economic and financial conditions in the core are likely to have material impact on the remainder of the network. However, the variation in density and the seemingly different functional role of some vertices vis-à-vis others suggests that a level of complexity exists within this graph system which would need to be further understood. Our concern then becomes how to systematically deconstruct the graph system in such a way that—irrespective of its complexity—we are able to further understand the underlying structure and functional characteristics of its building blocks (i.e., the vertices and how they are inter-related). Toward that end, we explore below various techniques and metrics.

C. Quantifying and Rank-Ordering Centrality

8. “Core” and “periphery”. Understanding which vertices belong at the core of the graph and which are peripheral is a necessary first step. Further, uncovering the correct order of the most important vertices for the graph as a whole vis-à-vis other important vertices, is also crucial. Together, these two pieces of information will later allow us to understand how the dynamics of the complex relationships unfold from the core outward, and more importantly from one peripheral part of the graph—via the core—to another.

9. Centrality measures. A methodologically robust way of quantifying the relative importance of vertices in the graph is to calculate a series of centrality measures as detailed below:

• Degree centrality: quantifies the number of connections any given vertex has to all others in the network. A vertex degree can be computed respectively as the sum of: incoming links (in degree); outgoing links (out degree); or all links (degree).

• Closeness centrality: measures the mean of the shortest path in terms of the number of paths, between one vertex and all others.

• Random walk betweenness centrality quantifies the importance of each vertex in relaying flows amongst all others. This can be approximated by the expected number of times that a random walk (or trade or financial flows) between any starting and ending vertex will pass through an intermediate set of vertices averaged over all starting and ending vertices.

• Eigenvector centrality: defines both the number and the quality of the connections any given vertex has within the network. Vertices with a large number of connections with lower connection weights may receive a lower eigenvector centrality value relative to points with fewer connections but with higher connection weights.

10. Most central economies. Based on the combination of these centrality measures, and for the available date used, we have identified the economies that display the highest centrality (higher than the 90th percentile for each measure). As evident in Table 1, the core of the trade and financial flows graph consists of 22 economies. In rank order of centrality, three distinct tiers appear at the core; the first two are dominated by Euro Area economies as well as Canada, China, Japan, Korea, Switzerland, the United Kingdom, and the United States. The final tier is largely made up of EMs along with Australia, Denmark, and Sweden.

Table 1.

Most Central Economies in Trade and Financial Flows

Table 1.

Most Central Economies in Trade and Financial Flows

Tier 1	Tier 2	Tier 3
China	Austria	Australia
France	Belgium	Denmark
Germany	Canada	India
Italy	Korea	Mexico
Japan	Netherlands	South Africa
United Kingdom	Spain	Sweden
United States	Switzerland	Taiwan, Province of China
		Thailand

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Table 1.

Most Central Economies in Trade and Financial Flows

Tier 1	Tier 2	Tier 3
China	Austria	Australia
France	Belgium	Denmark
Germany	Canada	India
Italy	Korea	Mexico
Japan	Netherlands	South Africa
United Kingdom	Spain	Sweden
United States	Switzerland	Taiwan, Province of China
		Thailand

11. Unpacking the system. What does centrality tell us that we do not already know? Understanding the core of the trade and financial flows graph, and how it is structured (i.e., who is at the core and in what ranking), confirms some existing priors, while revealing new results. Most importantly, it prompts us to address further issues concerning the complexity of the entire graph system. Revisiting Figure 1 above, along with the high centrality and core-tiering of specific economies, we can posit that the presence of some of these economies at the core reflects their high level of interaction in particular dimensions (trade, financial, or both) of the data we use. For instance:

• The presence of China along with several of its key trading partners at the core is indicative of its role in the Asian—and global—supply chains.

• The presence of key global financial intermediation centers reflects the importance of countries such as the United Kingdom, United States, and Switzerland in global financial flows, portfolio allocation, and management.

• Similarly, the presence of key EMs confirms the well known prior that, as such economies continue developing, they are becoming regional magnets for financial and trade flows.

• Overall, the core of the trade and financial flows graph in large part reflects many of the constituent economies in the Group of Twenty (G20).

12. Some surprises. Our measures of centrality also contain somewhat surprising results. Taking membership in the G20 as a representation of existing priors on identifying industrialized and developing countries that play the most systemically important role, we see that Argentina, Brazil, Indonesia, Saudi Arabia, Russia, and Turkey are absent, while Denmark, Sweden, Switzerland, Taiwan Province of China, and Thailand are part of the core. How can we explain the absence of oil exporting or significant emerging market economies from the core, while others (sufficiently proxied by other countries such as Austria-Germany and Belgium-France) appear? In addressing this, we are forced to seek a more nuanced understanding of the structural and functional properties of the trade and financial flows graph system. One meaningful way of doing this is via uncovering its underlying community (cluster) organization and the role of specific vertices within it.

D. From Networks (Graph) to Clusters

Cluster analysis lends itself to systematically uncovering and interpreting the natural organization of the vertices (countries) represented in any graph. In our case, we are concerned with how to understand country groupings—whether in the core or periphery—and in particular which countries form cohesive communities.

The Appropriate Cluster-Identification Methodology

13. Away from non-overlapping clusters. Cluster identification is essentially a problem of finding an unknown number of cohesive groups that are the underlying building blocks of a broader graph system. This can be done by imposing constraints on a maximizing problem; however, such constraints risk producing results that ignore the very complexity we are seeking to understand. Most cluster identification methods rely on partitioning algorithms which identify separable non-overlapping, non-nested communities as shown in Figure 2 below. While such algorithms successfully underscore the cohesive or hierarchical nature of some sets of links between groups of vertices, the less dense regions of links between groups become irrelevant. Adjacency between groups is not a trivial feature in trade and financial flows. As will be explained in detail in subsequent sections, adjacency between clusters can be utilized to define overlaps in clustering.

Architecture of Separable, Non-Overlapping Communities

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Architecture of Separable, Non-Overlapping Communities

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14. Toward overlapping clusters. While the tractability and efficiency of traditional partitioning algorithms are attractive, they are subject to some constraints on the number, size, or shape of the clusters to be identified. For example, such methods necessitate defining ex-ante the number of clusters into which the graph should be partitioned. In effect, the choice of the number of clusters to identify will have a non-trivial effect on the results; e.g., China would only be associated with the Asian supply chain economies and not with the United States, Germany would be associated only with large Euro Area economies and not with other EU economies. Hence, multiple valid solutions may be expected. As such, they are significantly limiting for our purposes of further understanding the underlying complexity of the graph system. Also, the partitioning usually focuses on cutting the graph system into clusters while minimizing the cost of edge elimination, thus, any single vertex can only belong to one cluster. This ignores the implications of overlapping or nested communities, and dilutes the potential for a richer understanding of the particular vertices which facilitate such overlaps and, therefore, of the set of interactions across economies.

Cluster Identification with Minimal Constraints

15. Clique percolation method. A recently developed cluster identification algorithm called the Clique Percolation Method (CPM) provides a feasible way of identifying clusters without imposing the constraints mentioned previously. In other words, it allows us to identify an unknown number of potentially overlapping clusters (i.e., cohesive country groups) with varied membership size. Utilizing CPM, we model the interaction amongst countries using global trade and financial flows to map out potential shock transmission paths between countries. Country groups which share very dense connections (based on trade, BIS, and portfolio flow data) are considered “clustered.” Clusters share overlap regions which are facilitated by a specific country or group of countries’ membership in multiple clusters. Membership in multiple clusters may allow countries to act as unique links through which the effects of economic or financial conditions may be transmitted from one cluster to another. Owing to their capacity to act as transmitters (and potentially amplifiers or mitigators) of shocks, countries comprising the cluster overlap regions are categorized as “gatekeepers.” The theoretical underpinnings of CPM are detailed in Annex 1. ^{Box 1} provides a step-by-step demonstration of how clusters are identified.

16. Richer network architecture. A much richer differentiation among groups of countries emerges in Figure 3 relative to the earlier presentation. In the first instance, CPM clearly yields 11 distinct clusters of varying sizes. The graph is also now separable into two clearly identifiable core regions, one surrounding the United States and China, and one surrounding Italy and Germany. Moreover, we can also identify a group of countries such as France, The Netherlands, and the United Kingdom which seem to sit in between both core regions. The next section elaborates on key implications of cluster-based analysis and concepts.

Preliminary Clustering based on Clique Percolation Method

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Preliminary Clustering based on Clique Percolation Method

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E. Cluster Analysis Results and Implications

Some economies serve as gatekeepers—linking different clusters and therefore transmitting (passing through, amplifying, or dampening) shocks. Groups of economies can together also play a gatekeeper role. The method allows for distinguishing individual gatekeepers and clusters of gatekeepers.

Gatekeeper Countries Versus Gatekeeper Clusters

17. Cluster-to-cluster relationships. CPM allows us to further understand cluster-to-cluster relationships. There is a threshold parameter, k, for defining cluster size (see Annex 1). For values of k between 5 and 8 which have been previously identified as the critical percolation region, a single cluster arises at the 8-clique level, which includes Australia, China, Indonesia, Japan, Malaysia, Singapore, Thailand, and the United States. We also identify three clusters at the 7-clique level, two of which are overlapping, while one stands separated.

18. Gatekeeper economies. Combining the clusters resulting from the 7 and 8 clique levels produces an interesting initial result. As evident in Figure 4, European economies appear clustered together, along with Tunisia and Algeria. The inclusion of Tunisia and Algeria in this cluster is on account of trade relations and remittances, while, China, Japan, Korea, and the United States act as gatekeeper countries linking key Middle Eastern economies and Pakistan to Asia. Also, on account of being members of adjacent clusters Korea, India, and Brunei are also clustered together despite having no connecting edges. In many respects, these are non-trivial results as they explicate clearly both the importance of relationship dynamics within developing Asian economies, as well as the role of their gatekeepers in linking them to oil exporters. Moreover, the analysis presents a unique result for the gatekeepers pertaining to Hong Kong SAR (see group K in Table 1 of main paper). Traditionally, Hong Kong SAR is viewed as a financial hub which is responsible for intermediating Asian savings. The results of our analysis contextualize further and add granularity by explicating the idea that the dynamic amongst the Asian economies (which are subject by varying degrees to capital flow restrictions) and the United States may potentially be the driving factor behind the role of Hong Kong (i.e., the gatekeepers’ real economic context drives the role of the equity financing hub).

Country Level View of First Clusters

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Country Level View of First Clusters

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Country Level View of First Clusters

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19. Gatekeeper clusters. There is also a clear internal organizational structure between clusters themselves (see Figure 5). Looking at the maximal overlap between clusters which takes place at the 6-clique level followed by the 5-clique level, we respectively identify 12 and 8 overlapping clusters containing 72 and 133 countries. The number of countries which are members in each cluster varies. For example at the 5-clique level, we see that cluster 1 is a giant cluster containing 117 countries. Moreover, we also see that the clusters are not only clustered into different yet overlapping groups. At first glance, the overlap between clusters appears to involve particular clusters (red circles). This suggests that the clusters situated in overlap region are gatekeeper clusters.

Structure of Clusters

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Structure of Clusters

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Structure of Clusters

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