metadata: authors: 0: author: Gould,David Michael
1: author: Kenett,Dror Yossef
2: author: Panterov,Georgi Lyudmilov
count: Europe,Central Asia
docna: 0: docna: Multidimensional connectivity : benefits,
            risks, and policy implications for Europe and Central Asia
docty: Policy Research Working Paper
subtopic: International Trade and Trade Rules,Economic Growth,Industrial Economics,Economic Theory & Research,Transport Services,Inflation,Marketing,Private Sector Economics,Private Sector Development Law
teratopic: Macroeconomics and Economic Growth,Law and Development,Private Sector Development,Industry,International Economics and Trade,Transport
abstracts: cdata!: International connections through trade,
            foreign direct investment, migration, the Internet, and
            other channels are critical for the transmission of
            knowledge and growth and form macroeconomic linkages. But
            how much knowledge is transmitted to a country is not only
            the result of the overall level of connectivity, but also to
            whom a country is connected, as well as how these
            connections complement each other. For example, being
            well-connected to an economy with wide-reaching global
            connections is likely to be a stronger conduit for knowledge
            transfers than being connected to an isolated economy.
            Likewise, connections are likely to complement each other.
            For example, ecommerce is often seen as a benefit of
            Internet connectivity, but without transport connectivity,
            ecommerce may not amount to much. This wider definition of
            connectivity, referred to as multidimensional connectivity,
            is broadened and explored in this study as it applies to
            Europe and Central Asia. Focusing on countries from the
            Europe and Central Asia region, the paper shows that
            multidimensional connectivity is an economically and
            statistically important determinant of future economic
            growth. The paper further discusses the potential risks and
            transfer of shocks that can result from cross-country
            economic connectivity. Furthermore, it provides some
            examples of how policy tools can be designed to leverage the
            benefits of connectivity channels and mitigate their risks.
repnme: repnme: Multidimensional connectivity : benefits,
            risks, and policy implications for Europe and Central Asia
display_title: Multidimensional connectivity :
            benefits, risks, and policy implications for Europe and
            Central Asia
listing_relative_url: /research/2018/05/29886009/multidimensional-connectivity-benefits-risks-policy-implications-europe-central-asia
topicv3: Private Sector Development m1326060 1921,Economic Growth m1326241 471,Transport m1326661 135,Inflation m1326709 0870F4727ACED1CF8525815C00471347,Trade m1326924 698
publishtoextweb_dt: 2018-05-11T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Law and Development,Private Sector Development,Industry,International Economics and Trade,Transport
no_of_pages: 41
author_keys: 0: author_key: 674224
1: author_key: 1544642
2: author_key: 1298828
model_extractions: WPS8438 Policy Research Working Paper 8438

# Multidimensional Connectivity

Benefits, Risks, and Policy Implications for Europe and Central Asia _David Gould Dror Y. Kenett Georgi Panterov_ Europe and Central Asia Region Office of the Chief Economist May 2018
Policy Research Working Paper 8438

# **Abstract**

International connections through trade, foreign direct investment, migration, the Internet, and other channels are critical for the transmission of knowledge and growth and form macroeconomic linkages. But how much knowledge is transmitted to a country is not only the result of the overall level of connectivity, but also to whom a country is connected, as well as how these connections complement each other. For example, being well-connected to an economy with wide-reaching global connections is likely to be a stronger conduit for knowledge transfers than being connected to an isolated economy. Likewise, connections are likely to complement each other. For example, ecommerce is often seen as a benefit of Internet connectivity, but without transport connectivity, ecommerce may not amount to much. This wider definition of connectivity, referred to as multidimensional connectivity, is broadened and explored in this study as it applies to Europe and Central Asia. Focusing on countries from the Europe and Central Asia region, the paper shows that multidimensional connectivity is an economically and statistically important determinant of future economic growth. The paper further discusses the potential risks and transfer of shocks that can result from cross-country economic connectivity. Furthermore, it provides some examples of how policy tools can be designed to leverage the benefits of connectivity channels and mitigate their risks.

This paper is a product of the Office of the Chief Economist, Europe and Central Asia Region. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The authors may be contacted at dgould@worldbank.org, gpanterov@worldbank.org, and dkenett@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Multidimensional Connectivity: Benefits, Risks, and Policy Implications for Europe and Central Asia<sup>1</sup>

David Gould<sup>a</sup> , Dror Y. Kenett<sup>b</sup> , Georgi Panterov<sup>c</sup>

> a World Bank, Email: dgould@worldbank.org

> b World Bank, Email: dkenett@worldbank.org

> c World Bank, Email: gpanterov@worldbank.org

Keywords: Economic growth, Economic connectivity, Trade, Globalization, Europe and Central Asia, Multilayer networks JEL: C54, F43, G15, G28, O47

> 1 Views and opinions expressed are those of the authors only and do not necessarily represent the views of the World Bank or any institution with which they are affiliated. We thank Ginestra Bianconi, Angel Bogoev, Michael Danziger, Dobrina Gogova, Shlomo Havlin, Aaditya Mattoo, Alessandro Spelta, Ananthanarayan Sainarayan, Hans Timmer, Xin Yuan, Tlek Zeinullayev for their useful comments, feedback, and support with data processing and analysis.

1
# 1. Introduction

Increased trade and financial relations together with various macroeconomic variables, such as exchange rates, interest rates, and equity prices, have resulted in increased economic linkages among countries. This has been further expedited by the growing global integration, and the cross‐border flow of trade, migration, technologies and knowledge. As such macroeconomic linkages increase, the debate has grown regarding the benefits and risks that result from such cross‐border linkages, or connectivity.

Investigating the role of connectivity across countries and across different economic activities has resulted in three main findings. First, regional connections through trade, FDI, migration, telecommunications and other channels over the past two decades have risen more rapidly than ECA’s connections outside the region, in part reflecting policies geared to increasing regional integration and the rising importance of regional value chains. However, countries in ECA that are linked to strong globally‐connected ECA countries, for example Germany or Great Britain, may nevertheless have experienced substantial increases in global connectivity as well. Among connectivity channels, ECA’s intraregional trade links are stronger than FDI links, while airline connections and labor market integration have increased sharply among European countries. Second, network connectivity measures for trade, FDI, migration, information and communication technology, airline flights and portfolio flows are all positively related to growth, and each is associated with higher growth over and above the influence of standard growth determinants. However, not all channels play an equally important role. Trade connectivity is perhaps the most important and is related to overall growth and the income growth of the bottom 40 percent of the income distribution. Increasing linkages in each form of connectivity are associated with higher growth, but at a decreasing rate, suggesting that a balanced connectivity profile along all dimensions of connectivity is more important than a large increase in one channel only. The growth impact of multidimensional connectivity is higher than the impact of each of the individual network indices, suggesting that overall connectivity is more important than each of the individual channels separately. Thus, policies to promote connectivity across trade, migration and FDI are likely more beneficial than focusing on enhancing only one channel, and reducing connectivity in one dimension may reduce the impact of growth from other channels. Third, greater international connectivity can increase a country’s exposure to international shocks, but may also mitigate shocks by enabling a country to increase its reliance on other links in its network. Both countries with low and high levels of connectivity tend to be more resilient to shocks in the global network, the first because of the limited number of partners that may become a source of shocks, the second because well‐diversified connections may provide alternative sources of, for example, finance or export demand. By contrast, countries in the “middle” of the connectivity spectrum, that is, those that are highly dependent on a few well‐connected countries, appear to be most susceptible to shocks that originate from, or affect, these countries.

Globalization often means different things to different people. For some, it is the large number of imported goods seen on store shelves. To others it is a social phenomenon that includes everyday exposure to a wide variety of cultures, peoples, foods, products, and spoken languages. In major cities throughout Europe and Central Asia (ECA) the change is perhaps most apparent, while in smaller towns or villages it may be less so. In Central Europe the look and feel of major cities is very different now than before the transition to market economies in the early 1990s. But even in the small towns in Western Europe, integration brought by the European Union and greater global connectivity has changed the look and feel of everyday life and economic opportunities. Regardless of where one is physically located, or how one observes globalization, the interconnectedness of the world is increasingly touching us either 2
directly by the people we encounter or indirectly through the items we purchase or foreign firms that employ us.

Since the early 1990s, the ECA countries have been radically transformed, as borders were opened and many hurdles impeding cross‐border connectivity were lowered. The move towards the common market in the European Union and the fall of the Iron Curtain had impacts well beyond trade – including positive impacts on income and income distribution. This trend towards income convergence with developed countries occurred despite intermittent external shocks, suggesting, in turn, that economic connectivity to regional and global markets has likely been an important driver of growth and improved standards of living. Since 2008/09, the global financial crisis, deepening geo‐political tensions, the refugee influx and sharp commodity price fluctuations have posed new challenges for the region, pointing, _inter alia_ , to the need to more fully understand the role that economic connectivity can play in preserving economic growth and incomes in times of political and economic flux.

ECA’s international economic bilateral connections with other countries and regions has expanded sharply over the past three decades, owing to greater global integration driven by lowering of costs to economic transactions, the breakup of the Soviet Union, and increasing integration within, and expansion of, the European Union. Enhanced international connectivity generally has been associated with growth, through the transmission of technologies across borders. This transmission is most effective when deep connections exist across different channels, and when countries are connected to other, well‐connected countries. This paper discusses the multidimensional character of connectivity. It assesses the impact of improved connectivity on income and income distribution, and it addresses the question of whether the region is optimally connected to other economic poles in the world.

Much of the empirical work done to date has recognized the importance of openness for economic growth, including through trade, foreign direct investment (FDI), the internet (information, communications, and technology—ICT), migration, and other forms of connectivity (Dollar, 1992, Sachs and Warner, 1995, Ben‐David, 1993, Edwards, 1998, Frankel and Romer, 1999, and Javorcik and Smarzynska, 2004, among others). While there are many nuances to the empirical findings, and questions remain regarding causality between outcomes and policies (Rodriguez and Rodrik, 2000), the association appears to be strong and intuitively appealing. Technologies embodied in goods, investments, and people are likely to be transmitted across borders, as long as the source and host countries are open and have the capacity to absorb these innovations. In other words, in addition to the gains from specialization that openness brings through each layer of connectivity, knowledge spillovers are also likely created. This leads not only to one‐time increases in output, but also, in the context of endogenous growth theory, long‐term increases in economic growth as the cost of acquiring new knowledge falls with an increasing stock of knowledge (Helpman, 2004; Romer, 1990).

To date, economic research has only examined one dimension at a time of partner connectivity and the relationship to economic growth. One main area of research has focused on macroeconomic linkages resulting from exchange rates, following the Mundell–Fleming model, which discusses how being an open‐ economy or incorporated into the global economy, means that a country has to adopt a strategic choice making behavior in handling volatilities of its macroeconomic variables especially the exchange rates (Fleming, 1962; Mundell, 1961, 1963). Furthermore, some research has focused on the link between monetary policies and interest rates across different countries (see for example Kung, 2015). Empirical research is available on the relationship between various types of trade and economic growth, FDI and 3
growth, the internet and growth, and migration and growth (Alfaro 2004; Borensztein 1998; Mountford 1997; Czernich 2011). More recent work has focused on using a global vector autoregressive model on different measures of macroeconomic linkages, to identify channels of shock transmissions (Hassan et al., 2017). But empirical and theoretical work has yet to examine how the _interplay_ between these various layers of connectivity complement each other. For example, internet connectivity has various direct avenues for influencing economic growth, including providing individuals the ability to quickly research products available in foreign countries, take online courses, and transact in services remotely, as well as serving as the backbone to facilitate greater deepening of cross‐border global supply chains. E‐commerce has been greatly enhanced by the availability of broadband internet. Nonetheless, without transport connectivity through roads, rail, shipping, and air transport, the effects of broadband connectivity as a channel to stimulate growth via e‐commerce would be greatly diminished.

More telling regarding the interplay between various forms of connectivity, is the role of migration and international travel, be it for permanent migration, foreign study, or tourism. While Gould (1994) first identified the complementary relationship between migration and trade between the home and host countries of migrants, subsequent research has also identified migration’s importance in influencing FDI and its direct influence on growth through knowledge transfers (Onodera 2008). Consequently, migration may not only be important for growth by directly transferring knowledge between the host and home countries, but also by facilitating knowledge embodied in trade and FDI flows through bridging market information gaps.

This paper finds that being connected to well‐connected countries matters for economic growth, but there is complementarity in the various types of connections that enhances growth as well. Countries can benefit from: (i) multiple types of economic links (such as trade, investment, migration, modern telecommunications, and transport) that underpin the movement of technologies and ideas; but also, (ii) the quality of connections in terms of knowledge spillovers and the indirect connections made through partners that are well connected. These are both aspects of inter‐connectedness that affect growth and growth spillovers.

# 2. Trends in Economic Connectivity

A fundamental prerequisite for identifying the complementarity between various forms of connectivity is the ability to identify the specific country links in the connectivity chain. For example, matching migration and trade flows between country partners is essential to identify the complementarity between migration and trade in enhancing economic growth. Knowing the size of overall trade and migration flows for a country is not sufficient to identify that trade from specific countries is facilitated by migration from those same countries.

Mapping these direct connections between countries also brings to light the potential importance of indirect connections. While two similar countries may have the same number and size of connections, they may be connected to very different countries. Being connected to “well‐connected” countries may provide greater opportunities for knowledge transfers from partners of partner countries ( <mark>Duernecker, Meyer, and Vega‐Redondo, 2014).</mark> For example, a dollar of trade between Algeria and Germany may provide greater knowledge spillovers than a dollar of trade between Algeria and Morocco, because Germany is much more connected to the global economy and is likely to be a source of advanced knowledge as well as a conduit for technology and knowledge from other countries it is connected to.

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The importance of direct and indirect connections between countries, as well as the complementarity between various types of connections for knowledge transfers and economic growth, lends itself to the use of _multilayer network analysis_ . Network analysis is simply a tool to study the direct and indirect connections between countries. Multilayer networks (Kivela et al., 2014) go beyond the notion of a single, one dimensional isolated network, and provide a description of the interactions between various types of connections (layers) in a larger network.

Economic links facilitate trade and the transfer of factors of production (capital, labor, etc.) and therefore impact the overall level of production. However, these links are also likely to facilitate the flow of ideas and innovation, and, hence, long‐run growth. But the strength of information flows is likely different for different economic connections. For example, the knowledge spillovers associated with merchandise trade are likely centered around the information embodied in the products traded (knowledge spillovers related to trade in processed food, for example, may be different from those related to trade in semiconductors).<sup>2</sup> FDI links are associated with a transfer of managerial, organizational, and corporate governance expertise. And migration flows can facilitate the transfer of knowledge directly, but also support less tangible cultural exchange, increase exposure to foreign languages, and bridge gaps in trust in business dealings that cannot always be narrowed through explicit contracting, particularly with differences in governance and legal systems.

As mentioned above, country and regional connectivity has typically been viewed as the size of trade relative to GDP or global trade. ECA’s share of global trade has declined since the early 2000s (figure 1a). Moreover, although intra‐regional and extra‐regional trade have grown, intra‐regional trade has grown more rapidly (figure 1b). Increased trade within ECA may reflect greater cooperation across institutional and regulatory dimensions with important implications for regional integration and convergence. Similar aggregate measures of connectivity (total FDI, migration, telecommunications, etc.) suggest that while regional integration has increased substantially, growth of global connections may not have kept up.

While past studies find evidence that greater trade openness and integration improves growth, these aggregate measures of integration may obscure the underlying bilateral connections and the importance of partner country connections. In other words, while ECA’s intra‐regional connectivity may be growing faster in the aggregate than extra‐regional connectivity, it is difficult to determine how well ECA countries are connecting to other ECA countries that are well connected globally. ECA global connectivity may actually be increasing for the average ECA country, if countries in ECA are linking to strong globally connected ECA countries. The following section examines the pattern of connections between countries and how countries are connected to the broader network of countries. Subsequently, the section uses this wider network of connectivity information to analyze types of connectivity, how the various layers of connectivity interact, and how connectivity might be associated with economic growth and shared prosperity.

> 2 See Hidalgo, C. and Hausmann, R., 2009.

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**Figure 1: Trends in intra‐regional trade in the ECA**

<!-- Start of picture text --> a. ECA’s share of global trade has been falling b. Intra‐regional trade growing faster than extra‐<br>regional trade<br>ECA Trade as a Share of Total World Intra‐ ECA trade vs Extra ECA trade<br>Trade (exports and imports) (billions of dollars)<br>37% 10000<br>35% 8000<br>33% 6000<br>31% 4000<br>29% 2000<br>0<br>27%<br>1996 1998 2000 2002 2004 2006 2008 2010 2012 2014<br>25%<br>1996 2000 2004 2008 2012 INTRA‐ECA EXTRA‐ECA<br><!-- End of picture text --> Source: Author’s calculations based on UNCTAD and World Bank Development Indicators While there are potentially hundreds of ways countries can connect with varying implications for the transfer of ideas, this paper focuses on six types of economic connections: trade, FDI, migration, information and communication technologies (ICT), air transport and portfolio financial flows. A summary of the data used is provided in Table 1. While other forms of connectivity may also be important for how knowledge transfers between countries and for economic growth, these data are the only ones available on a global and country to country basis. Subsequent sections will drill down into additional layers of connectivity (for example, land transport in ECA) as well as unique aspects of the layers of connectivity. This paper takes a broad macro view of the many layers of connectivity as a means to observe general trends in the strength of connections, how ECA countries are connected to each other and the rest of the world, and how these connections influence growth.

Table 1. Data used for measuring economic connectivity, including the data sources and sample period.

|Indicator Name|Description|Coverage|
|---|---|---|
|FDI|Total bilateral FDI stocks. Source: OECD|2002‐<br>2013|
|Trade|Bilateral total trade flows for manufacturing|2000‐|
||goods. Source: UNCTAD|2015|
|Migration|Total migration stocks. Source: Individual|2000 and|
||Countries’ Census Data, OECD and World Bank<br>estimates (See Artuc et. al 2017)|2010|

6
|ICT|Proxy for ICT flows. Estimated by combining|2003‐|
|---|---|---|
||bilateral duration of phone conversations and|2011|
||the bandwidth capacity between countries.<br>Source: Derived from TeleGeography data.||
|Airlines|Estimated bilateral number of flights (end|2002‐|
||destination) Source: ICAO|2012|
|Portfolio Flows|Total bilateral portfolio flows. Source: BIS,|2000‐|
||Consolidated Banking Statistics (CBS)|2014|

As an initial overview of ECA connectivity in the global context, we show graphically how countries in ECA and the rest of the world are connected in each layer of connectivity. We show data for the initial year and the last period available to see how connectivity in a particular dimension has changed over time. In Figures 2 to 7, ECA countries are highlighted in shades of blue, and the rest of the world is shown in shades of orange. The size of each country‐node is proportional to the size of its total connectivity in each layer of connectivity described. Outward arrows point to the two strongest bilateral partners. The methodology for plotting the countries attempts to show clearly the connections between countries in the global network of countries.<sup>3</sup> The largest country‐nodes are pulled to the outer boundaries of the graph, but the pull is counterbalanced by the number and strength of connections with partner countries. Consequently, country‐nodes will tend to be grouped together if they share common connections with well‐connected countries.

# _Trade_

Figure 2 is based on trade of manufactured goods between all the countries in the world in 2000 and 2014. The size of each country‐node reflects the total volume of trade (exports and imports) for each country, and the two outward arrows are pointed to each country’s two top export destinations. One of the most dramatic developments in global trade has been the emergence of China (CHN) since 2000, which has not only grown to one of the three largest traders, along with the United States (USA) and Germany (DEU), but also is pulled toward the center of the graph, with numerous connections to regional hubs in Europe, the Americas and Asia. ECA’s relative dominance in trade has declined, along with other regions, as China and other Asian countries’ share of global trade has increased. Interestingly, however, ECA country‐nodes are much closer to each other in recent years than in the past, reflecting the higher degree of regional integration and value chain development in Europe. Germany is the primary hub for ECA’s manufacturing

> 3 Country node placement utilizes the Barnes‐Hut algorithm <u>(http://arborjs.org/docs/barnes‐hut). The algorithm</u> attempts to place large country nodes closer to the edges of the graph as a means to more clearly show their numerous connections to smaller country nodes. The repulsion of the country nodes away from the center of the graph is proportional to their size. The repulsion away from the center of the graph is counterbalanced by the attraction forces due to how strongly each pair of countries are connected to each other. Once the forces of repulsion and attraction on the country nodes have been defined, the behavior of the entire graph under these forces may then be simulated as if it were a physical system. In such a simulation, the forces are applied to the country nodes, pulling them closer together or pushing them further apart. This is repeated iteratively until the system comes to a mechanical equilibrium state; i.e., their relative positions do not change from one iteration to the next. The positions of the country nodes in this equilibrium generate the graphical depiction of the network.

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connectivity has changed the most over the last decade due to deregulation and innovation, while portfolio financial flows have tended to be concentrated in a few dominate financial sectors that have changed only slightly.

This network analysis adds to previous and ongoing research on economic relationships and their influence on growth by not looking at one network layer independently of others, but by examining the many layers of connectivity together. Not only do individual connections matter but also their interdependence in economic relationships. Connectivity should be seen as a multidimensional concept: including trade, migration, finance, transport, communications, and other factors. Greater connectivity in one area may be a complement or substitute for connectivity in another area.

# 3. Connectivity and Income Growth

According to traditional economic growth models, an increase in trade, or other forms of connectivity, will have no impact on long‐run income growth. The _level_ of income will increase due to gains from specialization, but this will not lead to sustained increases in growth unless it has an impact on improving technological accumulation over time (i.e., the endogenous growth model, Romer, 1990). Thus, the main mechanism through which connections affect growth is via the transfer of knowledge and innovative ideas and technologies. Innovations are continuously generated globally, and they travel the world through the network of countries. Greater multidimensional connectivity increases the probability that an economy will absorb these new ideas and increase long‐run growth.

The empirical strategy we use for understanding how a country’s international connections and the interplay of these connections influence economic growth is three‐fold. First, we simply estimate a baseline growth model that includes standard explanatory variables, including the initial GDP per capita level, schooling, size of government, inflation, quality of governance, and investment rates (see also Helliwell, 1994). Second, we include the traditional measure of connectivity, trade/GDP, that is used in the economic literature on openness. Our interest is not so much replicating previous research, but rather determining a benchmark against which to compare network effects of connectivity. Third, we develop network centrality measures for each type of connection indicator (for example, trade, FDI, etc.) based on a modified Google’s PageRank algorithm (Page, 1999). This algorithm gives a higher ranking to countries that have a larger number of connections to well‐connected countries as well as connections to countries with a high “intrinsic value.” Intrinsic value in our context means a high propensity to generate and disseminate knowledge. We proxy this intrinsic value by the size of the country’s population and GDP per capita.

We modify and expand the analysis in Duernecker, Meyer, and Vega‐Redondo (2014) of the relationship between a network measure of trade and economic growth to other measures of connectivity (trade, FDI, migration, airline transport, portfolio flows, and ICT). We compare our six individual network centrality results with the relationship between traditional measures of connectivity (for example, overall trade to GDP) and growth, to determine whether network centrality measures are any better at describing long‐ run growth than the standard, non‐network, measures. The different variables, data sources, and sample periods, are summarized in Table 2.

14
Table 2: Summary of the variables, data sources, and sample period used for the growth models.

|Indicator Name|Description|Coverage|
|---|---|---|
|Initial GDP per capita<br>Governance|The logarithm of the initial value of GDP per<br>capita for the growth period in question<br>(2000‐2016). Source: World Bank World<br>Development Indicators (WDI).<br>Index of the quality of governance which takes<br>into account corruption, the rule of law and<br>the quality of institutions. Source: WDI.|2000‐<br>2016<br>2000‐<br>2016|
|Inflation|Measure of CPI change. Source: WDI.|2000‐<br>2016|
|Government Size|Total government expenditure as a share of<br>GDP. Source: WDI.|2000‐<br>2016|
|Years of Schooling|The average number of years of schooling.<br>Source: Barro‐Lee (www.barrolee.com).||

Finally, we develop a comprehensive measure of overall network centrality, referred to as multidimensional connectivity, that combines all six types of connectivity into a single network measure. This indicator takes into consideration the complementarity of the various forms of connectivity, as described in the introduction. Multidimensional connectivity is found to be significantly related to long‐ run growth, and provides a better explanation of long‐run growth than the individual connectivity channels. In other words, the sum is greater than the parts. As a robustness check, we develop an alternative index of network centrality, multiplex connectivity, which describes the complete network but does not impose the restriction that each layer of the network is a complement to other layers. This indicator has a similar, albeit less strong, relationship with growth than the multidimensional connectivity indicator.

# _3.1 Network centrality_

This section introduces a measure of centrality, or influence, based on the well‐known Google PageRank algorithm which was used to rank websites based on their links in the network. The algorithm was initially developed to rank websites in terms of their “importance” and “relevance” to a search query. Network analysis was a natural starting point for this problem because websites with more hyperlinks pointing at them were thought of as being of higher quality. In addition to the number of the incoming links, having more links from higher quality websites is yet another indicator of website quality. The innovation by Page (1999) consisted in modifying the popular network Eigenvector Centrality measure so that the centrality value of a website was proportional to the probability that a person clicking randomly on hyperlinks would 15
i i i= AY Ari c+ (i * Pi) k Axi k ia Yi Pi AdKAKi ke A Aki <u>Trade</u> ,; <u>FDI stock,; Migration Stock,; ICT flow,; Flights,; Portfolio Flows,;</u> A. = Ki <u>| GDP, GDP, POP, POP, POP, GDP,</u>
Each connection (total bilateral trade, total FDI stocks, bilateral migration stocks, ICT, airline transport and portfolio flows) is divided by a proxy for the size of the country (GDP or population). In the original PageRank algorithm, this feature is introduced by dividing by the total number of outgoing links of the partners. Therefore, the probability of getting from website A to website B by a random web surfer decreases as the number of outgoing links in A increases (there are more sites the surfer can land). In the case at hand, the probability of an idea reaching a specific country decreases with the population of the sending country.

Similar adjustments are necessary when one considers information flows between countries along the various networks. For example, conditional on an innovation being present in country A, the probability that a single migrant from A to B will carry this idea decreases with size of the population of A. Although large countries are more likely to generate ideas domestically, they need greater flows and deeper links in order to transmit those ideas to their partners. In this paper, it is argued that this measure is a good proxy for the probability of growth‐relevant knowledge generation by each country (either through learning from its connections or developing knowledge domestically).

# _3.2 Network Centrality Measures and Growth_

In this section, we estimate the importance for growth of the connectivity measures described in the previous section. We first estimate a standard cross‐country, long‐run model over 2000‐2016, where growth depends on the initial levels of GDP per capita, education, investment rate, governance, government size and inflation. We then add trade/GDP, the traditional measurement of openness, as an additional explanatory variable. Finally, we add each of our network measures of connectivity to determine whether network centrality measures are any better at describing long‐run growth than the standard, not‐network, measure.

Two adjustments are required to the network connectivity measures described above before including them in the model. First, we scale the value by population to account for the fact that more populous countries are expected to depend less on being connected to the rest of the world for innovations and growth than smaller countries, which, due to their size, naturally rely more on connectivity (e.g., China vs. Singapore). This has the effect of transforming connectivity into per capita terms. Second, because the network connectivity measure includes the country’s own level of GDP per capita (as well as GDP per capita of partner countries), we subtract the country’s own level of GDP per capita from the connectivity measure because it is already included as an explanatory variable in describing country growth. This, in effect, eliminates double counting. The intrinsic value of partner countries’ GDP per capita is still included in the network connectivity measure.

The estimation of the relationship between growth and the variables typically used in the empirical literature (and included here) faces several key challenges. Perhaps the most difficult concerns _endogeneity,_ often reflecting reverse causality, or the influence of the dependent variable (growth) on some of the independent variables (e.g. government size). Our main goal is to measure the contribution of our network connectivity measures to growth, after controlling for other variables (inflation, etc.) thought important to growth. However, both our connectivity measures and these other variables may themselves be determined, in part, by growth (they may not be _exogenous_ , as assumed in our estimation 17
procedure). Thus, most researchers using cross sections are only able to capture partial correlations instead of causality.

Our identification strategy attempts to reduce problems from endogeneity, although it does not eliminate them. First, we calculate the right‐hand side variables by taking the earliest observation available in the data at the start of the growth period. This of course does not correct all potential endogeneity problems, but it is indicative of a lack of reverse causality. Second, our measures of connectivity build on direct and indirect links for the various types of connectivity in the global network, and countries are only able to impact direct links and not indirect ones. By taking into consideration higher order indirect links, our connectivity measures are at least to some extent exogenous, or unaffected by growth of the country being measured. Moreover, for robustness we also included geographic distance between countries as a separate layer of connectivity to account for geographic proximity that may affect growth and the strength of connectivity channels simultaneously.<sup>8</sup> For a deeper treatment of endogenous relationships in economic growth we refer the reader to the rich literature (see, Frankel and Romer, 1999; Rodriquez and Rodrik, 2000; Helpman, 2008; Beck, 2008; Feyrer (2009) and Panizza, 2013).

This kind of estimation also may suffer from the existence of unobserved country effects (which are potentially correlated with the independent variables used in the empirical model). Furthermore, most variables are measured with considerable error. Since developing countries represent a large fraction of our sample, results depend on the reliability of the data. Hence, measurement error can be a source for inconsistent coefficient estimates.

We examine the growth effects of connectivity along each network layer separately (trade, FDI, migration, ICT, airlines connectivity and portfolio flows) in Table 3.

Table 3. Connectivity effects on overall income growth The dependent variable in each model is the annualized income growth (%) between 2000‐2016. All right‐hand‐side variables are transformed in logs and we take the first available observation for the growth period. There are 111 countries for which we are able to estimate each version of the model. The connectivity variables /PageRank are normalized using the standard normal distribution. Therefore, the size of the coefficient represents the growth impact of one standard deviation change. All model specifications include an intercept, which is not reported in the table.

||1|2|3|4|5|6|7|8|
|---|---|---|---|---|---|---|---|---|
|GDP per capitat=0|‐0.91***|‐1.10***|‐1.31***|‐1.29***|‐1.15***|‐1.06***|‐1.11***|‐1.11**|
|Years of schoolingt=0|2.46***|2.4***|1.7***|1.87***|1.60***|2.06***|1.99***|2.04***|
|Government sizet=0|‐9.24**|‐8.64**|‐5.81|‐5.24|‐4.91|‐5.44|‐5.21|‐5.79|
|Inflationt=0|1.02|0.99|2.92|2.75|2.54|2.1|1.82|1.73|
|Governancet=0|1.18|2.13|1.2|0.99|1.04|1.43|1.32|1.63*|
|Investment Ratet=0|0.160**|0.170***|0.190***|0.21***|0.20***|0.20***|0.20***|0.20***|
|Baseline Standard Connectivit<br>|y model||||||||
|Trade/GDPt=0||0.28|||||||
|Network Effects(PageRank)|||||||||

> 8 Including a layer of network connectivity that was determined solely by geographic (capital to capital) distance between countries was not a significant determinate of growth, nor did it change the empirical results related to our empirical inferences related to the multidimensional connectivity index described below.

18
|Trade Connectivity per<br>capitat=0<br>FDI Connectivity per capita<br>t=0|||0.61***|0.59***|||||
|---|---|---|---|---|---|---|---|---|
|Migration Connectivity per<br>capitat=0|||||0.34*||||
|ICT Connectivity per capita<br>t=0||||||0.12|||
|Portfolio Flows per capitat=0<br>Airline Connectivity per<br>capitat=0|||||||0.17|0.19*|
|Adj‐R<sup>2</sup>|0.54|0.53|0.59|0.58|0.56|0.54|0.55|0.56|

|Table 2. Network effects on overall incomegrowth<br>The dependent variable in each model is the annualized income growth (%) between 2000‐2016. All right‐hand‐side variables<br>we take the first available observation for the growth period. There are 86 countries for which we are able to estimate each ve<br>connectivity variables /PageRank are normalized using the standard normal distribution. Therefore the size of the coefficient r<br>impact of one standard deviation change.|are tra<br>rsion<br>epres|nsfo<br>of th<br>ents t|rmed i<br>e mod<br>he gro|n logs<br>el. The<br>wth|and<br>|
|---|---|---|---|---|---|
|1|2|3|<br>4|5|6|
|‐<br>1.|‐<br>1.|‐<br>1.|‐<br>1.|‐<br>1.|‐<br>1|
|3|2|1|0|1|.<br>|
|GDP per capita‐t0<br>1|9|5|6|1|1<br>|
|<br>*|*|*|*|*|1<br>|
|*|*|*|*|*|*<br>|
|*|*|*|<br>*|*|*|
||1.|1.|2.|1.|2.|
|1.<br>|8|6|0|9|0|
|Years of schooling‐t0<br>7<br>*|7<br>|0<br>|6<br>|9<br>|4<br>|
||*|*|*|*|*|
|*<br>*|*|*|*|*|*|
||*|*|<br>*|*|*|
|G i0<br>‐<br>5.|‐<br>5.|‐<br>4.|‐<br>5.|‐<br>5.|‐<br>5.|
|overnment sze‐t<br>8|2|9|4|2|7|
|1|4|1|<br>4|1|9|
|2.|2.|2.||1.|1.|
|Inflation‐t0<br>9|7|5|2.<br>|8|7|
|2|5|4|<br>1|2|3|
||0.|1.|1.|1.|1.<br>|
|<br>1.|||||6|
|Governance‐t0<br>|9|0|4|3||
|<br>2|9|4|<br><br>3|2|3<br>*|
|0.|0.|0.|0.|0.|0.|
|Investment Rate ‐ t0<br>1|2|2|2|2|2|
|9|1|0|0|0|0|

19
||0<br>*|*<br>*<br>*<br>*|
|---|---|---|
||*<br>*|*<br>*<br>*<br>*|
||*<br>*<br>*|*<br>*<br>*<br>*|
|Network Effects(PageRank)|||
||0.||
||6||
|Trade Connectivity per capita‐t0|1<br>*||
||*||
||*||
||0.||
||5||
|FDI Connectivity per capita‐t0|9<br>*||
||*||
||*||
|||0.|
|Migration Connectivity per capita‐t0||3<br>4<br>*|
|||0.|
|ICT Connectivity per capita‐t0||1|
|||2|
|||0.|
|Portfolio Flows ‐ t0||1<br>7|
|||0.|
|Airline Connectivity||1<br>9|
|||*|
||0.<br>0.|0.<br>0.<br>0.<br>0.|
|Adj‐R2|5<br>5|5<br>5<br>5<br>5|
||9<br>8|6<br>4<br>5<br>6|

Note: All coefficients are estimated with ordinary least squares regression. ***,**,* represent significance levels at 99%, 95% and 90% respectively.

Compared to the base model and the standard measure of openness (trade/GDP), nearly every network connectivity measure manages to increase the explanatory power (Adj‐R<sup>2</sup> ) of the standard growth equation, although not every network layer is statistically significant at the minimum 10 percent level. Deeper integration along each individual dimension is associated with stronger per capita GDP growth over the subsequent 16‐year period. Unlike the traditional measure of openness and connectivity (trade/GDP), the PageRank‐based index, which was designed to capture the knowledge spillovers from connections, is associated with higher long‐term growth in the case of international trade, FDI, migration and airline connectivity. A one standard deviation increase in the trade connectivity of a country is associated with more than half a percentage point (0.6%) higher annual economic growth over the long 20
term. The effect of FDI connectivity is similar (0.59%), and the effects of migration and airline connectivity markedly lower (0.34% and 0.19% respectively).

Connectivity can also boost shared prosperity. Economic channels by which the poor and bottom 40 percent may directly benefit from greater connectivity include improved access to finance and markets, changes in the return to capital and/or labor, exposure to technology and better governance, and changes in the relative prices of goods and services. Trade, for example, may enhance resource allocation across countries leading to improved opportunities for asset use by the bottom 40 percent of the income distribution (B40). Investment flows may generate new returns for the B40. As production becomes more competitive, the poor may also experience a mix of welfare gains and losses from relative price changes. Migration may open new opportunities, but also has implications for the labor market. Connectivity influences commerce and investment, but it also is a means to transfer ideas, technology, and institutional arrangements, which are all potential sources for spillovers to growth and may indirectly influence shared prosperity.

Table 4 summarizes the estimated impact of connectivity on the income growth of the poorest 40 percent of the income distribution in each country. Trade connectivity has the largest impact. In fact, the knowledge spillover effects from trade appear to be more important for the bottom 40 than for the top 60. However, the other measures of connectivity do not appear to play a statistically significant role in bottom 40 growth.

Table 4. Connectivity effects on Bottom 40 income growth The dependent variable in each model is the annualized bottom 40 income growth (%) between 2000‐2016. All right‐hand‐side variables are transformed in logs and we take the first available observation for the growth period. There are 88 countries for which we are able to estimate each version of the model. The connectivity variables /PageRank are normalized using the standard normal distribution. Therefore, the size of the coefficient represents the growth impact of one standard deviation change. All model specifications include an intercept, which is not reported in the table.

||1|2|3|4|5|6|7|8|
|---|---|---|---|---|---|---|---|---|
|GDP per capitat=0|‐0.77**|‐0.69*|‐1.19***|‐1.08***|‐0.69***|‐0.71*|‐0.75**|‐<br>1.77***|
|Years of schoolingt=0|2.1***|2.1***|2.32***|2.39***|2.15***|1.91**|2.65***|2.51***|
|Government sizet=0|‐7.37|‐7.38|‐3.61|‐9.05|‐10.38|‐6.4|‐8.05|‐5.72|
|Inflationt=0|2.61|2.62|5.69|6.21|5.08|5.23|4.01|0.96|
|Governancet=0|1.13|1.14|‐0.74|0.75|1.37|1.5|2.18|0.3|
|Investment Ratet=0|0.09*|0.08*|0.08*|0.13**|0.09*|0.12**|0.09*|0.09*|
|Baseline Standard Connectivity|model||||||||
|Trade/GDPt=0||0.02|||||||
|Network Effects(PageRank)|||||||||
|Trade Connectivity per capita<br>t=0|||1.49**||||||
|FDI Connectivity per capitat=0||||0.8|||||
|Migration Connectivity per<br>capitat=0|||||0.18||||
|ICT Connectivity per capitat=0||||||0.21|||

21
|Portfolio Flows per capitat=0|||||||‐0.13||
|---|---|---|---|---|---|---|---|---|
|Airline Connectivity per<br>capitat=0||||||||0.11|
|Adj‐R<sup>2</sup>|0.24|0.24|0.28|0.26|0.25|0.23|0.23|0.23|

Note: All coefficients are estimated with ordinary least squares regression. ***,**,* represent significance levels at 99%, 95% and 90% respectively.

# _3.3 Multidimensional Connectivity: Interplay of network connections and growth_

In this section, we develop two unique methods for combining each individual network layer (trade, FDI, migration, ICT, airline transport and portfolio flows) into a single total network measure of connectivity to address the complementarity between connectivity measures and their relationship to growth. Indeed, there appears to be a strong correlation between all measures of connectivity, with perhaps the exception of portfolio financial flows (Table 5). FDI and trade are the most correlated across connectivity layers, airline transport and migration less so, while portfolio flows is highly idiosyncratic. Intuitively, interplay between various forms of connectivity can be seen most clearly in migration and international travel. Much research has found that migration and trade tend to be complements (greater migration between two countries is associated with greater trade between them), and subsequent research has also identified migration’s importance in influencing FDI and its direct influence on growth through knowledge transfers (see, for example, Gould 1994, Onodera 2008, and others). Thus, people to people contact may be important for growth by directly transferring knowledge between the host and home countries, as well as indirectly by facilitating knowledge embodied in trade and FDI flows through bridging market information gaps.

Table 5: Correlation between connectivity layers is high, except for portfolio financial flows

||Trade|FDI|Migration|ICT|Airline|Portfolio Flows|
|---|---|---|---|---|---|---|
|Trade|1||||||
|FDI|0.9295*|1|||||
|Migration|0.7173*|0.7092*|1||||
|ICT|0.7107*|0.7882*|0.6789*|1|||
|Airline|0.8515*|0.9090*|0.6200*|0.8348*|1||
|Portfolio|||||||
|Flows|0.2560*|0.2751*|0.2624*|0.2286*|0.2697*|1|

The six network connectivity measures could be aggregated in a simple, ad hoc way (for example, taking averages of the network centrality measures). However, this is likely to result in a loss of important information and would not account for the interaction of various network layers and their effect on economic growth. For example, vastly different bilateral connectivity patterns in each dimension can result in similar average values. This is schematically described in Figure 8. In the left and right panels of the figure, country A has the same centrality index calculated using simple averages of modified PageRank centrality across three types of networks, represented by the three types of arrows (line, dash and dot). It is clear however, that the patterns of connections and the overall network for country A is vastly 22
different between the two cases. It is easy to show that using aggregation at the country level, the modified PageRank produces a higher centrality for country A in the case on the right compared to the one on the left.

**Figure 8:** Two examples of network connectivity and the modified PageRank of county A.

<!-- Start of picture text --> B C B C<br>A A<br>D<br>D<br><!-- End of picture text --> We therefore adopt a somewhat more intuitively appealing procedure for aggregating the connectivity measures. This includes calculating the weighted multiplicative average of the separate connectivity measures. The equation is: where ��� is the network information function and �, �, �, �, �, � are the estimated weights for each connectivity layer. The weights are calculated using the maximum likelihood procedure where the objective function was to maximize the goodness of fit of the growth equation (adjusted R‐squared).

Essentially, the six networks are collapsed into one network where each bilateral link is a function of each of the layers, as shown in Figure 9. The functional form used has several desirable features that have been well documented in other economic contexts. First, it imposes decreasing returns to scale, that is, having a large amount of one type of connection provides the country with decreasing informational returns. After some initial (low) threshold, an increase in connectivity will have less than a one‐to‐one increase in informational exchange. Second, this functional form allows imperfect substitutability of the channels in terms of transmitting growth‐relevant information. That is, a balanced increase in connectivity along each dimension would have a stronger impact on the bilateral informational link than a rapid increase in the connectivity along one layer only. It is very likely that these different channels complement each other in terms of the information they transmit. For example, a foreign investor is likely to be more successful in transferring know‐how in the host country if there already are deep links through migration and trade that can complement the information flows embedded in FDI.

Furthermore, the estimated weights on each of the network layers can be interpreted as the efficiency/importance of each channel in transmitting information that facilitates long term income 23
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each of the individual network indices (shown in Table 2). A one standard deviation increase in the multidimensional connectivity indicator is associated with 0.67% higher annualized growth. These results suggest that the overall connectivity profile of the country (one that combines all network layers) is more important than each of the individual layers separately. Moreover, in the combined network, trade has the highest importance, followed by FDI, and then migration. Neither ICT, airline transport, nor portfolio flows add additional information above these three connectivity channels. By contrast, the multidimensional measure does not add new information above the single network measure of trade connectivity in explaining changes in the growth of the incomes of the bottom 40 percent of the distribution.

Table. 6 Multidimensional Connectivity

|The dependent variable in each model is annual income g<br>transformed in logs. The PageRank coefficient is standardi<br>standard deviation.|rowth (%). All right‐hand‐side variables are<br>zed to represent the effect of a change of one<br> <br>|
|---|---|
||Overall Growth<br>B40 Growth<br> <br>|
|Multidimensional Connectivity Impact|0.67***<br>1.49***|
|Efficiency Exponents/Weight|s of Connectivity Channels|
|Trade Channel Efficiency|0.532<br>1|
|FDI Channel Efficiency|0.37<br>0|
|Migration Channel Efficiency|0.1<br>0|
|ICT Channel Efficiency|0<br>0|
|Airline Channel Efficiency|0<br>0|
|Portfolio Flows|0<br>0|
|Adj‐R<sup>2</sup>|0.61<br>0.28|

Note: ***,**,* represent significance levels at 99%, 95% and 90% respectively in an OLS regression. The values of the exponent parameters (efficiency exponents/weights) α,β,γ and δ were estimated using the maximum likelihood procedure where the objective function was to maximize the goodness of fit measure (adjusted R‐squared) 25
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In terms of overall levels in ECA sub‐regional multidimensional connectivity (Table 5), Northern, Southern, and Western Europe have the highest global ranking; Central Europe, Russia and Turkey have medium levels of global connectivity; while Eastern Europe, the Western Balkans, the South Caucasus, and Central Asia have the lowest levels of overall connectivity. Not surprisingly, absolute levels of connectivity are associated with higher levels of development.

**Table 7: Multidimensional Connectivity varies by ECA‐subregion, with the highest connectivity in the western part of the region, and lowest connectivity in the eastern part of the region**

|**ECA**|**Multidimensional**<br>|||||**Portfolio**|
|---|---|---|---|---|---|---|
|**Sub‐regions**|**connectivity**<br>**Trade**|**FDI**|**Migration**|**ICT**|**Airline**|**flows**|
|_Global ranking, fro_<br>High connectivity|_m the best to worst in combine_|_d connec_|_tivity (lower is_|_better)_|||
|Western Europe|8<br>8|8|18|9|11|26|
|Northern Europe|20<br>18|23|35|28|18|27|
|_of which Baltics_|_30_<br>_27_|_34_|_46_|_46_|_27_|_20_|
|Southern Europe|20<br>24|19|24|22|20|22|
|Medium Connectivi|ty||||||
|Central Europe|50<br>49|51|56|55|55|57|
|Russian Federation|56<br>53|55|58|62|71|39|
|Turkey|57<br>49|65|42|54|60|76|

27
|Low Connectivity<br>||||||||
|---|---|---|---|---|---|---|---|
|Eastern Europe|71|72|73|65|82|86|91|
|Western Balkans|74|73|78|40|61|67|84|
|Central Asia|76|80|79|51|87|83|91|
|South Caucasus|80|83|70|58|83|77|59|

Source: Own calculations. Note: Subregional indicators are median values of subregion’s countries.

Interestingly, although Central Asia and the South Caucasus rank relatively low on overall connectivity, they have also seen the greatest improvement from 2000 to 2014 (Figure 11). The South Caucasus has seen connectivity increase by nearly 75 percent, while Central Asia has seen connectivity increase by over 40 percent. Eastern Europe and Western Balkans, although also starting from relatively low levels, have not seen as rapid an increase, with connectivity increasing only 20 and 10 percent, respectively. The key challenge for these regions is to find ways to improve balanced connectivity, particularly easing constraints and facilitating trade, FDI, airline, and ICT connectivity. For the ECA region as a whole, connectivity has improved more than global connectivity, reflecting the integration process of the EU as well as strides taken in transition economies.

Figure 11: ECA’s connectivity has grown, but there are wide variations across subregions <!-- Start of picture text --> Growth in Connectivity (2000‐2014)<br>80%<br>70%<br>60%<br>50%<br>40%<br>30%<br>20%<br>10%<br>0%<br><!-- End of picture text --> Source: Own calculations. Subregional and global indicators are median regional averages.

The analysis of multidimensional connectivity and its relationship to economic growth can be useful in evaluating where countries can benefit the most in terms of reducing barriers to entry and facilitating linkages with well‐connected countries. It can also help identify which connections are likely to have the 28
largest impact on growth. For example, in China’s case, while the trade network is strong, the migration and FDI networks are weak in comparison. Likewise, taking the case of Kazakhstan, increasing FDI in Bulgaria would bring a higher increase in multidimensional connectivity than increasing FDI in Poland, despite Poland’s greater overall connectivity. This is due to the higher complementarity of Kazakhstan’s FDI to other pre‐existing connections with Bulgaria compared to Poland.

As a robustness test of the multidimensional connectivity indicator used above, a second approach to calculating multidimensional connectivity is evaluated using the recent techniques in the study of multiplex networks, where the functional form of the relationships is unknown. These multiplex networks do not rely on collapsing the network into a single layer and do not restrict the functional form (i.e., they do not rely on the Cobb‐Douglas functional form as used earlier). A benefit is that the functional form need not be assumed; the cost is that if economic theory suggests a particular relationship (i.e., complementarity between network layers), this information is not used.

Multiplex networks are observed in all types of complex systems, including economic, social, biological, infrastructure and socio‐technical systems. For example, the air transportation system is a socio‐technical system that exhibits many layers, all of them contributing to and essential for the overall functioning of the system. Interdependence among different layers of the air transportation system arises naturally because different airlines use the same airports. As a consequence, if an airport is closed, all the flights coming out of it (and in) stop for all the airlines. Another aspect of interdependence arises because for a flight to takeoff it needs both a crew and a plane. Similarly, banks are also connected (in often very complex ways) via their derivative positions, by overlap of portfolio composition, by joint exposure to the same creditors, etc. In other words, a multilayer network model of each system is essential to estimate the degree of resilience of the entire system to random events or attacks against some of its parts. The aim, then, would be to study potential contagion effects via multiple channels in first attempts at modeling multi‐dimensional network structures. For example, a description of the financial system as a three‐layer multilayer network, comprised of layers representing financial activities for funding, collateral, and asset layers, has been recently proposed by Bookstaber and Kenett (2016).

Given the surge of interest in multiplex networks, recently methodologies have been proposed to assess the centrality of nodes in multiplex, and more generally multilayer, structures. Halu et al. (2013) and Laccovacci et al. (2016) have proposed an algorithm that captures how the centrality of the nodes in a given layer of the multiplex can affect the centrality of the nodes in other layers. This effect is modeled by considering a PageRank algorithm based on the centrality of the nodes in the master layer. De Domenico et al. (2015) proposed instead to rank simultaneously nodes and layers of the multiplex network based on any previous measure of centrality stablished for single layer networks, including random walk processes that hops between nodes of the same layer and between nodes of different layers as well. The resulting centrality called "versatility" strongly awards nodes active (connected) in many layers, however the description was not intended to weight layers in any specific way.

Recently, Rahmede et al. (2017 have proposed a different approach, where they consider a random walk hopping through links of different layers with different probabilities determined by the centrality of the layers (influences). This is following the work of Sola et al. 2013)<sup>7</sup> where different measures for the centrality of the nodes given a set of in influences of the layers have been proposed. Rahmede et al. (2017) propose a ranking algorithm, called MultiRank, that is specified by a coupled set of equations that simultaneously determine the centrality of the nodes and the influences of the layers of a multiplex 29
network. The MultiRank algorithm applies to any type of multiplex network including weighted and directed multiplex network structures. Very generally, this algorithm proposes an extension to the classical PageRank centrality calculation, by coupling the centrality of the node to the influence of the layer it is active in. This is done by considering the node‐layer interaction as a bipartite network. Such a coupling provides new insights into the centrality of a node across different connectivity dimensions.

Similar to the measure of multidimensional connectivity described above, we consider the multilayer network of the individual flow networks. In this approach, we examine the multilayer network as a whole, and do not collapse the different flow layers one on another. Instead, we follow the approach developed by Rahmede et al. (2017) to calculate the Multiplex PageRank centrality (MPR). This approach assigns a measure of centrality to each country based on its connectivity across all the layers put together. A country’s centrality is measured by assigning a score based on its connectivity in one flow defined layer, and by assigning a score to the overall importance of a given economic flow defined layer. These two scores are calculated simultaneously and are co‐dependent.

Following the approach described above, we repeat the regression analysis using the same dependent and independent variables in the standard growth model, but instead use the standardized MPR centrality measure. This results in a statistically significant (albeit smaller) coefficient of the multiplex connectivity measure of 0.39 (p‐value = 0.02, Adj. R<sup>2</sup> =0.534). This alternative methodology confirms the importance of combining the multiple ways countries can connect, rather than simply focusing on one connection layer at a time, particularly for overall growth.

# 4. Trade‐offs and Resilience to Shocks

Although the long‐run effects of connectivity on growth appear to be positive, connectivity can also expose an economy to shocks and exacerbate crises. For example, Kaminsky and Reinhart (2000 and 2003) and Bae, Karolyi and Stulz (2003) show that financial sector linkages play an important role in propagating shocks. The 2005 commodity food price shock and the 2008 global financial crisis also demonstrated the cascade effects that shocks in one market can have in other markets.

Connectivity, however, may also mitigate shocks which originate in some country‐nodes in the network. For example, if a given country is well integrated in the network then a shock to one of its partners can be ameliorated by leveraging its other links to the remainder of the network.

This analysis provides supporting evidence for both these phenomena. Countries with low levels of connectivity are more resilient to shocks in the global network because they have few partners and less connections that would transmit shocks. On the other hand, countries with high levels of connectivity also appear to be less affected by shocks to the network. This is likely due to well‐diversified connections that can mitigate the severity of the shock. Countries in the “middle” of the connectivity spectrum appear to be most susceptible to international shocks. That is, they have low levels of diversified connectivity and are highly dependent on a few well‐connected countries and connections (which boosts their overall connectivity). They are particularly susceptible to shocks affecting one of the well‐connected countries where they derive access to global markets and connectivity.

Figure 12 shows this pattern. A 10 percent simultaneous, negative shock is simulated to three connections (trade, migration and FDI) in each of three “central” and well‐connected countries (Germany, USA and 30
Russia). The countries with the largest decline in their initial connectivity are those that are strongly connected to the country experiencing the shock and do not have strong connections to other partner countries. These countries tend to be in the middle‐range of centrality and receive their connectivity through a few well‐connected countries. A shock to one of these well‐connected countries would do the largest damage to their global connectivity.

Figure 12. Simulated impact on individual countries’ connectivity measure (modified PageRank) from a 10% decline in trade, FDI and migration in Germany, Russia and the United States.

<!-- Start of picture text --> Shock originating in Germany<br>(10 Percent fall in all types of connectivity)<br>0 0 0.2 0.4 0.6 0.8URYPAN 1NZL HKGAUS1.2 SGP CAN1.4 1.6<br>‐1‐2 AFG BFAATG TGO BLZBEN BRN ETH AZE TJK KGZARMGEOSWZBWAGUYPRYNAMBRBGABKWTMOZCMRLBNKENOMNJAMALBGHAECUMUSJORBHSQATGTMSLVDZADOMCYPPAKLVACRITTOTUNBLRNGAESTLTUCOLEGYSAUAREPERMARISRCHLARGZAF NORPRTFINLUXDNKTHAIDNINDMYSBRASWEIRLCHEJPNMEXESPITABELFRAGBRCHNUSA<br>BHR BIH BGR NLD<br>RUS<br>MKD<br>‐3 KAZ GRC SVK<br>CZE<br>HUN<br>‐4<br>MLT<br>SYR HRV TUR AUT<br>MDA<br>BGD<br>‐5 LKA POL<br>UKR<br>‐6 Initial level of connectivity<br>Change in level of connectivity<br><!-- End of picture text --> <!-- Start of picture text --> Change in level of connectivity<br><!-- End of picture text --> 31
<!-- Start of picture text --> Shock originating in USA<br>(10 Percent fall in all types of connectivity)<br>0 LUX<br>‐2 0 AFG BFA0.2 TGO BEN0.4BRNETH AZETJKKGZARMGEOSWZBWA0.6PRYNAMSYRGABMOZMDACMRLBNBHROMNLKAALBMKDMUSJOR0.8URYBGDBIHDZAKAZMLCYPLVA T BLRUNESTHRVLTUBGRSAUAREMARGRC1NZLUKRARGZAFSVKHKGNORPRTTURFINDNKTHAIDNHUNAUS1.2CZERUSMYSBRAAUTPOLSGPSWEIRLCHEESPITABELFRA1.4NLDGBRCHNDEU 1.6<br>QAT EGY CHL IND<br>‐4 BRB KENGHA PAKNGA<br>PAN<br>GUY JPN<br>‐6 ATG KWT BHS DOM COLPER CAN<br>ISR<br>CRI<br>‐8<br>ECU GTMSLV MEX<br>TTO<br>‐10<br>JAM<br>BLZ<br>‐12<br>Initial level of connectivity<br>‐14<br>Shock originating in Russia<br>(10 Percent fall in all types of connectivity)<br>0<br>0 0.2 0.4 0.6 0.8 1 1.2 SGP 1.4 1.6<br>‐0.02 LUX NLD<br>IRL<br>ARE AUSCZE SWECHE<br>NORFINDNK CANBEL FRA DEU<br>‐0.04 MLT HRV ISR HKGPRT AUT JPNESP<br>GBR<br>LTU ARG<br>‐0.06 URY CRITTO BGRNZL ZAFSVK TURHUN ITA<br>BLZ PRY QP A TN TUNBLRESTSAU UKRCHL BRA USA<br>‐0.08 KGZ JAMECUBHSSLVDOMCYP PER<br>GTM COL MYS<br>ARM LVA THA POL MEX<br>‐0.1 ATG BEN BRN GEOSWZBWAGUYNAMSYRBRBGABKWTMDACMRLBNBHRKENOMNLKAALBMKDGHAMUSJORBGDBIHDZAKAZPAKNGAEGYMARGRC IDNIND CHN<br>MOZ<br>‐0.12 AFG BFA TGO ETH AZE TJK<br>‐0.14 Initial level of connectivity<br>Change in level of connectivity<br>Change in level of connectivity<br><!-- End of picture text --> As Figure 12 shows, a 10% adverse shock to German trade, migration, and FDI has an important impact on most countries in the world due to the high centrality of Germany. (The left axis shows the change in connectivity and the horizontal axis shows the initial level of connectivity.) However, not surprisingly, the most affected countries are the smaller countries for which Germany is the main partner country, including countries in ECA, the Middle East, and parts of Asia. The largest decrease in connectivity, due to a 10% decline in Germany’s connectivity, is in Poland, Ukraine, and Sri Lanka, followed by Bangladesh, Macedonia, Croatia, and Turkey. However, due to the importance of Germany in the ECA network, even 32
well‐connected countries like Switzerland and the Netherlands experience a significant decline in their centralities. The least affected countries are the small Latin American countries and well‐connected Asian economies, like Singapore.

An adverse shock to US connectivity has an even stronger impact on most countries in the world due to the high centrality of the United States (compare the range of the left axes in all the graphs). However, not surprisingly, the most affected countries are the smaller countries for which the United States is the main partner country. The largest decrease in connectivity, due to a 10% decline in US connectivity, is in Jamaica and Belize followed by Guatemala and the Dominican Republic. Due to the importance of the United States in the international global network, even well‐connected large countries like Japan, Mexico and Canada experience a significant decline in their centralities. The least affected countries are the small European countries whose main trading partners are Germany, Great Britain, or Russia. Thus, Luxembourg, Estonia, the Slovak Republic and Lithuania barely experience any decline in their overall connectivity.

A 10 percent shock originating in Russia would have a modest impact on global connectivity (left axis). The shock would most affect countries that are closely tied to Russia, such as the former Soviet Republics, which are, in general, less connected to the global economy as a whole. In other words, they are highly reliant on Russia for connectivity to the world.

This framework allows for a multitude of scenarios, including impacts to just one dimension (say trade from China), or several dimensions across a subset of countries. However, a particularly pertinent one in recent times is a shock to Great Britain’s ties to the rest of the EU, the “Brexit” scenario.

Brexit would significantly affect the connectivity of ECA countries. Table 7 shows the effect on the overall connectivity index of ECA from a 10% reduction in all flows from Great Britain to the other EU 27 countries. Even though the other EU 27 countries are those affected directly by the shock, all of ECA is impacted by Brexit due to their indirect links to Great Britain and the EU countries. Smaller, well‐connected nations such as Malta, Ireland, Cyprus and Luxembourg would be the most affected countries from this assumed Brexit scenario. Alternatively, the countries in Central Asia and the Caucuses would be the least affected.

**Table 8: The ECA countries most affected and least affected by Brexit (percent decrease in Multidimensional Connectivity)**

|Most Affected(%)||Least Affected(%)||
|---|---|---|---|
|Great Britain|‐3.46864|Georgia|‐0.00105|
|Malta|‐1.35494|Kazakhstan|‐0.00109|
|Ireland|‐1.05116|Azerbaijan|‐0.00141|
|Cyprus|‐0.76504|Armenia|‐0.00153|
|Luxembourg|‐0.70449|Tajikistan|‐0.00194|
|Netherlands|‐0.65897|Kyrgyz Rep.|‐0.00234|
|Belgium|‐0.57851|Albania|‐0.00456|
|Sweden|‐0.30127|Bulgaria|‐0.00459|
|Spain|‐0.30023|Macedonia|‐0.00623|
|Denmark|‐0.28094|Latvia|‐0.00796|

33
Different regions in ECA have different exposures to types of connectivity shocks (trade, migration, FDI). For example, Western Europe is the most exposed to shocks in other Western European economies. Table 8 shows the largest two contributors to the decline in overall connectivity of each ECA sub‐region in response to a 10 percent shock in three network layers (trade, FDI, migration). Not surprisingly, the overall connectivity of Central Asia in terms of shocks to trade, FDI and migration is affected most by Russia (trade, FDI, migration), but also by China (trade and FDI), and migration (Germany). The rest of ECA appears to be more sensitive to trade shocks in other ECA countries, particularly Germany, as well as the United States. Belgium and the Netherlands have the greatest impact on overall connectivity for the ECA region due to shocks to FDI, due to their large role in trade logistics and finance. Migration shocks are transmitted to various ECA subregions via countries in close proximity, language similarities and historic ties.

Table 9: Transmission of Trade, Migration, and FDI shocks to ECA Subregions

||Largest origin countri<br>and Migration|es of shocks due to a 10 pe|rcent shock in trade, FDI|
|---|---|---|---|
|Region Affected|Trade Shock|FDI Shock|Migration Shock|
||Russian|Russian|Russian|
|Central Asia<br>Central Europe|Federation/China<br>Germany/<br>Netherlands|Federation/China<br>Germany/Austria|Federation/Germany<br>Germany/Austria|
|Western Balkans|Italy/Germany<br>Turkey/United|Austria/Hungary<br>Russian|Italy/Germany<br>Russian|
|South Caucasus<br>Eastern Europe<br>Russia|States<br>Russian<br>Federation/German<br>y<br>Germany/United<br>States|Federation/Kazakhstan<br>Russian<br>Federation/Germany<br>Germany/Switzerland|Federation/Ukraine<br>Russian<br>Federation/Poland<br>Germany/Ukraine|
|Turkey|Germany/Italy|Belgium/Netherlands|Germany/Netherlands|
|Southern Europe<br>Northern Europe<br>Western Europe|Germany/France<br>Germany/<br>Netherlands<br>Germany/Netherlan<br>ds|Belgium/Netherlands<br>Belgium/Netherlands<br>Belgium/Netherlands|Great Britain/Poland<br>Finland/Norway<br>Italy/Great Britain|

34
# 5. Example of using connectivity measures for investment decisions

Assume that a country like Kazakhstan would like to use its national sovereign wealth fund to invest USD100 million of its income from natural resources in Central Europe. Assume also that the risk‐adjusted rate of return in the region has been equalized by the market. Consequently, the government decides to choose a strategic destination for its investment, which would create future knowledge spillovers and innovation transfers. Table 10 lists the potential markets and their connectivity index.

Table 10. Potential markets and their multidimensional connectivity index.

|Potential Country<br>to place<br>Investment|Multidimensional<br>Connectivity Index of<br>Country|
|---|---|
|Poland|0.29|
|Hungary|0.27|
|Czech Rep.|0.26|
|Romania|0.25|
|Bulgaria|0.21|
|Slovenia|0.20|

Not surprisingly the country with the highest connectivity index is Poland. Poland is well integrated in European GVCs, and in particular Germany’s manufacturing industries. By virtue of its strong ties with the Western European economies, Poland has one of the highest overall connectivity indices in ECA, and the benefits of connecting with it are significant.

Table 11 Kazakhstan’s new multidimensional connectivity index after investing $100M in each of the respective markets.

|Country<br>where Kazakh<br>investment is<br>placed|Kazakhstan’s change in<br>Multidimensional<br>Connectivity (%)|
|---|---|
|Bulgaria|.00735|
|Poland|.00525|
|Czech Rep.|.00523|
|Hungary|.00519|
|Slovenia|.00515|
|Romania|.00510|

Somewhat counter‐intuitively, Kazakhstan achieves the highest connectivity increase by investing in Bulgaria and not in countries with better integration in the global network like Poland or Hungary.

There are two reasons for this result. First, having a balanced connectivity portfolio is superior, in terms of knowledge spillovers, to being well connected only in one dimension at the expense of the others. For example, migration may bridge information between countries and stimulate other types of economic connections, such as external investment, trade, and communications linkages. Kazakhstan has relatively 35
<!-- Start of picture text --> Kazakhastan's ranking chetse connectivity<br>(Ranking change from 20% increase in each type of<br>connectivity, by country or region)<br>35<br>30<br>25<br>20<br>15<br>10>0 |aD nl = oO ol. — ||mt=<br>World Germany China Russia<br>= Multidimensonal mTrade FDI Migration<br><!-- End of picture text -->
substitutability between the various layers, when it comes to information flows, complementary dominates. In fact, there might be a high degree of complementarity of the information flows that contribute to growth. Therefore, policies to promote balanced connectivity in many dimensions – one that focuses on trade, migration and FDI – is more beneficial than focusing on a policy to enhance only one. Indeed, reducing connectivity in one dimension may have adverse impacts on growth derived from other dimensions. Proposals to reduce migration flows, for example, may have adverse consequences for the growth‐enhancing benefits of trade and FDI flows.

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