1

John Loser & Edward Segel CS224W Final Project: Group 7 International Trade Cascades Introduction Global trade has increasingly entangled the economies of geographically distant countries. In this paper, we analyze how an economic shock in one country can cascade through trade networks to impact the economies of other countries. In particular, we examine how changes in a country’s growth can affect global trade flows and international growth. Traditional economic analysis often considers how a slowing economy affects the growth of its trading partners1. For example, a slowing US economy imports fewer goods from China and thus slows Chinese growth. However, the analysis usually stops here. There are additional second-order feedback effects which typically get ignored. For example, a slowing Chinese economy will in turn import fewer goods from the US, further slowing US growth beyond the initial slowdown. The international trade network is replete with these feedback loops. Prior work (Kali, Reyes) refers to these second-order phenomena as a “cascade of interdependent ripples” (pg. 6). These loops have become more complex over time as countries increasingly trade with multiple trading partners and global supply chains. The chart below shows the dramatic increase in global trade as a percent of world GDP, rising from 25% to 55% over the past several decades.

This paper first builds a model of the global trade network that exhibits (i) directional weighted edges, and (ii) a powerlaw distribution of degrees both regionally (between nearby countries) and globally (across all countries). We then compare how this model compares to the real-world trade network in terms of standard network measures such as degree distribution, transitivity, and diameter. We then test a model of global trade cascades on our model, showing how changes in a country’s growth affect growth in other countries via trade flows. Applying this algorithm to the real-world network, we show that the global economy has become increasingly sensitive to country-specific changes in growth due to trade cascades.

                                                                                                               1 http://www.economist.com/node/21559944

2

We also use our model to show how the economic-influence of countries changes over time, explaining the financial adage that “when the US sneezes, the world catches a cold”. Prior Work Both cascades and the global trade network have long been studied by both economists and network theorists. Below we discuss prior work to provide context for analyzing network cascades in global trade flows. Cascades are a primary topic of academic network research. In one paper, Watts2 investigates information cascades in networks, exploring the properties of connectedness that determine the susceptibility of a network to a cascade (defined here as the tendency for small perturbations in the network to affect large numbers of nodes). The author develops a model for a network driven binary decision, wherein each node determines its state as a function of its neighbor’s states. All nodes are initially set to the same state and a small perturbation is introduced in the graph. At each time step a node is updated random and the spread of the perturbation through time is observed. The author analyzes this general model as applied to an arbitrary random graph and derives formula for cascade size as a function of each node’s state update rule and the overall graphs connectedness (encapsulated by the random graph’s average degree). Notably, the author concludes that the distribution of vulnerable nodes (those that switch states with only one activated neighbor) is a critical indicator of cascade size, as the “triggering” of even a single sufficiently-large vulnerable cluster can be enough to create a cascade through the entire connected component. The paper appropriately focuses on the boundary conditions and nodes that result in cascades. Network theory has been applied to economic phenomena, though this is surprisingly uncommon. Schweitzer et al. provide a broad overview of emerging applications of network theory to macroeconomic questions3. The authors motivate the need for a network-driven approach to modeling the complexity and interconnectedness of economic networks ranging from international trade and supply chains to financial credit and investment networks. The authors categorize the existing literature as largely approaching network economies from a micro perspective, rooted in game-theoretic considerations, where the focus is on individual node behavior and the evolution of specific edge relationships. This research does not capture large-scale network characteristics that economic networks exhibit. For example, trade and banking linkages have been shown to exhibit scale-free properties while foreign direct investment (FDI) has been shown to observe a power-law scaling. The authors note the immaturity of this work, however and indicate a need for significant further research. In particular, the lack of research into information cascade behavior (a key feature of observed economic phenomena, which follow boom-bust cycles) is noted but little effort is made to place that research in the more central role it deserves. The exception to this assessment is by Kali and Reyes (2005) who explain the transmission of economic events through the structure of international trade networks, arguing that a country’s integration into the global trade network is directly related to its susceptibility to financial contagion. The authors observe the contagion aspect of financial crises, how “an initial country-specific event [is] rapidly transmitted to markets around the globe” (pg. 1). The research hope to answer the following question: do trade interdependencies help amplify or dissipate economic contagion? The authors find that a more interconnected trade network comes with pros and cons. A shock originating from a particular country (node) is more likely to cause contagion if that country is strongly integrated into the trade network.

                                                                                                               2 Watts.  A  simple  model  of  global  cascades  on  random  networks     3  Schweitzer  et  al.  Economic  Networks:  The  New  Challenges

3

However, a country that is well integrated into the global trade network is better able to diversify away the effects of incoming contagion. This analysis helps explain why some historical crises led to contagion (e.g. Asian crisis in 1997) while others didn’t (e.g. Latin America in 2000). Kali and Reyes use a binary approach to determine connections between nodes, drawing edges for any trade channels exceeding a certain threshold. The result is a node-matrix filled with 0s (no connection) and 1s (connection). This is certainly an appropriate “first pass” of the data. However, it ignores magnitudes of trade between countries. According to their methodology, countries with trade linkages of magnitudes {1,1,1,9} and {5,5,5,5}, have equally diversified trade networks, but in reality the first country is far more susceptible to a single partner node. Thus it is important to consider the magnitude and distribution of trade connections, especially since these distributions often observe “power law” distributions, with certain trade partners being far more important than others. Importantly, our analysis differs from the previous research by exploring cascades in the real-world directional weighted trade graph. Unlike Watts, we test cascades on a real-world graph that is powerlaw distributed with high clustering and preferential attachment. Unlike Kali and Reyes, we use weighted edges to capture which countries (nodes) have greater influences on the global economy through trade flows (edges). Overview of the Data The global trade network is comprised of exports and imports between countries. Importantly, for our network analysis, it is important to collect bilateral (i.e. country-to-country) trade data rather than each country’s aggregate trade with the world. Since one country’s exports is another country’s imports, the trade network can be fully described simply with only imports or only exports. Reported import numbers tend to be more accurate since custom agents typically use more rigorous accounting for goods entering the country (for tax collection purposes) than goods leaving the country.4 As a result, our data collection process focuses on imports to one country from another. In cases, where no bilateral import data is reported, we use the corresponding export data when available. We use bilateral trade data from two sources: (1) Correlates of War, and (2) UN Comtrade. Below we describe each of the sources: Correlates of War (COW) Trade Dataset5 provides annual bilateral trade data from 1870-2009, though not all countries contain the full history. All data is reported in current (2009) USD. Established at the University of Michigan, the COW organization “seeks to facilitate the collection, dissemination, and use of accurate and reliable quantitative data in international relations”6. UN Comtrade7 is the United Nations gold-standard trade database with monthly bilateral trade data from 1997-2012. Importantly, this dataset also provides bilateral trade data for specific product classifications (e.g. oil, electronics, vehicles). While not immediately relevant for this paper, this granularity will be important for our future work. The database can be accessed through an API.

                                                                                                               4 http://www23.statcan.gc.ca/imdb/p2SV.pl?Function=getSurvey&SDDS=2201&lang=en&db=imdb&adm=8&dis=2 5 http://www.correlatesofwar.org/COW2%20Data/Trade/Trade.html 6 http://www.correlatesofwar.org/ 7 http://comtrade.un.org/

4

We use COW to analyze how the global trade network has evolved over the past several decades. However, in future work we will refine this analysis using Comtrade since its granular monthly data enables more accurate parameter estimation. The visualization below presents an example of the network structure of the international trade data. We have created the global network for trade in oil. Each node represents a country, and the nodes are scaled according to the value of oil exports emanating from the country. The edges between country nodes represent trade in oil between two countries, with larger flows illustrated using thicker lines. Finally, we have highlighted the node and edges representing US trade to illustrate the highly connected nature of the trade network.

Finally, we collect GDP statistics for all countries to understand the contribution of trade to GDP growth (and consequently to a country’s demand for imports). Historical GDP data comes from the World Bank which provides annual GDP data for each country in current USD back to 1980.

Network Model While research regarding the weight distribution of international trade is uncommon, Serano and Boguna [1], among others, have observed that unweighted international trade linkages observe an approximate power-law distribution. We therefore generate a directed weighted graph in which the weights on each link are assigned according to a power-law distribution, with set proportions distributed both locally to reflect regional clustering and globally to reflect preferential attachment to the largest economies. The map below highlights the distribution of trade for the United States between both regional and global trade partners.8

                                                                                                               8 http://en.wikipedia.org/wiki/List_of_the_largest_trading_partners_of_the_United_States

5

We model the real-world trade network by distributing trade both locally and globally according to powerlaw distributions. Our simulated graph begins with a complete set of nodes and no edges. We then assign each node a magnitude m drawn randomly from a powerlaw distribution (α=2) to reflect the empirical distribution of GDP. We model regional connectedness for each node by establishing weighted directed edges to the n closest nodes (with proximity determined by node number in the graph). Edge weights are determined jointly by (i) a parameter dictating the percent pL of trade allocated locally, and (ii) the relative magnitudes of the destination nodes. We model global connectedness by establishing weighted directed edges to g nodes randomly drawn from the graph, where the probability of drawing a node is proportional to its magnitude m and the weight is again proportional to 1-pL and the relative magnitudes m of the destination nodes.

Cascade Model We model the impact of country-level shocks to growth and trade as cascades through a weighted directed graph, where each node represents a country and the weight on each edge indicates the value of bilateral trade between two countries. We use the convention that an edge points to the recipient country for each trade relationship. Thus the edge A → B represents exports from country A to country B (imports of B from A). We then examine information diffusion through this stylized network. Economically, shocks to trade propagate through the international trade network through their effects on growth. A country that has seen a sudden decline in exports (due to an external trade shock) will experience weaker than expected growth, holding other economic variables constant. This weaker than expected growth is typically reflected in a reduction in imports, as the affected country has less national income to spend on imported products. From the perspective of the country’s trading partners, this fall in imports can be seen as a shock to the trading partner’s exports to the initial country, thus transmitting the initial trade shock to all of the country’s trading partners, who in turn transmit it to their trading partners, and so on. Cascades are triggered by sending an impulse through one or more edges in the graph. At each subsequent time step, nodes aggregate the received impulses (that is, the total change in weight across all outgoing edges) and “respond” by emitting a uniform proportional impulse to the weights on all incoming edges (i.e. decreasing imports from all trading partners proportionally) in accordance with a linear response function 𝑦  =  𝑎𝑥, where x represents the aggregate received impulse and y the emitted impulse. All nodes are assumed to update simultaneously once per time step. The initial impulse

6

propagates through the network during subsequent time steps until the graph reaches an equilibrium, at which point the total effect of the initial impulse on the system can be examined. It is important to note that 𝑎  >  1  results in a positive feedback loop (amplifying the initial impulse) while 𝑎  <  

1   results in a negative feedback loop (dampening the initial impulse). In real-trade data, we expect 𝑎  <  1  

such that the initial impulse will diminish as it cascades through the network. This model allows for significant flexibility and generality in modeling economic shocks to the international trade network. For instance, a shock to growth in a single country A could be initially represented as a proportional decrease in the weight (value of trade) across all in-edges of node A (i.e. a uniform reduction in imports of A from all of its trading partners). Likewise, a shock to trade between two trading partners (i.e. a trade war or economic sanctions) could be modeled as a reduction in the weights on both edges connecting the two nodes. Analysis Methodology We first construct a stylized model of the trade network and compare the properties of the model with the properties of the real-world trade network. We analyze a series of cascades across the stylized graph in an effort to understand the general properties of cascades across such a network as a function of the magnitude and placement of the initial cascade. With this background in place, we construct networks for each year of available international trade data and examine cascades across these networks. We begin by analyzing a simplified version of our model in which the linear impulse response parameter is constant across countries, and we then turn to a more realistic version of our model in which the parameter is estimated via a country-level regression model of the form 𝑦  =𝑎  /  (𝑖𝑚𝑝𝑜𝑟𝑡𝑠  /  𝐺𝐷𝑃)  ∗  𝑥  , where again x is the aggregate export shock, y the transmitted import shock and a the calculated transmission coefficient. The additional term, 𝑖𝑚𝑝𝑜𝑟𝑡𝑠  /  𝐺𝐷𝑃 (imports as a percentage of total GDP for a given country), is a scaling parameter designed to account for the variation in trade openness between countries and within countries over time. Including this scaling factor allows us to more directly examine the country-specific variations in transmission sensitivity and assess their stability over time. Results Our results consist of two sections. First we compare the statistical properties of our network model to the real-world trade network. We then simulate cascades on our model to determine the model’s sensitivity to individual nodes. Finally, we simulate cascades on the real-world trade network and determine the global economy’s sensitivity to individual countries, both presently and historically over time. Model Results We first constructed a simulated trade network consisting of 179 nodes to match the number of countries in our real-world dataset. Based on empirical data, we vary regional trade from 10-30% of a country’s total trade, thus allocating more than 70% to global partners. We also vary the region size from 10-30 nodes. Both the simulated network and the real-world network are nearly fully-connected graphs due to the large number of edges. To analyze network properties, we trim the graph by only considering the top 20 out-

7

edges for each node, typically eliminating edges with less than 1% of total outgoing weight. Table 1 provides network statistics for both the real-world network and various simulated networks built from different parameters. Based on these statistics, our model does a good job capturing the characteristics of the real world network. Chart 1 shows the normalized in-degree distributions for both networks.

Table  1:  Simulated  Network  Summary  Statistics  

Chart  1:  In-‐Degree  Distribution  [i]  (Log-‐Log  Scale,  Normalized)  

We then apply our cascade model to our simulated network. We examine the relative importance of various nodes to the overall graph by analyzing the total cascade size produced by 1% shocks to node-size for each individual node. Table 2 shows the Top 10 influential countries from this simulation. Note

8

that larger countries have more impact than smaller countries—this reflects the fact that our model provides larger countries with more in-going degrees, thus allowing cascades to reach more countries.

Table  2:  Top  Nodes  by  Global  Impact    

Real-World Results We now turn to the economic properties of the real-world trade network. For our initial analysis, we used average trade and GDP data from the five years 2004-2009 to smooth out annual fluctuations and establish a baseline for the structure of the trade network. We examined the relative importance of various countries to the international trade network by analyzing the total cascade size for shocks to growth in each individual node. For each country, we assume that imports respond proportionally to GDP (i.e. that a 1% reduction in GDP would lead to 1% fewer imports) and apportion the total impulse to imports across all trading partners such that the impulse to any individual trading partner follows ∆𝑖𝑚𝑝𝑜𝑟𝑡𝑠𝑛  =∆𝐺𝐷𝑃∗  (𝑖𝑚𝑝𝑜𝑟𝑡𝑠𝑛  /  𝑖𝑚𝑝𝑜𝑟𝑡𝑠𝑡𝑜𝑡  ). By evaluating the total shock to world trade (and by extension world GDP, since trade factors directly into GDP accounting), we gain a measure of the importance and centrality of each country node to the overall trade network. Table 3 below lists the ten highest importance countries according to this metric, evaluated under both the linear model (with 𝑎=  .5) and the economic model (with 𝑎=  3).

Table  3:  Top  Countries  

 

 

9

Chart 2 shows the log-distribution of relative impact magnitudes. For these parameter values, the economic and linear models comport extremely closely both with each other and with observed trade and GDP relationships, though minor variation in node ranking is still evident.

Chart  2:  Log  distribution  of  relative  node  shock  impact  on  World  GDP  

 We examined the sensitivity of these results by varying the parameter a, which proxies for the trade openness of countries in the network, in order to understand the susceptibility of the international trade network to cascade behavior as globalization increases. As seen in Chart 3, our results indicate a clear non-linear relationship between trade openness and cascade size. It is clear that increasing openness to trade in the global economy increases, rather than decreases, the fragility and susceptibility to cascade of the overall system.

Chart  3:  Effect  of  1%  shock  to  highest  importance  node    

for  various  values  of  cascade  parameter  a.  

 

10

In order to capture time series data on changing cascade sensitivity in the international trade network, we constructed the trade network for each year from 1961 to 2009 and examined the cascade size for a global 1% GDP shock. In other words, we perturbed each trade network by simulating a simultaneous 1% shock to domestic demand (GDP) at every node, simulating the impact of a coordinated global shock such as that experienced during the 2008 Financial Crisis. We compared the final equilibrium trade levels to initial trade levels and projected these impacts to GDP, offering an insight into the multiplier effect created by trade cascades. Chart 4 below illustrates the evolution of this sensitivity over the period 1961-2009. We see a clear pattern of increasing connectivity interrupted temporarily during recession periods in 1980, 1990 and 2000, reaching peak connectivity in 2006 just prior to the onset of the financial crisis. By 2009, trade connectivity had fallen to levels last seen in the late 1990s, and it is highly likely that more up-to-date data would show further reduction in the level of global connectedness across the trade network.

Chart  4:  Ratio  of  initial  shock  to  final  cascade  impact  for  simultaneous  global  shocks,  1961-‐2009  

Finally, we examine the changing importance of countries to the international trade network over this period. Chart 5 below shows the evolution of node importance (using the same criteria as the table above) for several of the largest countries in the economy. Chart 6 removes the United States in order to highlight the dynamics between the other countries, most notably the rapid, almost exponential ascent of China to become the 2nd most influential and connected node for the global economy, trailing only the United States. These graphs strongly match economic intuition.

11

Chart 5: Evolution of Shock Significance for the Largest Nodes, 1961-2009.

Chart 6: Evolution of Shock Significance, 1961-2009, excluding United States

Conclusion We model cascade behavior through simulated and real-world trade networks. We demonstrate a non-linear relationship between the cascade parameter a and the magnitude of the resulting cascade. Increasing this parameter economically represents increasing a country’s openness to trade (defined as imports as % GDP). Our results show that a more open trade network amplifies the effect of individual country growth on the global economy. This contributes to our understanding of the magnitude of the recent financial crisis and its surprising consequences for global growth.