Stability of the world trade web over time
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My talk for a conference on Emergent Risk at Princeton in 2012. The paper discusses notions of stability and robustness in networks, with applications to the world trade web.
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Stability of the world trade web over time
- 1. Stability of the World Trade Web over time. Scott Pauls Department of Mathematics Dartmouth College Conference on Emergent Risk, Princeton University September 28-29,2012
- 2. Stability of the World Trade Web over time. Scott Pauls Department of Mathematics Dartmouth College Conference on Emergent Risk, Princeton University September 28-29,2012
- 3. Systemic and emergent risk “Whereas systemic risk is the threat that individual failures or accidents represent to a system through the process of contagion, emergent risk is the threat to the individual parts produced by their participation in and interaction with the system itself.” (Centeno and Tham) Conference on Emergent Risk, Princeton University September 28-29,2012
- 4. Stability and robustness Structure We use network models: actors are nodes, relationships are edges. Dynamics We construct dynamics to model exchanges between the actors. Robustness We define robustness in terms of responses to shocks. Conference on Emergent Risk, Princeton University September 28-29,2012
- 5. World Trade Web nodes are countries. edges are directed and weighted, giving the dollars that flow from country i to country j for traded goods. dynamics are given by the Income-Expenditure model. Barbieri, Katherine, Omar M. G. Keshk, and Brian Pollins. 2009. “TRADING DATA: Evaluating our Assumptions and Coding Rules.” Conflict Management and Peace Science. 26(5): 471-491. Conference on Emergent Risk, Princeton University September 28-29,2012
- 6. Income-Expenditure model propensity to spend debt Markov model Conference on Emergent Risk, Princeton University September 28-29,2012
- 7. Attacks on the system Edge deformation: policy decisions, sharp trade evolution. Bilateral edge deletion: war, collapse of trade agreement. Node deformation: internal collapse (e.g. bhat collapse in the 1980s) Node deletion: unrealistic but useful as a type of worst case scenario Maximal Extinction Analysis (MEA): really a worst case scenario! Conference on Emergent Risk, Princeton University September 28-29,2012
- 8. Power and robustness Income after rebalancing Total initial income Conference on Emergent Risk, Princeton University September 28-29,2012
- 9. WTWs are “robust yet fragile” Left hand side: TARGETED ATTACK The strength of maximal attacks of each type. Colored bars (and circles) indicate significance. Right hand side: RANDOM ATTACK Circles indicate the proportion of all possible attacks which are not significant. Conference on Emergent Risk, Princeton University September 28-29,2012
- 10. The role of connectance Conference on Emergent Risk, Princeton University September 28-29,2012
- 11. The role of connectance Conference on Emergent Risk, Princeton University September 28-29,2012
- 12. A closer look U.S./Canada link U.S. deformation Conference on Emergent Risk, Princeton University September 28-29,2012
- 13. Conclusions and the big picture We see evidence that increased connectance has two effects related to systemic risk. 1. On one hand, denser connections allow for more paths through which shocks may be mitigated. 2. But, on the other, denser connection patterns provide more paths along which collapse can spread. These two are in tension. With regard to emergent risk, we see an additional wrinkle related to connectance coupled with the topology of the network. 3. Denser connections allow for propagation of shocks which, while possibly mitigated overall, can have adverse impact on individual countries. Conference on Emergent Risk, Princeton University September 28-29,2012
- 14. Emergent and Systemic risk In our model, the tension is resolved in different ways depending on the size of the shock. Systemic risk a. Smaller shocks are easily absorbed into the system (and sometimes result in income increases!). b. But, there is a tipping point above which the larger shocks spark a substantial contagion effect. Emergent Risk c. Even with smaller shocks, we see evidence that mere participation in the WTW brings new risk. d. Large shocks amplify this risk. We need a new lexicon to describe these types of networks. Conference on Emergent Risk, Princeton University September 28-29,2012
Notas do Editor
- This is from the proposal describing the conference. In the work I’ll describe, our system is a network of trade relationships – measurements of the import/export business that countries do with one another. In that context, we are concerned with both of these types of risk and, in many ways, view them as aspects of a broader measure of risk inherent to the system. Robust participation in trade has obvious benefits in terms of income, availability of goods, mobility, etc. But that same participation creates vulnerability. Distant, and perhaps small, economic events can have disproportionate effects on other members of the trade network, even those not directly impacted by the event. So, in our work, emergent risk (as defined here) has a component of simple exposure to systemic risk but also a component of risk associated to the pattern of interactions across the network. We consider this in the context of globalization, which both pushes countries into the trade network and encourages them to trade more widely. This has structural consequences for the WTW. To what extent does this impact the risk (whether emergent or systemic) of the system?
- So, how do we assess these types of risk – our paradigm rests on the analysis of the response of the network to shocks.Given a (well defined) shock to the system, how does the system respond? What is the functional damage to the network?The interaction of the dynamics and the network topology are crucial.Earlier work in this direction: percolation, contagion, robust-yet-fragile categorization of router networks.
- The method we use is based on extinction analyses in ecology, primarily those done on food webs. Basic result – increasing connectance (i.e. network density) corresponds to increasing robustness.
- Our adjacency matrix is denoted by M - we use the import matrices from the Correlates of War project. 𝑀𝑖𝑗 is the $ amount of imports into country i from country j.Our adjacency matrix is denoted by M - we use the import matrices from the Correlates of War project. 𝑀_𝑖𝑗 is the $ amount of imports into country i from country j.
- In strength = $ of income from selling goods, Out strength = $ expended buying goods from others𝛼 is the percentage of income that you will spend,𝛽 is money spend over and above the income𝑚 is the Markov chain associated withM. If everything is computed from a fixed data matrix, then 𝐸𝑡 is constant over time.In strength = $ of income from selling goods, Out strength = $ expended buying goods from others𝛼 is the percentage of income that you will spend,𝛽 is money spend over and above the income𝑚 is the Markov chain associated withM. If everything is computed from a fixed data matrix, then 𝐸_𝑡 is constant over time.
- MEA: delete node of highest power, rebalance and repeat until 50% of the income has been removed.
- Power measures the strength of a given attack. Suppose an attack changes in total $ from 100,000 to 90,000. Then Power = 1-90000/100000=1-9/10=1/10.Robustness takes the maximum power over all attacks of a given type. Using 1-Power transforms this into a number which is low if power is high and vice versa.
- Take-away: for all attacks, targeted attacks are usually significant (i.e. the damage spreads) and for all but node deformations, random attacks are generally not significant. Hence RYF. But there is some nuance, some years buck this trend and node deformations show fragility for both types of attacks.
- For the smaller shocks, we see a similar trend to the food web results – as connectance increases, we see increased robustness as well. But, for the edge shocks, there seems to be a decay after a critical juncture at roughly 0.4.The weakest result is (again) for the node deformation.
- However, in the face of the maximal extinction analysis we see a different trend – increasing connectance corresponds to decreasing robustness.Notes:There is a structural transition in the 1970s which causes a temporary jump in robustness.the jagged black line is the mean robustness over a family of bootstrap null models. We gauge the significance of the results in terms of different null models. The black circles here are years when 𝑅𝑀𝐸𝐴 is outside of the 5-95% range for the same statistic over 100 bootstrap nulls.However, in the face of the maximal extinction analysis we see a different trend – increasing connectance corresponds to decreasing robustness.Notes:There is a structural transition in the 1970s which causes a temporary jump in robustness.the jagged black line is the mean robustness over a family of bootstrap null models. We gauge the significance of the results in terms of different null models. The black circles here are years when 𝑅_𝑀𝐸𝐴 is outside of the 5-95% range for the same statistic over 100 bootstrap nulls.
- Impact ratio = ∑𝐸5−∑𝐸0𝑡𝑜𝑡𝑎𝑙 𝑒𝑑𝑔𝑒 𝑤𝑒𝑖𝑔h𝑡 (RHS)Impact ratio = 𝐸5(𝑖)𝐸0(𝑖) (LHS)Bilateral link deletion: (a) 75% of the attacks do less damage than their edge weight (and some, the negative ones), create more income. 25% of the attacks do more damage. (b) 2006, US/Can is largest impact link, so we look at it closely. These are the same ratios, but country by country after US/CAN is deleted. They are ordered, from smallest to largest, by the mean network distance between the country and the US and Canada. Note that there is little association between these two. This is one indication of emergent risk. No matter how far you are from the epicenter of a crisis, you can have substantial risk just from your participation and the pattern of network interactions in the global network.Node deformation:Different picture, percentages flipped – 25% do less damage, 75% do more. Now, geographical association is more apparent. Impact ratio = (∑𝐸_5−∑𝐸_0)/(𝑡𝑜𝑡𝑎𝑙 𝑒𝑑𝑔𝑒 𝑤𝑒𝑖𝑔ℎ𝑡) (RHS)Impact ratio = (𝐸_5 (𝑖))/(𝐸_0 (𝑖)) (LHS)Bilateral link deletion: (a) 75% of the attacks do less damage than their edge weight (and some, the negative ones), create more income. 25% of the attacks do more damage. (b) 2006, US/Can is largest impact link, so we look at it closely. These are the same ratios, but country by country after US/CAN is deleted. They are ordered, from smallest to largest, by the mean network distance between the country and the US and Canada. Note that there is little association between these two. This is one indication of emergent risk. No matter how far you are from the epicenter of a crisis, you can have substantial risk just from your participation and the pattern of network interactions in the global network.Node deformation:Different picture, percentages flipped – 25% do less damage, 75% do more. Now, geographical association is more apparent.
- On b): Substantial questions here – is the tipping point so large that we should never expect shocks of that magnitude (i.e. “too big to fail”)? Do we really have a framework in which to properly evaluate this question? (see, 2008 financial crisis)