decoding complexity

complex systems update
I was recently asked to write something about the study The Network of Global Corporate Control in The Montreal Review. This is what I came up with...

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DECODING COMPLEXITY

THE ORGANIZING PRINCIPLES BEHIND OUR ECONOMY

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By James Glattfelder

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The Montreal Review, April 2012

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"We spend billions of dollars trying to understand the origins of the universe, while we still don't understand the conditions for a stable society, a functioning economy, or peace."

Dirk Helbing, Professor of Sociology at ETH in Zurich (source)

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It sounds paradoxical, but today it appears that we understand more about the universe than our society. We have created systems, that have outgrown our capacity to genuinely understand and control them. Just think about the Internet or the financial markets.

On the one hand, we are drowning in data. In 2007 Wired magazine heralded the arrival of the "Petabyte Age", plagued by the data deluge. Endless streams of data are continually flowing along global information super-highways, being stored in countless server farms around the world. On the other hand, while data can be mined and its potential harnessed, the biggest obstacle in understanding our own constructed socio-economic world has been nearly invisible. It came in the guise of a weltanschauung and is being currently conquered by a paradigm shift in understanding.

Our traditional ways of thinking and problem solving have been strongly shaped by the success of the reductionist approach taken in science. The fabric of the universe is broken down into its constituents, who's interactions are described by four fundamental forces. Information is boiled down to an irreducible physical entity: the bit. This thinking has been at the heart of the Scientific Revolution and the dawning of the Information Age, unlocking spectacular technological prowess. Put in the simplest terms, the focus has been on "things". Tangible, tractable and malleable.

Not so long ago, it was realized that there is an other, a more subtle dimension to our reality: things are not isolated! Ideas like interconnection, co-dependence and collective dynamics entered the stage. Indeed, this is the aspect of our world that has changed most in the past decades. While the things themselves still look pretty much the same, they have become highly networked and interdependent. The tools to grapple with this new era come from the field loosely known as complexity science.

In 1972 the Nobel laureate P. W. Anderson wrote an influential article in Science, planting the seeds for this new science, emerging from systems theory and cybernetics:

"At each stage [of complexity] entirely new laws, concepts, and generalizations are necessary [. . .]. Psychology is not applied biology, nor is biology applied chemistry."

Understanding a systems components' individual properties does not bring insights into how the system will behave as a whole. Indeed, the very concept of emergence fundamentally challenges our knowledge of complex systems: self-organization allows for novel properties to emerge, features not previously observed in the system or its components. The whole is literally more than the sum of its parts.

Although the paradigm shift, moving away from reducing to components towards analyzing interactions, seems to entail hopelessly complicated systems, it is a notable fact that also complex systems are characterized by laws and regularities. Most prominent are scaling-law distributions, also called power laws. Like a normal distribution, it quantifies what the frequency of an observed trait in a population is. Scaling-law distributions have been observed in an extraordinary wide range of complex systems: from physics, biology, earth and planetary sciences, computer science, demography and finance to the social sciences. In a nutshell, a scaling law says: most components are unimportant, very few are very important.

Regarding economics, already in 1897 V. Pareto observed that household income is distributed according to a scaling law. Called the Pareto principle, or the 80-20 rule, this still holds today. The aphorism introduced at the end of the last paragraph has a whole new quality, now that it describes the realm of human affairs: nearly all have very little and very few have very much. Suddenly a general organizing principle of reality has an unjust and undemocratic feel to it.

The Network of Global Corporate Control 

A recent example uncovering the patterns in an economic system, raising the issues of concentrated power, systemic risk and market competition, is the study: The Network of Global Corporate Control [1].

Complex systems find a natural formal representation as networks, where the links describe the interaction structures. The study of complex networks has been extremely fruitful in the past decade and has uncovered many features of the physical, biological and social worlds. This is quite remarkable, as complex systems are usually very hard to understand employing mathematical equations, i.e., applying the standard scientific approach.

In the study, ownership data of 30 million economic agents (i.e., natural persons, foundations, government agencies, listed and unlisted companies, etc.) from early 2007, located in 194 countries, was analyzed. By focusing on the 43,000 transnational corporations (TNCs) in the sample, a network was constructed with 600,000 nodes and 1,000,000 links (all numbers are approximations).

Already the topological structure of this ownership network reveals a surprising organizational structure. Whereas 64% of the TNCs are distributed among many small isolated clusters of a few nodes, the remaining 36% are located in a single giant connected network of 460,000 nodes. Interestingly, this minority of TNCs accounts for 94% of the total operating revenue of all TNCs. Moreover, the 460,000-node network has a tiny but distinct core of 1,300 nodes, seen in Figure 1.

Figure 1 (PLoS ONE)

By introducing a methodology that estimates the potential degree of control resulting from a network of ownership relations, it is possible to identify the most important nodes. It turns out that 730 top shareholders are able to control 80% of the operating revenue of all TNCs. Furthermore, combining the knowledge of the topology with the ranking of shareholders, it is revealed that the 1,300 nodes in the core are comprised of the most powerful nodes in the network: the top economic agents are interconnected and do not carry out their business in isolation (a small excerpt is given in Figure 2). Finally, the core is able to gain 39% of the potential control.

Although these numbers show an unprecedented high level of concentration, simulations suggest that this could all be the result of the interaction rules in the system. Contrary to common intuition, it is not necessary to have a puppet-master behind the scenes, orchestrating such a large concentration of power for self-enrichment. Inequality can be an emergent property. It is also an interesting side note, that the complex systems paradigm, with its empirical and data-driven foundation, its interaction-based methodology, is only very slowly being adopted in economics and finance.

Figure 2 (PLoS ONE)

Where Do we Go from Here?

These observations could possibly have very important implications for the global economy. The observed organizational patterns could endanger market competition and financial stability. "Too connected to fail" being the next predicament our economy faces. However, in order to validate these concerns an additional interdisciplinary effort is required.

This is the current state of things in dealing with socio-economic systems. We can improve our understand of their organizing principles, highlight potential weaknesses and looming threats. But to give concrete advice and formulate effective policies is a whole different story. Ambitious, long-term and highly-funded programs like futurICT (an EU FET Flagship Initiative), the UN's GlobalPulse or the US' Big Data R&D Initiative are currently trying to close this knowledge gap. The efforts aim at crafting new technologies and innovations building on a complex systems point of view, but are still at the level of data collection or project formulation.

Ideas relating to economics, finance, politics and society are very often tainted by individual ideologies. In contrast, decoding the complexity of our world by considering its interconnected and interactive nature, not only brings novel understanding, but perhaps also allows for a neutral perspective to emerge in the not too distant future. Reality is so complex, we need to move away from dogma.

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James B. Glattfelder holds a M.Sc. in theoretical physics and a Ph.D. in the study of complex systems, both from the Swiss Federal Institute of Technology. He co-authored the study "The Network of Global Corporate Control" which was recently covered in dozens of news media world-wide and sparked controversial discussions. He is a senior researcher at Olsen Ltd, a quantitative FX investment manager in Zurich, focusing on market-stabilizing algorithms. His interests include the philosophy of science next to societal issues. You can follow him here http://twitter.com/jnode and here http://gplus.to/jnode, and read his blog here http://j-node.blogspot.com/.

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[1] Stefania Vitali, James B. Glattfelder and Stefano Battiston; PLoS ONE 2011, 6(10): e25995; 2011
(Watch a TEDx talk about it.)

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the network of global corporate control - revisited

complex systems, vast amounts of data and self-organization...

We spend billions of dollars trying to understand the origins of the universe, while we still don't understand the conditions for a stable society, a functioning economy, or peace.

(D. Helbing quoted from here)

The publication The Network of Global Corporate Control --- watch a TEDx talk about it --- has gained quite some attention in the news (for instance, sciencenews.org and newscientist.com, which went viral) and the blogosphere (for instance, planetsave.com, physorg.com and johncarlosbaez.wordpress.com). Because some reactions have been particularly hostile, for instance Ms. Yves Smith from Naked Capitalism (see also our responses here and in their comment section), or have inspired the conspiracy theory camp, please let me recapitulate what our paper is and isn't and address some of the voiced concerns, in order to avoid misconceptions. (If you are only interested in our responses to critiques - for instance, computing control from ownership and the notion of control in the financial sector  - please see Section 8 below.)

Ownership network, more info and 3d video on youtube.

In a nutshell, it's an empirical and interdisciplinary effort to understand a vast economic dataset using methods from the study of complex networks. The analysis focuses, on the one hand on ownership, and on the other hand on control, and reports novel findings for both. It should be noted that ownership is an objective, measurable quantity and that control has to be estimated from it. As in all fields of science, classification and quantification are the first necessary steps in the process of in-depth understanding of novel phenomena.

You are also cordially invited to join the discussion at PLoS ONE, where our paper is "available for commenting and debate by the readers, making [it] the start of a scientific conversation".

1.) The dataset

It is comprised of ownership relations of 37 million economic agents (natural persons, families, foundations, government agencies, listed and unlisted companies, etc.) from early 2007, located in 194 countries. We identify and focus on about 43k transnational corporations (TNCs) in 116 countries, defining a network of 600k nodes.

It is Bureau van Dijk's commercial Orbis database, used, among others, by reinsurance companies, banks and government agencies.

We started in 2007 with our first cross-country study and then did this current global analysis. Yes, it would be very interesting to analyze a more recent network snapshot. However, it is also interesting to see the network shortly before the financial collapse in 2008. Moreover, other national ownership network studies have shown that clusters of powerful agents were very resilient and unaffected by external forces ([3] and [4]). So perhaps the observed power-structure in this 2007 dataset is still surviving the turmoil today...


2.) The research questions 

a.) What is the global architecture of ownership (e.g., TNCs may remain isolated, cluster in separated coalitions, or form a large connected component)?

b.) How is control distributed globally?

c.) Who are the key economic actors?

Sample of the international financial network, where the nodes represent
major financial institutions belonging to the core and the links give the 
strongest existing relations among them; node colors indicate different
geographical areas: EU (red), US (blue), other countries (green); the 
width and the darkness of the links show their weight; only the most 
prominent links are shown; the network shows a high connectivity, 
with many mutual cross-shareholdings as well as longer cycles; this 
indicates that the financial sector is strongly interdependent, which 
make the network vulnerable to instability, see [1] or [2].

3.) Methods

a.) Our novel methodology extends the known methods for computing control from ownership, and remedies their shortcomings.

b.) Control is proxied by the potential control over the TNCs operating revenue, referred to as network control in the paper. This estimate the percentage of control from the network of direct and indirect ownership relations (using three different models) and multiples this level of control with the operating revenue of the firms a shareholder is connected to (directly and indirectly).

c.) This measure of control can be understood as a quantity flowing through the network, as the methodology is highly attuned to indirect relations between nodes.

d.) Our study is also relevant to the field of complex networks in general, since the methodology can be applied to discover influential nodes in any network where resources are flowing along weighted directed edges.


4.) Novel findings

a.) The network is seen to organize as follows: there are many (~23k) small clusters of connected nodes (called weakly connected components) and then there is one huge connected component, where 77% of all the nodes are located. See the scaling-law distribution of the sizes of the weakly connected components in Figure S6 in the Supporting Information. Interestingly, although 64% of the TNCs are scattered among the many small connected components, they only account for 6% of the operating revenue. In other words, 1/3 of the TNCs are found in the huge connected component and represent nearly all the value. See Figure 2B in the main text.

b.) The topology of this largest weakly connected component has a tiny, but dominant core (in network speak: the largest strongly connected component defining a bow-tie topology) of about 1300 mostly US and GB financial intermediaries. This observation has possible implications for global systemic risk and global market competition (see more in item 7.).

c.) The economics literature would have us think that ownership relations of US and GB financial institutions should not organize as a tightly-knit group owning the majority in each other (i.e., cross-shareholdings and business groups,  the paradigm of widely held firms, and the Atlantic or stock market or arm's-length "type" of capitalism, see references in Section 1.2.2 in [1])

d.) The distribution of control (i.e., the potential control over the TNCs value) is unprecedentedly skewed. It takes the shape of a log-normal distribution (see Figure S3 of the Supporting Information) and is roughly an order of magnitude more unequally distributed than wealth (in developed countries). To give some numbers:
i.) 737 top economic agents in the network of 600508 nodes control 80% of the value (operating revenue) of the 43060 TNCs.
ii.) The core, comprised of 1318 nodes, holds 39% of the control.
iii.) There are 147 top agents in the core, controlling 38.4%.

e.) The top actors are in the core and hence are interconnected and do not carry out their business in isolation.

Observe, that findings a.) to c.) are based solely on the objective ownership data, and require no computation of control. Additional information here and here.


5.) Bottom line

a.) Economists are only slowly starting to turn their attention to economic networks. This said, there is an interesting gap in the literature regarding the tools and models used to do so (see Section 1.2.3 in [1]). This is the first analysis of a global dataset on ownership, using a complex networks approach.

b.) It is a starting point for future research. Determining the true implications is up to other scholars to debate on.

c.) Open question: is the core of top actors an emergent property or the result of planned coordination? We tend to think it is an emergent property of the network dynamics.


6.) What the paper isn't

a.) Pushing an economics or socio-political agenda.

b.) Promoting conspiracy theories.

c.) An exact, unambiguous measurement of real-world control.
"Because interpreting and analyzing these kinds of data is difficult, [Davis] says, the analysis serves more as  'an impression of the moon's surface you get with a telescope. It's not a street map.'" Gerald Davis, economist at the University of Michigan in Ann Arbor, quoted from here.

d.) Alleging that the top agents are colluding.


7.) Why study ownership networks?

a.) Previous studies looked at the impact of globalization forces and corporate governance reforms over time on the network topology and found that there was an unexpected resilient structure of powerful agents which was unaffected by these external forces [3,4].

b.) A cross-country analysis revealed that in markets with many widely held corporations (mostly in Anglo-Saxon countries), this local distribution of ownership actually goes hand in hand with a global concentration of ownership (and control), only visible from the bird's-eye view given by the network perspective [5].

c.) Complex ownership patterns, such as cross-shareholdings (e.g., when firms mutually hold shares of each other), are extensively studied motifs in the corporate governance literature and correspond to strongly connected components in networks. Previous studies (on small samples) have shown that cross-shareholdings significantly reduce competition. Accordingly, antitrust institutions all around the world take the existence of complex cross-shareholding structures very seriously. However, they lack the analytical and quantitative tools to deal with large networks.

d.) For some time economic theory has supported the idea that more connected networks are more stable. In contrast, recently, the work of some scholars as well as the view of some authoritative policy makers predict that a higher level of interconnections among financial institutions can lead to higher systemic risk [6].

e.) The network structure matters: the presence of indirect links can significantly amplify the control (or ownership) held by certain economic agents. If one defines the leverage as the ratio between the control we compute, which takes into account the whole network, and the direct control of agents, the resulting probability distribution is scale free (see Figure 4.10 and Section 4.3.3 in [1]). This means that some agents are able to gain a high level of control because of the presence of indirect ownership relations. Usually, this happens by shareholders having control over small firms, which in turn control larger corporations and so forth. Such ownership structures are also called pyramids but were never studied at a global level. Recall the pyramidal group of indirect ownership around Marco Tronchetti Provera, allowing him to control Telecom Italia, one of the world's largest telecom companies, with a disproportional small amount of equity.

f.) General network measures have meaning in ownership networks: the (scaling-law) distribution of the out-degree gives a measure of portfolio diversification (see Figure S5A in the Supporting Information); the distribution of the sizes of the weakly connected components gives a measure of how integrated or fragmented a market is (see the scaling-law distribution in Figure S6 in the Supporting information); the position of an agent in the network can be indicative of its importance.


8.) Problems'n'Answers:

P1: "OMG they discovered financial institutions hold shares! What a scandal!"
A1: It is obvious that large mutual funds own many shares. However, what we are saying is that the potential control they have is surprisingly high. A portfolio manager would arguably go for a diversification strategy and not a controlling one.

P2: "Everybody knows this. It is all so obvious."
A2: There is a big difference between suspecting the existence of a fact and in empirically demonstrating it. We are not aware of an existing study which gives actual empirical evidence of these findings, which some common wisdom indeed anticipated.
"'This is empirical evidence of what’s been understood anecdotally for years,' says information theorist Brandy Aven of the Tepper School of Business at Carnegie Mellon in Pittsburgh." (quote from here).

P3: "You cannot really infer control from ownership."
A3: The separation of ownership and control has been debated in the scholarly literature for decades (see references in Section 6.2.1 in [1]). Although there are many aspects which make the estimation of control from ownership hard to asses (nonvoting shares, dual classes of shares, multiple voting rights, golden shares, voting right ceilings, proxy votes, etc.), researchers have provided, and extensively used, different simple models believed to proxy the control gained from ownership, such as the linear model, assuming the one-share-one-vote principle, or a threshold model, assigning unequivocal control if the percentage of ownership exceeds the threshold. Quite a lot of attention has been devoted to the analysis of ownership and control of individual corporations and of small groups of firms, but never has a large ownership network been investigated. In [5] we added a novel model, that looks at the relative distribution of shares. Even with a small shareholding, if all others hold significantly smaller shares, this model assigns a high level of control.

We computed control using all three fundamentally different models. Neither the topology of the network, nor the distribution of control, nor the identity of the top holders significantly changes in these different scenarios. This unexpected robustness, or invariance, of such global control measures is encouraging, because it means that neither are the models computing arbitrary numbers, nor can the three models have the same bias in computing control the wrong way. So, although for individual agents the computation of direct control can appear arbitrary, the existence of this "aggregated" agreement in the computation is indeed a positive indication that the results are in fact not just spurious or an artifact of the model details. But, as we caution, these numbers are, in any case, an approximation.

P4: "But funds don't exert control."
A4: The question, if funds do or do not exert control, is still being debated in the scholarly literature. It is known that US mutual funds do not always seek to exert control. However, this applies only to them operating in the US. Indeed, the same funds have been shown to exert their power when operating in Europe. We are not aware of a systematic global study about the control financial institutions wield over the companies they have ownership in world-wide. Moreover, control is defined in these studies in a very specific way (for instance the propensity to vote against the management when it comes to issues of corporate governance). In any case, there are 49 mutual funds among the top 737 top holders.

Control can be exerted in ways which are not always visible. We state: "For example, a mutual fund owning some percent of a large corporation may try to impose job cuts because of a weak economic situation. This can happen: (i) without voting and (ii) although the fund does not plan to keep these shares for many years. In this case, the influence of the mutual fund has a direct impact on the company and its employees. Furthermore, mutual funds with shares in many corporations may try to pursue similar strategies across their entire portfolio." Moreover, studies on the network of directors, the boards they serve on, and the interlocks, have revealed these networks to be scale free [7]. This means a few directors are on very many boards. These ties could also be seen as potential channels, through which control can be exerted covertly, when the directors meet in person.

In being cautious, we cannot exclude that the top holders we identify do not globally exert their power in some way. Especially, if we allow for the fact, that control can also be exerted covertly. This is why we talk about potential power in the context of the control numbers we compute. Even if some top holders indeed do assume a passive role, this could be by their own choosing and change anytime.

For references, consult Section 6.2.5 in [1]. and generally Section 6.2 for more concerns that have been addressed.


9.) And finally...

As the world around us is becoming more complex and interconnected, and indeed so at an increasing speed, we believe in the following, in order to try and gain more understanding:

a.) Keep an open mind and question all assumptions, also supposedly established ones.

b.) Let the data speak, not dogmas.

c.) Take the interconnectedness serious: look for and try and understand the network behind complex phenomena.

d.) Use formal tools that can deal with huge amounts of data and complexity in general.


10.) Sources

[1] Ownership Networks and Corporate Control: Mapping Economic Power in a Globalized World, J.B. Glattfelder, 2010
[2] Industrial organization from a geographical and network perspective, S. Vitali, 2010
[3] (Kogut and Walker, 2001)
[4] (Corrado and Zollo, 2006)
[5] (Glattfelder and Battiston, 2009)
[6] (Battiston, Delli Gatti, Gallegati, Greenwald and Stiglitz; 2009)
[7] (Battiston and Catanzaro; 2004)