A new study by William Easterly and colleagues at NYU may be a significant breakthrough for the use of complexity science concepts in international development.

In the growing community of complexity thinkers in the aid sector, those with a qualitative mindset have been rather more prominent than those taking a quantitative approach. Published papers on complexity and aid to date have been predominately, if not exclusively, qualitative in nature. Given the quantitative basis of much of complexity thinking, a greater balance in the mix of approaches would be no bad thing.

The recent World Bank publication of a report by William Easterly, Ariell Reshef, and Julia Schwenkenberg  (all at NYU) on ‘power laws’ in international trade may be an important step towards achieving such a balance. To understand why, we need a bit of background on power laws and their use in different contexts.

There is a growing movement (lucidly described by McKinsey Strategy Principle Michelle Zanini in June 2009) whose focus is the application of quantitative complexity theory to social, economic and political issues. This work involves bringing so-called ‘hard’ scientists into the social science fold. One of the most notable examples is the geophysics and earthquake authority Didier Sornette, who also leads the Financial Crisis Observatory in Zurich – there are numerous others. The starting point of much of this work is that prediction in complex systems is impossible, or at least extremely difficult, because change is the products of many interdependent actors and factors. Such systems are characterised by cascades of events, known as sandpile effects, and as such are inherently unstable.

One of the widely accepted characteristics of complex systems is that the frequency and magnitude of outcomes can be described by a mathematical relationship called a “Power Law”. Power Law Curves are characterised by a short “head” of frequently occurring small events, dropping off to a long “tail” of increasingly rare but much larger ones.

Power Law Curves can be better understood by reference to another widely used mathematical tool, the Bell Curve. To take an example used by Mark Buchanan, if you set 500 salespeople to work independently on the telephones, then, according to bell curve thinking, their total weekly sales will almost always fall within a narrow range around some average; with large deviations proving very rare. The bell curve reflects an underlying and widely accepted theory for what happens when many independent events or actions contribute to some outcome – and underlies the widespread use of past averages as a guide to the future.

However, the Bell Curve is based on independent events. When one event influences another, as in interconnected complex systems, the bell curve does not apply. To continue Buchanan’s example, salespeople, in reality, rarely act completely independently. They are likely to be members of a product group, a regional body; they might meet to agree on goals and compare tactics, and they may compete for bonuses. In short, what one salesperson does has the potential to influence the behaviour of others, leading to collective swings in sales effectiveness. In such interdependent systems, power-law pattern frequently takes the place of the bell curve, because it is a rather more accurate tool. To take one example, in the case of market fluctuations, the bell curve predicts a one-day drop of 10 percent in the valuation of a stock just about once every 500 years. Power law approaches give a very different and more reliable estimate of such events occuring about once every five years.

As McKinsey analysis shows (see chart below), if the frequency of banking crises from 1970-2007 is plotted alongside their magnitude (measured by losses of GDP for each affected country) the result is a power curve. There is a short head of some  70 crises, each with losses of less than 15 percent of GDP, quickly falling off to a long tail of very few, very large crises .


Earthquakes, forest fires, and blackouts illustrate similar patterns, as the chart also shows. For example, from 1993 to 1995, Southern California registered 7,000 tremors at 2.0–2.5 on the Richter scale, falling off to the 1994 Northridge earthquake, at the end of the tail, with a magnitude of 6.7. Similar power laws can be found in US industrial production, in corporate bankruptcies, in terrorism and in global wars.

The Power Law Curve highlights a key property of complex systems: extremely large outcomes are more likely than they are in a normal, bell-shaped distribution, which implies a relatively even spread of values around a mean – in other words, shorter and thinner tails.
The above examples indicate that power law patterns, with their small, frequent outcomes mixed with rare, hard-to-predict extreme ones, exist in many aspects of the economy. The emerging view is that the economy is much like other complex systems characterised by power law behaviour.

With the NYU team’s discovery of power laws in international trade, we now have an example specific to development economics. Looking at manufacturing exports for a sample of 151 countries, and a range of 3000 products from the UN Comtrade database, Easterley et al document high degrees of concentration in the successful exports:

…For every country manufacturing exports are dominated by a few ‘big hits’ which account for most of the export value and where the ‘hit’ includes both finding the right product and finding the right market. Higher export volumes are associated with higher degrees of concentration, after controlling for the number of destinations a country penetrates. This further highlights the importance of big hits. The distribution of exports closely follows a power law…”

To give a few examples of big hits, out of 2985 possible manufacturing products in the dataset and 217 possible destinations for exports:

  • Egypt gets 23 percent of its total manufacturing exports from exporting one product – ceramic bathroom and kitchen items – to one destination, Italy, capturing 94 percent of the Italian import market for that product.
  • Fiji gets 14 percent of its manufacturing exports from exporting womens and girls cotton suits to the U.S., where it captures 42 percent of US imports of that product.
  • The Philippines gets 10 percent of its manufacturing exports from sending electronic integrated circuits and micro-assemblies to the US where it captures 80 percent of US imports of that product
  • Nigeria earns 10 percent of its manufacturing exports from shipping floating docks and special function vessels to Norway, making up 84 percent of Norwegian imports of that product.

On the basis of this analysis, Easterly and his fellow researchers conclude that ‘big hits’ cannot be identified through a policy of “picking winners” for export development. Specifically, the power law characterisation implies that the chance of picking a winner diminishes exponentially with the degree of success. Also, as developing countries are more exposed to the vagaries of product demand than rich ones, this further lowers the benefits from trying to pick single winners.

On the basis of this finding, the authors make some preliminary suggestions about the relative roles and importance of government and the market in ‘picking winners’. To find out more, read the paper, and wait for the trade specialists to battle it out (a debate has already started on the World Bank’s Private Sector Development Blog).

For all those with an interest in complexity sciences, a key point is that this study proves it is feasible to undertake quantitative analysis of complex global systems such as those dealt with by international aid agencies. With more such studies, we may be able to start to move beyond notions of complexity as a ‘useful metaphor’, as suggested by Duncan Green last year, and start talking about complexity as a recognisable, empirically provable property of the systems in which aid agencies operate.

When complexity is proved in this way, simplistic linear assumptions  based on extrapolation of past averages become meaningless. Proving the complexity of  real world systems  means accepting that the world works in a far more erratic and unpredictable way than our current mental models allow, and this means we need to start to question both our desire and and our ability to control the world.

To return to the point that started this article, this work does not negate the qualitative approaches to complexity. Rather it shows that multi-methods approaches to understanding complexity are possible in a development context, and they may well make the argument more powerfully (forgive the pun!) than an approach skewed towards just qualitative analysis. So, hats off to Easterly & Co for this important and timely analysis.

Join the conversation! 2 Comments

  1. Ben, I loved reading your blog and I found it very interesting. I’m really impressed with your work – it has helped me a lot.

  2. […] analysis and seismology (for more on comparisons between earthquakes and economic crises, see a 2009 Aid on the Edge of Chaos post): Seismologists may not be able to forecast earthquakes precisely but it would be deplorable if […]


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About Ben Ramalingam

I am a researcher and writer specialising on international development and humanitarian issues. I am currently working on a number of consulting and advisory assignments for international agencies. I am also writing a book on complexity sciences and international aid which will be published by Oxford University Press. I hold Senior Research Associate and Visiting Fellow positions at the Institute of Development Studies, the Overseas Development Institute, and the London School of Economics.


Economics, Public Policy, Reports and Studies, Trade