Power Curves Applied To Economy, Markets And Nature

This is an interesting study from The McKinsey Quarterly which dwells with power curves in "Power Curves": What Natural And Economic Disaster Have In Common

The power curve or the power law according to wikipedia.org,``A power law is a special kind of mathematical relationship between two quantities. If one quantity is the frequency of an event, the relationship is a power-law distribution, and the frequencies decrease very slowly as the size of the event increases. For instance, an earthquake twice as large is four times as rare. If this pattern holds for earthquakes of all sizes, then the distribution is said to "scale". Power laws also describe other kinds of relationships, such as the metabolic rate of a species and its body mass (called Kleiber's law), and the size of a city and the number of patents it produces. What this relationship means is that there is no typical size in the conventional sense. Power laws are found throughout the natural and manmade worlds, and are an active area of scientific research.

McKinsey suggests that the laws of nature can be applied to economies or marketplace, ``Scientists, sometimes in cooperation with economists, are taking the lead in a young field that applies complexity theory to economic research, rejecting the traditional view of the economy as a fully transparent, rational system striving toward equilibrium. The geophysics professor and earthquake authority Didier Sornette, for example, leads the Financial Crisis Observatory, in Zurich, which uses concepts and mathematical models that draw on complexity theory and statistical physics to understand financial bubbles and economic crises.

``Sornette aims to predict extreme outcomes in complex systems. Many other scientists in the field of complexity theory argue that earthquakes, forest fires, power blackouts, and the like are extremely difficult or even impossible to foresee because they are the products of many interdependent “agents” and cascades of events in inherently unstable systems that generate large variations. One symptom of such a system’s behavior is that the frequency and magnitude of outcomes can be described by a mathematical relationship called a “power law,” characterized by a short “head” of frequently occurring small events, dropping off to a long “tail” of increasingly rare but much larger ones...

``If, for instance, you plot the frequency of banking crises around the world from 1970 to 2007, as well as their magnitude as measured by four-year losses of GDP for each affected country, you get a typical power curve pattern, with a short head of almost 70 crises, each with accumulated losses of less than 15 percent of GDP, quickly falling off to a long tail of very few—but massive—crises . While the most extreme cases involve smaller, less developed countries, the same distribution also applies to more developed ones—and with much larger absolute values for GDP loss. Earthquakes, forest fires, and blackouts yield a similar power curve pattern—for instance, 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. The curve highlights a key property of the power law: 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 power law applied to the industrial production...

``These 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. This suggests that the economy, like other complex systems characterized by power law behavior, is inherently unstable and prone to occasional huge failures. Intriguing stuff, but how can corporate strategists, economists, and policy makers use it? This is still a young field of research, and the study of power law patterns may be part of the answer, but it isn’t too early to consider and discuss potential implications."

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