Economics And Physics: Strange Bedfellows?

ECONOMICS AND PHYSICS: STRANGE BEDFELLOWS? - Kousik Guhathakurta, Assistant Professor, Army Institute of Management

INTRODUCTION When there is bloodshed the world always take note. Poets romanticise. Massacres are termed as ‘revolution’ and the warmongers become heroes. But the real revolutions take place on a different plane altogether. The seeds of such revolution are independently born in the minds of great thinkers, the philosophers, the artists and the scientists of the world. Collectively they change the way we live our lives. From the day man discovered fire to this day of Human Genome Project, such revolutions have constantly overturned the wheels of civilisation. One such intellectual explosion is the theory of complexity, which is presently pervading all academic discipline giving birth to a new science. The Santa Fe Institute of Research at New Mexico is a pioneering research institute in this area. Even a cursory glance at the opening statement of its home page will tell us that a new science is emerging: “The Santa Fe Institute is devoted to creating a new kind of scientific research community, one emphasising multidisciplinary collaboration in pursuit of understanding the common themes that arise in natural, artificial, and social systems. This unique scientific enterprise attempts to uncover the mechanisms that underlie the deep simplicity present in our complex world” While economics is a study of social system, physics is a science devoted to unraveling the mysteries of nature. The new science attempts a marriage of these odd bedfellows. It may be admitted, however, that amongst the social sciences, economics is definitely the closest relative of natural sciences. A proof of that is the volume of advanced mathematical literature that dominates the academic world of economics. Sophisticated quantitative techniques form the foundation of most academic work in economics. In fact, several of the recipients of the Nobel Memorial Prize in Literature are mathematicians by training, including the mercurial John Nash for his contribution in Game Theory. Until recently, the body of economic literature, in spite of being highly mathematical in nature, did not borrow directly from the works of physics. Though several aspects of the economic and financial markets did attract the physicists, (the mood swings of the stock market for example, where physicists have often tried to practice the science of

probability, hoping to make some money in the game! Isaac Newton was known to have speculated heavily in stocks and lost twenty thousand pounds in the process!) they have started serious academic work in the field of economics only recently. Eminent physicists like Eugene Stanley, Doyne Farmer, J.P. Bouchaud and many others having joined the fray this new field has now started to gain real academic (to some extent practical too) respect. In fact, it was Eugene Stanley who coined the word ‘Econophysics’ to describe this new science, at a conference at, guess what, Kolkata! It may be added, however, that all these ‘econophysicists’ owe it to the pioneering works of Benoit Mandelbrot, the father of fractal geometry. The Nobel Prize awarded to Myron Scholes & Robert Merton for their famous Black-Scholes formula of derivative pricing, a formula that was based on the assumption that stock prices follow Geometric Brownian Motion, was perhaps a formal recognition of the possibility of marriage of these two sciences. EARLY CONNECTIONS The idea that financial or economic problems can be tackled with the help of tools borrowed from natural science is not new. It dates back to 1900 when Louis Bachelier, a student of Poincaré in Paris, proposed that fluctuations in the prices of stocks and shares could be viewed as random walk. His Ph.D. thesis actually contained remarkable results and insights, which anticipated not only Einstein’s theory of Brownian Motion, published in 1905, but also many of the post-war ideas in theoretical finance. Bachelier’s model, though elegant, was simplistic and failed to capture some of the critical aspects of market behavior. This was mainly because Bachelier assumed that the stock price fluctuations follow Gaussian distribution. That is why market crashes were absent in his model because portability of extreme events is miniscule in a Gaussian world. On the other hand, the economists also constantly drew inspiration from developments in physics, especially classical mechanics. Newton’s theories metamorphosed into more modern language of analytical mechanics in the hands of Lagrange, Hamilton and others. The elegance and power of analytical science did not escape the eyes of the economists. Economists like Walras, Jevons, Fischer, Pareto tried to map the formalism of physics

into the formalism of economy, replacing material points by economic agents. What is surprising is that the Newton Laplacian deterministic principles continued to enchant the economists even long after quantum physics had changed the world of physics into a stochastic one. In fact it took almost half a century for the ideas of Bachelier to reach the ivory towers of economic academicians. In fact one can trace the seeds of Black-Scholes equation to Bachelier only. THE DEVELOPMENT Considering the several developments in theoretical and empirical physics, one can conclude that perhaps in the 80s the economists missed a lesson from physics. The assumption of the Gaussian character of a stochastic process caused the models to move away from the actual price movements with large fluctuations. The concept of power law and fat-tailed distributions, quite common weapons in a physicist’s armory, attracted the attention of economists much later. In fact, rather than economists, a band of physicists have used these successfully in analysing market behaviour. Many other such alterations in economic systems ultimately led to non-linearity. That study of chaos is a major area of theoretical physics is common knowledge these days. What is interesting is that nowadays; studies of chaos, self-organised criticality, cellular automata and neural networks are seriously taken into account as economical and financial tools. The discussions this far may lead one to believe that the advent of physics in economists’ world has addressed only narrow field, namely financial markets. The application has pervaded other boundaries too. One such are is Firm Growth. In an economy all the firms interact with one another, the interactions changing as a function of time. This behaviour has motivated physicists to treat this as a critical phenomenon and try to predict universality in company growth. Closely related to this firm growth is the macroeconomic problem of income and wealth distribution. Since the phenomenal work of Pareto, power-law distribution of wealth is a well-established fact. Quite a number of empirical studies are being done and already the results are very encouraging. Statistical physicists are taking more and more interest in this subject.

Another area of development has been the study of Complex Networks of economy systems. Economy is a many-body system including agents as individuals, firms, countries, goods as produce, production and service, and subsystems as financial system, manufacturing, agriculture, service industry. And all of them interact with each other. A general way developed recently to describe such system is Complex Networks. In a complex network, a vertex represents every agent and the interaction between any two agents is described by a link between the two corresponding vertexes. Further more, the weight of links can be used as the strength of the interaction and a directed link can be used when the interaction is not symmetrical. MAJOR WORKS Though still at embryonic stage, there have already been some major breakthroughs in this new science. In the field of stock price fluctuations, there has been some important empiriacl studies done, including the group of physicists working with Eugene Stanley and Rosario Mantegna. They had worked with a large volume of data (of the order of 1 million data points!!) and developed a class of new mathematical distributions called truncated Lévy distribution. Apart from these there have been several other important studies as well (Rogério L. Costa, G.L. Vasconcelos, V. Plerou, P. Gopikrishman, L.A.N. Amaral, M. Meyer , J.-P. Bouchaud and M. Potters etc.) Several toy models have also been developed (e.g. the model by A. Krawiecki, J.A. Holyst and D. Helbing). Another important area of work have been the study of financial crashes, which have been likened to phase transitions (Didier Sornette et al.,). Several path-breaking studies have been done in the field of Distribution of firm sizes, GDP, personal income and wealth. Scientists have been able to generate reasonably good predictive models of growth and income distribution. On the economic networks, several studies have given interesting results on this aspect including the work on web trade. CONCLUSION There is no doubt that this intrusion of physics in to the world of economics has a possibility of enriching our understanding of economic systems. However, Many econophysicists acknowledge the presence in their field of an unusual amount of work

that they call ungrounded, misguided, or in some cases downright crazy. Pioneer econophysicist Jean-Philippe Bouchaud, whose company, Science & Finance, in Levallois, France, provides consultation to banks, says that many physicists have not invested sufficient time to learn about finance. Too many, he says, are dabbling in economics "as just an easy way to do some research." These aberrations notwithstanding, the marriage of these two great sciences is bound to have far-reaching implications on the future of our civilisation.