Scale invariance and universality in economicphenomena

Abstract

This paper discusses some of the similarities betweenwork being done by economists and by computational physicistsseeking to contribute to economics. We also mention some of thedifferences in the approaches taken and seek to justifythese different approaches by developing the argument that byapproaching the same problem from different points of view, newresults might emerge. In particular, we review two such newresults. Specifically, we discuss the two newly discoveredscaling results that appear to be `universal', in the sensethat they hold for widely different economies as well as fordifferent time periods: (i) the fluctuation of price changes ofany stock market is characterized by a probability densityfunction, which is a simple power law with exponent -4extending over 102 standard deviations (a factor of 108 onthe y-axis); this result is analogous to the Gutenberg-Richterpower law describing the histogram of earthquakes of a givenstrength; (ii) for a wide range of economic organizations, thehistogram that shows how size of organization is inverselycorrelated to fluctuations in size with an exponent ≈0.2. Neither of these two new empirical laws has a firmtheoretical foundation. We also discuss results that arereminiscent of phase transitions in spin systems, where thedivergent behaviour of the response function at the criticalpoint (zero magnetic field) leads to large fluctuations. Wediscuss a curious `symmetry breaking' for values of Σabove a certain threshold value Σc; here Σ isdefined to be the local first moment of the probabilitydistribution of demand Ω - the difference between thenumber of shares traded in buyer-initiated and seller-initiatedtrades. This feature is qualitatively identical to the behaviourof the probability density of the magnetization for fixed valuesof the inverse temperature.