Scale invariance and universality of economic uctuations

In recent years, physicists have begun to apply concepts and methods of statistical physics to study economic problems, and the neologism “econophysics” is increasingly used to refer to this work. Much recent work is focused on understanding the statistical properties of time series. One reason for this interest is that economic systems are examples of complex interacting systems for which a huge amount of data exist, and it is possible that economic time series viewed from a di erent perspective might yield new results. This manuscript is a brief summary of a talk that was designed to address the question of whether two of the pillars of the eld of phase transitions and critical phenomena – scale invariance and universality – can be useful in guiding research on economics. We shall see that while scale invariance has been tested for many years, universality is relatively less frequently discussed. This article reviews the results of two recent studies – (i) The probability distribution of stock price uctuations: Stock price uctuations occur in all magnitudes, in analogy to earthquakes – from tiny uctuations to drastic events, such as market crashes. The distribution of price uctuations decays with a power-law tail well outside the L evy stable regime and describes uctuations that di er in size by as much as eight orders of magnitude. (ii) Quantifying business rm uctuations: We analyze the Computstat database comprising all publicly traded United States manufacturing companies within the years 1974–1993. We nd that the distributions of growth rates is di erent for di erent bins of rm size, with a width that varies inversely with a power of rm size. Similar variation is found for other complex organizations, including country size, university research budget size, and size of species of bird populations. c © 2000 Elsevier Science B.V. All rights reserved.