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THE large-scale dynamical properties of some physical systems depend on the dynamical evolution of a large number of nonlinearly coupled subsystems. Examples include systems that exhibit self-organized criticality1 and turbulence2,3. Such systems tend to exhibit spatial and temporal scaling behaviour–power–law behaviour of a particular observable. Scaling is found in a wide range of systems, from geophysical4 to biological5. Here we explore the possibility that scaling phenomena occur in economic systemsa-especially when the economic system is one subject to precise rules, as is the case in financial markets6–8. Specifically, we show that the scaling of the probability distribution of a particular economic index–the Standard & Poor's 500–can be described by a non-gaussian process with dynamics that, for the central part of the distribution, correspond to that predicted for a Levy stable process9–11. Scaling behaviour is observed for time intervals spanning three orders of magnitude, from 1,000 min to 1 min, the latter being close to the minimum time necessary to perform a trading transaction in a financial market. In the tails of the distribution the fall-off deviates from that for a Levy stable process and is approximately exponential, ensuring that (as one would expect for a price difference distribution) the variance of the distribution is finite. The scaling exponent is remarkably constant over the six-year period (1984-89) of our data. This dynamical behaviour of the economic index should provide a framework within which to develop economic models.

The price reaction to a single transaction depends on transaction volume, the identity of the stock, and possibly many other factors. Here we show that, by taking into account the differences in liquidity for stocks of different size classes of market capitalization, we can rescale both the average price shift and the transaction volume to obtain a uniform price-impact curve for all size classes of firm for four different years (1995–98). This single-curve collapse of the price-impact function suggests that fluctuations from the supply-and-demand equilibrium for many financial assets, differing in economic sectors of activity and market capitalization, are governed by the same statistical rule.