Economic variability

The famous bell-shaped (normal) curve formulated by Gauss is based on the assumption that all of the variables are independent (uncorrelated). But information flow in networks is neither uniform nor instantaneous, so the normal distribution is generally inappropriate. Instead, distributions describing networks often have longer tails. So the likelihood of an extreme event is much greater.

In The (mis)Behavior of Markets, Mandelbrot and Hudson observed that market deviations do not follow the normal curve, and in fact the spread is considerably wider. They go on to describe some fractal-based statistical measures to describe this behavior. Mark Buchanan (Why economic theory is out of whack, New Scientist, July 2008) describes work of Sornette and Harras which points to a possible mechanism. The model described assumes that agents are not fully rational (as demanded by traditional economic theory) and base their actions on a combination of rational and network approaches. That is, they invest using information available from markets and the behavior of those with whom they network.

In 2004, Farmer proposed (What really causes large price changes?) the source of variability was due to the structure of a market’s limit order book. Many orders for stock are specified with a limit. Consider a stock currently selling for $13. A sell order might be placed for 10 shares when the price rises to $14, or a bid order placed to buy when the price drops to $12. The problem is that orders do not occupy every possible slot on the price continuum. A bid order for 100 shares might have to be filled with 40 shares at $13 (the most available) and 50 shares at $14, and finally 10 shares at $17, yielding a mean share price of $13.90. These discontinuities in price can yield huge swings in markets.

In 2008, Bouchard proposed (Wealth condensation in a simple model of economy) severe market swings were due to agents following one another rather than external information (news).

On the display of the distribution of wealth

The traditional tool for the display the distribution of wealth is the histogram. In this format, wealth is typically displayed along the horizontal axis and the frequency (number of occurrences) along the vertical. The histogram suffers from shortcomings. One is that wealth can take on an enormous range of values, and another is any power law characteristics will not be clearly evident. As an alternative, Lorenz proposed where the cumulative wealth is assigned to the vertical scale, and the cumulative population to the horizontal — both shown as a percentage.

A straight line connecting all the percentage points of equal value would indicate a perfectly uniform distribution of wealth, thus any deviation from this line becomes a measure of wealth inequity. This inequity is quantified by calculating the Gini coefficient which is the area between the uniform line and the actual data (scaled to the range 0–1).

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