RESEARCHERS APPLIED STATISTICAL PHYSICS PRINCIPLES TO EXPLAIN WEALTH DISTRIBUTION

An interview with Jean-Philippe Bouchaud, 40, french physicist at Service de Phisique de l'État Condensé, Centre d'Études de Saclay, Gif-sur-Yvette, Paris, France, and founder of Science & Finance, a research company specialized in quantitatuve finance, a division of Capital Fund Management, based in Paris. He co-authored an article about a model of wealth distribution based on the famous Pareto's Power-Law and his "tail" distribution. The paper concludes that favoring exchanges seems to be an efficient way to reduce inequalities. Also favouring a network economy and developing connectivity between economic agents reduces inequalities.

Vilfredo Pareto, italian economist and sociologist, was one of the leaders of the so-called Lausanne School, founded by León Walras in the XIX century. Before Pareto changed political direction (towards non-democratic ideas of Sorel and Mussolini type), in his Cours d'Économie Politique, published in 1896 and 1897, presented an exposition of the so-called Pareto's Law of income distribution. He argued that in all countries and times the wealth distribution follows a regular logarithmic pattern captured in image as a "tail" - in the right end a small fraction of the population owned the majority of the wealth. For instance, in the States, 300 thousand (less than 1,5% ) owns 10% of the wealth. It's common that 90% of the total wealth is owned by only 5 to 15% of the population.

Jean-Philippe is a Ph.D in physics, was awarded the IBM young scientist prize in 1990 and is co-author of Theory of Financial Risks, published by Cambridge University Press, 2000.

Science & Finance web site
Article "Wealth Condensation in a simple model of economy" co-authored by Jean-Philippe Bouchaud and Marc Mézard, published in Physica review February 2000
Article mentioned at Harvard Business Review, April 2002 edition, by Mark Buchanan in "Wealth Happens"
Buy the book "Theory of Financial Risks"

By Jorge Nascimento Rodrigues, editor of www.gurusonline.tv

How it happened that two physicists, you and Marc Mézard, get envolved in this economic research about wealth distribution? Why you decided to study this problem and how statistical physics helps to understand this kind of social problems?

I personally have always been attracted intellectually by economic problems, in particular economical and financial statistics. The trigger was however meeting someone working in a bank who told me that the statistics of market crashes could have a lot in common with the problems of statistical mechanics I was studying at the time. This spurred my interest and I finally created a company, Science & Finance, to explore the possible connections between the methods and ideas of statistical physics (that apply
to many different fields already, from biophysics to population dynamics, from bird flocks to traffic jams and earthquakes) and finance. We have found a very large number of connections and useful ideas. Statistical physics is the science of complex, collective effects. So it is quite natural that it should also apply to economics, which is the science of collective human effects. In the case of the Pareto distribution, we were looking, with Marc Mezard, for the simplest model of economy where agents exchange goods and speculate, and found an equation exactly identical to one that we had already studied in physics, that leads to a Pareto equilibrium distribution of wealth.

Adam Smith model about wealth creation and distribution by means of an invisible hand is valid?

No, there is no rationality or optimisation of any kind in our model. Everything is in a sense random; the only crucial assumption is that exchanges and returns are proportional to wealth.

Pareto power-law of wealth distribution is a systemic law? Is it a law of economic life that emerges naturally?

Yes and no. In our model, as soon as the above very reasonable assumption is made (exchanges and returns are proportional to wealth itself), which corresponds to an invariance of the laws of economics
with respect to a change of the currency unit, a Pareto tail is found. But there are possible violations of this law of proportionality, for example, increasing marginal tax rates like in France. Also, this does not apply for small wealths, because there are fixed social minima and minimum living expenses that set a particular wealth scale. So the Pareto law only describes the TAIL of large wealths/incomes, as found empirically. We have nothing to say about the WHOLE distribution.

What was the impact in wealth distribution of the 6 trillion dollars "loss" in the last crashes of Nasdaq and DowJones? (Common middle class people invested in the bubble period assuming their wealth will improve).

We find that larger volatility of returns create more inequalities. In this case, it is obvious that some individuals did extremely well by pulling out of the market before the crash. On average and in the long run, crashes create inequalities. A stable market would not create very strong contrasts between investment returns.

Are we assisting in USA and Europe a transition period to an economy with more wealth condensation in a few super-rich?

I don't think so, even if the Pareto index might well have decreased in recent years. A limitation to wealth condensation is the death of individuals and the corresponding redistribution of wealth. In our model, this decreases the possibility of occurence of the wealth condensation. But if life was longer, we might be in the super rich phase.

Can you explain in a simple way the network effect on wealth creation and distribution? (In the new economy period, we have talked of the law of more generates more in a network).

The more connected the network, the smaller the probability that wealth is not 'transmitted', in a sense. This is like the Internet: by having multiple paths between any two nodes, there is robustness against failures of some of these paths, and the messages are transmitted. In our model, having only one path between a rich individual and a poor one does not make very probable the possibility of levelling
off the inequality. On the other hand, through the multiple paths connecting the two in a well connected economy, the poor can benefit in different ways of the activity of the rich. Using your word: increased connectivity helps trickling down wealth.

According to your model, income taxes can reduce inequalities? In what conditions?

Yes, income taxes always reduce inequalities in our model. These can even kill the Pareto tail if the marginal tax rates are increasing like in France, where, depending on the range of income, your tax can go from 0 to 54%. However, since most of the income of large wealth comes from capital gains, this is not really operative.

In what conditions capital taxes can reduce inequalities?

In our model, we have found the curious result that if the product of the wealth tax is not redistributed equally but used, for example, to reduce the debt or to finance specific projects, the result could be an increase of inequalities.

Changing VTA (for instance increasing) can affect in a negative way exchanges and wealth distribution?

VAT has two opposite effects: seen as a tax it tends to decrease inequalities, but its side effect of reducing exchanges leads to increased inequalities. It should be an optimal value of VAT such that the inequality reduction is strongest, but this goes beyond the scope of our model.

Cutting taxes to the upperlevel incomes can favour productive investment and entrepreneurship and trickle down wealth?

Our model is not rich (if we may say) enough to deal with this issue.

Cutting taxes to companies and banks can favour productive investment and trickle down wealth?

Same answer.

Are you thinking to continue this kind of research?

Yes, in different directions. Our model is a first very rough approximation to reality. We believe that one needs to build a richer and more complete `toy-'model of economy. It will be too complicated to solve mathematically, but if the ingredients are realistic and the behaviour of human agents properly modelled, one will perform numerical simulations of this model, as one does for airplane profiles for example, where the hydrodynamical equations cannot be solved mathematically. Then, various scenarios can be tried before taking political decisions, for instance on those two questions labove. The development of such models will however probably take years to achieve. Simpler situations, like the behaviour of agents in stock markets, will probably help. This is our focus for the time being.