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Buchanan: A chilling mathematical model of inequality

First Published      Last Updated Mar 16 2016 02:48 pm

Economists have offered various explanations for the frustrating slowness of global growth, from excessive debt to a shifting balance of power bringing an end to an American century. A new analysis suggests there's one that deserves greater attention: the chilling effect of inequality.

Think of an economy as a large network of individuals and firms who make and use things, interact and exchange with one another. Any party can, in principle, transact with any other, buying and selling, the only constraint being the budget of the buyer. Economists have studied network models of this sort — called random exchange economies — to explore how normal trading activity might (or might not) make an economy approach equilibrium.



Now some European physicists have used such a model to examine a different question: How does a significant change in inequality affect the overall level of exchange? Their study makes use of some fairly abstruse mathematics coming from physics, developed precisely for messy network problems of this kind. What they find is troubling, although not all that surprising — rising inequality tends to undermine exchange.

The reason is quite simple. As inequality gets more pronounced, a larger fraction of the population faces more stringent budget constraints, and the spectrum of possible economic interactions open to them narrows. Fewer people have the wherewithal to engage in economic activity. This mathematical economy actually demonstrates a sharp transition, akin to the abrupt freezing of a liquid, as the level of inequality exceeds a certain threshold. Worryingly, the wealth distribution in the U.S. over the past few decades has been moving ever closer to this critical edge.

To be sure, the model is far from complete, and can only suggest possibilities. That said, it gets at the intricacies of exchange in a way that traditional macroeconomic models do not. Moreover, the effect of budget constraints on people's economic capabilities makes intuitive sense. There is every reason to believe that more realistic models would show a similar dynamic, changed only in minor details.

This inequality mechanism has nothing to do with ordinary recessions and the usual business cycle. Significant changes in the distribution of wealth take place much more slowly — an attribute consistent with what many economists have identified as the different and more profound nature of the current global slump. The concept of secular stagnation that Larry Summers has popularized could have a number of contributing causes, including rising inequality.

If so, the inequality diagnosis opens up interesting possibilities for policy solutions. The researchers found another interesting effect — a "trickle up" flow of wealth quite different from the usual "trickle down" picture of supply-side economics. In an economy with appreciable inequality, capital tends to flow from those with less to those with more, generating a cascade of transactions along the way. Hence, policy interventions aiming to spur economic activity should work better if they inject money into the system at the lower end, rather than from the top.

This fits with the argument that quantitative easing — in which central banks purchase securities — may ultimately be misguided. Such a policy is supposed to encourage spending by propping up the prices of stocks and bonds, which tends to boost wealth only at the top end of the distribution. Central bankers might have a more powerful and beneficial effect if they instead injected money directly into the accounts of citizens, who could then use it to pay down debts or spend as they like.

The idea of such "people's quantitative easing" is gaining popularity, and for good reason. It would more directly attack the budget constraints holding back the vast number of individuals on whom economic growth depends.

 

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