Mathematician Michael Edesess has a dose of reality for economists.
“Economics pretends to be mathematics, but it is not mathematics,” he says. “There is a major difference. No mathematician uses a term in a formula, or a statement of a theorem, unless that term has first been defined with excruciating precision.”
And while economists may think they’ve defined terms like “aggregate demand” or “economic growth,” Edesess suggests they talk to a mathematician. “Economists may think they’ve defined them, but they should try reading some real mathematics to see what a precise definition truly is,” he says. “The economists, I think, leave the work of definition to be inferred from the way the terms are used in the formulas. This, to me, is weird.”
Using a recent blogosphere debate between Steve Keen and Paul Krugman as a jumping off point, Edesess offers a mathematician’s insight into some of the key problems with economic theory and economic debate. The lack of precise definitions produces some distinct symptoms, as the Krugman-Keen argument shows: “The amazing thing is that, in this debate, one side or the other will present what appears to be a very simple proof that they are right – and yet the other side is not persuaded in the least.”
He traces this problem back to what he suggests is the cause: “The source of all the confusion, in my view, is the idea that if you can’t measure something and model it mathematically, it has no meaning. There is too much mathematics used and expected in economics, and too much of it is of poor quality and distorts the ideas it is meant to undergird.”
This mathematical hubris is at the heart of the “the critical state of economic theory has been exacerbated by the financial crisis” – a crisis that was in part created by the overreliance on precise but not accurate mathematical models used as if the real world were made up of mere numbers.
This reliance on mathematics can be traced back to an economics that has falsely aspired to the certainty of a mathematical science like physics (which, in reality, is far less well-defined and precise than economists seem to believe). But, as Edesess also suggests in relation to a part of the Keen-Krugman debate, “causality runs both ways.”
The desire of the business community and society for the illusion of certainty has created significant short-term incentives for economists to provide this false reassurance. But the long-term costs were well demonstrated by the 2008 financial crisis and its aftermath, which we’re still dealing with. Economists too often ignored the real world – and key issues like inequality, financial instability, and innovation – in favor of precise but not accurate numbers, like, as Edesess notes, aggregate demand or GDP.
If economists want to remain relevant they have to return mathematics and the precision it offers to its proper place in the discipline. Math should be a tool that economists use, not an end goal in and of itself. And economists must focus on addressing humanity and morals and ethical dilemmas, which lie at the heart of it all.