Friday, September 11, 2009

Krugman on Math in Economics

Paul Krugman (following up on the article I linked to a few days ago) discusses the role of mathematics in economic theory:

Math in economics can be extremely useful. I should know! Most of my own work over the years has relied on sometimes finicky math — I spent quite a few years of my life doing tricks with constant-elasticity-of-substitution utility functions. And the mathematical grinding served an essential function — that of clarifying thought. In the economic geography stuff, for example, I started with some vague ideas; it wasn’t until I’d managed to write down full models that the ideas came clear. After the math I was able to express most of those ideas in plain English, but it really took the math to get there, and you still can’t quite get it all without the equations.

What I objected to in the mag article was the tendency to identify good math with good work. CAPM is a beautiful model; that doesn’t mean it’s right. The math of real business cycle models is much more elegant than that of New Keynesian models, let alone the kind of models that make room for crises like the one we’re in; that makes RBC models seductive, but it doesn’t make them any less silly.

In intermediate micro, we won't get too sophisticated with our math, but Krugman's right, the part of the value of writing down and solving mathematical models for economic phenomena, is that such models occasionally yield results that were not intuitively obvious (but ultimately make lots of sense).

It also follows that any model, based in math, that yields conclusions that are not intuitively obvious are the most important; that is, an important hypothesis would have seemingly false or outlandish assumptions. Otherwise, its results will not help us predict or learn anything new. If math helps us reach these unintuitive results, then it is a good tool. Still, I agree with Krugman that math alone does not serve as absolute proof; we should use other forms of reasoning before accepting and applying a new model.
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