Tuesday, September 8, 2009

Krugman on Mathematics and the Failure of Economics

Probably anyone who is interested in this article has already seen it, but Paul Krugman put out an article in Sunday's New York Times Magazine called "How Did Economics Get It So Wrong?". The article is very well-written, but a bit unsatisfying as it combines Krugman's more standard worries about macroeconomics with a short attack on financial economics. I am trying to write something right now about the ways in which mathematics can lead scientists astray, and one of my case studies in the celebrated Black-Scholes model for option pricing. Hopefully I can post more on that soon, but here is what Krugman says about it and similar models which are used to price financial derivatives and devise hedging strategies.

My favorite part is where Krugman says "the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth". But he never really follows this up with much discussion of the mathematics or why it might have proven so seductive. Section III attacks "Panglossian Finance", but this is presented as if it assumes "The price of a company's stock, for example, always accurately reflects the company's value given the information available". But, at least as I understand it, this is not the "efficient market hypothesis" which underlies models like Black-Scholes. Instead, this hypothesis makes the much weaker assumption that "successive price changes may be considered as uncorrelated random variables" (Almgren 2002, p. 1). This is the view that prices over time amount to a "random walk". It has serious problems as well, but I wish Krugman had spent an extra paragraph attacking his real target.

Almgren, R. (2002). Financial derivatives and partial differential equations.
American Mathematical Monthly, 109: 1-12, 2002.


Brian said...

I think the phrase "efficient markets hypothesis" is ambiguous in practice, and this is leading to some of the confusion. In the terminology that John Quiggin uses here, and which I think is helpful, Krugman is attacking the semi-strong version, and you're putting forward in reply the weak version.

This kind of terminological confusion has costs. The weak version is at least sorta kinda backed up by the data. But people then use that fact to support policies that only make sense conditional on the strong, or semi-strong, versions.

Chris Pincock said...

Brian, thanks for the comment and the very useful link. I wasn't aware of these distinctions, so it is good to see them critically discussed along with the supposed policy links.

I have taken a book out from the library that criticizes the weak efficient market hypothesis, but not yet read it: Lo and McKinley, A Non-Random Walk Down Wall Street. A superficial look at it suggests that it is actually quite hard to refute the claim that some random walk fits stock prices, but this is just because there are many refinements.