Physics Envy (again)

Seeing as I've covered the topic a few times already, here is an interesting - and surprisingly amusing - presentation by Andrew Lo of MIT, based on a paper he has co-authored with (physicist) Mark T. Mueller: "WARNING: Physics Envy May be Hazardous To Your Wealth!"

Lo's discussion is somewhat contextualised towards financial economics and markets, but he certainly builds his case by first discussing economics in general:

(HT: Bill Easterly. The actual presentation begins around the 03:10 mark)

As I see it, Lo and Mueller's general propositions dovetail nicely with the arguments that I (and many others for that matter) have put forward in the past. For instance (+/-07:05), focusing on when to use your tools rather than simply throwing them to one side:

So what we thought we would do in this paper is to try to trace the origins of physics envy and then see whether or not it really is the cause of crisis, or when it is and when it isn't, and how we might deal with it in a somewhat more productive manner than simply saying that quant is broken and we should forget all about all of this fancy mathematics.

Because, frankly, when I first came across this very popular sentiment that quant is at the root of financial evils, I have to say that it struck me a little bit odd. It's a bit like blaming arithmetic and the real number system for accounting fraud. It's true that they're involved, but you're sort of missing a piece!

Among the many interesting points Lo makes, it's also intriguing to see how reverent he is to the supposed father of physics envy, Paul Samuelson. For example, at (+/-) 12:45 he defends Samuelson against a charge of blind physics envy by quoting a passage from the latter's famous dissertation:

[O]nly the smallest fraction of economic writings, theoretical and applied, has been concerned with the derivation of operationally meaningful theorems. In part at least this has been the result of the bad methodological preconceptions that economic laws deduced from a priori assumptions possessed rigor and validity independently of any empirical human behavior. But only a very few economists have gone so far as this. The majority would have been glad to enunciate meaningful theorems if any had occurred to them. In fact, the literature abounds with false generalization. (Samuelson, 1947, p. 3) 

[Editors note: Samuelson goes on to add (p. 4): "By a meaningful theorem I simply mean a hypothesis about empirical data which could conceivably be refuted, if only under ideal conditions." Karl Popper anyone? I would also note that Lo makes repeated reference to the need for empirical testing as a means of validating economic theory, at the same time as he is wide-eyed about the problems we may encounter in doing so.]

Moving back to main thrust of the presentation and paper, Lo and Mueller follow Frank H. Knight in focusing on the distinction between two types of randomness: risk and uncertainty. The former - "risk" - refers to the type of randomness that lends itself to prediction, while the latter - "uncertainty" - is everything else. (You can skip to 14:10 if you want to see a nice illustration of this distinction via the Ellsberg's Paradox and our behavioural reaction to it.) Lo and Mueller develop this concept of Knightian Uncertainty further by proposing a more refined taxonomy:

1. Complete Certainty (e.g. Newton's three laws... for certain frames of reference)
2. Risk Without Certainty (Known probability distributions)
3. Fully Reducible Uncertainty (You can get close to Level 2 by testing a model with sufficient sample size that produce known/observable outcomes) 
4. Partially Reducible Uncertainty (There will always be some level of unknowable randomness that you can't transform into quantifiable risk. Bayesian methods are likely to be more appropriate...)
5. Irreducible Uncertainty (The realm of religion and astrology... E.g. "What is the meaning of life?")

The problem comes in when investors (and social scientists) mistake the level of the continuum that they are  operating in. While we may find ourselves in, say, Level 3... often we are closer to Level 4. Being overconfident about our level of certainty is, in effect, what characterises physics envy. Lo and Mueller conclude by offering a framework to best determine when quantitative analysis and mathematical modelling will be most useful to resolving an economic problem.

THOUGHT FOR THE DAY: Knowing when to use your tools is just as important as knowing how to use them. Also, the ultimate test for any model - mathematical or otherwise - should always be how well it describes real-life data.

PS - The issue of uncertainty is the source of some of the most interesting work that's being done in the field of climate change economics. I hope to write a brief introduction for the layman sometime in the future, but take a look here and here if you feel inspired.