## Wednesday, November 2, 2011

### A Question about Modeling Uncertainty

Clearly pretending that uncertainty and risk are the same thing is bad - Keynes pointed this out ninety years ago now and lots of people have made that same point since then. Conceptually it's not hard to make that distinction, but it's harder to model - and "neoclassical" (for lack of a better term) models of behavior under uncertainty often come under criticism because they assume a probability distribution.

My question is this: Even in cases of fundamental uncertainty, people don't crawl into a hole, suck their thumbs, and whimper. They guess. Sometimes the guess is completely wrong - they don't consider the prospect of something, which is the same as assuming a zero percent probability of it when there is actually a non-negative probability. This is sort of an "unknown unknowns" situation. It's not even on their radar so they proceed as if it's not an option worth considering. My point is, what is there that's really lost if we model uncertainty as subjective probability that is wrong?

One potential problem is that I can assess something that is uncertain with a vague guess of 50% likelihood, and I can assess something that has a very well known probability distribution with a sure expectation of 50%. Presumably we don't want to treat those two as the same if I know that I am less sure about the former than the latter.

Just thinking out loud here. I think a lot of problems that come up - like Keynesian uncertainty - drive people to throw up their hands and toss out neoclassicism. It seems to me that if what we're trying to understand is human behavior, then humans still behave as if there's a certain probability distrubtion attached to uncertain events - even if that's not the real distribution or if the real distribution can't be calculated.

UPDATE: And Knight, obviously. I told Jeff Friedman he had a moral obligation to all future generations to cite Keynes in addition to Knight in his recent article on uncertainty, so I suppose I ought to live by my own advice. I've got nothing whatsoever against Knight - I just have more in the front of my mind the application of Keynes's work on the subject to actual economics, so he usually comes to mind first.

1. I think you might want to read Michael Emmett Brady's articles again.

http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=1033456

If you don't wish to read by Brady, then I recommend Daniel Ellsberg's work on decision-making under uncertainty. Keynes's weight of evidence index and interval estimate approach to probability (with upper and lower bounds) throw a spanner into the Subjective Expected Utility hypothesis.

If you don't want to read Daniel Ellsberg or Michael Emmett Brady, I suggest reading Benoit Mandelbrot, who distinguishes between "mild risk" and "wild risk" in probability applied to financial markets.

The Society for Imprecise Probability - Theories and Applications (SIPTA) has published research on something called a "Choquet integral" approach to probability, which vindicates George Boole and John Maynard Keynes.

http://www.sipta.org/

But unless I'm misunderstanding your question, my point is this - subjective probability and Keynes's interpretation of probability and uncertainty are fundamentally different.

2. I think you might want to read Michael Emmett Brady's articles again.

http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=1033456

If you don't wish to read by Brady, then I recommend Daniel Ellsberg's work on decision-making under uncertainty. Keynes's weight of evidence index and interval estimate approach to probability (with upper and lower bounds) throw a spanner into the Subjective Expected Utility hypothesis.

If you don't want to read Daniel Ellsberg or Michael Emmett Brady, I suggest reading Benoit Mandelbrot, who distinguishes between "mild risk" and "wild risk" in probability applied to financial markets.

The Society for Imprecise Probability - Theories and Applications (SIPTA) has published research on something called a "Choquet integral" approach to probability, which vindicates George Boole and John Maynard Keynes.

http://www.sipta.org/

But unless I'm misunderstanding your question, my point is this - subjective probability and Keynes's interpretation of probability and uncertainty are fundamentally different.

3. Off topic, but I notice Russ and Don don't engage you any more. Russ's challenge is what, a whole 5 days old now?

My premise is that CH is not about discussion and more about advertising. When was the last time you were allowed to question the merits of Chevy *during* the Chevy commercial?