Martin Weitzman has an excellent piece in the Sept. 07 American Economic Review that provides exactly that. He argues that papers using a Rational Expectations Equilibrium (REE) approach generate the equity premium puzzle (it's too big), the risk free rate puzzle (it's too low) and the equity volatility puzzle (it's too volatile compared to fundamentals), by incorrectly assuming that the underlying density generating growth shocks is known to agents. Simply replacing the known variance with an estimated variance (changing the normal density to a student-t density) can actually REVERSE the puzzles.
Maybe I should let him tell it:
"Intuitively, a normal density “becomes” a Student-t from a tail-thickening spreading-apart of probabilities caused by the variance of the normal having itself a (inverted gamma) probability distribution. There is then no surprise from expected utility theory that people are more averse qualitatively to a relatively thick-tailed Student-t child distribution than they are to the relatively thin-tailed normal parent which begets it. A much more surprising consequence of expected utility theory is the quantitative strength of this endogenously-derived aversion to the effects of unknown variance-structure. The story behind this quantitative strength is that thickened posterior left tails represent structural uncertainty about rare disasters that terrify people. This fear-factor effect holds for any utility function having everywhere-positive relative risk aversion."
So fear of rare events whose generating distributions are not known can cause the puzzles we see without any excessive amount of risk aversion by agents. I think this is a very nice and important paper.
4 comments:
Not sure I follow all of this, but would like to if you could translate into regular speak. One simple minded question--your concluding sentence makes me ask, is this similar in nature to Talib's Black Swan?
Given the variation in income or consumption over the sample period used for calibration, People demand too high of a return to bear risk (the equity premium puzzle) and will sacrifice a lot of return to eliminate risk (the risk free rate puzzle). These puzzles have vexed economists. there are tons of papers trying to explain them, but few do it well and none do it simply.
What Weitzman does is argue that we can't use the sample mean and variance as if they were the population mean and variance. Simply taking into account that the population variance is unknown and estimated (parameter uncertainty) makes the potential for bad events more likely than what we can infer from the frequencies in our sample in the way it has been done so far. He goes further and assumes the true parameters are evolving and people are using Bayesian updating to try and figure them out, but they don't get there. This parameter uncertainty then is permanent and when taken into account can explain why we observe the equity premium and risk free rates that we do observe.
I am sorry to say that I am not familiar enough with "the black swan" to comment except to say that Weitzman doesn't cite it!!
Thanks, that makes perfect sense now. So much so, in fact, it's a wonder no one thought of that before. I guess that's what will make this an important paper.
Very intriguing.. I like the way you brought this one up. I do agree that this is a nice piece and important paper. Anyway, if you have time, take a visit at my Download Games website. :)
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