Wednesday, December 24, 2014

More Piling On Cochrane: Why He Cannot Go Back To Being Taken Seriously Even About Asset Pricing

Oh, I cannot resist.  Since his effort to  dump on Keynesians in the WSJ, lots of people have been piling on John Cochrane, showing that nearly all his claims are not only laughingly bogus, but seriously unsupported even in his own column, such as failing even to mention a single supposedly Keynesian economist who forecast a return to recession as a result of budget sequestration, a centerpiece of his embarrassing column.  A sampling can be found Mark Thoma's links for today at economistsview, sort of a Christmas Eve special.

In any case, what caught my attention and is pushing me into  the piling on as well is a remark Brad DeLong made in his post at the link entitled "Cochrane ought to simply say..."  He suggests that Cochrane has made such a big fool of himself out of all this that he should just go back to working on asset pricing.  I am going to argue that even in that arena, he has made a bit of a fool of himself and should also be ignored to some extent, even though he has a long and respectable publication record in the area.

So, what is his problem?  He is one of the leading figures in finance who has simply ignored dealing seriously with the phenomenon of "fat tails," more properly known as kurtosis (or even as leptokurtosis), which are widely known to be ubiquitous in many financial time series.  This is  more a subject for Nassim Taleb, although he pushes things further to talk about full-blown Keynesian-Knightian uncertainty that he calls "black swans," arguing that modeling fat tails is a matter of "grey swans" because we can estimate various probability distributions that show them, and that the crash of 2008 was obviously coming, whereas true black swan uncertainty involves there being no probability distribution at all.

Where does Cochrane fail to do this?  In his widely used and admired grad textbook, _Asset Pricing_.  Let me say that indeed this is a well written book that does a good job of covering most of the material in standard financial  economics related to asset pricing.  However, it has one very unfortunate and peculiar lacuna, not corrected as of the last time I checked.  He simply does not discuss the existence of kurtosis or fat tails in most  financial time series.  The words "fat tails" "kurtosis" and "leptokurtosis" simply do not appear in his famous book. Nowhere, nada, not at all.

Now I have encountered admirers of his who argue that he does address the issue.  The defense in this case rests on noting that when he presents the theory of stochastic discount factors, he does note specifically which of the theorems hold when returns are non-Gaussian (allowing kurtosis) and which only hold when returns are Gaussian, that is normal, without any fat tails.  However, he fails to go on anywhere else in the book to discuss how to deal with the cases where they are not normal. I  note that some of the competitors to his book, such as that by Cambell, Lo, and MacKinlay, do at least talk about this issue and the fact that most returns are kurtotic, even if they do not say a whole lot about it. (It must be recognized that dealing with fat tails formally is hard, with copulas being one way that practitioners have attempted to do so, with the use of one of those, the bivariate normal Gaussian one developed by David Li becoming implicated in the blowing up of AIG in 2008, leading Li to escape to China.)

What is really curious here is that at the time of the crash in 2008, when he was criticized for not talking about fat tails, Cochrane defended himself by noting that Eugene Fama, also at Chicago Booth and his father-in-law to boot, knew all about fat tails because he had worked with Benoit Mandelbrot at one point, one of the earliest people to point out that asset returns have fat tails and proposed using fractals to study the phenomenon.  Indeed, Fama initially supported Mandelbrot's argument that variances are asymptotically infinite, but then turned against him on this matter (they do not appear to be so empirically), although ignoring evidence that fourth moments (kurtosis) may actually be so.  In any case, Cochrane claimed that even though Fama abandoned Mandelbrot on this issue, he knew about asset returns having fat tails and that anybody who studied with him knew this.  Maybe this is so, but there seems to be might little evidence that Cochrane has been passing this on to  his students, even though he is reputedly a good teacher.

BTW, I posted once on this specific matter previously at the time of the death of Benoit Mandelbrot.  One commenter argued then that what financial economists did instead of looking at kurtosis of the overall distributions was instead to focus on volatility clustering by using ARCH/GARCH models, and so on, which is true.  I noted then that these suffer from the problem that they do not model the exogenous shocks that set off the clusters, although such clusters clearly exist.  In any case, it remains true that Cochrane and his closest allies have continued to largely ignore the fat tails phenomenon, and this makes him look pretty pathetic in terms of why anybody should take him really seriously even in his area of most basic research.

Barkley Rosser

PS:  And Merry Christmas to all who celebrate it!


Julio said...

"leptokurtosis" should have been "kleptokurtosis".

lgm said...

Fat tails and kurtosis are different things. Most non-gaussian distributions have non-zero kurtosis. But many of those have thin tails. If you use kurtosis to estimate the tail distribution, you're likely to get it wrong.

If you look at histograms of, say, one day S&P500 returns, you will see a central peak higher than the gaussian with the same variance. That's kurtosis too, but not fat tails.