From a letter to Brian Caplan and ccing Andrew Gelman.
Brian,
As a prologue, I cced Andrew Gelman who is a professor of Poli Sci at Columbia and a very prominent Bayesian Statistician. He too has written on the sparsity of Bayesian economics and I cced him because I thought he too would find this email of interest given his very public advocacy of all methods Bayesian in science (and social sciences!) and having had interactions with Andrew before, I know he may even want to post this on his own blog! (seehttp://andrewgelman.com/ -- It is truly high quality).
The comments section on your post (on the blog posthttp://econlog.econlib.org/archives/2009/11/why_arent_acade.html#91157) are closed which is most natural due to its age.
I thought nonetheless I should write to you about Bayesian Econometricians as an addendum. Obviously some commentatorswere wrongly disposed to think economists do not have the bandwidth to understand Bayes’ rule. It is a much deeper historical (hysteresis) problem. I would not say that Phillips or Granger do not have the bandwidth—far from it. Surprisingly, they are wrong-headedabout their philosophy as though the Pearson-Neymann Fisherphilosophy (repeated experiments, really now? In economics? Guffaw! LoL!) was the most applicable to economics alone even though it is increasingly out of favour in the physical sciences. This is so wrong it is hard to fathom. Meanwhile, most economists I speak with know full well how Bayes’ rule works if they have never actually used it in practice!
In physics, many prominent physicists are active supporters of the Many Worlds Interpretation (i.e., http://en.wikipedia.org/wiki/Many-worlds_interpretation) as opposed to the dominant Copenhagen Interpretation - Hawkings among others. Edwin Jaynes claimed that the Copenhagen school with its’ god-like Observers was a form of Mind Projection Fallacy. The big difference is Jaynes and Jeffreys(and Hawkings) all believe that probability is in the mind of the beholder. It measures our own lack of information. For Einstein, God does not roll dice. Reality is all deterministic even if the equations are not.
I don’t see why Economics should be different. We do not know how economic agents will act. Does that make them “random”? As though randomness was some physical property assigned to possible states of the world? No not in any way. Randomness is in the mind of the person who does not know all. De Finetti and Ramsey, Savage and Jeffreys (and Richard Jeffrey, see e.g.,http://en.wikipedia.org/wiki/Richard_Jeffrey) were all onto something very real when it was often quashed by the (then) orthodoxy of Fisherian school with all its triple negatives (“we cannot fail to reject the null hypothesis of X” Tell me who really knows what that means?).Bayes must be accepted if only because Ockham’s razor tells us, the interpretation is far easier in the long run. Meanwhile interpreting probabilities using DBAs (Dutch Book Arguments) a la Ramsey, gives them a very real (risk-neutral) pricing interpretation. Uncertainty then is an inability to find a unique mid. It all makes sense in a self-consistent economics interpretation sort of way. Why rely on ontological arguments for the existence of some other-worldly probability that has physical meaning when it only need be a unique price a la information markets!?!?
What is truly shocking is that Statistics departments have come fullswing and are full of Bayesians or agnostics (e.g., Donald Rubin and Brad Efron ), who use both Bayesian and (modern) frequentist methods (e.g., Bootstrap, Cross validation, frequentist nonparametrics) whenever they suit the problem to hand. But some of the best Bayesian stats goes on outside statistics departments (e.g.,in Poli Sci, see Andrew Gelman’s website, http://andrewgelman.com/ or Simon Jackman, http://jackman.stanford.edu/blog/ or in Physics and Comp Sci Departments, usually in areas of Machine Learning, e.g., David MacKay, Judea Pearl, et al). Nonetheless this world outside economics is Bayes’ friendly! (see e.g.,http://videolectures.net/ for a plethora of pro-Bayes’ lectures from CS and other areas, and see http://www.youtube.com/watch?v=8oD6eBkjF9o for the reception that the likes of Google gives authors who advocate Bayes’ rule—author S B McGrayne of The Theory That would Not Die). Bayesian methods now form the basis for much of Machine Learning, probably the most successful version of Artificial Intelligence there is, giving good reason for theirprominence in CS departments.
But Econometrics departments are full of die-hard Frequentists --Phillips and Granger and Gouriereux et al with their shockinglycomplex assumptions, complex mathematics, large sample theory (when was an economics sample ever that large? The only large sample is the one they generate using their computers!), etc -surprisingly wedded to their philosophy.
We can probably count the Bayesian Econometricians on the fingers of one hand—Zellner, Sims, Koop, Lancaster-- Maybe that’s it? (see e.g., http://en.wikipedia.org/wiki/Bayesian_econometrics). I don’t understand why! Some areas (e.g., I(0), I(1)-stationarity, cointegration theory) do not lend themselves to Bayesian analysis (Sims famously called it a prior on a set of measure 0, to which Phillips replied that the Jeffreys’ prior (for a hypothesis not a model??? I never heard of a Jeffreys’ prior for a hypothesis before this or after this paper!) should in fact have a Dirac mass appropriately placed). In the end, Sims’analysis is more elegant, less formalistic, easier to understand and allows plenty of explosive forecasts in the predictive densities! Some Bayesians have tried to wed the two although it makes for the unnatural priors on concentrated on cones (of rank one matrices!).Much easier to forget it all and use a Minnesota Prior!
And surprisingly, virtually every economist and finance PhD I have ever spoken with talks regularly about their priors and posteriors in reference to models, to visions of reality, etc. All of their principal agent models have some sort of prior or posterior in them even if Bayesian updating is not explicit. It figures well into the way they seereality. Most theoretical economists/finance PhDs will have complicated (DSGE) models for reality which, when it comes down to it, justify a few RHS variables in a simple regression and they do an OLS or GLS if they’re really sophisticated, and are done with it. Theyopt for ease (and linearity) in their PhD theses! In fact, I think F Black was one of the few theoreticians who didn’t seem to take on Bayes’wholeheartedly (see his paper on Noise-- http://www.e-m-h.org/Blac86.pdf). He speaks of knowledge all the time but forgets Bayes! It is clear that epistemological interpretations are far easier than others.
But the econometricians are all die-hard. Why? It is econometricians who are the truly egregious sinners here, not wanting to state what they believe because it in the end sounds just plain ridiculous. This state of affairs is enough to make one opt for the religious fervour of Bayesians as one can see in the zeal of Zellner or the stridency of Sims (to alliterate!). I can only imagine it is because the math is harder. As a former math (asst) prof who used to do lots of convergence theory (weak-star in the sense of measures, weal in this or that Sobolev sense, etc), there is an appeal to the mostly impenetrable and completely unintuitive analysis. Quasi-MLE and simulated method of moments. Wow. Amazing what you can do with millions of computer generated observations. Too bad we only have one historical path in reality—the stock market only did as it did once and we can’t seem to generate any other reasonable histories -- As a realist I see little sense in the methods.
For me, a PhD in Applied Math (in Nonlinear PDE) who never used a statistical method before learning (the frequentist) methods in fashion in Wall St, I found Bayes’ theory and philosophy a major relief. No more triple negatives. No more having to explain the craziness of hypothesis testing and why you chose 10% rather than 5% or 1% as a CI (because I got the results I wanted????). I only wish I could be more of a Bayesian in practice!!!
I might even liken the use of Bayesian methods in Economics to the use of Sabrmetrics in Baseball. There will come a time when the revolution happens and the frequentists will just have to stand back and give in, or be swamped.
Should we make it an active plan to promote Bayesian methods in Economics departments? To grow a new generation of Econometricians who are freed from the shackles of overly formalistic large sample theory favoured by frequentists? Should all intro courses in Econometrics be taught out of Koophttp://www.amazon.co.uk/Bayesian-Econometrics-Gary-Koop/dp/0470845678 or Lancasterhttp://www.amazon.co.uk/Introduction-Modern-Bayesian-Econometrics/dp/1405117206/ref=sr_1_4?s=books&ie=UTF8&qid=1373363994&sr=1-4&keywords=bayesian+econometrics? Should we actively work on the demise of a school of philosophy (frequentist theory or its “bastard child” propensity theory) which are so obviously lacking in any sensible interpretation?
Any comments or answers to my queries would be most welcome.
Best regards,
Nick Firoozye
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