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Don’t idealize “risk aversion”

Richard Thaler writes (click here and search on Thaler):

Both risk and risk aversion are concepts that were once well defined, but are now in danger of becoming Aetherized [this is Thaler’s term for adding free parameters to a model to make it work, thus destroying the purity and much of the value of the original model]. Stocks that earn surprisingly high returns are labeled as risky, because in the theory, excess returns must be accompanied by higher risk. If, inconveniently, the traditional measures of risk such as variance or covariance with the market are not high, then the Aetherists tell us there must be some other risk; we just don’t know what it is.

Similarly, traditionally the concept of risk aversion was taken to be a primitive; each person had a parameter, gamma, that measured her degree of risk aversion. Now risk aversion is allowed to be time varying, and Aetherists can say with a straight face that the market crashes of 2001 and 2008 were caused by sudden increases in risk aversion. (Note the direction of the causation. Stocks fell because risk aversion spiked, not vice versa.)

I don’t know anything about the stock market (except that I lost a lot of money when it crashed a couple years ago) so I pass on that .

But I am bothered by Thaler’s implication that all was good in the good old days when “he concept of risk aversion was taken to be a primitive; each person had a parameter, gamma, that measured her degree of risk aversion.” First off, why shouldn’t risk aversion vary over time? Young people are different from old people, life circumstances change, and cultural norms change as well. (In fact, Thaler in his parenthetical above seems to have no problem with risk aversion “spiking” as the result of a stock market crash.)

My second problem is with that single parameter gamma. As we’ve discussed endlessly on this blog (and as Yitzhak has demonstrated mathematically), people generally exhibit a level of uncertainty-aversion that is not consistent with any parameter gamma in a curving utility function. (See section 5 of this article from 1998. I actually mailed a copy of that article to Thaler back when it came out, so maybe he will recall it.)

In short, the classical risk aversion model does not capture actual aversion to risk.

To back to Thaler’s analogy to astronomy, the traditional risk aversion and utility model is like the old-fashioned geocentric model of the universe–without the epicicyles. Thaler is annoyed at people adding epicycles (“aether”) to make the model work. But my problem is with the original model. If you really need need need to have a utility model for risk aversion–I argue that you don’t–then you better add some epicycles or your model will be completely useless. I understand the appeal of a lost world of simplicity, but you can’t get that back. There’s no returning to the world of Neumann and Morgenstern or even Luce and Raiffa. There’s no way to go but forward. Thaler recognizes this in his own research–huge contributions on the border of psychology and economics, going well beyond naive utility theory–so I think this thing he wrote is an atypical descent into nostalgia.

P.S. Thaler also writes, “there is no need for a term that refers to something that does not exist.” That sounds reasonable enough, but . . . unicorns!

8 Comments

  1. Concept Modeling…

    […] copy of that article to Thaler back when it came out, so maybe he will recall i […]…

  2. C Ryan King says:

    In defense of Aetherists, recall your earlier article on how over-parameterizing often gives a useful interpretation, and then you slap some constraints / identifying assumptions on to make it estimable.

    In the example given, the too-strong assumption is probably independence; once things start to move people remember their irrational anxiety. Hey, then you have an interpretable parameter again (contagion) whose time course is something you can study (information diffusion).

  3. Jack says:

    The basic model ("primitive… one parameter gamma") is invaluable for pedagogical purposes: to introduce basic models, the idea of risk aversion, establish classical results, and then let students try to estimate the parameter using data, and when they flounder, discuss the limits of the model and different ways the literature has tried to tackle the problems, especially empirically. Thaler seems to want a return to parsimony, but if the data reject the model, what should we do?

  4. Tal Yarkoni says:

    I'd be surprised if Thaler has any deep commitment to the classic one-parameter prospect theory formulation where gamma representing loss aversion. I simply read him as saying that when the empirical data blatantly contradict an existing model, the thing to do is rethink the fundamental assumptions of the model, and not to just patch it with another parameter. The classic risk aversion model was a crude approximation to the truth that at least had the benefit of mathematical elegance; newer formulations that add parameters ad hoc end up losing the elegance without gaining anything in understanding. The context to keep in mind is that every time Thaler and other behavioral economists publish a paper that seemingly turns classical assumptions on their head (e.g., by showing that people don't exhibit consistent preferences), the response from many (certainly not all) economists is to add a parameter to their existing models that allows them to go on ignoring the fundamental point being made. I don't think Thaler's point is that the old models were good, just that adding parameters ad hoc is the wrong way to improve them.

    • andrewgelman says:

      Tal:

      I see your point, but when Thaler writes, "I am planning to refer to the time-varying variety of risk aversion as Aether aversion," that sounds to me like he thinks the good old non-time-varying variety is fine. If we're going to be talking about risk aversion at all, I'd prefer the time-varying variety.

      • Tal Yarkoni says:

        The problem with time-varying risk aversion (and I can't claim to speak for Thaler here, but I think this is what he's getting at) is that it completely abdicates explanation and becomes close to circular. Much of the economic enterprise is predicated on the idea that people have consistent preferences (even though those preferences may be very strange). Once you allow time-varying preferences into your model, you can "explain" away almost any finding you observe. Can the model handle the fact that risk-seeking investors suddenly became risk-averse following the crash? Sure, because you just need to posit that their preferences changed. But the problem is that your model could have explained the opposite shift equally well–or pretty much any other pattern. Even violations of transitivity become moot: it's not that I like A > B > C > A; it's just that in between your asking me about A vs. B and C vs. A, my preferences must have changed. So you can no longer falsify the model, because literally any behavior can be explained in terms of transient changes in preferences. I think that's the problem here, and not simply the fact that there are additional free parameters in the model.
        That said, I also see your point, and maybe part of Thaler's objection really does stem from excessive attachment for the classic risk aversion model. I guess the real question is how he would react to a more complex risk aversion model that allowed preferences to vary over time in a constrained (i.e., non-Aetherized way)–e.g., by taking into account measurable personality differences or environmental conditions.

  5. BWV says:

    another fundamental problem with the concept is defining risk naively as "risk of loss". The equity markets are dominated by professional money managers whose performance is measured against passive benchmarks over short time periods. The real risk they analyze is that of underperfoming their benchmark. Assuming these money managers are rational actors, they are managing their career risk with at least equal attention as the funds of their clients. They are well aware that as the market goes up more often than it falls they are more likely to be fired for underperfoming a bull market than be fired for underperforming in a market decline. There is also a herding dynamic, as one only gets fired for being wrong and alone. Therefore they are incented to own a riskier basket of securities than the market as a whole, particularly if the market has been performing well.

  6. Mayo says:

    Gelman didn't say whether he ever made back his stock losses, I assume not, but I've kept that in mind for a day like today with the market crash. We may be witnessing a point once again where it is very possible to double invested funds…. as I luckily managed to do last time. Does statistical/risk analysis trump stock-market intuition/psychology/knowledge of nitty -gritty details of a company? Probably not. But…