“It would be as if any discussion of intercontinental navigation required a preliminary discussion of why the evidence shows that the earth is not flat”

I’ve been ranting lately about how I don’t like the term “risk aversion,” and I was thinking it might help to bring up this post from last year:

This discussion from Keynes (from Robert Skidelsky, linked from Steve Hsu) reminds me of a frustrating conversation I’ve sometimes had with economists regarding the concept of “risk aversion.”

Risk aversion means many things, but in particular it is associated with attiitudes such as preferring a certain $30 to a 50/50 chance of having either $20 or $40. The standard model for this set of attitudes is to assume a nonlinear function for money. It is well known that reasonable nonlinear utility functions do not explain this sort of $20/30/40 attitude (see section 5 of this little article, for example); nonetheless the curving utility function always comes up in discussion, requiring me to waste a few minutes before going on, explaining why it doesn’t explain the phenomenon.

It would be as if any discussion of intercontinental navigation required a preliminary discussion of why the evidence shows that the earth is not flat. . . .

13 thoughts on ““It would be as if any discussion of intercontinental navigation required a preliminary discussion of why the evidence shows that the earth is not flat”

  1. $20, $30, $40 is the wrong conversation. Sure, with such small amounts, any curvature in the utility curve will be hugely magnified when extended to serious money, as Andrew points out.

    In my classes I discuss with the students what would be serious money for them: amounts ranging from $10,000 (a significant fraction of their tuition) to $1,000,000 (getting close within a factor of a few to not ever having to work again, if wisely invested).

    There has to be a serious difference between the value of the items before any utility/loss conversation makes any sense.

    So, between a 50/50 chance of $1,000,000 and a sure $300,000, my class this year was pretty indifferent. It took going down to $100,000 before most took the gamble. (I had one risk-taker who was happy to gamble against a sure $500,000 and even more; and there were one or two who wouldn't even take the gamble against a sure $100,000.)

  2. I don't think you are thinking about risk aversion correctly. While I'm sure some people may take $10 over a 55% chance of $20, there is a very different explanation for such behavior suggested by your subsequent post about Nigerians: trust of the experimenter. A certainty of $10 is verifiable; and experimenter who fails to deliver lied. Even a 99% chance of $20 is going to come up zero some of the time and is much harder to verify; the experimenter certainly has an incentive to pad the zeros. Such logic means that the thought experiment behind risk aversion is exceedingly difficult to test empirically and experimental tests should be viewed with care.

    If the public actually were willing to give up $1 to insure a $10 risk, insurance companies would be substantially wealthier than they are. Even the equity premium puzzle, which suggests people are unnaturally risk averse given the rate of return on stocks relative to that of federal government bonds (2008-9 nonwithstanding), doesn't produce this kind of risk aversion.

    While there are indubitably challenges to the empirical validation of risk aversion, the argument you promote isn't one of them. To parody, the argument says "some people may be excessively risk averse so the theory is flawed."

    My recollection is that choice models that do not satisfy expected utility are vulnerable to dutch books. This is a pretty solid reason for accepting expected utility, at least as a working model. This doesn't entail people being averse to risk, but does entail people having a value of wealth function.

  3. Bill, Preston: Definitely. I have no problem with the discussion at large monetary scales, and I have no problem with considering different psychological explanations for most people's strong preference for the $30. My problem is that, if I bring up the $20/30/40 example, economists (even those who should know better) bring up the nonlinear utility function as their first explanation–their first line of defense, as it were, against any implication that people might have irrational preferences. My point is:

    (a) The nonlinear-utility-function argument is irrelevant to any discussion of the $20/30/40 problem. You might as well attribute the weather on a blustery Chicago day to the pressure of neutrinos coming from the sun. It's just the wrong sort of explanation.

    (b) More generally, it's exhausting to have conversations in which the first step ia a careful discussion of the $20/30/40 problem, just to explain that, no, what is called "risk aversion" doesn't need to have anything to do with a nonlinear utility function. Or, for that matter, with "risk" (given that there's actually no risk involved in that example, all of which is free money. I mean, you could call it "risk" but then that's just the name you're giving to any uncertainty. If you want to use that sort of definition, I'd prefer you just call it "uncertainty" to avoid misleading connections with the English language).

    The study of uncertainty aversion and even risk aversion is fine–important, even–but I don't think it's helped by the fact that the nonlinear-utility-function model is always the first thing that's brought up. I'm not kidding that economists I've talked to reflexively use that model to explain the $20/30/40 phenomenon.

  4. But I think that's because economists are busy teaching rather than listening. When I ask you a hypothetical, no one wants to hear the (correct) answers given above by Profs McAfee and Jeffreys, ie, your hypothetical doesn't express an important part of the world we economists want to explain. So, we fall back on the way we learned it and try to shoehorn in this hypothetical into stuff we learned (but never applied seriously) in graduate school. Then, since the hypothetical is in that sense a trick question, we discover it has counterfactual implications, so we backtrack.

    Let's try an analogy: It's a little like Taleb making fun of statisticians for always using normal errors. They often do as a first approximation, or when in teaching mode. And indiscriminate use of normal errors is something no statistician does. But it doesn't mean it's not the first thing dragged out when in teaching mode.

  5. If statisticians are using the normal distribution when they shouldn't, and it's hurting them, then I think it's very appropriate for Taleb to make fun of them.

    I'm skeptical of your implied claim that people (economists, statisticians, etc.) are saying dumb things in class but then are getting it right in their applied work. I think it's much more plausible that many people–even top researchers–haven't thought things through and are stuck in what Lakatos et al. would call degenerate research programs (or, to be more precise, degenerate aspects of their research programs).

  6. A quick response: first, it's not clear to me that they are using it when they shouldn't. Most of Taleb's claims, I think, go to a parody view of what statisticians are actually doing. Second, I suspect most of the people you talk to about these issues aren't really using then in their applied work at all, rather than investing in a degenerate program. (By the way, I'm a huge fan of Lakatos.) That's not to say that I don't think there aren't any degenerate research programs in economics — I just don't think this one of them. I think it highly unlikely that they say dumb things in class related to their own work. Indeed, in my experience, when talking about their own work, you're likely to get a much more nuanced view than you really wanted… like adjustments for spherical oblateness in intercontinental navigation before a discussion of longitude.

  7. Economics has more than its share of people for whom belief in theory clouds their vision of the world. (Hence the famous joke about the $10 bill on the ground.) Economists suffer the normal level of Maslow's "when your only tool is a hammer, every problem looks like a nail." But doesn't your rant share Maslow's problem? Risk aversion is a *valuable* tool. It isn't relevant at $10 gambles for most Americans but your characterization is like saying computers aren't useful because they won't clean bathrooms.

  8. Preston:

    I think utility theory is great, both in theory and even in practice (which is why I devoted a chapter of Bayesian Data Analysis to it). And I have no problem with the study of risk aversion–that is, of the psychological/economic phenomenon of aversion to risk. I also think it's a good idea to study aversion to loss (not the same thing as risk, for example people don't seem to even like to lose $10, but that's hardly a "risk" in the usual sense of the word) and aversion to uncertainty (as in the $20/30/40 example). All three of these phenomena seem interesting to me, and important enough that it's worth keeping them as three separate concepts. Heck, I even like the game Risk.

    But . . . I think that equating risk aversion to the declining utility of money is a mistake that doesn't help anybody. Given the well-known phenomenon of uncertainty aversion (even apart from loss aversion or risk aversion), I don't think it makes sense to use people's preferences over gambles, at whatever scale, to try to assess their utility functions.

    I'm sure that there are lots of useful tools that people have for addressing these problems in applied economic analysis; as noted above, my frustration comes from always having to clear the air about risk aversion, uncertainty aversion, etc. I really think the term "risk aversion" does more harm than good, by leading people to think that there's one single concept that handles all these different psychological/economic phenomena.

  9. I don't disagree; a lot of related but different behaviors are often wrapped up in risk aversion, and risk aversion in the form of concave utility ought to be restricted to gambles that are an appreciable amount of income. This is pretty much a cornerstone of finance and to toss it out because it has been confused by some with ambiguity aversion or status quo points or other ideas.

    Using utility as a function of money is a convenience, justified in general equilibrium by the the indirect utility function.

  10. I would define a person as "risk averse" if he always prefers the expected value of two different wealth levels to a gamble between them (using known probabilities). I agree that "uncertainty aversion" would be a better term, but we're stuck with history here.

    Given that definition, then I claim that if someone is risk averse for all wealth levels and probabilities, and one can summarize that person's behavior by a vNM utility function, that function must be concave.

    However, I agree that you can't really summarize most peoples' behavior using a vNM utility function. But this is a problem with the vNM utility function, not the concept of risk aversion per se, which is purely behavioral — it is based on choice behavior that is described completely independently of whether or not those choices can be described by a particular form of a utility function. (Of course there are many people that aren't risk averse, at least for some gambles — Las Vegas is full of them.)

  11. Hal:

    I agree. If "risk aversion" is used as a term to describe behavior consistent with aversion to risk, I have no problem with it. My problem is with the assumption that such behavior can be described by a utility function.

  12. @Andrew;

    Is your objection then to one or more of the axioms which guarantee the existence of a function, f, that maps the relation X is riskier than Y, to a real number, such that X is riskier than Y iff f(X) > f(y)?

  13. Michael:

    No. My problem is the immediate rush to take any behavior (for example, the notorious indifference between "$30" and "55% chance of $40, 45% chance of $20" and attribute it to a curving utility function for money, rather than simply a negative utility for uncertainty.

    The curving utility function for money does not fit the data (as explained in my paper and in Yitzhak's, if you curve the utility function enough to fit the preferences described above, you get a utility function that makes no sense, a utility function where $1,000,000,000 is barely distinguishable from $300), whereas a negative utility for uncertainty does fit the data.

    From a normative standpoint, I don't think it makes sense to have a negative utility for uncertainty, but description is different.

    As for the sharply-curving utility function for money: well, that's neither normatively nor descriptively appropriate. And it frustrates me that people treat this model as a baseline.

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