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Risk aversion is not a thing

I came across this post by Alex Tabarrok arguing that people should be given one rather than two doses of a new vaccine. I know nothing about these vaccines but my attention was drawn to this statement from Alex:

We should vaccinate 6 million people with first dose NOW. It is deadly cautious to hold second dose in *reserve*.

His phrase, “deadly cautious,” reminds me of a problem that I’ve had for a long time regarding ideas such as caution and risk aversion.

We have this phrase, “risk aversion,” that’s used a lot in social science. But what does it mean? I argue that caution or risk aversion is a state of mind more than it is a clearly defined economic concept.

For example, in the vaccination setting, is it risk averse to give everyone two doses (that’s safer for each person getting the dose)? Or is it risk averse to give out just one dose so you can vaccinate more people (as this could minimize tail risk in terms of total deaths)?

Another example comes up when shopping. Is it risk averse to save your money (because you might need it later)? Or is it risk averse to spend it now (because one in the hand is better than two in the bush)? Saving somehow seems more risk-averse than spending, but it’s not clear to me that this alignment stands up to scrutiny.

None of this is meant to express any comment on Alex’s particular recommendations. It’s just that his framing of “deadly caution” reminded me of the emptiness of the often-used but, I believe, poorly-understood concept of risk aversion.

This has come up before:

Risk aversion is a two-way street

Don’t idealize “risk aversion” (and don’t idealize celebrity economists who are patronizingly trying to explain things to you)

Slipperiness of the term “risk aversion”

More on risk aversion etc etc etc

Risk aversion and money

“Loss aversion” isn’t always

“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”

“It’s as if you went into a bathroom in a bar and saw a guy pissing on his shoes, and instead of thinking he has some problem with his aim, you suppose he has a positive utility for getting his shoes wet”

P.S. This also relates to our earlier post from today and a bit to this one too.


  1. Joshua says:

    > Another example comes up when shopping. Is it risk averse to save your money (because you might need it later)? Or is it risk averse to spend it now (because one in the hand is better than two in the bush)?

    They had a huge sale at the store today. I had to buy a lot of things I wasn’t expecting to buy and don’t particularly need – because I saved so much money I couldn’t afford to pass it up.

  2. Yuling Yao says:

    I think risk aversion= choosing a convex loss function, for which some type of Jensen’s inequality will encourage to distribute the utility more evenly (saving for future rather than consuming all now, giving up cold fusion after a few years try, buying ETF rather than individual stocks, rao-blackwellization in Monte Carlo, etc.)
    If the dose vs expected effect is linear (1 dose is 50% effective, 2 doses are 100% effective in expectation) and the utility is the sum of all individual effective probability (in contrast to, say the max), then the Jensen’s inequality encourages to vaccinate more individuals. On the other hand, the dose effect is generally not linear (often, concave), hence there is no easy worked out solution and both narratives can make sense.

    • There’s decent evidence that one dose of the current vaccines is nearly as effective as two. Furthermore to hold one dose in reserve as if the company isn’t going to ramp up production and deliver more later so we need to be sure that we can double dose this small group of people now… Is insane.

      This article covers it pretty well

      • dhogaza says:

        For Pfizer that data showing it is nearly as effective is for preventing a symptomatic case starting on Day 14 after the first shot until Day 21 when the second shot is given.

        Nothing in the Phase III trial evaluated durability of the immune effect after one shot.
        With the two shot regime, it’s known it lasts at least two months and given the very few number of cases during that period certainly longer.

        Also nothing in the Phase III trial measured how effective the vaccine is at preventing infection, a key consideration if the vaccine is going to reduce the rate of spread of the disease. There is data from their non-human primate trial that preceded the human trials that indicate it is effective, and the one statement I’ve seen from them on this is that they expect the two-shot regime to be at least 50% effective in reducing transmission, and probably much better. I’d be amazed if they didn’t trial one-shot and two-shot treatments and compare them in the non-human primate trials.

  3. Robert says:

    Isn’t this just “being risk averse with respect to outcome X may be the opposite of risk averse for outcome Y”? I don’t see why this makes risk aversion more slippery than any other term that leaves a context implicit. It seems to me like you could throw away most of statistics with this complaint; taking every concept that depends on a variable X, removing all mention of X, and then saying that the concept is ill-defined. “Expected outcomes aren’t a thing: is a coin flipped 1000 times expected to be 50% heads (average) or not (50/50 will rarely happen)?” Anyone who understands mean and variance sees the implication of conflict in this statement as faulty, but you seem to regard risk aversion as different and I’m not seeing why.

  4. MJ says:

    “For example, in the vaccination setting, is it risk averse to give everyone two doses (that’s safer for each person getting the dose)? Or is it risk averse to give out just one dose so you can vaccinate more people (as this could minimize tail risk in terms of total deaths)?”

    From the sound of it, both options can be rationalized by risk averse preferences. It’s not an either/or proposition. Risk aversion can take many forms — one risk averse person may prefer the latter and another risk averse person could prefer the former. Risk aversion isn’t deterministic in terms of choice in most situations (unless there is stochastic dominance, which isn’t happening in your example).

    “Another example comes up when shopping. Is it risk averse to save your money (because you might need it later)? Or is it risk averse to spend it now (because one in the hand is better than two in the bush)? Saving somehow seems more risk-averse than spending, but it’s not clear to me that this alignment stands up to scrutiny.”

    It would depend on the (subjective) probabilities associated with the various events you’re describing, i.e. job loss or financial collapse that wipes out savings. What you’re describing here is just a compound lottery. Given utility and subjective probabilities, it’s trivial to calculate risk preference for this situation.

    Risk aversion is quite clearly defined economically. The mistake seems to be in thinking that it’s some universal axiom, rather than specific to the lottery in question. It’s perfectly rational to be risk averse over some lotteries and risk seeking over other lotteries.

  5. elin says:

    Risk aversion is definitely the wrong framing for this. Right now the only data we have on single doses is based on the period between the first and second dose. It shows about 52% efficacy. We don’t know if that changes with more time and we also don’t know if a single dose might reduce severity if you do get the virus or might reduce your chances of transmitting it. We also don’t know a lot of other things like what happens with longer or shorter intervals or if someone gets two (or three) different vaccines. The FDA has standards for making judgements on these, and they actually also, as we have seen, deal with risk in a variable way such as compassionate use, emergency use, and so on. It could be that by the summer there is much more knowledge and at the same time lower risk groups are starting to get vaccinated and they might make a decision at that time to go with lower efficacy, but that’s a decision that has a known, standard process. We may have better therapies at that point as well, not to mention wider access to them.

    • Dale Lehman says:

      Yes, risk aversion aside, this particular context touches on another theme we’ve discussed frequently on this blog. Tabarrok (and Cowen, his co-conspirator) frequently display the predilection of economists to think that their knowledge of economics suffices for them to be experts in everything. Perhaps all disciplines do this, although I find it most irritating among my fellow economists. Tabarrok is not an expert on infectious diseases but believes that his knowledge of economics is enough to make policy decisions regarding the best policy for these vaccines. Let’s just say I don’t share his belief.

      • jim says:

        I guess the problem arises for several reasons:

        1) once a problem can be placed into a general framework with a limited number of constraints, the benefit of specific subject expertise is drastically reduced;

        2) not every epidemiology problem is a *biology* problem; This is a relatively simple distribution problem and Tabarrok – like many other educated people – has sufficient expertise to assess it;

        4) the public health hierarchy hasn’t distinguished itself during this pandemic for its bold foresight and decision making and is more or less inviting critics with it’s bumbling.

    • But in what universe does it make sense to reserve half your doses so you can double dose all the people on your list even if no further doses of the vaccine are ever made? Because we know billions of doses are going to be made! We should absolutely dose many people once and then wait for the next shipment to do more people once and critically important people for second doses… And roll out this way rather than being strict about 2 doses for everyone

      • Dale Lehman says:

        I’m actually shocked that Daniel and jim are ready to support the single dose/twice as many people option. Sure, it has some logic – but what evidence do we have that one dose will work? It is certainly not my expertise, nor do I think it is Tabarrok’s. And I haven’t seen any evidence that a single dose will work. And I believe that public health professionals would be considering such options. So, I am very reluctant to substitute a conjecture, without evidence, that flies in the face of what the vaccine manufacturers believe.

        Further, I don’t agree with jim’s suggestion that the credibility of the “public health hierarchy” has been damaged so much that perhaps Tabarrok and “many other educated people” should be trusted over that hierarchy. Sure they have made mistakes – big ones. But I haven’t reached the point of ignoring their advice in favor of “educated” economists.

        • elin says:

          All we really know at this point is that for 2 weeks the people who got the first dose did better than placebo, but there were not enough cases in that time span to really conclude anything. It’s promising but no more than that.

          With the flu vaccine the elderly get a stronger formulation. Perhaps by the time we get past the highest risk groups we will have some more evidence and some of the other variations will have accumulated enough cases to be able to estimate efficacy for the less high risk. That might include one dose or two doses spread out over longer time. I think pregnant and lactating women will be studied soon (they were excluded from the initial studies) as might children under 16. In those cases trying single dose might make sense. But the size of these trials is 35k or more which allowed accumulating enough cases over a few months. With one dose compared to two doses (since that is the standard of care) it will take a long while. And that’s me, not an expert, but reading the journal articles and CDC reports.

      • Carlos Ungil says:

        If you’re going to ignore the label, why stop there? Instead of two doses to each patient, or one, give them one quarter of a dose. You can then vaccinate eight times as many people!

    • Anonymous says:

      Can I get the source on the 52% efficacy of a single-shot? I’ve been seeing this graph:

      Eyeballing it, it looks to be more than 50% effectiveness in the first month, accounting for the week or so before it kicks in. But I haven’t done actual analysis, and don’t know the domain, so I’d like to read more.

    • dhogaza says:

      “Risk aversion is definitely the wrong framing for this. Right now the only data we have on single doses is based on the period between the first and second dose. It shows about 52% efficacy.”

      The efficacy is close to the two-dose regime for Day 14 through Day 21 (second dose). The 52% number includes the two week period, during which the amount of neutralizing antibodies is building.

      “… or might reduce your chances of transmitting it.”

      That’s the key, and they don’t actually know if this is true for the two-shot regime, either, at least for the human trials. They do have data from their non-human primate trial that suggests the vaccine does reduce transmission. They would not have pulled the decision to go with a two-shot regime out of their ass, any more than the Shingrx people did. They probably have data from in vitro and non-human primate testing that gave them a target for what level of antibody titers they should aim for, and that combined with tolerance for the vaccine led them to a two-shot regime.

      • elin says:

        Yes I do think many people are ignoring both that they know a lot from phase 1 and that they know things from animal studies. These vaccines were also not created from scratch, they build on what was learned from SARS-1 work when that seemed likely to cause a pandemic.

        People also are ignoring that it is a normal part of things to continue to develop and test formulations and protocols after initial approval.

  6. Dzhaughn says:

    How about framing it as Blame Aversion? Certain failures result in a greater loss of status than others. The cost of that loss of status has to be part of a decision analysis.

    Approving a bad vaccine is very much worse for the FDA than getting a good one 6 months later. Lots of people who were vaccinated getting the disease is bad optics, too. If controversy leads to people deciding against getting vaccinated, that’s bad public health policy.

    There’s a limit to how many mistakes the public will tolerate from anyone. Well, from almost everyone.

  7. James says:

    This has nothing to do with risk aversion. Risk aversion is about individual preference and can be derived from the decreasing marginal utility of some good. Risk aversion describes why most people would choose 1 million dollars in the bank over a 50/50 shot at 2 million dollars (let’s pretend 0% tax rate).

    This debate is about how much society should be worried about uncertainty of impacts, which is completely different. This is decision making under real uncertainty about what the consequences of different vaccine delivery trials might be, and with different values and preferences around how to choose from distributions over outcomes. Yes, some people might prefer 100K certain deaths over a coin flip between 50K and 150K deaths, but risk aversion really isn’t a helpful language.

    • rm bloom says:

      Individuals never have the chance to make choices like the one in the jejune example above. Consequently when “economists” speak ex-cathedra about what individuals would or would not do in such “circumstances” they might as well be telling us that martians prefer to eat this variety of marmalade with their waffles on martian christmas. It would be bending over backwards to even call such constructions counterfactual conditionals. The individual who is faced with a difficult decision, certainly is in a bind — does he spend his last paycheck to fix the car or visit the doctor, say. Well it depends on the circumstances. He may have money in the bank; he may not. His father-in-law may be generous; he may not be. The distinction between exogenous and endogenous factors conditioning this specific person’s action is not so easily made. The economist tells us, well, yes, but we can be quite certain of one thing, which is every person carries with him a schedule so-to-speak, according to which he will make his “bets” in favor of such-and-such and in avoidance of such-and-such. An invariant mathematical function, Voila! Rubbish. His “function” on Tuesday when he’s feeling up is not the same as his “function” on Wednesday when he’s feeling down. Perhaps, says the economist, this schedule is only an idealization, of what this individual *means* to do, when (and only when) he’s at his most rational best; when he’s not drunk, or feverish or enraged at the TV news; i.e. when he’s acting as he *ought* (if he were a reasonable chap), though not always when he’s acting as he actual does. Adler, the psychologist, tells a joke about the cult of the Prophetess who’d announced to her followers one day that the world would be coming to an end the following Wednesday. The faithful followers of course sold all their worldly belongings anticipating that these things would be of no use in the conflagration. And when, the following week, the prediction proved false, the assembly, in a very ill humor, confronted her and asked what was the meaning of this? With a mysterious smile, the prophetess explained, “Yes, I did say the world would come to an end this Wednesday; but you must realize of course, that *your* Wednesday is not *my* Wednesday!”

      • MJ says:

        “The economist tells us, well, yes, but we can be quite certain of one thing, which is every person carries with him a schedule so-to-speak, according to which he will make his “bets” in favor of such-and-such and in avoidance of such-and-such. An invariant mathematical function, Voila!”

        No economists believe this. “Utility maximization” is a theoretical construct that allows us to (very accurately) describe and predict market behavior. We don’t believe that humans actually solve a convex programming problem each time they make a decision any more than rocket scientist believe in Newtonian action at a distance, or a Bayesian believes that a likelihood is an IID normally random variable. Tractable science requires abstraction.

        • rm says:

          How accurately did economists predict market behavior; earlier this year? Last year? Did the economists have some preternatural foresight, so that their equations told them remarkably what sort of turmoil the whole world would be struggling with at this time? What about before the crash of 2008? 1987? Have there been aggregates (like Gelman’s Economist aggregated Poll set) of predictions made which indicate the extent to which these predictions are doing anything other than merely putting an interval around the noise — which is able of course to capture almost any event next month, short of a catastrophe (which of course is never predicted)?

  8. Anon says:

    You might not understand risk aversion, but it doesn’t mean it’s not a thing. Have you seriously engaged with the academic literature on risk aversion? If not, why? Assuming you haven’t: Try reading about something a bit more carefully before you say that it doesn’t exist! Or else hot takes like these are better left for Twitter.

    • Andrew says:


      To be clear: Yes, people are often averse to risk. In that sense, risk aversion is definitely real. But I think it is better understood as a psychological than an economic phenomenon, and I think it’s generally a mistake to think of risk-averse behavior or preferences as being a utility-maximizing response to a nonlinear utility function.

      • rm bloom says:

        Or a utility-maximizing response to a nonlinear utility function, which is itself a dynamic function, depending upon time, on the time-history of the individual, the present circumstances surrounding that individual, the time-history of those surroundings, his present family circumstances, the time-history of that family circle; and likewise the city and state and country in which he finds himself; not to mention the city block; and we might as well throw in the tides, which do effect the weather after all; but then we must consider the motions of the moon; the other major and minor planets; and so on. This holy grail — the “personal utility function” — an “equation” if one allows for maybe a countable infinity of time-varying terms; one group for every person in the individual’s “local group”; second order terms for all those persons in the local group of the subject’s local group; and so on. Perhaps there is a cosmological principal here? Maybe a Nobel-class physicist has something to say about it after all. Maybe God is an academic, too.

      • MJ says:

        Can you clarify what you mean by this? Surely you can’t be claiming that risk preference is not relevant for economic behavior, or the study thereof…

  9. Min says:

    I suppose that the Pfizer vaccine and the Moderna vaccine require a booster only a few weeks after the initial shot because of pilot studies. It does seem that we have evidence that the first shot is pretty effective. But is it effective enough for the vaccinated person to engage in the same degree of social contact as before the pandemic? If so, why the boosters? If not, what behavior is safe?

    Besides, the vaccines were not tested for infectivity. Just because your body can fight off the virus successfully if you are infected does not mean that you are not shedding the virus to others for some time.

    Does Tabarrok know something nobody else knows?

    • Don Baccus says:

      “I suppose that the Pfizer vaccine and the Moderna vaccine require a booster only a few weeks after the initial shot because of pilot studies.”


      “the vaccines were not tested for infectivity.”

      Pfizer has some data from their early non-human primate trials, and Moderna did some serological testing, that supports them being effective at reducing transmission. I would imagine that Moderna has data from their pre-human trials, too. I’m sure the two-shot regime wasn’t pulled out of their collective rear ends but, as you say, based on data from their early studies.

    • Jonathan says:

      What is missing from Alex’s discussions is the views of people who developed the vaccines. There may be very good reasons why they expect that a single dose has a high risk of having too weak or too transient an impact. I would value those views more than those of Alex on this matter.

    • Dale Lehman says:

      This just came out today: For the record, I can’t locate the purported statement by Klugman on twitter, but that could be because I am (proudly) social media impaired. Nor have I seen the evidence of 90% effectiveness from a single dose. This could all be true – but on the other hand, the standards for what are taken as “facts” seem to be degraded daily.

  10. Renzo Alves says:

    “One can perish from an excess of caution.”

  11. Petros Boutselis says:

    My humble opinion is that “risk-averse” is a decision-making qualitative rule that expresses things like the ones discussed above. However, being qualitative means that in order to be operationalized, additional elicitation efforts would be required. On the other hand, and given no other data to proceed, having a “risk-averse” attitude suggests being “conservative” in the choices for a course of action, which again suggests applying something like a “maxmin” strategy in decision making under uncertainty.

  12. Dale Lehman says:

    Risk aversion is a real thing – and it can be defined in terms of willingness to take a fair bet. That doesn’t mean it has to be defined that way – many concepts can have multiple definitions, but the simplest one suffices for many purposes. What this post illustrates, however, is that the definition does not help us examine any real choice. All choices involve risks regardless of the decision make – there is no certainty equivalent option. We always choose between alternative risky courses of action – that differ according to probabilities, consequences, and knowledge. Another important feature of the choice involves reversibility – if/when a mistake is made, how many of the consequences are irreversible? Once a particular definition of risk aversion is chosen, application of that definition to any particular decision will require consideration of all these dimensions. Risk aversion alone will not enable a decision to be reached.

  13. Avery says:

    The term “Abundance of Caution” is quite popular among government and corporate officials in recent years, as a defense of their actions that might be viewed as arbitrary or questionable.

    Also, the “Precautionary Principle” was a popular social science concept in previous decades.

    Questions of risk hinge upon risk to who (?), personal risk or collective risk to a group or general population.

    (the 2-dose Pfizer vaccine option is officially stated as a safety measure to reduce adverse side effects among individuals — a single full-strength dose obviously would speed up mass inoculations and greatly reduce logistics problems)

  14. Anonymous says:

    ” is it risk averse to give everyone two doses (that’s safer for each person getting the dose)? Or is it risk averse to give out just one dose so you can vaccinate more people (as this could minimize tail risk in terms of total deaths)?”

    Speaking of context, this statement misstates Tabarrok’s argument, which presumes that the second dose will be available for everyone eventually, but *possibly* not in a timely fashion. The question he asks is framed by the context of the *possibility* of *temporarily* running out of vaccine.

    This is his claim: given that a single dose is likely to be effective to a significant degree, and given that the second dose will come soon no matter what, it makes more sense to give the first dose to as many people as possible, rather than to use the current supply to give half as many people two doses.

  15. JIM says:

    It’s clear from empirical data that in general / on average people make rational choices when they have the freedom to do so. By that I mean rational in so far as the risks are known and the people aren’t disabled (e.g., addicts, mental health issues etc). The only reason the question arises at all is because some political groups want a justification to take people’s ability / right to chose away and thereby confiscate the wealth that the right to choose generates.

    The idea that every individual needs to make a finely adjusted calculation for every decision or even a major life decision is silly. Most people don’t do that because they don’t need to: they simply observe what has been successful for other people and copy them. It may not be the *exact* optimal solution, but it’s usually close enough.

    • rm bloom says:

      “It may not be the *exact* optimal solution, but it’s usually close enough.”

      The presumption that there is *an* optimal action to be taken in every circumstance; and that our actions can be ranked by their closeness to it. This is the sort of Ptolemaic idealization that cannot fail to explain; but because it cannot fail to explain, it explain nothing. What measure of optimality is relevant depends upon where you stand and whom you ask. It is not merely that “a dollar is worth more to a beggar than to a millionaire”. One beggar might not grovel for a dime let alone a dollar; and some millionaires have been know not to part with a dime. The value in the transaction may have nothing at all to do with money. The motive to act one way or another may be pride; it may be humility; it may be sadness; joy; religious feeling; it may be nostalgia; dementia; clairvoyance….

      Eighty some years ago physicists had to come to terms unexpectedly with what seemed fundamental limitations on the classical mechanistic paradigm; that if *only* we had sufficiently precise information on the state of every particle in the system (or in the universe!) at an earlier time, *then* we could — “with enough computational agility and power” — figure where the system (or the entire universe!) would find itself at some subsequent time. At the present juncture it still remains a seeming paradox, but (look at the Bell phenomenon) the consensus would appear that even a single so-called ‘photon’ does not travel through space and time with a well-defined polarization access; until that is it interacts with a measuring device.

      Perhaps the Laplacian conceit has just moved house; from its 19th century domain in physics; to its present-day certitudes in respect to “economic man”.

  16. D.O. says:

    Sorry, I didn’t read all previous posts, maybe it was already covered, but I think that though the concept of risk aversion can be viewed as “psychological” it can be a part of a straightforward model with a clear menaing. For example,we can look at hedging or insurance. You give up a bit of money on average to prevent or cusion catastrophic loss. The other side of the transaction can withstand dispertion better, partially by pulling risks. In this sense, risk aversion is simply the result of finite resources, which is pretty real and is not some philosophical black hole.

    Now, to the vaccine. Suppose unvaccinated person has probability to catch virus (over some period of time) p0, single-dose vaccinated p1, and double-dose vaccinated p2 and there is no interaction (not very realistic, but whatever). If there are 2 doses for 2 people then “single dose for both” regime has smaller expected number of people getting sick if 2*p1 < p0 + p2. Variance is 2p1(1-p1) in the first scenario and p0(1-p0)+p2(1-p2) in the second. It means that "risk averse behavior" is to take "two doses for one person" approach when p0+p2< 2p1 < p0+p2 -(p0^2+p2^2-p0*p2)/(2-p0-p2). There might or might not be a good reason for this "risk aversion", but it can be made precise. Of course, using variance as a measure of risk might not make sense, but then choose a measure that makes it.
    Sorry if I made some mistake in the calculation.

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