Behavioral economists have a concept called loss aversion. It’s almost always described something like this:

“Loss aversion implies that one who loses $100 will lose more satisfaction than another person will gain satisfaction from a $100 windfall.”
Wikipedia, as of December 2015

Sounds eminently reasonable, right? Some might say so reasonable, in fact, that it’s crazy that those darn neoclassical economists don’t incorporate such an obvious, fundamental fact about human nature in their models.

It is crazy – because it’s not true! The pop definition of loss aversion given above – that ‘losses hurt more than equivalent size gains’ – is precisely the concept of diminishing marginal utility (DMU) that is boringly standard in standard price theory.

Loss aversion is, in fact, a distinct and (perhaps) useful concept. But somewhat obnoxiously, behavioral economists, particularly in their popular writings, have a tendency to conflate it with DMU in a way that makes the concept seem far more intuitive than it is, and in the process wrongly makes standard price theory look bad.

I’m not just cherry-picking a bad Wikipedia edit. I name names at the bottom of this post, listing where behavioral economists – Thaler, Kahneman, Sunstein, Dubner, etc. – have (often!) given the same misleading definition. It’s wrong! Loss aversion is about reference dependence.

To restate, what I’m claiming is this:

  1. Behavioral economists use an incorrect definition of loss aversion when writing for popular audiences
  2. This incorrect definition is in fact the property of DMU that is assumed in all of neoclassical economics
  3. DMU is much more intuitive than the real definition of loss aversion, and so by using a false definition of loss aversion behavioral economists make neoclassical economics look unnecessarily bad and behavioral economics look misleadingly good

Let me walk through the difference between DMU and loss aversion painstakingly slowly:

Diminishing marginal utility
“Diminishing marginal utility” is the idea that the more you have of something, the less you get out of having a little bit more of it. For example:

If you own nothing but $1,000 and the clothes on your back, and I then give you $100,000, that is going to give you a heck of a lot more extra happiness then if you had $100 million and I gave you $100,000.

An important corollary follows immediately from this: losses hurt more than gains!

I made a super high quality illustration to depict this:

What we have here is a graph of your utility as a function of your wealth under extremely standard (i.e., non-behavioral) assumptions. The fact that the line flattens out as you get to higher wealth levels is the property of DMU.

We can also see that equivalently sized losses hurt more than gains. As you go from 10k wealth to 2k wealth (middle green line to bottom green line), your utility falls by more than the amount your utility rises if you go from 10k wealth to 18k wealth (middle green to top green lines), despite the change in wealth being the same 8k in both directions.

Standard economics will always assume DMU, thus capturing exactly the intuition of the idea described in the above Wikipedia definition of loss aversion.

More mathematically – and I’m going to breeze through this – if your utility is purely a function of your wealth, Utility=U(W), then we assume that U'(W)>0 but U''(W)<0, i.e. your utility function is concave. With these assumptions, the result that U(W+ε)-U(W) < U(W)-U(W-ε) follows from taking a Taylor expansion. See proof attached below.

Loss aversion
Loss aversion is a consequence of reference dependence and is an entirely different beast. The mathematical formulation was first made in Tversky and Kahneman (1991).

In words, loss aversion says this: Suppose you have nothing but the clothes you’re wearing and $10,000 in your pocket, and then another $10,000 appears in your pocket out of nowhere. Your level of utility/happiness will now be some quantity given your wealth of $20,000.

Now consider a situation where you only own your clothes and the $30,000 in your pocket. Suppose suddenly $10,000 in your pocket disappears. Your total wealth is $20,000 – that is, exactly the same as the prior situation. Loss aversion predicts that in this situation, your level of utility will be lower than in the first situation, despite the fact that in both situations your wealth is exactly $20,000, because you lost money to get there.

Perhaps this concept of loss aversion is reasonable in some situations. It doesn’t seem crazy to think that people don’t like to lose things they had before.

But this concept is entirely different from the idea that ‘people dislike losses more than they like gains’ which sloppy behavioral economists go around blathering about. It’s about reference dependence! Your utility depends on your reference point: did you start with higher or lower wealth than you currently have?

In their academic papers, behavioral economists are very clear on the distinction. The use of math in formal economic models imposes precision. But when writing for a popular audience in the less-precise language of English – see below for examples – the same economists slip into using an incorrect definition of loss aversion.

Conclusion
So, please, don’t go around claiming that behavioral economists are incorporating some brilliant newfound insight that people hate losses more than they like gains. We’ve known about this in price theory since Alfred Marshall’s 1890 Principles of Economics.

 

Addendum
It’s kind of silly for me to write this post without naming names. Here we go:

1. Richard Thaler, one of the founding fathers of behavioral economics, in his 2015 bestseller, Misbehaving:

2. Richard Thaler, in the 2008 bestseller, Nudge:

3. Cass Sunstein (Oct. 2015), Harvard law and behavioral economics professor:

4. Daniel Kahneman, Nobel Prize-winning behavioral economist, in his 2011 bestseller, Thinking Fast and Slow:

5. Stephen Dubner (Nov. 2005):

6. New York Times (Dec. 2013):

7.The Economist (Feb. 2015):

I should note that Tversky and Kahneman in their original paper describing loss aversion are admirably clear in their usage of the concept: the title of their QJE paper is Loss Aversion in Riskless Choice: A Reference-Dependent Model, explicitly highlighting the notion of reference dependence.

References

 

6 Responses to Loss aversion is not what you think it is

  1. Charles Kupferberg says:

    Hey Basil, good job explaining the difference between DMU and loss aversion. I'm a little confused as to the necessity of your defending of neoclassical economics in this piece, there is no attack on it as far as I can tell in any of these snippets. Rather pop behaviorial economics simply seem to have rebranded DMU (a concept whose roots are far older than economics) to make themselves sounds smarter and more innovative. I always liked the sports analogy to describe loss aversion and reference dependence, losing a baseball game hurts a lot more if you give up a walkoff home run in the bottom of the ninth than if your team closes the gap at the end but still loses, either way you still lose by the same margin but the second scenario is preferred to the first.
    Best,
    Charles Kupferberg

  2. This explains a tiny, tiny amount of the effect, but the size of the effect is out of all proportion to DMU. E.g. if I misplace a lens cap or a recharging cable I will spend ridiculous amounts of time looking for it; time I could easily spend doing something fun (leisure time is expensive) or earning money to get several new ones.

    Furthermore, recouping a loss is also disproportionately satisfying.

    I suspect that neurologically it's tied to similar emotions such as grief (which teaches us to not do things that cause grief).

  3. Koenfucius says:

    I think you are making a mountain out of a molehill, as well as misrepresenting (or misunderstanding) the concept of loss aversion.

    The colloquial references to loss aversion are indeed not very precise, and could technically describe Diminishing Marginal Utility just as much as Loss Aversion.

    But I wonder to what extent this really is a problem. The context is generally very clear: the authors are not taking about a loss/gain of thousands, but often of just a few dollars/euros/pounds. Even the Wikipedia example could barely be said to refer to DMU rather than LA (you'd need to be very close to the origin for the utility curve to show a material difference between the gain in utility when wealth increases by $100 and the loss of utility when wealth decreases by $100.

    Your second reference to Thaler in Nudge is even so specific as to indicate the empirically observed factor 2. This ratio occurs at most once for every possible value of one's wealth when you look at the DMU curve, and is therefore obviously not what Thaler is referring to.

    I doubt very much that Behavioural Economists "somewhat obnoxiously tend to conflate DMU with LA". It is not because the description used can also refer to DMU, that - as you appear to imply - they are really talking about DMU. They refer to a very clear and well described phenomenon, and it is not DMU.

    Yes, maybe they are guilty of sloppy language, but then again if you are in the process of popularizing science, you sometimes need to give up some rigour in order not to lose your audience. In this case, I doubt that anyone is being misled, when example after example shows that, even for exceedingly small amounts, the loss is experienced as twice as significant as an equivalent gain.

    But when you are saying:

    "But this concept is entirely different from the idea that ‘people dislike losses more than they like gains’ which sloppy behavioral economists go around blathering about."

    you are being disingenuous. LA is not 'entirely different' from the idea that people dislike losses more than they like equivalent gains. LA is much closer to that definition than DMU - on your "super high quality illustration" someone with a wealth of $20k, looking at a loss or gain of $5 will not experience a material difference in utility differential according to DMU - yet he or she will definitely experience loss aversion as described by Behavioural Economists.

    "Your utility depends on your reference point: did you start with higher or lower wealth than you currently have?"

    Loss Aversion is experienced (by and large) irrespective of the wealth you start with.

    The "brilliant newfound insight" is not DMU (which, as you say, has been known for a long time), but quite distinct from it. It is definitely also not - as commenter Charles Kupfer suggests - a "rebranding of DMU".

  4. Biagio says:

    Basil: Thanks for this very helpful comment.

    Koenfucius: "LA is not 'entirely different' from the idea that people dislike losses more than they like equivalent gains."

    I think there is actually a clear difference between the two. Under DMU, losses and gains of equal sizes are compared with one another based on the 'changes' they each cause to utility. Under LA, on the other hand, there is no gain vs loss comparison involved, the reference level of wealth must be specified and be the same in the two cases (with and without loss), and loss aversion is measured in terms of its impact on the 'level' of utility derived from the given (reference) level of wealth. In other words, LA gives a value to the psychological effect of a loss for any given (reference) level of wealth, and doesn't say anything about gains. Am I correct?

  5. Koenfucius says:

    @Biagio: Kahneman and Tversky say "losses loom larger than gains" in their Prospect Theory paper. It seems to me to be inevitable that loss aversion must say something about gains too: the 'aversion' to which it refers needs to be in relation to something else.

    DMU suggests that the utility of an additional gain or loss is a function of the current level of wealth. DMU does not mention equivalent gains and losses; it refers the gain (or loss) and their utility to he level of wealth.

    LA suggests that the utility of a given gain is smaller than the utility corresponding to an equivalent loss, irrespective of the level of wealth from which one starts.

    • Ray Lopez says:

      @Koenfucious - Jeez man, you waited over a year to reply to a commentator? As for the author, I think he made a useful post and your post was trying to move the goalposts. Indeed, the smaller the distance on the utility function the more DMU looks like LA, but that's not to detract anything from the OP, Basil.

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