# Question on loss aversion

I have a question on loss aversion, as I am confused.  I keep seeing loss aversion defined like this:

our tendency to feel sadder about losing, say, \$1,000 than feeling happy about gaining that same amount

But this sounds like diminishing marginal utility to me.  I mean, the \$1,000 dollars I’m losing provides me with a greater level of satisfaction than an addition \$1,000 would provide me with.

My feeling was that loss aversion was a situation where my satisfaction would be lower in a situation where I lost \$10,000 and ended up with \$40,000 than it would be in a situation where I gained \$10,000 and ended up with \$40,000 – even though in both situations my endowment was the same.

I thought loss aversion was about an additional payoff relevant factor (namely that the direction of the change in my outcomes is also payoff relevant, as well as the strict outcomes) not an arbitrary way of framing diminishing marginal utility.

If someone could explain where I am making a mistake it would be much appreciated 🙂

17 replies
1. Andrew Coleman says:

Hi Matt
My simple understanding is based on the difference between valuing a probabilistic outcome or raffle using standard expected utility theory and prospect theory (or loss aversion theory). Consider a raffle that has outcomes (x1,x2,..xn) with probabilities (pi,p2,..pn), where x includes all your wealth ie initial wealth plus raffle outcomes. With standard utility theory, the value of the raffle is p1U(x1) + p2U(x2)..+pnU(xn) where U(.) is a utility function. The diminishing marginal utility comes in through the utility function; if this is concave, an agent gets much lower utility from a poor outcome than a good outcome, and therefore will value the raffle much less than its expected value.

In prospect theory, the losses and gains are valued. Suppose we start with wealth Y. Then rather than valuing the raffle in terms of the final outcomes (x1..xn) we value it in terms of gains and losses. For a utility function V(.), this could be written as p1 V(x1-Y)+ p2 V(x2-Y)…+pnV(xn-Y). We no longer value the raffle in terms of what we can purchase with the proceeds, but according to whether or not the prizes make us better off or worse off. Moreover, the raffle will be evaluated quite differently according to our value Y.

Standard utility theory does recognize that how much money we have initially will affect the way we value different prizes, but it doesn’t recognize that if we start at different places Y0 and Y1 and have different raffles that lead us to the same objective distribution of outcomes (x1,…Xn), our valuation of the same outcomes depends on initial position Y.

I find the concept a little mindbending because most of the raffles we usually think about give as a certain amount of additional cash if we win. The twist Tversky and Kahneman put on it was to consider raffles that take us to the same final outcomes, and argue (and provide evidence) that the path we take to these outcomes matters to the way we value these outcomes.

This post comes with a warning that I am not a behavioural economist and often don’t know precisely what I am talking about. So go and read one of the most impressive papers ever written, Econometrica 1979

2. Robbie says:

Here’s my understanding… the less formal explanation.

Diminshing marginal utility says that your absolute wealth is more important than relative changes. Suppose you have a game that will let you win or lose \$10. Diminishing marginal utility would say that if you have, say, \$100, then losing \$10 will lose you 10 utils, but gaining \$10 will give you 8 utils. So if you gain \$10 then lose \$10, you’re back to the same place.

With prospect theory, the change is more important than the absolute position. So if you gain \$10 it gives you 8 utils (say), but if you lose \$10 it will lose you \$10 utils. This will of course change with wealth, but not on a 1:1 basis.

3. Matt Nolan says:

“The twist Tversky and Kahneman put on it was to consider raffles that take us to the same final outcomes, and argue (and provide evidence) that the path we take to these outcomes matters to the way we value these outcomes.”

This is what I considered to be the essence as well – the “reference dependence” of the impact of a change. If this is indeed the essential part of loss aversion then I don’t think the definition getting thrown around is correct – I think people need to explain that it is a difference between the valuing of a loss and a gain that leads to the SAME outcome.

Without it being premised on the fact that the objective outcome the concept seems a bit weak – as it can be mixed with diminishing marginal utility.

I am concerned about this, as it is the third time in the last fortnight I have heard loss aversion described as “valuing making \$X less than the value foregone from losing \$X” – and if people start to believe this definition dodgey people may try to make diminishing marginal utility sound like “a irrational phenomenon” … then again maybe I’m an economists version of a conspiracy theorist 😉

4. rauparaha says:

I don’t think it’s about the same outcome, really. Loss aversion is represented in prospect theory by the kink in the utility curve at the reference point. The utility function is steeper over losses than gains. So the point is that your marginal gain in utility for wealth increases is less than your marginal loss in utility for wealth decreases.

5. Matt Nolan says:

But it is kinked at the reference point right. So when looking at counterfactuals you can only conclusively say that loss aversion is occurring (instead of diminishing marginal utility) when you compare the payoff from a situation with a loss and a situation with a gain that lead to the same outcome – as this removes the impact of diminishing marginal utility completely, only leaving loss aversion

6. rauparaha says:

@Matt Nolan
I’m not sure what you mean, Matt. Prospect theory doesn’t have an additive utility function, so there isn’t diminishing marginal utility in the sense that I think you’re intending. But I’m not really sure what you’re intending to say, either…

7. Matt Nolan says:

I, in my intense lack of clarity, mean to say that “if we want to actually observe loss aversion we need a clear counterfactual”.

People keep saying “if we are hurt more by a loss than we enjoy a gain we are showing loss aversion” – but that doesn’t seem complete enough to me, because we can have diminishing marginal utility. As a result, I fear that people will take this definition, and apply it to cases where there is simply diminishing marginal utility.

However, if they can illustrate a case where someone values the loss more highly than the gain even though the eventual outcome is the same then it rules out diminishing marginal utility – and they can justifiably use the idea of loss aversion and discuss bounded rationality and any associated policy recommendations.

8. Matt Nolan says:

Also I would note that I am looking at revealed actions here – I want the appropriate counterfactual to discuss realised data. I can’t observe the shape of the utility function I can only observe actions – which is why I have a feeling the definition in bold in the post is a bit inappropriate for that.

9. rauparaha says:

@Matt Nolan
“even though the eventual outcome is the same”

This is the bit that doesn’t make sense to me. Why is ending up in the same place important if we don’t have an additive utility function? What’s important, surely, is having a static frame of reference so our reference point is the same for each scenario.

PT has diminishing sensitivity to changes in wealth, but the idea of diminishing marginal returns as the level of wealth increases don’t come into it, do they? If they did then the PT value function would be state dependent and I don’t think it is.

10. Matt Nolan says:

“What’s important, surely, is having a static frame of reference so our reference point is the same for each scenario.”

Indeed. But if we don’t know the shape of the utility function then we can only say that this is the case if we are heading to the exact same point following each shock right?

If we assumed that diminishing marginal returns didn’t hold then we don’t have to worry – as treating a \$10 loss differently to a \$10 gain would imply loss aversion. But in the absence of that assumption I don’t see how it is clear.

“PT has diminishing sensitivity to changes in wealth, but the idea of diminishing marginal returns as the level of wealth increases don’t come into it, do they?”

My question depends on whether people have diminishing marginal returns to increases in the level of wealth – not whether it is assumed in PT.

As far as I know it is fair to assume that people have diminishing marginal returns to wealth – and as a result the above definition in bold could describe a situation that involves diminishing marginal utility and/or loss aversion.

In that sense, I don’t think it is fair to look at a person and say “since you are more concerned about losing \$10 than you are happy about gaining \$10 you are loss averse” as the actual outcomes associated with each of those \$10 is different.

Thanks for your comments BTW rauparaha – I am sorry if I’m slow getting it 😛

11. Matt Nolan says:

I’d also note that saying that they are risk averse in gains and risk loving in losses is the same as comparing it to an objective reference point, as in this – that is what PT does, and that is a way I am agreeing with.

I am disagreeing with the quote – which says that loss aversion (which is supposedly broader than PT) is simply a case where the pain of a loss exceeds the happiness of a gain. This seems incomplete to me.

12. rauparaha says:

@Matt Nolan
Loss aversion isn’t really about risk preference. You could be risk neutral and loss averse. The question you seem to be asking is “what experimental design could distinguish between loss aversion and diminishing marginal utility as explanations for an endowment effect?” Is that right? Cos if it is then I’ll look up a study when I have a minute.

13. Matt Nolan says:

“Loss aversion isn’t really about risk preference. You could be risk neutral and loss averse”

I thought that loss aversion directly implied that people’s revealed risk preference was asymmetric between gains and losses?

“The question you seem to be asking is “what experimental design could distinguish between loss aversion and diminishing marginal utility as explanations for an endowment effect?” Is that right? Cos if it is then I’ll look up a study when I have a minute.”

Sort of – if you look at the initial post the entire point was to ask if the definition in bold was an appropriate definition of loss aversion.

I wasn’t even arguing about the endowment effect because the definition didn’t say anything about the endowment effect. If it did, it would be closer to loss aversion.

With the endowment effect we find that people value something more highly when they have it right? So if you don’t own a cup you will pay \$X for it, if you do own it you will only sell it for \$X+\$Y where Y>0. That is definitely loss aversion as you are measuring comparable conterfactuals.

In the definition in bold that is not the case. You currently have \$10,000 and you illustrate that you are more hurt from losing \$1,000 and having \$9,000 than from gaining \$1,000 and having \$11,000. This doesn’t seem like an example of the endowment effect, and it doesn’t clearly illustrate loss aversion for me – especially given that the change in value could be the result of diminishing marginal utility.

Ultimately, I am saying that framing loss aversion as “feeling sadder about a loss than a gain” is not a sufficient condition for the result – we could observe that in the absence of loss aversion.

I feel that the definition in bold could be abused – my impression was that loss aversion was about reference dependence, and a asymmetric preference regarding the direction of change. If this is the case this is more specific than the idea that “people value a loss more heavily than a gain”

14. rauparaha says:

My definition of loss aversion: abs(MU(gain in wealth)) < abs(MU(loss of wealth)).

Essentially it explains the difference between willingness-to-pay and willingness-to-accept which is an endowment effect. Surely the \$1000 gain/loss difference is about endowment. Either you have it and you're going to lose it or you don't have it and you're going to get it. Is the WTP for it less than the WTA for losing it? Yes, even for a risk neutral person. Obviously this is kinda backwards to value money in terms of a good that provides utility, but the principle holds.

"Ultimately, I am saying that framing loss aversion as “feeling sadder about a loss than a gain” is not a sufficient condition for the result – we could observe that in the absence of loss aversion."

I think that's the key: the bold doesn't define loss aversion, it describes an observation that we can explain with loss aversion. You could plausibly explain that simple observation many ways. However, the best way we have at the moment is loss aversion.

The full quote makes that clear:
"Their pioneering work addressed money illusion and other psychological foibles, such as our tendency to feel sadder about losing, say, \$1,000 than feeling happy about gaining that same amount."

What you are painting as a definition is actually an observation that loss aversion can plausibly explain. It's not a definition of it.

15. Matt Nolan says:

“Essentially it explains the difference between willingness-to-pay and willingness-to-accept which is an endowment effect.”

“What you are painting as a definition is actually an observation that loss aversion can plausibly explain. It’s not a definition of it.”

My impression when I read it was that they were using this as an example of loss aversion. To me an example is like a loose way of defining something. Now in this case the same example could clearly be explained with diminishing marginal utility – which I think heavily reduces its usefulness as an example.

I have heard that example being used for explaining loss aversion 3 times in the last 2 weeks and I’m not comfortable with it – as I feel that there are too many plausible alternative explanations to make is a clear example of loss aversion.

I am genuinely concerned that this type of definition could lead to the concept of loss aversion being “over-applied” to cases where we are actually only observing diminishing marginal utility.

16. porno says:

I have heard that example being used for explaining loss aversion 3 times in the last 2 weeks and I’m not comfortable with it – as I feel that there are too many plausible alternative explanations to make is a clear example of loss aversion.