Behavioral Econs 101: The endowment effect and loss aversion Part 1 – Prospect Theory

In this third installment of our Behavioral Econs 101 series(for parts 1 and 2, see here, and here) we finally turn to a discussion of the endowment effect. Why do losses feel so much more painful than an equivalent gain feels good? Why are we reluctant to give up something we already own, even if we had obtained the item for free or at a heavily discounted price? Why do the prices that we are willing to pay for something often differ significantly from the prices that we are willing to accept to sell the same item?

by HK Lim

This piece explores how we can understand these perplexing(well at least to “standard” economics) observations of economic life, but first we need to lay the groundwork for understanding how economists have traditionally thought about utility and choice.

Richard Rossett’s wine collection and the endowment effect

Before we get ahead of ourselves, what exactly is the endowment effect? One of the best examples I’ve come across comes from the 2017 Economics Nobel laureate Richard Thaler(1980), in recounting his amusing observations regarding Richard Rossett(who was at the time also the chairman of the University of Rochester’s economics department) and his wine collection. Rossett told Thaler that he had bottles in his cellar that he had purchased a long time ago for $10 that were now worth over $100. A local wine merchant was actually also willing to buy some of Roseett’s older bottles at current market prices. Now, Rossett said he would occasionally drink one of those bottles on special occasions but would never pay $100 to acquire one, Rossett also did not sell any of his own bottles to the local wine merchant. From the perspective of “standard” microeconomics, this behavior is confounding. If Rossett was willing to drink a bottle that he could sell for $100, then drinking it had to be worth more than $100, right? But in that case, why would he not also be willing to pay for a comparable bottle? In fact, Rossett refused to purchase any bottle that cost even close to $100.

In Richard Thaler’s words, “As an economist, Rossett knew such behavior was not rational, but he couldn’t help himself.” This was the endowment effect at work. To properly understand why such behavior happens, we will first need to understand economists’ traditional theory of utility and risky choice before looking to see how it should be modified.

Bernoulli, von Neumann, Morgenstern and risk aversion

While the bulk of economics’ development of the formal treatment of the theory of utility and decision making in risky environments(expected utility theory) can be traced to John von Neuman and Oskar Morgenstern’s publication of “The Theory of Games and Economic Behavior” (1944), these ideas had much earlier roots. In fact, Daniel Bernoulli in 1738 came up with the very notion of risk aversion in his study of the St Petersburg Paradox.

The St Petersburg Paradox: Suppose you are offered a gamble where you keep flipping a fair coin until it lands heads up. If you obtain tails on your first flip you win $2, if you obtain tails on your second flip you win $4, and so on, with the winning payout doubling each time. The “average” payout (to be precise, the mathematical expectation of the payout which is ½ x $2 + ¼ x $4 + 1/8 x $8 +… ) corresponds to an infinite sequence, so the question is why won’t any rational gambler agree to pay any finite amount to play this game? Daniel Bernoulli’s solution was to suppose that people derive diminishing value from increases in their wealth, giving rise to risk aversion.

“The determination of the value of an item must not be based on the price, but rather on the utility it yields…. There is no doubt that a gain of one thousand ducats is more significant to the pauper than to a rich man though both gain the same amount.”

Bernoulli came up with risk aversion by supposing that people’s happiness(or utility in textbook economics parlance) increases as they get wealthier but at a diminishing rate. Simply stated, as an individual’s wealth grows, the impact of a particular increment in wealth, say $10000, decreases. In this setup, a windfall of $10000 would go almost unnoticed to someone as rich as Warren Buffet but to a poor inner city family’s sole breadwinner earning minimum wage, such a windfall would be almost unimaginably life-changing.

Box.1 The St. Petersburg Paradox

(Source: the Stanford Encyclopedia of Philosophy)

What von Neumann and Morgenstern did was to derive rules from the set of axioms of rational choice theory and thereby deduce how a person following such axioms(a detailed discussion of the validity of these axioms is best saved for a future piece) would behave while making risky decisions. [These axioms were mainly technical requirements to ensure that consumer preferences were “well-behaved”, consistent and amenable to analysis using optimization methods.] What they showed was that if one were to “satisfy” these axioms, one’s decision making process would fall completely in line with their theory(expected utility). Their logic was irrefutable, provided of course one actually satisfied these axioms. [This is a big proviso, and in a future post we will discuss violations of these axioms in more detail.]

I. Diminishing marginal utility and “standard” expected utility theory

To understand utility’s diminishing sensitivity to a fixed increment wealth windfall(of $10000) and how this relates to risk aversion, let us consider Fig.1.

Fig.1 Diminishing marginal utility

In Fig.1, the utility function(the curve in black) gives an individual’s happiness or utility(measured on the vertical axis) corresponding to each level of wealth(as measured on the horizontal axis). In Fig.1, for the same fixed increment of $10000, we see that the increase in utility(happiness) for someone starting out with much less initial wealth is larger than that of someone who is already much richer. This captures the idea of diminishing marginal utility that all budding economists are introduced to early in their training. [Whether they get excited about it is another question.]

II. Risk aversion

How does the shape of this particular utility curve capture risk aversion? Well, for starters, the curve is concave(with respect to the horizontal axis, you can imagine looking up from the horizontal axis) and according to expected utility theory, the correct way to think about the choice between an uncertain bet versus a sure thing should be as follows. [Side note: Economists “measure” utility in units of “utils.” Yes really.]

Fig.2 Risk aversion

With diminishing marginal utility, as we trace the utility curve to higher levels of wealth and utility, a fixed increment in wealth will produce smaller and smaller increase in utility. That is what is meant by diminishing marginal utility.

Now consider Fig.2 and suppose we are initially at some level of wealth E. Consider an even bet giving a $200 or $0 payout each with probability ½ versus the choice of a certain payout of $100(this can easily be generalized to arbitrary probabilities and payouts). Now according to expected utility theory, the decision of whether to take up the bet or choose the sure thing depends on the “expected” utility of such a bet(“expected” here has a technical meaning similar to an average) which corresponds to utility level C’ in Fig.2.

Note that point C lies on the straight line AB and is its midpoint(as it must since it’s an even weighted average of two outcomes) and maps horizontally to point C’ with corresponding payout corresponding to total wealth F. On the other hand, a certain payout of $100(with total wealth F) corresponds to point D and gives utility D’ as illustrated in Fig.2. Now clearly D’ is greater than C’, and this implies that the utility derived from the sure thing of $100 is preferred to(or dominates) the utility from the risky bet. This is risk aversion, the individual prefers the the sure thing to the risky bet because the utility is higher in the former compared to the latter calculated through expected utility theory. This conclusion also holds true for any combination of probabilities for risky bets and gives an expected utility corresponding to a point somewhere on the straight line AB. Risk aversion simply means that all points on the straight line AB lie below the utility curve for that wealth range. [Aside: risk-seeking individuals would on the other hand have utility curves that lie below the straight line AB.] This averaging process is what gives the “expected” in expected utility theory. And yes, it is terribly confusing terminology if I may say so myself.

III. Prospect Theory

So far, we have just re-iterated what “standard” textbook microeconomics tells us is the correct way to choose between a risky bet with an uncertain payoff and a sure thing. Enter the psychologists Daniel Kahneman(winner of the 2002 Economics Nobel Prize) and Amos Tversky with their proposed radical re-working of how we should think about utility and risky choices in their seminal paper “Prospect Theory: An Analysis of Decision under Risk” (1979). Their approach proposed a major conceptual change in how we should think about utility because up until this point, economists had almost always exclusively assumed that people experienced a diminishing marginal utility of wealth(as depicted in Fig.1). [[Kahneman and Tversky chose the name “Prospect Theory”(renamed from the original Value Theory) precisely because this term was meaningless, and would only become meaningful if their theory somehow took hold in the broader judgement and decision making community. Which indeed it did.]

While this simple assumption can be credited with getting some of the basic psychology right(Kahneman and Tversky use the term psychophysics of choice), this wasn’t quite the whole picture. Kahneman and Tversky’s key insight was to propose that we turn our attention from levels of wealth to changes in wealth to be consistent with how humans typically experience life. For example, suppose Mike who earns $70,000 annually receives an unexpected year-end bonus of $4500. Does he consider this bonus in the context of his lifetime expected earnings, where it’s most likely negligible? Or instead think to himself, “wow, an extra $4500 to spend!” Humans tend to think about and experience life in terms of changes and not levels, and this fundamental psychological observation was key in helping Kahneman and Tversky understand various the paradoxical features of risky decision making better.

With this key insight that instead of levels of wealth, one should really be thinking in terms of changes in wealth, we can reformulate our understanding of expected utility and better understand how humans assess risky bets more accurately. It’s best at this point to give a graphical illustration of Kahneman and Tversky’s proposed version of the utility value function, depicted in Fig. 3.

Fig.3 Prospect Theory’s value function

The S shaped curve in Fig.3 above represents the value function of Prospect Theory and has several important features. First, the horizontal axis now measures changes in wealth in gains or losses. Second, the diminishing sensitivity(diminishing marginal utility) that arises from the concavity of “standard” utility theory’s value curve(as illustrated in Fig.1 and Fig.2) is retained but now applies to changes in wealth(gains as well as losses) instead of levels. Note crucially that the losses portion of the value curve also exhibits diminishing sensitivity and this will be important for our later discussion. Third, the portion of the value curve that corresponds to losses(to the left of the vertical utility axis) is steeper than the analogous portion for equivalent gains and thus gives loss aversion. What this means is that losses hurt more than the “feel good” of gains and by some estimates is thought to be at least twice as painful to an equivalent monetary gain. From a utility perspective, a loss will not be offset by an equivalent gain! This last feature produces the “endowment effect” which we see arises precisely because of loss aversion.

Thus, this S-shaped value curve of Kahneman and Tversky’s Prospect Theory proposed a stunning modification to how economists have traditionally thought about utility and risky choice. Changes are really the way that humans experience life, and the fact that humans(as opposed to textbook economics’ homo economicus, rational economic man’s Mr Spock) experience diminishing sensitivity to changes away from the status quo ties in very closely to psychology’s Weber-Fechner Law which says that the just-noticeable difference in any variable is proportional to the magnitude of that variable. The particular shape of the value function from Prospect Theory captures all of this.

IV. Revisiting Richard Rossett’s wine bottles

With our newfound knowledge of Prospect Theory’s value function and an understanding of loss aversion, we can re-cast the perplexing case of Richard Rossett’s wine bottles in a completely new light. In Prospect Theory, the fact that losses hurt at least twice as much as gains make one feel good gives rise to loss aversion and this underpins the endowment effect. If we were to take away a bottle of Rossett’s wine, the loss that he would feel would be more than equivalent to twice the gain he would feel upon acquiring a similar bottle. This is because in giving up a bottle, Rossett would have to give up something he already owns and take a “loss.” This also explains why Rossett would never buy a bottle worth the same market price as one already in his wine collection. The endowment effect was at work all the time!

V. Risk-averse for gains and risk-seeking for losses

Keeping in mind the features of Fig.3, and following a similar argument to that given in section II(and Fig.2) but now for changes in wealth instead of levels, we see that while we would expect risk aversion for gains for Prospect Theory’s value function, the same argument implies that we would expect people to be risk-seeking for losses! Yes, you read that right. For the losses region of the Prospect Theory value function(see Fig.3) the value function curve would lie below the straight line joining two points, but since losses are painful and since the pain of losing an additional $100 is less than the pain of losing the first $100, people will often be willing to take the risk of losing more for the chance to get back to no loss at all. In particular, the urge to get back to no loss at all is in fact due to loss aversion! This goes a long way to explaining why gamblers already down on their luck often are willing to bet the house at the end of the day.

To close out this piece, let’s try a little experiment that very neatly demonstrates the ideas we have just discussed. Consider the following two scenarios and determine your choices for each

Problem 1

Assume that you are $400 richer than you are today and are offered a choice between

A.    A sure gain of $100, or

B.    A 50% chance to win $200 or a 50% chance to lose $0.

Problem 2
Assume that you are $600 richer than you are today and are offered a choice between

A.    A sure loss of $100, or

B.    A 50% chance to lose $200 or a 50% chance to lose $0.

What were your choices under each scenario? Most people select choice A for Problem 1 and choice B for Problem 2. Now note that if the two Problems were reformulated in terms of levels of wealth instead of changes(by incorporating the first line of how much you are richer into the options A and B), you actually have identical scenarios in both Problem 1 and Problem 2. Wait a minute! If you chose choice A for Problem 1 and choice B for Problem 2, you are risk-averse for gains and risk-seeking for losses in this particular pair of scenarios! Isn’t that shocking?! Well, maybe not so much in light of what you now know about Prospect Theory. Don’t worry, you’re in the good company of humans since the majority of participants presented with this experiment made very much the same paradoxical choices.

In our next installment of Behavioral Economics 101 we shall explore more examples of the endowment effect at work. Once you start looking, the endowment effect really is everywhere! Stay tuned.

References

1) Thaler, R.H, 1980. Toward a positive theory of consumer choice. Journal of Economic Behavior & Organization, vol, vol 1, issue 1, 39-60.

2) von Neumann, J., and Morgenstern, O. 1944. The Theory of Games and Economic Behavior, . Princeton: Princeton University Press.

3) Kahneman, D., and Tversky, A. 1979. Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47(2), pp. 263-291.