Topic and Abstract 2:30 Graham Loomes Opening Remarks Department of Economics, University of Warwick

November 4 Speaker(s) Topic and Abstract 2:30 Graham Loomes Opening Remarks Department of Economics, University of Warwick

2:30 - 3:50 Rosario Macera Expectation-Based Reference-Dependent Preferences: Theory, Evidence and Department of Economics, Applications University of Warwick The current challenge of reference-dependent preferences is the specification of the reference point. This talk overviews the theory and evidence of expectation- based reference-dependent preferences, which proposes that the reference point corresponds to the agent's recent (rational) expectations about outcomes. After summarizing the theory and re-exploring old prospect-theory-related puzzles that motivated the theory, we will review recent supportive laboratory and field evidence as well as unsolved puzzles. We wrap up by overviewing the economic applications done to pricing, contracts and social preferences.

THE QUARTERLY JOURNAL OF ECONOMICS Vol. CXXI November 2006 Issue 4

A MODEL OF REFERENCE-DEPENDENT PREFERENCES*

BOTOND KO˝ SZEGI AND MATTHEW RABIN

We develop a model of reference-dependent preferences and loss aversion where “gain–loss utility” is derived from standard “consumption utility” and the reference point is determined endogenously by the economic environment. We assume that a person’s reference point is her rational expectations held in the recent past about outcomes, which are determined in a personal equilibrium by the requirement that they must be consistent with optimal behavior given expectations. In deterministic environments, choices maximize consumption utility, but gain–loss utility inﬂuences behavior when there is uncertainty. Applying the model to consumer behavior, we show that willingness to pay for a good is increasing in the expected probability of purchase and in the expected prices conditional on purchase. In within-day labor-supply decisions, a worker is less likely to continue work if income earned thus far is unexpectedly high, but more likely to show up as well as continue work if expected income is high.

I. INTRODUCTION How a person assesses the outcome of a choice is often determined as much by its contrast with a reference point as by intrinsic taste for the outcome itself. The most notable manifes-

* We thank Paige Skiba and Justin Sydnor for research assistance, and Daniel Benjamin, B. Douglas Bernheim, Stefano DellaVigna, Xavier Gabaix, Edward Glaeser, George Loewenstein, Wolfgang Pesendorfer, Charles Plott, An- drew Postlewaite, Antonio Rangel, Jacob Sagi, Christina Shannon, Jean Tirole, Peter Wakker, seminar participants at the University of California—Berkeley, the Harvard University/Massachusetts Institute of Technology Theory Seminar, Princeton University, Rice University, the Stanford Institute for Theoretical Economics, and the University of New Hampshire, graduate students in courses at the University of California—Berkeley, Harvard University, and the Massa- chusetts Institute of Technology, and anonymous referees for helpful comments. We are especially grateful to Erik Eyster, Daniel Kahneman, and Nathan Novem- sky for discussions on related topics at the formative stage of this project. Ko˝szegi thanks the Hellman Family Faculty Fund, and Rabin thanks the MacArthur Foundation and the National Science Foundation for ﬁnancial support.

1133 1134 QUARTERLY JOURNAL OF ECONOMICS tation of such reference-dependent preferences is loss aversion: losses resonate more than same-sized gains. In this paper we build on the essential intuitions in Kahneman and Tversky’s [1979] prospect theory and subsequent models of reference dependence, but flesh out, extend, and modify these models to develop a more generally applicable theory. We illustrate such applicability by establishing some implications of loss aversion for consumer behavior and labor effort. We present the basic framework in Section II. A person’s utility depends not only on her K-dimensional consumption bundle c but also on a reference bundle r. She has an intrinsic “consumption utility” m(c) that corresponds to the outcome-based utility classically studied in economics. Overall utility is given by u(c͉r) ϵ m(c) ϩ n(c͉r), where n(c͉r) is “gain–loss utility.” Both consumption utility and gain–loss utility are separable across ϵ ¥ ͉ ϵ ¥ ͉ dimensions, so that m(c) k mk(ck) and n(c r) k nk(ck rk). Because the sensation of gain or loss due to a departure from the reference point seems closely related to the consumption value ͉ ϵ attached to the goods in question, we assume that nk(ck rk) ٪␮ Ϫ ␮ (mk(ck) mk(rk)), where satisfies the properties of Kah- neman and Tversky’s [1979] value function. Our model allows for both stochastic outcomes and stochastic reference points, and assumes that a stochastic outcome F is evaluated according to its expected utility, with the utility of each outcome being the average of how it feels relative to each possible realization of the reference point G: U(F͉G) ϭ͐͐u(c͉r) dG(r) dF(c). In addition to the widely investigated question of how people react to departures from a posited reference point, predictions of reference-dependent theories also depend crucially on the under- studied issue of what the reference point is. In Section III we propose that a person’s reference point is the probabilistic beliefs she held in the recent past about outcomes. Although existing evidence is instead generally interpreted by equating the reference point with the status quo, virtually all of this evidence comes from contexts where people plausibly expect to maintain the status quo. But when expectations and the status quo are different—a common situation in economic environments—equating the reference point with expectations generally makes better predictions. Our theory, for instance, supports the common view that the “endowment effect” found in the laboratory, whereby random owners value an object more than nonowners, is due to loss aversion—since an owner’s loss of the object looms larger A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1135 than a nonowner’s gain of the object. But our theory makes the less common prediction that the endowment effect among such owners and nonowners with no predisposition to trade will disappear among sellers and buyers in real-world markets who expect to trade. Merchants do not assess intended sales as loss of inventory, but do assess failed sales as loss of money; buyers do not assess intended expenditures as losses, but do assess failures to carry out intended purchases or paying more than expected as losses. Equating the reference point with expectations rather than the status quo is also important for understanding financial risk: while an unexpected monetary windfall in the lab may be assessed as a gain, a salary of $50,000 to an employee who expected $60,000 will not be assessed as a large gain relative to status-quo wealth, but rather as a loss relative to expectations of wealth. And in nondurable consumption—where there is no object with which the person can be endowed—a status-quo-based theory cannot capture the role of reference dependence at all: it would predict, for instance, that a person who misses a concert she expected to attend would feel no differently than somebody who never expected to see the concert. While alternative theories of expectations formation could be used, in this paper we complete our model by assuming rational expectations, formalizing (in an extreme way) the realistic assumption that people have some ability to predict their own behavior. Using the framework of Ko˝szegi [2005] to determine rational expectations when preferences depend on expectations, we define a “personal equilibrium” as a situation where the stochastic outcome implied by optimal behavior conditional on expectations coincides with expectations.1 We also define a notion of “preferred personal equilibrium,” which selects the (typically unique) personal equilibrium with highest expected utility. We show in Section III that in deterministic environments preferred personal equilibrium predicts that decision-makers maximize consumption utility, replicating the predictions of classical reference-independent utility theory. Our analyses in Sec- tions IV and V of consumer and labor-supply behavior, however, demonstrate a central implication of our theory: when there is

1. Expectations have been mentioned by many researchers as a candidate for the reference point. With the exception of Shalev’s [2000] game-theoretic model, however, to our knowledge our paper is the first to formalize the idea that expectations determine the reference point and to specify a rule for deriving them endogenously in any environment. 1136 QUARTERLY JOURNAL OF ECONOMICS uncertainty, a decision-maker’s preferences over consumption bundles will be influenced by her environment. Section IV shows that a consumer’s willingness to pay a given price for shoes depends on the probability with which she expected to buy them and the price she expected to pay. On the one hand, an increase in the likelihood of buying increases a consumer’s sense of loss of shoes if she does not buy, creating an “attachment effect” that increases her willingness to pay. Hence, the greater the likelihood she thought prices would be low enough to induce purchase, the greater is her willingness to buy at higher prices. On the other hand, holding the probability of getting the shoes fixed, a decrease in the price a consumer expected to pay makes paying a higher price feel like more of a loss, creating a “comparison effect” that lowers her willingness to pay the high price. Hence, the lower the prices she expected among those prices that induce purchase, the lower is her willingness to buy at higher prices. Our application in Section V to labor supply is motivated by some recent empirical research beginning with Camerer et al. [1997] on flexible work hours that finds some workers seem to have a daily “target” income. We develop a model where, after earning income in the morning and learning her afternoon wage, a taxi driver decides whether to continue driving in the afternoon. In line with the empirical results of the target-income literature, our model predicts that when drivers experience unexpectedly high wages in the morning, for any given afternoon wage they are less likely to continue work. Yet expected wage increases will tend to increase both willingness to show up to work, and to drive in the afternoon once there. Our model therefore replicates the key insight of the literature that exceeding a target income might reduce effort. But in addition, it both provides a theory of what these income targets will be, and—through the fundamental distinction between unexpected and expected wages—avoids the unrealistic prediction that generically higher wages will lower effort. Beyond improvements in specific substantive predictions, our general approach has an attractive methodological feature: because a full specification of ␮٪ allows us to derive both gain–loss utility and the reference point itself from consumption utility and the economic environment, it moves us closer to a universally applicable, zero-degrees-of-freedom way to translate any existing reference-independent model into the corresponding reference- A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1137 dependent one. Although straightforward to apply in most cases, our model falls short of providing a recipe for entirely formulaic application of the principles of reference-dependent. Psychologi- cal and economic judgment is needed, for instance, in choosing the appropriate notion of “recent expectations.” And there are also settings where the same principles motivating our approach suggest an alternative to our reduced-form model. We discuss such shortcomings and gaps, some possible resolutions, as well as further economic applications, in Section VI.

II. REFERENCE-DEPENDENT UTILITY We specify a person’s utility for a riskless outcome as u(c͉r), ϭ ʦ ޒK ϭ where c (c1,c2,...,cK) is consumption and r ʦ ޒK (r1,r2,...,rK) is a “reference level” of consumption. If c is drawn according to the probability measure F, the person’s utility is given by2

(1) U͑F͉r͒ ϭ ͵ u͑c͉r͒ dF͑c͒.

As is clearly necessary in our framework developed below, where we assume that the reference point is beliefs about outcomes, we allow for the reference point itself to be stochastic. Suppose that the person’s reference point is the probability measure G over ޒK, and her consumption is drawn according to the probability measure F. Then, her utility is

(2) U͑F͉G͒ ϭ ͵͵ u͑c͉r͒ dG͑r͒ dF͑c͒.

This formulation captures the notion that the sense of gain or loss from a given consumption outcome derives from comparing it with all outcomes possible under the reference lottery. For example, if the reference lottery is a gamble between $0 and $100, an outcome of $50 feels like a gain relative to $0, and like a loss relative to $100, and the overall sensation is a mixture of these

2. Despite the clear evidence that people’s evaluation of prospects is not linear in probabilities, our model simplifies things by assuming preferences are linear. 1138 QUARTERLY JOURNAL OF ECONOMICS two feelings.3 That a person’s utility depends on a reference lottery in addition to the actual outcome is similar to several previous theories.4 With the exception of the model in Gul [1991]—which can be interpreted as saying that the certainty equivalent of a chosen lottery becomes the decision-maker’s reference point—none of these theories provide a theory of reference-point determination, as we do below. While preferences are reference-dependent, gains and losses are clearly not all that people care about. The sensation of gain or avoided loss from having more money does significantly affect our utility—but so does the absolute pleasure of consumption we purchase with the money. Therefore, in contrast to prior formulations based on a “value function” defined solely over gains and losses, our approach makes explicit the way preferences also depend on absolute levels. We assume that overall utility has two components: u(c͉r) ϵ m(c) ϩ n(c͉r), where m(c) is “consumption utility” typically stressed in economics, and n(c͉r) is “gain–loss utility.” For simplicity—and for further reasons discussed in Ko˝szegi and Rabin [2004]—we assume that consumption utility is addi- ϵ ¥K tively separable across dimensions: m(c) kϭ1 mk(ck), with ٪ each mk differentiable and strictly increasing. We also assume ͉ ϵ ¥K ͉ that gain–loss utility is separable: n(c r) kϭ1 nk(ck rk). Thus, in evaluating an outcome, the decision-maker assesses gain–loss utility in each dimension separately. In combination with loss aversion, this separability is at the crux of many implications of reference-dependent utility, including the endowment effect. Beyond saying that a person cares about both consumption

3. See Larsen et al. [2004] for some evidence that subjects have mixed emotions for outcomes that compare differently with different counterfactuals. Given the features below, our formula also implies that losses relative to a stochastic reference point count more than gains, so that a person who gets $50 is more distressed by how it compares with a possible $100 than she is pleased by how it compares with a possible $0. We are unaware of evidence on whether this, or an alternative speciﬁcation where the relief of avoiding $0 outweighs the disappointment of not getting the $100, is closer to reality. We believe few of the results stressed in this paper depend qualitatively on our exact formulation. We discuss this assumption in more detail in Ko˝szegi and Rabin [2005] in the context of risk preferences, where it is crucial. 4. Our utility function is most closely related to Sugden’s [2003]. The main difference is in the way a given consumption outcome is compared with the reference lottery. In our model, each outcome is compared with all outcomes in the support of the reference lottery. In Sugden [2003], an outcome is compared only with the outcome that would have resulted from the reference lottery in the same state. See also the axiomatic theories of Gul [1991], Masatlioglu and Ok [2005], and Sagi [2005]. A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1139 and gain–loss utility, we propose a strong relationship between the two. While it surely exaggerates the tightness of the connec- tion, our model assumes that how a person feels about gaining or losing in a dimension depends in a universal way on the changes in consumption utility associated with such gains or losses:5

nk͑ck͉rk͒ ϵ ␮͑mk͑ck͒Ϫmk͑rk͒͒, where ␮٪ is a “universal gain–loss function.”6 We assume that :␮٪ satisfies the following properties A0. ␮( x) is continuous for all x, twice differentiable for x 0, and ␮(0) ϭ 0. A1. ␮( x) is strictly increasing. A2. If y Ͼ x Ͼ 0, then ␮( y) ϩ ␮(Ϫy) Ͻ ␮( x) ϩ ␮(Ϫx). A3. ␮Љ( x) Յ 0 for x Ͼ 0, and ␮Љ( x) Ն 0 for x Ͻ 0. ␮Ј ␮Ј ϵ␭Ͼ ␮Ј ϵ ␮Ј ͉ ͉ A4. Ϫ(0)/ ϩ(0) 1, where ϩ(0) limx30 ( x ) and ␮Ј ϵ ␮Ј Ϫ͉ ͉ Ϫ(0) limx30 ( x ). Assumptions A0–A4, first stated by Bowman, Minehart, and Rabin [1999], correspond to Kahneman and Tversky’s [1979] explicit or implicit assumptions about their “value function” defined on c Ϫ r. Loss aversion is captured by A2 for large stakes and A4 for small stakes. Assumption A3 captures another important feature of gain–loss utility, diminishing sensitivity: the marginal change in gain–loss sensations is greater for changes that are close to one’s reference level than for changes that are further away. We shall sometimes be interested in characterizing the implications of reference dependence with loss aversion but with-

5. In a single-dimensional model, Ko¨bberling and Wakker [2005] also assume that the evaluation of gains and losses is related to consumption utility. Our formulation extends their insight to multiple dimensions. As one way to motivate that gain–loss utility is related to changes in consumption utility in each dimension, consider a person choosing between two gambles: a 50–50 chance of gaining a paper clip or losing a paper clip, and the comparable gamble involving $10 bills. It seems likely that she would risk losing the paper clip rather than the money, and do so because her sensation of gains and losses is smaller for a good whose consumption utility is smaller. Yet since m٪ is approximately linear for such ٪ small stakes, the choice depends almost entirely on the comparison of nk across dimensions, so that any model that does not relate gain–loss assessments to consumption utility is not equipped to provide guidance in this or related examples. Note that once ␮٪ is fixed, unless A3Ј below holds, affine transformations .6 of m٪ will not in general result in affine transformations of our model’s overall utility function. While this raises no problem in applying our model once the full utility function u(⅐͉⅐) is specified (or empirically estimated), it does mean that when deriving our model from a reference-independent model based on consumption utility alone, the specification of ␮٪ must be sensitive to the scaling of consumption utility. 1140 QUARTERLY JOURNAL OF ECONOMICS out diminishing sensitivity as a force on behavior. For doing so, we define an alternative to A3: A3Ј. For all x 0, ␮Љ( x) ϭ 0. This utility function replicates a number of properties commonly associated with reference-dependent preferences. Proposition 1 establishes that fixing the outcome, a lower reference point makes a person happier (Part 1); and preferences exhibit a status quo bias (Parts 2 and 3):

PROPOSITION 1. If ␮ satisfies Assumptions A0–A4, then the following hold. 1. For all F,G,GЈ such that the marginals of GЈ first- order stochastically dominate the marginals of G in each dimension, U(F͉G) Ն U(F͉GЈ). 2. For any c, cЈ ʦ ޒK, c cЈ, u(c͉cЈ) Ն u(cЈ͉cЈ) f u(c͉c) Ͼ u(cЈ͉c). 3. Suppose that ␮ satisfies A3Ј. Then, for any F,FЈ that do not generate the same distribution of outcomes in all dimensions, U(F͉FЈ) Ն U(FЈ͉FЈ) f U(F͉F) Ͼ U(FЈ͉F).

Parts 2 and 3 mean that if a person is willing to abandon her reference point for an alternative, then she strictly prefers the alternative if that is her reference point. Under Assumptions A0–A4, this is always true for riskless consumption bundles, but counterexamples can be constructed to show that the analogous statement for lotteries requires a more restrictive assumption such as A3Ј. ٪Proposition 2 establishes that in the special case where m is linear, our utility function u(c͉r) exhibits the same properties :٪as ␮

PROPOSITION 2. If m is linear and ␮ satisﬁes Assumptions A0–A4, K then there exists {vk}kϭ1 satisfying Assumptions A0–A4 such that, for all c and r,

K ͑ ͉ ͒ Ϫ ͑ ͉ ͒ ϭ ͸ ͑ Ϫ ͒ (3) u c r u r r vk ck rk . kϭ1

Insofar as for local changes m٪ can be taken to be much closer to linear than ␮٪, Proposition 2 says that for small changes our utility function shares the qualitative properties of A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1141 standard formulations of prospect theory.7 This equivalence does not hold when the changes are large or marginal consumption utilities change quickly. This is a good thing. If, for instance, a person’s reference level of water is a quart below the level needed for survival, loss aversion in ␮٪ will not induce loss aversion in u(c͉r): she would be much happier about a one-quart increase in water consumption than she would be unhappy about a one-quart decrease. More importantly, when large losses in consumption or wealth are involved, diminishing marginal utility of wealth as economists conventionally conceive of it is likely to counteract the diminishing sensitivity in losses emphasized in prospect theory.8

III. THE REFERENCE POINT AS (ENDOGENOUS)EXPECTATIONS In comparison to the extensive research on preferences over departures from posited reference points, research on the nature of reference points themselves is quite limited. While we hope that experiments and other empirical work will shed light on this topic, our model makes the extreme assumption that the reference point is fully determined by the expectations a person held in the recent past. Speciﬁcally, a person’s reference point is her probabilistic beliefs about the relevant consumption outcome held between the time she ﬁrst focused on the decision determining the outcome and shortly before consumption occurs.9 While some evidence indicates that expectations are important in determining sensations of gain and loss, our primary motivation for this assumption is that it helps unify and reconcile existing interpretations and corresponds to readily accessible intuition in many examples.10 The most common assumption, of course, has been that the reference point is the status quo. But in virtually all experiments

7. The proof of Proposition 2 shows that, quantitatively, the degree of loss .٪aversion observed in u(c͉r) is less than the degree assumed in ␮ 8. The tension between consumption utility and gain–loss utility in the evaluation of losses has been emphasized by prior researchers; see, e.g., Kahne- man [2003] and Ko¨bberling, Schwieren, and Wakker [2004]. 9. Our theory posits that preferences depend on lagged expectations, rather than expectations contemporaneous with the time of consumption. This does not assume that beliefs are slow to adjust to new information or that people are unaware of the choices that they have just made—but that preferences do not instantaneously change when beliefs do. When somebody finds out five minutes ahead of time that she will for sure not receive a long-expected $100, she would presumably immediately adjust her expectations to the new situation, but she will still five minutes later assess not getting the money as a loss. 10. For examples of some of the more direct evidence of expectations-based counterfactuals affecting reactions to outcomes, see Mellers, Schwartz, and Ritov [1999], Breiter et al. [2001], and Medvec, Madey, and Gilovich [1995]. 1142 QUARTERLY JOURNAL OF ECONOMICS interpreted as supporting this assumption, subjects plausibly expect to keep the status quo, so these studies are also consistent with the reference point being expectations. For instance, procedures that have generated the classic endowment effect might plausibly have induced a disposition of subjects to believe that their current ownership status is indicative of their ensuing ownership status, so that our expectations-based theory makes the same prediction as a status-quo-based theory. Indeed, our theory may be useful for understanding instances where the endowment effect has not been found. One interpretation of the rare excep- tions to laboratory findings of the effect, such as Plott and Zeiler [2005], is that they have successfully decoupled subjects’ expectations from their initial ownership status. Similarly, the field experiment by List [2003], which replicates the effect for inexpe- rienced sports card collectors but finds that experienced collectors show a much smaller, insignificant effect, is consistent with our theory if more experienced traders come to expect a high probability of parting with items they have just acquired. And the important limits on the endowment effect noted by Tversky and Kahneman [1991] and Novemsky and Kahneman [2005]—that budgeted spending by buyers and successful reduction of inventory by sellers are not coded as losses—are clearly also predicted by our model: parties in market settings expect to exchange money for goods.11 Consider also an instance of reference dependence commonly discussed in economics: employees’ aversion to wage cuts. A wise inconsistency has pervaded the application of the reference-point- as-status-quo perspective to the laboratory versus the labor market: a decrease in salary is not a reduction in the status-quo level of wealth—it is a reduction from the expected rate of increase in wealth. While good judgment and obfuscatory language can be used to variously deem aversion to losses in current wealth (when we reject unexpected gambles) versus aversion to losses in increases in current wealth (when we are bothered by wage cuts) versus aversion to losses in increases in the rate of increase of current wealth (when we are bothered by not getting an expected pay raise) as the relevant notion of loss aversion, our model not

11. Indeed, while researchers such as Novemsky and Kahneman [2005] seem to frame these examples as determining some “boundaries of loss aversion,” we view them more narrowly as determining the boundaries of the endowment effect. As we demonstrate in Section IV, loss aversion does have important implications in markets—but the endowment effect is not among them. A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1143 only accommodates all these scenarios—but predicts which is the appropriate notion as a function of the environment. Finally, a status-quo theory of the reference point is especially unsatisfying when applied to the many economic activi- ties—such as food, entertainment, and travel—that involve fleet- ing consumption opportunities and no ownership of physical as- sets. If a person expects to undergo a painful dental procedure, finding out that it is not necessary after all may feel like a gain. Yet there is no meaningful way in which her status-quo endowment of dental procedures is different from somebody’s who never expected the procedure, so irrespective of expectations a status- quo theory would always predict the same gain–loss utility of zero from this experience. Our model of how utility depends on expectations could be combined with any theory of how these expectations are formed. But as a disciplined and largely realistic first pass, we assume that expectations are fully rational. To illustrate with an example analyzed in more detail in Section IV, suppose that a consumer had long known that she would have the opportunity to buy shoes, and faced with price uncertainty, had formed plans whether to buy at each price. If given the reference point based on her expectation to carry through with these plans, there is some price where she would in fact prefer not to carry through with her plans, our theory says that she should not have expected these plans in the first place. More generally, our notion of personal equilibrium assumes that a person correctly predicts both the environment she faces—here, the market distribution of prices— and her own reaction to this environment—here, her behavior in reaction to market prices—and taking the reference point generated by these expectations as given, in each contingency maximizes expected utility. Formally, suppose that the decision-maker has probabilistic beliefs described by the distribution Q over ޒ capturing a distribution over possible choice sets {Dl}lʦޒ she might face, where each ʦ ⌬ ޒK Dl ( ). In the first and weaker of two solution concepts we consider, rational expectations is the only restriction we impose: ʦ DEFINITION 1. A selection {Fl Dl}lʦޒ is a personal equilibrium ʦ ޒ Ј ʦ ͉͐ Ն Ј͉͐ (PE) if for all l and F l Dl, U(Fl Fl dQ(l )) U(F l Fl dQ(l )).

If the person expects to choose Fl from choice set Dl, then given her expectations over possible choice sets she expects the 1144 QUARTERLY JOURNAL OF ECONOMICS

͐ distribution of outcomes Fl dQ(l ). Definition 1 says that with those expectations as her reference point, she should indeed be willing to choose Fl from choice set Dl. Of existing models, our notion of PE is most related to the notion of “loss-aversion equilibrium” that Shalev [2000] defined for multiplayer games as a Nash equilibrium fixing each player’s reference point, where the reference point is equal to the player’s (implicitly defined) reference-dependent expected utility. Al- though Shalev does not himself pursue this direction, reformu- lating his notion of loss-aversion equilibrium using our utility function and applying it to individual decision-making corresponds to PE.12 As we shall illustrate in Section IV, there may be multiple PE: it may be that if a person expects to buy shoes at a particular deterministic price, she prefers to buy them, and if she expects not to buy, she prefers not to buy them. Since the decision-maker has a single utility function, she can always rank the PE outcomes in terms of ex ante expected utility. Insofar as a person is free to make any plan so long as she will follow it through; therefore, she will choose her favorite plan: ʦ DEFINITION 2. A selection {Fl Dl}lʦޒ is a preferred personal ͐ ͉͐ equilibrium (PPE) if it is a PE, and U( Fl dQ(l ) Ն ͐ Ј ͉͐ Ј Fl dQ(l )) U( F l dQ(l ) F l dQ(l )) for all PE selections Ј ʦ {F l Dl}lʦޒ. To see how the solution concepts work, consider the shoe shopper from above. Her choice set at the time of the purchase decision is the decision of whether to buy at the (ex ante possibly unknown) price she faces. Her reference point is the probabilistic distribution over money outlays and shoe acquisitions determined by her planned behavior in each choice set—her plans whether to buy at each possible price—combined with the distribution over possible choice sets—her beliefs about the prices she might face. PE requires her planned behavior in each choice set to

12. Proposition 3 below is also related to Shalev’s [2000] Proposition 2 showing that pure-strategy Nash equilibria are always myopic loss-aversion equilibria. Insofar as they provide a framework for having utility depend on beliefs, personal equilibrium is also very closely related to Geanakoplos, Pearce, and Stacchetti’s [1989] notion of psychological Nash equilibrium in games. But since in a psychological game a player’s utility can only depend on her own (possibly higher-order) beliefs about other players’ strategies, it seems impossible to reformulate our model in that framework. A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1145 be optimal given this reference point, and PPE requires her to choose the PE plan with highest ex ante expected utility.13 While PE and PPE may in general exhibit different properties, our main results and intuitions in this paper hold for both concepts. Except where we wish to make explicit how the concepts differ, we have therefore chosen examples where there is a unique PE, so that the set of PE and PPE coincide. Before considering speciﬁc contexts, we note a simple and striking feature of our general model. When a loss-averse decision-maker’s choice set is deterministic and all choices in it are deterministic, the predictions of PPE are identical to those of a model based solely on consumption utility:

PROPOSITION 3. Suppose that Q is a lottery putting probability 1 on a choice set consisting of all convex combinations of a set D* of deterministic outcomes. If A3Ј holds, then a lottery is a PPE if and only if it puts probability 1 on an outcome that is Ј a solution to argmaxcЈʦD*m(c ). Any deterministic consumption level c that maximizes consumption utility is a PE: if the decision-maker had expected c, another outcome would both lower consumption utility and lead to sensations of loss in dimensions where it falls short of c. Furthermore, notice that ex ante expected gain–loss utility is zero for deterministic outcomes, and because losses from comparing an outcome to a counterfactual loom larger than the symmetric gains, it is negative for nondeterministic lotteries. Hence, c yields strictly greater ex ante expected utility than any deterministic outcome that does not maximize consumption utility, and also than any nondeterministic lottery. This means both that c is a PPE, and that the latter possibilities cannot be.

13. The above glosses over a key way that our model is underspecified. A premise of our model is that preferences depend on expectations formed after the decision-maker started focusing on a decision. The specification of Q should correspond to this timing, and is therefore an important interpretational matter in any application. As an illustration, if the shoe shopper had been thinking about her possible purchase for a long time, her expectations from before she knew the price will affect her preferences, and the appropriate Q is the lottery representing her probabilistic beliefs over prices. But if she only considered the possible purchase upon seeing shoes at the store, Q should be the deterministic lottery corresponding to the relevant price at the time. Because PE is simply an application to our environment of the more general definition in Ko˝szegi [2005], Theorem 1 of that paper establishes that, if ͐ Dl dQ(l ) is convex and compact, a PE exists. Since the set of PE is closed and U(F͉F) is continuous in F, a PPE also exists. 1146 QUARTERLY JOURNAL OF ECONOMICS

Because u(c͉c) ϭ m(c), Proposition 3 implies that in deterministic environments, not only does loss aversion not affect behavior, it also does not affect welfare. These statements are not true for PE: as we illustrate in Section IV, if a person comes to anticipate choosing an option that does not maximize consumption utility, she may carry it out to avoid the sensation of loss associated with switching to another option. But more importantly, as many of our results in Sections IV and V highlight, in environments with uncertainty even applying PPE reference dependence can hugely inﬂuence behavior.

IV. SHOPPING In this section we use our model to study how a consumer’s valuation for a good is endogenously determined by market conditions and her own anticipated behavior. Suppose that there are two dimensions of choice, with m(c) ϭ ϩ ʦ c1 c2, where c1 {0,1} reflects whether or not a consumer has ʦ ޒ a pair of shoes, and c2 is her dollar wealth. This means that we can think of her “intrinsic value” for shoes as $1. To isolate the :consequences of loss aversion, we assume that ␮٪ satisfies A3Ј ␮( x) ϭ ␩x for x Ͼ 0, and ␮( x) ϭ ␩␭x for x Յ 0. In this formulation, ␩ Ͼ 0 is the weight the consumer attaches to gain– loss utility, and ␭ Ͼ 1 is her “coefficient of loss aversion.” We normalize her initial endowment to (0,0). Whatever the consumer expected, she assesses a price p paid for shoes as some combination of loss and forgone gain. Adding this gain–loss sensation to her consumption value for money, her disutility from spending on the shoes is between (1 ϩ ␩) p—her disutility if she had expected to pay p or more—and (1 ϩ ␩␭) p— her disutility if she had expected to pay nothing. By a similar argument, the consumer’s total utility from getting the shoes is between 1 ϩ ␩ and 1 ϩ ␩␭. Hence, the expectations most conducive to buying induce a disutility of (1 ϩ ␩) p from spending money and a utility of 1 ϩ ␩␭ from getting the shoes, so that no matter her expectations the consumer would never buy for prices Ͼ ϵ ϩ ␩␭ ϩ ␩ p pmax (1 )/(1 ). Conversely, even given the expectations least conducive to buying, the consumer buys for all prices Ͻ ϵ ϩ ␩ ϩ ␩␭ p pmin (1 )/(1 ). The above implies that if shoes are available at a certain Ͼ price p, then for p pmax there is a unique PE in which the Ͻ consumer does not buy, and for p pmin there is a unique PE in A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1147 which she buys. In addition, with a deterministic price, expecting to buy in fact creates the preferences most favorable for buying, and expecting not to buy creates the preferences least favorable ʦ for buying. Hence, for p [ pmin,pmax], buying for sure and not buying for sure are both pure-strategy PE.14 Intuitively, if the consumer had expected to get the shoes, she would feel a loss of shoes if she did not buy, and her aversion to this loss leads her to buy even at relatively high prices. In contrast, if she had expected not to buy, buying would result in a loss of money, and her aversion to this loss leads her not to buy. But as an application of Proposition 3, the consumer’s PPE is typically unique: she buys if and only if p Ͻ 1.15 Reference dependence leads to more interesting behavior when prices are uncertain. In this case, changes in the price distribution can significantly affect a consumer’s willingness to pay a particular price.16 To examine the consumer’s willingness to pay without wor- rying about how her behavior feeds back into her expectations, we Ͻ suppose that she expects the price pL pmin with probability qL and Ͼ ϭ Ϫ the price pH pmax with probability qH 1 qL, and consider the “out-of-equilibrium” question of whether she buys at the intermediate price pM. Our calculations are limiting cases of environments 17 where pM occurs with a small probability. Given the assumptions above, the consumer will buy the shoes at price pL, but not at price pH. Hence, she expects to consume shoes and spend pL with probability qL, and not to consume shoes or spend money with probability qH. As a result, her utility from buying at price pM is

14. In the interior of this range, there is also a unique mixed-strategy equilibrium, where the consumer buys with probability q ϭ [(1 ϩ ␩␭) p Ϫ (1 ϩ ␩)]/[␩(␭ Ϫ 1)(p ϩ 1)] ʦ [0,1], and is indifferent between buying and not buying. This equilibrium is unstable by analogy to conventional notions of instability. 15. To avoid cumbersome presentation, for the remainder of the paper a statement of the form “if and only if x Ͻ y” will be used to mean “if x Ͻ y and only if x Յ y.” 16. One implication of this distribution-dependence is that different mechanisms that are traditionally considered equivalent, “incentive compatible” ways of eliciting preferences should yield different answers. For instance, the Becker- DeGroot-Marschak [1964] value-elicitation procedure commonly used in experimental work under the presumption that any induced or subjective expectation by subjects should yield the same—intrinsic—value, according to our model would yield different results depending on expectations. Hence, our model tells us that not only does this procedure not work in practice—it does not work in theory, either. 17. In Ko˝szegi and Rabin [2004], we show how to solve for the set of personal equilibria for any price distribution faced by the consumer, and how the principles we establish with our three-price examples extend to such distributions. We also show that sufﬁcient price uncertainty implies that the PE is unique. 1148 QUARTERLY JOURNAL OF ECONOMICS

(4) 1 Ϫ pM

ϩ qH͑␩ Ϫ ␩␭pM͒

Ϫ qL␩␭͑ pM Ϫ pL͒. The ﬁrst line is the consumption utility from buying. The second line is gain–loss utility from comparing buying with not buying, which is assessed as a gain of 1 pair of shoes and a loss of pM dollars. The third line is gain–loss utility from comparing buying at pM with buying at the expected purchase price pL, Ϫ which leads to no gain or loss in shoes and a loss of pM pL dollars. The consumer’s utility from not buying is

(5) qL͑␩pLϪ␩␭͒.

Relative to the expectation to buy, not buying is a gain of pL dollars and a loss of one pair of shoes. We consider consumer behavior in several different situations by comparing these expected utilities from buying and not buying. First, suppose that the good may be available for free: ϭ pL 0. Then, using expressions (4) and (5), the consumer buys the shoes at pM if and only if ␩(␭ Ϫ 1) (6) p Ͻ 1 Ϫ ͑1 Ϫ q ͒ . M L 1 ϩ ␩␭

The right-hand side of the above inequality is increasing in qL. Since the consumer expects to spend nothing no matter what, an increase in qL only increases her expectation to get the shoes and hence the loss she will feel if she does not buy. This “attachment effect” increases her willingness to pay. Ն ϭ Now suppose that pL 0 and qL 1. Then, comparing expressions (4) and (5), the consumer buys the shoes at price pM if and only if ␩͑␭ Ϫ 1͒ (7) p Ͻ 1 ϩ p ⅐ . M L 1 ϩ ␩␭

The right-hand side of this inequality is increasing in pL. Hence, in violation of the law of demand, a decrease in the price distribution decreases the consumer’s willingness to pay for the shoes. If there is a possibility of acquiring the shoes at a low price, by comparison the consumer considers paying the higher price pM to be a loss. The greater the difference between pM and pL, the A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1149 greater is the sense of loss, and the more this “comparison effect” decreases her willingness to pay. This violation of the law of demand occurs in our model solely because of the feedback of the environment into expectations: for any fixed expectations, the consumer’s demand is downward- sloping. But because lowering the prices at which she had expected to buy changes her view of paying higher prices, she might be led not to buy at those prices.18 The above illustrations of the attachment and comparison effects can be generalized to broader principles regarding the consumer’s reaction to different types of price decreases. If prices drop from above the consumer’s reservation price to below it, this boosts demand not only by the direct effect of lower prices, but also because the reservation price itself increases: since the consumer now expects to buy with higher probability, she becomes more attached to the idea of having the good. If prices drop from a level at which she would have bought anyway, then the price decrease intensifies the sense of loss a consumer feels from comparing buying at a high price to other possible purchase prices, reducing her demand at higher prices. While Proposition 3 says that (if applying PPE) consumption utility fully governs consumer behavior in deterministic environments, the above results show that the same is very much not true in stochastic ones. As inequality (6) indicates, there may be a unique PE in which the consumer does not buy the shoes for some prices below their intrinsic value; and as inequality (7) shows, she may be induced to buy even for some prices above their intrinsic value. Price uncertainty may in fact induce a shopper to behave in a way that does not maximize her overall utility among strategies available to her. As an example, suppose that she faces equiprob- able prices of zero or one-half. It is easy to check that for any ␩ Ͼ 0 and ␭ Ͼ 1 the unique PE is to buy at both prices. Yet as ␭ 3 ϱ, the disutility from paying one-half as compared to nothing ap- proaches infinity, with other parts of the consumer’s PE utility, as

18. The logic behind the attachment and comparison effects can shed light on nonequilibrium situations in which buyers believe that the price is lower than it actually is. For example, car dealers sometimes use the strategy of “throwing a lowball,” promising a very low price and attempting to raise it once the consumer gets used to the expectation of buying—using the attachment effect to sell at a price that would otherwise be too high. Our model says this strategy may backfire if the high price looks too awful compared with the expected price, but car dealers presumably make it their business to be well calibrated about which combinations of expected and actual prices are most successful in the situations they face. 1150 QUARTERLY JOURNAL OF ECONOMICS well as her utility from expecting and carrying through a plan never to buy, remaining the same. Hence, for a sufficiently high ␭, the consumer is worse off than if she were unable to buy the shoes. Intuitively, since the consumer values the shoes, she buys whenever the price is very low. The attachment to the good induced by realizing that she will do this, however, changes her attitudes toward the purchase decision. If the price turns out to be higher, she must choose between a loss of money and a loss of shoes. While buying is her best response to her expectations, it is still worse than if she could have avoided the risk of loss by avoiding the expectation of getting the shoes in the first place. More generally, because the consumer does not internalize the effect of her ex post behavior on ex ante expectations, the strategy that maximizes ex ante expected utility is often not a PE.

V. DRIVING A literature has recently emerged studying the relationship between labor supply and wages of workers with flexible daily work schedules.19 While strongly disagreeing about the extent of this behavior and whether it is irrational, Camerer et al. [1997] and Farber [2004, 2005] analyzing New York city taxi drivers all find a negative relationship between earnings early in the day and duration of work later in the day. Studies analyzing participation decisions as a function of expected wages, on the other hand, find a positive relationship between earnings and effort: Oettinger [1999] finds that stadium vendors are more likely to go to work on days when their wage can be expected to be higher, and Fehr and Goette [forthcoming] show bicycle messengers sign up for more shifts when their commission is experimentally increased. The negative relationship between earnings early and work later in the day found in this literature can be thought of in terms of drivers having a daily “target income.” To our knowledge, all existing research assumes that the target is exogenous, and none specifies its determinants. A person’s target, however, is likely to be endogenous to her situation. If a driver generally makes around $200 a day, her target is probably close to $200; if she

19. See Goette, Huffman, and Fehr [2004] and Farber [2004] for useful reviews of this literature. A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1151 generally makes $300, it will be $300. If there are days (such as holidays) where she predictably makes more money than average, her target on those days will be higher; and on days she does not drive, it is presumably zero. In this section we analyze labor-supply decisions with such endogenous targets. We find that a driver’s response to wage changes depends on whether those changes were predictable: (a) she is more likely to go to work on days her wage is predictably higher, and (b) once at work she is likely to work more at a given realized wage when those predicted wages are higher, but (c) she may drive less when her wages are unpredictably high. By endogenizing the target as the driver’s expectations, our theory contributes to the literature in a few ways. Most fundamentally, feature (b) above reverses the problematic implication of fixed-income-target models that predictably higher wages lower effort. In addition, because the model predicts how targets vary between drivers and for a driver from day to day, it may qualify the interpretation of existing empirical studies of the target-income hypothesis and aid substantially in de- signing new tests. Finding that the reference-dependent model best fits the data if the target is allowed to vary across drivers and days, for instance, Farber [2004] concludes that such variation—implicitly equated with indeterminacy—undermines the usefulness of the concept of target income. But assuming that expectations reflect the empirical patterns of average income, our model provides a way of allowing realistic variation in targets without introducing degrees of freedom. Finally, while this literature seems to assume that reference dependence is limited to income, our model assumes that effort is also reference-dependent. Although we follow the literature in referring to the phenomenon as income-targeting, in fact we obtain a negative relationship between unexpectedly high income and effort without a priori assuming that only income is reference dependent. Formally, a taxi driver decides each day whether to go to work in the morning, and, if she does, whether to continue driving in the afternoon. Denote by em her morning participation decision, where em ϭ 1 if she drives and em ϭ 0 if she does not. Define her afternoon driving decision, ea ʦ {0,1}, similarly. Driving in the morning yields income Im, and driving in the afternoon brings in Ia. Im and Ia are independent random variables. If the driver works in the morning, she learns her afternoon wage Ia before 1152 QUARTERLY JOURNAL OF ECONOMICS deciding whether to drive in the afternoon. The driver has daily loss-averse preferences over her income and driving time. Her consumption utility is linear in each of the two dimensions, with m ϩ a ϭ m ϩ a m ϩ a ϭ m ϩ a m1(I I ) I I and m2(e e ) f(e e ), where f is the per-unit consumption-utility cost of effort. Assume again that ␮( x) ϭ ␩x for x Ͼ 0 and ␮( x) ϭ ␩␭x for x Յ 0. We solve for properties of PPE.20 As in the previous section, to develop intuition, we consider an “out-of-equilibrium” situation. The driver expects the morning m income to be wE with probability one, and the realized morning m income is wR . Although when expected income changes, typically so does realized income, to highlight the conceptual distinction between expected and surprise wage changes we perform com- m m parative statics separately with respect to wE and wR . The driver a Ͼ ϩ ␩␭ ϩ ␩ ϵ expects the afternoon wage to be wH [(1 )/(1 )] f a Ͻ ϩ ␩ ϩ ␩␭ ϵ wmax or wL [(1 )/(1 )] f wmin with probabilities qL ϭ Ϫ and qH 1 qL, respectively, and the realized afternoon wage a is the intermediate value wR. These assumptions imply that if the driver works in the morning, then no matter her expectation a she will work in the afternoon if the wage is wH, and not work if a the wage is wL. To be able to demonstrate all the effects of interest within this simple model, we assume that at midday the driver is short but within reach of her expected morning in- m Ϫ a Ͻ m Յ m come: wE wR wR wE . Since our main interest is in the driver’s behavior if she works, we first investigate the properties of PPE, labeled “participation PPE,” in which she shows up; we turn below to whether showing up is indeed a PPE. With the above distributions, the cabbie expects to work in the afternoon with probability qH, and m m ϩ a to earn wE if she drives in the morning only, and wE wH if she drives all day. Her utility if she continues to work is then m ϩ a Ϫ wR wR 2f ϩ ͑␩͑ m ϩ a Ϫ m͒Ϫ␩␭ ͒ qL wR wR wE f Ϫ ␩␭͑͑ m ϩ a ͒Ϫ͑ m ϩ a ͒͒ qH wE wH wR wR . The first line is the consumption utility from working all day. The second line is gain–loss utility from comparing driving all day m ϩ with driving only in the morning, which leads to a gain of wR

20. Appropriately restated, the results we stress hold for PE as well, with more complicated characterizations due to the multiplicity of equilibria. A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1153

a Ϫ m wR wE in income and a loss of f in work effort. Finally, the third line is the loss from comparing working all day with her expectation to work all day, which feels like a loss because the m ϩ a m ϩ a driver earns wR wR instead of wE wH. The utility from not working is m Ϫ ϩ ͑␩ Ϫ ␩␭͑ m ϩ a Ϫ m͒͒Ϫ ␩␭͑ m Ϫ m͒ wR f qH f wE wH wR qL wE wR . Hence, the driver continues to work so long as ͓1 ϩ ␩ ϩ q ␩͑␭ Ϫ 1͔͒ f Ϫ q ␩͑␭ Ϫ 1͒͑wm Ϫ wm͒ a Ն L L E R (8) wR . 1 ϩ ␩ ϩ qH␩͑␭ Ϫ 1͒

Finally, if the expected income level is realized in the morning m ϭ m (wR wE ), this inequality becomes

1 ϩ ␩ ϩ q ␩͑␭ Ϫ 1͒ a Ն L (9) wR f. 1 ϩ ␩ ϩ qH␩͑␭ Ϫ 1͒ Notice that this last inequality does not depend on the expected morning wage. With an expectations-based income target, a fully anticipated increase in the morning wage leaves the driver on average equally far from her target in the middle of the day—and hence does not affect her willingness to continue work. By contrast, the driver is more likely to drive even at a moderate afternoon wage if the probability qH of a high afternoon wage is increased. Intui- tively, an increase in the expected afternoon wage increases the driver’s target income as well as her expectation to work, making lower income more painful and work less painful. Unlike the prediction of reduced work in ﬁxed-income-target models, these results imply that (depending on the form of increase) anticipated wage increases either increase work effort or leave it unaffected. Examining how a divergence between expected and realized incomes affects the driver’s work effort, however, shows that our model does capture the core intuition in the target-income ﬁnd- ings of Camerer et al. [1997]. Since the right-hand side of inequal- m ity (8) is increasing in wR , when the driver’s morning income is lower she requires a lower afternoon income to induce her to keep working. Intuitively, if a driver earns less money than she expected early in the day, she will be more willing to work later, so as to mitigate the losses from falling short of her target. Finally, inequality (8) shows one more sense in which increases in expected income increase the driver’s willingness to work: an in- 1154 QUARTERLY JOURNAL OF ECONOMICS

m crease in the predicted morning wage wE has a positive effect on the afternoon work decision for any given morning wage.21 Based on the above, it is easy to derive the driver’s participation decision. Since the afternoon work decision is independent m m of wE , an increase in wE merely shifts the entire income distribution from participation to the right. Hence, showing up is more likely to be part of a PPE. This result is consistent with the ﬁndings of Oettinger [1999] and Fehr and Goette [forthcoming] that the elasticity of participation with respect to predictable wage variation is positive. Although these intuitions do not fully extend to all stochastically dominant increases in the income distribution, they do generalize to simple shifts in it.22 Suppose that the driver’s morning income has two additive components, a constant wm and a continuously distributed “surprise” part w˜ m ϳ Fm with bounded support. Her afternoon income is the continuously distributed a ϳ a គ ៮ គ Ͻ ៮ Ͼ 23 random variable I F [w,w], where w wmin and w wmax. Proposition 4 establishes some properties of PPE as a function of the driver’s beliefs about income described by the triple (wm,Fm,Fa).

PROPOSITION 4. The following hold for any ␩ Ͼ 0 and ␭ Ͼ 1. 1. For any participation PPE there is a function g : ޒ 3 m [wmin,wmax] such that for any w˜ , the driver contin- ٪ues work if and only if Ia Ն g(w˜ m). The function g is increasing, and is strictly increasing at w˜ m if Fm(w˜ m ϩ g(w˜ m)) Ϫ Fm(w˜ m) Ͼ 0. ,(If g٪ describes a participation PPE for (wm,Fm,Fa .2 it also describes a participation PPE for any (wmЈ,Fm,Fa) such that wmЈ Ն wm.

21. It bears emphasizing that only an increase in the realized morning income has a negative effect on willingness to drive in the afternoon. Because an a increase in the realized afternoon income wR does not affect the driver’s reference point, our model predicts (as does virtually any model) that such an increase m a increases the driver’s willingness to work. Hence, in cases when both wR and wR increase—when surprises in the wage are positively correlated over the course of a day—the overall effect on work effort is ambiguous. 22. Speciﬁcally, it is parts 2 and 3 of Proposition 4 below regarding the driver’s participation decision that does not extend to all shifts. If, for instance, the variance in income increases signiﬁcantly along with an increase in the mean, the driver’s expected utility in a PE involving participation may decrease because of the variance. 23. These assumptions ensure that if the driver works in the morning, then for any Im there is a positive probability that she continues work, and a positive probability that she does not. A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1155

3. For any Fm and Fa, there is a constant wគ m such that participation is part of a PPE for (wm,Fm,Fa) if and only if wm Ն wគ m, and nonparticipation is a PPE for (wm,Fm,Fa) if and only if wm Յ wគ m. In the proposition, g(w˜ m) is the driver’s “reservation wage” for driving in the afternoon as a function of the surprise compo- nent of the morning wage. Part 1 shows that g٪ is increasing, so that the driver has negative labor supply elasticity with respect to surprises in the morning wage. Part 2 says that once the morning wage is sufﬁciently high to induce participation, it is only surprises relative to expectations that determine the driver’s afternoon work decision. This means that an increase in the expected morning wage does not affect the afternoon work decision if it is matched by an increase in the actual wage, but makes the driver more likely to continue work if it is not borne out in the actual wage (which therefore represents a worse surprise). Part 3 shows that an increase in the expected morning wage makes the driver more likely to show up to work.

VI. CONCLUSION By directly constructing reference-dependent utility from consumption utility and assuming that the reference point is endogenously determined as rational expectations about outcomes, our theory provides an algorithm for translating a “classical” reference-independent model into the corresponding reference-dependent one. This helps render it highly portable and generally applicable. While we illustrated some implications of our framework for consumer and labor-supply decisions, there are many other domains where it can be applied. In the context of risk preferences, Ko˝szegi and Rabin [2005] and Sydnor [2005] show that an expectations-based theory may help explain very different reactions consumers have to insuring anticipated risks versus reacting to unanticipated risks. In auction theory, since expectations of winning an auction affect the desire to do so, different auction designs predicted in current theory to be reve- nue equivalent may in fact generate different revenues because of different expectations induced. In intertemporal choice, Stone [2005] shows how expectations-based preferences can generate behavior that can be mistaken for present-biased preferences in the sense of Laibson [1997] and O’Donoghue and Rabin [1999] or 1156 QUARTERLY JOURNAL OF ECONOMICS temptation disutility in the sense of Gul and Pesendorfer [2001], since surprising oneself with immediate consumption tends to be more pleasurable than inherently unsurprising planned future consumption. In principal-agent models, performance-contingent pay may not only directly motivate the agent to work harder in pursuit of higher income, but also indirectly motivate her by changing her expected income and effort. In bargaining, early posturing might be used not only to influence the other’s beliefs about achievable outcomes, but also to influence her preferences over outcomes by this change in beliefs.24 And while firms are presumably not directly subject to reference-dependent utilities, Heidhues and Ko˝szegi [2005, 2006] show that their responses to consumer loss aversion have important implications for wage and price setting in imperfectly competitive markets. Several features, however, leave our framework short of providing a formulaic way to apply reference dependence to all economic contexts. Our model takes as given the set of consumption dimensions over which gain–loss utility is separately defined. While in most applications it is appropriate to identify these dimensions with the physical consumption dimensions, with this approach our theory (or any theory) of reference dependence would in some cases make bad predictions.25 Ko˝szegi and Rabin [2004] argue that gain–loss utility should be defined over “hedonic” dimensions of consumption that people experience as psychologically distinct; in some situations, judgment is needed to identify these dimensions. And as noted in Section III, even more judgment is required in determining the moment of first focus. There are also contexts to which this paper’s model does not apply, but to which alternative models using the same psychological principles would apply. When considerable time passes between a decision and consumption, by the time consumption takes place the reference point—which we assume is recent expectations—will pre-

24. For related intuitions outside of our personal-equilibrium framework, see DeMeza and Webb [2003] on principal-agent theory and Compte and Jehiel [2003] on bargaining theory. 25. Consider, for instance, a decision-maker making choices over Tropicana and Florida’s Natural premium orange juices, two separate consumption goods she enjoys but can barely distinguish. Would she be willing to trade six ounces of Tropicana juice she had expected to consume for eight ounces of Florida’s Natural juice? If the trade were coded as a loss in the Tropicana dimension and a gain in the Florida’s Natural dimension, under usual parametrizations she would not. However, if the person does not view the juices she consumes as substantively different experiences, she would presumably accept the trade. A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1157 sumably reﬂect the decision made. In the purchase of extended warranties, for instance, whether or not a good breaks is typically realized long after the decision of whether to buy the warranty. Ko˝szegi and Rabin [2005] consider an approach to incorporating such possibilities into a rational-expectations model. While the utility-maximization approach in this paper suggests that people maximize reference-dependent preferences corresponding to true experienced well-being, there are reasons to doubt that this is so. Substantial evidence indicates that people “narrowly bracket”: They do not fully integrate decisions at hand with other decisions and events. Ignoring the way gains and losses from different decisions cancel each other out leads to overweighting of gains and losses. People may also overattend to losses and gains because they underestimate how quickly they will adapt to these changes.26 On both of these accounts, the nature and scope of reference-dependent choices seems to reﬂect mistakes our fully rational model does not capture.

APPENDIX:PROOFS Proof of Proposition 1 1. Obvious. 2. Suppose not; that is, suppose that u(c,cЈ) Ն u(cЈ,cЈ) and u(c,c) Յ u(cЈ,c). Adding these and using the deﬁnition of u implies that (10) m͑c͒ ϩ m͑cЈ͒ ϩ n͑c͉cЈ͒ ϩ n͑cЈ͉c͒ Ն m͑c͒ ϩ m͑cЈ͒ ϩ n͑c͉c͒ ϩ n͑cЈ͉cЈ͒. Eliminating m(c) ϩ m(cЈ) from both sides and using the deﬁni- tion of n٪, this reduces to

K ͸ ͓␮͑ ͑ ͒Ϫ ͑ Ј͒͒ ϩ ␮͑ ͑ Ј͒Ϫ ͑ ͔͒͒ Ն (11) mk ck mk ck mk ck mk ck 0. kϭ1 By A2, and using that c cЈ, this is a contradiction.

26. See Kahneman and Tversky [1979], Thaler [1985], Kahneman and Lovallo [1993], Benartzi and Thaler [1995], and Read, Loewenstein, and Rabin [1999] on the role of narrow bracketing in loss aversion, and Kahneman [1991] and Loewenstein, O’Donoghue, and Rabin [2003] on the role of underestimating adaptation. 1158 QUARTERLY JOURNAL OF ECONOMICS

3. We prove that for any F,FЈ ʦ ⌬(ޒK),

U͑F͉F͒ ϩ U͑FЈ͉FЈ͒ Ͼ U͑F͉FЈ͒ ϩ U͑FЈ͉F͒.

This is obviously sufﬁcient to establish the claim by contradiction. Let the marginals of F and FЈ on dimension k (that is, the distribution of outcomes in dimension k generated by F and FЈ) Ј be Fk and Fk, respectively. Noticing that expected consumption utilities are the same on the two sides, it is sufﬁcient to prove that

͵͵ ␮͑m ͑c ͒Ϫm ͑r ͒͒ dF ͑c ͒ dF ͑r ͒ϩ͵͵ ␮͑m ͑c ͒ k k k k k k k k k k

Ϫ m ͑r ͒͒ dFЈ͑c ͒ dFЈ͑r ͒ Ն ͵͵ ␮͑m ͑c ͒ k k k k k k k k

Ϫ m ͑r ͒͒ dF ͑c ͒ dFЈ͑r ͒ϩ͵͵ ␮͑m ͑c ͒ k k k k k k k k

Ϫ mk͑rk͒͒ dFkЈ͑ck͒ dFk͑rk͒

Ј for all k, and the inequality is strict for any k for which Fk F k. ϭ Ј The inequality obviously holds with equality when Fk F k,sowe Ј establish that it holds strictly when Fk F k. Since ␮ satisﬁes A3Ј, there is an ␣ Ͼ 0 such that for any x ʦ ޒ we have ␮( x) ϩ ␮(Ϫx) ϭϪ␣͉x͉. Using this and dividing by Ϫ␣/2, the above becomes

(12) ͵͵ ͉m ͑c ͒ Ϫ m ͑r ͉͒ dF ͑c ͒ dF ͑r ͒ ϩ ͵͵ ͉m ͑c ͒ k k k k k k k k k k

Ϫ m ͑r ͉͒ dFЈ͑c ͒ dFЈ͑r ͒ Ͻ 2͵͵ ͉m (c ) k k k k k k k k

Ϫ mk(rk)͉ dFk(ck) dFЈk(rk).

For real x,a,b, let x ʦ ((a,b)) denote that x is between a and b (i.e., that x ʦ (a,b)ifa Ͻ b and x ʦ (b,a)ifb Ͻ a). Also, let I٪ denote the indicator function. Then, the above inequality can be rewritten as A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1159

͵͵͵ I͓ x ʦ ͑͑m ͑c ͒,m ͑r ͔͒͒͒ dx dF ͑c ͒ dF ͑r ͒ k k k k k k k k

ϩ ͵͵͵ I͓ x ʦ ͑͑m ͑c ͒,m ͑r ͔͒͒͒ dx dFЈ͑c ͒ dFЈ͑r ͒ k k k k k k k k

Ͻ 2͵͵͵ I[ x ʦ ((m (c ),m (r )))] dx dF (c ) dFЈ(r ). k k k k k k k k

Reversing the order of integration, the above becomes

(13) ͵ Pr ͓x ʦ ͑͑m ͑c ͒,m ͑r ͔͒͒͒ dx k k k k ckϳFk,rkϳFk

ϩ ͵ Pr ͓x ʦ ͑͑m ͑c ͒,m ͑r ͔͒͒͒ dx k k k k ckϳFkЈ,rkϳFkЈ

Ͻ 2͵ Pr [x ʦ ((m (c ),m (r )))] dx. k k k k ckϳFk,rkϳFkЈ We prove that the above is true weakly point-by-point, and Ϫ1 ϭ strictly on a set of positive measure. Let Fk(mk ( x)) p( x) and Ј Ϫ1 ϭ Ј Ј F k(mk ( x)) p ( x). Notice that since Fk F k, there is a set of positive measure such that p( x) pЈ( x). The probability that x is on a line segment of two points mk(ck) and mk(rk), where ck Ϫ and rk are chosen independently according to Fk is 2p( x)(1 p( x)). Similarly, the probability that it is between two such points Ј Ј Ϫ Ј when ck and rk are chosen according to F k is 2p ( x)(1 p ( x)). And the probability that it is between two such points when ck Ј and rk are chosen according to Fk and F k, respectively, is p( x)(1 Ϫ pЈ( x)) ϩ pЈ( x)(1 Ϫ p( x)). It is sufﬁcient to prove that

p͑ x͒͑1 Ϫ p͑ x͒͒ ϩ pЈ͑x͒͑1 Ϫ pЈ͑x͒͒ Յ p͑ x͒͑1 Ϫ pЈ͑x͒͒ ϩ pЈ͑x͒͑1 Ϫ p͑ x͒͒ and that the inequality is strict for a set of positive measure. This is true since ( p( x) Ϫ pЈ( x))2 Ն 0 and the inequality is strict whenever p( x) pЈ( x). Proof of Proposition 2 ϭ Ϫ ϩ ␮ Ϫ Let vk( x) mk( x) mk(0) (mk( x) mk(0)). Since mk is linear for each k, 1160 QUARTERLY JOURNAL OF ECONOMICS

K ͑ ͉ ͒ Ϫ ͑ ͉ ͒ ϭ ͸ ͓ ͑ ͒ Ϫ ͑ ͒ ϩ ␮͑ ͑ ͒Ϫ ͑ ͔͒͒ u c r u r r mk ck mk rk mk ck mk rk kϭ1

K ϭ ͸ ͓ ͑ Ϫ ͒ Ϫ ͑ ͒ mk ck rk m 0 kϭ1

ϩ ␮͑mk͑ck Ϫ rk͒Ϫmk͑0͔͒͒ K ϭ ͸ ͑ Ϫ ͒ vk ck rk . kϭ1 A0 and A1 are obviously satisﬁed. Notice that for any y Ͼ x Ͼ 0,

vk͑Ϫy͒ ϩ vk͑y͒ ϭ ␮͑mk͑ y͒Ϫmk͑0͒͒ ϩ ␮͑Ϫ͑mk͑ y͒Ϫmk͑0͒͒͒

Ͻ ␮͑mk͑ x͒Ϫmk͑0͒͒ ϩ ␮͑Ϫ͑mk͑x͒Ϫmk͑0͒͒͒ ϭ vk͑Ϫx͒ϩvk͑ x͒ ␮ since mk is increasing and satisﬁes A2. Thus, vk satisﬁes A2. A3 is obvious, given the linearity of mk. Next,

vЈ͑Ϫx͒ mЈ͑0͒ ϩ ␮ЈϪ͑0͒mЈ͑0͒ 1ϩ␮ЈϪ͑0͒ k ϭ k k ϭ Ͻ ␭ lim Ј͑ ͒ Ј͑ ͒ϩ␮Ј ͑ ͒ Ј͑ ͒ ϩ␮Ј ͑ ͒ . xn0 vk x m k 0 ϩ 0 m k 0 1 ϩ 0 This completes the proof. Proof of Proposition 3 Without loss of generality, let (as in Sections IV and V) ␮( x) ϭ ␩x for x Ͼ 0 and ␮( x) ϭ ␩␭x for x Յ 0. Suppose that c ʦ Ј Ј ʦ argmaxcЈʦD* m(c ). Then, by deﬁnition, for all c D* ͸ ͓ ͑ Ј͒ Ϫ ͑ ͔͒ Յ ͸ ͓ ͑ ͒ Ϫ ͑ Ј͔͒ mk c k mk ck mk ck mk c k .

k:mk͑ckЈ͒Ͼmk͑ck͒ k:mk͑ckЈ͒Ͻmk͑ck͒ Therefore, using that m(cЈ) Յ m(c), ͑ Ј͉ ͒ ϭ ͑ Ј͒ ϩ ͸ ␮͑ ͑ Ј͒Ϫ ͑ ͒͒ Յ ͑ ͒ u c c m c mk c k mk ck m c k ϩ ͸ ␮͑ ͑ Ј͒Ϫ ͑ ͒͒ mk c k mk ck k ϭ ͑ ͒ ϩ ␩ ͸ ͓ ͑ Ј͒Ϫ ͑ ͔͒ m c mk c k mk ck

k:mk͑c kЈ͒Ͼmk͑ck͒ Ϫ ␩␭ ͸ ͓ ͑ ͒Ϫ ͑ Ј͔͒ Յ ͑ ͒ϭ ͑ ͉ ͒ mk ck mk ck m c u c c ,

k:mk͑c kЈ͒Ͻmk͑ck͒ which implies that c is a PE choice. A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1161

To show that c is a PPE, it is sufﬁcient to prove that it is preferred ex ante to all feasible choices within the decision-maker’s choice set (not only PE choices). We show that for any distribution F over D*, we have U(F͉F) Յ ͐ m(cЈ) dF(cЈ)(Յ m(c)). We prove dimension by dimension. The gain–loss utility part of U(F͉F) in dimension k is

1 (14) ͵͵ ͓␮͑m ͑c ͒Ϫm ͑r ͒͒ 2 k k k k

ϩ␮͑mk͑rk͒Ϫmk͑ck͔͒͒ dFk͑ck͒ dFk͑rk͒. By assumption A2, this is nonpositive. Finally, to show that a lottery F that is nondeterministic or does not maximize m٪ is not a PPE, we show that c is strictly preferred to these outcomes ex ante. This is obvious for deterministic outcomes ٪ that do not maximize m . And for a nondeterministic Fk, expression (14) is strictly negative, establishing the claim for that case as well.

Proof of Proposition 4 1. Suppose that the driver expects to work in the afternoon with probability q, and her daily income net of wm to be distributed according to H٪. If the driver’s realized morning income net of wm is w˜ m, then her utility from working in the afternoon for wage Ia is (15) wm ϩ w˜ m ϩ Ia Ϫ 2f ϩ ␩

w˜ mϩIa ͵ ͓͑w˜ m ϩ Ia͒Ϫw͔ dH͑w͒Ϫ␩␭ Ϫϱ

ϱ ͵ ͓w Ϫ͑w˜ m ϩ Ia͔͒ dH͑w͒Ϫ͑1 Ϫ q͒␩␭f, w˜ mϩIa while her utility from not working is

w˜ m (16) wm ϩ w˜ m Ϫ f ϩ ␩ ͵ ͓w˜ mϪw͔ dH͑w͒ Ϫϱ

ϱ Ϫ␩␭ ͵ ͓w Ϫ w˜ m͔ dH͑w͒ϩq␩ f. w˜ m 1162 QUARTERLY JOURNAL OF ECONOMICS

Hence, she works if (17) ͑1 ϩ ␩͒Iaϩ␩(␭ Ϫ 1)Ia͑1 Ϫ H͑w˜ m ϩ Ia͒͒ ϩ ␩͑␭ Ϫ 1͒

w˜ mϩIa ͵ ͑w Ϫ w˜ m͒ dH͑w͒ Ն ͓1 ϩ ␩ ϩ͑1 Ϫ q͒␩͑␭ Ϫ 1͔͒ f. w˜ m Notice that the left-hand side of inequality (17) is greater than or equal to (1 ϩ ␩)Ia, and the right-hand side is less than or ϩ ␩␭ ⅐ a Ͼ equal to (1 ) f. Hence, for any I wmax, the left-hand side is greater. Conversely, the left-hand side is less than or equal to [1 ϩ ␩ ϩ ␩(␭ Ϫ 1)H(w˜ m)] ⅐ Ia Յ (1 ϩ ␩␭) ⅐ Ia, while the right- hand side is greater than or equal to (1 ϩ ␩) ⅐ f. Hence, for any a Ͻ I wmin, the left-hand side is lower. Since the left-hand side of the inequality is strictly increasing and continuous in Ia while the a a ʦ right-hand side is constant in I , there is a unique I [wmin, m wmax] where the two sides are equal. Call this value g(w˜ ). Clearly, the driver works in the afternoon whenever Ia Ͼ g(w˜ m), but not if Ia Ͻ g(w˜ m). The left-hand side of inequality (17) is differentiable in w˜ m, with the derivative being Ϫ␩(␭ Ϫ 1)[H(w˜ m ϩ Ia) Ϫ H(w˜ m)] Յ 0. Hence, g٪ is nondecreasing, and whenever H(w˜ m ϩ g(w˜ m)) Ϫ m Ͼ m a Ͻ H(w˜ ) 0, it is strictly increasing at w˜ . Since prob[I wmin] Ͼ 0, for any realized morning wage the probability that the driver does not work in the afternoon is positive. Thus, H(w˜ m ϩ g(w˜ m)) Ϫ H(w˜ m) Ͼ 0ifFm(w˜ m ϩ g(w˜ m)) Ϫ Fm(w˜ m) Ͼ 0. This completes the proof. 2. Let a “compulsory-work PPE” refer to a PPE in the decision problem in which the driver must work in the morning. Notice that any participation PPE is a compulsory-work PPE, and in a compulsory-work PPE the expressions (15) and (16) describe the driver’s utilities from working and not working in the afternoon. Now since wm additively enters both the driver’s utility from working in the afternoon (expression (15)) and her utility from not working in the afternoon (expression (16)), if H٪ and q describe a compulsory-work PPE for some (wm,Fm,Fa), they describe a compulsory-work PPE for any (wmЈ,Fm,Fa): with the same expectations of behavior as a function of w˜ m, the same behavior remains optimal. Suppose that a compulsory-work PPE described by H٪ and q is a PPE for some (wm,Fm,Fa). Then, by the above argument H٪ and q also describe a compulsory-work PPE for any (wmЈ,Fm,Fa) such A MODEL OF REFERENCE-DEPENDENT PREFERENCES 1163 that wmЈ Ն wm. Furthermore, since (relative to the former compulsory-work PPE) in the latter compulsory-work PPE the distribution of income is just shifted to the right by a constant, increasing the driver’s expected utility by the same constant, this compulsory-work PPE is also a PPE. 3. Notice that for any Fm and Fa, the set of wm such that a compulsory-work PPE for (wm,Fm,Fa) is a PPE for (wm,Fm,Fa)is closed. And clearly a compulsory-work PPE is a PPE for a sufﬁ- ciently large wm, and not a PPE for a sufﬁciently small wm. Combining these facts with part 2, the set of wm for which a compulsory-work PPE is a PPE is of the form [wគ m,ϱ) for some wគ m ʦ ޒ. Since PPE exists and has nonparticipation whenever it is not a participation PPE, this means that nonparticipation is a PPE for any wm Ͻ wគ m. Since the set of wm for which nonparticipation is a PPE is also closed, nonparticipation is a PPE for wm ϭ wគ m. Finally, since an increase in wm shifts the distribution of income from participation to the right while leaving income from nonparticipation unchanged, nonparticipation cannot be a PPE for any wm Ͼ wគ m.

DEPARTMENT OF ECONOMICS,UNIVERSITY OF CALIFORNIA,BERKELEY

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Keith M. Marzilli Ericson and Andreas Fuster†

May 19, 2010

Abstract

Evidence on loss aversion and the endowment eﬀect suggests that people evaluate outcomes with respect to a reference point. Yet little is known about what determines reference points. We conduct two experiments that show that reference points are determined by expectations. In the ﬁrst experiment, we endow subjects with an item and randomize the probability they will be allowed to trade it for an alternative. Subjects that are less likely to be able to trade are more likely to choose to keep their item, as predicted when reference points are expectation-based, but not when reference points are determined by the status quo or when preferences are reference-independent. In the second experiment, we randomly assign subjects a high or low probability of obtaining an item for free and elicit their willingness-to-accept for it. Being in the high probability treatment increases valuation of the item by 20-30%.

JEL classification: C91, D03, D11, D81, D84 Keywords: reference points, expectations, loss aversion, endowment effect, willingness-to-accept, experimental economics ∗An earlier draft was entitled “Expectations as Endowments: Reference-Dependent Preferences and Ex- change Behavior” (first draft: November 12, 2009). We thank Anat Bracha, Keith Chen, Lucas Coffman, Tom Cunningham, Drew Fudenberg, Lorenz Goette, Botond K˝oszegi,Judd Kessler, David Laibson, George Loewenstein, Rosario Macera, Sendhil Mullainathan, Matthew Rabin, Al Roth, and seminar audiences at Harvard, the Whitebox Graduate Student Conference at Yale SOM, and the University of Basel for helpful comments and discussions. We gratefully acknowledge support from the Russell Sage Foundation through the Small Grants Program in Behavioral Economics. †Address: Department of Economics, Harvard University, Littauer Center, 1805 Cambridge St., Cam- bridge, MA 02138. E-mail: [email protected] and [email protected]

1 1 Introduction

A wide literature suggests that people evaluate outcomes with respect to a reference point. In Kahneman and Tversky’s (1979, 1991) highly influential prospect theory, individuals value gains and losses and are loss averse around a reference point. Yet the determination of the reference point was left imprecise. It has often been taken to be the status quo (Samuelson and Zeckhauser, 1988), meaning that individuals are reluctant to give up things they currently possess. However, K˝oszegiand Rabin (2006, 2007, 2009) (henceforth KR) argue that reference points are determined by recent expectations about outcomes, which need not correspond to the status quo. Since individuals often expect to keep the status quo, much evidence is consistent with either method of determining reference points. This study provides new experimental evidence that reference points are shaped by expectations. We present two experiments in which we manipulate expectations separately from endowments. In the first experiment, we endow all subjects with the same item (a mug), and randomize the probability that they will be allowed to exchange that item for an alternative (a pen). We show that when subjects are more likely to expect to keep their endowed item (because they have a low probability of being allowed to exchange), they are more likely to choose to keep their item if given the opportunity to exchange. In the second experiment, we randomize the probability that subjects will be given a mug for free. All subjects also know that with probability 10%, they instead have a choice between the mug and money. We elicit their mug/money choices for varying amounts of money, which provides us with a measure of their willingness-to-accept (WTA) for the mug. Subjects that have a higher chance of getting the mug for free have a higher WTA. These results are predicted when expectations determine reference points, but not by theories that identify the reference point with the status quo or by theories in which preferences do not depend on reference points. Evidence on how reference points are determined is necessary to predict when we should expect behavior to be affected by loss aversion, and will help economists choose between competing models of reference-dependent preferences.1 Moreover, our experiments and the theory of expectation-based reference points can help reconcile different findings regarding the presence or absence of endowment effects in exchange experiments (Knetsch, 1989; Plott and Zeiler, 2007; Knetsch and Wong, 2009) and experiments comparing the WTA of current owners to the willingness-to-pay (WTP) of current non-owners (Kahneman, Knetsch, and Thaler, 1990; Plott and Zeiler, 2005). We argue that in the typical exchange experiment, procedures can influence subjects’

1Recent theoretical and empirical applications of reference-dependent preferences with expectation-based reference points include Mas (2006), Heidhues and K˝oszegi(2008), Crawford and Meng (2009), Herweg, M¨uller,and Weinschenk (2009), and Pope and Schweitzer (2009).

2 perceptions of the likelihood that they will be able to exchange their endowed item for an alternative, or that they might also be given the alternative. Most discussions of such experiments implicitly assume that reference points are given by current endowments, in which case these perceptions should not matter for behavior. However, as the results from our first experiment show, such expectations dramatically impact subjects’ propensity to exchange. Our second experiment shows that expectations also matter for monetary valuation of goods and provides a quantitative measure of their effect. The first experiment leaves open the question of how quantitatively important the effects of expectation-based reference points are. It is possible, for instance, that a majority of subjects is simply near-indifferent between the two items, so that even a small effect of our expectation manipulation could lead to large differences in exchange proportions. We thus design a second experiment to provide an estimate of the quantitative magnitude of the effect of expectation-based reference points on WTA. Estimating this magnitude in an experiment is difficult because of the many other idiosyncratic factors that may influence subjects’ valuation of the items used in the experiment. For this reason, we also elicit the WTA for a second item, a pen. We use WTA for the pen to control for subject-specific valuation of university merchandise, thereby improving statistical power. Our results show that subjects who had a high (80-90%, depending on their indicated WTA) expectation of leaving with the mug valued the mug about 20-30% higher than subjects who were unlikely (10-20% chance) to leave with the mug, an effect that is both statistically and economically significant. We argue that our estimate of the effect of (likely) ownership on “true” valuation is cleaner than the ones obtained in typical experiments comparing the WTA of owners to the WTP of non-owners. As argued by Plott and Zeiler (2005), the often-observed gap between these measures may be driven by subject misconceptions due to experimental procedures, such as a misunderstanding of the value elicitation mechanism, or by the use of a “buy low, sell high” heuristic that does not necessarily reflect true valuation. However, as already pointed out by KR (2006), providing subjects with extensive instructions and training in the use of the value elicitation mechanism may lead them to expect the possibility of trade once they receive their item, in which case reference-dependent preferences with expectation- based reference points are perfectly consistent with the absence of a WTA-WTP gap found by Plott and Zeiler (2005). Thus, cleanly estimating the effect of ownership on valuation from the comparison of WTA and WTP is a very difficult task. Our experiment instead focuses only on WTA and holds everything other than the expected likelihood of leaving with the mug exactly constant across subjects in different treatments. Therefore, treatment differences can be driven only by differences in expected ownership of the item. Thus, our

3 second experiment contributes to the large literature that studies the effect of ownership on valuation and its consequences for policy (see e.g. Korobkin 2003 on the endowment effect’s implications for legal analysis). There is little other research that directly examines the effect of expectations on reference points. Knetsch and Wong (2009) conduct exchange experiments using a variety of procedures, and discuss their results in terms of the KR theory. However, they do not manipulate expectations explicitly as we do in our first experiment, and do not directly test the theory of expectation-based reference points.2 The study by Smith (2008) is close to our second experiment, in that he tests whether a higher (lagged) probability of receiving an item increases subjects’ valuation of that item (as measured by the WTA of subjects that end up receiving the item and the WTP of subjects who do not). He cannot reject the null hypothesis that lagged expectations do not matter for valuation. However, he does not attempt to proxy for idiosyncratic factors that may affect valuation as we do, and as a consequence his standard errors are large enough that he would not have had the power to detect reasonably sized effects (e.g. a $1, or 15-25%, change in valuation).3 Abeler, Falk, Götte,and Huffman (2009) conduct a real-effort experiment in which subjects are equally likely to receive a fixed payment or to be paid according to their effort, and only learn which case applies after they stop working. When the amount of the fixed payment is higher, subjects work more. This is predicted by KR, as subjects want to avoid being disappointed by potentially getting paid less than their fixed payment.4 A potential concern with this study is that randomization into the low or high fixed payment condition is not made transparent to subjects. As a consequence, subjects may make (potentially mistaken) inferences from the amount of the fixed payment about the “appropriate” amount of effort to provide (e.g., the fixed payment could be seen as an indication of how much the experimenter expects participants to work).5 We provide evidence that transparent randomization can be important: in pilot sessions of our first experiment, randomization into treatments was not made transparent, and subjects made inferences about the relative value of the items which then influenced their behavior. Our two experiments make randomization transparent, and these inferences disappear. We thus confirm that expectations affect reference points, and

2Section 4.3 will discuss their experiments in more detail. 3Another potential reason why he finds no effect may be that valuations are elicited after subjects learn whether or not they receive the item for free, so that the reference point may already have adjusted to having the item (or not having it) for sure. 4See also a related study by Gill and Prowse (2010) who find evidence for disappointment aversion in a two-person sequential-move tournament. 5The concern that subjects might conform to their interpretation of appropriate effort is distinct from anchoring or gift-exchange motives, which Abeler et al. control for and find no evidence of in additional treatments. See Section 4.2 for more detail.

4 furthermore provide new evidence that expectations matter not only for eﬀort provision, but also for valuation of goods, an issue of fundamental importance to economics.

2 Experiment 1: Expectations and Exchange Behavior

Our ﬁrst experiment is a variation of the classic Knetsch (1989) experiment, with many procedural details following Plott and Zeiler’s (2007) “loss emphasis treatment.” We endow subjects with an item (a university travel mug) and randomly and transparently manipulate the probability with which a subject will have the opportunity to exchange her item for an alternative (a silver metal university pen).6 We ﬁrst derive the theoretical predictions, then describe our experimental procedures, and present the results.

2.1 Theoretical Predictions for Behavior

In this section, we compare how expectations aﬀect the exchange behavior of three types of individuals: an individual with classical preferences (no loss aversion), one with loss aversion around a reference point given by the status quo, and one with loss aversion around a reference point determined by expectations (as in KR 2006).7 Consider an individual who is endowed with a mug and expects to have the option to exchange this mug for a pen with probability p. After being given some time to think about the situation, she is then asked to register a decision: if the option to exchange materializes, would she like to exchange? Let individuals have utility functions u(c|r) that can depend both on consumption c and reference r. Consumption and reference levels have multiple dimensions; for exchange behavior, only the “mug” dimension and the “pen” dimension are relevant. Utility on the th k dimension is composed of direct consumption utility uk and gain-loss utility with respect r to that dimension’s reference level of utility uk. Total utility from a consumption outcome c is then given by:   X  r  u(c|r) = uk + µ(uk − uk) ,  |{z} | {z }  k∈{mug,pen} Consumption utility Gain-loss utility where µ has the properties of the Kahneman-Tversky value function. For simplicity, we

6Both items have a retail value of around $8. In a typical endowment effect experiment, half the subjects would be endowed with a mug and the other half with a pen. We chose to endow all our subjects with the same item (which we randomly picked by flipping a coin before our very first session) in order to get sufficient power for testing the hypothesis that expectations affect exchange behavior. 7A more detailed exposition is provided in the Theory Appendix.

5 follow Section IV of KR (2006) and assume µ to be a piecewise linear function with a kink at zero that captures loss aversion: µ(x) = ηx for x > 0 and µ(x) = ηλx for x ≤ 0, where η ≥ 0 is the weight on gain-loss utility and λ > 1 is the individual’s loss aversion coefficient. This specification nests classical preferences that do not feature gain-loss utility (η = 0). Throughout, when referring to individuals with reference-dependent preferences, we assume η > 0. Now we consider two different specifications of the reference point. If the reference point is given by the status quo, which is that the individual owns the mug but not the pen, then r r we simply have upen = 0 and umug = umug In contrast, in KR’s specification, the reference point is determined by the individual’s probabilistic beliefs about outcomes, or in other words, her expectations. KR assume that individuals calculate an outcome’s gain-loss utility as follows: they compare each dimension’s consumption utility from the actual outcome to that of each possible outcome, producing a series of gain-loss µ (·) terms. Each possible outcome’s µ (·) is then weighted by the probability with which the individual expected that outcome to occur.8 Furthermore, an individual’s reference point is endogenous to her plans, as the probabilities of different states of the world occurring may depend at least in part on her decisions. In our example, if the KR individual plans not to exchange, then her reference point is the same as in the status quo case — she keeps the mug for sure. If instead she decides to exchange conditional on having the possibility to do so, the two states of the world she considers for her gain-loss utility are rend w/pen = {1 pen, 0 mugs} and rend w/mug = {0 pens, 1 mug} , which occur with probability p and 1 − p, respectively. Her utility of consumption bundle c given her expectations is then pu c|rend w/pen + (1 − p) u c|rend w/mug . If the exchange oc-

curs, then she gains or loses nothing with respect to rend w/pen, but with respect to rend w/mug,

she gains upen and loses umug. Thus, her total utility of this outcome would be her consump-

tion utility upen plus her gain-loss utility (1 − p) η (upen − λumug). Similarly, if the exchange

does not occur, her total utility would be umug + pη (umug − λupen). Following KR, we assume that the individual acts so as to maximize her expected utility given her reference point (which itself is determined by her plan), and chooses the plan that leads to the highest expected utility, given her rationally-forecasted future actions.9

Now, let individuals vary in their value for the mug and for the pen; assume that (umug,

8In this application, no predictions would change if reference points were instead simply given by the expected consumption utility in each dimension, in the spirit of Bell (1985). 9In the language of KR, we assume throughout the main part of the paper that the individual plays the “preferred personal equilibrium.” However, the theoretical prediction on the eﬀect of p is the same when using the less restrictive “personal equilibrium” concept, or K˝oszegiand Rabin (2007)’s “choice-acclimating personal equilibrium,” which assumes that reference points are determined by the individual’s decision, not her plan. See the Theory Appendix for more details.

6 upen) are distributed according to some population distribution function. The following proposition shows that increasing the probability p with which an individual is allowed to exchange increases the expected proportion of individuals who choose to exchange when reference points are determined by expectations, but not when reference points are given by the status quo or when individuals do not have gain-loss utility.

Proposition 1 If reference points are determined by expectations, then increasing p increases the expected proportion of individuals who choose to exchange. The probability p of having the option to exchange does not aﬀect the decision to exchange if reference points are given by the status quo or otherwise unaﬀected by expectations, or if there is no gain-loss utility (η = 0).

Proof. When reference points are given by the status quo, the utility of exchanging is greater

than the utility of keeping the mug if and only if p [upen + η (upen − λumug)] + (1 − p)umug > 1+ηλ umug, which holds if and only if upen > 1+η umug and thus does not depend on p. A similar condition, not dependent on p, holds for any ﬁxed reference point. When η = 0, the individual

desires to exchange if and only if upen > umug. However, when reference points are determined by expectations, an individual desires to exchange if and only if the expected utility of planning to exchange (and following through on the plan) is greater than the expected utility of planning to keep the mug (and keeping it). As

the Theory Appendix shows, this is true when (upen − umug)+η (1 − p) (1 − λ)(upen + umug) >

0. Note that upen > umug is a necessary condition for the individual to desire to exchange, as for p < 1 the second term is negative due to loss aversion. The second term gets less negative as p increases. Therefore, an individual who chooses to keep the mug under one value of p will always do so for lower values of p, but may instead choose to exchange for higher values of p.

Intuitively, for an individual who has classical preferences, the decision of whether to exchange is inﬂuenced only by the consumption utilities she derives from the two items. On the other hand, an individual who is loss averse around the status quo may not be willing to give up the mug he owns for the pen, even if the pen has higher consumption utility, due to the loss he feels from moving away from the status quo. However, this loss, and therefore the decision, is independent of whether the chance of the exchange occurring is high or low. Meanwhile, for an individual with KR preferences, the cost imposed by the gain-loss utility in case she decides to exchange must be outweighed by the gain in consumption utility from getting the pen instead of the mug, and this is less likely to happen the lower is p. On the other hand, as p → 1, gain-loss utility becomes relatively less important. In the extreme, if such an individual were certain to be able to exchange, she would prefer to do so

7 if and only if the consumption utility from the pen exceeds the one from the mug, exactly like a classical individual.

2.2 Procedures10

Upon arrival at the lab, each subject is seated at a carrel with a mug and a pen on it. We then flip a coin in front of each subject individually. The coin’s sides are labeled “1” and “9”, and we give each subject an index card with their resulting number on it. Subjects then start reading instructions on their computer screen. Subjects are told that they own the mug in front of them, and that each participant will leave the experiment with either a mug or a pen. They are then informed that at the end of the session, they may have the option to exchange their mug for the pen, if they so desire, and that this option will occur if and only if a ten-sided die that we roll individually for each subject at the end of the study comes up lower than or equal to the number on their index card. Thus, subjects whose coin came up “1” have a 10% chance of having the option to exchange (we will refer to them as being in Treatment T L, for low probability of being able to trade) while subjects who got a “9” have a 90% chance of being able to exchange their mug for the pen if they would like (Treatment T H ). After this first round of instructions, and after an experimenter reads the most important parts out loud, subjects answer some demographic questions and then fill out the first part of a 44-item “Big Five” personality questionnaire (John, Donahue, and Kentle, 1991). The purpose of this questionnaire is to distract subjects from the main decision we are interested in, and also to provide them with some time to plan their decision as to whether or not to exchange the mug. After they finish answering the first 22 questions, we remind them of the instructions and procedures for the (possible) mug-pen exchange, in order to make sure they understand, and also to make them think about their choice. Then, after they answer the second 22 questions of the questionnaire, subjects are asked to make a choice conditional on the die coming up lower than or equal to the number on their index card.11 This allows us to observe a decision for each subject, not just the ones for which the decision actually turns out to apply, which is similar to the strategy method often used in experimental games.12

10More details on both experiments are provided in the Methods Appendix. 11They are asked to check one of the following: If the the die comes up [1 in Treatment T L; 1 to 9 in Treatment T H ]: I want to keep the mug; or I want to trade the mug for the pen. 12As is further discussed in the Theory Appendix, eliciting a subject’s decision conditional on a choice set being reached is theoretically equivalent to asking the subject to choose once the choice set is reached, if by then the subject has made her plan. This is because KR (2006) posit that reference points are determined by lagged expectations. An interesting avenue for future research would be to test this prediction and investigate how quickly reference points adapt. However, if in our experiment we were to only elicit decisions after the uncertainty was resolved, we would need a prohibitively large number of subjects to examine decisions in

8 Before rolling the die, we ask some additional questions, as described in Section 4.1. The experiments were run at the Harvard Decision Science Laboratory. A total of 45 subjects (23 females; mean age 21), all of them undergraduate students at the university, participated. We conducted 10 sessions with between 3 and 7 subjects per session. Half the sessions were run on one day in late October 2009, the other half over two days in early November. Subjects received a show-up fee of $10, and the experiment took about 20 minutes.13

2.3 Results

RESULT 1: Subjects that have a 10% chance of being able to exchange are signiﬁcantly less likely to be willing to exchange than subjects that have a 90% chance. The proportion of subjects who choose to exchange in Treatments T L and T H are 22.7% and 56.5%, respectively (p=0.033, two-sided Fisher’s exact test).

Thus, we confirm the prediction of KR (2006) that reference points matter for choice, and that they are determined by expectations. The effect is large: subjects in Treatment T H are 34 percentage points, or one and a half times, more likely to choose to exchange than subjects in Treatment T L. As a test of the robustness of the result, Table 1 reports the estimated marginal effects from probit regressions that predict the probability a subject chooses to exchange from a treatment indicator and other covariates that may be related to their choice. Among the covariates we consider, gender significantly predicts the desire to exchange: column (2) shows that females seem to like the pen relatively more than males. However, the gender effect does not drive our result, as our treatments were perfectly gender- balanced. Column (3) shows that when both treatment and gender indicators are included as regressors, the indicator for Treatment T H is still significant at p < 2%. Furthermore, column (4) shows that adding subject age and an indicator for the day on which the session took place does not change the result either. If anything, the estimated treatment effect becomes even larger.14

the 10% possibility-of-trade condition. 13In the November sessions, the subjects afterwards participated in a second, completely unrelated experiment. The fact that these experiments were unrelated was made very clear to participants, and they were told that the ﬁrst experiment involved the mugs and pens while the second involved choosing between various payment amounts. The results below demonstrate that behavior was similar in the October and November sessions. 14The robustness of the eﬀect across subsets of sessions is strong: the proportions of subjects in Treat- ments T L and T H who wanted to exchange were 23.1% and 53.9% in our October sessions (13 subjects per treatment) and 22.2% and 60.0% in our November sessions (9 subjects in Treatment T L, 10 subjects in Treatment T H ).

9 3 Experiment 2: Expectations and Valuation

3.1 Theoretical Predictions for Behavior

3.1.1 Eﬀect of Expectations on WTA

To provide a quantitative measure of the effect of expectation-based reference points, we now consider how WTA for an item is affected by expectations of getting that item. As in the case of exchange behavior, this section shows that expectations affect WTA of individuals with loss aversion around a reference point determined by expectations, but not that of individuals with reference-independent preferences or with a reference point given by the status quo. Consider an individual who is told the following: she will receive a mug for free with

probability p, which varies between individuals and is either high (pH = 0.8) or low (pL = 0.1). Moreover, with small probability q (=0.1) the individual will receive the opportunity to choose between receiving the mug or various amounts of money. With probability 1 − p − q, the individual expects to get nothing. Individuals’ WTA in case they have the opportunity to trade the mug for money is elicited using an incentive-compatible modified Becker-DeGroot- Marschak (1964) (BDM) mechanism. How do expectations affect WTA under different theories of the reference point? As before, let consumption utility have multiple dimensions, here a “mug” dimension and a “money” dimension. We parameterize the consumption utility of money as being linear, but this is not crucial. Proposition 2 shows that the probability p of getting the mug for free alters WTA for the mug if reference points are determined by expectations, but has no effect under other theories of the reference point.

Proposition 2 If reference points are determined by expectations, then increasing the probability p of getting the mug for free affects the WTA for the mug. For any values of the parameters η > 0 and λ > 1, there is a q small enough such that increasing p unambiguously increases WTA for the mug. The probability p does not affect WTA if reference points are given by the status quo or otherwise unaffected by expectations, or if there is no gain-loss utility (η = 0).

Proof. The Theory Appendix shows that for q = 0, WTA for the mug is given by η(λ−1) 15 1 + 1+η p umug, which is increasing in p. This expression does not depend on p when η = 0, or if λ = 1. The Appendix also considers the case when q > 0, and shows that in our 1+η case, for η > 0, λ > 1, a suﬃcient condition for WTA to be increasing in p is q < 2η(λ−1) .

15This is the case considered by Smith (2008).

10 If the status quo (no mug, no money) is the reference point, or if η = 0, then WTA for the mug simply gives the utility of the mug. For any ﬁxed reference point, WTA may depend on λ and η, but will not depend on p.

Denote by WTAmug an individual’s WTA for the mug, which is affected by p under KR preferences. The intuition underlying Proposition 2 is the same as for Proposition 1’s results for exchange behavior: a higher probability of getting the mug for free increases the weight on the mug in the individual’s reference point. Here, however, WTAmug is also affected by q, the probability that the results of the BDM mechanism are implemented, because the endogenous probability of receiving money or a mug in this case affects the reference point.

The Appendix shows that WTAmug is unambiguously increasing in p for q small enough; for q = 0.1, as in our experiment, it is sufficient that λ ≤ 5. This is a mild restriction, as it is unlikely that losses loom more than five times larger than gains. Examining the limit as q goes to zero (q = 0.1 is small in our experiment) clarifies the

intuition: when p = 0,WTAmug simply gives the consumption utility of the mug, umug. When 1+ηλ p = 1, getting the mug is the full reference point, and WTAmug = 1+η umug, which depends η(λ−1) on both η and λ. For intermediate values of p, we have WTAmug = 1 + 1+η p umug. Thus, the eﬀect of changing expectations is proportional to umug, suggesting the use of the logarithmic functional form to identify the eﬀect of p as a percentage change in WTA.

3.1.2 Improving Power

Previous studies such as Smith (2008) have found large variance in subjects’ WTA or WTP for items similar to university mugs, which might make it difficult to detect even a reasonably sized effect of expectations on WTA. To improve statistical power, we control for individual-specific valuation of university merchandise by eliciting WTA for an unrelated item, a university pen. Holding expectations constant, WTA for both the mug and pen will be affected by similar factors, such as individual wealth and attachment to the university. Hence, by controlling for WTA for the pen, the unexplained variance in WTA for the mug will be reduced and a more precise estimate of the effect of expectations can be obtained. Consider the following situation. After the individual provides her WTA for the mug, but before she learns whether her choice applies, she is given a surprise decision. She is shown a pen and her WTA for the pen, WTApen, is elicited using the same modified BDM mechanism as for the mug. The pen-related BDM mechanism will be implemented with probability q, in addition to the probability q that the mug-related BDM mechanism will be implemented.16

16Thus, there are four possible states of the world: with probability p, the individual receives the mug independently of any decisions made; with probability q she receives one of her choices between the mug and money; with probability q she receives one of her choices between the pen and money; and with probability

11 Proposition 3 veriﬁes that WTApen is unaﬀected by p for theories of the reference point that

do not depend on expectations, and that if a higher p increases WTAmug, then WTApen will

not decrease in p. Thus, controlling for individual WTApen will not lead to a predicted eﬀect

of p on WTAmug when there is no such eﬀect.

Proposition 3 The probability p of getting the mug for free has no eﬀect on WTA for the pen if reference points are given by the status quo or otherwise unaﬀected by expectations, or if there is no gain-loss utility. If expectations are determined by reference points and WTA for the mug is increasing in p, then WTA for the pen will weakly increase in p.

Proof. As in Proposition 2, if the reference point is the status quo (no mug, no money, no pen), then WTA for the pen simply gives the utility of the pen. For any ﬁxed reference point, WTA may depend on λ and η, but will not depend on p. Now suppose reference points are determined by expectations. If mugs and pens are the same dimension of utility, then the derivation is the same as for Proposition 2, and raising

p increases WTApen. If mugs and pens are independent dimensions of utility, then when

q = 0, the utility of getting the pen is upen + η (upen − pλumug) and that of getting $WTApen

is WTApen + η (WTApen − pλumug) . At the indiﬀerence point, these expressions must be

equal; p cancels and WTApen is independent of the treatment. The Appendix takes the

case where q > 0, shows that WTApen does not depend directly on p but does depend

positively on WTAmug, as WTAmug will affect the amounts of money the individual expects to receive. This effect is proportional to q. We use the implicit function theorem to show that dW T Apen > 0 for interior values of WTA ,WTA . dW T Amug pen mug The proposition shows that there is a tradeoff: while controlling for WTApen would not give us a false positive (a positive estimate when the true effect is zero), doing so might attenuate our estimate of the effect of expectations. If reference points are determined

by expectations, WTApen may be aﬀected by p for two reasons. First, mugs and pens may overlap in dimensions of utility, if for instance the relevant utility dimension were “university

merchandise.” In this case, p will have a similar eﬀect on WTApen and WTAmug. Second,

p may aﬀect WTApen indirectly: since p aﬀects WTAmug, it alters individuals’ expectations

of how much money they will receive. This indirect eﬀect on WTApen is of the same sign

as the eﬀect on WTAmug, and is proportional to q, which is small in our context and thus likely undetectable.17

Our results below show that controlling for WTApen increases the precision of our treat-

ment eﬀect on WTAmug without reducing the point estimate. We cannot statistically reject

1 − p − 2q she receives nothing. 17 Another way in which WTAmug could affect WTApen is via anchoring, which would raise WTApen when p is high and also attenuate our estimated effect. We find no evidence of this.

12 a zero effect of p on WTApen, consistent with “mug” and “pen” being in different utility dimensions and the indirect effect through the expected money receipt being small (due to q being low).

3.2 Procedures

Upon arrival at the lab, each subject is seated at a carrel with a mug on it. We then flip a coin in front of each subject individually. The coin’s sides are labeled “1” and “8”, and we give each subject an index card with their resulting number on it. Subjects then start reading instructions on the computer screen in front of them. Subjects are told that if a ten-sided die that we roll individually for each subject at the end of the study comes up lower than the number on their index card, they will receive the mug in front of them for free and leave with it at the end of the experiment. They are also told that if the die comes up 9, they will have the option to keep the mug or exchange it for a randomly determined amount of money between $0 and $10.18 Thus, subjects whose coin came up “1” have a 10% chance of receiving the mug without making a choice (we will refer to them as being in Treatment M L, for low probability of getting the mug) while subjects who got an “8” have an 80% chance of receiving the mug without making a choice (Treatment M H ). Subjects in both treatments have a 10% chance of having a choice between the mug and money. The next phase of the experiment is then identical to Experiment 1. The experimenter reads the most important parts of the instructions out loud; subjects fill out a personality questionnaire in two parts, and get reminded in the middle that they may get the mug for free or have the possibility to choose between the mug and money. They are then told that they will now make choices (on a list) between different monetary amounts or keeping the mug (and not getting the money), and that, if the die comes up 9, they will receive their choice from one randomly selected row. Subjects then make their choices for dollar amounts ranging from $0 to $9.57, in increments of $0.33.19 They are also told that their decisions will only be revealed to the experimenters in case the die comes up such that one of their choices applies. Once they have made their choices for the case in which the die comes up 9, they get surprised by a page of instructions that informs them that if the die comes up 8 (in which case they previously expected to get neither the mug nor money), they will get their choice

18While the ten-sided die we used for Experiment 1 had numbers from 1 to 10, the die we used for this study had numbers from 0 to 9. 19The increments were chosen in order to avoid focal numbers as much as possible. The software enforced a single switching point and required that subjects make a choice in all the rows, improving data quality. For more details, see the Methods Appendix.

13 between a pen and a randomly determined dollar amount. It is made very clear to the subjects that their choice for this contingency does not in any way influence what they will get in case the die does not come up 8. They are handed a pen to inspect, and are then again asked to make choices between keeping the pen and different dollar amounts ($0 to $9.57, in $0.33 increments). The experiments were again run at the Harvard Decision Science Laboratory. A total of 112 subjects (66 females; mean age 22), all of them either undergraduate (83 subjects) or graduate (29 subjects) students at Harvard, participated. We conducted 16 sessions with between 3 and 11 subjects per session, across five days in April and May 2010. Subjects received a show-up fee of $10, and the experiment took about 20 minutes.20

3.3 Results

RESULT 2: Subjects that have a high chance of leaving with the mug value the mug signiﬁ- cantly higher than subjects that have a low chance of leaving with the mug. We estimate that being in treatment M H instead of M L increases willingness-to-accept for the mug by 20-30%.

Based on the individual coin flips, 52 subjects were in treatment M H and 60 subjects in treatment M L. We start by simply comparing the mean WTA for the mug across treatments.21 On average, subjects in the M H treatment request $4.12 to give up the mug, while the mean WTA of subjects in the M L treatment is $3.74. While these averages are in the right direction to support our theoretical predictions, they are far from statistically significantly different (p=0.44, two-sided t-test), due to the large between-subjects variation (the standard deviation of WTAmug is around 2.5 in both treatments).

However, as explained in Section 3.1.2, we also elicit the WTA for the pen, WTApen, to control for individual-specific variation in WTA for university memorabilia. Looking at subject-level differences between the amounts people are willing to accept in exchange for the mug or for the pen, WTAmug − WTApen, the treatment effect indeed moves closer towards significance: on average, subjects in the M H treatment require $0.92 more to give up the mug than to give up the pen, while the corresponding average for the M L treatment is only $0.02. This treatment difference is borderline significant using a nonparametric Fisher-

20As in experiment 1, the subjects afterwards participated in a second, completely unrelated pilot experiment, and the fact that these experiments were unrelated was made very clear to subjects. 21In our main analysis, we measure WTA as the midpoint between the highest amount for which the subject prefers keeping the item and the lowest amount at which she prefers returning the item in exchange for the money. For subjects who prefer keeping the item for all amounts, we set their WTA to $9.57 (the highest amount we offer them). We control for this censoring in some of our regressions (by using Tobit or interval regressions) and find that it does not materially affect our results.

14 Pitman permutation test of the equality of distributions (p=0.053).22,23 Differences in absolute values between the WTA for the mug and the pen are, however, not the correct functional form according to the theory. As described in Section 3.1.1, the effect of a high probability of getting the mug should be approximately proportional to the consumption utility of the mug, or, as we will implement it, linear in logs. The mean H L ln(WTAmug) is 1.30 in Treatment M and 1.11 in Treatment M ; a difference that is not quite significantly different (Fisher-Pitman p=0.18). However, when we consider the subject- level difference between ln(WTAmug) and ln(WTApen), we find a mean of 0.33 for subjects in the M H treatment and 0.01 for subjects in the M L treatment. This difference is significant at conventional levels (Fisher-Pitman p=0.02; Wilcoxon-Mann-Whitney p=0.09).24 Thus, controlling for idiosyncratic variation in WTA enables us to reduce noise and detect the treatment effect.

Regression analysis allows for a more ﬂexible relationship between ln(WTAmug) and

ln(WTApen), and allows us to control for demographic characteristics and potential day- specific effects that may influence individuals’ preference for the mug versus the pen. It can also address the censoring that occurs in a few cases at the top or the bottom of the WTA scale. Our main regression equation is

H 0 ln (WTAmug,i) = α + β · Mi + γ ln (WTApen,i) + ψ Xi + i

H H where Mi is an indicator that equals one for subjects in treatment M . If expecting to get the mug with a high probability increases WTA for the mug, as predicted by the KR theory, we expect β > 0. If instead preferences are reference-independent, or if reference points are given by the status quo, we expect β = 0. Table 2 shows that we ﬁnd strong support for the KR theory. Column (1), where we H regress ln(WTAmug,i) on the treatment indicator Mi only, restates the result that without

controlling for WTApen, β is positive but not quite statistically signiﬁcant. However, as

predicted in the discussion in Section 3.1.2, once we add ln(WTApen,i) as an additional regressor in order to reduce idiosyncratic noise, β increases in magnitude to 0.27 and becomes signiﬁcant at p <0.05 (column (2)). It remains signiﬁcant and increases even further in

22All tests reported in this paper are two-sided. The Fisher-Pitman test is a more powerful alternative to the better known Wilcoxon-Mann-Whitney test, which here gives a p-value of 0.10. See Kaiser (2007) for further discussion. 23 L The average WTA for the pen, WTApen, is somewhat higher in the M treatment ($3.72) than in the M H treatment ($3.20), but the distributions are not statistically significantly different (Fisher-Pitman p=0.27; p=0.61 if instead we use ln(WTApen)). 24Subjects that indicate a $0 WTA for either the mug or the pen, meaning they would rather have nothing than leaving with the item, get dropped when we use ln(WTA). There are five such subjects in M H (two of which indicate a $0 WTA for both items) and three in M L.

15 magnitude (to 0.3) if we add demographic and day controls (column (3); note that the signs of the coeﬃcients on age and female are consistent with what was found in Experiment 1)

or use a Tobit that accounts for the few censored observations (at WTAmug=9.57; column

(4)). In column (5), we allow for a more ﬂexible relationship between ln(WTAmug,i) and

WTApen,i by using a cubic function in WTApen,i instead of ln(WTApen,i). This also enables us to include the two subjects with WTApen,i = 0 in the sample. The point estimate of the treatment effect decreases slightly but remains significant at p < 0.05. Taken together, these results indicate that WTA for the mug increases by 20-30% when subjects have a high probability of getting the mug. In Table A.2 in the Empirical Appendix, we conduct a number of additional robustness checks which show that our result is robust H to adding an interaction term Mi · ln(WTApen,i), session fixed effects, or to the use of an interval regression that accounts for the fact that we only observe bounds on subjects’ WTA. Also, we show that if we run regressions in levels rather than in logs, the estimated treatment effect is generally borderline significant (at p < 0.1, and at p < 0.05 if we use

interval regression) once WTApen and demographic characteristics are added as regressors.

4 Discussion

4.1 Psychological Mechanisms Underlying Expectation-Based Ref- erence Points

In both our experiments, we find that increasing the expectation of getting an item makes subjects more reluctant to give up the item. These results support models of reference- dependent preferences in which expectations shape the reference point. There are various psychological mechanisms that could lead expectations to have an effect on preferences, and KR do not take a stance on the mechanism in the brain that would yield the preferences they propose. Although economists need not examine psychological mechanisms in order to apply KR preferences, doing so can suggest further avenues of inquiry for both theorists and empiricists. One psychological mechanism underlying expectation-based reference points may be an “attachment effect,” related, for instance, to the “emotional attachment mechanism” discussed by Ariely et al. (2005). A higher probability of ending up with an item may increase the time or intensity with which an individual thinks about the item, leading her to become attached to the item. This in turn increases the chance that the reluctance to lose this “endowment” created by expectations outweighs the potential consumption utility surplus the alternative item may provide.

16 Questions asked to subjects in Experiment 1 provide suggestive evidence consistent with this mechanism. After they made their choices (but before the die was rolled to determine whether their decision applied), subjects were asked to indicate agreement or disagreement with the following statements on a scale from 1 (disagree strongly) to 5 (agree strongly):

1. I like the mug better than the pen.

2. Since the beginning of the session, I have spent some time thinking about how I would use the pen.

3. Since the beginning of the session, I have spent some time thinking about how I would use the mug.

4. Since the beginning of the session, I have spent more time thinking about the mug than about the pen.

Table A.1 in the Empirical Appendix summarizes the results. Consistent with the choice evidence, subjects in Treatment T L (mildly) significantly more strongly agree with the statement that they like the mug better than the pen. Subjects in both conditions are about equally likely to agree to having spent some time thinking about using each item. However, subjects in Treatment T L more strongly agree to having spent more time (between the moment we explained the decision situation and the moment they made their decision) thinking about the mug than about the pen (means: 3.95 v. 3.17; Fisher-Pitman p=0.061). This latter fact is consistent with the “attachment mechanism” discussed above, or with “Query Theory” (Johnson et al., 2007), which argues that values are constructed by posing queries to oneself. In our context, individuals with high expectations of keeping the item may pose themselves different queries and think more about the mug, producing a change in valuation. Other complementary psychological mechanisms may also be at work, leading individuals to display behavior consistent with KR preferences. For instance, cognitive dissonance (Festinger, 1957) may lead subjects who expect to get an item to choose to like it more. Further, construal level theory predicts that low-probability events are mentally represented as psychologically distant (Wakslak et al., 2006), thereby affecting their incorporation into the reference point.

4.2 Subject Misconceptions and Transparent Randomization

Subjects in experiments make inferences from the decision environment they are put in. While this fact is true in general, Plott and Zeiler (henceforth PZ) (2007) suggest that it is particularly important to control for such inferences in experiments that try to test whether

17 reference-dependent preferences affect exchange behavior. They argue that if subjects in the typical exchange experiment are not told that which item they receive first was determined randomly, they may (mistakenly) infer that this item is superior to the one they can exchange it for, which makes them reluctant to exchange. To prevent this, PZ explicitly tell subjects that which item they get first was randomly determined, as will be discussed further in the next subsection. In a pilot for our exchange experiment, we found evidence that subject misconceptions from non-transparent randomization do indeed matter for behavior. Before settling on the design reported in Section 2, we ran sessions in which we did not make the random assignment to treatments obvious to subjects. A total of 63 subjects participated in 15 sessions conducted at the end of July 2009; 32 were randomly assigned (without their knowledge) to Treatment T˜L and 31 to Treatment T˜H . Subjects in these treatments had the same probabilities of being able to exchange as in T L and T H , respectively, and received very similar instructions, except that they were not told the source of the probability they would be permitted to exchange (see Methods Appendix for more details). The results went in the opposite direction of the ones in our main sessions reported in Section 2.3. In Treatment T˜H , 29.0% of subjects chose to exchange, while in Treatment T˜L, 62.5% chose to exchange, and the difference in proportions is statistically significant at p = 0.011 (Fisher’s exact test). After the first few sessions, we realized that this may have been due to a value inference effect: subjects who were given a low (10%) probability of being able to exchange their mug for the pen may have inferred that the pen must therefore be more valuable. We then added a question to the debriefing survey in which we ask subjects which item they believe has higher retail value, on a five-point scale from “definitely pen” to “definitely mug.” Consistent with the value inference hypothesis, among the 19 subjects in Treatment T˜L who answered the question, 13 (or 68.4%) indicated that they believed that the pen “definitely” or “probably” had higher retail value, while the same was true for only four out of 14 (28.6%) of subjects in Treatment T˜H . A Fisher-Pitman test indicates that the distributions of responses to the question are significantly different at p = 0.04. This value inference effect disappears when randomization is made transparent by flipping a coin in front of each subject.25 Thus, we conclude that, in the pilot, our test of expectation-based reference points was confounded by an experimental design that created

25The final row of Appendix Table A.1 shows that the answers to the debriefing question about relative retail value do not differ significantly across treatments in our main sessions, suggesting that our explicitly random assignment to treatments prevented subjects from inferring anything about the relative values of the two items. We asked the same question after Experiment 2, also finding only small and insignificant treatment differences (means: 2.75 in Treatment M H , 2.68 in Treatment M L; Fisher-Pitman p=0.82).

18 subject misconceptions about the relative values of the two items. The pilot may also speak to the relative strength of expectation-based reference points versus value inference. While we find evidence in favor of the KR theory in our clean treatments, the effect of loss aversion can be more than outweighed by (perceived) value signals provided by probabilities. This observation was part of the motivation behind Experiment 2, the goal of which was to get a clean measure of the strength of the effect of expectation-based reference points on behavior. While our pilot results provide evidence that subtle cues in the experimental environment can have a strong influence on subjects’ behavior, as hypothesized by PZ (2007), it is interesting to note that in a sense subjects behave in a way opposite to what PZ conjecture. They worry that subjects may mistakenly believe that the experimenter is altruistic towards them and endows them with the more valuable good. However, our pilot results are more consistent with the subjects believing that the experimenter is selfish and wants to prevent them (through a low probability of letting them exchange) from getting the more valuable good.26 Misconceptions from non-transparent randomization may affect the results of other research. For instance, in Abeler et al. (2009), subjects are randomized into a low or high fixed payment condition. They are then equally likely to be paid a piece rate or to receive this fixed payment and only learn which case applies after they stop working. Abeler et al. find that subjects in the high fixed payment condition work more and that a significant fraction of subjects stop working right when their piece rate earnings equal the fixed payment they may receive. These findings, like our results, are consistent with subjects having reference- dependent preferences with a reference point determined by expectations. However, because randomization into treatments was not transparent to subjects in Abeler et al.’s experiment, their results could also be driven in part by subjects’ (mistaken) inference. In particular, subjects may have taken the fixed payment as a signal of the expected effort level in the experiment (for instance, they could think that the fixed payment they may receive instead of their piece rate earnings was calibrated to be close to the piece rate earnings the average participant accumulates), and their behavior may (consciously or unconsciously) be affected by this.27

26In line with this discussion, Knetsch and Wong (2009) point out that if individuals have classical preferences, it seems more reasonable for them to assume that the experimenter assigns items in a cost- minimizing way rather than being altruistic towards subjects. 27Note that this concern is different from the alternative concern that subjects stop working when their piece rate earnings equal the fixed payment because the amount of the fixed payment is particularly salient and may thus serve as a focal point or anchor. Abeler et al. can rule out this explanation for their findings through some clever additional treatments. They also conduct a further additional treatment to show that their result is not driven by gift exchange motives (i.e., subjects wanting to reciprocate in response to the generosity of the possible fixed payment).

19 4.3 Reconciling Previous Experiments

4.3.1 Exchange Behavior

Our findings, along with the KR theory, can help reconcile the varied findings of previous experiments on the presence or absence of the endowment effect and on WTP-WTA gaps. The classic early experiment demonstrating the endowment effect was conducted by Knetsch (1989), who endowed subjects with either a mug or a chocolate bar and found that substantially fewer subjects exchanged their item for the alternative than predicted by classical theories. Such exchange asymmetries have usually been interpreted as resulting from loss aversion around a reference point given by current endowments. However, a natural interpretation in terms of the KR theory is that, until the opportunity to exchange is offered to participants, they fully expect to leave the experiment with the item they were endowed with, so that expectations and endowments coincide. PZ (2007) argue that Knetsch’s findings (and those of other researchers who replicated Knetsch’s experiment) were largely driven by certain features of his experimental procedures. PZ alter Knetsch’s procedures in various ways and demonstrate that such changes can have a large impact on the existence and magnitude of exchange asymmetries. They interpret this result as evidence that the endowment effect observed in earlier studies is not due to non-standard features of subjects’ preferences. However, when experimental procedures are altered, subjects’ expectations of which item(s) they will leave the experiment with may also change. In particular, PZ’s procedures may have made subjects believe that they would also be given a pen, or that there would be an opportunity to exchange the mug for the pen.28 In terms of the KR theory, the reference point of a subject who expects to receive both a mug and a pen is umug in the mug dimension and upen in the pen dimension. When she then gets surprised by the announcement that to obtain a pen, she has to give up her mug, she necessarily feels a loss in one dimension, and therefore chooses the item with the higher consumption utility. Similarly, a subject who expects to be able to exchange for sure will optimally plan to do so if the consumption utility of the pen is higher than the one provided by the mug, and therefore will not exhibit behavior predicted by theories that take the status quo as the reference point. Thus, while PZ show that the endowment effect can disappear when certain experimental

28Their two treatments in which no exchange asymmetries are observed, the “full set of controls” and the “loss emphasis treatment,” begin as follows (p. 1459): “We began these sessions by informing the subjects that mugs and pens would be used during the experiment. Subjects were then told that a coin was ﬂipped before the start of the experiment to determine which good, the mug or the pen, would be distributed ﬁrst. We then distributed mugs to the subjects and announced, ‘These mugs are yours.”’ In their “loss emphasis treatment,” PZ use somewhat stronger language to convey subjects’ entitlement to the endowed good; they say “The mug is yours. You own it.”

20 procedures are used, they do not directly manipulate or measure subjects’ expectations that they will leave with a mug or pen. While they argue that previously observed exchange asymmetries are not due to reference-dependence but rather classical preferences interacting with experimental procedures, their results are also consistent with the endowment effect being driven by reference-dependent preferences, but with a reference point determined by expectations, not current endowments. Other work has found an “endowment effect” even when subjects do not formally own an item. Knetsch and Wong (2009) find exchange asymmetries in an experimental treatment in which they give subjects an item, but tell them they do not yet own the item (but will own it at the end of the session). They interpret this finding as evidence in favor of KR, and interpret the PZ procedures as providing only a “weak reference state.” In this treatment, there is no upfront announcement to subjects that they will be able to alternatively get the other item at the end. In another treatment, Knetsch and Wong closely follow the PZ procedures, except that they explicitly tell subjects that at the end they will have the option to exchange, and confirm the absence of an endowment effect under these conditions.29

4.3.2 Valuation Behavior: WTP and WTA

A robust debate continues on when WTP-WTA gaps exist and whether they should be interpreted as evidence for reference-dependent preferences (see Isoni, Loomes, and Sugden 2010 and the reply by PZ 2010). In a classic paper, Kahneman et al. (1990) find that initial ownership of an item seemed to affect valuation of that item. They find large gaps between WTP and WTA for mugs, even though initial endowments were randomly assigned. These results have been interpreted as evidence for prospect theory and loss aversion. PZ (2005) reexamine this paradigm and dispute that the mere fact of endowment affects preferences. They instead argue that subject misconceptions drive the WTP-WTA gap and show that with extensive training in the BDM mechanism and anonymity, there is no statistically significant gap between WTP and WTA for mugs.30 Our results and the KR theory can help reconcile the findings of Kahneman et al. (1990) and PZ (2005). KR theory taken by itself predicts WTP-WTA gaps only when buyers and sellers of the good have different expectations of keeping the good. In the original Kahneman et al. experiments, endowments may (or may not) have induced an expectation of continued ownership of the good. Either way,

29They do not discuss that the announcement of having the possibility to exchange for sure will lead KR to predict no endowment effect. Knetsch and Wong have a third treatment, in which they find a significant exchange asymmetry even though subjects are told early on that they will have the option to exchange their item if they would like. They speculate that this finding may be due to the randomization procedure used, but it could also be due to the classic endowment effect. 30However, both Plott and Zeiler (2005) and Isoni et al. (2010) do find WTP-WTA gaps in lotteries. Isoni et al. and Plott and Zeiler (2010) debate various reasons for this differential finding.

21 we agree with PZ that many factors other than reference-dependence—bargaining heuristics, misunderstanding the BDM mechanism, etc.—may contribute to differences between WTP and WTA in these experiments. Yet just as in the exchange experiments, the procedures and training used by PZ may not have induced a difference between buyers and seller in their expectations of keeping the mug, as subjects may anticipate the possibility of trade. Thus, the absence of WTP-WTA gaps in their experiments is not surprising when reference points are determined by expectations.31 More generally, isolating the “pure” effect of reference-dependence on valuation is a daunting task, because even if the BDM mechanism is well understood, motivations that can be seen as consistent with classical preferences may be driving observed WTP-WTA gaps. An emphasis by the experimenter on the differences in roles of buyers and sellers, or placing the item in front of sellers but not buyers, can help induce a difference in expectation of keeping the item. However, these procedural details can also be seen as providing information or cueing strategic reactions (PZ 2010). Furthermore, sellers may be reluctant to sell what they could consider a gift or a trophy, and both buyers and sellers may want to signal their “bargaining savviness,” especially in a classroom setting. Our second experiment, which directly manipulates expectations and holds everything else constant across treatments, circumvents these problems and provides clean evidence of a statistically and economically significant effect of reference-dependence on valuation. We cannot directly speak to whether WTP-WTA gaps observed elsewhere are due to differences in expectations as opposed to a possible direct effect of endowment or other factors, but our results suggest that researchers examining WTP-WTA gaps should directly induce or at least elicit buyers’ and sellers’ expectations that they end up with the good they are buying/selling. In sum, PZ (2005, 2007) show that the mere fact of endowment, independent of expectations, may not lead to increases in valuations of goods. However, their results should not be taken as an indication that in general, reference-dependent preferences do not matter for exchange and valuation behavior, once one recognizes that the reference point may be determined by expectations which do not necessarily correspond to current endowments. Our results suggest that to the extent endowments affect expectations (as they often do outside the lab), endowments will lead to increased valuation of a good.

31This may also explain the ﬁnding by List (2003) that experienced traders do not seem to display the endowment eﬀect (see DellaVigna 2009 for further discussion).

22 5 Conclusion

The endowment effect is a seminal finding from psychology and economics research and a major source of evidence for the claim that individuals are loss averse. Yet, recent research has explored the limits of the endowment effect and found conditions under which it does not appear. Our results and the K˝oszegi and Rabin (2006) theory suggest that an “endowment effect” of some sort is real, but operates via expectations instead of mere ownership. In two simple experiments, increasing subjects’ expectations of leaving with an item has an effect on exchange behavior (they are more likely to choose to keep the item) and valuation (they demand more compensation to give up the item). We thus provide evidence that individuals’ reference points are determined, at least in part, by expectations. The implications for policy and legal analysis of expectation-based reference points are often similar to those of status-quo-based reference points, since ownership often carries with it the expectation of keeping a good. Yet there may be consequential differences. For instance, loss aversion may not operate in markets where individuals expect to trade, such as markets for tradeable pollution (e.g. carbon) permits. While we show that expectations are an important determinant of reference points, we cannot rule out that other factors, such as social norms, aspirations, salience, and history, may also influence the reference point. Untangling these factors suggests an interesting direction for future research.

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26 Table 1: Determinants of Desire to Exchange Mug for Pen Pr(choose to exchange) (1) (2) (3) (4) Treatment T H .338∗∗ .353∗∗ .402∗∗∗ (.137) (.139) (.154) Female .249∗ .270∗ .291∗ (.141) (.145) (.163) Age .103 (.066) Day indicators No No No Yes # observations 45 45 45 45 Notes: Displayed coefficients are predicted marginal effects from probit regressions (in case of dummy variables, for a discrete change from 0 to 1). Dependent variable: Indicator variable = 1 if subject wants to exchange. Standard errors in parentheses. Level of significance:*p < 0.1, **p < 0.05, ***p < 0.01

Table 2: Determinants of Willingness-to-Accept for the Mug (1) (2) (3) (4) (5) Treatment M H .194 .266∗∗ .306∗∗ .308∗∗ .290∗∗ (.143) (.124) (.128) (.126) (.13) ∗∗∗ ∗∗∗ ∗∗∗ ln(WTApen) .524 .560 .568 (.091) (.093) (.091) Female -.199 -.213∗ -.191 (.131) (.128) (.133) Age -.052∗ -.050∗ -.046∗ (.027) (.026) (.027) Day indicators No No Yes Yes Yes Other controls Cubic in WTApen # observations 106 104 104 104 106

Notes: Dependent variable: ln(WTAmug). (1), (2), (3) and (5) are OLS regressions; (4) displays predicted marginal eﬀects from a Tobit that takes into account censoring at WTAmug = 9.57. All regressions contain a constant, and except for (1) also an indicator for WTApen = 9.57 (which indicates that a subject’s WTA for the pen may be censored; p > 0.3 in all regressions). Regressions with ln(WTApen) as explanatory variable drop two subjects with WTApen=0. Standard errors in parentheses. Level of signiﬁcance:*p < 0.1, **p < 0.05, ***p < 0.01

27 A Theory Appendix

A.1 General Theory

The main objective of KR (2006) is to extend Kahneman and Tversky’s (1979) prospect theory and to bring it closer to “standard” economic theory. In their formulation, the utility of a decision-maker (henceforth DM) depends both on her consumption c and on how this consumption compares to a reference level r. They assume separability between “consumption utility” m(c) and “gain-loss utility” n(c|r). Consumption and reference lev-

els can have multiple dimensions, so that c = (c1, c2, ..., cK ) and r = (r1, r2, ..., rK ), and it is assumed that both forms of utility are additively separable across dimensions, such PK PK that m(c) = k=1 mk(ck) and n(c|r) = k=1 nk(ck|rk). Total reference-dependent utility (henceforth RDU) of an outcome c given reference level r is then given by

K K X X u(c|r) = mk(ck) + µ(mk(ck) − mk(rk)), k=1 k=1 | {z } | {z } cons. utility m(c) gain−loss utility n(c|r)

where µ(·) is continuous and strictly increasing, and has the properties of the Kahneman- Tversky value function: loss aversion (a kink at zero) and diminishing sensitivity. In what follows, we will use the piecewise linear speciﬁcation (as in Section IV of KR, 2006) µ(x) = ηx for x > 0 and µ(x) = ηλx for x ≤ 0, where η > 0 is the DM’s weight on gain-loss utility and λ > 1 her loss aversion coeﬃcient. In KR, the reference point is based on expectations of future outcomes, so that it is in fact a reference lottery given by probability measure G : RK → R over consumption utility in each of the k dimensions. Thus the RDU of outcome c given expectations G is Z U(c|G) = u(c|r)dG(r).

This formulation implies that when evaluating a dimension ck of a consumption outcome c, the DM compares it separately to each possible value that this dimension could take according to the reference lottery, and weights it by the probability of this outcome in the reference lottery. But what exactly determines the reference lottery? KR employ the concept of personal equilibrium (PE), which requires the following:

• the DM has a plan for every contingency that she can possibly face in a given decision situation;

28 • her reference lottery is based on her expectation to put these plans into action once she knows which contingency applies; and

• her actions maximize expected RDU, given her reference lottery.

The timing of a decision situation in which PE applies is as follows:

• t = −1: DM starts focusing on the decision; knows all the possible choice sets she might face at t = 1 and the probabilities with which they occur;

• t = 0: DM makes plans for each possible choice set, thereby setting her reference lottery;

• t = 1: ‘Nature’ determines the choice set the DM actually faces. The DM follows through on her plan for this choice set, which then yields either a deterministic or a probabilistic outcome.

The PE concept requires the DM’s actions at t = 1 to be optimal given her beliefs at t = 0, beliefs formed at t = 0 to be rational given her plans, and her plans to be “credible” in the sense that at t = 1 the DM has no incentive to deviate from them (akin to subgame perfection in standard multi-player game theory). KR emphasize that it is possible for multiple PEs to exist in a given situation. An example: assume the consumption utilities resulting from actions x and y are not too diﬀerent. Then, one equilibrium may be for the DM to plan on x and indeed do x, but another one may be for her to plan on y and do y (because if she planned on y and ended up doing x, she would feel a loss from not getting the consequence of y, which may outweigh a possible consumption utility advantage of x). In such a case KR’s preferred way of equilibrium selection is to take the PE that gives the DM the highest expected RDU, the preferred personal equilibrium (PPE).

A.2 Derivation of KR Portion of Proposition 1

Denote subject i’s consumption utility from the mug by umug and the consumption utility 1 from the pen by upen. The treatment variable is p, the probability with which the subject will be able to exchange the mug (which she is endowed with) against the pen. Each subject will have to indicate whether she wants to exchange the mug for the pen (but her decision

1 Throughout, we assume upen, umug ≥ 0, i.e. that subjects weakly prefer both receiving the mug for sure and receiving the pen for sure to receiving nothing.

29 only applies with probability p; with probability 1 − p, she keeps the mug independently of her decision). We will refer to her two possible actions as “exchange” and “keep.” The subjects know the choice sets that they may face, but are unable to commit to a decision until the end of the session. In terms of the timeline from the previous subsection, the moment when we announce to subjects that they own the mug and may have the possibility to exchange the mug against a pen comprises t = −1. t = 0 is then the time span during which the subjects plan what they are going to do at t = 1, and this plan determines their reference lottery. The moment when they make their decision is t = 1. Note that we elicit a decision from all subjects, independently of whether their decision to exchange or not will in fact matter. In terms of the KR theory, such a situation (occurring at t = 1) is no different from the alternative in which we first roll the die and then only elicit a decision if the appropriate number comes up. At this point, the plan is made, and whether we elicit it as a plan or as an actual choice should not make a difference, given KR’s assumption that preferences depend on lagged expectations.

We now examine how the conditions on umug and upen for a subject to choose “exchange” in a PE or (more restrictively) the PPE vary with our treatment variable p.2

If a subject plans to choose “exchange” if given the choice, then she expects rend w/pen to occur with probability p and and rend w/mug to occur with probability 1 − p. Her utility of outcome c, given her expectations, is then

U (c|“exchange”) = pu c|rend w/pen + (1 − p) u c|rend w/mug .

If she follows through with her plan, her gain-loss utility in the diﬀerent outcome cases is as follows:

• if her decision applies (which happens with probability p): p·0+(1−p)η(upen −λumug)

• if it does not apply (which happens with probability 1−p): pη(umug −λupen)+(1−p)·0

Therefore, her expected utility from sticking to her plan to say “exchange” is given by3

EU(“exchange”|“exchange”) = p [U ({1 pen, 0 mugs} |“exchange”)] + (1 − p)[U ({0 pens, 1 mug} |“exchange”)]

= p[upen + (1 − p)η(upen − λumug)]

+(1 − p)[umug + pη(umug − λupen)]

2We limit our focus to pure-strategy equilibria. 3The notation U(“x”|“y”) means “utility from action x if the reference lottery is (the result of plan) y.”

30 Meanwhile, if having planned to exchange, she deviates and chooses to say “keep” instead,

her gain-loss utility would equal pη(umug − λupen) for sure, and her total expected utility would be equal to

EU(“keep”|“exchange”) = umug + pη(umug − λupen).

Choosing to exchange is then a PE if and only if EU(“exchange”|“exchange”) ≥ EU(“keep”|“exchange”), which boils down to the condition

1 + η(λ + p(1 − λ)) u ≥ u . pen mug 1 + η(1 − p(1 − λ)) | {z } ≡X(p)

As λ > 1 and η > 0 we have that

1 + ηλ 1 1 + η X0(p) < 0,X(0) = > 1,X = 1, and X(1) = < 1. 1 + η 2 1 + ηλ

In words, this means that as the probability p of getting the possibility to exchange the mug for the pen increases, the consumption utility a subject gets from the pen necessary for

“exchange” to be a PE decreases (relative to umug), such that “exchange” is a PE for more

(umug, upen) pairs. 1 If p is high (p > 2 ), “exchange” may be a PE even if upen < umug. However, in such a case, 4 “keep” is a PE as well, and it may indeed be the PPE. We have EU(“keep”|“keep”) = umug (there is no gain-loss utility when the subject is certain to keep the mug). Thus, “exchange” would be the PPE if and only if EU(“exchange”|“exchange”) ≥ EU(“keep”|“keep”), or

p(upen − umug) + η[p(1 − p)(upen − λumug) + (1 − p)p(umug − λupen)] ≥ 0,

which simpliﬁes to

(upen − umug) + η (1 − p) (1 − λ)(upen + umug) ≥ 0.

For p < 1, “exchange” can be the PPE only if the pen gives higher consumption utility

(upen > umug), as the second term is negative due to loss aversion (λ > 1). Crucial for our

hypothesis, note that as p is increased, “exchange” is the PPE for more pairs of upen and

umug (the required consumption utility surplus from the pen becomes smaller), as increasing

4 1+ηλ It is easy to show that “keep” is a PE if upen ≤ 1+η umug, which is always the case if upen < umug and if “exchange” is not a PE.

31 p makes the second term less negative. K˝oszegiand Rabin (2007) introduce an alternative equilibrium concept, the “choice- acclimating personal equilibrium” (CPE), which applies in situations where the DM determines the reference lottery by her actual choice, instead of with her plan. In general, the CPE may yield diﬀerent predictions from the (P)PE concept (which KR 2007 rename “unacclimating personal equilibrium”). However, the CPE applies only in cases in which uncertainty is resolved long after actions are committed to. In both our experiments, subjects cannot commit to their decision before the end of the decision situation, but are given ample time to think about it between the beginning of the experiment and the moment they make their choice, making (P)PE the appropriate concept. Furthermore, in this experiment, CPE would make the exact same prediction as PPE, as the expected utility from

saying “keep” is simply umug, while the expected utility from saying “exchange,” knowing that this will then determine the reference lottery, is the same as given in the expression for EU(“exchange”|“exchange”). Thus, the prediction that a higher p should increase the proportion of subjects that indicate that they would like to exchange is robust to the use of all the diﬀerent equilibrium concepts proposed by KR.

A.3 Derivation of KR Portion of Propositions 2 and 3

In the second experiment, subjects are put in the following situation: at t = −1, they are

told that at t = 1, they will receive a mug with probability pi ∈ {pL, pH }. With probability q, they instead enter a Becker-DeGroot-Marschak (1964) (BDM) mechanism where for different amounts of money between $0 and $10 they have to indicate whether they prefer receiving the mug or the money. With probability 1 − p − q, they do not get the mug or a choice between mug and money. t = 0 is the time span during which subjects plan what to do at t = 1, which determines their reference lottery. A subject’s plan here corresponds to an amount at which the subject is indifferent between ∗ receiving $Wmug and receiving the mug. Then, when entering the BDM mechanism, the ∗ subject (consistent with her plan) chooses the mug for any amount below $Wmug and the money otherwise. Proposition 2 states that for any pair of parameters η > 0 and λ > 1, ∗ there exists a q small enough such that Wmug unambiguously increases in p for both the PE and the PPE equilibrium concepts. We give the proof of the proposition for the continuous BDM case; subjects actually make a discrete decision for different amounts, but this does not affect the results. Assume that a price x is drawn from a uniform distribution over [$0, $10].5 Subjects indicate an indifference

5The statement in Proposition 2 also holds for other distributions, which however make the proof less

32 ∗ ∗ point Wmug, their WTA. (All subjects indicate their Wmug, even though their decision only matters with probability q. As in Experiment 1, eliciting their plan is theoretically equivalent ∗ to eliciting their actual choice if the BDM choice set is reached.) If x < Wmug the subject ∗ keeps the mug and gets no money; if x ≥ Wmug, the subject gets $x but no mug. A PE requires that subjects’ choices must be consistent: a plan will be of the form ∗ ∗ ∗ “choose ‘mug’ if x < Wmug, choose ‘money’ if x ≥ Wmug,” where Wmug is assumed to be in the interior of the interval (0, 10). Call this plan Ω. For plan Ω to be a PE, it must be implementable, and thus the subject must be indiﬀerent between receiving the mug and ∗ receiving $Wmug (because if she were not, she would have an incentive to deviate from her plan). Thus, it must be the case that

∗ U ({1 mug, $0|Ω}) = U 0 mugs, $Wmug|Ω

Under plan Ω, the possible outcomes are:

q ∗ •{ 1 mug, $0} with probability p + 10 Wmug

•{ 0 mug, $0} with probability 1 − p − q

∗ q ∗ •{ 0 mug, $x} for x ∈ Wmug, 10 with probability 10 10 − Wmug

Getting a mug involves a gain of a mug relative to getting nothing and a loss relative to ∗ ∗ ∗ getting $x ≥ Wmug. Similarly, getting $Wmug involves a loss of a mug and gain of $Wmug ∗ ∗ relative to getting a mug, a gain of $Wmug relative to getting nothing, and a loss of x−Wmug ∗ relative to getting $x > Wmug. Continue to denote subject i’s consumption utility from the

mug by umug, and let utility of money be linear with scale normalized to one. Using the piecewise linear gain loss function described above, we have " # q Z 10 U ({1 mug, $0|Ω}) = umug + η (1 − p − q)(umug) + (umug − λx) dx 10 ∗ Wmug " # (1 − p − q) W ∗ + p + q W ∗ W ∗ − λu ∗ ∗ mug 10 mug mug mug U 0 mugs, $Wmug|Ω = Wmug + η q R 10 ∗ − λ ∗ x − W dx 10 Wmug mug

∗ where the integrals are the loss from not getting x > Wmug. The indiﬀerence condition at ∗ Wmug is then satisﬁed if the two expressions are equal. ∗ 1+η(1+(λ−1)p) Consider the case when q = 0. Then, there is a unique PE Wmug = umug 1+η , which is therefore the PPE. This is the unique solution and it does not depend on the

tractable.

33 subject’s planned action.6 When q > 0, it is possible that multiple PE exist. Rearranging the indiﬀerence condition ∗ gives a quadratic equation for Wmug : q h h u ii W ∗ 2 η (λ − 1)−W ∗ 1 + η 1 + (λ − 1) q 1 − mug +u [1 + η (1 + (λ − 1) p)] = 0 mug 10 mug 10 mug

Write this as AW 2+BW +C = 0. Hence, there are at most two roots of this equation, and only two possible values of W consistent with a PE. Call these values W + and W −. We restrict attention to the lower root W −, as W + gives the perverse case in which WTA for the mug + decreases in the consumption utility of the mug ( dW /dumug < 0). Moreover, a sufficient + + 1+η umug condition for W to be a non-interior root (W > 10) is η(λ−1) > q 1 + 10 , which is satisfied whenever q is low enough. Now, assume the lower root W − is real, so that we have an interior solution. Then, simple algebra shows that dW − > 0, as dW − = umug[η(1+(λ−1))] > 0. dp dp (B2−4AC)1/22A For Proposition 3, consider the surprise WTA elicitation for the pen, the results of which will be implemented with probability q, replacing part of the probability space in which the subject expected to get nothing. Since it is a surprise, subjects give their indifference ∗ point Wpen while reference points stay fixed (because they are assumed to be given by lagged expectations). In this case, reference points are the same as the mug case derived above. ∗ Then, for the indifference condition to hold at Wpen, we must have U ({1 pen, $0|Ω}) = ∗ U 0 pens, $Wpen|Ω . We have

" Z 10 # q ∗ q U ({1 pen, $0|Ω}) = upen+η upen + p + Wmug (−λumug) + (upen − λx) dx 10 10 ∗ Wmug

( )! " # 0 pens, $W ∗ 1 − q + q W ∗ W ∗ U pen = W ∗ + η 10 mug pen ∗ ∗ pen q ∗ q R 10 ∗ |Ω,W > W − p + W λumug + λ ∗ W − x dx mug pen 10 mug 10 Wmug pen   1 − q + q W ∗ W ∗ ( ∗ )! 10 mug pen 0 pens, $Wpen ∗  q ∗  U = Wpen + η  − p + 10 Wmug λumug  ∗ ∗ ∗ |Ω,Wmug < Wpen  q R Wpen ∗ q R 10 ∗  + ∗ W − x dx − λ ∗ x − W dx 10 Wmug pen 10 Wpen pen

∗ ∗ Take Wmug > Wpen. Then at the indiﬀerence condition we have, after simpliﬁcation: h q i (1 + η) u = W ∗ + η 1 + (λ − 1) q + (1 − λ) W ∗ W ∗ pen pen 10 mug pen

6 ∗ Hence, Wmug would also be a CPE: a CPE must maximize expected utility given that the plan determines the reference-point. But when q = 0, the reference point is not aﬀected by plans.

34 which does not depend directly on p. Applying the implicit function theorem gives

∗ q ∗ ∗ dWpen h h q ∗ ii ηWmugWpen (λ − 1) = ∗ · 1 + η 1 + (λ − 1) q − Wmug (λ − 1) 10 dWmug 10

∗ dWpen ∗ which yields ∗ > 0 since W < 10. dWmug mug ∗ ∗ Similarly, for the case in which Wmug < Wpen, simplifying the indiﬀerence condition and using the implicit function theorem gives

∗ h q ∗ i dWpen h h q ∗ ii η (λ − 1) Wmug = ∗ · 1 + η (1 + (λ − 1) q) − Wpen (λ − 1) 10 dWmug 10

∗ dWpen ∗ which again gives ∗ > 0 since W < 10. dWmug mug

B Empirical Appendix

B.1 Experiment 1

Table A.1 summarizes the questionnaire responses from subjects in our exchange experiment. Questions 1 to 4 were asked after the subjects made their conditional choice as to whether to exchange or not, but before they knew whether their choice would apply or not. Question 5 was asked as part of the debrieﬁng questionnaire at the end of the study.

B.2 Experiment 2

Table A.2 contains multiple robustness checks of the results discussed in Section 3.3. Regres-

sions (1) to (3) use ln(WTAmug) as the dependent variable, as in the analysis in the main

text, while regressions (4) to (9) instead use WTAmug in levels. H In regression (1), we add an interaction term Mi · ln(WTAmug,i) to our main regression to allow for the possibility that the relation between ln(WTAmug) and ln(WTApen) to differ across treatments. This coefficient on this interaction term is negative but not significant. Regression (2) uses session dummies instead of date dummies as in the main text, which increases the estimate of the treatment effect somewhat. Column (3) shows the results from an interval regression that explicitly allows for the fact that we only know bounds on subjects’ WTA.7 The treatment effect remains significant at p < 0.05, with a nearly unchanged point estimate compared to the analysis in the text.

7The diﬀerent intervals in which subjects’ WTA can lie are: $0 (assuming nobody would be willing to pay to not have to take an item); [$0, $0.33]; [$0.33, $0.66]; . . . [$9.24, $9.57]; [$9.57, ∞).

35 Table A.1: Subject Evaluations of the Mugs and Pens in Experiment 1 Treatment Question LH p-value 1) “I like the mug better than the pen.” 3.95 3.26 .081 (1.17) (1.25) 2) “Since the beginning of the session, I have spent 2.95 3.35 .387 some time thinking about how I would use the pen.” (1.46) (1.23) 3) “Since the beginning of the session, I have spent 4.09 4.00 .878 some time thinking about how I would use the mug.” (0.87) (1.09) 4) “Since the beginning of the session, I have spent 3.95 3.17 .061 more time thinking about the mug than about the pen.” (1.13) (1.40) 5) “Which item do you think has higher retail value?” 3.50 3.26 .547 (1.14) (1.01)

Notes: Questions 1) to 4) were asked after subjects made their decision as to whether they would like to trade, and are answered on a scale from 1 (strongly disagree) to 5 (strongly agree). Question 5) was asked as part of the debriefing questionnaire, and is answered on the following scale (with the corresponding number in brackets): “Definitely Pen” (1), “Probably Pen” (2), “About the same” (3), “Probably Mug” (4), “Definitely Mug” (5). Standard deviations in parentheses. p-values are from a two-sided nonparametric Fisher-Pitman test.

Regression (4) shows that simply comparing WTAmug across treatments does not yield

a significant treatment effect. However, once WTApen is added as a regressor, the estimated treatment effect increases in magnitude, as in the log case, and is significant at p < 0.1 (column (5)). Column (6) adds demographic controls, while column (7) displays the marginal

eﬀects from a Tobit regression that takes into account censoring at WTAmug = 0 and

WTAmug = 9.57. Columns (8) and (9) display results from interval regressions, and show that once demographic characteristics are added as regressors, the treatment effect is significant at p < 0.05. Overall, we conclude that the results from estimating our main equation (in logs) are robust to a variety of different regression specifications.

36 Table A.2: Determinants of Willingness-to-Accept for the Mug: Robustness

Dependent variable: ln(WTAmug) Dependent variable: WTAmug (1) (2) (3) (4) (5) (6) (7) (8) (9) Treatment M H .559∗∗ .37∗∗∗ .297∗∗ .596 .765∗ .81∗ .777∗ .774∗ .814∗∗ (.228) (.134) (.13) (.496) (.426) (.419) (.448) (.425) (.413) ∗∗∗ ∗∗∗ ∗∗∗ ln(WTApen) .616 .438 .531 (.115) (.095) (.093) H Tr. M × ln(WTApen) -.252 (.179) ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ WTApen .536 .577 .571 .547 .587 37 (.099) (.098) (.104) (.098) (.096) Female -.759∗ -.796∗ (.432) (.426) Age -.16∗ -.156∗ (.087) (.086)

#observations 104 104 104 112 112 112 112 112 112 Notes: All regressions other than (2) (which uses session indicators) also contain indicators for the different days on which sessions were run (none of which ever reach a significance level p < 0.2) and an indicator for WTApen = 9.57 (which indicates that a subject’s WTA for the pen may be censored; p > 0.3 in all regressions). Standard errors in parentheses. Level of significance:*p < 0.1, **p < 0.05, ***p < 0.01