Lagged Beliefs and Reference-Dependent Utility Alec Smith∗ October 6, 2008
∗
Department of Economics,
University of Arizona,
Tucson,
AZ 85721-0108,
USA. e-mail:
[email protected]. I am grateful to Martin Dufwenberg for advice and guidance. I also thank Joseph Cullen, Erik Eyster, Glenn Harrison, Kate Johnson, Botond K˝oszegi, Erkut Ozbay, and attendees of the 2007 Mannheim Empirical Research Summer School and the 2007 North American Meetings of the Economic Science Association for helpful comments and suggestions. Financial support from the Economic Science Laboratory and the Institute for Behavioral Economics at the University of Arizona is much appreciated.
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Abstract The K˝oszegi-Rabin model of reference-dependent preferences proposes that the reference point to which consumption outcomes are compared is endogenously determined as a function of lagged, probabilistic beliefs. This paper presents an experiment designed to test some predictions of the K˝oszegi-Rabin model. The design controls for potential confounds suggested by their theory. The experimental results support their prediction of an endowment effect but do not show the attachment effect predicted by their model.
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Introduction
Prospect theory (Kahneman and Tversky, 1979) and related models of reference-dependent preferences assume that utility is derived from the comparison of consumption outcomes to some reference point. The models also incorporate loss aversion: in the evaluation of consumption outcomes, losses are given greater weight than gains. A common objection to reference-dependent preference models is that the reference point is a “free parameter” (Pesendorfer, 2006) to be determined subjectively by the researcher. In two recent papers K˝oszegi and Rabin (2006; 2007), (henceforth KR) address this concern. They propose a model of reference-dependent preferences in which a decision-maker (DM) derives utility from the comparison of consumption outcomes with his recent probabilistic beliefs about outcomes. KR suggest that these lagged beliefs about consumption are the reference point. In their solution concept the reference point is endogenously determined as a function of the DM’s beliefs regarding the choice set he will face and his planned action for each possible choice set. In their 2006 paper KR apply their model to two decision problems: intertemporal supply of labor and consumption. In the application to labor supply (“Taxi Driving”) their model is broadly consistent with the target income hypothesis studied by Camerer, Babcock,
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Loewenstein, and Thaler (1997) and Goette, Huffman, and Fehr (2004).1 In the application to consumer behavior (“Shopping”) KR make two new predictions about behavior. The attachment effect predicts that a DM’s valuation for a commodity will be will be an increasing function of the lagged probability of possessing it. The comparison effect predicts that a DM’s valuation for a commodity will be (stochastically) increasing in the price the DM expected to pay for the commodity. In addition to these conjectures, KR also predict an endowment effect. The endowment effect predicts that owners of a commodity will value it more highly than prospective buyers.2 The experiment described in this paper tests for an attachment effect after endowing subjects with a binary lottery over a commodity prize. The experiment has two stages. The first stage is the lottery which is intended to induce a reference point. The second stage elicits values. The treatment variable is the probability of winning the prize (High (H) or Low (L)) in the first-stage lottery. Immediately after resolution of the lottery, prizes are awarded and subjects are “surprised” with a Becker-Degroot-Marschak (BDM) mechanism (Becker, deGroot, and Marschak, 1964) to elicit their valuations for the commodity. Prize winners are given a seller version of the BDM mechanism while those who don’t win are given a buyer version. KR’s model predicts an attachment effect: assignment to treatment H is predicted to increase valuations. Because Willingness-to-Accept (WTA) is elicited from prize-winners while Willingness-to-Pay (WTP) is elicited from non-winners, KR’s model also predicts an endowment effect: in each treatment WTA is predicted to exceed WTP. By randomly assigning subjects to treatment, varying between treatments the probability of winning the 1
The target income hypothesis states that workers set a short-term income target which serves as the reference point. The resulting prediction is that workers supply more labor when wages are low and less when high, in contrast to classical predictions that workers should supply more labor when wages are high. KR’s model makes similar predictions to classical models of intertemporal labor supply when the wage is as expected, but when the wage is a surprise, KR’s prediction follows the target income hypothesis. 2 The term “endowment effect” is due to Thaler (1980); see also Tversky and Kahneman (1991) for a model of loss aversion in riskless choice. The endowment effect contradicts classical predictions that the difference between willingness-to-pay (WTP) and willingness-to-accept (WTA) should be negligible if income effects are small or the commodity has many substitutes (Willig, 1976; Hanemann, 1991).
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prize in the binary lottery, and eliciting valuation for the commodity immediately after the binary lottery is resolved, the experimental design attempts to exogenously induce a reference point and to control for endogenous reference point formation. If the reference point is lagged beliefs, as KR suggest, then the attachment effect suggests that DM’s valuation for the commodity will depend on the probability of winning in the first stage. The rest of the paper is organized as follows: Section 2 presents KR’s general model and the application to consumer behavior. Section 3 describes the experimental design and hypotheses. Section 4 presents the experimental results, and Section 5 offers concluding remarks. The instructions and forms used in the experiment are in the appendix.
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Theoretical Background
Kahneman and Tversky (1979; 1991) model decision-making with a value function which has the following properties: 1) Reference Dependence: the arguments of the value function are gains and losses relative to some reference point; 2) Loss Aversion: losses weigh more heavily than same-sized gains; and 3) Diminishing Sensitivity: the marginal contribution of gains and losses to the value function diminishes with distance from the reference point. A typical value function is shown in Figure 1. KR modify and extend prospect theory in several ways. In their model DM’s derive utility from consumption as well as from gains and losses. KR define their utility function over deterministic outcomes and reference points, and then allow for both stochastic consumption and stochastic reference points. KR propose that lagged beliefs about consumption are the reference point, and provide a model of reference point determination, personal equilibrium, in which the reference point is determined from the DM’s beliefs about the choice sets he will face and the choices he will make from each set in the support of his beliefs. Finally, KR assume that DM’s evaluate risky options according to their expected utility, in contrast with prospect theory where DM’s are assumed to transform probabilities with a nonlinear
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Figure 1: Kahneman and Tversky’s value function
weighting function. In applications of prospect theory, the reference point is frequently assumed to be the status quo. KR’s specification of the reference point as recent beliefs about outcomes makes it possible to apply their model to situations where DM’s beliefs about the future differ from the status quo. For example, suppose a decision-maker (call her Ann) expects to receive a TV (with some probability) for her birthday. Ann’s belief about the event that she receives a TV is incorporated into her reference point. If Ann doesn’t receive the TV then KR predict that Ann’s willingness to pay for the TV will increase in the probability she assigned to receiving the TV, so long as Ann’s reference point does not change. The intuition is that the greater the probability Ann assigned to receiving the TV, the greater the “sense of loss” she experiences when she doesn’t receive it. Then loss aversion (in the TV dimension of consumption) leads her to pay more when given the opportunity to buy the TV than she would have if she had not expected to receive the TV at all.
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2.1
KR’s model
In this section I provide a brief overview of K˝oszegi and Rabin (2006); for details see their paper. Formally, given a consumption level c ∈ Rn and a reference level r ∈ Rn , KR’s utility function u : Rn × Rn → R is defined as
u(c|r) =
n X
mk (ck ) +
k=1
Consumption utility is m(c) =
P
k
n X
µ(mk (ck ) − mk (rk ))
k=1
mk (ck ), where for each k ∈ {1, . . . , n}, mk (·) is a strictly
increasing and differentiable function. Gain-loss utility in each consumption dimension is µ(mk (ck ) − mk (rk )), where µ(·) has the properties of Kahneman and Tversky’s (1979) value function. KR allow r to be determined by the probability measure G over Rn . This formulation allows them to link the reference point with beliefs. Given G, the utility from some deterministic consumption level c is calculated by comparing the consumption utility from c to the DM’s beliefs about consumption and computing Z U (c|G) =
u(c|G)dG(r)
If the consumption level is given by the probability measure F over Rn , then utility is Z Z U (F |G) =
u(c|r)dG(r)dF (c)
In addition to specifying a utility function which allows for both the objects of choice and the reference point to be stochastic, KR propose a model of reference point determination, personal equilibrium (PE). In a PE, the DM has exogenously given beliefs about the possible choice sets he will face. For example, he might have beliefs about his future income or about the prices he might face. The reference point is determined endogenously as a result of the DM’s planned choices 6
for each possible choice set. A PE is a form of rational expectations in which the DM both correctly predicts his choice sets and his behavior when facing those choice sets, and does not want to deviate from his plan when actually faced with any given choice set. Although KR’s model does not explicitly specify the timing aspects of their model, they do often state that the appropriate reference point is “recent expectations” and that the specification of beliefs about choice sets should correspond to “expectations formed after the decision-maker started focusing on the decision.” KR equate surprise with “out-of-equilibrium” decision-making. In their model surprise occurs when a DM is faced with a choice set to which he assigns negligible probability. For example, suppose there are two choice sets D1 and D2 . The DM believes he will face D1 with probability α ∈ [0, 1] and D2 with probability (1 − α). Given these beliefs suppose his PE plan is to choose F1 from D1 and F2 from D2 . As α approaches 0, then the DM’s planned behavior when facing D1 has little influence on his reference point. If in fact he does face D1 then the DM will still behave as if his reference point is the outcome F2 ∈ D2 . KR’s decision-maker evaluates his expected utility correctly, but with a reference point determined by lagged beliefs. A key premise of KR’s model is that reference point updating is “slower” than belief updating, and so preferences change more slowly than beliefs.
2.2
Consumer Behavior
Consider a DM who derives utility from a consumption bundle (c1 , c2 ) ∈ R2 , with c1 representing ownership of a commodity and c2 is the DM’s dollar wealth. The DM’s endowment is (0, w). The DM has K˝oszegi-Rabin utility with m1 (1) − m1 (0) = v and m2 (c2 ) = c2 ), so consumption utility is linear in wealth. Assume the gain-loss function is piecewise linear, so that µ(x) =
ηx
if x > 0,
ηλx if x ≤ 0
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Here η > 0 is the weight the DM attaches to gain-loss utility, and λ > 1 measures the DM’s loss-aversion. The DM’s problem is to determine the prices at which he would be willing to buy or sell one unit of the commodity. Assume the DM evaluates his gain-loss utility with respect to the reference point L, a binary lottery in which the decision-maker receives one unit of the commodity with probability q, and receives nothing with probability 1 − q. This reference point can be interpreted as exogenously given or alternatively one can consider the personal equilibrium in which the DM expects to face the lottery L with probability (1 − α) and some other choice set D with probability α. Letting α approach 0, the contribution of outcomes from D to gain-loss utility will be minimal, and so for very small α the DM will evaluate choices from D as if L is the reference point. The DM will compare the utility from buying at some price p with L as the reference point, to the utility from not buying again with L as the reference point. The DM’s maximum willingness to pay (WTP) will be the price at which he is indifferent between buying and not buying: U (not buy at p|L) = U (buy at p|L) that is, if
m1 (0) + w + qηλ(−v) = m1 (1) + (w − p) + (1 − q)ηv + ηλ(−p) p =
1 + η + qη(λ − 1) v = WTP 1 + ηλ
(1)
Alternatively, leaving the reference point fixed at L, the, DM’s minimum willingnessto-accept (WTA) will be the price at which he is indifferent between selling the item and keeping it: U (sell at p|L) = U (keep|L)
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m1 (0) + (w + p) − qηλv + ηp = m1 (1) + w + (1 − q)ηv p(1 + η) = v + (1 − q)ηv + qηλv p =
1 + η + qη(λ − 1) v = WTA 1+η
(2)
The right-hand side of Equations 1 and 2 is increasing in q, the probability of receiving the commodity for free. As q increases, so does the DM’s valuation (WTP or WTA) for the item. This is KR’s attachment effect. The numerator in the expressions for WTP and WTA is the same, but the denominator is larger for WTP. This difference between WTP from Equation 1 and WTA from Equation 2 results from the fact that the price paid p by the buyer is evaluated as a loss for the buyer but as a gain for the seller. This result leads to an endowment effect: seller’s valuation is predicted to be greater than buyers. In this case the result is derived from loss aversion over wealth.
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Experimental Design and Hypotheses
Given the specification of the reference point as lagged beliefs, an experimental design studying how behavior varies with a belief-dependent reference point might either elicit beliefs (e.g. with a scoring method) or induce beliefs by endowing subjects with a lottery (Hurley and Shogren, 2005). Because scoring might influence subject’s reference point, the design employed belief induction. Stage 1 of the design was a binary lottery intended to induce a reference point in subjects. In Stage 2, subjects participated in a value-elicitation procedure in order to measure the effect of varying the Stage 1 lottery. After taking their seats subjects were given a packet of instructions (see the Appendix) and a bag containing 10 marbles, some of which were blue and some of which were white; an example is shown in Figure 2. The instructions stated that the experiment would have two parts, and that the first part was a drawing for a prize. Participants were asked to count the
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number of marbles of each color, and were informed that if they drew a blue marble, they would win the prize. Before the drawing subjects were given an opportunity to examine the prize. The treatment variable in the experiment was the probability of winning the water bottle in the Stage 1 - specifically the number of blue marbles and white marbles assigned to each subject. In Treatment L, subjects were assigned 1 blue marble and 9 white marbles. In treatment H, subjects were assigned 7 blue marbles and 3 white marbles.
Figure 2: Sample packet of marbles provided to subject.“51” was a subject identification number.
The prize was a 32-ounce polycarbonate water bottle, manufactured by NALGENE Outdoor; an example is shown in Figure 3. The bottle had the University of Arizona logo on it and was virtually identical to bottles which retail in the university bookstore for $13.95 plus tax3 Subjects were not told the retail price, though several subjects did ask about it. The particular prize was chosen because students on campus are frequently seen carrying similar products and it seemed likely that most subjects would be willing to pay some positive amount for the bottle. After the subjects had an opportunity to examine the marbles and the water bottle, the experimenters walked around the room with a small bag. Participants were asked to put the marbles they had been assigned in the bag and to then draw a marble. The bag was made 3
The bottles were custom ordered and had a slightly different logo design than those sold in the bookstore.
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Figure 3: A sample of the water bottle used as a prize.
of dark cloth and was small enough so that subjects could not see into it when they reached in to draw a marble. After each subject drew marbles, the container was emptied and the next subject was asked to repeat the procedure, until all the subjects drew marbles. After all subjects had a chance to draw, prizes (the water bottles) were given to subjects who had drawn a blue marble, and subjects were asked to wait for the next part of the experiment. After the prizes were awarded, instructions for Stage 2 were handed out. In Stage 2 the Becker, deGroot, and Marschak (1964) mechanism was implemented to elicit subject’s values for the water bottle. The instructions were titled either ‘Seller Information Sheet’ and ‘Buyer Information Sheet’ depending on the results of the Stage 1 drawing. See the Appendix for copies of the instructions. After the instructions were handed out subjects were shown ping-pong balls with prices ranging from $0.00 to $21.00, in increments of $0.30. The balls were then placed in a bingo cage while subjects filled out their record sheets. Participants were asked to check all prices up to their maximum buying price, for buyers, and all prices above their minimum selling price, for sellers. It was clearly stated that “if you have indicated that you will buy (sell) at the price that is drawn from the bingo cage, then you buy (sell) at that price.” Next, the various seller and buyer information sheets were collected. Then a ball was
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drawn from the cage in full view of the subjects and the resulting price was written on the whiteboard at the front of the lab. Afterwards subjects were called individually, by subject identification number, to another room in the laboratory to privately settle trades and conclude the experiment. Table 1 describes the treatment assignment process in the experiment. The experiment was designed such that there are four data points: Measures of willingness-to-pay for each treatment (WTP-L and WTP-H) and measures of willingness-to-accept for each treatment (WTA-L and WTA-H. Participants were randomly assigned to treatments via independent draws of a Bernoulli random variable with the propensity of assignment to treatment H equal to 0.75. Because the probability of obtaining the prize is 0.1 in treatment L and 0.7 in treatment H, treatments were approximately balanced in terms of observations on WTP and WTA (since P (Treatment L) × P (not win|L) = .25 × .9 = .75 × .3 = P (Treatment H) × (P (not win|H). So there are many more observations of WTA-H than of WTA-L. WTP was selected for balancing because it matches the “Shopping” example in K˝oszegi and Rabin (2006).
Treatment H L
P(win) 0.7 0.1
Table 1: Treatment Assignment Propensity P(win) × Propensity (1-P(Win))× Propensity 0.75 0.525 0.225 0.25 0.025 0.225
The first hypothesis about the experimental results from the attachment effect: Hypothesis 1. Attachment Effect. 1a WTP-H > WTP-L Willingness-to-pay among buyers will be higher in Treatment H than in Treatment L. 1b WTA-H > WTA-L Willingness-to-accept among sellers will be higher in Treatment H than in Treatment L. 12
The intuition for both hypotheses 1a and 1b is that if subject’s reference point is the first stage lottery - or simply is influenced by the first stage lottery - then subjects evaluate gains and losses relative to that reference point. The calculations in Section 2.2 show that the loss experienced from not winning the item is increasing in the probability of winning. The incentive to avoid these losses results in a higher predicted WTP (WTA) for the object in Treatment H than in Treatment L. KR also predict an endowment effect. The endowment effect results from loss-aversion: DMs are biased towards the status quo because losses count more than gains in evaluating potential actions. For those who did not win the prize, buying is always a loss in the money dimension, while for those who did win selling is always a gain. Because of loss aversion, gains count less than losses, and sellers require a higher price to compensate them for the loss of the item than buyers are willing to pay to obtain the item. Hypothesis 2. Endowment Effect. 2a WTP-H < WTA-H Buyers’ willingness-to-pay in Treatment H will be less than seller’s willingness-toaccept. 2b WTP-L < WTA-L Buyers’ willingness-to-pay in Treatment H will be less than seller’s willingness-toaccept. To control as much as possible for endogenous reference point formation, no details about the Stage 2 task were provided in advance, so that subjects were “surprised” by the BDM mechanism in Stage 2. After the marble drawing, while prizes were awarded subjects were simply asked to wait for the second part of the experiment. If subjects had been told in advance that they would be given the opportunity to buy or sell, then their reference point might include that information, diminishing the effect of the Stage 1 lottery on elicited values. 13
Plott and Zeiler (2005) show that subject misunderstanding of the BDM mechanism may distort reported values. However, the principal measure of interest in this experiment were the differences between WTP (WTA) in Treatments L and H. Presumably any distortion would be the same for buyers and sellers in each treatment, since treatment assignment was random. Thus the main issue with using the BDM mechanism in the design is that variation in elicited values resulting from subject misunderstanding might obscure the attachment effect. Other than the BDM mechanism, two commonly used incentive compatible value elicitation mechanisms are the English (ascending) auction or the Vickrey (second-price) auction. The English auction was ruled out because of its dynamic structure. Several researchers have suggested that real-time learning occurs in that mechanism (e.g. Rutstr¨om, 1998). Learning has the potential to alter the reference point, and because the goal of the experiment was to study the effect of induced, lagged beliefs on valuation, the English auction was ruled out for use in this design. In Vickrey auctions, some researchers have suggested that anticipated valuations of others might influence bids (Knetsch, Tang, and Thaler, 2001). So, because this experiment employed a “one-shot” design, and to encourage subjects to focus on their own valuations, the BDM mechanism was used. Because surprise was an important feature of the design, care was taken to avoid deception in the experiment. The scenario in this experiment is a little bit different from KR’s model in that the lottery which induces the reference point is resolved before valuations are elicited, unlike in KR where surprise results when a DM expects one choice set and faces another. While implementing the BDM mechanism immediately after endowing subjects with the lottery (and not drawing marbles) would more closely resemble KR’s model, such a design would clearly involve deception, the use of which is prohibited at the Economic Science Laboratory. The important issue is that KR specify the reference point as lagged beliefs. Given this specification, the hypothesis that the first stage lottery should affect values elicited in the BDM mechanism seems like a reasonable interpretation of their model, even if the
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first stage lottery is somehow mixed with other beliefs.
4
Results
6 experiment sessions were conducted June 7-15, 2007. All sessions took place at the Economic Science Laboratory (ESL) at the University of Arizona. Subjects were given a showup fee of $10 upon arrival.4 After the subjects arrived they were seated in the lab. Participants were undergraduates who had signed up to be recruited by the ESL’s email-based recruiting software. The maximum number of subjects per session was 14, and the minimum was 6. The experimental data is contained in Table 2. The mean of WTP-L was 4.12 and the mean of WTP-H was 4.22. The mean WTA-L was 6.8, and mean WTA-H was 7.30. Figures 4(a) and 4(b) show the histograms of WTP and WTA for each treatment. Table 2: Individual Data and Summary Statistics Session Treatment L Treatment H WTP-L WTA-L WTP-H WTA-H 0.9, 1.5, 1.8, 1.8, 0.3, 8.1, 9.0, 12.0 1 3.0, 3.0, 4.5, 9.0 7.5, 9.0 10.2 1.5, 6.3 1.2, 5.1, 5.1, 5.1, 2 7.2, 10.2, 12.0, 12.0 3.0 0.9, 0.9, 1.5, 1.8, 15 1.2, 3.0, 3.0, 5.1, 3 7.5, 10.8, 11.1, 15.0 7.2 1.5, 1.8, 2.1, 3.9 3.0, 4.2, 5.1, 5.1, 4 6.0, 12.0 5 3.0, 3.9, 7.5 3.0, 9.0, 9.9 9.0, 10.2, 10.2 6 2.4 3.0 3.0, 5.1, 10.2, 13.8 Mean 4.12 6.80 4.22 7.30 Std. Dev. 2.76 3.62 4.28 3.95 n 15 3 14 33 The results do not support the hypothesis of an attachment effect. A Mann-Whitney/Wilcoxon test for equality of distributions of WTP-L and WTP-H fails to reject the null hypothesis that the distributions are equal (p-value .43). A Mann-Whitney/Wilcoxon test for equality 4
In Sessions 5 and 6 Subjects were given the showup fee after the marble drawing. This had a small effect which is discussed below.
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of distributions of WTA-L and WTA-H fails to reject the null hypothesis that the distributions are equal (p-value .77). While the comparison of WTA-L and WTA-H suffers from the low number of observations of WTA-L, taken together the results suggest that the first stage lottery does not have an effect on behavior in the BDM mechanism. The data do support the hypothesis of an endowment effect. A Mann-Whitney/Wilcoxon rank sum test for equality of distributions of WTP-H and WTA-H rejects the hypothesis that the two distributions are equal (p = 0.02). A Mann-Whitney/Wilcoxon test for equality of distributions fails to reject the hypothesis that WTP-L and WTA-L are equal (p = .21). However, the number of observations (3) for WTA-L is low as a result of the unbalance design of the experiment. After aggregating by treatments, a Mann-Whitney/Wilcoxon test for equality of distributions of WTP and WTA rejects the hypothesis that the two distributions are equal (p = .001). In Session 5, the showup payment was inadvertently made after the marble drawing. This appeared to raise subject valuations, and the procedure was repeated in session 6 to investigate the effect further. Delaying payment led to an increase in WTP, which is statistically significant (p = .056) using a Mann-Whitney test which compares WTP in Sessions 5-6 with WTP in Sessions 1-4, after aggregating across treatments. Including Sessions 5 and 6 in the data analysis does not affect the conclusion that the data support an endowment effect but not an attachment effect. Showup fees are standard at the Economic Science Laboratory and most other experimental economics labs. The reason for paying the showup fee immediately upon arrival in the laboratory was to control as much as possible for subject beliefs about their payoff from the experiment. That the delayed showup fee affects WTP is potentially consistent with KR’s model when subject’s beliefs about the showup fee are included in the model. Further investigation of the effect of changing beliefs about showup payments is deferred to future research.
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(a) Willingness-to-pay by treatment
(b) Willingness-to-accept by treatment
Figure 4: Histogram of results
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Concluding Remarks
It is not surprising that an endowment effect was observed in the experiment. Such an effect is predicted by KR’s model and by many other reference dependent models. The endowment effect would be expected if the stage 1 lottery was eliminated from the design. Why then, was no attachment effect observed in the experimental data? One explanation which is consistent with KR’s model is that DMs may require more time to incorporate a lottery into their reference point than was provided in the experiment. Strahilevitz and Loewenstein (1998) varied the time of endowment with various (deterministic) prizes and showed that increased time of ownership led to a larger endowment effect. It is possible that the attachment effect works in a similar way. Alternatively, it may be that DMs update their reference points quickly, and that as soon as subjects in the experiment were awarded prizes, they updated their reference points to reflect their current endowments. For deterministic events, it is well known that DMs do update their reference points almost immediately. Kahneman, Knetsch, and Thaler (1990) refer to the “instant endowment effect” where endowment with an item immediately changes the reference point. Instant reference point updating together with the endowment effect is consistent with status quo bias models such as Masatlioglu and Ok (2005). Novemsky and Kahneman (2005) point out that the important contribution of KR is that intentions matter in the determination of the reference point. For intentions to matter, a DM must make plans which are contingent upon the choice sets in the support of his beliefs. In both the example given at the beginning of section 2, and in the experimental design, the reference point is purely dependent on beliefs about outcomes. In neither case is there an opportunity for intentions to influence the reference point (except possibly to show up at the experiment). It may be that when the reference point is the endogenously determined distribution of consumption outcomes resulting from the DM’s beliefs about possible choice sets and his plan for each set in the support of his beliefs, rather than an exogenously given lottery as in this experiment, that lagged beliefs affect behavior. 18
The question raised by the experiment is: how rapidly and under what circumstances is new information is incorporated into the reference point? The results suggest that reference point updating is fast enough to obscure any influence of lagged beliefs when uncertainty is resolved and when DM’s have limited ability to make choices which influence the reference point. Future experimental study might involve allowing for choices to influence the reference point, for example by allowing subjects to choose from a menu of lotteries over various consumption items and then eliciting values. Another design might vary the time with which subjects are endowed with the lottery. Further work is necessary to better understand the mechanisms which lead to reference-dependent behavior. In summary, KR propose a model of endogenous reference point determination in which the reference point is lagged beliefs about consumption outcomes. This paper described an experiment which studied whether lagged beliefs influence valuation for a simple commodity in a manner consistent with the “shopping” model of K˝oszegi and Rabin (2006). While KR predict an endowment effect and this prediction is supported by the experimental data, the main result of the experiment is a failure to support the hypothesis that subject behavior will exhibit an attachment effect.
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