Sunk Decision Points: A Unified Theory of the Endowment

Effect and Present Bias∗

Peter Landry†

February 8, 2014

Abstract

This paper presents a utility-based model in which situational cues compel an

agent to consider the associated consumption decision. The premise gives rise to a

unified account of the endowment effect and present bias that, unlike prevailing

behavioral theories of inconsistent preferences, captures both ‘anomalies’ (and

without extra parameters). Among other features, the model captures evidence

that the endowment effect and present bias are often inactive (and that cues,

such as exposure to the good, can activate them), as well as key properties of

prospective memory — e.g. the effect of mere reminders and value in forgetting in

that successful recall carries an opportunity cost. Stemming from the hypothesis

that the anomalies are linked, the model offers testable new predictions, including

a form of crowding out between the endowment effect and present bias. A method

to deactivate both anomalies is also proposed, the viability of which fits with

related evidence.

∗I thank Attila Ambrus, Peter Arcidiacono, Mike Dalton, Rachel Kranton, and PhilippSadowski for helpful feedback.†Division of the Humanities and Social Sciences, California Institute of Technology, MC

228-77, 1200 E. California Blvd, Pasadena, CA 91125. E-mail: plandry@caltech.edu.

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1 Introduction

The standard economic model of decision-making is built on the premise that

preferences are consistent, yet behavioral researchers — drawing heavily on ex-

perimental evidence — have highlighted compelling challenges to this assump-

tion. One of the most well-known such “behavioral anomalies” is the endowment

effect, i.e. the tendency of those who receive a good to value it more than they

otherwise would.1 The endowment effect is typically captured by models of loss

aversion, which depart from consistent consumption preferences by adopting a

utility function that depends on a reference point (e.g. current assets) from which

losses hurt more than gains help.2 A second important behavioral anomaly is

present bias, i.e. disproportionately steep impatience to delay immediate re-

wards.3 Present bias is typically captured by (quasi-)hyperbolic discounting,

given as βδt with “present bias” factor β < 1, which departs from consistent

time preferences by devaluing future utilities at a nonconstant rate.4,5

While relaxing the explicit assumption of consistent preferences, the loss aver-

sion and hyperbolic discounting models maintain an implicit assumption regard-

ing the decisions that an agent considers. That is, both the standard model and

its behavioral counterparts take the underlying decision problem as given. In

dynamic settings, the same consumption decision arises once in every period by

assumption. Hence, situational factors cannot affect when or whether the deci-

sion is considered, nor can different decisions be considered at different times.

When interpreting experimental research through this lens, it is presumed that

the decisions a subject considers are independent of experimental protocols. For

instance, receiving a good or being asked to evaluate an intertemporal tradeoff in-

1See Thaler (1980), Knetsch (1989), or Kahneman et al. (1990).2See Kahneman and Tversky (1979), Tversky and Kahneman (1991), and Koszegi and Rabin

(2006). When referencing the “loss aversion model(s),” I will implicitly include (and notdifferentiate between) pure ownership- and newer expectations- based approaches because theyare not distinguished by the typical laboratory illustration of the endowment effect, which isthe formal setting considered in this paper.

3For example, the mean annual discount rates inferred from the median willingnesses todelay $250 in Thaler’s (1981) study were 219% over one month from the present, yet only 14%over the next 9 years, 11 months. Also see Benzion et al. (1989) or Kirby (1997).

4See Laibson (1997) and O’Donoghue and Rabin (1999).5Here and throughout, “endowment effect” and “present bias” will refer to the associated

behaviors, as opposed to their formal connotations as models based on inconsistent preferences.

2

volving the good (i.e. time-preference elicitation) — as in the typical experiments

that reveal the endowment effect and present bias, respectively — are assumed

to have no effect on whether the subject considers the decision to consume the

good.

While maintaining consistent preferences, this paper presents a model in which

the decisions we consider can depend on the situations we encounter. Namely, sit-

uational “cues” induce decision points in that they compel the agent to consider

the associated consumption decision.6 A cue also entails a decision opportunity

cost, understood as the loss due to the inability to fully engage other possible

activities when “thinking about” the decision of interest. It follows that expo-

sure to a cue increases the effective utility of owning the associated good; or put

differently, a good is most valuable to you when you’re already thinking about

consuming it.

The model accounts for both behavioral anomalies of interest in a manner

that maps to the typical experiments that reveal them. To start, Section 4

shows how the endowment effect arises when receiving a good is modeled as a cue

(inducing a decision point), as the willingness-to-accept (WTA) to sell a received

good exceeds a potential buyer’s ex-ante willingness-to-pay (WTP). Due to the

irreversibility of the induced decision point, simply receiving the good makes

the agent “invested” in the consumption decision. Hence, the endowment effect

exists because the decision point is “sunk” — or more precisely, the accompanying

decision opportunity cost is sunk — for a potential seller but not for a potential

buyer, where the WTA-WTP gap quantifies the cost of being “stuck” having to

think about consuming a good that is no longer available for consumption.

In Section 5, time-preference elicitation is modeled as a cue, giving rise to

present bias. Analogous to receiving a good, simply being asked to choose be-

tween an immediate good and a future good makes the agent think about — and

therefore become invested in — consumption at the time of elicitation, while

choosing the future good entails being stuck having to think about the foregone

immediate good. The form of the apparent present bias β depends on whether

6While focusing on addiction, Landry (2014) also models cues as decision points. For otherrepresentations of cues in economics, which also focus on addiction, see Laibson’s (2001)preference-based approach and Bernheim and Rangel’s (2004) treatment of cues as triggersof mistaken consumption.

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or not choosing the future good guarantees an accompanying future decision

point. If so, β < 1 embodies a “fixed-cost” present bias (as in Benhabib et al.,

2010), which reflects the “extra” opportunity cost from having to re-think about

consumption after elicitation. This fixed-cost present bias also captures the well-

documented “magnitude effect” whereby individuals exhibit greater patience for

high-value than low-value goods.

For the case in which it is uncertain whether a decision point will accompany

the future good, β < 1 reflects the possibility that the agent will be thinking

about something else when the future good becomes available. This characteri-

zation fits with the observation that individuals sometimes forget — while cues

can serve as reminders — to carry out a future plan.7 Related to this, the model

accommodates value in forgetting due to the opportunity cost inherent in remem-

bering; this implied tradeoff between forgetting and remembering is consistent

with evidence that remembering to perform a given task is associated with re-

duced performance on a secondary task (Park et al., 1997; Smith, 2003; Smith

et al., 2007).

Sections 4 and 5 collectively demonstrate that, contrary to the mainstream

view, the endowment effect and present bias are both compatible with consistent

preferences. In doing so, the model fits with evidence (reviewed in Section 7) that

both anomalies can be activated by situational cues, as well as the related “mere

exposure” and “mere question” effects, whereby exposure to or being asked about

a good increases one’s valuation of it.8 Furthermore, unlike prevailing behavioral

models, the current framework simultaneously captures both anomalies — and

without requiring additional parameters. That is, relative to the most stripped-

down version of the standard decision-making model, only one new parameter

is needed: the “natural” per-period probability of considering the decision of

interest in the absence of a cue.

Section 6 characterizes a method to control for sunk decision points. In par-

ticular, the theory predicts that both anomalies vanish when their typical ex-

periments are modified to include the ex-ante receipt of an appropriately-timed7See Ericson (2011) for evidence on forgetting. For evidence that cues can function as

reminders or nudges to carry out the associated behavior, see Karlan et al. (2012).8For example, Peck and Shu (2009) and Bushong et al. (2010) document the effect of

physical exposure. The mere question effect is covered by Sprott et al. (2006), among others.See Section 7.2 for additional references and discussion.

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“auxiliary good” (e.g. a replica of the primary good). Receiving the auxiliary

good eliminates the endowment effect because it sinks the decision point for all

subjects: even potential buyers who do not receive the primary good will as-

suredly consider the decision to consume it. Hence, WTP for the primary good

rises to the level of WTA, which matches evidence that subjects do not exhibit

an endowment effect for goods that they already own, as well as its manifestation

as a rise in WTP instead of a drop in WTA (Morewedge et al., 2009). Present

bias is similarly eliminated by the ex-ante endowment of a future auxiliary good

— to be received at the time associated with the future good offered in elicita-

tion — because it sinks the future decision point. In this case, the consumption

decision is not only considered with certainty at elicitation, but also at the time

the future good would be acquired (even if the immediate good is chosen). This

result extends to a general auxiliary endowment sequence, which fits with the

apparent lack of present bias when time preferences are elicited over sequences

of outcomes.9

While carrying a new interpretation of the experimental evidence, the model

also features a novel link between the endowment effect and present bias, as

both anomalies arise because the agent rationally values a good more when she

is already thinking about consuming it. Formally tightening this proposed link,

Section 7 demonstrates that in an idealized experimental setting, the two anoma-

lies’ standard laboratory measures are in fact equal: i.e. β = WTPWTA

< 1. This

equality is not a coincidence because both measures quantify the effective de-

valuation of a good when its decision point is not yet sunk. For example, in

the endowment effect experiment, a potential buyer in essence devalues the non-

endowed good by β relative to a potential seller’s valuation — even though the

good is immediately available. Conversely, in the typical present bias experi-

ment, the future good’s value reflects WTP, while the immediate good’s value

reflects WTA — even though the subject is not endowed with it ex-ante.

Along these lines, the theory offers some new predictions to test the hypothesis

that the endowment effect and present bias share a common basis, such as: (i)

hidden versions of each anomaly are generated in the experiments known to

produce the other — for example, the theory predicts that the typical endowment

9See Loewenstein and Prelec (1991, 1993). For an elaboration and caveats, see Footnote 45.

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effect experiment activates a hidden “present bias” that could be uncovered if

the experimenter attempts to compare the endowed good’s value to that of a

future good; and (ii) “crowding out” between the endowment effect and present

bias would occur in an experiment designed to simultaneously detect both in

that the combined strength of the two anomalies would be significantly weaker

than would be implied by the standard notion that their underlying mechanisms

are distinct.10,11

Lastly, Section 8 shows how the hypothesized “artificial” separation between

the endowment effect and present bias can extend to the field. That is, in for-

malizing conventional means of field inference, a detection threshold arises that

partitions the domains for which each anomaly is observable. In particular, only

the endowment effect can be detected for goods with “raw” value above the

threshold in that market prices will reveal a WTA-WTP disparity; below the

threshold, only present bias can be detected in that agents will value commit-

ment, as evidenced by a willingness to pay a cost to avoid receiving the good.

This result complements the laboratory analysis in addressing why, if they are

supposedly variations of an equivalent “sunk decision points” rationale, the en-

dowment effect and present bias are still generally inferred in different settings.

2 Related Theories

Although the current approach is distinguished in its attempt to unify the anoma-

lies, the theory can be related to existing theories that seek to explain one or the

other anomaly without the usual behavioral model. To start, Huck et al. (2005)

propose an evolutionary basis for the endowment effect, suggesting that it can

improve one’s bargaining position in bilateral trade. Gintis (2007) also posits an

adaptive advantage, suggesting that an endowment effect could have facilitated

10For instance, suppose a subject is endowed with an immediately available good at the timeof time-preference elicitation (and thus has the option to exchange it for a future good thatis not in her endowment). In this combined experiment, either WTP

WTA or β (or both) would becloser to their classical value of 1 than when they are measured in separate experiments, ceterisparibus.

11The proposed coexistence between the anomalies is not far off suggestive evidence (reviewedin Section 7.2) that their associated cues may trigger the other anomaly; namely, present biashas been linked to physical contact with a good, while an endowment effect has been linked tomerely asking questions about the good.

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enforcement of private property rights in the absence of legal institutions (which

are a relatively modern invention). Isoni (2011) and Weaver and Frederick (2012)

emphasize the role of reference prices in arguing that the endowment effect fits

better with “bad deal aversion” than loss aversion. Bordola et al. (2012) suggest

that the endowment effect can arise because due to the influence of context on

the salience of goods’ attributes, which in turn affects the degree to which these

attributes are weighted in choice. Ungureanu (2012) demonstrates how the en-

dowment effect can arise due to locally-limited knowledge of one’s own utility

function.12

As for present bias, Sozou (1998) suggests that it can arise without hyperbolic

discounting if a Bayesian updater does not know the hazard rate that determines

whether future payoffs will be realized. Dasgupta and Maskin (2005) instead at-

tribute present bias to uncertainty with respect to when future payoffs will be

realized. Havely (2008) demonstrates how present bias can be explained by non-

linear termination probabilities (which can be interpreted as a mortality rate or

as the likelihood a reward will disappear). Ok and Masatlioglu (2007) show how

relaxing the assumption of transitive time preferences can give rise to present

bias. Rubinstein (2003) argues that a “similarity” heuristic in evaluating differ-

ent rewards across time can explain behavioral patterns typically attributed to

hyperbolic discounting. Lastly, Robson and Samuelson (2009) offer an evolution-

ary hypothesis in which present bias emerges amidst aggregate uncertainty in

the form of a discount rate that falls with age, due to the imperfect correlation

of aggregate shocks to agents’ survival probabilities.

3 Model

3.1 Benchmark Setup

In each period, t = 0, 1, 2, . . ., a utility-maximizing agent with consistent time

and consumption preferences might consider the decision to consume a particu-12Also of note, Plott and Zeiler (2007) informally propose (and experimentally test) a few

alternatives to loss aversion in explaining experimental illustrations of the endowment effect,such as: other-regarding preferences towards the experimenter (i.e. subjects view their endow-ment as a gift, making them feel somewhat obligated to keep it), perceived signaling of thegood’s relative value by way of the fact that the experimenter chose to endow the subject withit, and informational cascades stemming from the observation of other subjects’ choices.

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lar good. The decision points are defined as the times that the agent considers

this decision. For ease of exposition, we assume that the good is perfectly perish-

able.13 We also assume (implicitly) that the instantaneous utility from consump-

tion is strictly increasing.14 Hence, in period t, the agent optimally chooses to

consume her full period-t endowment of the good (which may be zero) if and only

if t is a decision point.15 If t is not a decision point, the agent engages in some

outside opportunity, e.g. perhaps a different consumption decision is considered.

Since the return to this outside opportunity is equivalent to the opportunity cost

of a decision point, it will be referred to as the decision opportunity cost. For

simplicity, the decision opportunity cost is normalized to 1 (in absolute value).

The benchmark refers to the control setting in which the agent is not (yet)

subjected to an “experiment.” For all t in the benchmark, the endowment of the

good is normalized to zero and the decision point probability is fixed to some

π ∈ (0, 1). The benchmark expected lifetime utility is thus given by

U =∞∑t=0

δt(1− π) =1− π1− δ

,

where δ ∈ (0, 1) is a constant discount factor.

3.2 Alternate Scenarios: Endowments and Cues

Now suppose the agent is subjected to alternate, “experimental” scenarios. Rel-

ative to the benchmark, an alternate scenario may involve changes to the en-

dowment stream, to the decision point probabilities, or both. Let e(τ) denote a

time-τ endowment of the good with consumption value e > 0 (i.e. consuming

the good brings e utils). For a scenario that features an endowment of this form

but does not include any other changes to the benchmark, the expected lifetime

utility is given by

U [e(τ)] = U + πδτe.

13As shown in Appendix A.8, all results are (qualitatively) robust to consideration of durablegoods.

14Equivalently, we could instead model an indivisible good for which its consumption bringspositive utility.

15Thus, we abstract from the possibility that the agent considers consuming the good, butchooses not to. We maintain such assumptions to keep the model as simple and standard aspossible.

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This expression implies that the present value of the endowed good, πδτe, is its

discounted consumption value weighted by the decision point probability π. This

weighting by π follows because e(τ) provides e utils in period τ if and only if τ

is a decision point (otherwise the good perishes).

Exposure to a cue associated with the consumption good will formally describe

a situational factor that increases the probability of a decision point relative to

the benchmark probability, π. Thus, exposure to a cue precludes the outside op-

portunity, which reflects the idea that a cue “distracts” the agent from whatever

else she happens to be doing, and compels her to consider the consumption deci-

sion associated with the cue. For simplicity, we assume that a cue at t guarantees

a decision point at t and leaves all other decision point probabilities unaffected.16

Also, to avoid ambiguity when translating real-world cues into the model, only

situational factors that are exclusively associated with the primary consumption

good will induce a decision point; in particular, exposure to a situation that is

symmetrically associated with the primary consumption good and with an out-

side opportunity or with a different good (such as money) will not affect the

decision point probability.17

Absent any accompanying changes to the endowment stream, the expected

lifetime utility associated with a single cue at t is

U [t] = U − (1− π)δt. (1)

Hence the cue’s cost, (1 − π)δt, is the discounted decision opportunity cost,

weighted by the benchmark probability that t would not have been a decision

point in the absence of a cue. Thus 1−π represents the expected decision oppor-

tunity cost attributable to a cue, and will be referred to as such from this point

forward.18

16This assumption isolates the immediate impact of a cue and treats it as a binary event. SeeSubsection 3.3 for a discussion of this assumption.

17If a cue is associated with multiple and different goods/activities, (at least) one must beincluded in the outside opportunity. Since the agent’s attention is a limited resource and thusmay be partially diverted from the primary good when such combined cues are present, it isnot necessarily clear whether their net effect would be to increase or decrease the decision pointprobability. To abstract from this ambiguity, the model simply assumes that the net effect iszero.

18As defined here, the expected decision opportunity cost of a cue is expressed relative to— and not to be confused with — the expected opportunity cost of a decision point in the

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For a scenario that involves a cue at t and an endowment of the good, e(τ),

the expected lifetime utility is:19

U [t; e(τ)] =

{U − (1− π)δt + πδτe if t 6= τ

U − (1− π)δt + δτe if t = τ(2)

As shown here, cues and endowments will be separated by a semicolon in the

argument of U . From equation (2), if the endowment and the cue do not coincide

(t 6= τ), the net value of both is simply the sum of their individual values.

However, if they do coincide (t= τ), then the weight π on the endowed good’s

discounted consumption value vanishes, which follows because the cue guarantees

a decision point at the time of the endowment. The increase in utility when the

endowed good coincides with the cue highlights the inefficiency in “thinking

about” consuming a good and having it available for consumption at different

times. Put differently, it is best to possess a good when considering the decision

to consume it — otherwise the agent may forget (with probability 1 − π) to

consume the good when it is available.20,21

3.3 Simplifications in the Cue Representation

While it will suffice to illustrate the main properties of the model, the cue repre-

sentation described in the previous subsection — in which a cue at t guarantees

a decision point at t and leaves all other decision point probabilities unaffected

— is limited in its realism. First, this “simple cue” abstracts from any effect be-

yond the present, even though cues realistically may affect future decision points.

For instance, an individual may remember past cues or a cue may be a catalyst

benchmark, which is just π.19In general, a scenario can involve sequences of cues and endowments: {ti}, {ej(τj)}.

The corresponding lifetime utility expression is U [{ti}; {ej(τj)}] = U − (1 − π)∑i δti +∑

j:τj∈{ti}δτjej + π ·

∑j′:τj′ /∈{ti}

δτj′ ej′ . As in (2), the cost of a cue at t is (1− π)δt, while the

value of an endowment e(τ) is δτe if it coincides with a cue and is πδτe if it does not.20Note that not considering the decision to consume (i.e. thinking about something else) and

forgetting to consume are, in essence, equivalent in the current framework, which follows fromthe feature that the agent consumes e(τ) if and only if τ is a decision point.

21As addressed in Appendix A.8, this mismatch between the decision point and possession ofthe good when t 6= τ is still costly for a durable good e(τ), in which forgetting at τ does notpreclude its eventual consumption. Rather, if τ is not a decision point, the value of the goodis subject to additional discounting, out to the time it is eventually consumed.

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for planning future decision points — e.g. setting a mental reminder, or using

an external planning device (such as a calendar).22 Appendix A.9 considers the

almost-as-simple case of a lagged decision point, in which a cue at t induces a

decision point in t+1, but leaves all other decision point probabilities unaffected;

here it is shown that the results derived from the simple cue model extend to the

case in which a cue’s effect is felt in the next period.23

The simple cue representation also abstracts from potential uncertainty re-

garding the induced decision point. Realistically, a cue may only raise the

likelihood of a decision point without guaranteeing it. With uncertainty and

persistence, cues could be ranked in terms of their salience.24 In contrast, any

two cues must be equally salient in the current setup. Moreover, since the first

cue guarantees the decision point, a second and concurrent cue has no additive

effect (even though realistically two cues are likely more salient than one, all else

equal). Though superfluous for the formal results, consideration of uncertainty

and persistence will be helpful to informally address real-world intricacies that

the simple cue representation does not readily motivate; uncertainty and persis-

tence also represent potentially promising generalizations of the basic model for

future research.22Dramatic examples of cue persistence can be seen in the realm of addiction. For instance,

when a drug addict attempting to quit cold turkey encounters a cue for the drug, it may inducea prolonged craving, in which the abstinent addict is continually preoccupied with “thoughts”of drug use. The example also alludes to the notion that the extent to which a cue “endures”beyond the present can depend on the chosen course of action when the cue is encountered,as in Landry (2014). For instance, choosing not to consume a craved good likely brings anear-term escalation of decision points due to the unsatisfied craving. If the good is durable,the physical presence of unconsumed portions can also invite continued decision points.

23As another basic way to model persistence, a cue at t could guarantee decision points int and in t + 1. This case is equivalent to a scaled version of the simple cue model withoutpersistence and with a perishable good. That is, the expected decision opportunity cost wouldbecome (1 + δ)(1 − π), provided that realized cues do not overlap in that they are separatedby at least one period without a cue. This scaling of the decision opportunity cost by (1 + δ)follows because the cue precludes the outside opportunity both ‘today’ and ‘tomorrow.’

24Suppose π∗t ∈ [π, 1] denotes the decision point probability at t = 0, 1, . . ., in a scenario thatfeatures a single cue at time-zero (without loss of generality). Then

∑t δt(π∗t − π) would be a

natural measure of the cue’s salience since this sum quantifies the cue’s “impact,” given as thepresent expected value of the induced decision point sequence.

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4 A Receipt-Induced Endowment Effect

4.1 The Endowment Effect Experiment

In the typical endowment effect experiment, some subjects are given (endowed

with) a good, while others are not.25 All subjects must then choose between

the good or some amount of money. That is, subjects who initially receive the

good are prospective sellers who can either sell the good or keep it, while the

remaining subjects are prospective buyers who can either buy the good or keep

their money. In this context, ‘willingness-to-pay’ (WTP) refers to the maximum

price that a prospective buyer is willing to pay for the good, while ‘willingness-to-

accept’ (WTA) is the minimum price that a prospective seller is willing to accept

to relinquish the good. The endowment effect is revealed by this experiment if

WTA exceeds WTP, where a large WTA-WTP disparity (or a small WTP/WTA

ratio) signifies a strong endowment effect.

4.2 Receiving the Good as a Cue

To formally consider the typical endowment effect experiment, receiving the good

is now modeled as a cue.26 Thus, if the agent receives e(τ), τ will be a decision

point. For this experiment and without loss of generality, we will only consider

a time-zero endowment of the good, e(0). Let vP (e) denote the agent’s WTP for

the good, defined as the net value from receiving it; WTA, denoted by vA(e), is

then defined as the value of retaining e(0) upon its receipt. WTP and WTA can

be interpreted as the prices to a buyer and to a seller, respectively, such that the

net return to a transaction is zero. Relative to the benchmark, WTP and WTA

25See Horowitz and McConnell (2002) for a review of experimental research on the endowmenteffect.

26Note that following the criteria given in Section 3.2, the opportunity to buy or sell the gooddoes not constitute a cue. This follows because buying and selling opportunities essentiallyboil down to a choice between two goods — the primary consumption good and a numerairegood (i.e. money) — and only situations that are exclusively associated with a single good aremodeled as cues. To be sure, the emergence of an endowment effect in this section is robustto generalizations of the exclusivity requirement that allow, for instance, a potential buyer’sdecision point probability to exceed π. See Appendix A.10 for an elaboration.

12

are thus given by:

vP (e) = U [0; e(0)]− U,

vA(e) = U [0; e(0)]− U [0].(3)

Here, WTP is the expected utility gain from receiving the good and WTA is

the ensuing loss upon relinquishing it.27 Since relinquishing the good does not

change the fact that it had been received, the benchmark utility does not enter

WTA; rather, the scenario in which e(0) is relinquished still entails a cue at t=0.

Due to the irreversibility of this cue, simply receiving the good makes the agent

“invested” in the associated consumption decision. Quantifying this investment,

the first result captures the endowment effect:

Proposition 1 [Endowment Effect] vA(e)− vP (e) = 1− π > 0.

Here and in all subsequent results, the benchmark is the base for comparison

unless otherwise specified; all proofs are in the appendix.

Proposition 1 establishes a WTA-WTP disparity, equal to the expected de-

cision opportunity cost, 1 − π. This endowment effect reflects the cost of being

“stuck” having to consider the decision to consume a good that was immediately

relinquished upon its receipt.28 Thus, by causing the recipient to “think about”

consumption, receiving the good causes its value to rise from its benchmark value

— put differently, this WTA-WTP disparity exists because the decision point is

sunk for a prospective seller, but not for a prospective buyer.29 Observe if π = 1,

as in the standard decision-making model, there would be no WTA-WTP dispar-

ity; this lack of an endowment effect for π = 1 follows because the cue (receiving

the good) would no longer carry a decision opportunity cost if the decision would

have been considered regardless.

27If the “default” scenario is something other than the benchmark, i.e. if it involves sequencesof cues {ti} and of endowments {ej(τj)}, the general forms for WTP and WTA are: vP (e) =U [0 ∪ {ti}; e(0) ∪ {ej(τj)}]− U [{ti}; {ej(τj)}] and vA(e) = U [0 ∪ {ti}; e(0) ∪ {ej(τj)}]− U [0 ∪{ti}; {ej(τj)}] (respectively).

28In the language of loss aversion, the loss from relinquishing the good exceeds the gain fromreceiving it because the loss is the good’s full consumption value, while the gain is only itsnet value, i.e. the consumption value minus the expected decision opportunity cost from itsreceipt.

29To reiterate, variations on the phrase “sunk decision point” are used as shorthand to referto the sunk decision opportunity cost.

13

The emergence of an endowment effect in Proposition 1 is robust to notions

of cue persistence discussed in Section 3.3. In fact, if we maintain that receiving

the good guarantees the present decision point, the endowment effect would

strengthen with cue persistence because the total expected decision opportunity

cost underlying the WTA-WTP disparity would exceed 1 − π if receiving the

good sinks additional decision points beyond the present. That is, a seller of

the good may continue to “reminisce” or “think about” using the good after

selling it due to the continued decision points that were effectively sunk when

the good was initially received.30 It similarly follows that, with cue persistence,

the endowment effect can exist even for goods that were received “yesterday.” In

contrast, using our simple cue model without persistence, Proposition 1 implies

that there will be no endowment effect for goods at the time that they are “ripe”

(or available) for consumption if they were received in the past; e.g. there is no

WTA-WTP disparity at τ for an endowment e(τ) if it was received in τ − 1.

5 An Elicitation-Induced Present Bias

5.1 The Present Bias Experiment

The typical experimental illustration of present bias is based on a time-preference

elicitation protocol that involves asking subjects to choose between an immedi-

ately available good and a future endowment of the same good, but of a higher

quantity or value. From a subject’s responses, the analyst makes inferences on

the form of the subject’s discount function. The total elicited discount from the

present to a future time τ is calculated as the ratio of a presently-available good’s

value to the value of a good at τ such that the subject is indifferent between the

two. A present bias is then revealed if the elicited discount function is quasi-

hyperbolic, i.e. if it takes the form βδτ for τ > 0, where β < 1 is the present bias

factor (Laibson, 1997; O’Donoghue and Rabin, 1999).

30The notion that receiving the good could induce future decision points (via cue-inducedplanning) would likely be important in understanding the endowment effect for mugs — theclassical endowment effect illustration (Kahneman et al., 1990) — in the context of the model,as mugs are generally not used immediately upon receipt. Recall, the robustnesses of Propo-sition 1 to durable goods and to a basic form of cue persistence are established in AppendicesA.8 and A.9, respectively.

14

5.2 Elicitation of Time Preferences as a Cue

To formally consider the typical present bias experiment, time-preference elici-

tation is now modeled as a cue.31 The elicited discount function, denoted by Dτ ,

measures the total discount from elicitation at t= 0 (without loss of generality)

to the time of the future good e(τ) that is offered as an option. Thus, Dτ is

defined as the unique value such that the agent is indifferent between e(τ) and

Dτe(0).32

To compute Dτ we still need to know more about the elicitation protocol

because when the future good e(τ) is chosen, the period-τ decision point prob-

ability remains ambiguous. If the agent receives e(τ) in period τ , then τ must

be a decision point since receiving the good is a cue. That said, it is conceivable

that τ may not be a decision point even if e(τ) is chosen, e.g.: (i) elicitation may

only involve a choice among hypothetical rewards;33 (ii) the subject may have

to remember to claim the future reward; or (iii) a good that is not yet ripe for

consumption may be acquired at the time of elicitation (e.g. choosing between

one yellow banana and two green bananas). To account for these possibilities,

the term non-cueing is used to refer to a good for which its acquisition does not

induce a decision point — in contrast to a “received” good.34

Proposition 2 [Present Bias] Dτ = βδτ , where β < 1 is given by:

(i) β = 1− (1− π)/e for received goods,

(ii) β = π for non-cueing goods.

31Note that time-preference elicitation is exclusively associated with a single good, as both ofthe subject’s options are endowments of the primary consumption good. Thus, time-preferenceelicitation meets the criteria for a cue from Section 3 — unlike buying and selling opportunitiesin the endowment effect experiment, which are symmetrically associated with a numeraire good(i.e. money) in addition to the primary good. See Appendix A.10 for additional discussion onthis distinction as it relates to the main results.

32Put differently, if elicitation reveals that the agent is indifferent between e∗(0) and e(τ),then Dτ = e

e∗ . Note that Dτ may implicitly depend on e (as well as on π).33When hypothetical rewards are involved, it is often unclear whether subjects ought to

choose the alternative that they would prefer to have had in their pre-existing endowment,in which case the future good may not be evaluated as if it involves a cue, or to choose thealternative that they would prefer to receive into their endowment at that time. This ambiguityis evident in an excerpt from the sample instructions in Thaler’s (1981) classic study: “choosebetween: (A.1) One apple today. (A.2) Two apples tomorrow.”

34That is, if e(τ) is a non-cueing good then choosing it in the elicitation task does not affectthe decision point probability at τ .

15

From part (i), elicitation induces a present bias for received goods in the

form of a “fixed-cost” present bias, in which the agent appears to discount as if

future returns entail a fixed cost from which present returns are exempt. This

fixed cost for future returns equals the expected decision opportunity cost and

is attributable to the property that time-preference elicitation at t=0 sinks the

decision point for the immediate good, but not for the future good.35 From

part (ii) of Proposition 2, elicitation induces a present bias for non-cueing goods,

equal to the benchmark decision point probability. In this case, present bias arises

because an accompanying decision point is only guaranteed for the immediate

good (since it coincides with elicitation). If the future good is chosen, with

probability π the agent will not consider the decision to consume it, in which

case the good perishes.36

Together, parts (i) and (ii) of Proposition 2 show that an elicitation-induced

present bias will exist with or without our previous assumption that receiving

the good induces a decision point. In both cases, the present bias reflects the

extra incentive to own a good when its decision point is already sunk from time-

preference elicitation. As with the endowment effect, present bias (in both forms)

disappears if π = 1 in that Dτ = δτ . For received goods, this disappearance of

present bias reflects that the expected decision opportunity cost from receiving

a future good is zero if the future decision point was assured regardless. For

non-cueing goods, present bias disappears because the agent will always consider

the consumption decision — meaning it is certain that the good will not perish

— since decision points are guaranteed in all periods with π = 1.

5.3 Magnitude Effect (for Received Goods)

Observe from part (i) of Proposition 2 that a received good’s consumption value

nontrivially enters the expression for β. This dependence implies:

35To see that the fixed cost equals the expected decision opportunity cost, observe that thetime-zero value associated with receiving e(τ) is βδτe = δτ (e− (1−π)), while the present valuefrom receiving e(0) is just e. For a formal consideration and evidence of fixed-cost present-bias,see Benhabib and Bisin (2005) and Benhabib et al. (2010).

36With durable non-cueing goods, the elicited present bias instead reflects the “extra” dis-counting from the time that the future good is first available until the time of its eventualconsumption (i.e. the first decision point on or after the time the good first becomes availablefor consumption). See Appendix A.8 for details.

16

Corollary 1 [Magnitude Effect] For received goods, Dτ increases with e.

Hence, the elicited discount function for received goods is increasing in the

good’s consumption value. This corollary captures the widely-documented mag-

nitude effect — an inherent feature of a fixed-cost present-bias — whereby indi-

viduals exhibit greater patience for large rewards than for small rewards, ceteris

paribus.37 Here, the magnitude effect exists because the expected decision op-

portunity cost of a future, receipt-induced decision point is comparatively small

when the received good’s consumption value is large. That is, if the agent chooses

the received future good e(τ), the nuisance from having to consider the decision

(again) at τ is relatively minor if the future reward e is large.

5.4 Memory and Cue Persistence

The current treatment of present bias relates to aspects of memory. To start,

the present bias for non-cueing goods reflects the intuitive (and empirically sup-

ported) notion that people sometimes “forget” to carry out their plans or in-

tentions for the future. For example, subjects in Ericson’s (2011) experiment

had to choose between a smaller payment to be automatically given to them six

months later and a larger payment that they had to remember to claim after the

same six-month waiting period; roughly half of the subjects who chose the larger

payment did not remember to claim it.

Furthermore, receiving a future good in essence serves as a reminder to con-

sume it. The the notion that such a reminder works as a “nudge” to perform

the associated behavior likewise matches introspection and evidence.38 While

a reminder may on balance be beneficial (i.e. provided e > 1 − π), there can

also be value in forgetting because the decision opportunity cost is avoided if

37In addition to Benhabib et al.’s (2010) evidence of a fixed-cost present bias, the magnitudeeffect is evident from survey data in Thaler (1981), Benzion et al. (1989), and Green et al.(1997). Also see Loewenstein and Prelec (1992) or Frederick et al. (2002) for discussion andadditional references. For a recent axiomatization of the magnitude effect, see Noor (2011).

38Karlan et al.’s (2012) field study shows how mere reminders can be effective increasingindividuals’ propensity to save. As the authors note, not only does the hyperbolic discountingmodel fail to explain the effect of reminders on behavior, the fact that reminders matter alsopoints to a different channel through which inconsistent behavior typically attributed to time-inconsistent preferences can arise.

17

the agent does not remember to consider consumption.39 This implied tradeoff

between remembering and forgetting — as well as its conception in terms of an

opportunity cost — fits with laboratory evidence that successfully remembering

to perform a given task is associated with reduced performance on a secondary

task (e.g. Park et al., 1997; Smith, 2003; Smith et al., 2007).

Both forms of present bias in Proposition 2 are robust to cue persistence.40

Similar to its effect on the WTA-WTP disparity, cue persistence can exacerbate

the elicited fixed-cost present bias because the total corresponding opportunity

costs are higher if receiving the good has an enduring effect on decision points

beyond the present. For non-cueing goods, however, cue persistence would gen-

erally weaken present bias because elicitation at t = 0 could then raise the

decision point probability at τ above the benchmark value, thereby increasing

the likelihood that the agent remembers to consume. Bearing in mind that the

present bias for non-cueing goods reflects the probability of remembering to con-

sume, a realistic specification of cue persistence motivated by an understanding

of memory would likely enhance the model’s predictive power. For example, the

likelihood of remembering to consume e(τ) is probably higher if τ = 1 than if

τ = 100. In particular, incorporating the (empirically-supported) hyperbolic “re-

tention function” would give rise to the appearance of the smoother hyperbolic

discount function, as opposed to the cruder quasi-hyperbolic form.41

6 Controlling for Sunk Decision Points

In contrast to their usual interpretations as evidence against consistent pref-

erences, the endowment effect and present bias emerged in preceding sections

because goods are rationally valued more by those who are already considering

39Recall from Section 3.1 that the agent optimally chooses to consume a good if and only ifshe considers the decision to consume it. Hence, remembering to consume and rememberingto consider the decision to consume can, in effect, be regarded as equivalent.

40Save for unreasonably extreme cases. For example, if elicitation is so salient that it guaran-tees decision points for all t (the agent never again considers any decision besides the decisionto consume this particular good), present bias would disappear because, in essence, we wouldhave π = 1.

41Lee’s (2004) estimates from individual retention data favor a hyperbolic memory model overalternative specifications such as an exponential and a quasi-hyperbolic-equivalent retentionfunction.

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the associated consumption decision. While quantifying the influence of such

sunk decision points on the valuation of goods may have merit, if the aim is

to test preference consistency assumptions, the results suggest that standard

experiments may not be suitably controlled.

Can we control for sunk decision points? As discussed, if decision points are

guaranteed in all periods (π = 1), both anomalies vanish. Although guaranteeing

decision points for all t is not a practical experimental control, with our simple

cue concept that lacks persistence, decision points would only need to be induced

in periods relevant to the valuation problem. Namely, suppose the benchmark is

modified such that the agent receives an auxiliary good, denoted by a(τ). Here

τ will be the period for which some, but not all participants in the original

experiment will have an induced decision point. This modified benchmark will

be referred to as the auxiliary-appended benchmark.

6.1 Disappearance of the Endowment Effect

The next result shows that the endowment effect from Proposition 1 disappears

in the auxiliary-appended benchmark:

Proposition 3 [WTA-WTP parity] From the auxiliary-appended benchmark,

vA(e) = vP (e), both of which equal vA(e) in benchmark.

The WTA-WTP disparity vanishes here because receiving the auxiliary good

a(0) guarantees a decision point at t = 0 regardless of whether or not the agent

receives the primary good e(0) — i.e. receiving the auxiliary good sinks the

decision point even for potential buyers of the primary good. Only WTP changes

from its benchmark value because, to a recipient of e(0), receiving a(0) as well

does not affect the time-zero decision point probability, implying that WTA is

unaffected. This disappearance of the endowment effect and its attribution to

an increase in WTP (as opposed to a decrease in WTA) are both consistent

with Morewedge et al.’s (2009) finding that potential buyers of a coffee mug that

already own an identical mug are generally willing to pay the price demanded by

sellers.

Proposition 3 ought to remain valid even if the auxiliary good is a different

good that, when received, triggers the same consumption decision as the primary

good. Since different goods may be used in a similar fashion, it is plausible

19

that such (possibly imperfect) “decision-point substitutes” exist. This concept

fits with Chapman’s (1998) finding that the endowment effect is significantly

stronger between a writing utensil and a chocolate than between two different

types of writing utensils (or between two different types of chocolates).42 For

example, receiving an “auxiliary pen” would control for the endowment effect

from receiving a pencil if both items cause the agent to consider writing. However,

the endowment effect should persist if the auxiliary good triggers a different

decision altogether — e.g. a chocolate cannot serve as a proper control for a

pencil because receiving the chocolate would not compel the agent to consider

writing.

6.2 Disappearance of Present Bias

The same principle that eliminated the endowment effect can be applied to elim-

inate present bias. That is, an exponential discount function is elicited if it is

assured that the agent will receive an auxiliary good at the time associated with

the primary future good offered in the elicitation task:43

Proposition 4 [Exponential Discounting] From the auxiliary-appended bench-

mark, Dτ = δτ.

Receiving the auxiliary good a(τ) eliminates present bias because it sinks

the decision point at τ , offsetting the elicitation-induced decision point at t =

0. Proposition 4 holds for both received and non-cueing goods, although it is

easier to conceive implementation with received goods for consistency with how

the auxiliary good is acquired. For received goods, there is no longer a fixed-

cost present bias as in part (i) of Proposition 2 because the associated fixed

cost at τ (i.e. the expected decision opportunity cost) is “paid” ex-ante in the

42That is, individuals endowed with a chocolate tend to be much less reluctant to exchangeit for a different type of chocolate than to exchange it for a writing utensil (and vice versa).Similar evidence is provided by Hanemann (1991) and by Shogren et al. (1994) who find thatgoods with more substitutes in the marketplace feature a smaller WTA-WTP gap than goodswith fewer substitutes.

43Stated differently, if the original procedure compared e∗(0) to e(τ), then now the pairs{(e∗+a)(0), a(τ)} and {a(0), (e+a)(τ)} are effectively compared. In the current setting, receivinga(0) for both options is extraneous, but it may be a helpful control in practice to ensure thepresent cue is as potent as the future cue even when the agent opts for the alternative withthe larger consumption value at τ .

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auxiliary-appended benchmark. For non-cueing goods, there is no longer any

doubt whether the agent will consider consumption at τ because receiving a(τ)

guarantees the decision point; hence the value of e(τ) is no longer weighted by

π, which was the elicited β from Proposition 2, part (ii).

Although it would have been extraneous, Proposition 4 would still hold if

the agent also received an additional, time-zero auxiliary good, a(0). In this

case, both alternatives in the elicitation task would effectively reduce to a pair

of nonzero endowments — one at t= 0 and one at τ — that differ only in their

per-period consumption values.44 Hence, Proposition 4 suggests that there would

be no present bias when eliciting preferences over sequences of outcomes at pre-

specified times. This fits with the apparent lack of present bias when discount

rates are inferred from preferences over sequences of outcomes (Loewenstein and

Prelec, 1991, 1993).45 Intuitively, present bias would not be apparent here be-

cause the periods for which the agent receives some amount of the good — and

hence the periods for which the agent considers the decision — are fixed ex-ante

and thus do not depend on the chosen endowment sequence.46

7 Linking the Endowment Effect and Present Bias

So far, several similarities between the endowment effect and present bias have

emerged. The results from Sections 4-5 show how both behavioral anomalies can

be inferred from consistent preferences in conventional experimental settings.

Both anomalies were attributable to the increase in a good’s effective value when

44For example, if utility is linear and the consumption value of the immediate primary goodis e∗, the elicitation task would entail asking the subject to choose between: (i) endowmentsat t = 0 and at τ worth a+ e∗ and a, respectively, or (ii) endowments at t = 0 and at τ wortha and a+ e, respectively.

45In fact, Loewenstein and Prelec document revealed negative time preferences, as improv-ing sequences of outcomes tend to be favored over nonimproving sequences. The simple cuerepresentation cannot account for revealed negative time preferences. That said, if receivinge(τ) has a persistent and positive effect on decision point probabilities after τ where the degreeof persistence (i.e. salience beyond its present impact) rises with e, then improving sequencescould become more favorable to mitigate the decision opportunity costs in the interim periodswhen no endowment is received.

46The logic is the same for sequences that involve more than a pair of endowments. If anauxiliary good is received in all t = 0, 1, 2, . . ., the disappearance of present bias — and also ofthe endowment effect — can be understood in light of the fact that the induced sequence ofdecision points is, in essence, a reduction to standard discrete-time.

21

its decision point is “sunk.” Moreover, both anomalies were activated by cues.

Basic comparative statics reinforce the connection, as increasing π brings both

the WTP/WTA ratio and the elicited present bias β closer to unity. Although

it was normalized to 1, it is also straightforward to posit changes to the decision

opportunity cost and to see, for received goods, that increases would make both

anomalies more pronounced. Finally, Section 6 shows how both anomalies vanish

using the same experimental control — an auxiliary endowment of the good.

7.1 Laboratory Coexistence and Equivalence

Despite the similarities described above, the link between the endowment effect

and present bias can be formally tightened. In fact, their standard laboratory

measures are equal:47

Proposition 5 [Equivalence] For received goods, vP (e)/vA(e) = β < 1.

Thus, the WTP/WTA ratio and the elicited present bias factor are equal. This

equality is not a coincidence because both measures express, when considering the

decision to consume a good, the share of that good’s value that is not attributable

to the fact that its decision point is already sunk. That is, both WTP/WTA

and β are equal to the ratio of the benchmark value from receiving a good to its

value conditional on a cue-induced decision point. Proposition 5 also suggests

that the typical endowment effect experiment could be reinterpreted in terms

of a “hidden” present bias, and vice versa. That is, in the endowment effect

experiment, a received good is evaluated as if the agent has a present bias for it,

in that an unowned good — despite being immediately available — is devalued

by the present bias β < 1 relative to the received good. By the same logic, the

immediate good in time-preference elicitation is evaluated as if it has already

been received, suggesting that the present bias experiment effectively compares

WTA for the immediate good to WTP for the future good.

Instead of reinterpreting one anomaly in terms of the other, we could regard

both as existing simultaneously. That is, since receiving the good and time-

preference elicitation induce decision points that are identical (for our purposes),47To be sure, both the WTA-WTP disparity and the WTP/WTA ratio could be regarded as

a “standard measure” of the endowment effect. In light of this, Proposition 1 was expressedin terms of the WTA-WTP disparity — which is generally not equal to the elicited β — topreserve the suspense for Proposition 5.

22

Proposition 5 also suggests that either experiment can generate both anomalies,

only one of which is explicitly “noticed.” For instance, physically receiving a good

in the endowment effect experiment activates a coexisting “present bias” that

remains hidden because such experiments do not compare the received good’s

value to that of a future good. Conversely, time-preference elicitation in the

present bias experiment raises the immediate good’s value from its benchmark

WTP to its WTA, but this coexisting “endowment effect” likewise remains hidden

because these experiments do not compare the immediate good’s value to its value

in the absence of elicitation.

The proposed “overlap” between the endowment effect and present bias could

be tested by modifying either experiment to incorporate the defining feature of

the other. For instance, if the present bias experiment is modified such that

the subject receives the immediate good ex-ante and is then given the option

to trade it for the future good, then accounting for the WTA-WTP disparity

would substantially diminish the inferred present bias (bringing β closer to 1),

and vice versa. The same “crowding out” would arise if an unowned good is

delayed to τ > 0 in the endowment effect experiment, in which case accounting

for the present bias β < 1 in the subject’s valuation of the unowned good would

substantially diminish the WTA-WTP disparity, and vice versa.48

7.2 Related Evidence and Other Shared Features

Existing research lends credence to the notion that the endowment effect and

present bias have a shared basis. To start, many studies show that being asked

questions about a good (as in the present bias experiment) can increase one’s

willingness to buy it; for instance, Morwitz et al. (1993) find that merely ask-

ing “how likely are you to buy a car?” led to a 37% rise in car purchases.49

48With the simple cue assumption, there would be complete crowding out. With persistenceand/or uncertainty, however, two simultaneous cues — namely, receiving the good and time-preference elicitation — could be more salient than either cue in isolation, which implies thatthere would generally only be partial crowding out. In contrast, the standard view that treatsthe endowment effect and present bias as distinct phenomena would imply zero crowding out inthat if vP /vA and β are measured (separately) in their typical experiments, then an unowned-and-delayed good would be devalued by βvP /vA relative to a received-and-immediate good(above and beyond discounting via δt) in such a combined experiment.

49One could argue that asking “how likely are you to...?” could have a fundamentally differenteffect on decision-making than questions about intertemporal tradeoffs because the former

23

Analogously, while several studies demonstrate that physical contact with (or

exposure to) a good can induce an “endowment effect” (with or without ac-

tual ownership), others have noted it can induce behavior reminiscent of present

bias.50 Since physical contact with the good is the textbook example of a cue,

these studies also provide support for the model’s feature that both anomalies

are cue-activated, which is not the case in the loss aversion and hyperbolic dis-

counting models.51

The model’s implication that opportunity costs inherent in cues underly both

anomalies also has empirical backing. For instance, Frederick et al. (2009) find

that cues to consider the opportunity costs associated with buying a good lead to

a decrease in WTP. Brendl et al. (2003) likewise show that when cigarette and

popcorn cues are present, unrelated goods are valued less. These effects could

arise because exposure to a cue associated with one good reduces the decision

point probability associated with another good. Similarly, when subjects are

asked questions that emphasize the past or the future, present bias weakens

(Radu et al., 2011). Siegel and Rachlin (1995) likewise find that pigeons exhibit

less present bias for an immediate reward when they must repeatedly peck a

key associated with a future reward immediately prior to their decision.52 These

examples also support the notion that cues’ capacity to activate (or deactivate)

question may implicitly suggest doing the behavior. However, implicit suggestions do notappear to be driving this “mere question” effect in light of Levav and Fitzsimons’s (2006)finding that asking “how likely are you not to...?” and asking “how likely are you to...?”change behavior at the same rate. See Sprott et al. (2006) for additional background on andexamples of this mere question effect.

50Studies demonstrating an induced endowment effect due to physical contact or exposureinclude Reb and Connolly (2007), Wolf et al. (2008), Peck and Shu (2009), and Bushong etal. (2010); the link to present bias is highlighted by Loewenstein (1996) and Laibson (2001).Noting that reference-point effects are traditionally related to the endowment effect but not topresent bias, the anomalies’ coexistence is further bolstered by Hoch and Loewenstein’s (1991)observation that present bias can emerge due to situational factors that shift one’s referencepoint.

51In the realm of impulsive choice, the capacity of uninformative cues to induce apparentpresent bias has been characterized as the “greatest limitation” of the hyperbolic discountingmodel by Ainslie (2010), whose earlier experiments laid the groundwork for the model (Ainslie,1974, 1975). For neuropsychological evidence that cues can activate present bias, see McClureet al. (2004).

52Similar to the human study, the logic here presumes that repeated pecking of the “fu-ture” key diverts attention from the present — or more specifically, reduces the decision pointassociated with present consumption.

24

the opportunity costs underlying both anomalies may be traceable to the role

of cues in causing people (or birds) to “think about” particular behaviors at

particular moments in time.

8 Field Inference

In the laboratory, it makes sense that the endowment effect and present bias

are not found together since neither of their experiments attempt to detect the

other anomaly. Yet this only partially explains why, if they are variations of an

equivalent incentive to own a good when its decision point is sunk, the anomalies

are commonly regarded as distinct because they are also not found together in the

field. Since cues activate both anomalies in the current framework, field versions

should in principle exist because cues exist in the field. However, since field cues

cannot be introduced on command, the previous consideration of laboratory cues

will be insufficient for field inference.

For the endowment effect, field inference is possible in conventional goods

markets because WTA and WTP map to prices. Accordingly, field studies have

demonstrated the endowment effect in numerous market settings.53 Field infer-

ence of present bias, however, is not typically based on markets for the primary

goods for which present bias is deemed relevant. Instead, present bias is inferred

from demand for (pre-)commitment devices that eliminate the availability of the

primary good. The logic behind such inferences follows because commitment

reveals (and present bias implies) that the availability of a good can be desirable

‘today’ yet undesirable from ‘yesterday’s’ perspective.54

53Such settings include: an insurance market (Johnson et al., 1993), a sportscard market(List, 2003), and a stock market (Furche and Johnstone, 2006). List’s study features aninteresting disclaimer as it demonstrates a strong endowment effect for inexperienced tradersonly, while experienced traders’ behavior is more or less consistent with neoclassical demandtheory. The induced decision point concept embeds a natural explanation for this finding:since experienced traders are accustomed to trading the sportscards they receive, it is quiteplausible that a sportscard becomes a cue to consider the decision to trade it — as opposed tothe decision to “consume” it. Consequently, the cue does not heighten the incentive to havethe card because the card becomes associated with a different activity (trading) that does notinvolve keeping it. See Coursey et al. (1987) for similar evidence that the WTA-WTP gapshrinks with market experience.

54As O’Donoghue and Rabin (1999) describe, “Researchers looking for empirical proof oftime-inconsistent preferences often explore the use of self-limiting ‘commitment devices’ (e.g.,Christmas clubs, fat farms), because such devices represent ‘smoking guns’ that cannot be

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To consider field inference of present bias, define commitment value, denoted

by vC(e), as the value of a commitment device that restricts the availability

of e(0) by preventing it from being received. In the field, present bias is only

detected if commitment value is positive (vC > 0). To detect the endowment

effect, WTP must be positive (vP > 0) because an agent must voluntarily buy

the good (and also find a willing buyer to sell it to) for a WTA-WTP disparity

to be observable. Given these restrictions, the next result shows that the two

anomalies are never simultaneously detected in the field.

Proposition 6 [Mutually-Exclusive Field Inference]

(i) If e > 1 − π, then vP (e) > 0 > vC(e), so that the endowment effect can be

detected (but not present bias).

(ii) If e < 1 − π, then vC(e) > 0 > vP (e), so that present bias can be detected

(but not the endowment effect).

For a given good e(0), field inference of one anomaly precludes field inference

of the other because WTP and commitment value must have the opposite sign

(unless both are zero). From part (i), only the endowment effect is detected

for ‘good’ goods, in which the consumption value exceeds the expected decision

opportunity cost. Since the net value of receiving a ‘good’ good is positive, there

is no demand for a commitment device that prevents it from being received, so

that present bias will not be detected. From part (ii), only present bias is detected

for ‘bad’ goods, in which the consumption value is less than the expected decision

opportunity cost. Since the net value of receiving a ‘bad’ good is negative, there

is no demand for it and thus no observable WTA-WTP disparity to reveal an

endowment effect.

While mutual-exclusivity in field inference is robust to generalizations dis-

cussed earlier, the threshold consumption value, e = 1−π, between ‘good’ and

‘bad’ goods may vary.55 With cue persistence, the total expected decision oppor-

tunity costs from receipt — and hence the threshold for e — may far exceed 1−π.

explained by any time-consistent preferences.” For a review of commitment devices, see Bryanet al. (2010).

55That is, vP > 0 still holds for ‘good’ goods but not for ‘bad’ goods, while the opposite holdswhen vC > 0, so that the endowment effect but not present bias can be detected if the netexpected utility from receiving a good is positive (and the reverse if the net expected utility isnegative).

26

Consequently, the WTA-WTP disparity and commitment value could dwarf the

cost associated with having to consider just one “extra” decision.56 Even with

such generalizations, the field versions of the endowment effect and present bias

both arise because receiving a good sinks the decision point, thereby raising its

effective value.

Along with their relegation to separate laboratory experiments, Proposition 6

reinforces how a potential link between the endowment effect and present bias can

go unnoticed since a separation is inevitable from conventional field inference.

That said, unlike in the laboratory, the anomaly that can be inferred in the

field depends on the relevant good’s consumption value. Thus, although the

field versions of both anomalies arise due to a shared motive to own a good

when the decision point is sunk, their connotations can fundamentally differ.

Namely, while the endowment effect is a feature of goods that were desirable to

begin with, present bias reflects a qualitative (and temporary) change in that its

activating cue can, in essence, transform something that the agent does not want

into something that the agent wants. Although these characterizations fit with

the usual connotations of each anomaly, the “induced wanting” aspect of present

bias could also be regarded as a striking illustration of loss aversion because it

illustrates how someone can even be averse to losing a good that they did not

want in the first place.

Proposition 6 also suggests that the endowment effect and present bias can

be detected in the field for different “quantities” of the same good. To illustrate,

consider a 10-cent coupon and a $10 coupon (perhaps electronic) for a common

consumption good. Both coupons would be valued at the time that the con-

sumption good is purchased. However, many would go out of their way to opt

out of a mailing list or to apply a spam filter to prevent the 10-cent coupon from

being received, but would also willingly pay to subscribe to a mailing list or to

purchase a booklet to receive the $10 coupon. Hence, it is plausible that there

is commitment value with respect to the 10-cent coupon yet a positive WTP for

56Without cue persistence, commitment value is probably too small to meaningfully motivatedemand other than as a theoretical possibility. With cue persistence, however, commitmentvalue can be very large. Landry (2014) shows how persistence can be particularly salient inthe context of addiction. In fact, when faced with a craving, the addict will optimally consumeharmfully addictive goods for which the direct cost of consumption outweighs its benefits, asa means to delay unwanted decision points (i.e. cravings) in the short run.

27

the $10 coupon, but not vice versa. It follows that conventional field inference

would reveal a present bias but not an endowment effect with respect to the

10-cent coupon, while the opposite would hold for the $10 coupon; thus, merely

changing the consumption value e may cause one anomaly to appear and the

other to disappear, as Proposition 6 suggests.57

9 Conclusions

When parting with an endowed good or forgoing an immediate reward, we may

find ourselves stuck thinking about what might have been — if only for a moment.

Such unproductive thoughts therefore carry an opportunity cost, which ought

to nudge a rational utility-maximizer towards keeping an endowed good and

towards immediate gratification, all else equal. While formalizing these ideas,

this paper presented a model in which cues can compel someone to consider a

particular decision that they weren’t already thinking about. In doing so, the

model provided a new and unified theoretical account of two important anomalies

in behavioral economics: the endowment effect and present bias. Relative to

the prevailing loss aversion and hyperbolic discounting models that capture the

endowment effect and present bias, respectively, the sunk decision points model

was distinguished in several ways, such as:

(i) Both anomalies were captured at once (and without requiring additional pa-

rameters). In comparison, the loss aversion model does not address present

bias, while hyperbolic discounting does not address the endowment effect.

(ii) The anomalies were traced to a common source, as both arose due to the57Avoiding the 10-cent coupon might not jibe with standard connotations of commitment —

in large part because using or receiving the coupon does not entail costly future consequences.Nonetheless, efforts to avoid the 10-cent coupon would qualify as demand for commitment andtherefore constitute “evidence” of present bias, according to conventional field inference. Toinsulate it from conventional notions involving intertemporal tradeoffs, one could argue thatthis demand for commitment has nothing to do with present bias, but instead emerges becausetime spent thinking about the coupon is more valuable than the 10-cent savings from having it.Yet this is the essence of present bias (and also the endowment effect) in the current context.Namely, commitment value is attributable to the accompanying decision opportunity costs.Even in the case of a tempting drug, to use a more traditional example, present bias likelywouldn’t just reflect the immediate distraction cost, but also the enduring drain on decision-making faculties (a more opaque form of the decision opportunity cost) with cue persistence— see Section 3.3.

28

heightened incentive to own a good when already considering the decision

to consume it. Thus, the endowment effect and present bias coexisted as

two different flavors of a unified concept. This contrasts the usual charac-

terizations of the anomalies as distinct behavioral phenomena.58

(iii) The endowment effect and present bias were both activated by cues. This

cue-activation feature fits with evidence discussed in Sections 6 and 7.

(iv) Receiving an (appropriately-timed) “auxiliary good” caused both anoma-

lies to disappear, in line with the findings that ownership of an identical

good eliminates the endowment effect and that eliciting time preferences

over sequences of outcomes eliminates present bias. In contrast, the endow-

ment effect and present bias cannot be “turned off” in the loss aversion and

hyperbolic discounting models (respectively).

(v) The sunk decision points model preserved consistent preferences. In doing

so, we saw that both the endowment effect and present bias are compatible

with consistent preferences (contrary to the mainstream view).

By preserving consistent preferences the model also depicts behavioral eco-

nomics and utility theory as closer relatives than their usual portrayal would

suggest.59 Namely, if we accept that fixed preferences is a central tenet of stan-

dard (i.e. expected and discounted) utility theories and that “fixed decision

points” is merely a convenient simplifying assumption, then the current frame-

work’s accommodation of the endowment effect and present bias suggests that

utility theory can account for some of its own “anomalies.” It may also be note-

worthy that the “missing” utility parameter used to reconcile the two anomalies

with consistent preferences was a form of opportunity cost, as it shows how a fun-

damental concept from within economics can be useful in addressing challenges

to the foundations of economic theory.

58As discussed in Section 7, there is ample evidence to support the notion that the endowmenteffect and present bias share a common basis.

59While equally relevant for riskless choice, the endowment effect is cited as evidence for theloss aversion model as an alternative to expected utility theory, the standard model of choiceunder uncertainty (von Neumann and Morgenstern, 1944). Present bias is instead regardedas the main challenge to discounted utility theory, the standard model of choice over time(Samuelson, 1937; Koopmans, 1960).

29

The preservation of consistent preferences also has normative appeal because

the appropriate criterion for welfare comparisons is simply lifetime expected util-

ity. In contrast, there is invariably a subjective element to welfare analysis in

leading behavioral theories in that the analyst has multiple options in choos-

ing the “correct” preferences that represent well-being. With loss aversion, this

normative ambiguity exists because both WTA and WTP could be regarded as

the welfare-appropriate measure of value; with (quasi-)hyperbolic discounting,

it is analogously open to interpretation whether or not the present bias β < 1

belongs in the discount function that maps to well-being.60 In resolving these

ambiguities, the sunk decision points approach emphasizes the distinction be-

tween whether or not the agent is already considering the consumption decision

of interest.61 If not, the appropriate welfare standard — as derived from the

benchmark lifetime expected utility — is based on WTP and omits β from the

discount function, which fits with the associated literatures’ tendencies to favor

WTP over WTA and to use exponential discounting, δt, for welfare analyses.62 If

the agent is considering the decision ex-ante, welfare calculations would instead

be based on WTA and β would be included in the discount function.

As alluded to earlier, the basic framework is amenable to some potentially

interesting extensions. Incorporating cue persistence and cue uncertainty, as en-

visioned in Section 3.3, would likely expand the model’s descriptive reach.63 It

could also be worthwhile to relax the one-to-one mapping between cues and de-60Put differently, welfare comparisons could be based on the time preferences of the “current

self” or of the “future self.” As Strotz (1956) writes in his classic treatment of time-inconsistentpreferences: “consumer sovereignty has no meaning in the context of the dynamic decision-making problem. The individual over time is an infinity of individuals, and the familiar prob-lems of interpersonal utility comparisons are there to plague us.” The normative ambiguityinherent in the loss aversion and hyperbolic discounting models is discussed in Tversky andKahneman (1991) and O’Donoghue and Rabin (1999), respectively.

61While it restores normative objectivity, the approach does introduce a complication forempirically-based welfare calculations because the analyst must now ascertain whether (orwhen) the agent is considering the relevant consumption decision.

62Knetsch (1989, 2010) and Bateman et al. (1997) discuss the use of WTP instead of WTAfor welfare calculations; the omission of β is addressed by O’Donoghue and Rabin (1999, 2003).

63Persistence and uncertainty may offer channels through which expectations can influencevaluations. In particular, if the likelihood and/or frequency with which a subject “thinks about”a good rises with the probability of obtaining it, so would the psychological “investment” in thegood, in terms of sunk decision points. While the consideration of such probabilistic settingswere outside the scope of this paper, the premise would fit with evidence that the endowmenteffect is largely a product of expectations (see Ericson and Fuster, 2011).

30

cision points. For instance, if substitute goods can trigger the same consumption

decision, the endowment effect and present bias would both be weaker for goods

with readily available substitutes, as experimental evidence discussed in Section

6.1 suggests; intuitively, a cue-induced decision point could be “salvaged” with-

out the particular good associated with the cue if a close substitute is at hand

— e.g. if receiving a pen compels the recipient to consider writing a letter, then

the loss from losing the pen could be cushioned by a readily-available pencil.

Alternatively, a single good could trigger different decisions, where the re-

alized decision point would depend on an endogenously-determined association

strength. For example, if trading a good strengthens the association between

having the good and the decision to trade it — while weakening the association

between the good and the decision to consume it — it would be expected that ex-

perience trading mitigates the endowment effect, again as experimental evidence

suggests.64 Money is an especially striking (and thorny) example of a good that

does not map to a single decision point.65 To start, different amounts of money

likely induce different decision points for the same individual — e.g. receiving $1

may induce a “candy bar” decision point, while $25,000 may induce a “new car”

decision point. Moreover, since it can be used for a wide range of consumption

activities as well as for deferred consumption via savings or investments, different

individuals likely have very different associations with money and hence different

ideas of how to spend it.

64See List (2003). Engelmann and Hollard (2010) similarly find that forcing individuals totrade an endowed good eliminates the endowment effect in subsequent tests.

65Horowitz and McConnell (2002) report that the WTA-WTP disparity is smallest in experi-ments that use some form of money. This fits with the notion that money would inflict a minordecision opportunity cost since it has many uses besides any particular consumption activity.Moreover, for liquidity-unconstrained individuals, forgoing an imminent opportunity to havemoney does not generally preclude the activity that the money would have been used for. AsFrederick et al. (2002) note, choices between money and other readily tradeable rewards inprinciple should not reveal anything about time preferences.

31

A Appendix

A.1 Proof of Proposition 1

From equation (3),

vA(e)− vP (e) = U − U [0].

Substituting U [0] = U − (1− π) from equation (1) gets the desired result.66 �

A.2 Proof of Proposition 2

Given time-zero elicitation, for received goods, the expected lifetime utilities

associated with e(τ) and Dτe(0) are, respectively,

U [0, τ ; e(τ)] = U − (1− π)− (1− π)δτ + eδτ

U [0;Dτe(0)] = U − (1− π) +Dτe.

The indifference condition is Dτe = δτ (e− (1− π)), which establishes part (i).

For non-cueing goods, the associated expected lifetime utilities are:

U [0; e(τ)] = U − (1− π) + πeδτ

U [0;Dτe(0)] = U − (1− π) +Dτe.

Now the indifference condition is Dτe = πδτe, which establishes part (ii). �

A.3 Proof of Corollary 1

Holds because e′ > e implies δτ(1− 1− π

e′)> δτ

(1− 1− π

e

). �

A.4 Proof of Proposition 3

Given the receipt of a(0), WTP for e(0) is the value with both endowments minus

the value with a(0) only, while WTA for e(0) is the value with both endowments

66To preserve the suspense for Proposition 1, this substitution — which would have madethe existence of a WTA-WTP gap trivially apparent — was not inserted into equation (3). (Inturn, Proposition 1 was formulated in a particular way to preserve the suspense for Proposition5, as discussed in Footnote 47.)

32

minus the value with a(τ) only, conditional on receipt of e(0):67

vP (e) = U [0, 0; a(0), e(0)]−U [0; a(0)] = U [0; (a+e)(0)]−U [0; a(0)] = e,

vA(e) = U [0, 0; a(0), e(0)]−U [0, 0; a(0)] = U [0; (a+e)(0)]−U [0; a(0)] = e.

Thus vA(e) = vP (e). �

A.5 Proof of Proposition 4

Given time-zero elicitation of time-preferences, the value of receiving e + a at τ

and a now versus receiving a at τ and Dτe+ a now are, respectively,

U [0, τ ; a(0), (e+ a)(τ)] = U − (1− π)− (1− π)δτ + a+ (e+ a)δτ

U [0, τ ; (Dτe+ a)(0), a(τ)] = U − (1− π)− (1− π)δτ +Dτe+ a+ aδτ .

The indifference condition is Dτe = δτe, which gives the desired result. �

A.6 Proof of Proposition 5

From equations (1), (2), and (3),

vP (e)

vA(e)=

U [0; e(0)]− UU [0; e(0)]− U [0]

= 1− 1− πe

,

which is the definition of β (for received goods) as given in Proposition 2, part

(i). �

A.7 Proof of Proposition 6

vP (e) =U [0; e(0)]− U = e− (1− π),

vC(e) =U − U [0; e(0)] = (1− π)− e = −vP (e).

67Note that since they correspond to the same period, the valuation associated with havingboth the auxiliary and primary endowments only needs one cue in its argument, i.e. a(0)and e(0) can enter U ’s argument as (a + e)(0). As with WTP, a second cue in the valuationassociated with having both endowments will be redundant in expressing WTA. Now, however,the redundancy also exists in the expression associated with relinquishing e(0). Hence, sincereceiving a(τ) assures a decision point at t = 0, conditioning on having received e(0) is irrelevantto the valuation.

33

Therefore, the sign of e− (1− π) must agree with the sign of vP (e) and disagree

with the sign of vC(e). �

A.8 Generalization to Durable Goods

Now assume the good is durable. Then the benchmark expected lifetime utility

and the expected lifetime utility with a cue at t are unchanged:

U =∞∑t=0

δt(1− π) =1− π1− δ

, U [t] = U − (1− π)δt.

The expected lifetime utility for the endowment e(τ) is now

U [e(τ)] = U +∞∑k=0

πδτ+k(1− π)ke = U +eπδτ

1− δ(1− π),

where π · (1 − δ(1 − π))−1 is the expected excess discount from the time of the

endowment to the time of its eventual consumption (i.e. at the first cue on or

after τ).

For a scenario that involves a cue at t and an endowment e(τ), the expected

lifetime utility is thus

U [t; e(τ)] =

U − (1− π)δt + eδτ if t = τ,

U − (1− π)δt +eπδτ

1− δ(1− π)if t 6= τ.

(4)

It is readily verifiable that Proposition 1, part (i) of Proposition 2, Corollary

1, and Propositions 3–6 do not need to be changed to accommodate durable

goods because they hold exactly as they did for perishable goods. For part (ii) of

Proposition 2, the result holds except we need to modify the measured present

bias factor for non-cueing goods, as it is now given by

β =π

1− δ(1− π)< 1.

This expression can be derived from the indifference condition U [0; e(τ)] =

U [0;Dτe(0)] using Equation (4). �

34

A.9 Generalization to Cue Persistence

Now assume cues induce decision points “tomorrow,” i.e. a cue in t induces a

decision point in t+ 1. This extension is nontrivial only if today’s decision point

remains uncertain, so for simplicity, assume that a cue in t does not affect the

decision point probability in t.

In this case, we now have:

U [0] = U − δ(1− π).

Therefore, as with Proposition 1, there is still a WTA-WTP disparity, except

now

vA(e)− vP (e) = U − U [0] = δ(1− π).

To show that part (i) of Proposition 2 carries over, use:

U [0, τ ; e(τ)] = U − δ(1− π)(1 + δτ ) + (π + δ(1− π))δτe,

U [0;Dτe(0)] = U − δ(1− π) + (π + δ(1− π))Dτe.

Solving for the elicited discount function from the indifference condition gives

Dτ = βδτ , as desired, where the elicited present bias factor for received goods is

now given by:

β =

(1− δ(1− π)

(π + δ(1− π))e

)< 1.

Note that β, as defined here, is increasing in e, which establishes the magnitude

effect from Corollary 1.

For part (ii) of Proposition 2, we assume τ ≥ 2 to avoid complications from

interference between the decision-point induced by elicitation and the future

endowment’s acquisition. Using the above expressions, we again get Dτ = βδτ ,

except for non-cueing goods we now have:

β =π

π + δ(1− δ)(1− π)2< 1.

For Proposition 3, as before, we have vA(e) = vP (e) = U [0; (a + e)(0)] −U [0; a(0)], so that the auxiliary good still eliminates the WTA-WTP disparity.

For Proposition 4, the indifference condition used to solve for the elicited

35

discount function is U [0, τ ; a(0), (e+ a)(τ)] = U [0, τ ; (a+Dτe)(0), a(τ)], where:

U [0, τ ; a(0), (e+a)(τ)] = U − δ(1−π)(1+δτ ) + (a+(e+a)δτ )(π+δ(1−π)),

U [0, τ ; (a+Dτe)(0), a(τ)] = U − δ(1−π)(1+δτ ) + (a+Dτe+aδτ )(π+δ(1−π)).

This implies Dτ = δτ , as desired.

Noting that the elicited present bias factor for received goods in this setting

is given by β = δ(1− π)[(π + δ(1− π))e]−1, Proposition 5 still holds because

vP (e)

vA(e)=

U [0; e(0)]− UU [0; e(0)]− U [0]

= 1− δ(1− π)

(π + δ(1− π))e.

Proposition 6 still holds because, as before, vP (e) = −vC(e).

A.10 More on the Exclusivity Requirement for a Cue

Colloquially, the emergence of an endowment effect in the current framework

rests on the premise that the overall tendency for a potential seller to “think

about” the primary consumption good after choosing to sell it is greater than

that of a potential buyer who ultimately chooses to pass on buying the good,

all else equal. The simplifying assumption that the associated decision point

probability for a potential seller is 1 while it is π < 1 for a potential buyer —

with this latter property stemming from the exclusivity requirement for a cue

(see Footnote 17) — is merely a crude, binary representation of the idea that such

a discrepancy exists. Note, the existence of present bias rests on the analogous

premise that the tendency to think about an unchosen good is greater at the

time of time-preference elicitation than at the time associated with the future

good — i.e. the extent to which a subject who chooses the immediate good is

stuck thinking about the future good is less than the extent to which a subject

who chooses the future good is stuck thinking about the immediate good.

To elaborate, it is probably true that potential buyers in the endowment

effect think about the good more than they would in the benchmark setting

because the benchmark does not include the option to buy the good — let alone

any other mention of (or reference to) the good. That said, it does not seem

plausible that mere participation as a potential buyer would be as salient of a

cue (in terms of the expected, aggregate, sunk decision opportunity costs) as

36

the “composite” cue that the potential seller is exposed to because the potential

seller physically receives the good immediately before (and in addition to) the

exchange opportunity.68 Precisely explicating the difference in the extent to

which potential sellers and buyers are “invested” (via sunk decision points) in

the primary consumption good is outside the scope of this paper and would

require drawing on notions of cue persistence and uncertainty (see Section 3.3).

That said, the fact that such a discrepancy in salience exists is sufficient to

motivate the key, qualitative results with or without the exclusivity requirement

for a cue and the other simplifying assumptions on decision point probabilities.

For instance, if the decision point probability associated with participation as

a potential buyer increases from its benchmark value to some π′ ∈ (π, 1), there

would still be an endowment effect (in which case the WTA-WTP gap would

be 1 − π′ > 0). In this light, assuming the decision point probability is π for

potential buyers while keeping it at 1 for potential sellers can be regarded as a

crude, reduced form representation — mainly intended to conserve on parameters

— of a more realistic and dynamic characterization of sunk decision points for

each type.

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