Expectation-Based Reference-DependentPreferences

Rosario Macera

November, 2010

Motivation

Ï Outcome assessments depend on contrasts with a referencepoint, where losses resonate more than same sized gains(Kahneman and Tversky (1979) Prospect Theory).

Ï What is the reference point?

Ï Candidates:

1. Status Quo or Endowment (PT)2. Aspiration/Goals3. Social Comparison4. Expectations

Ï Kőszegi and Rabin (2006,2007,2009) model this last idea.

Basic IdeaKőszegi and Rabin (2006)

Ï The reference point corresponds to the agent’s recentexpectations about the relevant outcomes.

Ï How does the agent form expectations? Rationally.

Ï Three comments:

1. Model is based on PT2. As close to the mainstream as possible.3. Consequentialist evaluation

Outline

I The Kőszegi and Rabin (2006) model

II Indirect evidence

III Direct evidence

IV Theoretical Applications: Pricing, Contracts, Auctions andSocial Preferences

I. The ModelThe Utility Function

Ï Agent’s utility flow out of consumption c for a given (fixed)reference point r is

u(c)︸︷︷︸

Consumption Utility

+µ(

u(c)−u(r))

︸ ︷︷ ︸

Gain-Loss Utility

where µ(·) is the PT value function.

Ï When consumption is stochastic c ∼ F , the agent computesEU:

EU(F |r)=

∫[

u(c)+µ(

u(c)−u(r))]

dF

Ï When reference point is stochastic r ∼G , take EU again:

EU(F |G )=

∫∫[

u(c)+µ(

u(c)−u(r))]

dGdF

Ï Assume separability if consumption has several dimensions.

I. The ModelThe Reference Point and Personal Equilibrium

Ï What is G? the agent’s recent expectations about F .

Ï Agent forms those expectations rationally.

⇒ He only forms expectations he knows he will be willing tofollow ex-post.

⇒ Action must be credible

Definition

An action inducing F is a Personal Equilibrium (PE) ifEU(F |F )ÊEU(F ′|F ) for any F ′.

Ï Preferred Personal Equilibrium (PPE) is the PE thatmaximizes utility.

Ï When the agent has time to “acclimate" to her plans:

Definition

An action inducing F is a Choice-Acclimating Personal Equilibriumif EU(F |F )ÊEU(F ′|F ′) for any F ′.

The Simplest Example

Ï A risk neutral agent has been offered a lottery(0.5◦X ,0.5◦−Y ), where X >Y .

Ï He has two possible actions: accept the lottery (a) or notaccept it (na).

Ï What is his EU if he planed to accept the lottery and heexecutes his plan?

(1) If X is realized, then he gets consumption utility X .Ï Because of RE gain-loss utility is 0.5µ(X −X )+0.5µ

(

X −(−Y ))

⇒ Total utility is X +0.5µ(X +Y )> 0(2) If −Y is realized, then he gets consumption utility −Y .

Ï Because of RE gain-loss utility is0.5µ(−Y −X )+0.5(−Y − (−Y ))

⇒ Total utility is −Y +0.5µ(

− (X +Y ))

< 0

Ï His total utility is therefore:

EU(a|a)= 0.5(X −Y )︸ ︷︷ ︸

>0

+0.5[

µ(

X +Y)

+µ(

− (X +Y ))]

︸ ︷︷ ︸

<0 because of loss aversion

Ï What is his utility of deviating towards na having planned a?

EU(na|a)= 0+ [0.5µ(0−X )+0.5µ(0− (−Y ))]

= 0.5[

µ(−X )+µ(Y )]︸ ︷︷ ︸

<0

Ï Is a PE? ⇔ EU(a|a)ÊEU(na|a)Ï Not necessarily! The action a is not necessarily credible given

the expectations it generates.

Ï Notice:

1. Only one domain.2. The agent cannot affect the probability distribution.

I. The ModelSome Predictions

ClaimEquilibrium Expected Gain-Loss Utility is always negative

ClaimUnder certainty agents with expectations-based RD preferencesbehave as standard consumption utility maximizers.

There is more to “Psychology and Economics" than to BehavioralEconomics !

II.Indirect EvidenceRationalization of Puzzles in the PT literature

(1) No loss aversion on money?

Ï Budgeted spending by buyers and successful reduction ofinventory by sellers are not coded as losses (Tversky andKahneman (1991) and Novemsky and Kahneman (2005))

Ï No when money expenses are expected.

(2) How is that agents are so risk loving and so risk averse at thesame time?

Ï Kőszegi and Rabin 2007 show that agents are more willing totake risk when they have expected the risk but they are averseto risk when they have expected to insure themselves againstrisk.

(3) Agents value a lottery less than its worse outcome?

Ï Yes! Gneezy, List and Wu (2006) GLW

Ï Kőszegi Rabin (2007) show that if an agent has time to planand if gain-loss utility is sufficiently important relative toconsumption utility, an agent can choose a dominated lottery.

Ï Why? Equilibrium expected gain-loss utility is always negative!Ï These agents really dislike uncertainty!

(4) The Endowment Effect as a manifestation of loss aversion.

4.1) Does the Endowment effect exists at all?Ï Plott and Zeiler (2005, 2007): WTA and WTP gap disappears

with certain experimental procedures (practice rounds andanonymity).

⇒ Practice rounds affect the reference point: agents expect totrade and thus they don’t feel endowed with the mug.

4.2) Does experience wash away loss aversion?Ï List (2003,2004) List , Haight and List (2005) find that

experienced traders do not exhibit a WTA/WTP gap.⇒ More experienced agents expect to trade.

4.3) If the WTA and WTP gap is true, then how is that there aremarket transactions at all???!

⇒ Because usually people who engage in a market transactionexpect to trade: neither selling nor giving up on money isassessed as a loss!

(4) Labor SupplyÏ Absent income effects, labor supply is upward slopping due to

the substitution effect.Ï Camerer et al. (1997) use three data sets of hours worked and

daily earnings for New York cab drivers to test this hypothesis.They find a negative elasticity.

Ï Income Targeting: taxis drive up to they meet a daily incometarget.

Ï BUT: evidence that agents do work more when expectedincome is higher (Oettinger (1999 JPE) and Fehr and Goette(2007 AER).)

Ï The Kőszegi and Rabin model says that the distinctionbetween expected and unexpected wage increase.

Ï Farber (2005) tries to overcome the econometric problems inCamerer et al. (wage fluctuations are correlated with marginalcost of effort and division bias.)

Ï He finds that before controlling for driver fixed effects, theprobability of stopping work is significantly related to realizedincome that day. Including controls, however, the effectdisappears.

FandG

III. Direct Evidence“New York City Cabdrivers’ Labor Supply Revisited: Reference-Dependent Preferenceswith Rational-Expectations Targets for Hours and Income" Crawford and Meng (2009)

Ï Drivers have an expectation about wage and hours to work.

Ï They use sample averages as proxi for rational expectations(without including the day in question).

Ï Finding:Ï When early earnings are high, hours (but not income) has a

strong and significant effect on stopping probability; and whenthey are low this pattern is reversed.

III. Direct Evidence“Family Violence and Football: The Effect of Unexpected Emotional Cues on ViolentBehavior" (Card and Dahl, 2010)

Ï Police reports of violent incidents on Sundays during theprofessional football season in the US (NLS).

Ï 1) Home games on Sunday afternoons typically attract 25% ormore of the local television audience 2) Well organized bettingmarkets (expectations are observable!)

Ï Data on 866 games.

Ï Findings:Ï Upset losses (defeats when the home team was predicted to

win by 4 or more points) lead to a 10 percent increase in therate of at-home violence by men against their parters.

Ï In contrast, losses (defeats when the game was expected to beclose) have small and insignificant effects.

Ï Upset wins (when the home team was predicted to lose) alsohave little impact on violence as predicted by loss aversion.

Ï These are stronger in more salient games (traditional rival)

III. Direct Evidence“Expectations as Endowments: Evidence on Reference-Dependent Preferences fromExchange and Valuation Experiment" Marzilli Ericson and Fuster (2010)

Ï Endowment Effect Lab experiment where they manipulatetrading expectations directly.

Ï Endow all subjects with the same item (a mug), andrandomize the probability that they will be allowed toexchange the mug for a pen.

Ï 10 sessions, 45 subjects.

Ï Two treatments: 10% or 90% chance to be allowed toexchange.

Ï FindingsÏ 56.7% of subjects with a high probability of trading (90%)

trade if they get the chance to.Ï 22.7% of subjects with a low probability of trading (10%)

trade if they get the chance to.

III. Direct Evidence“Is Tiger Woods Loss Averse? Persistent Bias in the Face of Experience, Competition,and High Stakes" Pope and Schweitzer (2009)

Ï Study how a RP affects the golfer’s performance on PGATOUR (series of tournaments.)

Ï In each tournament, golfers attempt to minimize the totalnumber of shots they take across 72 holes.

Ï Two definitions of the RP: (1) par (the typical number of shotsa player takes to complete a hole) (2) the average score oneach hole by the entire field of golfers.

Ï Golfers who complete a hole one stroke under par shot a“birdie" and those who complete a hole one stroke over parshot a “bogie".

Ï Prediction: players choose higher effort when in the lossdomain (bogie).

Ï Finding: On average golfers make birdies 2-3% less often thanthey make bogies.

Ï A good thing: very experienced players!

III. Direct Evidence“Reference Points and Effort Provision" Abeler et al. (2009)

Ï Study how effort responds to changes in expectations aboutthe wage.

Ï Agents work on repetitive task and decide whether to stopafter each trial. With probability 0.5 they are paid a piece-rateor a fix rate.

Ï Prediction: the higher the fix wage, the longer the agents work.

Ï Main Result:Ï Fixed payment of 3 euros, subjects stop working after

accumulating 7.37 euros on average.Ï Fixed payment of 7 euros, subjects stop on average at 9.22

euros.

IV. Applications: Pricing

(1) “Competition and Price Variation when Consumers are LossAverse" Heidues and Kőszegi (2008) AER

Ï Fact: Nonidentical competitors charge identical prices (“focal"prices).

Ï Modify the Salop (1979) model of price competition withdifferentiated products by adding loss averse consumers.

Ï Main Prediction: When firms face common stochastic costs afocal-price (symmetric) equilibrium exists.

Ï Loss aversion on money: agents really dislike paying priceshigher than expected meanwhile the gain from paying lowerprices is mild.

IV. Applications: Pricing

(2) “Regular Prices and Sales" Heidues and Kőszegi (2010)

Ï Fact: Supermarkets have regular prices and sales prices.

Ï Study the a monopolist’s optimal price distribution whenselling to a loss-averse consumer.

Ï Main Prediction: Set a low price with a low probability and ahigh and sticky “regular" price with the complementaryprobability.

Ï Sale prices are set such that it is not credible for the consumernot to buy at these prices.

Ï This creates an attachment effect that makes the agent buy atthe regular price.

IV. Applications: Contracts

(1) “Binary Payment Schemes: Moral Hazard and Loss Aversion"Herweg, Müller and Weinschenk (2010) AER.

Ï Fact: Real-world contracts are much simpler than thosepredicted by the classical theory.

Ï Analyze a standard static moral hazard problem with agentswith Kőszegi and Rabin (2006) preferences.

Ï Main Prediction: Optimal contract is much simpler: involvesless uncertainty. If agent is risk neutral optimal contract isbinary.

IV. Applications: Contracts

(2) “Intertemporal Incentives Under Loss Aversion" Macera (2010)

Ï Fact: real-world contracts use delayed uncertainty to motivateagents even when they could use present uncertainty.

Ï Classical model of repeated moral hazard predicts principalshould use present and future uncertainty to motive agents.

Ï Analyze a standard dynamic moral hazard problem with agentswith Kőszegi and Rabin (2009) dynamic preferences.

Ï Main Prediction: Optimal contract defers all uncertainty to thefuture allowing the principal to pay fix wages in the present.

IV. Applications: OthersAuctions and Social Preferences

(1) “Multi-dimensional reference-dependent preferences insealed-bid auctions—How (most) laboratory experiments differfrom the field" Lange and Ratan (2010) GEB.

Ï Study first-price auctions with Kőszegi and Rabin (2006)preferences.

Ï Agents in first-price auctions overbid.

(2) “Reference-Dependent Social Preferences" Esteves-Sorensonand Macera (2010)

Ï Study whether the effect of monetary incentives depend ontheir capacity of surprising the agent.

Ï Study a principal-agent problem on a gift-exchangeenvironment whit fix wages.

Ï Develop a model of social reference-dependent preferences topredict the response of effort to surprising wage increases.

Ï Test it on the field.

:: thank you ::

“The Uncertainty Effect: When a Risky Prospect is Valued Less than its

Worse Outcome”

Gneezy, List, Wu (2006), QJE

Ï Individuals provided a maximum WTP or buying price foreither (i) a $50 gift certificate to a local bookstore; (ii) a $100gift certificate to the same local bookstore; or (iii) a lottery inwhich they were equally likely to receive either the $50 or $100gift certificate.

Ï Buying prices were elicited using an incentive-compatibleBecker, DeGroot, and Marschak mechanism: They placed asealed envelope containing a randomly determined offer y infront of each individual. Participants were told that they wouldbuy the respective prize at y if and only if xÊy.

Back to Evidence

“Does Market Experience Eliminate Market Anomalies?"John List, (2003) The Quarterly Journal of Economics

Ï Field experiment on a sport card fair.

Ï Random assignment of (same value) sports memorabilia A orB.

Ï Subjects with below-average training switch only 6.8% of thetime.

Ï Subjects with above-average training switch 46.7% of the time.

Ï Results are not due to self-selection of loss averse people intoless -experienced: following up unexperienced subjects into afuture fair, find that WTA/WTP gap decreases.

Back to EE

“Do Workers Work More if Wages Are High? Evidence froma Randomized Field Experiment"Fehr and Goette (2007) AER

Ï Field experiment on the labor supply of bike messengers whochoose how long to work within a shift.

Ï They randomly assign forty-four messengers into two groups.Each group receives a 25 percent higher commission for thedeliveries for just one month in two different months.

Ï Findings:Ï Bike messengers in the treatment group work 30% more shifts

but within each shift, they do 6% fewer deliveries.Ï To discard the effects of a convex cost of effort they measure

loss aversion in the lab.Ï Bike messengers that display loss aversion exhibit a more

negative response.

Back to Labor Supply

(Some) References

Ï Card, D and Dahl, G. “Family Violence and Football: The Effect of Unexpected

Emotional Cues on Violent Behavior" IZA Working Paper, 2010.

Ï Haigh and List “Do Professional Traders Exhibit Myopic Loss Aversion? An

Experimental Analysis" (2005) Journal of Finance.

Ï List, John“Does Market Experience Eliminate Market Anomalies?".QJE (2003)

Ï List, John “Neoclassical Theory Versus Prospect Theory: Evidence from the

Marketplace" (2004) Econometrica.

Ï Plott,C and Zeiler, K. “The Willingness to Pay-Willingness to Accept Gap, the

"Endowment Effect," Subject Misconceptions, and Experimental Procedures for

Eliciting Valuations" AER (2005).

Ï Novemsky, Nathan, and Daniel Kahneman, “The Boundaries of Loss Aversion",

Journal of Marking Research, XLII (2005), 119Ð128.

Ï Plott,C and Zeiler, K. “Exchange Asymmetries Incorrectly Interpreted as

Evidence of Endowment Effect Theory and Prospect Theory?" AER (2007).