“Constructed” preferences SS200 Colin Camerer

    Preferences: “complete, transitive” u(x), tradeoffs among goods  Historical note: Axioms not empirically well-founded. They were designed to provide simple mathematical framework for aggregation (utility  demand) and because Pareto won the “what is utility?” battle “Constructed” suggests expression of preference is like problem solving:   Will you vote for John Kerry? Answered by rapid intuition (tall, good hair) and/or deliberate logic (positions on issues) Alternative views of preference:   Learned (reinforcement, “locked in a closet” story) “Discovered” (Plott, implies path-independence) Hybrid view: Combination of predisposition (e.g., language, “preparedness”), learning and logic

“Constructed” preference: effects

      Context-dependence (comparative) Description-dependent “framing (descriptions guide attention) Reference-dependence (changes, not levels; anchoring) Some values “protected”/sacred (health, environment) Is too much choice bad?

Open questions:      Are effects smaller with familiar choices? Experts? Markets?

New predictions (e.g. “big tip” labor supply experiment) Cross-species (pigeons, rats, capuchins)

Preferences and utility theory: A guide for neuroscientists Colin Camerer, Caltech

  Utility theory: numerical accounting for choices   Bundles of goods Risky and ambiguous “gambles” (EU, SEU)  Choices over time (discounted utility) Representation theorems:   Find mathematical structures that map onto (“represent”) observable choices U(x) > U(y) iff x  y numbers preferences

EU: Preferences over risk

  How do people weigh and combine likelihoods and outcomes?     Gambling Risky investment (stocks, college, mates) Insurance Social risks (terrorism, global warming) Notation: f(x) is a risk with probability f(x) of outcome x

    

Where utility theories come from

Axiomatic  Decompose representations into logical “bones”  Find sets of axioms that are mathematically equivalent to numerical representations Empirical  What mathematical functional forms fit choice data?

Evolutionary  What preference structures would have adapted? (e.g., Robson JEcLit 01, JEcPers 02) Neural  Do brain structures obey axioms?

Ideal: All four criteria should cohere

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Possible decision rules

Maximin   Choose risk with the best worst outcome f*=argmax g [min x x] Safety-first/VAR  Choose best EV with p(loss) below a threshold  f*=argmax g Σ x xg(x) subject to Σ x<0 g(x)

The rise (and fall?) of expected utility

  Why EU?

 EV-maximization Σ x xg(x) easily disproved  St. Petersburg paradox …but EU is a simple generalization of EV  Axioms:  Completeness of preference (including transitivity)   Continuity (“solvability”)  If f  g  h then there exists p such that pf+(1-p)h  g Cancellation (independence)  If f  g then pf+(1-p)z  pg+(1-p)z for all z, p>0 Axioms imply EU form U(g)=Σ x u(x)g(x)  Degree of risk-aversion: -u ’’ (x)/u ’ (x) (Arrow-Pratt)

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What’s wrong with the axiomatic approach

Axioms are useful if they are more than equivalent representations transparent Easier to judge normative content than descriptive Is generality a seductive illusion?

  Thou shalt not kill Always cancel common consequences  Always tell the truth Competing axioms are difficult to compare  E.g. independence versus betweeness if f  g then f  pf+(1-p)g  g for all 1>p>0



Cancellation is logically sensible but perceptually unnatural

Allais common consequence problem:  A: $1 M or? (.10, $5 M; .89, $1 M; .01, 0)  B: (.11, $1 M; .89,0) or? (.10,$5 M; .89,0; .01, 0)



Cancellation is logically sensible but perceptually unnatural

Allais common consequence problem:   A: $1 M or? (10, $5 M; .89, $1 M; .01, 0) B: (.11, $1 M; .89,0) or? (.10,$5 M; .89,0; .01, 0)  Majority choose $1M in A and (.10,$5M) in B  Violates EU   A pair is (.11,$1M) or (.10,$5M) with common (.89,$1M) B pair is (.11,$1M) or (.10,$5M) with common (.89,0)

 

Cancellation is logically sensible but perceptually unnatural

Allais common consequence problem:  A: $1 M or? (10, $5 M; .89, $1 M; .01, 0)   B: (.11, $1 M; .89,0) or? (.10,$5 M; .89,0; .01, 0) A’: (.11,$1M; .89, $1M) or? (.10, $5 M; .89, $1 M; .01, 0) Brain craves whole gestalts, not decompositions

Compliance with axioms often depends on unnatural representations

  58% choose C over D Sensible?  Source: Kahneman-Tversky JBus 86

   

Axioms require unnatural representations

BUT! D “first-order stochastically dominates” C (FOSD) A and B rearrange C and D to make dominance transparent KT: B chosen 100%, D chosen 42%

FOSD is only detectable if a table is constructed (or compare

CDF’s). Mas-Collel: But they would be fired!”

   

Choice is a psychological process Will depend on many factors

Description-invariance (framing, reference dependence) Actual study with n=792 docs (Harvard Med, Brigham &Women’s, Hebrew U; McNeil et al JAMA ’80s)  treatment 1 yr 5 yrs choice Surgery 10% 32% 66% 53% Radiation 0% 23% 78% 47%    treatment 1 yr 5 yrs choice Surgery 90% 68% 34%

82%

Radiation 100% 77% 22% 18% both frames 60% 40%

Choice is a psychological process

  Procedure-invariance (pref. reversal)  Prefer p-bet (.95, $4) over $ bet (.30,$16) …but price p-bet higher Context-invariance  Disappointment (across states [columns])   Regret (between choices [rows]) 1/3 1/3 1/3 A 10 0 5 B 0 5+e 10 Is regret an overadapted learning signal? (Gilovich-Medvec Olympic medalists study)

Many variants of expected utility

 Source: Camerer JRiskUnc 88, Edwards (Ed) Utility Theories, 92

Useful tool: Marschak-Machina triangle for representing 3-outcome gambles

   Outcomes x3>x2>x1 Each point is a gamble Theories dictate indifference curve shape

  EU is equivalent to   Linear indiff curves Parallel Allais common consequence effect  curves get steeper toward upper left

Different theories predict different indifference maps

Facts from experimental studies:

 Betweenness (linear indiff curves) often violated (Prelec, 90 JRU, Camerer-Ho JRU 94):  If you prefer (.34,$20k)  (.17,$30k) …should prefer (.34,$20k) to any mixture But most pick (.01,$30k.;.32,$20k)  (.32,$20k) Sensitive to compound lottery reduction though

More facts from experiments

   Violations are larger when some probabilities are low [inside the triangle]  nonlinear w(p) is crucial Animal behavior (rats) similar to humans (Kagel et al) Small effect of experimental stakes  Paying real money reduces noise, creates more significant EU violations  Source: Camerer, 95; Harless-Camerer 94 Econometrica

Prospect theory, I

   Key features:  Reference-dependence, nonlinear w(p) Nonlinear weighting of probability   Zeckhauser bullet example, 6  5 and 1  0 Inflection (sensitivity), elevation (risk attitude)   KT (’92 JRU) w(p)=p γ/ /(p γ +(1-p) γ ) 1/γ Prelec (98 E’metrica) w(p)=1/exp((ln(1/p) γ )  Large overweighting of low probabilities  γ=.7 w(1/10)=.165, w(1/100)=.05, w(1/1,000,000)=.002

Morgenstern 79 J Ec Lit:  [Like Newtonian mechanics] The domain of our axioms on utility theory is also restricted…For example, the probabilities used must be within certain plausible ranges and not go to .01 or even less to .001, then be compared with other equally tiny numbers such as .02 etc.”

Prospect theory value function: Note kink at zero and diminishing marginal sensitivity (concave for x>0, convex for x<0)

Empirical weighting functions

SEU: Ambiguity and risk

     Derive subjective (“personal”) probabilities from bets between “states” s SEU form is Σ s u(x(s))p(s) Ellsberg paradox:  p(s) cannot express both likelihood and “ weight of evidence ” or ambiguity (One) resolution: p(A)+p(not-A) < 1  P(A)/p(not-A) is likelihoood  1-p(A)-p(not-A) is reserved belief Caution: Updating given new information is tricky…

Ambiguity-aversion with knowledge questions

1. Ambiguity Aversion (with Ming Hsu et al)

   Ambiguity is uncertainty about probability, created by missing information that is relevant and could be known Does “weight of evidence”/ambiguity matter?

Longstanding debate  Savage: No  Logic overrides discomfort of not knowing   Keynes, Knight, Ellsberg, experiments: Yes Many new theories (Gilboa-Schmeidler et al)  Pessimism over sets of beliefs  Nonadditive beliefs (“missing” probability is “reserved belief”)

Historical suggestion: Distinct neural processes in ambiguity vs risk

"But if certain uncertainties in the problem were in cloudy or fuzzy form, then very often there was a shifting of gears and no effort at all was made to think deliberately and reflectively about the problem. Systematic decomposition of the problem was shunned and an over-all 'seat of the pants' judgment was made which graphically reflected the temperament of the decision maker.“ (Raiffa, 1963)

Ambiguity vs risk is important in social science     Home bias in equity markets (1-2%/yr), insurance, incomplete contracting, entrepreneurship, “rolloff” in voting, political incumbency advantage, brand loyalty, law (“not proven” in Scottish law), game theory Ambiguity-aversion  pure demand for information even if it doesn’t affect a decision  E.g. medical overtesting, “sunshine laws” in politics Inflames hindsight bias in manager-worker “agency” relationships Permits encoding bias:  US Senate Iraq report; “…led intelligence community to interpret cloud” ambiguous evidence as conclusive of a WMD program…”; Bush: “it might come in the form of a mushroom

Ambiguity-aversion as emotion-driven pessimism     Risk case:  P(red)=P(blue)=.5

Ambiguous case      w(red)=w(blue) but don’t add to 1 1-w(red)-w(blue) is “reserved belief” …a “vigilance” signal expressed by limbic system?

Bet on red is valued    w(red)u($10)= P(red)u($10) - [P(red)-w(red)]u($10) risky part pessimism look for neural dissociation Measure strength of ambiguity aversion by w(red)=P(red) γ γ>1 ambiguity-aversion, γ=1 neutrality γ  Logit “softmax” model P(bet red>x)=1/(1+exp[λ*[x ρ -10 ρ P(red) γ ]])

      Description dependent “framing” (descriptions guide attention) Analogy to figure-ground in perception Actual study with n=792 docs (Harvard Med, Brigham &Women’s, Hebrew U; McNeil et al JAMA ’80s)  treatment 1 yr 5 yrs choice Surgery 10% 32% 66% 53% Radiation 0% 23% 78% 47%  treatment 1 yr 5 yrs Surgery 90% 68% 34% Radiation 100% 77% 22% choice both frames 82% 60% 18% 40%     Asian disease problem (-200 vs (1/3) of -600 / +400 vs (2/3) 600 Pro-choice vs pro-life Politics: “spin” (Lakoff)    e.g. aren’t we better off w/ Hussein gone? Liberation vs. occupation …other examples? Supply-side response: Competitive framing; which frame “wins”?

Some new frontiers

     Animal model  Animals exhibit all EU violations humans do Field studies Imagined vs. learned probabilities (Erev, Weber et al Psych Sci) Emotion and nonlinear w(p) (Hsee Rottenstreich Psych Sci) Neural foundations

Prospect theory, I

  Key features:  Reference-dependence, nonlinear w(p) Reference-dependence   Extension of psychophysics (e.g. hot-cold) U(x-r)  U(.) “reflects” (gamble over losses)  Loss-aversion  Q: Is loss-aversion a preference or a forecasting mistakes (underestimates emotional “immunity” a la Tim Wilson-Dan Gilbert)?

Loss-aversion in savings decisions (note few points with y-axis actual utility <0) Chua & Camerer 03 -50

Actual Utility Vs Optimal Utility

-30 50 40 30 20 10 0 g 10 -20 -30 -40 -50

Optimal Utility Gains/Losses

Data Points Jack Knife Regression 30 50

Reference-dependence modelling (Koszegi-Rabin, 05)    Two problems in prospect theory:   Is v(c-r) the only carrier of utility? Probably not… How is r “chosen”? Perceptual? Expectations? How are expectations chosen? KR solution    U(c|r)= m(c)+µ(m(c)-m(r)) and “surprise” utility separable into consumption For distributions F, F*=argmax F ∫ c u(c|r)dF(c) For reference distribution G, F*=argmax F ∫ c ∫ r u(c|r)dF(c)dG(r) Axioms:       A0: µ(x) continuous, twice differentiable (for x≠0), µ(0)=0 A1: µ(x) strictly increasing (µ’(x)>0) A2: If y>x>0, then µ(y)+µ(-y)<µ(x)+µ(-x)  (convexity of disutility is weaker than concavity of utility) A3: µ’’(x)≤0 for x>0 and µ’’(x)≥0 for x<0 A3’: For all x≠0, µ’’(x)=0 A4: lim x-->0 µ’(-|x|) / lim x-->0 (reflection effect) (piecewise linear utility) µ’(|x|) = λ > 1 (coef. of loss-aversion)

Economic domain Instant endowment effects for goods Choices over money gambles Asymmetric price elasticities for consumer product increases & decreases Loss-aversion for goods relative to money Loss-aversion relative to initial seller “offer” Reference-dependence in two-part distribution channel pricing Aversion to losses from international trade Surprisingly few announcements of negative EPS and negative year-to-year EPS changes Disposition effects in housing Disposition effects in stocks Disposition effects in stocks Daily income targeting by NYC cab drivers Equity premium puzzle Consumption: Aversion to period utility loss citation(s) Type of data Kahneman-Knetsch-Thaler (1990) Kahneman and Tversky (1992) Putler (1992), Hardie-Fader Johnson (1993) Bateman et al (2004) ADD NAMES Chen, Lakshminarayanan, Santos (2005) Ho-Zhang (2005) Field data (survey), goods experiments Choice experiments Supermarket scanner data Choice experiments Capuchin monkeys trading tokens for stochastic food rewards Bargaining experiments Estimate λ 2.29

2.25

2.40, 1.63

1.30

2.70

2.71

Tovar (2005) DeGeorge, Patel and Zeckhauser (1999) Genesove & Mayer (2001) Odean (1998) Weber and Camerer (1999) Camerer-Babcock Loewenstein-Thaler (1997) Benartzi-Thaler (1997) Chua and Camerer (2004) Non-tariff trade barriers, US 1983 Earnings per share (EPS) changes from year to year for US firms Boston condo prices 1990-97 Individual investor stock trades Stock trading experiments Daily hours-wages observations (three data sets) 1.95-2.39

US stock returns Savings-consumption experiments

Monkey loss-aversion

    (a,b,c) means display a, then pay b or c One: stochastic dominance Two: reference dependence (risky) Three: reference dependence (riskless)

  

Reference-dependence

Sensations depend on reference points r  E.g. put two hands in separate hot and cold water, then in one large warm bath  Hot hand feels colder and the cold hand feels hotter Loss-aversion ≡ -v(-x) > v(x) for x>0 (KT 79)  Or v’(x)| + < v’(x) | …a “kink” at 0; “first-order risk aversion” aka focussing illusion?

Requires theory of “mental accounting”  What gains/losses are grouped together?

  When are mental accounts closed/opened?

Conjecture: time, space, cognitive boundaries matter  Example: Last-race-of-the-day effect (bets switch to longshots to “break even”, McGlothlin 1956)

Reference-dependence modelling (Koszegi-Rabin, 05)    Prop 1: If µ satisfies A0-A4, then “reference point preference” follows  (If A3’), then for F and F’, U(F|F’) ≥U(F’|F’)  ≥U(F’|F) U(F|F) Big move: What is reference distribution?  Impose “personal equilibrium”: r=F*   Pro: Ties reference point to expected actions Con: If µ(x) is a “prediction error” designed for learning, r=F* means there is nothing to learn Implication: Can get multiple equilibria (buy if you plan to buy, don’t buy if you don’t)  Role for framing/advertising etc. in choosing an equilibrium (supply side response)

Endowment effects (KKT JPE ’90)

KKT “mugs” experiment (JPE ‘90)

Reference-dependence and endowment effects

  Koszegi-Rabin applied to pens (x p ), $ (x d ) Utility is direct plus “transition utility” t(.)

u

(

x p

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x d

;

y p

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y p

if

y p y p

  0 , 0 ,  ω is weight on ref-dependent utility, λ is strength of loss-aversion

  

Endowment effects analysis

Choosing (choice-equivalent P c )  Reference points r(p)=r(d)=0   U(gain pen)=b+ωb U(gain P c )= P c + ωP c Equating gives P c =b Selling (selling price P s )  Reference points r(p)=b, r(d)=0    U(“lose” pen, gain $) U(keep pen, gain 0)= b Equating gives P Buying price P b = s =

b

( 1 1 

b

( 1  1   )      )

P S

     

b

 1   

P S

 Prices ordered by P s >P c >P b iff λ, ω>0

Plott-Zeiler review

Data from young (PCC) and old (80 yr olds) using PZ instructions (Kovalchik et al JEBO in press 04)

Plott-Zeiler (AER 05) results: replication (top) vs mugs-first (bottom)

“Status quo bias” and defaults in organ donation (Johnson-Goldstein Sci 03)

Disposition effects in housing (Genesove and Mayer, 2001)     Why is housing important? It's big:  Residential real estate $ value is close to stock market value.

It’s likely that limited rationality persists      most people buy houses rarely (don't learn from experience). Very emotional ("I fell in love with that house"). House purchases are "big, rare" decisions -- mating, kids, education, jobs Advice market may not correct errors buyer and seller agents typically paid a fixed % of $ price (Steve Levitt study shows agents sell their own houses more slowly and get more $). Claim:  People hate selling their houses at a "loss" from nominal [not inflation adjusted!] original purchase price.

Boston condo slump in nominal prices

G-M econometric model

Model: Listing price L_ist depends on “hedonic terms” and m*Loss_ist (m=0 is no disposition effect) …but *measured* LOSS_ist excludes unobserved quality v_i …so the error term η_it contains true error

and

unobserved quality v_i …causes upward bias in measurement of m Intuitively: If a house has a great unobserved quality v_i, the purchase price P^0_is will be too high relative to the regression. The model will think that somebody who refused to cut their price is being loss-averse whereas they are really just pricing to capture the unobserved component of value.

Results: m is significant, smaller for investors (not owner occupants; less “attachment”?)

Cab driver “income targeting” (Camerer et al QJE 97)

Cab driver instrumental variables (IV) showing experience effect

Capuchins obey law of demand (K. Chen et al 05)

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“Arbitrary” valuations

Stock prices?

Wages (what are different jobs really worth?)  Depends on value to firm (hard to measure)  & “compensating differentials/disutility (hard to measure) Exotic new products Housing (SF  Pittsburgh tend to buy “too much house”; Simonsohn and Loewenstein 03) Exec comp'n (govt e.g. $150k for senator, vs CEO's, $38.5 million Britney Spears)

Anchored valuation: Valuations for listening to poetry framed as labor (top) or leisure (bottom) (Ariely, Loewenstein, Prelec QJE 03 and working paperhttp://sds.hss.cmu.edu/faculty/Loewenstein/downloads/Sawyersubmitted.pdf

What econ. would happen if valuations are arbitrary?

         Perfect competition  price=marginal cost…anchoring influences quantity, not price; expect large Q variations for similar products Attempts to influence the anchor (QVC home shopping, etc., "for you just $59.95”). Advertising!!!

If social comparison/imitation is an anchor, expect geographical, temporal, social clustering (see this in law & medical practice) E.g., CEO pay linked to pay of Directors on Board's comp'n committee. Geographical differences in housing prices, London,Tokyo, NYC, SF. Interindustry wage differentials for the same work (Stanford contracts out janitorial service so it doesn't have to pay as much; cf. airline security personnel??) Sports salaries: $100k/yr Miami Dolphins 1972 vs $10million/yr modern football Huge rise in CEO comp'n from 1990 (42 times worker wage) to 2000 (531 times); big differentials between US and Europe Consumers who are most anchorable or influenceable will be most faddish -- children and toys!!? (McDonald's happy meal etc)

1/n heuristic & partition dependence in the lab (cf. “corporate socialism”, Scharfstein & Stein, at corporate level)

Experimental markets & prob judgment              

1. Abstract stimuli vs natural events??

pro: can precisely control information of individuals can conpute a Bayesian prediction con: maybe be fundamentally different mechanisms than for concrete events...

2. Do markets eliminate biases?

Yes: specialization Market is a dollar-weighted average opinion Uninformed traders follow informed ones Bankruptcy No: Short-selling constraints Confidence (and trade size) uncorrelated with information Camerer (1987): Experience reduces pricing biases but *increases* allocation biases Contingent claims markets:

Markets enforce correct prices..BUT probability judgment influences

allocations and volume of trade (example: Iowa political markets)

 

Choice-aversion

How to model “too much choice”?    Anticipated regret from making a mistake “grass is greener”/buyer’s remorse Direct disutility for too-large choice set (e.g. too complex) Policy question:  Markets are good at expanding institution for limiting choice?  choice…what is a good Example: Bottled water in supermarkets   Limit “useless” substitution? What is the right amount? Pro-govt example: Swedish privatized social security    Offered hundreds of funds Default fund is low-fee global index (not too popular) Most popular fund is local tech, down 80% 1 st yr



Is too much choice bad?

Jams study (Iyengar-Lepper):   6 jams 24 jams 40% stopped, 30% purchased 60% stopped, 3% purchased  Assignment study:   Short list Long list 74% did the extra credit assignment 60% did the extra credit assignment     Participation in 401(k) goes down 2% for every 10 extra funds Shoe salesman: Never show more than 3 pairs of shoes… Medical  65% of nonpatients said they would want to be in charge of medical treatment…but only12% of ex-cancer patients said they would Camerer conjecture: The curse of the composite   Paraphrased personals ad: “I want a man with the good looks of Brad Pitt, the compassion of Denzel Washington…” Is there “too much” mate choice in big cities?

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IIlusions of transparency

“Curse of knowledge”

Difficult to recover coarse partition from fine-grained one Piaget example: New PhD’s teaching EA Poe, “telltale heart” Computer manuals “ The tapper” study (tapping out songs with a pencil)

Hindsight bias

Recollection of P_t(X) at t+1 biased by whether X occurred “I should have known!” “You should have known” (“ignored warning signs”) --> juries in legal cases (securities cases) implications for principal-agent relations? 

Spotlight effect (Tom Gilovich et al)

  

Eating/movies alone Wearing a Barry Manilow t-shirt



psychology: Shows how much we think others are attending when they’re not

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Some references

         Camerer 1995 Handbook Expl Econ Camerer & Harless 94 Econometrica Camerer 1989 JRiskUnc, Edwards 92 edited book Camerer World Congress Ec’ic Society 05 (avail 11/05) John Hey chapter (Kreps-Wallis book) 97 (more pro-EU) Starmer J Ec Lit 2002 John Quiggin, Duncan Luce 2000+ books Annual Rev Psych articles on decision making (Shafir LeBoeuf 2000 et al) Camerer Behavioral Game Theory , Princeton, 2003