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10/8/08 Prospect Theory Sendhil Mullainathan Economics 2030 Fall 2008 Outline of Talk • What is Prospect Theory? • Empirical Evidence for Prospect Theory • Experimental Challenges • Theoretical Work and Important Application Areas • Big Picture Observations Outline of Talk • What is Prospect Theory? • Empirical Evidence for Prospect Theory • Experimental Challenges • Theoretical Work and Important Application Areas • Big Picture Observations 1 10/8/08 What is Prospect Theory? • A collection of extremely clever experiment that illustrate a few core ideas. • So presentation of this theory will be less “theory” and more “experiment” • One of the two stalwarts of behavioral economics (present bias/hyperbolic discounting/self-control is the other) Some Evidence • [8] Choose between two bets – A : (.25 $6000) – B : (.25 $4000; .25 $2000) Some Evidence • [8’] Choose between two bets – A : (.25 -$6000) – B : (.25 -$4000; .25 -$2000) 2 10/8/08 Some Evidence • [8] Choose between two bets (N=68): – A : $6000 at 25% chance (18% chose) – B : $4000 at 25% chance and $2000 at 25% chance (82% chose) • [8’] N=64 people were asked to choose between two bets: – A : -$6000 at 25% chance (70% chose) – B : -$4000 at 25% chance and -$2000 at 25% chance (30% chose) Prospect Theory Subjects who have already been given $1000 are subsequently asked to choose either • a certain reward of $500 (84%) • or a 50% chance of earning $1000 (16%) A different sample of subjects are given $2000, and asked to choose either • a certain loss of $500 (31%) • or a 50% chance of losing $1000 (69%) • a certain reward of $1500 • a 50% chance of earning $1000 and a 50% chance of earning $2000 General Lesson • Losses vs. Gains matters • Risk seeing in losses, risk averse in gains • Losses and gains can be framed 3 10/8/08 Some Evidence • [9] (N = 152). Imagine that the US is preparing for the outbreak of an unusual Asian disease which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the programs are as follows: – A : If program A is adopted 200 people will be saved – B : If program B is adopted there is a one third probability that 600 people will be saved and a two-thirds probability that no people will be saved. • Which of the two programs would you favour? Some Evidence • [9] (N = 152). Imagine that the US is preparing for the outbreak of an unusual Asian disease which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the programs are as follows: – A : If program A is adopted 200 people will be saved (72%) – B : If program B is adopted there is a one third probability that 600 people will be saved and a two-thirds probability that no people will be saved. (28%) • Which of the two programs would you favour? Some Evidence • [10] (N = 155). Imagine that the US is preparing for the outbreak of an unusual Asian disease which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the programs are as follows: – C : If program C is adopted 400 people will die – D : If program D is adopted there is a one third probability that nobody will die and a two-thirds probability that 600 people will die. • Which of the two programs would you favour? 4 10/8/08 Some Evidence • [10] (N = 155). Imagine that the US is preparing for the outbreak of an unusual Asian disease which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the programs are as follows: – C : If program C is adopted 400 people will die (22%) – D : If program D is adopted there is a one third probability that nobody will die and a two-thirds probability that 600 people will die. (78%) • Which of the two programs would you favour? Implications • Losses and gains can be created by the framing of the question Some Evidence • [11] (N = 86). Choose between – A : 25% chance to win $240 and 75% chance to lose $760 – B : 25% chance to win $250 and 75% chance to lose $750 5 10/8/08 Some Evidence • [11] (N = 86). Choose between – A : 25% chance to win $240 and 75% chance to lose $760 (0%) – B : 25% chance to win $250 and 75% chance to lose $750 (100%) • In Problem [11] it is easy to see that option B dominates A, and all respondents chose accordingly. Some Evidence • [12] (N = 150). Imagine that you face the following pair of concurrent decisions. First examine both decisions, then indicate the options you prefer: – Decision (i). Choose between: • C: A sure gain of $240 • D: 25% chance to gain $1000 and 75% chance to gain nothing – Decision (ii). Choose between: • E: A sure loss of $750 • F: 75% chance to lose $1000 and 25% chance to lose nothing Some Evidence • [12] (N = 150). Imagine that you face the following pair of concurrent decisions. First examine both decisions, then indicate the options you prefer: – Decision (i). Choose between: • C: A sure gain of $240 (84%) • D: 25% chance to gain $1000 and 75% chance to gain nothing (16%) – Decision (ii). Choose between: • E: A sure loss of $750 (13%) • F: 75% chance to lose $1000 and 25% chance to lose nothing (87%) 6 10/8/08 Implications • Losses loom larger than gains • Value function implied – Concave in gains – Convex in domain of losses – Loss curve around zero is steeper than gain curve The Hypothetical Value Function Value Concave in gains Loss curve steeper than gains Losses Gains Convex in losses Beliefs in Prospect Theory The Creation of Decision Weights From Probabilities 7 10/8/08 Beliefs in Prospect Theory • EU: Probabilities enter linearly • Prospect theory: Probabilities enter as “decision weights” by means of a function Some Evidence • [1] Consider the following choice put to N = 66 people: – A : $6000 at .45 chance [EV = 2700] – B : $3000 at .90 chance [EV = 2700] Some Evidence • [1] Consider the following choice put to N = 66 people: – A : $6000 at .45 chance [EV = 2700] (14% chose) – B : $3000 at .90 chance [EV = 2700] (86% chose) 8 10/8/08 Some Evidence • [1] Consider the following choice put to N = 66 people: – A : $6000 at .45 chance [EV = 2700] (14% chose) – B : $3000 at .90 chance [EV = 2700] (86% chose) • [1’] Now consider the following problem put to N = 66 people – A : $6000 at .001 chance [EV = 6] – B : $3000 at .002 chance [EV = 6] Some Evidence • [1] Consider the following choice put to N = 66 people: – A : $6000 at .45 chance [EV = 2700] (14% chose) – B : $3000 at .90 chance [EV = 2700] (86% chose) • [1’] Now consider the following problem put to N = 66 people – A : $6000 at .001 chance [EV = 6] (73% chose) – B : $3000 at .002 chance [EV = 6] (27% chose) Some Evidence • [2] Consider the following choice put to N = 72 people: – A : 5000 at .001 chance [EV = 5] (72% chose) – B : 5 at 1 (certainty) [EV = 5] (28% chose) • [2’] Also consider the following choice put to N = 72 people – A : -5000 at .001 chance [EV = -5] (17% chose) – B : -5 at 1 (certainty) [EV = -5] (83% chose) 9 10/8/08 Evidence for Certainty Effect • [3] Zeckhauser asked respondents to imagine that they were forced to play Russian Roulette. However, in this game they were given the opportunity to purchase one bullet from the loaded gun. The respondents were asked – [A] How much they would be willing to pay for the chance to reduce the number of bullets from four to three – [B] How much they would be willing to pay for the chance to reduce the number of bullets from one to zero? • Most respondents were willing to pay much more for [B] the reduction of the chance of death from 1/6 to zero than for [A] the chance to reduce the probability of death from 4/6 to 3/6 More Evidence • [4] Consider the following two stage game put to N = 85 people. In the first stage there is an 85% chance to end the game without winning anything, and a 25% chance to move to the second stage. If you reach the second stage, you have a choice between: – A : a sure win of $30 [EV = 30] (74% chose) – B : 80% chance to win $45 [EV = 36] (26% chose) • Your choice must be made before the game starts, i.e., before the outcome of the first stage is known. More Evidence • [4] Consider the following two stage game put to N = 85 people. In the first stage there is an 85% chance to end the game without winning anything, and a 25% chance to move to the second stage. If you reach the second stage, you have a choice between: – A : a sure win of $30 [EV = 30] – B : 80% chance to win $45 [EV = 36] • Your choice must be made before the game starts, i.e., before the outcome of the first stage is known. 10 10/8/08 More Evidence • [5] Consider a problem put to N = 81 people. Which of the following options do you prefer? – C : 25% chance to win $30 [EV = 7.5] – D : 20% chance to win $45 [EV = 9] More Evidence • [5] Consider a problem put to N = 81 people. Which of the following options do you prefer? – C : 25% chance to win $30 [EV = 7.5] (42%) – D : 20% chance to win $45 [EV = 9] (58%) Non-monetary evidence of certainty effect • [6] N=72 people asked to choose between – A : 50% chance to win a three week tour of England, France and Italy (22% chose) – B : A one-week tour of England with certainty (78% chose) • [6’] N=72 people asked to choose between – C : 5% chance to win a three week tour of England, France and Italy (67% chose) – D : A 10% chance of a one-week tour of England (33% chose) 11 10/8/08 Undervaluing intermediate probabilities • [7] Suppose you are considering buying insurance against flooding, but are hesitating because of the high premiums. Your friendly insurance agent comes with an alternative offer. You can have the insurance at less than half the premium and you will be fully covered if the flood takes place on an even numbered day, but not covered at all if the flood takes place on an odd numbered day. Would you take this revised offer? • Most people reject this offer of probabilistic insurance Hypothetical Probability Weighting Function 1.0 1. Discontinuity (Certainty Decision Effect) Weight: 2. Underwighting (p) Intermediate probabilities .5 3. Overweighting Very small probabilities .5 1.0 Stated Probability: p Summary of Prospect Theory • Editing phase – Organizes options into relevant values, reference points and probabilities. Bracketing • Evaluation phase – Maps real probabilities of bracketed prospect to subjective “decision weights” through a “ ” function – Maps objective “values” into a function defined in terms of losses and gains from reference point – Choose the prospect of highest value 12 10/8/08 Editing Operations • Coding as gain or loss – People normally perceive outcomes as “gains” or “losses”. The decision as to whether a gain or loss is involved in a prospect depends on the reference point, which the statement (“framing”) of prospect can affect – Ex: 50/50 chance to gain 100 or lose 100 versus nothing? • Segregation – Riskless components of a prospect are segregated from risky components • Simplification – Complex prospects are simplified to more manageable prospects • These are by far the weakest part of prospect theory. Summary of Prospect Theory • Value Function – Losses vs. gains – Risk averse in gains; risk seeking in losses – Loss aversion • Probability weighting function – Certainty effect – Underweighting intermediate probability – Overweighting very small probabilities • Bracketing matters – Value function: Narrow bracketing and framing of reference points – Weighting function: pooling of events and p vs. 1-p More Evidence • Endowment Effect • Risk aversion in small gambles • Mental Accounting 13 10/8/08 Kahneman-Knetsch-Thaler • Observed numerous experiments showed willingness to pay-willingness to accept disparity in survey questions. Experiment • Subjects given tokens or not with valuations – Each owner and non-owner provided willingness to pay/accept. – Demand and supply curves mapped out. Market clearing price determined. Transactions implemented • Half subjects given mugs – All examined mug, either own or neighbors • Again, market set. • How many trades do you expect? 14 10/8/08 A Gamble • What X makes you indifferent between (1, $X) and (.5 $0; .5 $20) Interpreting this • Expected utility theory .5Eu(w + 20) + .5Eu(w) = Eu(w + x) – What do you expect x to be? • Prospect Theory. Could be: .5v(20) + .5v(0) = v(x) – Why do I write “could be”? • Rabin’s calibration theorem 15 10/8/08 Source : M. Rabin and R.H.Thaler (2001), Anomalies- Risk Aversion, Journal of Economic Perspectives, pages 219-232 Rabin’s Calibration Theorem • Intuition – Use concavity to force the utility function to get flatter and flatter – Key is that you turn down the bet at many wealth levels Mental Accounting • This illustrates importance of bracketing • Mental accounting investigates at greater length. – Framing is not just about losses/gains – It is also about which gambles are segregated or integrated – Elusive editing module of prospect theory 16 10/8/08 Multiattribute Problem • [13] N=88. Imagine that you are about to purchase a jacket for $125 and a calculator for $15. The calculator salesman informs you that the calculator that you wish to buy is on sale for $10 at another branch of the store, located 20 minutes drive away. Would you make a trip to the other store? • 68% said “Yes” Multiattribute problem • [13’] N=93. Imagine that you are about to purchase a jacket for $125 and a calculator for $15. The jacket salesman informs you that the jacket that you wish to buy is on sale for $120 at another branch of the store, located 20 minutes drive away. Would you make a trip to the other store? • Only 29% of N=93 respondents were willing to drive to the other store to save $5 on as $120 jacket Interpreting in Prospect Theory • Implied Coding • Costs t to save s v g (g) + v$ ( p) compared to v g (g) + v$ ( p + s) + v t ( t) 17 10/8/08 Which Account? • [14] N = 200. Imagine that you have decided to see a play and paid the admission price of $10 per ticket. As you enter the theatre, you discover that you have lost the ticket. The seat was not marked and the ticket cannot be recovered. • Would you pay $10 for another ticket? Which Account? • [14] N = 200. Imagine that you have decided to see a play and paid the admission price of $10 per ticket. As you enter the theatre, you discover that you have lost the ticket. The seat was not marked and the ticket cannot be recovered. • Would you pay $10 for another ticket? • Yes (46%). No (54%) Which Account?, ctd • [14’] N = 183. Imagine that you have decided to see a play where admission is $10 per ticket. As you enter the theatre, you discover that you have lost a $10 bill. • Would you still pay $10 for a ticket for the play? • Yes (88%). No (12%). 18 10/8/08 Which Account?, ctd • [14’] N = 183. Imagine that you have decided to see a play where admission is $10 per ticket. As you enter the theatre, you discover that you have lost a $10 bill. • Would you still pay $10 for a ticket for the play? Why might this be happening? • Conjecture Lost ticket v g ( play 20) vs v$ ( 10) Lost money v g ( play 10) + v$ ( 10) vs v$ ( 10) Outline of Talk • What is Prospect Theory? • Empirical Evidence for Prospect Theory • Experimental Challenges • Theoretical Work and Important Application Areas • Big Picture Observations 19 10/8/08 Empirical Evidence • Labor Markets • Asset markets • Some examples of framing Card Hyslop Taxi Cab Drivers Camerer Babcock Lowenstein Thaler 20 10/8/08 Taxi Cab Drivers Taxi Cab Driver Controversy • Fail to find it for hot dog vendors in stadium • Farber’s reanalysis of other cab driver data finds weak evidence • What to think of the former? – Latter is easy to understand Field • Law School Students • Lottery to receive financial aid – Winners receive tuition assistance • Must repay if they do not go into public interest law – “Losers” receive loan • Waived if they go into public interest law 21 10/8/08 Labor Markets • Under-explored – Ex: Do people search differently given their last wage might be a reference wage? – Do incentive/promotion schemes take into account features of loss aversion? Bonuses? 22 10/8/08 Odean • Looks for direct evidence of prospect theory in asset markets • In investor behavior. • How do they buy or sell stocks? 23 10/8/08 Other asset markets • Genesove-Mayer examine housing markets Interpretation • Higher loss means higher selling price • Other Facts – Higher loss means longer time to sell – But also higher sales price – Interesting aside: Implied return on waiting pretty high 24 10/8/08 Outline of Talk • What is Prospect Theory? • Empirical Evidence for Prospect Theory • Experimental Challenges • Theoretical Work and Important Application Areas • Big Picture Observations List’s Experiment • Baseball Card Show – Dealers and non-dealers • Give them card A or card B (randomly) – Examine willingness to switch List 25 10/8/08 Interpretation • Does experience remove loss aversion? • Observations: – 95% of the subjects kept the final good. Why is this odd? – Note what prospect theory says Keep B if v(A) + v( B) < 0 Keep A if v(B) + v( A) < 0 – Do you see a different way to explain the List effect? – How to reconcile with Odean? Outline of Talk • What is Prospect Theory? • Empirical Evidence for Prospect Theory • Experimental Challenges • Theoretical Work and Important Application Areas • Big Picture Observations Theoretical Work • Careful application of prospect theory • Where do reference points come from? 26 10/8/08 Odean Revisited • Barberis and Xiong Stock drops in price v( pcurrent p purchase ) – Why does selling affect this? – Ask whether utility only happens at realization • Notice centrality of bracketing Consumption Model • Simple Euler equation • What if there are multiple assets? • How do we convert this to equity pricing? Equity pricing model 27 10/8/08 Calibrating this model • Mehra Prescott, 1890-1979 – Rate of return on equity is about .06 – Std dev of consumption growth: .036 – Std dev of stock market: .167 – Correlation: .40 – Covariance: .0024 • Implies: =25 Benartzi Thaler • Investors invest in stocks and bonds • Observe performance of portfolio in time intervals • Loss averse investors • What is the implication of variance now? – Does it depend on frequency of observation? • How different is this from traditional risk? • Notice relation to Barberis and Xiong’s point 28 10/8/08 Interesting findings • At around evaluation of year, stock and bond roughly equal – At existing equity premium. Barberis-Huang-Santos • Observe that in calibrations this is not enough – BT is not an equilibrium model. – Does not produce enough stock return volatility. • How to price risk in even more? Barberis Huang Santos • Standard utility function in consumption • Utility over wealth – Defined over current gains/losses (X) – Impact of S, wealth, relative to lagged reference points captured in z. Allows changing reference points (mental accounting) – Key feature: Wealth movements matter independent of consumption • Show they can calibrate such a model to explain equity premium. 29 10/8/08 Koszegi Rabin • Reference Points Koszegi Rabin Koszegi Rabin • How are reference points selected? • Rational expectations – Lottery over choice sets – Individuals forecast what they would choose in each choice set – This forecast sets the reference point 30 10/8/08 Koszegi Rabin Koszegi-Rabin • Implications: – Multiple personal equilibria – Stochastic price decrease can decrease sales – Loss aversion may not manifest itself in some market cases • Note that this is already a prediction of PT. But it was a vague prediction • Observations: – How to think about nominal wage rigidity? – Does this explain List’s experiment? Outline of Talk • What is Prospect Theory? • Empirical Evidence for Prospect Theory • Experimental Challenges • Theoretical Work and Important Application Areas • Big Picture Observations 31 10/8/08 Big Picture Observations • Notice less work on framing • Notice centrality of reference points – Empirical work – Theoretical conceptualization • Notice centrality of bracketing – Very little understood theoretically or empirically – Experimental work has been hard going 32

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