Prospect Theory

Document Sample
Prospect Theory Powered By Docstoc
					                                           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

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:25
posted:10/10/2011
language:English
pages:32