Prospect Theory Warwick Economics Summer School Prospect Theory Eugenio Proto University of Warwick, Department of Economics July 19, 2016 Prospect Theory, 1 of 44 Prospect Theory Outline 1 General Introduction 2 The Expected Utility Theory 3 Main Departures from Expected Utility 4 Prospect Theory 5 Empirical Evidence Finance Economic Development Housing Markets Labor Market Domestic Violence 6 Summary Prospect Theory, 2 of 44 Prospect Theory General Introduction Behavioral Economics Economics and Psychology were not separated Adam Smith: The theory of Moral Sentiments Jeremy Bentham, the psychological underpinnings of Utility Francis Edgeworth, concept of envy in Utility Functions Prospect Theory, 3 of 44 Prospect Theory General Introduction Behavioral Economics, cont'd Neoclassical Revolution separated clearly Psychology and Economics Economics like a natural (and not a social) science Psychology has too unsteady foundations Utility can be defined as an ordinal (and not a cardinal) object Rejection of the hedonistic assumptions of Benthamite Utility Neoclassical economists expunged the psychology from economics Prospect Theory, 4 of 44 Prospect Theory General Introduction Behavioral Economics, cont'd Some early Criticism to the neoclassical economy from Irwing Fisher, J.M. Keynes,, Herbert Simon More from Allais (1953), Ellsberg (1961), Markowitz (1952), Strotz (1955), following the Expected Utility Theory and the discounted utility models Kahneman and Tversky (1979) on expected utility, Thaler (1981) and Loewenstain and Prelec (1992) (on discounted utility), Happiness Economics on Hedonic foundations of Utility Neuroscience looks for the bases of Individual Behavior Neuroscience gives steadier foundations to psychology Toward a unique discipline? Prospect Theory, 5 of 44 Prospect Theory The Expected Utility Theory Outline 1 General Introduction 2 The Expected Utility Theory 3 Main Departures from Expected Utility 4 Prospect Theory 5 Empirical Evidence Finance Economic Development Housing Markets Labor Market Domestic Violence 6 Summary Prospect Theory, 6 of 44 Prospect Theory The Expected Utility Theory Expected Utility Individuals generally, ceteris paribus, prefer certainty to uncertainty a prospect is a vector of probabilities and Consequences (q = (x1; p1; :::; xn; pn)) they take decision over a prospect H; p; L; (1 − p), following a utility function Eu = pu(H) + (1 − p)u(L) (1) 1 is defined Expected Utility Individuals prefer r1 = (800; 1) to r2 = (1000; 0:85; 0; 0:15) note that E(r1) < E(r2). Prospect Theory, 7 of 44 Prospect Theory The Expected Utility Theory Main Tenets of EU 1 The overall Utility of a prospect is the expected Utility, Eu 2 The Utility is defined over final wealth rather than gain and losses 3 Risk aversion: u is concave (u00 < 0) 4 Preferences are independent on the manner the prospects are described Prospect Theory, 8 of 44 Prospect Theory Main Departures from Expected Utility Outline 1 General Introduction 2 The Expected Utility Theory 3 Main Departures from Expected Utility 4 Prospect Theory 5 Empirical Evidence Finance Economic Development Housing Markets Labor Market Domestic Violence 6 Summary Prospect Theory, 9 of 44 Prospect Theory Main Departures from Expected Utility Main Departures from EU 1 Non Linear Decision Weights 2 Individuals reason in terms of loss and gains rather than final outcome 3 Loss aversion 4 Framing Effects Prospect Theory, 10 of 44 Prospect Theory Main Departures from Expected Utility Non Linear Decision Weights Expected Utility requires a linear response to variation of probability Experimentally: raising the probability from 0.39 to 0.40 has much less impact than increasing the probability from 0.99 to 1, or 0 to 0.01 (certainty effect) Prospect Theory, 11 of 44 Prospect Theory Main Departures from Expected Utility Non Linear Decision Weights: Allais Paradox Problem 1: A = (2500; 0:33; 2400; 0:66; 0; 0:01) or B = (2400; 1) Problem 2: C = (2500; 0:33; 0; 0:67) or D = (2400; 0:34; 0; 0:66) choosing B and C is not consistent with EU theory, u(2400) > 0:33u(2500) + 0:66u(2400) or 0:34u(2400) > 0:33u(2500) The second inequality is inconsistent with C > D (assume u(0) = 0) Problem 2 is obtained from Problem 1, by eliminating .66 of winning 2400 Eliminating a large chance of winning alters the ordering Prospect Theory, 12 of 44 Prospect Theory Main Departures from Expected Utility Non Linear Decision Weights: Allais Paradox; cont'd Problem 3: A = (4000;:80) or B = (3000; 1) Problem 4: C = (4000; 0:20) or D = (3000; 0:25) choosing B and C is not consistent with EU theory, Problem 4 is obtained from Problem 3, by dividing all probabilities of a positive outcome by 4 Reducing the probability of winning from 1 to .25 has a greater effect than reducing it from .8 to .2 Certainty effect Prospect Theory, 13 of 44 Prospect Theory Main Departures from Expected Utility Non Linear Decision Weights Problem 7: A = (6000; 0:45) or B = (3000; 0:90) Problem 8: C = (6000; 0:001) or D = (3000; 0:002) choosing B and C is not consistent with EU theory, Problem 8 is obtained from Problem 7, by dividing all probabilities of a positive outcome by 45 Violation of the Independence axiom With high probability of winning individuals are risk averse with low individuals are more risk seekers Prospect Theory, 14 of 44 Prospect Theory Main Departures from Expected Utility Willingness to Pay vs Willingness to Accept (Kahneman, Knetsch and Thaler 1990) Markets for: Tokens and Mugs Willingness to Pay is the maximum price an individuals want to pay a good Willingness to Accept is the minimum compensation demanded by the owner to sell a good Standard Assumptions imply that WTA ≈ WTP Prospect Theory, 15 of 44 Prospect Theory Main Departures from Expected Utility Willingness to Pay vs Willingness to Accept Market for Tokens and Mugs (6 USD) in an experiment involving the exchange of a mug (6 USD value), some individuals were endowed with a mug, some other with the money to buy this mug at a price 8.75 I will sell I will not sell at a price 8.25 I will sell I will not sell For the token: WTP = WTA for the mug the Median WTP = 2.75 and the Median WTA = 5.25 Similar Experiments were conducted with pens, folding binoculars, lottery tickets etc. Prospect Theory, 16 of 44 Prospect Theory Main Departures from Expected Utility Willingness to Pay vs Willingness to Accept Why WTA > WTP? Endowment Effect Mugs belong to sellers' endowment but not to the Buyers' endowment A manifestation of Loss aversion Prospect Theory, 17 of 44 Prospect Theory Main Departures from Expected Utility Framing Effects and status quo The EU theory implies that choices are invariant to the way options are described. An outbreak of a disease is expected to kill 600 people. Program A : 200 people will be saved (72%) Program B : 1/3 probability to save 600 people, 2/3 probability that no people will be saved (28%) Program A (reframed) : 400 people will die (22%) Program B (reframed) : 1/3 probability that nobody will die, 2/3 that no people will be saved (78%) In the first version the reference is:\everybody will die". In the second version is \nobody will die". Individuals prefer the status quo. Prospect Theory, 18 of 44 Prospect Theory Main Departures from Expected Utility Framing of Gains and Losses Decision frames: Individuals evaluates outcome separately rather than jointly Hedonic Frames: Individuals aggregate losses and segregate gains : who is happier someone who win 50 and 25 in two lotteries (64%) or someone that wins 75 in one lottery (36%)? Prospect Theory, 19 of 44 Prospect Theory Prospect Theory Outline 1 General Introduction 2 The Expected Utility Theory 3 Main Departures from Expected Utility 4 Prospect Theory 5 Empirical Evidence Finance Economic Development Housing Markets Labor Market Domestic Violence 6 Summary Prospect Theory, 20 of 44 Prospect Theory Prospect Theory Prospect Theory \Transforming" the EU theory to accommodate some of the above anomalies V = pu(x) + (1 − p)u(y) is the value function for the Expected Utility V = π(p)v(x) + (1 − π(p))v(y) where π(p) is a decision weight which reflect the overall impact of p on the value of the prospect v is a function different from utility u Prospect Theory, 21 of 44 Prospect Theory Prospect Theory Prospect Theory: the function v Individuals reason in terms of loss and gains, they are risk averse in gains and risk lovers in losses, A difference between a gain of 100 to 200 appears larger than a difference between 1100 and 1200 The difference between a loss of -100 and -200 appears larger than difference between -1100 and -1200 The effect of a change diminishes with the distance to the reference point: principle of diminishing sensitivity Hence v 00(x) < 0 for x > 0 and v 00(x) > 0 for x < 0 Prospect Theory, 22 of 44 Prospect Theory Prospect Theory Prospect Theory : the function v cont'd Prospect Theory, 23 of 44 Prospect Theory Prospect Theory Prospect Theory : the weighting function π(p) the principle principle of diminishing sensitivity applies to π(p) The natural reference for p are certainty p = 1 and impossibility p = 0 an increase of 0.1 in the probability of winning a prize has more impact when it changes to probability from 0.9 to 1 or from 0 to 0.1 than from 0.5 to 0.6 diminishing sensitivity gives rise to a weighting function π(p) concave near 0 and convex near 1 implies subadditivity for unlikely event and superadditivity near certainty Prospect Theory, 24 of 44 Prospect Theory : the weighting function π(p) Prospect Theory Empirical Evidence Outline 1 General Introduction 2 The Expected Utility Theory 3 Main Departures from Expected Utility 4 Prospect Theory 5 Empirical Evidence Finance Economic Development Housing Markets Labor Market Domestic Violence 6 Summary Prospect Theory, 26 of 44 Prospect Theory Empirical Evidence Finance The Equity Premium Puzzle (Benartzi and Thaler 1995) Stocks' returns are more volatile than bonds' returns The average return to stocks is 8% higher than the average return to bonds this would imply an unrealistically high degree of risk aversion, i.e.