Prospect Theory

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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

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

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

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

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. lotteries (51.2K, 1) and (50K, 1/2; 100K, 1/2) should be equivalent Since stocks have negative returns more often than bonds, this can be explained with the loss aversion.

Prospect Theory, 27 of 44 Prospect Theory Empirical Evidence Finance The Disposition Eﬀect (Shefrin and Statman 1985)

Individuals hold stock that have lost value too long and are eager to sell stocks that have gained value following the standard theory, price expectation should drive this choice trading volumes for stocks that have fallen in price is lower than for stocks that have risen in a field experiment from a brokerage firm investors held losing stocks a median of 124 days and held winners only 104 days a similar effect exists in the housing market: when the house price falls the volume of the sales fall as well.

Prospect Theory, 28 of 44 Prospect Theory Empirical Evidence Finance The Disposition Eﬀect: Finance (Odean (JF, 1998))

Do investors sell winning stocks more than losing stocks? Individual trade data from Discount brokerage house (1987-1993) Share of realized gains: RealizedGains PGR = (2) RealizedGains + PaperGains Share of realized Losses: RealizedLosses PLR = (3) RealizedGains + PaperGains

Prospect Theory, 29 of 44 Prospect Theory Empirical Evidence Finance The Disposition Eﬀect, Odean (JF, 1998))

PGR and PLR for the Entire Data Set This table compares the aggregate Proportion of Gains Realized ~PGR! to the aggregate Pro- portion of Losses Realized ~PLR!, where PGR is the number of realized gains divided by the number of realized gains plus the number of paper ~unrealized! gains, and PLR is the number of realized losses divided by the number of realized losses plus the number of paper ~unrealized! losses. Realized gains, paper gains, losses, and paper losses are aggregated over time ~1987– 1993! and across all accounts in the data set. PGR and PLR are reported for the entire year, for December only, and for January through November. For the entire year there are 13,883 realized gains, 79,658 paper gains, 11,930 realized losses, and 110,348 paper losses. For December there are 866 realized gains, 7,131 paper gains, 1,555 realized losses, and 10,604 paper losses. The t-statistics test the null hypotheses that the differences in proportions are equal to zero assuming that all realized gains, paper gains, realized losses, and paper losses result from independent decisions.

Entire Year December Jan.–Nov.

PLR 0.098 0.128 0.094 PGR 0.148 0.108 0.152 Difference in proportions -0.050 0.020 -0.058 t-statistic -35 4.3 -38

Prospect Theory, 30 of 44 Prospect Theory Empirical Evidence Finance The Disposition Eﬀect, Odean (JF, 1998))

Prospect Theory, 31 of 44 Prospect Theory Empirical Evidence Economic Development Mental Accounting eﬀects For the Poor (Bertrand, Mullainathan, Shaﬁr. 2004

Money is not fungible Liquidity, current account , assets are perceived differently Differential marginal propensities to consume (MPC) current income (where MPC is high), current assets (where MPC is intermediate), future income (where MPC is low). Consumption functions thus end up being overly dependent on current income, Importance to induce poor people to open a saving account Savings, help investments and efficiently smooth consumptions

Prospect Theory, 32 of 44 Prospect Theory Empirical Evidence Housing Markets Loss Aversion in the Housing market (Genesove-Mayer , 2001)

For houses sales, natural reference point is previous purchase price, P0 Loss Aversion: Unwilling to sell house at a loss

General Prediction, when aggregate prices are low Higer prices P relative to fundamentals

Bunching at purchase price P0 Lower probability of sale p(P) Longer waiting on market

Prospect Theory, 33 of 44 Prospect Theory Empirical Evidence Housing Markets Loss Aversion in the Housing market (cont’d)

Listing price Li,t

Lossi,t = Pˆi.t − P0 Pˆ is the real market value (estimated) Listing price increases with the Loss

Prospect Theory, 34 of 44 Prospect Theory Empirical Evidence Housing Markets Loss Aversion in the Housing Market (cont’d)

LOSS AVERSION AND LIST PRICES DEPENDENT VARIABLE: LOG (ORIGINAL ASKING PRICE), OLS equations, standard errors are in parentheses.

(1) (2) (3) (4) (5) (6) All All All All All All Variable listings listings listings listings listings listings

LOSS 0.35 0.25 0.63 0.53 0.35 0.24 (0.06) (0.06) (0.04) (0.04) (0.06) (0.06) LOSS-squared -0.26 -0.26 (0.04) (0.04) LTV 0.06 0.05 0.03 0.03 0.06 0.05 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) Estimated 1.09 1.09 1.09 1.09 1.09 1.09 value in (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) 1990 Estimated 0.86 0.80 0.91 0.85 price index (0.04) (0.04) (0.03) (0.03) at quarter of entry Residual from 0.11 0.11 0.11 last sale (0.02) (0.02) (0.02) price Months since -0.0002 -0.0003 -0.0002 -0.0003 -0.0002 -0.0003 last sale (0.0001) (0.0001) (0.0001) (0.0001) (0.0001) (0.0001) Dummy No No No No Yes Yes variables for quarter of entry Constant -0.77 -0.70 -0.84 -0.77 -0.88 -0.86 (0.14) (0.14) (0.13) (0.14) (0.10) (0.10) R2 0.85 0.86 0.86 0.86 0.86 0.86 Prospect Theory, 35 of 44Number of 5792 5792 5792 5792 5792 5792 observations

Prospect Theory Empirical Evidence Housing Markets Eﬀect of the experience and loss Aversion

(1) (2) (3) (4) All All All All Variable listings listings listings listings

LOSS x owner-occupant 0.50 0.42 0.66 0.58 (0.09) (0.09) (0.08) (0.09) LOSS x investor 0.24 0.16 0.58 0.49 (0.12) (0.12) (0.06) (0.06) LOSS-squared x owner-occupant -0.16 -0.17 (0.14) (0.15) LOSS-squared x investor -0.30 -0.29 (0.02) (0.02) LTV x owner-occupant 0.03 0.03 0.01 0.01 (0.02) (0.02) (0.01) (0.01) LTV x investor 0.053 0.053 0.02 0.02 (0.027) (0.027) (0.02) (0.02) Dummy for investor -0.02 -0.02 -0.03 -0.03 (0.014) (0.01) (0.01) (0.01) Estimated value in 1990 1.09 1.09 1.09 1.09 (0.01) (0.01) (0.01) (0.01) Estimated price index at quarter of 0.84 0.80 0.86 0.82 entry (0.05) (0.04) (0.04) (0.04) Residual from last sale price 0.08 0.08 (0.02) (0.02) Months since last sale -0.0002 -0.0003 -0.0001 -0.0002 (0.0002) (0.00015) (0.0001) (0.0001) Constant -0.80 -0.76 -0.86 -0.84 (0.16) (0.16) (0.14) (0.16) R2 0.85 0.85 0.86 0.86 Number of observations 3687 3687 3687 3687

Prospect Theory, 36 of 44 Prospect Theory Empirical Evidence Labor Market New York Cab Drivers (Camerer, Babcock, Loewenstein and Thaler, 1997)

cab drivers in New York lease their cabs for a ﬁxed fee for up to 12 hours They work long hours when there is low demand (sunny days) and short hours when there is high demand (rainy days) The standard theory would predict the opposite This is consistent with the loss aversion of cab drivers ﬁx a daily target and are averse to fall short of it. Inexperienced drivers feature this behavior more than experienced ones

Prospect Theory, 37 of 44 Prospect Theory Empirical Evidence Labor Market New York Cab Drivers (Camerer, Babcock, Loewenstein and Thaler, 1997)

Prospect Theory, 38 of 44FIGURE I Hours-Wage Relationships Prospect Theory Empirical Evidence Domestic Violence Domestic Violence (Card and Dahl, QJE 2011))

Consider a man in conﬂicted relationship with the spouse What is the eﬀect of an event such as the local football team losing or winning a game? With probability h the man loses control and becomes violent Assume h = h(u) with h0 < 0 and u the underlying utility Denote by p the ex-ante expectation that the team wins

Prospect Theory, 39 of 44 Prospect Theory Empirical Evidence Domestic Violence Implication from Reference dependent utility)

The more a win is expected, the more a loss is costly in terms of utility, the more likely it is to trigger violence The (positive) eﬀect of a gain is higher the more unexpected (lower p)

Prospect Theory, 40 of 44 Prospect Theory Empirical Evidence Domestic Violence Data)

Domestic violence (NIBRS) Football matches by State Expected win probability from Las Vegas predicted point spread Separate matches into Predicted win (+3 points of spread) Predicted close Predicted loss (-3 points)

Prospect Theory, 41 of 44 Prospect Theory Empirical Evidence Domestic Violence Results

Prospect Theory, 42 of 44 Prospect Theory Empirical Evidence Domestic Violence Results

Unexpected loss increases domestic violence No effect of expected loss No effect of unexpected win, if anything increases violence Effect disappears within a few hours of game end – Emotions are transient

Prospect Theory, 43 of 44 Prospect Theory Summary

Summary

Main departures from EU theory Prospect Theory can accommodate most of them several applications Finance Labor Market Economic Development Housing Market Domestic Violence

Prospect Theory, 44 of 44