econ 219b psychology and economics: applications (lecture 6)...feb 26, 2020 · auto collision...

Econ 219B

Psychology and Economics: Applications

(Lecture 6)

Stefano DellaVigna

February 26, 2020

Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 26, 2020 1 / 106

Outline

1 Reference Dependence: Full Prospect Theory

2 Reference Dependence: Insurance

3 Reference Dependence: Finance

4 Reference Points: Forward vs. Backward Looking

5 Reference Dependence: Domestic Violence

6 Reference Dependence: Endowment Effect

7 Reference Dependence-KR: Effort

8 Social Preferences Wave I: Altruism

9 Workplace Effort: Altruism


Reference Dependence: Full Prospect Theory

Section 1




Introduction

Two key features of evidence so far1 Focus not on Risk

Much of the laboratory evidence on prospect theory is on risktakingYet, field evidence considered so far (mostly) does not directlyinvolve riskHouse Sale, Merger Offer, Effort, Labor Supply, Job SearchNow consider explicitly settings with risk: insurance andfinancial choices

2 Focus on Loss Aversion exclusivelyNow examine settings where probability weighting plays roleDiminishing sensitivity also in finance


Reference Dependence: Insurance

Section 2

Reference Dependence: Insurance


Reference Dependence: Insurance Sydnor (2010)

Introduction

Sydnor (AEJ Applied, 2010) on deductible choice in the lifeinsurance industry

Menu Choice as identification strategy as in DellaVigna andMalmendier (2006)

Slides courtesy of Justin Sydnor


Dataset50,000 Homeowners-Insurance Policies

12% were new customers Single western stateOne recent year (post 2000)Observe

Policy characteristics including deductible1000, 500, 250, 100

Full available deductible-premium menuClaims filed and payouts by company

Summary Statistics

VariableFull

Sample 1000 500 250 100

Insured home value 206,917 266,461 205,026 180,895 164,485(91,178) (127,773) (81,834) (65,089) (53,808)

8.4 5.1 5.8 13.5 12.8(7.1) (5.6) (5.2) (7.0) (6.7)

53.7 50.1 50.5 59.8 66.6(15.8) (14.5) (14.9) (15.9) (15.5)

0.042 0.025 0.043 0.049 0.047(0.22) (0.17) (0.22) (0.23) (0.21)

Yearly premium paid 719.80 798.60 715.60 687.19 709.78(312.76) (405.78) (300.39) (267.82) (269.34)

N 49,992 8,525 23,782 17,536 149Percent of sample 100% 17.05% 47.57% 35.08% 0.30%

Chosen Deductible

Number of years insured by the company

Average age of H.H. members

Number of paid claims in sample year (claim rate)

* Means with standard errors in parentheses.

Deductible PricingXi = matrix of policy characteristicsf(Xi) = “base premium”

Approx. linear in home valuePremium for deductible D

PiD = δD f(Xi)

Premium differencesΔPi = Δδ f(Xi)

⇒Premium differences depend on base premiums (insured home value).

Premium-Deductible Menu

Available Deductible

Full Sample 1000 500 250 100

1000 $615.82 $798.63 $615.78 $528.26 $467.38(292.59) (405.78) (262.78) (214.40) (191.51)

500 +99.91 +130.89 +99.85 +85.14 +75.75(45.82) (64.85) (40.65) (31.71) (25.80)

250 +86.59 +113.44 +86.54 +73.79 +65.65(39.71) (56.20) (35.23) (27.48) (22.36)

100 +133.22 +174.53 +133.14 +113.52 +101.00(61.09) (86.47) (54.20) (42.28) (82.57)

Chosen Deductible

Risk Neutral Claim Rates?

100/500 = 20%

87/250 = 35%

133/150 = 89%

* Means with standard deviations in parentheses

Potential Savings with 1000 Ded

Chosen DeductibleNumber of claims

per policy

Increase in out-of-pocket payments per claim with a

$1000 deductible

Increase in out-of-pocket payments per policy with a

$1000 deductible

Reduction in yearly premium per policy with

$1000 deductible

Savings per policy with $1000 deductible

$500 0.043 469.86 19.93 99.85 79.93 N=23,782 (47.6%) (.0014) (2.91) (0.67) (0.26) (0.71)

$250 0.049 651.61 31.98 158.93 126.95 N=17,536 (35.1%) (.0018) (6.59) (1.20) (0.45) (1.28)

Average forgone expected savings for all low-deductible customers: $99.88

Claim rate?Value of lower deductible? Additional

premium? Potential savings?

* Means with standard errors in parentheses

Back of the Envelope

BOE 1: Buy house at 30, retire at 65, 3% interest rate ⇒ $6,300 expected

With 5% Poisson claim rate, only 0.06% chance of losing money

BOE 2: (Very partial equilibrium) 80% of 60 million homeowners could expect to save $100 a year with “high” deductibles ⇒ $4.8 billion per year

Consumer Inertia?Percent of Customers Holding each Deductible Level

0

10

20

30

40

50

60

70

80

90

0-3 3-7 7-11 11-15 15+

Number of Years Insured with Company

%

1000

500

250100

Chosen DeductibleNumber of claims

per policy

Increase in out-of-pocket payments per claim with a $1000 deductible

Increase in out-of-pocket payments per policy with a $1000 deductible

Reduction in yearly premium per policy with

$1000 deductible

Savings per policy with $1000 deductible

$500 0.037 475.05 17.16 94.53 77.37 N = 3,424 (54.6%) (.0035) (7.96) (1.66) (0.55) (1.74)

$250 0.057 641.20 35.68 154.90 119.21 N = 367 (5.9%) (.0127) (43.78) (8.05) (2.73) (8.43)

Average forgone expected savings for all low-deductible customers: $81.42

Look Only at New Customers

Bounding Risk Aversion

1)ln()(,1)1(

)()1(

==≠−

=−

ρρρ

ρ

forxxuandforxxu

Assume CRRA form for u :

)1()(

)1()1(

)()1(

)()1(

)1()( )1()1()1()1(

ρπ

ρπ

ρπ

ρπ

ρρρρ

−−

−+−−−

=−

−−+

−−− −−−−

HHHLLL PwDPwPwDPw

Indifferent between contracts iff:

CRRA Bounds

Chosen Deductible W min ρ max ρ

$1,000 256,900 - infinity 794 N = 2,474 (39.5%) {113,565} (9.242)

$500 190,317 397 1,055 N = 3,424 (54.6%) {64,634} (3.679) (8.794)

$250 166,007 780 2,467 N = 367 (5.9%) {57,613} (20.380) (59.130)

Measure of Lifetime Wealth (W): (Insured Home Value)

Interpreting Magnitude

50-50 gamble: Lose $1,000/ Gain $10 million

99.8% of low-ded customers would rejectRabin (2000), Rabin & Thaler (2001)

Labor-supply calibrations, consumption-savings behavior ⇒ ρ < 10

Gourinchas and Parker (2002) -- 0.5 to 1.4Chetty (2005) -- < 2

Model of Deductible Choice

Choice between (PL,DL) and (PH,DH)π = probability of lossEU of contract:

U(P,D,π) = πu(w-P-D) + (1- π)u(w-P)

PT value:V(P,D,π) = v(-P) + w(π)v(-D)

Prefer (PL,DL) to (PH,DH)v(-PL) – v(-PH) < w(π)[v(- DH) – v(- DL)]

Prospect Theory

No loss aversion in buyingNovemsky and Kahneman (2005) (Also Kahneman, Knetsch & Thaler (1991))

Endowment effect experimentsCoefficient of loss aversion = 1 for “transaction money”

Köszegi and Rabin (forthcoming QJE, 2005)Expected payments

Marginal value of deductible payment > premium payment (2 times)

So we have:

Prefer (PL,DL) to (PH,DH):

Which leads to:

Linear value function:

)]()()[()()( LHHL DvDvwPvPv −−−<−−− π

][)( ββββ λπ LHHL DDwPP −<−

DwPWTP Δ=Δ= λπ )(

= 4 to 6 times EV

Choices: Observed vs. Model

Chosen Deductible 1000 500 250 100 1000 500 250 100

$1,000 87.39% 11.88% 0.73% 0.00% 100.00% 0.00% 0.00% 0.00% N = 2,474 (39.5%)

$500 18.78% 59.43% 21.79% 0.00% 100.00% 0.00% 0.00% 0.00% N = 3,424 (54.6%)

$250 3.00% 44.41% 52.59% 0.00% 100.00% 0.00% 0.00% 0.00% N = 367 (5.9%)

$100 33.33% 66.67% 0.00% 0.00% 100.00% 0.00% 0.00% 0.00% N = 3 (0.1%)

Predicted Deductible Choice from Prospect Theory NLIB Specification:

λ = 2.25, γ = 0.69, β = 0.88

Predicted Deductible Choice from EU(W) CRRA Utility:

ρ = 10, W = Insured Home Value

Alternative ExplanationsMisestimated probabilities

≈ 20% for single-digit CRRAOlder (age) new customers just as likely

Liquidity constraintsSales agent effects

Hard sell?Not giving menu? ($500?, data patterns)Misleading about claim rates?

Menu effects

Reference Dependence: Insurance Barseghyan et al. (2013)

Barseghyan et al. (2013)

Barseghyan, Molinari, O’Donoghue, and Teitelbaum (AER2013)

Micro data for same person on 4,170 households for 2005 or2006 on

home insuranceauto collision insuranceauto comprehensive insurance

Estimate a model of reference-dependent preferences withKoszegi-Rabin reference points

Separate role of loss aversion, curvature of value function, andprobability weighting

Key to identification: variation in probability of claim:home insurance � 0.084auto collision insurance � 0.069auto comprehensive insurance � 0.021



Predicted Claim Probabilities



Summary

This allows for better identification of probability weightingfunction

Main result: Strong evidence from probability weighting,implausible to obtain with standard risk aversion

Share of probability weighting function

With probability weighting, realistic demand for low-deductibleinsurance

Follow-up work: distinguish probability weighting fromprobability distortion


Reference Dependence: Finance

Section 3




Background

Equity premium (Mehra and Prescott, 1985)

Stocks not so riskyDo not covary much with GDP growthBUT equity premium 3.9% over bond returns (US, 1871-1993)

Need very high risk aversion: RRA ≥ 20

Benartzi and Thaler (QJE 1995): Loss aversion + narrowframing solve puzzle

Loss aversion from (nominal) losses � Deter from stocksNarrow framing: Evaluate returns from stocks every n months


Reference Dependence: Finance Benartzi and Thaler (1995)

Narrow Framing

More frequent evaluation � Losses more likely � Fewer stockholdings

Calibrate model with λ (loss aversion) 2.25 and full prospecttheory specification � Horizon n at which investors areindifferent between stocks and bonds


Reference Dependence: Finance Benartzi and Thaler (1995)

Narrow Framing

If evaluate every year, indifferent between stocks and bonds

(Similar results with piecewise linear utility)

Alternative way to see results: Equity premium implied asfunction on n


Reference Dependence: Finance Barberis’s Finance Work

Reference Dependence and Finance

Nick Barberis’s work in Handbook of Behavioral Economics

Slides courtesy of Nick

Extra Figures on Disposition Effect – Odean (1998)

There are two hypotheses to be tested. The first is that investors tend tosell their winners and hold their losers. Stated in terms of realization ratesfor gains and losses this is:

HYPOTHESIS 1: Proportion of Gains Realized . Proportion of Losses Realized(for the entire year).

The null hypothesis in this case is that PGR # PLR. The second hypothesisis that in December investors are more willing to sell losers and less willingto sell winners than during the rest of the year. That is:

HYPOTHESIS 2: Proportion of Losses Realized 2 Proportion of Gains Realizedin December . Proportion of Losses Realized 2 Proportion of Gains Realizedin January–November.

The null hypothesis here is: PLR 2 PGR in December # PLR 2 PGR inJanuary through November.

B. Results

Table I reports the PGR realized and the PLR realized for the entire year,for January through November, and for December. We see that for the entireyear investors do sell a higher proportion of their winners than of theirlosers. For both Hypothesis 1 and Hypothesis 2 the null hypotheses can berejected with a high degree of statistical significance. A one-tailed test of thefirst null hypothesis, PGR # PLR, is rejected with a t-statistic greater than35. The second null hypothesis, PLR 2 PGR in December # PLR 2 PGR in

Table I

PGR and PLR for the Entire Data SetThis 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 thenumber of realized gains plus the number of paper ~unrealized! gains, and PLR is the numberof 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, forDecember only, and for January through November. For the entire year there are 13,883 real-ized gains, 79,658 paper gains, 11,930 realized losses, and 110,348 paper losses. For Decemberthere 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 zeroassuming that all realized gains, paper gains, realized losses, and paper losses result fromindependent decisions.

Entire Year December Jan.–Nov.

PLR 0.098 0.128 0.094PGR 0.148 0.108 0.152Difference in proportions 20.050 0.020 20.058t-statistic 235 4.3 238

Are Investors Reluctant to Realize Their Losses? 1783


Reference Dependence: Finance Barberis’s Finance Work

Reference Dependence and Finance

Ben-David and Hirshleifer (2012)

66

Figure 2. V-Shapes in the Likelihood of Selling or Buying Additional Shares

Likelihood of Selling Stock Likelihood of Buying Additional Shares Day 1 Day 1

Day 5 Day 5

Day 20 Day 20


Prospect theory applications

[1]

• the cross-section of stock returns

– one-period models

– new prediction: the pricing of skewness

– probability weighting plays the most critical role

[2]

• the aggregate stock market

– multi-period models

– try to address the equity premium, non-participation,volatility, and predictability puzzles

– loss aversion plays a key role; but probability weight-ing also matters

[3]

• trading behavior (and the cross-section, revisited)

– multi-period models

– try to address the disposition effect and other trad-ing phenomena

– all aspects of prospect theory play a role

13

Prospect theory applications, ctd.

Note:

• prospect theory models capture a very intuitive idea

– that, when they invest, people think explicitly abouthow much money they could make, or lose

• one difficulty is defining the “gains” and “losses” peo-ple think about

– gains and losses in total wealth, financial wealth,stock market holdings, individual stocks?

– annual gains and losses?

– is a gain a return that exceeds zero, or one thatexceeds the risk-free rate or the investor’s expecta-tion?

• in the absence of a full theory of how gains and lossesare defined, we try specifications that appear plausible

– e.g. focus on annual gains and losses in financialwealth

14

The cross-section

Barberis and Huang (2008), “Stocks as Lotteries...”

• single period model; a risk-free asset and J risky assetswith multivariate Normal payoffs

• investors have identical expectations about securitypayoffs

• investors have identical CPT preferences

– defined over gains/losses in wealth (i.e. no narrowframing)

– reference point is initial wealth scaled up by therisk-free rate, so utility defined over W = W1 −W0Rf

– full specification is:

V (W ) =∫ 0−∞ v(W ) dπ(P (W ))−

∫ ∞0 v(W ) dπ(1−P (W ))

(continuous distribution version of Tversky andKahneman, 1992)

Then:

• the CAPM holds!

– i.e. prospect theory gives the same prediction asthe EU model

– see also De Giorgi, Hens, and Levy (2011)

15

The cross-section, ctd.

• to make more interesting predictions, break away fromthe multivariate Normal assumption

– introduce a small, independent, positively skewedsecurity into the economy

• obtain a novel prediction: the new security earns anegative excess return

– skewness itself is priced, in contrast to concave EUmodel where only coskewness with market matters

• equilibrium involves heterogeneous holdings

(assume short-sale constraints for now)

– some investors hold a large, undiversified positionin the new security

– others hold no position in it at all

– heterogeneous holdings arise from non-unique globaloptima, not from heterogeneous preferences

• since the new security contributes skewness to theportfolios of some investors, it is valuable, and so earnsa low average return

16


0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.1610

8

6

4

2

0

2

4

6

810–3

x

Util

ity

Figure 3. A Heterogeneous Holdings Equilibrium

Notes: The figure shows the utility that an investor with cumulative prospect theory preferences derives from adding a position in a positively skewed security to his current holdings of a Normally distributed market portfolio. The skewed security is highly skewed. The variable x is the fraction of wealth allocated to the skewed security relative to the frac-tion of wealth allocated to the market portfolio. The two lines correspond to different mean returns on the skewed security.

17


Applications

• low average return on IPOs

– IPO returns are highly positively skewed

– Green and Hwang (2012) show that IPOs predictedto be more positively skewed have lower long-termreturns

• low average return of distressed stocks, bankrupt stocks,OTC stocks (Eraker and Ready, 2015)

• low average return of out-of-the-money options on in-dividual stocks

– Boyer and Vorkink (2014) find that stock optionspredicted to be more positively skewed have lowerreturns

• low average return of out-of-the-money index calls andindex puts, and the variance premium (Baele et al.,2019)

• low average return on stocks with high idiosyncraticvolatility (Ang et al., 2006; Boyer, Mitton, Vorkink,2010)

• diversification discount (Mitton and Vorkink, 2010)

21

The aggregate stock market

Can prospect theory help us understand empirical factsabout the aggregate stock market?

• Benartzi and Thaler (1995) propose that prospect the-ory can help explain the equity premium puzzle

• specific finding:

– the prospect theory values of the historical distri-bution of annual U.S. stock returns and of the his-torical distribution of annual U.S. bond returns areapproximately equal

• interpretation: the high equity premium makes thestock market competitive with the bond market inthe eyes of prospect theory investors

– without it, the stock market would be unappealing,due to loss aversion

• loss aversion and annual evaluation play importantroles here

– “myopic loss aversion”

24

The aggregate stock market, ctd.

• Benartzi and Thaler (1995) do not incorporate theirideas into an equilibrium model with endogenouslydetermined prices

• Barberis, Huang, and Santos (2001) take up this task

– construct a model where the representative agentderives utility from consumption and from gainsand losses in financial wealth

• Barberis and Huang (2009) address the same chal-lenge using a different modeling approach

– see also Andries (2013) and Pagel (2013)

25


• Barberis, Huang, and Santos (2001) consider an econ-omy with three assets: risk-free (Rf,t), stock market(RS,t+1), non-financial asset (RN,t+1)

• representative agent maximizes:

E0

∞∑t=0

⎡⎢⎢⎢⎣ρ

t C1−γt

1− γ+ b0ρ

t+1C−γt v(GS,t+1)

⎤⎥⎥⎥⎦

GS,t+1 = St(RS,t+1 −Rf,t)

v(x) =

⎧⎪⎪⎨⎪⎪⎩

xλx

forx ≥ 0x < 0

, λ > 1

– here, GS is the annual gain or loss in financialwealth, measured relative to the risk-free rate

i.e. BtRf,t + StRS,t+1 − (Bt + St)Rf,t

where Bt and St are risk-free and stock marketholdings

– v(·) captures loss aversion; concavity/convexity andprobability weighting are ignored for now

• for “reasonable” parameters, the model generates alarge equity premium

26


The role of narrow framing

• Barberis, Huang, and Santos (2001) assume a mildlevel of narrow framing

– gains and losses in financial wealth

• loss aversion over total wealth fluctuations may notproduce as large an equity premium

– nor generate non-participation in the stock market(Barberis, Huang, Thaler, 2006)

• a stronger level of narrow framing can also be assumed

The role of probability weighting

• De Giorgi and Legg (2012) bring probability weightingand concavity/convexity into the Barberis and Huang(2009) framework

– they show that probability weighting can signifi-cantly increase the equity premium

– because the aggregate market is negatively skewed

28


Note:

• we are using frameworks in which investors derive util-ity from fluctuations in financial wealth, not just con-sumption

• we can justify this in terms of “mental accounting”

– to try to ensure good future consumption outcomes,investors track wealth fluctuations on a regular ba-sis

– an increase in wealth is “good news” and becomesassociated with a positive utility burst

– a decrease in wealth is “bad news” and becomesassociated with a negative utility burst

30

II. Disposition effect (CC)

• Odean (1998) studies the trading activity, from 1987-

1993, of 10,000 households with accounts at a large

discount brokerage firm

• whenever an investor sells shares of a stock, classify

each of the stocks in her portfolio on that day as one

of:

– “realized gain”, “realized loss”, “paper gain”, or

“paper loss”

• add up total number of realized gains and losses and

paper gains and losses over all accounts over the sam-

ple, and compute:

PGR =no. of realized gains

no. of realized gains + no. of paper gains

PLR =no. of realized losses

no. of realized losses + no. of paper losses

(e.g. PGR is “proportion of gains realized”)

• the disposition effect is the finding that PGR > PLR

– specifically, 0.148 = PGR > PLR = 0.098

21

II. Disposition effect (CC), ctd.

The most obvious potential explanations fail to capture

important features of the data

• e.g. informed trading

– the subsequent return of winners that people sell

is higher than that of losers they hold on to

• e.g. taxes, rebalancing, transaction costs

Two non-standard hypotheses have gained prominence

• an irrational belief in mean-reversion

• an explanation based on prospect theory and narrow

framing

At first glance, prospect theory and narrow framing do

seem to generate a disposition effect

• in a formal model, however, Barberis and Xiong (2005)

find that prospect theory often predicts the opposite

of the disposition effect

22


• consider a simple portfolio choice setting

– T + 1 dates: t = 0, 1, . . . , T

– a risk-free asset, gross return Rf each period

– a risky asset with an i.i.d binomial distribution

across periods:

Rt,t+1 =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

Ru > Rf with probability 12

Rd < Rf with probability 12

, i.i.d.

• the investor has prospect theory preferences defined

over her “gain/loss”

– simplest definition of gain/loss is trading profit be-

tween 0 and T, i.e. WT −W0

– we use WT −W0RTf

– call W0RTf the “reference” wealth level

23


Does prospect theory predict a disposition effect?

• construct a simulated dataset of how 10,000 prospect

theory investors trade NS stocks over T periods

– simulate a T -period path through the binomial tree

for 10, 000×NS stocks

– for each path, earlier analysis tells us how the in-

vestor trades along the path

• now follow Odean’s (1998) exact methodology for com-

puting PGR and PLR

– if PGR > PLR, there is a disposition effect

• parameter values:

– set (P0,W0) = (40, 40) for each stock

– set Rf = 1 and σ = 0.3

– set (α, λ) = (0.88, 2.25)

– Barber and Odean (2000) report NS = 4

– range of values of µ and T

29

Table 2: For a given (µ, T ) pair, we construct an artificial dataset of how 10,000investors with prospect theory preferences, each of whom owns NS stocks, eachof which have expected return µ, would trade those stocks over T periods. Foreach (µ, T ) pair, we use the artifical dataset to compute PGR and PLR, wherePGR is the proportion of gains realized by all investors over the entire tradingperiod, and PLR is the proportion of losses realized. The table reports PGR/PLRfor each (µ, T ) pair. Boldface type identifies cases where the disposition effectfails (PGR < PLR). A hyphen indicates that the expected return is so low thatthe investor does not buy any stock at all.

µ T = 2 T = 4 T = 6 T = 12

1.03 - - - .55/.50

1.04 - - .54/.52 .54/.52

1.05 - - .54/.52 .59/.45

1.06 - .70/.25 .54/.52 .58/.47

1.07 - .70/.25 .54/.52 .57/.49

1.08 - .70/.25 .48/.58 .47/.60

1.09 - .43/.70 .48/.58 .46/.61

1.10 0.0/1.0 .43/.70 .48/.58 .36/.69

1.11 0.0/1.0 .43/.70 .49/.58 .37/.68

1.12 0.0/1.0 .28/.77 .23/.81 .40/.66

1.13 0.0/1.0 .28/.77 .24/.83 .25/.78

41


What is the investor’s strategy at time 1?

• we focus on situations in which the expected risky

asset return is not too low

• after a gain at time 1, the investor takes a position

such that, after a poor time 2 return, she ends up

with a small gain

– since v(·) is only mildly concave over gains, she

gambles to the edge of the concave region, but no

further

• after a loss at time 1, the investor takes a position

such that, after a good time 2 return, she again ends

up with a small gain

– since v(·) is convex over gains, she gambles to the

edge of the convex region, but not much beyond

31


So why does the disposition effect fail?

• for the investor to buy the stock at all at time 0, in

spite of her loss aversion, it must have a relatively high

expected return

– this implies that the time 1 gain is larger than the

time 1 loss in magnitude

– it also implies that, after a gain, the investor gam-

bles to the edge of the concave region

• but it takes a larger position to gamble to the edge of

the concave region after a gain, than it does to gamble

to the edge of the convex region, after a loss

⇒ the investor takes more risk after a gain, than after

a loss, contrary to the disposition effect

32

Trading behavior, ctd.

• an alternative gain-loss utility approach can generatethe disposition effect more reliably

– one based on “realization utility”

– the idea that investors derive utility directly fromrealized gains and losses (Shefrin and Statman,1985)

• e.g. if you buy a stock at $40 and sell it at $60

– you get a jolt of positive utility at the moment ofsale, based on the size of the realized gain

• what is the source of realization utility?

– people often think about their investing history asa series of investing episodes

– and view selling a stock at a gain as a “good”episode

⇒ when an investor sells an asset at a gain, hefeels a burst of pleasure because he is creating apositive new investing episode

35


• Barberis and Xiong (2012), “Realization Utility,” studylinear realization utility, coupled with time discount-ing

Assets

• a risk-free asset, with net return of zero

• N risky assets, “stocks”; stock i has price process

dSi,t

Si,t= μdt + σdZi,t

– μ and σ are the same for all stocks

The Investor

• at each time t, he either allocates all of his wealth tothe risk-free asset, or all of his wealth to one of the Nstocks

– time t wealth is Wt

• if he is holding stock at time t, let Bt be the cost basisof the position

• if he sells stock at time t, he pays a transaction costkWt

36


Key assumption:

• if, at time t, the investor switches his wealth from astock to the risk-free asset or to another stock, hereceives realization utility of

u((1− k)Wt −Bt)

• he also faces the possibility of a random liquidity shock

– the shock arrives according to a Poisson processwith parameter ρ

– when a shock hits, the investor sells his asset hold-ings and exits the asset markets

• the investor maximizes the discounted sum of expectedfuture realization utility flows

– δ is the time discount rate

– we take u(x) = x

37


Solution

• if the expected return on stocks is low, the individualinvests in the risk-free asset forever

• if the expected return on stocks is high enough, hebuys a stock at time 0

– and sells it only if its value rises a certain percent-age amount above purchase price

– he then immediately reinvests in another stock,and so on

38


• applications:

– the disposition effect

but also:

– “excessive trading”

– the underperformance of individual investors evenbefore transaction costs

– the greater turnover in bull markets

– the greater selling propensity above historical highs

– the negative premium to volatility in the cross-section

– the fact that overpriced assets are also heavily traded

39

Reference Points: Forward- vs. Backward-Looking

Section 4

Reference Points: Forward- vs.

Backward-Looking



So Far: Backward-Looking Reference Point

Most papers so far assume assume a backward-looking referencepoint

Salient past outcomes

Purchase price of homePurchase price of sharesAmount withheld in taxesRecent earnings



So Far: Backward-Looking Reference Point

Status quo

Ownership in endowment effect

Cultural norm

52-week high for mergersRound numbers (as running goals)Number of strokes in a put

For bunching and shifting test, reference point needs to be

DeterministicClear to the researcher

For other predictions, such as in job search, exact level lesscritical



What About Forward-Looking?

Koszegi and Rabin (QJE 2006; AER 2007): forward-lookingreference points

Reference point is expectations of future outcomesReference point is stochasticSolve with Personal Equilibria

Motivations:

Motivation 1: It often makes sense for people to compareoutcomes to expectationsMotivation 2: Reference point does not need to be assumed

Evidence so far:

Reference point for police arbitrationReference point for watching sports games



Forward-Looking Reference Point

Drawbacks of forward-looking reference points:

Stochastic � Lose sharpest tests of reference dependence(bunching and shifting)(Reference point is often taken as expectation, rather than fulldistribution, to simplify)Often multiplicity of equilibria

Next, cover papers designed to test reference points asexpectations:

Endowment effectEffort



Future Research

Future research: Would be great to see papers with referencepoint r

r = αr0 + (1− α) rf

r0 backward-looking / status quo reference pointrf forward-looking reference pointWhat weight on each component?


Reference Dependence: Domestic Violence

Section 5




Introduction

Consider a man in conflicted relationship with the spouse

What is the effect of an event such as the local (American)football team losing or winning a game?

With probability h the man loses control and becomes violent

Assume h = h (u) with h′ < 0 and u the underlying utilityDenote by p the ex-ante expectation that the team winsDenote by u(W ) and u(L) the consumption utility of a loss



Introduction

Using a Koszegi-Rabin specification, then ex-post the utility from awin is

U (W |p) = u(W ) [consumption utility]

+p [0] + (1− p) η [u (W )− u (L)] [gain-loss utility]

Similarly, the utility from a loss is

U (L|p) = u(L) + (1− p) [0]− λpη [u (W )− u (L)]

Implication:

∂U (L|p) /∂p = −λη [u (W )− u (L)] < 0

The more a win is expected, the more a loss is painful � themore likely it is to trigger violenceThe (positive) effect of a gain is higher the more unexpected(lower p)


Reference Dependence: Domestic Violence Card and Dahl (2011)

Testing the Predictions

Card and Dahl (QJE 2011) test these predictions using adata set of:

Domestic violence (NIBRS)Football games by StateExpected win probability from Las Vegas predicted point spread

Separate matches into

Predicted win (+3 points of spread)Predicted closePredicted loss (-3 points)



Testing the Predictions



Findings

1 Unexpected loss increases domestic violence

2 No effect of expected loss

3 No effect of unexpected win, if anything increases violence

Findings 1-2 consistent with ref. dep. and 3 partially consistent(given that violence is a function of very negative utility)

Other findings:

Effect is larger for more important gamesEffect disappears within a few hours of game end � Emotionsare transientNo effect on violence of females on males


Reference Dependence: Endowment Effect

Section 6

Reference Dependence: Endowment Effect


Reference Dependence: Endowment Effect Plott and Zeiler (2005)

Plott and Zeiler (AER 2005)

Plott and Zeiler (AER 2005) replicating Kahneman,Knetsch, and Thaler (JPE 1990)

Half of the subjects are given a mug and asked for WTAHalf of the subjects are shown a mug and asked for WTPFinding: WTA ' 2 ∗WTP



Model

How do we interpret it? Use reference-dependence in piece-wiselinear form

Assume only gain-loss utility, and assume piece-wise linearformulation (1)+(3)Two components of utility: utility of owning the object u (m)and (linear) utility of money pAssumption: No loss-aversion over moneyWTA: Given mug � r = {mug}, so selling mug is a lossWTP: Not given mug � r = {∅}, so getting mug is a gainAssume u {∅} = 0



This implies:

WTA: Status-Quo ∼ Selling Mug

u{mug} − u{mug} = λ [u {∅} − u{mug}] + pWTA or

pWTA = λu{mug}WTP: Status-Quo ∼ Buying Mug

u {∅} − u {∅} = u{mug} − u {∅} − pWTP or

pWTP = u{mug}It follows that

pWTA = λu{mug} = λpWTP

If loss-aversion over money,

pWTA = λ2pWTP



Results

Result WTA ' 2 ∗WTP is consistent with loss-aversion λ ' 2

Plott and Zeiler (AER 2005): The result disappears with

appropriate trainingpractice roundsincentive-compatible procedureanonymity



Interpretation 1

Endowment effect and loss-aversion interpretation are wrong

Subjects feel bad selling a ‘gift’Not enough training



Interpretation 2

In Plott-Zeiler (2005) experiment, subjects did not perceive thereference point to be the endowment

Koszegi-Rabin: Assume reference point (.5, {mug}; .5, {∅}) inboth cases

WTA:[.5 ∗ [u{mug} − u{mug}]+.5 ∗ [u{mug} − u {∅}]

]=

[.5 ∗ λ [u {∅} − u{mug}]+.5 ∗ [u {∅} − u {∅}]

]+pWTA

WTP:[.5 ∗ λ [u {∅} − u{mug}]+.5 ∗ [u {∅} − u {∅}]

]=

[.5 ∗ [u{mug} − u{mug}]+.5 ∗ [u{mug} − u {∅}]

]−pWTP

This implies no endowment effect:

pWTA = pWTP



Testing Koszegi-Rabin

Following papers: manipulate probability of exchange to testKoszegi-Rabin

Ericson and Fuster (QJE 2011): KR evidenceHeffetz and List (JEEA 2015): no KR evidence

Cerulli-Harms, Goette, and Sprenger (AEJ Micro, 2019)

Endowment effect in classroomVary probability p of forced exchange: owner must sell, buyermust buyFor probability p = 0.5, owner in KR sense is only owner withprob. 0.5, and buyer is owner with p = 0.5 � Should be noendowment effect


Reference Dependence: Endowment Effect Cerulli-Harms, Goette, and Sprenger (2019)

Prediction

For p > 0.5 � Reverse endowment effect


Reference Dependence: Endowment Effect Cerulli-Harms, Goette, and Sprenger (2019)

Results

What do they find? Mostly, full endowment effect, no KR


Reference Dependence-KR: Effort

Section 7

Reference Dependence-KR: Effort


Reference Dependence-KR: Effort Abeler et al. (2011)

Abeler, Falk, Goette, Huffman (AER 2011)

Return to our earlier real-effort set up

Individuals put in effort e, with cost c (e)

Value of effort v (e|r) affected by a reference point

Assume now that the reference point r is a la Koszegi-Rabin

� Evidence that subjects shift effort and bunch at this referencepoint?

Design to disentangle forward- versus backward-lookingreference points



Design

Individuals put real effort

First training: for 4 minutes count as many zeros in tables ascanThen, real task:

Decide how long to work, for up to 60 minutes (smart designchoice, as higher elasticity of effort than tasks to do in fixedamount of time)With probability 1/2, paid piece rate time effort, p ∗ e, p = .2With probability 1/2, paid T eurosVary whether TLow = 3 or THi = 7



Standard Model

maxe

T + pe

2− c (e)

−− > e∗ = c ′−1 (p/2)

Solution does not depend on target T



Reference-Dependent Model

Reference-dependent model, with gain-loss utility: Assume referencepoint is pe with prob. 1/2, T with prob. 1/2

If pe < T , utility v (e|r) is (with prob. 1/2 paid pe, with prob.1/2 paid T ):

T + pe

2+

1

2η

[1

2(pe − pe) +

1

2λ (pe − T )

]+

+1

2η

[1

2(T − T ) +

1

2(T − pe)

]

=T + pe

2+

1

4η (λ− 1) (pe − T )



Reference-Dependent Model

If pe > T , utility is

T + pe

2+

1

2η

[1

2(pe − pe) +

1

2(pe − T )

]

+1

2η

[1

2(T − T ) +

1

2λ (T − pe)

]

=T + pe

2− 1

4η (λ− 1) (pe − T )



F.O.C. for Effort

The f.o.c. for effort are

p

2+

p

4η (λ− 1)− c ′ (e∗) = 0 if pe < T

p

2− p

4η (λ− 1)− c ′ (e∗) = 0 if pe > T

Thus, should see

bunching at THigher effort for higher T



Results

KR effect on effort, though smaller than one would expect

Anchoring can be confound


Reference Dependence-KR: Effort Gneezy et al. (2017)

Gneezy, Goette, Sprenger, Zimmermann (JEEA

2017)

Focus on possible confound in design of Abeler et al. paper

Subject are paid a piece rate with p = 0.5 and with p = 0.5 arepaid TReference point T is also salient choice

Remove with alternative design:

Subjects are paid $0 with prob. pSubjects are paid $14 with prob. qSubjects are paid piece rate with prob. 1− p − q = 0.5

This removes salience-based bunching at T since $0 or $14 arenot salient points


Reference Dependence-KR: Effort Gneezy et al. (2017)

Gneezy et al. (JEEA 2017)

(a): Like Abeler et al. but also use ref pt L = 0, L = 14(b): Do stochastic designKey result: do not replicate Abeler et al. findingGneezy et al. The Limits of Expectations-Based Reference Dependence 871

Panel (a) Panel (b)

FIGURE 2. Average accumulated earnings across treatments. Standard error bars correspondingto C/! one robust standard error. Panel (a): Average accumulated earnings for each value of Lfrom treatments (0, 0.5, NA, L). Panel (b): Average accumulated earnings for each value of p fromtreatments (p, q, 14, 0). Observations from subtreatments (0, 0.5, NA, 0) and (0, 0.5, NA, 0)8 as wellas for subtreatments (0, 0.5, NA, 7) and (0, 0.5, NA, 7)8 are combined.

4. Results

A total of 265 subjects participated in our nine conditions. Over all treatments, subjectson average solved 39.64 tables, leading to accumulated earnings of $7.93. The averagetime subjects worked on the task was 33.30 min. Table 1 provides means and standarddeviations for all experimental conditions and Figure 2 summarizes our key findings.The key measure of effort will be Accumulated Earnings, we!. Accumulated earningsare graphed against the expected value of the manipulated payments, pH C qL, withseparate series for our two predictions.

4.1. Changing Outcomes

To test Prediction 1, we first consider treatments (0, 0.5, NA, 3) and (0, 0.5, NA, 7),the two treatments from Abeler et al. (2011). Figure 2, Panel (a) and Table 1 showthat, as predicted by theories of expectations-based reference dependence and found inAbeler et al. (2011), effort increases as we move from a fixed payment of $3 to a fixedpayment of $7. In the two envelope conditions, subjects on average stop working at

Downloaded from https://academic.oup.com/jeea/article-abstract/15/4/861/2965616by University of California, Berkeley/LBL useron 21 February 2018


Reference Dependence-KR: Effort Summary

Summary on Reference Points

Much research remains to be done on reference pointdetermination

Not much support for forward-looking reference pointsEmphasis on backward-looking reference pointsCan estimate reliable speed of adjustment?Much faster in Thakral and To than in DellaVigna et al.

Need more designs that ‘reveal’ reference points

Use bunching?


Social Preferences Wave I: Altruism

Section 8




Pure Altruism

First set of models (since 1970s): Pure altruismSelf with payoff xs

Other with payoff xoSelf assigns weight α to Other’s utility:

U = u (xs) + αu (xo)

First used to model within-family altruism (Becker, 1981;Becker and Barro, 1986)Still very useful benchmark model


Workplace Effort: Altruism

Section 9

Workplace Effort: Altruism


Workplace Effort: Altruism Bandiera, Barankay, and Rasul (2005)

Bandiera-Barankay-Rasul (QJE, 2005)

Impact of relative pay versus piece rate on productivity

Standard model:

Piece rate: Worker i maximizes

maxei

pei − c (ei )

e∗iP = c ′−1 (p)

Relative pay: Worker i maximizes

maxei

pei − γ∑

j 6=i

ejI − 1

− c (ei )

e∗iRP = e∗P = c ′−1 (p)



Assume simple altruism

Simple Altruism model:

Ui = ui + α∑

j 6=i

uj

Piece rate: Worker maximizes

maxei

pei − c (ei) + α∑

j 6=i

[pej − c (ej)]

Same solution as with α = 0Relative pay: Worker i maximizes

maxei

pei−γ∑

j 6=i

ejI − 1

−c (ei )+α∑

j 6=i

pej − γ

∑

q 6=j

eqI − 1

− c (ej)

Solution

c ′ (e∗iRP) = p − αγ (I − 1) – > e∗iRP < e∗iP



Experiment Details

Test for impact of social preferences in the workplace

Does productivity increase when switching to piece rate?

Use personnel data from a fruit farm in the UK

Measure productivity as a function of compensation scheme

Timeline of quasi-field experiment:First 8 weeks of the 2002 picking season � Fruit-pickerscompensated on a relative performance scheme

Per-fruit piece rate is decreasing in the average productivity.Workers that care about others have incentive to keep theproductivity low

Next 8 weeks � Compensation switched to flat piece rate perfruitSwitch announced on the day change took place



Results: Productivity

Dramatic 50 percent increase in productivity



Results: Other

No other significant changes

Is this due to response to change in piece rate?No, piece rate went down � Incentives to work less(substitution effect)



Robustness Checks

Results robust to controls

Results are stronger the more friends are on the field



Interpretations

Two Interpretations:Social Preferences:

Work less to help othersWork even less when friends benefit, since care more for them

Repeated Game

Enforce low-effort equilibriumEquilibrium changes when switch to flat pay

Test: Observe results for tall plant where cannot observeproductivity of others (raspberries vs. strawberries)



Results: Comparison

Compare Fruit Type 1 (Strawberries) to Fruit Type 2(Raspberries)

No effect for Raspberries

� No Pure Social Preferences. However, can be reciprocity

Important to control for repeated game effects � Fieldexperiments


Workplace Effort: Altruism Hjort (2014)

Hjort (QJE, 2014)

Social preferences among co-workers as function of ethnicity

Kenya flower plantTeams of 3: one supplier, two processorsPiece rate (at least initially) for two processors, and suppliergets pay for average productivity



Manipulate Team Composition

Different team ethnicity configurations of Luos and Kikuyu:

Vertically mixed teams � Work less hard to sort flowersHorizontally mixed teams � Sort fewer flowers to non-coethnicFindings strikingly aligned to predictions of model



Results



Explanations

Two further pieces of evidence:1 Period of ethnic animosity and violence2 Switch to team pay for the processors

Prediction of first change:

Exacerbate patterns

Prediction of second change:

Reduce effect in horizontally-mixed teamsNot in vertically-mixed teams



Results



Next Lecture

Social Preferences

Wave I: AltruismWave II: Warm GlowWave III: Inequity AversionWave IV: Social Pressure, Social Signalling, and Social Norms


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