Econ 219B
Psychology and Economics: Applications
(Lecture 6)
Stefano DellaVigna
February 21, 2018
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 1 / 101
Outline
1 Reference Dependence: Golf
2 Reference Dependence: Job Search
3 Reference Dependence: Applications with Full Prospect Theory
4 Reference Dependence: Insurance
5 Reference Dependence: Equity Premium
6 Reference Points: Forward vs. Backward Looking
7 Reference Dependence: Endowment Effect
8 Reference Dependence-KR: Effort
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 2 / 101
Reference Dependence: Golf
Section 1
Reference Dependence: Golf
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 3 / 101
Reference Dependence: Golf Pope and Schweitzer (2011)
Pope and Schweitzer (AER 2011)
Last example applying the effort framework: golf
To win golf tournament, only thing that matters is total sum ofstrokes
Yet, each hole has a “suggested” number of strokes (“parvalue”)
That works as a reference point
Pope and Schweitzer (AER 2011)
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 4 / 101
1
PGA TOUR40-50 tournaments per/year~150 golfers per tournament4 rounds of 18 holes~$5M total purse – very convex
GolfStart at the tee, end by putting on the greenTotal # of strokes determines the winnerPar values of 3, 4, or 5Eagle, birdie, par, bogey, and double bogey
Is Tiger Woods Loss Averse (Pope & Schweitzer, AER, 2011)
2
3
– PGA Tour ShotLinks data from 2004 to 2009
– 239 Tournaments, 421 golfers (with more than 1,000 putts each), ~2.5 million putts
– X, y, and z coordinates for every ball placement within a centimeter on the green
– Focus on putts attempted for eagle, birdie, par, bogey, or double bogey
“A 10-footer for par feels more important than one for birdie. The reality is, that’s ridiculous. I can’t explain it in any way other than that it’s subconscious. And pars are O.K. – Bogeys aren’t.” - Paul Goydos
Data
4
6
Reference Dependence: Job Search
Section 2
Reference Dependence: Job Search
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 10 / 101
Reference Dependence: Job Search DellaVigna et al. (2017)
DellaVigna, Lindner, Reizer, Schmieder (QJE 2017)
Job Search in Hungary
Example where identification is not from comparing gains fromlosses
Identification comes from
how much at a loss relative to reference pointreference point adapts over timeaim to identify reference point adaptation
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 11 / 101
Introduction
Introduction
Large literature on understanding path of hazard rate fromunemployment with different models.Typical finding: There is a spike in the hazard rate at theexhaustion point of unemployment benefits.
⇒ Such a spike is not easily explained in the standard (McCall /Mortensen) model of job search.
⇒ To explain this path, one needs unobserved heterogeneity of aspecial kind, and/or storeable offers
Reference-Dependent Job Search 2 / 34
Introduction
Germany - Spike in Exit Hazard0
.02
.04
.06
.08
.1.1
2.1
4
0 5 10 15 20 25Duration in Months
12 Months Potential UI Duration 18 Months Potential UI Duration
AllHazard − Slopes differing on each side of Discontinuity
Source: Schmieder, von Wachter, Bender (2012)Reference-Dependent Job Search 3 / 34
Introduction
Simulation of Standard model
0 2 4 6 8 10 12 14 16 180
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Period (months)
Haza
rdRate
Hazard Rate, Standard
Predicted path of the hazard rate for a standard model withexpiration of benefit at period 25
Reference-Dependent Job Search 4 / 34
Model
Model - Set-up
We integrate reference dependence into standard McCall /Mortensen discrete time model of job searchJob Search:
Search intensity comes at per-period cost of c(st), which isincreasing and convexWith probability st , a job is found with salary wOnce an individual finds a job the job is kept forever
Optimal consumption-savings choice
Individuals choose optimal consumption ct (hand-to-mouthct = yt as special case)
Individuals are forward looking and have rational expectations
Reference-Dependent Job Search 4 / 47
Model
Utility Function
Utility function v(c)Flow utility ut(ct |rt) depends on reference point rt :
ut(ct |rt) ={
v(ct) + η(v(ct)− v(rt)) if ct ≥ rtv(ct) + ηλ(v(ct)− v(rt)) if ct < rt
η is weight on gain-loss utilityλ indicates loss aversionStandard model is nested for η = 0
Builds on Kahneman and Tversky (1979) and Kőszegi and Rabin(2006)
Note: No probability weighting or diminishing sensitivity
Reference-Dependent Job Search 5 / 47
Model
Reference Point
Unlike in Kőszegi and Rabin (2006), but like in Bowman,Minehart, and Rabin (1999), reference point isbackward-lookingThe reference point in period t is the average income earnedover the N periods preceding period t and the period tincome:
rt =1
N + 1
t∑
k=t−Nyk
Reference-Dependent Job Search 6 / 47
Model
Key Equations
An unemployed worker’s value function is
V Ut (At) = maxst∈[0,1];At+1
u (ct |rt)−c (st)+δ[stV
Et+1(At+1) + (1− st)V Ut+1(At+1)
]
Value function when employed:
V Et+1(At+1) = maxct+1u (ct+1|rt+1) + δV Et+2(At+2).
Solution for optimal search:
c ′ (s∗t ) = δ[V Et+1 (At+1)− V Ut+1 (At+1)
]
Solve for s∗t and c∗t using backward induction
Reference-Dependent Job Search 7 / 47
Model
How does the model work?
Consider a step-wise benefit schedule
T T+N50
100
150
200
250
300
350
400
450
Periods
Ben
efit
Leve
l
Benefit
What are the predictions of the standard vs.reference-depedent model without heterogeneity?
Reference-Dependent Job Search 8 / 47
Model
Example: Hazards under Two Models
T T+N50
100
150
200
250
300
350
400
450
Periods
Ben
efit
Leve
l
Benefit
Hazard Rate, Standard Model Hazard Rate, Ref.-Dep. Model
T T+N0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08Hazard rate in the Standard Model
Haz
ard
Rat
e
Periods
Reference-Dependent Job Search 9 / 47
Model
Example: Hazards under Two Models
T T+N50
100
150
200
250
300
350
400
450
Periods
Ben
efit
Leve
l
Benefit
Hazard Rate, Standard Model Hazard Rate, Ref.-Dep. Model
T T+N0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08Hazard rate in the Standard Model
Haz
ard
Rat
e
PeriodsT T+N
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08Hazard rate in the Reference Dep. Model
Haz
ard
Rat
e
Periods
Reference-Dependent Job Search 10 / 47
Model
Example: Hazards under Two Models
Consider the introduction of an additional step-down after T1periods, such that total benefits paid until T are identical:
T1 T T+N0
50
100
150
200
250
300
350
400
450
Periods
Ben
efit
Leve
l
Benefit
What are the predictions of the standard vs. ref.-dep. model?
Reference-Dependent Job Search 11 / 47
Model
Example: Hazards under Two Models
T1 T T+N0
50
100
150
200
250
300
350
400
450
Periods
Ben
efit
Leve
l
Benefit
Hazard Rate, Standard Model Hazard Rate, Ref.-Dep. Model
T1 T T+N0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08Hazard rate in the Standard Model
Haz
ard
Rat
e
PeriodsT1 T T+N
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08Hazard rate in the Reference Dep. Model
Haz
ard
Rat
e
Periods
Reference-Dependent Job Search 12 / 47
Evidence from Hungary UI Benefits in Hungary
Benefit schedule before and after the reform
270 90
$342
$222
$171
$114
360
Mon
thly
UI B
enef
it
Number of days since UI claim 180
1st tier (UI) 2nd tier (UA)
Social Assistance (HH income dependent)
44,460
68,400
34,200
22,800
Before Nov, 2005 schedule
After Nov, 2005 schedule
Note: Eligible for 270 days in the first tier, base salary is higher than114,000HUF ($570), younger than 50.→ Benefit-Schedule Macro Context Institutional Context
Reference-Dependent Job Search 13 / 47
Evidence from Hungary UI Benefits in Hungary
Define before and after
Reference-Dependent Job Search 14 / 47
Evidence from Hungary Reduced Form Results
Hazard rates before and after0
.01
.02
.03
.04
.05
.06
.07
.08
0 200 400 600Number of days since UI claim
before afterSamplesize: 11867
Hazard by Duration
Survival Rate Reemployment Wages
Reference-Dependent Job Search 15 / 47
Evidence from Hungary Reduced Form Results
Interrupted Time Series Analysis
.1.1
5.2
.25
Sea
sona
lly a
djus
ted
haza
rd r
ate
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7Quarter
hazard at 210−270 days hazard at 270−330 days
Before Placebo Test After Placebo Test
Reference-Dependent Job Search 17 / 47
Model Estimation Estimation Method
Structural Estimation
We estimate model using minimum distance estimator:
minξ
(m (ξ)− m̂)′W (m (ξ)− m̂)
m̂ - Empirical Moments (without controls)
35 15-day pre-reform hazard rates35 15-day pre-reform hazard rates
W is the inverse of diagonal of variance-covariance matrixFurther assumptions about utility maximization:
Log utility: v(c) = log(c)Assets A0 = 0, Borrowing limit L = 0, Interest rate R = 1Cost of effort c(s) = kj s
1+γ
1+γ
Reference-Dependent Job Search 18 / 47
Model Estimation Estimation Method
Estimation Method
Parameters ξ to estimate:
λ loss component in utility functionN speed of adjustment of reference point15-day discount factor δ (fixed at δ = 0.995 for hand-to-mouthcase)Cost of effort curvature γUnobserved Heterogeneity: kh, km and kl cost types, and theirproportions (only one type for ref. dep. model)
Fixed parameters:Gain-loss utility weight η = 0 (standard model), η = 1 (ref.-dep.model) LinkReemployment wage fixed at the empirical median Link
Start with hand-to-mouth estimates (ct = yt)
Reference-Dependent Job Search 19 / 47
Model Estimation Hand-to-Mouth Estimates
Standard Model, 3 types (Hand-to-Mouth)
0 50 100 150 200 250 300 350 400 450 500 550Days elapsed since UI claimed
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
haza
rd r
ate
Hazard rates, actual and estimated
Actual Hazard, BeforeEstimated Hazard, BeforeActual Hazard, AfterEstimated Hazard, After
Reference-Dependent Job Search 20 / 47
Model Estimation Hand-to-Mouth Estimates
Ref.-Dep. Model, 1 types (Hand-to-Mouth)
0 50 100 150 200 250 300 350 400 450 500 550Days elapsed since UI claimed
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
haza
rd r
ate
Hazard rates, actual and estimated
Actual Hazard, BeforeEstimated Hazard, BeforeActual Hazard, AfterEstimated Hazard, After
Reference-Dependent Job Search 21 / 47
Model Estimation Estimates with Consumption-savings
Incorporating Consumption-Savings
Previous results have key weaknessReference-dependent workers are aware of painful loss utility atbenefit decreaseShould save in anticipationRuled out by hand-to-mouth assumption
Introduce optimal consumption:In each period t individuals choose search effort s∗t andconsumption c∗tEstimate also degree of patience δ and β, δ
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Model Estimation Estimates with Consumption-savings
Standard model (Optimal Consumption)
0 50 100 150 200 250 300 350 400 450 500 5500
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Days elapsed since UI claimed
haza
rd r
ate
Hazard rates, actual and estimated
Actual Hazard, BeforeEstimated Hazard, BeforeActual Hazard, AfterEstimated Hazard, After
Standard model with 3 cost types and estimated δ performs nobetter than with hand-to-mouth assumption
Reference-Dependent Job Search 24 / 47
Model Estimation Estimates with Consumption-savings
Ref.-Dep. model (Optimal Consumption)
0 50 100 150 200 250 300 350 400 450 500 550Days elapsed since UI claimed
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
haza
rd r
ate
Hazard rates, actual and estimated
Actual Hazard, BeforeEstimated Hazard, BeforeActual Hazard, AfterEstimated Hazard, After
Reference-dependent model with estimated δ performs wellBUT: estimated δ = .9 (bi-weekly) – not realistic
Reference-Dependent Job Search 25 / 47
Model Estimation Estimates with Consumption-savings
Ref.-Dep. model - Discount Factor Estimated
Ref.-Dep. Model - β estimated Ref.-Dep. Model - δ estimated
0 50 100 150 200 250 300 350 400 450 500 5500
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Days elapsed since UI claimed
haza
rd r
ate
Hazard rates, actual and estimated
Actual Hazard, BeforeEstimated Hazard, BeforeActual Hazard, AfterEstimated Hazard, After
0 50 100 150 200 250 300 350 400 450 500 550Days elapsed since UI claimed
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
haza
rd r
ate
Hazard rates, actual and estimated
Actual Hazard, BeforeEstimated Hazard, BeforeActual Hazard, AfterEstimated Hazard, After
The reference-dependent model with β, δ performs about equally well- Laibson (1997), O’Donoghue and Rabin (1999), Paserman (2008),Cockx, Ghirelli and van der Linden (2014)Estimated β̂ = 0.58 with δ = .995, reasonableNoticed: maintained naiveté
Reference-Dependent Job Search 26 / 47
Model Estimation Estimates with Consumption-savings
Benchmark Estimates (Optimal Consumption)
Structural estimation of Standard and Ref.-Dep. models - Optimal Consumption(1) (2) (3) (4)
Standard RefD. Standard RefD.Discounting: Delta Delta Beta BetaParameters of Utility functionUtility function ν(.) log(b) log(b) log(b) log(b)Loss aversion λ 4.92 4.69
(0.58) (0.62)Gain utility η 1 1Adjustment speed of reference 184 167.5point N in days (11) (11.2)δ 0.93 0.89 0.995 0.995
(0.01) (0.02)1 1 0.92 0.58
β (0.01) (0.19)Parameters of Search Cost FunctionElasticity of search cost γ 0.4 0.81 0.07 0.4
(0.04) (0.16) (0.01) (0.2)Model FitGoodness of fit 227.5 194.0 229.0 183.5Number of cost-types 3 1 3 1
Reference-Dependent Job Search 27 / 47
Model Estimation Estimates with Consumption-savings
Goodness of fit by Impatience
Extra dividend of optimal consumption: Estimate patience
Unemployed workers estimated to be very impatientImpatience too high in δ model, but realistic with β, δ model⇒ Evidence supporting present-bias
Ref.Dep. Model - SSE by (by-weekly)δ Ref.-Dep. Model - SSE by β
●
benchmark estimates
Conclusion
Ongoing Work: Survey
Key prediction of different models on search effort
Search Effort, Standard model Search Effort, Reference Dependence
T T+N0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08Hazard rate in the Standard Model
Haz
ard
Rat
e
PeriodsT T+N
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08Hazard rate in the Reference Dep. Model
Haz
ard
Rat
e
Periods
⇒ Ideally we would have individual level panel data on searcheffort
Reference-Dependent Job Search 45 / 47
Conclusion
Ongoing Work: Survey
Build on Krueger and Mueller (2011, 2014):Large web based survey among UI recipients in NJ5% participation rateNo benefit expiration in their sample
Reference-Dependent Job Search 46 / 47
Conclusion
Ongoing Work: Survey
Conduct SMS-based survey in 2017 in Germany with IABTwice-a-week ‘How many hours did you spend on search effortyesterday?’
Follow around 10,000 UI recipients over 4 months.Use discontinuity in benefit duration (6/8/10 months) to getcontrol groupExamine in particular search effort around benefit expiration
Advantages of SMS messages:
Very easy to reply / low cost to respondent.A lot of control, easy to send reminders etc.
Reference-Dependent Job Search 47 / 47
Reference Dependence: Full Prospect Theory
Section 3
Reference Dependence: Full Prospect Theory
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 41 / 101
Reference Dependence: Full Prospect Theory
Introduction
Two key features of evidence so far1 Focus not on Risk
Much of the laboratory evidence on prospect theory is on risktakingField evidence considered so far (mostly) does not directlyinvolve riskHouse Sale, Merger Offer, EffortNow evidence explicitly on settings with risk: insurance andfinancial choices
2 Focus on Loss Aversion exclusivelyNow examine settings where probability weighting plays roleDiminishing sensitivity also in finance
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 42 / 101
Reference Dependence: Insurance
Section 4
Reference Dependence: Insurance
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 43 / 101
Reference Dependence: Insurance Sydnor (2010)
Introduction
Sydnor (AEJ Applied, 2010) on deductible choice in the lifeinsurance industry
Menu Choice as identification strategy as in Del
laVigna and Malmendier (2006)
Slides courtesy of Justin Sydnor
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 44 / 101
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
Features of ContractsStandard homeowners-insurance policies (no renters, condominiums)Contracts differ only by deductibleDeductible is per claimNo experience rating
Though underwriting practices not clearSold through agents
Paid commissionNo “default” deductible
Regulated state
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 differences
ΔPi = 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:
Getting the bounds
Search algorithm at individual levelNew customers
Claim rates: Poisson regressionsCap at 5 possible claims for the year
Lifetime wealth:Conservative: $1 million (40 years at $25k)More conservative: Insured Home Value
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 −−−
Parameter values
Kahneman and Tversky (1992)λ = 2.25β = 0.88
Weighting function
γ = 0.69
γγγ
γ
ππππ 1
))1(()(
−+=w
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
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Reference Dependence: Insurance Barseghyan et al. (2013)
Predicted Claim Probabilities
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 65 / 101
Reference Dependence: Insurance Barseghyan et al. (2013)
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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 66 / 101
Reference Dependence: Insurance Barseghyan et al. (2013)
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 67 / 101
Reference Dependence: Insurance Barseghyan et al. (2013)
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 68 / 101
Reference Dependence: Equity Premium
Section 5
Reference Dependence: Equity Premium
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 69 / 101
Reference Dependence: Equity Premium
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 ≥ 20Benartzi 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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 70 / 101
Reference Dependence: Equity Premium 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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 71 / 101
Reference Dependence: Equity Premium 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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 72 / 101
Reference Dependence: Equity Premium Other Examples
Other Narrow Framing Work
Barberis, Huang, and Santos (QJE 2001)
Piecewise linear utility, λ = 2.25
Narrow framing at aggregate stock level
Range of implications for asset pricing
Barberis and Huang (2001)
Narrowly frame at individual stock level (or mutual fund)
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 73 / 101
Reference Points: Forward- vs. Backward-Looking
Section 6
Reference Points: Forward- vs.
Backward-Looking
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 74 / 101
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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 75 / 101
Reference Points: Forward- vs. Backward-Looking
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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 76 / 101
Reference Points: Forward- vs. Backward-Looking
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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 77 / 101
Reference Points: Forward- vs. Backward-Looking
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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 78 / 101
Reference Points: Forward- vs. Backward-Looking
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?
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 79 / 101
Reference Dependence: Endowment Effect
Section 7
Reference Dependence: Endowment Effect
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 80 / 101
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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 81 / 101
Reference Dependence: Endowment Effect Plott and Zeiler (2005)
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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 82 / 101
Reference Dependence: Endowment Effect Plott and Zeiler (2005)
This implies:
WTA: Status-Quo ∼ Selling Mugu{mug} − u{mug} = λ [u {∅} − u{mug}] + pWTA or
pWTA = λu{mug}WTP: Status-Quo ∼ Buying Mug
u {∅} − u {∅} = u{mug} − u {∅} − pWTP orpWTP = u{mug}
It follows that
pWTA = λu{mug} = λpWTPIf loss-aversion over money,
pWTA = λ2pWTP
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 83 / 101
Reference Dependence: Endowment Effect Plott and Zeiler (2005)
Results
Result WTA ' 2 ∗WTP is consistent with loss-aversion λ ' 2Plott and Zeiler (AER 2005): The result disappears with
appropriate trainingpractice roundsincentive-compatible procedureanonymity
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 84 / 101
Reference Dependence: Endowment Effect Plott and Zeiler (2005)
Interpretation 1
Endowment effect and loss-aversion interpretation are wrong
Subjects feel bad selling a ‘gift’Not enough training
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 85 / 101
Reference Dependence: Endowment Effect Plott and Zeiler (2005)
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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 86 / 101
Reference Dependence: Endowment Effect Plott and Zeiler (2005)
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
Go over Goette, Harms, and Sprenger (2016)
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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 87 / 101
Reference Dependence: Endowment Effect Goette, Harms, and Sprenger (2016)
Prediction
For p > 0.5 � Reverse endowment effect
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 88 / 101
Reference Dependence: Endowment Effect Goette, Harms, and Sprenger (2016)
Results
What do they find? Mostly, full endowment effect, no KR
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 89 / 101
Reference Dependence-KR: Effort
Section 8
Reference Dependence-KR: Effort
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 90 / 101
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 pointAssume 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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 91 / 101
Reference Dependence-KR: Effort Abeler et al. (2011)
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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 92 / 101
Reference Dependence-KR: Effort Abeler et al. (2011)
Standard Model
maxe
T + pe
2− c (e)
−− > e∗ = c ′−1 (p/2)
Solution does not depend on target T
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 93 / 101
Reference Dependence-KR: Effort Abeler et al. (2011)
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 )
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 94 / 101
Reference Dependence-KR: Effort Abeler et al. (2011)
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 )
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 95 / 101
Reference Dependence-KR: Effort Abeler et al. (2011)
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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 96 / 101
Reference Dependence-KR: Effort Abeler et al. (2011)
Results
KR effect on effort, though smaller than one would expect
Anchoring can be confound
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 97 / 101
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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 98 / 101
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
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 99 / 101
Reference Dependence-KR: Effort Gneezy et al. (2017)
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?
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 100 / 101
Reference Dependence-KR: Effort Gneezy et al. (2017)
Next Lecture
Social Preferences
Wave I: AltruismWave II: Warm GlowWave III: Inequity AversionWave IV: Social Pressure, Social Signalling, and Social Norms
Stefano DellaVigna Econ 219B: Applications (Lecture 6) February 21, 2018 101 / 101
Reference Dependence: GolfPope and Schweitzer (2011)
Reference Dependence: Job SearchDellaVigna et al. (2017)
Reference Dependence: Full Prospect TheoryReference Dependence: InsuranceSydnor (2010)Barseghyan et al. (2013)
Reference Dependence: Equity PremiumBenartzi and Thaler (1995)Other Examples
Reference Points: Forward- vs. Backward-LookingReference Dependence: Endowment EffectPlott and Zeiler (2005)Goette, Harms, and Sprenger (2016)
Reference Dependence-KR: EffortAbeler et al. (2011)Gneezy et al. (2017)