Y. Masatlioglu and N. Uler
University of Michigan
Do Reference Points Influence Economic Outcomes?
Standard Neoclassical Theory: If transactions costs are small enough, reference points
should not influence rational consumers.
In practice, defaults make an enormous difference: Organ donation Car insurance Car purchase options Consent to receive e-mail marketing Savings Asset allocation
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Reference-Dependent Behavior
Endowment Effect The gap between WTA and WTP
Status Quo Bias People often stick with their default options
Reference Effect Reference points alter one's choices even when agents do not stick to the reference point itself
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The Reference Effect
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r
y
x
Good 1
Goo
d 2 STATUS QUO BIAS
x is more likely to bechosen from the set {x, y} when x is the endowment,
REFERENCE EFFECTx is more likely to bechosen from the set {x, y, r} when there is an endowment, r.
Reference-Dependent Models
• Behavioral Models (Positive Approach)Tversky and Kahneman (1991)
• Rational Models (Normative Approach)Masatlioglu and Ok (2005, 2007, 2009)
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Tversky and Kahneman (1991)(Loss Aversion Model (LA))
• Reference dependence
• Loss aversion
• Diminishing sensitivity
)]()([)( iii
iii ruxugxrU
][][ agag ii
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ig concave for a > 0, convex for a < 0
Shortcomings of the LA model
• Non-convex Indifference Curves
• Unusual Cyclical Choices
• Accommodates not only Status Quo Bias but also Status Quo Aversion
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Unusual Preference Cycles Munro and Sugden (2003) show that one can find three alternatives,
x, y and z such that
)()( yUzU yy
)()( zUxU zz
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)()( xUyU xx
xyzx xyz
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Loss Aversion Model predicts Status Quo Aversion EXAMPLE: Consider an environment in which an agent needs to choose
among pairs (x,m), where x and m stand for the units of a private good and money, respectively.
0)(20
)(020
)(8.0
8.0
aifaaifa
agaifaaifa
ag mx
*)(*)(),(*)*,( mmgxxgmxU mxmx
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€
U(0,0)(1,100) >U(0,0)(0,103)
Choose between “one mug and $100” and “no mug and $103” when there is no reference:
€
U(1,100)(1,100) <U(1,100)(0,103)
Now, status quo is “one mug and $100” what would you do?
STATUS QUO AVERSION !!!
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Constant Loss Aversion (CLA)
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We say Constant Loss Aversion if there is no diminishing sensitivity or constant sensitivity (gi is linear).
While Loss Aversion Model (i) permits non-convex indifference curves and intransitive preferences(ii) accommodates not only status quo bias but also status quo aversion,
While Constant Loss Aversion does not suffer from these implications, it is much more restrictive than the LA model.
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The Multi-criteria Choice ModelMasatlioglu and Ok (2005)
If y is chosen when x is the status quo point, then, y must be chosen when y is itself the status quo.
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Axiom of Status Quo Bias
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Movie
Sports
r1
r2 r
Acceptable alternatives
when r is status quo
Assume that r is the status quo
u2
u1
U = w1u1+w2u2
Masatlioglu and Ok, 2005 (The SQB Model)
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Loss Aversion vs. Status Quo Bias
Loss Aversion Model
Status Quo Bias Model
)(xrU
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Q(r)Bxmax
)(xU
Bxmax
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The Generalized SQB ModelMasatlioglu and Ok (2009)
)()()()(
rUyUrQyrQr
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Q(r)xmaxS
)(xU
such that Mental Constraint
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The Procedural RD Model Masatlioglu and Ok (2007)
)()()( rQyQrQy iii
)()()()(
rUyUrQyrQr
i
i
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otherwiseSS
(r)2Qx(r)1Q{r} if(r)1Qx
max
)(xU
such that
Another generalization of SQB model with two mental constraints, Q1and Q2
Some Facts about Experiment
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Conducted at C.E.S.S. (NYU) A total of 99 subjects Money and Chocolate Each subject answered 16 questionsOn average, earned $14 including the $7 show-up
fee and also some chocolates
Experimental Design
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r1
r5 r2r3r7
r6 r4
y
x
r0 Money
Bel
gium
Cho
cola
te
A Screen Shot from the Experiment
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Experimental Design: Theoretical Predictions
r1 r2
Classical Choice Theory
y y Yes
y x No
x x No
x y No
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r1
r2
y
x
r0 Good 1
Goo
d 2
There are four possible cases:
Assume that y is preferred to x when there is no reference point.
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Loss Aversion Model
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x
r2
y
r1
LA model favors x
Good 1
Good 2
r1 r2 LA CLA
y y Yes Yes
y x Yes Nox x Yes Yesx y No No
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SQB ModelAcceptable Alternatives Choice
r1 r1 x x
r2 r2 x y y
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r1
x
y
r2
SQB model favors y
u2
u1
u2
u1
r1 r2 SQB
y y Yes
y x Nox x Yesx y Yes
Good 1
Good 2
Generalized SQB Model
r1 r2 SQB GSQB
y y Yes Yes
y x No Yesx x Yes Yesx y Yes Yes
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Q(r1)
r2 Q(r2)
r1
x
y Q(r) ∩ B Choice
r1 r1 x y y
r2 r2 x x
GSQB model is indecisive
Good 1
Good 2
Procedural R-D ModelElimination
ChoiceQ1(r) ∩ B Q2(r) ∩ B
r1 r1 r1 x y y
r2 r2 x - x
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x
Q1(r1)
Q2(r1)
r2
y
Q1(r2)
Q2(r2)
r1
PRD model is also indecisive
r1 r2 SQB PRD
y y Yes Yes
y x No Yesx x Yes Yesx y Yes Yes
Good 1
Good 2
Theoretical Predictions for r1 r2
Tversky - Kahneman Masatlioglu - Ok
CLA LA SQB GSQB PRD
r1→ r2 - Favors x Favors y Indecisive Indecisive
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r1
r2
y
x
r0 Money
Belgium Chocolate
Theoretical Predictions
Tversky - Kahneman Masatlioglu - Ok
CLA LA SQB GSQB PRD
Group 1
r0→ r5 - I - - I
r0→ r6 - I - - I
r0→ r7 - I - - I
Group 2
r1→ r2 - x y I I
r3→ r4 - x y I y
r5→ r6 - x - - I
r5→ r7 - y - - I
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r1
r5 r2r3r7
r6 r4
y
x
r0
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Reference Effect: Preference Reversals
No reversal 269 %73Reversal 97 %27# Obs 366
r1→ r2 r3→ r4 r5→ r6 r5→ r7
r1 r2 r3 r4 r5 r6 r5 r6
No reversal 40 33 42 40 32 30 25 27Reversal 14 21 14 16 5 7 11 9# subjects 54 56 37 36
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Comparison of the Models
Tversky - Kahneman Masatlioglu - Ok Classical TheoryCLA LA SQB GSQB PRD
Total 65 89 68 75 93 48
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Explanatory Power of the Models (in percentages)
Selten’s Measure of Predictive Success
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Conclusion
• Existence of the reference effect• An experiment that distinguish between the
models of reference-dependence. • R-D Models make different predictions
regarding the reference effect. • We find that both the PRD and LA models
explain approximately 90 percent of the data.
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THANK YOU
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A Sample Question from the Experiment
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Is SQB Axiom too strong?
)},,({)},,({yzyczxyxcy
)},,({ xzxcz
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Take x = CUNY, y = OSU and z = UM
OSU = c({CUNY, OSU},CUNY)
UM = c({OSU, UM},OSU)
But CUNY = c({CUNY, UM},CUNY)
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Relaxing SQB Axiom?
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Weak Status Quo Bias
andimplies
implies
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