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Measuring tastes for equity and aggregatewealth behind the veil of ignorance
Jan HeuferErasmus University Rotterdam and Tinbergen Institute
Jason ShachatDurham University and Wuhan University
Yan XuErasmus University Rotterdam and Tinbergen Institute
September 2019
Problem: efficiency vs. equity
• How do people make trade-offs between aggregate wealth anddistributional equality among social members?
• a big cake with an uneven split• a small cake with an equal split
• Harsanyi’s (1953) Veil of Ignorance (VoI) framework:
• choose a wealth distribution for all social members• ignorant of individual position on the income ladder• know ex-ante that each position is equally likely
1
Problem: efficiency vs. equity
• How do people make trade-offs between aggregate wealth anddistributional equality among social members?
• a big cake with an uneven split• a small cake with an equal split
• Harsanyi’s (1953) Veil of Ignorance (VoI) framework:
• choose a wealth distribution for all social members• ignorant of individual position on the income ladder• know ex-ante that each position is equally likely
1
A VoI choice problem for a two-person economyRi
ch
Poor
xA
yA A
Rich
Poor
budget: y + qx = z
xA
yA A
xB
yB B
45◦
x
y
• efficiency: x + y• equity: x
x+y• trade-offs?
2
A VoI choice problem for a two-person economy
Rich
Poor
xA
yA A
Rich
Poor
budget: y + qx = z
xA
yA A
xB
yB B
45◦
x
y
• efficiency: x + y• equity: x
x+y• trade-offs?
2
A Risk choice problem for an individual DM?Ri
ch
Poorx∗
A
y∗A A
xB
yB B
45◦
x
y
• Good state: Rich• Bad state: Poor• Lotteries: A and B
3
A Risk choice problem for an individual DM?Ri
ch
Poorx∗
A
y∗A A
xB
yB B
45◦
x
y
• Good state: Rich• Bad state: Poor• Lotteries: A and B
3
Problem: Risk and social preferences conflate behind VoI
VoI preference 6= social preference over efficiency-equity trade-off= risk preference?
∆(VoI preference, risk preference) ≡ “pure social preference”
This paper:
• measure the “pure social preference”
• relationships between risk and “pure social preference”
4
Problem: Risk and social preferences conflate behind VoI
VoI preference 6= social preference over efficiency-equity trade-off= risk preference?
∆(VoI preference, risk preference) ≡ “pure social preference”
This paper:
• measure the “pure social preference”
• relationships between risk and “pure social preference”
4
Problem: Risk and social preferences conflate behind VoI
VoI preference 6= social preference over efficiency-equity trade-off= risk preference?
∆(VoI preference, risk preference) ≡ “pure social preference”
This paper:
• measure the “pure social preference”
• relationships between risk and “pure social preference”
4
Remedy: paired choice problems
45◦
x∗Risk
y∗Risk
x
y
(a) Risk Problem
45◦
x∗VoI
y∗VoI
x
y
(b) VoI Problem
A classification of social preferences:• equity-preferring: x∗
Risk < x∗VoI
• socially agnostic: x∗Risk = x∗
VoI• efficiency-preferring: x∗
Risk > x∗VoI
5
Remedy: paired choice problems
45◦
x∗Risk
y∗Risk
x
y
(c) Risk Problem
45◦
x∗VoI
y∗VoI
x
y
(d) VoI Problem
A classification of social preferences:• equity-preferring: x∗
Risk < x∗VoI
• socially agnostic: x∗Risk = x∗
VoI• efficiency-preferring: x∗
Risk > x∗VoI
5
Induced budget experiment
we create forty budget sets y + qx = z , where• expenditure z ∈ {50, 80, 110, 140, 170, 200, 230, 260} and• price q ∈ {1, 2, 3, 4, 5}.
45◦
100
100
200
200
Rich
/goo
dst
ate
weal
th
Poor/bad state wealthx
y
6
Experimental interface
7
Experimental procedures
• 10 sessions totalling 92 subjects
• Subjects recruited from undergraduate and master students atXiamen University
• Within-subject design with paired choice problems• 40 choices per subject for Risk treatment• 40 choices per subject for VoI treatment
• One of 80 choices is randomly selected for payment
• Randomization fiesta: interface, treatment order, budgetorder, slider’s initial location, random match for VoI
• Duration of each session is 100 minutes on average andaverage payment is 55+10 Yuan
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Choices by illustrative subjects: similar choices
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VoI Choices of Subject 89
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Choices by illustrative subjects: different choices
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The BIG takeaway: individual treatment effects
−0.13
0
25
50
75
100
−20 0 20
24 equity-pref24 equity-pref
17 efficy-pref
24 equity-pref
17 efficy-pref
51 agnostic
xVoI − xRisk: mean and 95% confidence interval for each subject11
The BIG takeaway: individual treatment effects
−0.13
0
25
50
75
100
−20 0 20
24 equity-pref
24 equity-pref
17 efficy-pref
24 equity-pref
17 efficy-pref
51 agnostic
xVoI − xRisk: mean and 95% confidence interval for each subject11
The BIG takeaway: individual treatment effects
−0.13
0
25
50
75
100
−20 0 20
24 equity-pref
24 equity-pref
17 efficy-pref
24 equity-pref
17 efficy-pref
51 agnostic
xVoI − xRisk: mean and 95% confidence interval for each subject11
The BIG takeaway: individual treatment effects
−0.13
0
25
50
75
100
−20 0 20
24 equity-pref24 equity-pref
17 efficy-pref
24 equity-pref
17 efficy-pref
51 agnostic
xVoI − xRisk: mean and 95% confidence interval for each subject11
Reduced form demand curves by clusters
• Risk reduced demand curves are the same for three clusters.• VoI reduced demand curves differ across three clusters.
12
Reduced form demand curves by clusters
• Risk reduced demand curves are the same for three clusters.• VoI reduced demand curves differ across three clusters.
12
Misclassification due to large variations?
−0.13
0
25
50
75
100
−20 0 20
51 agnostic
−0.13
0
25
50
75
100
−20 0 20
51 agnostic
−0.13
0
25
50
75
100
−20 0 20
51 agnostic
Can we do better in classifying social preference types?
13
Misclassification due to large variations?
−0.13
0
25
50
75
100
−20 0 20
51 agnostic
−0.13
0
25
50
75
100
−20 0 20
51 agnostic
−0.13
0
25
50
75
100
−20 0 20
51 agnostic
Can we do better in classifying social preference types?
13
Misclassification due to large variations?
−0.13
0
25
50
75
100
−20 0 20
51 agnostic
−0.13
0
25
50
75
100
−20 0 20
51 agnostic
−0.13
0
25
50
75
100
−20 0 20
51 agnostic
Can we do better in classifying social preference types?
13
Misclassification due to large variations?
−0.13
0
25
50
75
100
−20 0 20
51 agnostic
−0.13
0
25
50
75
100
−20 0 20
51 agnostic
−0.13
0
25
50
75
100
−20 0 20
51 agnostic
Can we do better in classifying social preference types?
13
Roadmap for further analyses
• non-parametric revealed preference analyses
• rationality: GARP violation, Afriat’s CCEI and its power
• homotheticity: HARP violation, HEI and its power
• Classification: relative convexity of Risk versus VoIindifference curves
• parametric structure estimation analyses
• rational choices ⇔ maximize a well-behaved utility function
• Classification: relative concavity of Risk versus VoI utilityfunctions
14
Conclusion
• We construct an instrument to measure individual’s preferenceover the trade-off between equity and efficiency behind VoI.
• Both risk and social preferences are highly heterogeneous, butconsistent with maximizing (maybe) non-homothetic utilities.
• Individual risk preferences are uncorrelated with socialpreferences over efficiency and equity.
• Aggregate level: socially agnostic
• Individual level: clear clusters of equity-preferring,efficiency-preferring and socially agnostic
• Classification: statistical, non-parametric and parametric
15
Thank you for your attention!
Contributions to the literature
• Three DM’s perspectives in eliciting social preferences:• as a dictator in front of a VoI: multiple motives include warm
glow, selfish, efficiency, equity, maxmin ect.– Engelmann and Strobel (2004); Charness and Rabin (2002)
• as a disinterested social planner behind a VoI: problem ofincentive compatibility– Traub et al. (2005,2009); Hong et al. (2015)
• as a society member behind a VoI:– Frignani and Ponti (2012): binary choices– Schildberg-Horisch (2010): fixed trade-offs
• Elicitation methods with linear budget experiments:• elicit social preferences with the dictator game: Andreoni and
Miller (2002); Fisman et al. (2007).• elicit risk preferences: Choi et al. (2007, 2014)
16
CCEI for participants and random choices
0.6 0.7 0.8 0.9 1.
10%
20%
30%
40%
50% VoIRisk
0.6 0.7 0.8 0.9 1.
5%
10% randomchoice sets
Figure: Histogram of the CCEI for 92 subjects and for 10,000 randomchoices over the budget sets. 17
HEI for participants and random choices
0.6 0.7 0.8 0.9 1.
5%
10% VoIRisk
0.6 0.7 0.8 0.9 1.
5%
10% randomchoice sets
Figure: Histogram of the HEI for 92 subjects and for 10,000 randomchoices over the budget sets.
18
A revealed preference comparison of relative convexity of Risk versusVoI indifference curves
Partially Revealed More Convex (PRMC) is a binary relationship tocompare local convexity.
• two lotteries: S : (4, 6) and R : (2, 14)• Alice prefers S � R• Bob prefers R � S• whose indifference curve is more convex at S?
In our within-subject design, Alice and Bob correspond to eitherRisk-self or VoI-self of the same DM.
• Risk-PRMC: S is a choice in Risk task ⇒ efficiency-preferring• VoI-PRMC: S is a choice in VoI task ⇒ equity-preferring
19
Classifications based on curvature comparisons
Compare global convexity?
• unorderable: Risk-PRMC and VoI-PRMC hold at least once;• effciency-preferring: Risk-PRMC holds at least once while
VoI-PRMC never holds;• equity-preferring: VoI-PRMC holds at least once while
Risk-PRMC never holds;• socially agnostic: Risk-PRMC and VoI-PRMC never hold.
different similar
efficiency-preferring equity-preferrring un-ordable socially agnostic
26 (28.3%) 30 (32.6%) 20 (21.7%) 16 (17.4%)
20
Structure estimation of a subjective EU model
• maximize a subjective expected utility model αu(x) + u(y)
• assume CRRA utility function: u(x) = x1−ρi1−ρi
• VoI treatment dummy ρVoI = ρRisk + DVoI · ρdiff
• solving UMP yields the optimal allocation choices:
ln(x∗/y ∗) =
ln(ω) if ln(α)− ρ ln(ω) ≤ ln(q),
− 1ρ [ln(q)− ln(α)] if ln(α) < ln(q) < ln(α)− ρ ln(ω),
0 if ln(q) ≤ ln(α).
• estimate α, ρRisk and ρdiff for each subject
min80∑
j=1
[ln(
x j
y j
)− ln
(x j∗
y j∗
)]2
21
Classifications based on curvature differences ρdiff
0.07
0
20
40
60
−1 0 1
(a) EU model
0.11
0
20
40
60
−2 0 2
(b) SEU model
Figure: The estimated curvature differences ρdiff based on (e) expectedutility and (f) subjective expected utility model for each participant.
22
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