Inequality Aversion: Theory
and Empirical Evidence
Josephine Böge, Maren Kämmerer,
Gerelmaa Gerelsaikhan & Javkhlan Tahery Boeini
Content
1 Introduction and theory of Inequity Aversion
2 Inequity Aversion in Economic Experiments
 Ultimatum Game
 Dictator Game
 Market Game (Proposer vs. Responder Competition)
3 Criticism
4 Empirical evidences and studies on Inequality Aversion
1. Inequity Aversion
 People behave differently in various situations
 Behave selfish according to rationality and
competitive markets
 Behave according to social norms, eg. fairness,
reciprocity or altruism
 Can this be explained in one simple model?
 Fehr & Schmidt: YES!
Assumption: Additional to self-interested people,
there is a fraction of people motivated by
fairness considerations
1. Theory I
“An individual is inequity averse if he dislikes
outcomes that are perceived as inequitable.”
xi ; xj
= monetary payoff
αi
= player i’s disutility of having less than player j
βi
= player i’s disutility of having more than player i
1. Theory II
Preferences with Inequity Aversion *
* Fehr & Schmidt, “A Theory of Fairness, Competition, and Cooperation”, Quarterly Journal of Economics, 1999, p.815-886
2.1 Ultimatum Game I
 Payoff (Proposer)
x1 = 1-s
 Payoff (Responder) x2 = s
 Self-interest model:
 Responder accepts any s ∈ (0,1)
 Responder indifferent in accepting or declining s = 0
 Unique Subgame Perfect Equilibrium: Proposer offers s = 0,
responder accepts
Numerous experiments refute this prediction
2.1 Ultimatum Game II
1. No offers s > 0.5
3. No offers s < 0.2
2. Majority of offers s [0.4,0.5] 4. Low offers are frequently rejected
* Fehr & Schmidt, “A Theory of Fairness, Competition, and Cooperation”, Quarterly Journal of Economics, 1999, p.827
2.2 Dictator Game
 Payoff (Dictator)
x1 = 1-s
 Payoff (Beneficiary) x2 = s
 Self-interest model: Dictator makes the decision s = 0
Numerous experiments refute this prediction
Percentage of offers
Dictators choices
20 %
s=0
60%
0 < s < 0.5
20%
s = 0.5
Fehr & Schmidt, “A Theory of Fairness, Competition, and Cooperation”, Quarterly Journal of Economics, 1999, p.847
study of Forsythe, Horowitz, Savin and Sefton (1994)
2.3 Market Game:
Proposer Competition
 Only concern payoff: responder accepts any s > 0
 Subgame perfect equilibrium: two proposers offer one
good, responder has advantage
 Proof:
 All players offer
 If player i increases offer → increases probability to get
chosen
 Turns inequality towards other proposers to his advantage
 cannot be subgame perfect equilibrium, needs to
be at least 2 sellers offering
→ no single player can enforce an equitable outcome
2.3 Market Game:
Responder Competition
 Self-interest model:
 Responder accepts any s > 0
 Indifferent about accepting or rejecting s = 0
 Subgame perfect equilibrium: Proposer offers s = 0,
one responder accepts offer
→ Experiment shows model holds true
 As long as there is one responder accepting s = 0
no other can prevent an inequitable outcome
→ Even very inequitable-averse responders try to
use the unavoidable inequality to have an
advantage (accepting low offers)
3. Critics on Inequality
Aversion
 Theories by Fehr & Schmidt doubtful
 Misquoting their own theorems
 Inflating their own results
 Statements and arguments full of confusion
 Limited applicability and no deeper explanatory power
 F & S change basic assumptions of selfishness by
introducing a utility function which will permit equity
to enter the individuals‘ preferences
 Utility function depends on the material payoffs of all
individuals – Only deviation from traditional theory
3.1 Ultimatum Game I
 Proposers do not offer > ½ of the surplus
 Finding the distribution of their ß‘
 Responder faces with offer < ½ of the surplus
 Uses a to accept or reject the offer
 Need to have detailed information on offer
rejection rates by responders to find the distribution
of a‘s
 But: the information is not given by Fehr & Schmidt
3.1 Ultimatum Game II
 Fehr & Schmidt‘s proposed a,ß distribution gives
only rough intervals of ß‘s
 Proposers who offered 0.5 have ß ≥ ½
 For these 40% of population F&S have arbitrarily
chosen ß = 0.6
 Calibration of distributions of a, ß‘s are used to
explain the experimental behavior in different games
3.2 Dictator Game
 F & S provide insight why the theory of inequity
aversion can explain the behavior in experiments
of dictator games, but they do not try to explain
it using the calibration
 They did not use the Dictator Game to calibrate their
model
 Incompatible with data: The model predicts that
offers will be 0 or exactly 0.5, which is typically not
the case
3.3 Market Game: Proposer
Competition I
 Responder is restricted to consider only the highest
offer → prevents from practicing any inequality
aversion he may have
 Responder who receives 2 offers (whole cake & half
cake) is restricted to choose between accepting offer
1 or rejecting it and having 0 and is not allowed to
consider the offer 0.5
 Preventing from choosing the equitable point
 F&S do not differ on how high the inequity aversion is
but this game does not allow the inequity aversion to
be arbitrarily high → one player is not allowed to have
or practice inequity aversion
3.3 Market Game: Proposer
Competition II
 If no restriction and the responder is allowed to
accept or reject any offer and he is endowed with
high inequity aversion, ß >
, the only equilibrium is
the equitable partition in which all the proposers offer
½ and the responder accepts it
 → responder can force an equitable outcome
irrespective of how selfish the other players are
 F&S do not consider this
 Contrary to F&S: It shows that fairness considerations do
matter even in competitive situations and F&S’s theory is
not compatible with the experimental observations on
competitive markets
3.3. Market Game:
Responder Competition I
 Single proposer makes an offer to a number of
responders
 F&S: to obtain an outcome which is close to the
competitive equilibrium the proposer and at least one
of the responders need to be sufficiently selfish
 If proposer’s ß is not too high, ß <
, and if one of the
responders is willing to accept a low share of the surplus
 All other responders are forced to accept this share in
equilibrium
 Closeness of the equilibrium to the competitive outcome
depends on the most selfish responder & proposer’s
selfishness
3.3 Market Game:
Responder Competition II
 If the single proposer is sufficiently inequity averse, ß<
,
the only equilibrium is one in which he proposes ½ and all
accept it
 Contrary to F&S: A single player can enforce an equitable
outcome
 F&S ignore the condition on the proposer’s selfishness and
misquote the proposition
 → F&S’s general principle does not apply to Proposer and
Responder competition
4.1 Inequality aversion in
country studies
Selected OECD countries’ income redistribution
Country & year
Gini before taxes Gini after taxes
and transfers
and transfers
% changes
Germany, 1994
43.6
28.2
-35.3
Denmark, 1994
42.0
21.7
-48.3
Sweden, 1994
48.8
23.4
-52.1
Italy, 1993
51.0
34.5
-32.4
United States,
1995
45.5
34.4
-24.5
OECD, 1997
4.1 Inequality aversion in
country studies
 Estimation methods are various: E.g. linking to preand post-government income distribution
 Germany:
 The residents are not inequality-averse themselves
 The state cannot make any contribution towards
reducing inequality and increasing wellbeing
 Any action taken by the state increases the
burden on middle income civilians
4.2 Inequality aversion in
companies
 Optimal employment contracts:
 Employees are inequality-averse
 Employees are inequality-neutral  Case 1
 Employers offer contracts ‘off-equilibrium’
 Employees feel ‘guilt’ or ‘envy’ when the employer’s
demand is not met
 What would the optimal contract be in this case?
4.3 Inequality aversion in
healthcare sector
 Private healthcare insurance
 Uniform public healthcare
• in which everyone receives the same care and
pays the same healthcare premiums
 Supplemental healthcare insurance
• Option to purchase extra insurance
References
 Fehr E. & Schmidt K. M., 1999: A Theory Of Fairness,
Competition, And Cooperation, The Quarterly
Journal of Economics, 114 (3), Aug, pp 817-868
 Schwarze J. & Härpfer M., 2003: Are People
Inequality Averse, and Do They Prefer Redistribution
by the State? A Revised Version, ZA DP No. 974,
Discussion paper series
 Leach S., 2009: Income Disparity, Inequity Aversion
and the Design of the Healthcare System,
Scandinavian Journal of Economics 111(2), pp 277–
297
 Bergh A., 2008: A critical note on the theory of
inequity aversion, The Journal of Socio-Economics
 Shaked, A., 2005: The Rhetoric of Inequity Aversion,
NAJ Economics
Thank you for your attention!