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 2. Majority of offers s [0.4,0.5]

3. No offers s < 0.2 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

 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)

2.3 Market Game: Responder Competition

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

Country & year Gini before taxes and transfers

Gini after taxes 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

Selected OECD countries’ income redistribution

OECD, 1997

4.1 Inequality aversion in country studies

  Estimation methods are various: E.g. linking to pre-

and 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!