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On the Methodology of Inequity Aversion Theory

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K. Binmore and A. Shaked. Experimental Economics: Science or What ?http://www.econ3.uni-bonn.de/shaked/topics/ScienceOrWhat.pdf, 2007

A. Shaked. The Rhetoric of Inequity Aversion. Seehttp://www.najecon.org/naj/cache/666156000000000612.pdf, 2005

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• Behavioral Economics

• Neoclassical economics does not assume ‘selfishness’

• Backward Induction. Refuted in Experiments (UG, Camerer)

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Testing Theories Scientifically• Prediction state range, use new data, replicating

experiments

• Logic (A→B)

• Cherry Picking: the events that a theory predicts, rival theory, multiple predictions.

• Fitting floating parameters

• Honesty: methodology, floating parameters, footnotes, appendices

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Inequity Aversion theory

the envy parameter,

the discomfort of being rich

α β

An individual is characterized by a pair

The population is described by a distribution of pairs

(a joint distribution of , )

α, β

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• Infinite parameters

• Consistent with a spectrum of outcomes.

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For 2 players dividing 1 unit:

x - α 1 - 2x x 0.5U x =

x - β 2x - 1 x 0.5

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For 2 players dividing 1 unit:

x - α 1 - 2x x 0.5U x =

x - β 2x - 1 x 0.5

x

U

0 0.5 1

0.5

-α

β ≤ 0.5

β ≥ 0.5

28 Juneconvexity ?Changing the peak ??

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• What is ‘fair’ depends on the context. Earning one’s share. Eckel’s gold star. Different cultures.

• Inequity Aversion is context-free

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The QJE. paper

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In their invited lecture F&S say:

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"The objective is rather to offer a first test for whether there is a chance that our theory is consistent with the quantitative evidence from different games. Admittedly, this test is rather crude.“ "Clearly, the above computations provide only rough evidence in favor of our model."

QJE

"Using the data that is available from many experiments on the ultimatum game, Fehr and Schmidt calibrate the distribution of α and β in the population. Keeping this distribution constant, they show that their model yields quantitatively accurate predictions across many bargaining, market and co-operation games."

INVITED:

and a year later:

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The UG does not determine the parameters. The model is under-identified, The data allows much freedom in choosing the parameters

x

U

0 0.5 1

0.5

-α

β ≤ 0.5

β ≥ 0.5

40% proposed 0.5, hence β ≥ 0.5

40% were offered 0.5 their α is undeterminedNo Joint distribution 1+ 2

αα

The Calibration

It is assumed that the proposers know the distribution of

α’s among the responders.

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The Calibration

They add this perfect correlation, in the appendix, to fit Fehr Gächter’s Public Goods Game with Punishmentwithout referring to it in the text

Why 0.6 ? They admit they chose it to fitFehr Gächter’s Public Goods Game with Punishment

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In the

2006

they no longer say they calibrated the model , but rather that they chose parameters that are consistent with the UG data.

But they used the data of other experiments for their ‘calibration’.This is a fitting rather than a predicting exercise.

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Public Goods game with Punishment

• Public Goods Games with/without Punishments

• Stranger/Partner design

• Experienced / Inexperienced players

In the first stage of the Public Goods Game with Punishment, each subject can simultaneously contribute towards a common pool, whose value is then enhanced and eventually redistributed to all players (including any free riders).

This standard Public Goods Game (without punishments) is then modified so that the subjects can punish each other at a second stage. Each player is informed of the contributions of the others, and then has the opportunity to reduce the payoff of a selected victimby 10% on payment of a small cost.

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Public Goods Games with punishments: Contributions ≥ 16: about 27% Contributions ≥ 15: about 40%

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F&S choose to explain the partner/experienced designalthough they claim to be interested in one-shot games

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I/A theory and PGG with punishments

Theorem: If there are ‘conditionally cooperative enforcers’ in the population, with high α and β, and β ≥ 0.6 and ALL other players have α = β =0, then for each

level of contribution x there is an equilibrium in which all contribute x.

This is why they introduced the correlation and β =0.6

This is inconsistent with the calibration

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I/A theory and PGG with punishments

Theorem: If there are ‘conditionally cooperative enforcers’ in the population, with high α and β, and β ≥ 0.6 and ALL other players have α = β =0, then for each

level of contribution x there is an equilibrium in which all contribute x.

This is inconsistent with the calibration

I/A theory and PGG with punishments

Theorem: If there are ‘conditionally cooperative enforcers’ in the population, with high α and β, and β ≥ 0.6 and ALL other players have α = β =0, then for each

level of contribution x there is an equilibrium in which all contribute x.

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I/A theory and PGG with punishments

Theorem: If there are ‘conditionally cooperative enforcers’ in the population, with high α and β, and β ≥ 0.6 and ALL other players have α = β =0, then for each

level of contribution x there is an equilibrium in which all contribute x.

Inequity Aversion predicts a continuum of equilibria with contributions in the range 0% - 100%

F&S choose the 100% contribution prediction, because it is efficient.

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Money-maximizing (selfish) theory and PGG with punishments

Subgame perfection is refuted

Nash equilibria (a threat to punish which is not realized since the other contributed) predicts contributions

The last game in a sequence is not played like a one-shot game.

In infinitely repeated games all individually rational outcomes are equilibria.

This can be achieved in finitely repeated games with some ‘irrational’ players(gang of four).

(Experimental behavior in finite horizon games is close to the predicted behavior in infinitely horizon game.)

The theory predicts the whole range of contributions

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100 % contributions

no contributions

I - A theory Money-max (selfish) theory

The Predictions of the Theories

F&S claim that Inequity Aversion predicts 100% contributionsand the ‘selfish’ theory predicts no contributions

S.P.E.

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Contract Games

"Using the data that is available from many experiments on the ultimatum game, Fehr and Schmidt calibrate the distribution of α and β in the population. Keeping this distribution constant, they show that their model yields quantitatively accurate predictions across many bargaining, market and co-operation games."

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Contract Games

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A principal offers a contract to an agent.

The agent can then exert a costly effort which produces a payoff for the principal.

The principal may offer the agent an Incentive, Trust or a Bonus contract.

In an incentive contract the principal may invest in verification technology, he names a wage, he demands an effort level and specifies a fine to be paid if the agent made a lower effort.

In a Bonus contract the principal names a wage, an effort level and a bonuswhich he may pay. Here, neither the agent’s effort nor the principal’s bonus arecontractually enforceable.

A Trust contract is like the bonus contract without the last stage, the stage in which the principal may pay a bonus.

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F&S assume in these papers that there are 60% individuals with α = β =0, and 40% with α = 2, β =0.6

Keeping the distribution constant ???

The QJE calibration

α = 2 ????

FS describe this new 40-60 distribution as a ‘simplification’ of the QJE calibration, as ‘following’ it and as being ‘in accordance with’ the QJE calibration.

They do not offer a discussion of when it is permitted to change a calibration.

In the proposed equilibrium an agent of this typedoes not play like a selfish agent

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Proposed Equilibrium

All principals offer the bonus contract.

Selfish agents choose high effort.

I-A agents choose low effort.

I-A principals pay bonus (equalizing payoffs) to selfish agents.

The calibrated theory (40-60) predicts that (bonus contract will be chosen)

40% of the agents choose low effort.

60% of the agents choose high effort

Of these 60% agents 40% (i.e. 24%) would be paid a bonus

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The calibrated theory (40-60) predicts that (bonus contract will be chosen)40% of the agents choose low effort.60% of the agents choose high effortOf these 60% agents 40% (i.e. 24%) would be paid a bonus

These simple predictions (40,60,24%) are not tested by F&S and are refuted.

The % of fair agents and principals are not equal and vary in the 3 experiments.

The bonuses paid do not equate payoffs

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F&S test only ‘qualitative’ predictions of the theory.

But they add that the model makes some surprisingly accurate quantitative predictions.

The qualitative predictions:

1. Choice of contract

2. Bonuses increase with effort (but how?) (diagram)

3. Bonus contract is more efficient than a trust contract (belief in I-A principals)

4. Some agents do not exert high effort (disbelief in I-A principals)

The surprising quantitative predictions:

The experimental average wage, average effort and average bonus are as predicted

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return

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What is the explanatory value of Inequity Aversion Theory?

What is the explanatory value of Inequity Aversion Theory?