Presentation at the HLEG thematic workshop on "Inequality of Opportunity", 14 January 2015, Paris, France, http://oe.cd/HLEG-workshop-inequality-opportunity-2015

1. 1
Equality of opportunity:
key concepts
Erik Schokkaert (Department of
Economics, KU Leuven and
CORE, UCLouvain)

2. 2
Introduction
• Egalitarian approaches: equality of what? Growing
criticism on welfarist (subjective well-being)
approaches. Individuals should not be compensated for
expensive tastes.
• The issue of responsibility has invaded social choice
and political philosophy (“luck egalitarianism”) in recent
decades.

3. 1. Philosophical foundations
• John RAWLS, A theory of justice (1971):
– autonomous moral agents must get the freedom and
assume responsibility of pursuing their own personal
conception of the good life.
– resulting differences in well-being are their own
responsibility.
• Ronald DWORKIN, What is equality? (1971)
– personal talents and handicaps to be seen as
internal resources.
– a good distribution of resources must be
endowment-insensitive but ambition-sensitive.
3

4. 4
From preferences to control?
• Richard ARNESON (1989), Gerald COHEN (1989),
John ROEMER (1993)
– individuals should only be held responsible for
characteristics and decisions that are within their
own control (e.g. not for preferences that are
“imposed” upon them by their education)

5. Formal economic theory
• Define an outcome function:
𝑦𝑖 = 𝑓 𝑥𝑖 = 𝑓(𝑐𝑖, 𝑟𝑖)
– “mechanism” determining the outcome (however
measured).
– two sets of variables: “compensation”
(circumstances/types) and “responsibility” (effort).
– typical example of circumstance: SES parents.
• QUESTION: how to “measure” inequality if we want to
“compensate” individuals for differences in c while
holding them “responsible” for differences in r?
5

6. • The formal framework is “general”, in that it holds for all
possible responsibility cuts.
• Existing conditional approaches (e.g. socio-economic
health inequalities) are just primitive versions of this
general framework.
• I will come back to the question of the “responsibility
cut” at the end. For the moment, let us follow the
“control” approach.
6

7. 2. Normative choices
• Implementing responsibility-sensitive egalitarianism
requires taking a position on two issues:
– what to “equalize”?
– how to introduce “responsibility”?
• Let us assume (for convenience) that we can
distinguish “discrete” types, i.e. groups of individuals in
identical circumstances.
7

8. Question 1: compensation
1. EX ANTE COMPENSATION: equalize the “value” of
the opportunity sets of the different types.
8

9. effort (r)
outcome (y)
type A
type B
9

10. Question 1: compensation
1. EX ANTE COMPENSATION: equalize the “value” of
the opportunity sets of the different types.
– Example: “average incomes” per type.
2. EX POST COMPENSATION:
∀𝑖, 𝑗 with 𝑟𝑖 = 𝑟𝑗, 𝑦𝑖 = 𝑦𝑗
10

11. effort (r)
outcome (y)
type A
type B
11

12. • Special case: if everybody exerts the same effort, this
implies pure outcome egalitarianism.
• Ex ante compensation and ex post compensation are in
general incompatible.
12

13. Question 2: “responsibility”
• How to treat individuals at different effort levels?
• Thought experiment: what to do if everybody is of the
same “type” (same circumstances)?
• Two approaches:
1. “Utilitarian reward” (Roemer)
2. Liberal reward (Fleurbaey)
13

14. effort (r)
type A
type B
“Utilitarian reward” (John Roemer, 1994,
1998)
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outcome (y)

15. • IF everybody is of the same “type” (has the same
circumstances), maximize the sum of outcomes.
15

16. 16
“Liberal reward” (Marc Fleurbaey, 2008)
• Outcome differences between two persons of the same
type should not be affected by the redistribution.
• IF everybody is of the same “type” (has the same
circumstances), there is no need for redistribution. (“On
average, the system gets it right”).

17. Yet another impossibility...
• Both liberal reward and utilitarian reward are
incompatible with ex post compensation.
17

18. 3. Inequality measures
• The number of empirical applications is rapidly growing,
but not all of them are closely linked to the social choice
background.
• In general, distinction between “direct” and “indirect”
approaches.
• Example: direct, ex ante
𝐼 𝑦𝑡
i.e. inequality in the average incomes per type.
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19. 19
Conditions for a good inequity measure
• CONDITION 1 (NO INFLUENCE OF LEGITIMATE
DIFFERENCES). A measure of unfair inequality should
not reflect legitimate variation in outcomes, i.e.
inequalities which are caused by differences in the
responsibility variables.
• CONDITION 2 (COMPENSATION). If a measure of unfair
inequality is zero, there should be no illegitimate
differences left, i.e. two individuals with the same value for
the responsibility variables should have the same
outcome.

20. Direct, ex post: direct unfairness
• Fix a reference value for the responsibility variables and
calculate
𝑦𝑖
𝐷𝑈
= 𝑓 𝑐𝑖, 𝑟 .
• Calculate the inequality 𝐼(𝑦𝑖
𝐷𝑈
).
• By construction this measure can only capture
“illegitimate inequality”. However, it does not satisfy
“compensation”.
20

21. Inequality in fairness gaps
• Fix a reference value for the circumstance variables
and calculate a “norm” outcome for i:
𝑦𝑖
𝑁𝑂𝑅𝑀
= 𝑓 𝑐, 𝑟𝑖 .
• Calculate the distance between the norm outcome and
the actual outcome. This is called the “fairness gap”:
𝑓𝑔𝑖 = 𝑦𝑖 − 𝑦𝑖
𝑁𝑂𝑅𝑀
.
• Calculate the inequality 𝐼 𝑓𝑔𝑖 .
• This measure satisfies compensation, but includes also
some “legitimate” inequalities.
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22. Indirect approach
• It has become popular in the literature to calculate
“inequality of opportunity” as
𝐼 𝐼𝐸𝑂𝑃 = 𝐼 𝑦𝑖 − 𝐼(𝑦𝑖
𝑁𝑂𝑅𝑀
).
• Yet this is a very strange measure.
– EXAMPLE: take 𝑦 𝑁𝑂𝑅𝑀
= 20, 40 .
– Compare two income distributions: (20, 40) and
(40,20).
– These will give the same value for 𝐼 𝐼𝐸𝑂𝑃
.
• Not surprisingly, the (scarce) empirical evidence shows
that 𝐼 𝑓𝑔𝑖 ≫ 𝐼 𝐼𝐸𝑂𝑃. 22

23. 4. Implemention with imperfect info
• In practice, information will be incomplete. The
estimation result will be
𝑦𝑖 = 𝑓 𝑐𝑖
𝐼
, 𝑟𝑖
𝐼
, 𝑟𝑒𝑠𝑖 .
• Usually, some circumstance variables are easily
observed (e.g. SES of parents).
• Yet, if description of types is incomplete, estimated
inequality will be a lower boundary of actual inequality.
23

24. 𝑦𝑖 = 𝑓 𝑐𝑖
𝐼
, 𝑟𝑖
𝐼
, 𝑟𝑒𝑠𝑖
• “Effort” is very often not observed, and even
conceptually more difficult.
– e.g. number of hours worked?
• What if effort and circumstances are correlated? Can
individuals be held responsible for the effort distribution
of their type?
– RIA (Roemer’s identifying assumption): effort of individual i
measured by the percentile (s)he occupies in the outcome
distribution of his (her) type. VERY CONVENIENT!
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25. • An alternative? Try to estimate a structural model:
𝑦𝑖 = 𝑓 𝑐𝑖, 𝑟𝑖
𝑟𝑖 = 𝑔(𝑐𝑖, 𝑧𝑖)
• Some have argued that it is sufficient to estimate a
reduced form 𝑦𝑖 = ℎ 𝑐𝑖 , as the indirect effect of effort
through circumstances would then be captured by the
reduced form effect of 𝑐𝑖.
– This does not work for all measures and/or non-linear
specifications.
– Moreover, some variables may play a double role. Example:
health care as an outcome, age differences signal needs
differences (r-variable in this setting), but may also lead to
discrimination.
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26. 𝑦𝑖 = 𝑓 𝑐𝑖
𝐼
, 𝑟𝑖
𝐼
, 𝑟𝑒𝑠𝑖
• Most difficult issue, as the residual will capture “luck”,
but also the effects of misspecification and omitted
variables.
• Treatment of luck?
– Dworkin: brute luck vs option luck.
– Trannoy et al.: luck as a third category.
• Often the residual is simply neglected. The
interpretation of this practice will depend on the
inequality measure used. Better: lower and upper
boundary?
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27. 5. The responsibility cut
• “Responsibility as control” is the most popular
approach, but it faces huge difficulties.
27

28. 28
Responsibility as control
• Seems intuitively very attractive and dominates the
empirical work.
• “Genuine control” requires that one also corrects for
interindividual differences in (internal) choice-making
abilities and in the (external) environment (in so far as it
is not chosen by the individual).

29. 29
Problem 1: determinism and free will
• Is there any room left for “control” in a deterministic
world, if we better and better can understand and
explain behaviour?
• In general, in a world where the belief in determinism
seems great, “it is difficult to expand equality of
opportunity in ways that satisfactorily address the
constraining effects of social circumstance, gender
socialisation, cultural convictions and so on, without
undermining the idea of people as responsible agents”
(Phillips, J. Pol. Philosophy, 2006)

30. 30
Problem 2: the economic model
• in models of “rational choice”, individual decisions are
analysed as resulting from a mechanical optimization
exercise with a given objective (preferences) and a
given set of options (determined by budget set and
possibly additional constraints).
• in this model, genuine choice is an elusive notion.

31. A possible way out?
• Responsibility practices in a given society. Even if we
cannot choose freely, as human beings we need the
feeling that we are to some extent free, and society
needs to impose rules that give citizens a “feeling” of
responsibility.
• This makes the responsibility cut time- and society-
dependent (John Roemer).
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32. 32
Responsibility for preferences
• Back to Rawls and Dworkin: individuals are held
responsible for their preferences (their conceptions of a
good life), even if these preferences are not chosen/are
not under their control.
• Dworkin: respect for individuals implies respect for their
preferences with which they identify (when people
endorse their preferences, it is bizarre to consider these
as a piece of bad luck)

33. 33
Autonomy and freedom (Fleurbaey, 2008)
• Responsibility is not something which justifies
disadvantages, but something which is assumed by
individuals when they accept liabilities: justified by
independent fairness principles.
• Autonomous individuals must have the freedom to
practice the activity of choice as much as desired and
possible.

34. 34
How to recover preferences?
• a structural model is needed to identify preferences.
• NOTE:
– if the outcome of interest is well-being, this leads to
simple egalitarianism in terms of a concept of well-
being that does respect preferences without being
subjective utility.

35. 35
Conclusion
• (In)equality of opportunity comes in different forms:
– control vs preferences.
– liberal vs utilitarian reward.
– ex post vs ex ante compensation.
• A variety of measures is available, satisfying well-
defined axioms. For egalitarians, inequality in the
fairness gaps seems the most attractive.
• Booming empirical literature of variable quality adds to
the confusion.

36. • In my view, it is scientifically sound and ethically
attractive to clearly distinguish between the “estimation”
and the “evaluation” stage:
– STEP 1: try to understand as well as possible the
relationship between the outcomes and the different
circumstance, responsibility, mixed variables. Do not
put the empirical analysis in the straitjacket of a
simplified normative theory.
– STEP 2: implement an attractive inequality measure.
– STEP 3: take care to calculate upper and lower
bounds. Think explicitly about the residuals.
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