Unfair inequalities in health and health care
Marc Fleurbaey and Erik Schokkaert
CORE DISCUSSION PAPER
Unfair inequalities in health and health care
Marc FLEURBAEY 1 and Erik SCHOKKAERT2
Inequalities in health and health care are caused by different factors. Measuring "unfair"
inequalities implies that a distinction is introduced between causal variables leading to
ethically legitimate inequalities and causal variables leading to ethically illegitimate
inequalities. An example of the former could be life-style choices, an example of the latter is
social background. We show how to derive measures of unfair inequalities in health and in
health care delivery from a structural model of health care and health production: “direct
unfairness”, linked to the variations in medical expenditures and health in the hypothetical
distribution in which all legitimate sources of variation are kept constant; “fairness gap”,
linked to the differences between the actual distribution and the hypothetical distribution in
which all illegitimate sources of variation have been removed. These two approaches are
related to the theory of fair allocation. In general they lead to different results. We propose to
analyse the resulting distributions with the traditional apparatus of Lorenz curves and
inequality measures. We compare our proposal to the more common approach using
concentration curves and analyse the relationship with the methods of direct and indirect
standardization. We discuss how inequalities in health care can be integrated in an overall
evaluation of social inequality.
Keywords: equity in health care delivery, health inequality, social welfare
JEL Classification: D63, I10
1 University Paris-Dauphine, CNRS, LSE and IDEP, France. E-mail: marc.fleurbaey@univ-
2 Department of Economics, KULeuven and CORE, Université catholique de Louvain, Belgium. E-mail:
This paper has benefited from comments by E. van Doorslaer, D. Hausman, Aki Tsuchiya, Dirk Van de
Gaer, Tom Van Ourti and audiences in Copenhagen, Lille and Rotterdam. Financial support from DREES-
MiRE and INSERM under convention 05/186 is also gratefully acknowledged.
This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated
by the Belgian State, Prime Minister's Office, Science Policy Programming. The scientific responsibility is
assumed by the authors.
There is by now a very large literature on different aspects of inequity in health, both
from a theoretical and from an empirical point of view. This literature focuses mainly
on socioeconomic inequalities in health and in the delivery of health care (Wagstaff and
Van Doorslaer, 2000a). While different methods (including the calculation of odds ratios)
have been proposed in the public health literature (Mackenbach and Kunst, 1997), the
concentration curve has become the workhorse in most health economic studies. Recently,
a number of papers have been published which propose a welfare economic foundation for
its use (Wagstaff, 2002; Koolman and van Doorslaer, 2004; Bleichrodt and van Doorslaer,
2006) or advocate alternative approaches (Bommier and Stecklov, 2002; Becker et al.,
2005; Abul Naga and Geoffard, 2006; Zheng, 2006; Dias and Jones, 2007; Fleurbaey,
When moving from the measurement of inequality (in health or in health care) as such
to socioeconomic inequality, one implicitly assumes that policy-makers are more concerned
or should be more concerned about some causes of observed overall inequality, such as
socioeconomic background, than about other causes. In the literature on health inequality,
it is implicitly accepted that health inequalities within a socioeconomic group are less
problematic than health inequalities between socioeconomic groups. And in the literature
on equity in health care delivery, it is quite reasonably taken for granted that differences
in use which reflect differences in needs are not only unproblematic, but even desirable.
All in all, this strongly suggests that some inequalities are "legitimate" while others are
not. The most obvious justification for making this distinction between "legitimate" and
"illegitimate" differences is that the former can be attributed to causes that belong to
individual responsibility. Given this background, it is striking that, while there are clear
links between the literature on income inequality and the literature on socioeconomic
inequalities in health and in health care, there has been until now hardly any link with
the growing literature in social choice on equity, responsibility and compensation (Roemer,
1998; Fleurbaey, 2008). This paper tries to bridge part of that gap.
As soon as one formulates the problem of illegitimate or "unfair" inequalities in this
general framework, one is immediately confronted with the observation that, in addition
to socioeconomic background, there are many more causes of inequalities that may be a
cause of ethical concern. Why should we then focus almost exclusively on socioeconomic
inequalities in health care consumption? Is it less problematic if someone is denied health
care because she lives in another region of the country? (Or, for that matter, in another
country?) Why should we not be interested in equality of health as such? Because part of
these health differences is unavoidable, or not created by socioeconomic institutions? And,
suppose we restrict ourselves to avoidable health inequalities, why then focus again almost
exclusively on socioeconomic health inequalities? And what if socioeconomic differences
in health can to some extent be explained by differences in lifestyle? In this paper we will
define an "equitable" situation as a situation without unfair inequalities - and inequalities
are defined as unfair when they follow from causes which do not belong to the sphere
of individual responsibility. The socioeconomic background of individuals is one of these
causes - but, although very important, it is not the only one. It is necessary to get a more
complete perspective on these different causes.
The method we propose consists of three steps. In the first (explanatory) step one
has to construct a structural model to estimate the relative importance of the different
causes of inequality and to get a better insight into their possible interactions. In a
second (normative) step, one decides which of these causes lead to legitimate and which
to illegitimate (or unfair) inequalities. The third step involves the measurement of these
unfair inequalities. We will focus on the choices to be made in that third step.
There are of course different opinions in society with respect to what belongs to
the sphere of individual responsibility. Some will claim that equality of access is a better
criterion than equality of use, because individuals should be held responsible for their own
choices. Some will claim that health differences following from differences in life-style are
not problematic, because individuals should be held responsible for their smoking and
drinking behavior. Some will claim that health differences reflecting differences in age
or in genetic endowments are not unfair, because they are unavoidable. But in each of
these cases there are also proponents of the opposite view. We will show how different
views about equity (or about unfair inequalities) can be interpreted as different views
about where to draw the line between legitimate and illegitimate causes of differences, i.e.
as different options taken in the second step referred to above. Our method to measure
inequality (the third step) works for any of these options and can therefore accommodate
many different ethical views. This has the advantage that one can also compare the results
for different approaches within one general encompassing framework.
In our view, unfair inequalities in the health domain cannot be separated from unfair
inequalities in other domains. The overall social objective is to minimize unfair inequalities
in welfare. Health is important because it is one of the most crucial dimensions of welfare.
Health care is important because it contributes to better health, and perhaps also directly
to a higher welfare level. Although there is this clear hierarchy, we agree that it is useful
to consider also inequalities at the lower levels, not in the least because health care and
health policy are separate policy domains.
We introduce our basic concepts in section 2 for a simple case with two variables. We
propose two possible approaches to measuring unfair inequalities. Direct unfairness refers
to inequalities in health or health care after one has removed the effect of all legitimate
variables. The fairness gap measures the distance between the actual distribution and
a fair distribution in which all the effects of illegitimate variables have been removed.
We show why, in general, these two approaches do not yield the same results. Section
3 sketches the broad contours of a structural model of health and health care. Section
4 shows how the concepts from section 2 and the structural model of section 3 can be
combined to conceptualize unfair inequalities in health care and in health. We also discuss
within our framework the problem of aggregating the different elements in the health care
vector for the purpose of measuring inequity. In section 5 we argue that some additional
normative choices have to be made when moving from the empirical model to the calcu-
lation of inequality. We show that direct unfairness is analogous to direct standardization
and that the calculation of the fairness gap is related to indirect standardization, when the
latter technique is reinterpreted to include all relevant variables. In section 6 we compare
our approach to the traditional work on socioeconomic inequalities using the concentra-
tion curve and we suggest one possible way to integrate health issues in a broader concern
for equality of welfare. Section 7 concludes.
We focus on conceptual issues with respect to the definition of unfair inequalities
and we do not really go into problems of implementation. Although we are well aware
that the level at which, e.g., health is measured, may have an influence on the measure-
ment instruments to be used (see, e.g., van Doorslaer and Jones, 2003; Erreygers, 2006),
we completely neglect this issue.1Moreover, throughout the paper we work within an
absolute approach to measuring inequalities. This means that we will be referring to
absolute Lorenz curves and to inequality measures which satisfy translation invariance,
i.e. which do not change when a constant is added to all the elements of the vector. This
is not in line with the dominant practice in economic inequality measurement (including
the measurement of socioeconomic inequalities in health and health care), in which rela-
tive Lorenz curves and scale invariant inequality measures have been much more popular.
Our choice in favour of the absolute approach brings our paper more closely to the social
literature on responsibility and compensation where absolute distances have been used
more often than relative proportions. However, this choice is not necessary, and all the
axioms and results of this paper can be easily reformulated within a relative approach.
2Direct unfairness and the fairness gap: a simple
Let us introduce the basic issues of this paper with a simple example. For illustrative
purposes, we will focus on inequalities in health. In later sections, we will apply the
same ideas in a more elaborate model and also consider the issue of equity in health care
delivery. Let us assume that the health of individual i (i = 1,...,n) is determined by her
1Although we will be concerned with measurability and comparability of individual welfare in the very
income yiand by her life-style li2, i.e.
Neglecting all problems of measurability -as we will do throughout the paper- it would be
straightforward to construct Lorenz curves for health or to calculate inequality in health.
However, from an ethical point of view, we are mainly interested in ethically objectionable
or unfair inequalities. Let us for the sake of the argument take it for granted that health
inequalities due to differences in life-style are unproblematic, because we want to hold
people responsible for these.3Therefore, a measure of unfair inequalities should not reflect
health differences due to differences in life-style. In our simple example, this means that
we only want to measure so-called "socioeconomic inequalities in health".
How to go from "overall inequality" to "unfair inequality"? One way to approach
the problem is to see it as an exercise of removing from the overall inequality measure all
differences which are due to lifestyle. What then should remain is a measure of health
inequalities due to income differences, and to income differences only. In general (but
very loose) terms, we can summarize this condition for later reference as
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.
Another approach starts from the concept of a fair distribution. In our example, in
a fair distribution there should be no health inequalities due to income differences. This
implies that if two individuals have the same life style, they should have the same health
2For the purpose of this simple example, we use income as an indicator of socio-economic status. As
we will see in the next section, in a broader setting individuals may be held partly responsible for their
income. Moreover, in the real world the health situation of the individuals is determined by many more
variables, not in the least their genetic endowment. We come back to this issue in the later sections. For
the purpose of the simple example in this section, we assume that all these other variables are identical
for all individuals.
3This starting point can be -and has been- hotly debated. We will return to that issue later on in the
paper. At this stage, we only want to illustrate the basic issues related to measuring unfair inequalities.
level, whatever their income. Again, more generally (but very loosely) formulated, we can
say that a measure of unfair inequality should satisfy the following condition:
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 respon-
sibility variable should have the same outcome.
At first sight, both conditions are perfectly clear and it seems obvious that a good
measure of unfair inequality should satisfy both. However, there is a basic problem in
that the two conditions are incompatible as soon as the effect of income on health is
not independent of the life-style. This basic problem is well documented in the social
choice literature and discussed in a long series of publications (a synthesis can be found
in Fleurbaey, 2008). Its consequences, however, have not yet been fully realized in the
literature on the measurement of socioeconomic inequalities in health care or in health.4
Without going into the formal details, we can use our example to convey the basic in-
tuition in a straightforward way. Let us first introduce two methods to measure unfair
inequality. These two methods are closely related to the concepts of conditional equality
and egalitarian-equivalence in the literature on fair allocation (see, e.g., Fleurbaey, 2008).
The first method (conditional equality) focuses on condition 1. It removes the legit-
imate differences by fixing the value of liin (1), i.e. by defining a "corrected" value of
healthehi= h(yi,el). This is the health level that individual i with income yiwould reach
traditional apparatus of Lorenz curves and inequality measures. We propose to call this
if he had the reference lifestyle. Inequality ineh can immediately be measured with the
inequality direct unfairness. By construction, a measure of direct unfairness can only
reflect variation due to income differences, since differences in life style are kept constant.
Therefore it satisfies condition 1. However, there is no reason why it would satisfy con-
dition 2: if there is no inequality ineh, this does not at all guarantee that two individuals
4Gravelle (2003) and van Doorslaer et al. (2004) touch the issue, but do not really go into the
with the same life style will also have the same health level.
normative implications. Schokkaert et al. (1998) and Schokkaert and Van de Voorde (2004, 2006) have
shown its relevance for the problem of risk adjustment.
The latter condition is satisfied automatically by a second method (egalitarian-
equivalence), in which we first explicitly define a fair distribution, i.e. a distribution
in which all the illegitimate sources of variation have been removed. A straightforward
way to do this is to fix the value of yiin (1) and to define a reference health level for i as
i= h(y∗,li). In a fair distribution, the difference between this ideal reference situation
and the actual situation should be zero or at least equal for all i. Unfair inequality can
therefore be measured by applying the traditional inequality measurement apparatus to
the vector (hi− h∗
clear that it satisfies the compensation condition 2. However, in general it does not sat-
i). We call this the approach of the fairness gap. It is immediately
isfy condition 1: the fairness gap may be influenced by life style, because the differences
h(yi,li) − h(y∗,li) may depend on the value taken by the variable li.
In general, the two approaches will not yield the same conclusions. Measures of
direct unfairness satisfy condition 1, but not condition 2. Measures of the fairness gap
satisfy condition 2, but not condition 1. There is one interesting case in which they do
coincide, however. Suppose that eq. (1) is additively separable, i.e. that it can be written
as h(yi,li) = f(yi) + g(li). This implies that the effect of income differences on health is
independent of the life style (and vice versa). In this case, direct unfairness measures the
inequality in the vector (f(yi) + g(el)), while the fairness gap measures the inequality in
the vector (f(yi)−f(y∗)). The two will give the same result in our absolute measurement
A picture may illustrate the issues. Take income to be a continuous variable and
suppose there are two different lifestyles in society, denoted lAand lB. The figure shows
the functions hA
i= h(yi,lA) and hB
i= h(yi,lB). We assume that lAis the healthier lifestyle
5Remember that we opt in this paper for an absolute approach to inequality measurement, in which
adding a constant to all elements of a vector does not change inequality. As mentioned before, the
same basic intuitions hold also for the relative approach. To be more specific, one could instead define
the fairness gap in relative terms: hi/h∗
i. With this formulation, the direct unfairness and the fairness
gap approaches are equivalent if the health function is multiplicatively separable: h(yi,li) = f(yi)g(li).
Indeed, one then hasehi= f(yi)g(el) and hi/h∗
i= f(yi)/f(y∗). In this case, relative inequality measures
and the Lorenz curve are identical forehiand for hi/h∗
Figure 1: Direct unfairness and the fairness gap
and that for both lifestyles there is a positive relationship between health and income.
Differences in health due to differences in lifestyle are considered to be unproblematic,
but fairness requires that all individuals with the same lifestyle should have the same
health level whatever their income position, i.e. that the curves in the figure should be
When measuring direct unfairness, we fix the lifestyle at a reference value. Let us
say that we focus on one specific curve (say, we puteh ≡ hB). We will then measure the
are contained in the striped area in the Figure. It is obvious that this procedure does
inequality in the distances between this curve and the horizontal line x.6These distances
not satisfy the compensation condition: indeed we fully neglect the unfairness which
is implicit and (in this case larger) for lifestyle hA. On the other hand, the procedure
satisfies condition 1, since the only health differences reflected in the inequality measure
by construction are due to differences in income.
6Given that we focus on absolute inequality measures, the exact position of line x does not matter, as
long as it is horizontal.
When we calculate the fairness gap, we fix y at a given level (say y∗) and we compute
for each individual the difference between his actual health and the health level that he
would reach with his actual lifestyle in the hypothetical situation that he had income y∗.
These distances are contained in the shaded areas in the Figure. Note that condition 2 is
now satisfied: all individuals are taken into account and the fairness gap will only be zero
if both health curves are horizontal. However, the fairness gap also takes into account
the fact that the slopes of the curves hAand hBare different, while we ideally would like
to neutralize the effect of life style differences, and, hence, the differences in the slopes.
Therefore, the fairness gap does not satisfy condition 1. Both approaches lead to the
same result if the only difference between hAand hBis a vertical shift. This is the case
of additive separability.
Note that we basically propose to use the standard apparatus of inequality mea-
surement to the corrected health outcomes or to the individual fairness gaps: we do
not work with concentration curves, as is the dominant procedure in the literature on
socioeconomic inequalities in health. There are two reasons for this. First, the use of
concentration curves is only possible if one considers inequality in one dimension (e.g.
income) with a natural ordering which can be used to construct the concentration curves.
Our approach allows for many legitimate and illegitimate variables. Second, even if one
only considered socioeconomic inequalities we still think that there are severe limitations
to the use of concentration curves. In the following sections, we will come back to these
issues more explicitly.
3A sketch of a structural model
Fairness does not only relate to socioeconomic inequalities. Some variables influencing
health or health care can be considered to be legitimate, others are ethically objectionable
sources of differences. Moreover, as the simple example in the previous section has shown,
the empirical interactions between these different variables may have a crucial influence on
the inequality measurement. It is therefore necessary to have a structural model in mind
when thinking about specific measures of unfair inequality. Starting from a structural
model makes it possible to close part of the gap between the large health economics
literature on explaining health and health care differences and the normative literature
on unfair inequalities. In this section we will organize our thinking by introducing such a
structural model in very general terms. Of course, many simplifications are needed if one
wants to apply the model to real empirical data. We will return to this issue in section 5.
We state that the health level hiof individual i is produced by a health technology
H(.), which can be written as follows
where miis a vector of medical consumption (e.g. the number of GP visits, the number
of specialist visits, pharmaceutical consumption and so on), ciis a vector of consumption
goods, including life style goods (smoking, drinking, physical activities), oiis a vector of
job characteristics (including leisure), and siis social background. We therefore leave open
the possibility that, in addition to life style and job characteristics, there is also a direct
effect of social background on health. Further crucial variables are ei, the genetically
determined health endowment, and εi, which is a (stochastic) health shock. The health
technology, as described in (2), is determined mainly by biological considerations and
is objectively given to the individual. However, individual behavior has an influence on
health through the choices of mi, ciand oi.
Labour income yiis endogenous and is determined through a mixture of endowments
and choice variables:
yi= Y (ci,oi,hi,ai,si)
where ai is the innate productive capacity of the individual, for which she cannot be
held responsible. Earnings capacities are also influenced by the present health status of
the individual. Individual choices of leisure and job characteristics oiwill endogenously
determine gross labour income yi. Note that we again include social background explicitly:
this is meant to capture not only the effect of discriminatory practices by employers, but
also the differences in the quality of the social networks that are available to various
individuals and that will influence their search behavior and their final outcomes.
To model the individual choices of mi,ciand oi, we assume that individuals maximize
a utility function Ui(mi,ci,oi,hi).7We thus assume that mienters the utility function
directly. With this we want to capture the idea that individuals may have specific tastes
about medical care consumption, for which they can (perhaps) be held responsible. They
also care for their health. However, the health production function (2) is not perfectly
known to individuals and there may also be differences between social groups in this
respect. Representing the information available to individual i by Ii, we explicitly define
her "perceived" health production function as
and we assume that choices are based on this perceived health production function.
Individuals maximize their utility under a budget constraint, which we write as
pci+ B(mi,ri) = yi− T(yi,ci) − ρ(ri,ei)
where yi is income, T(yi,ci) gives taxes paid (or transfers received) as a function of
labour income and consumption, and p are the consumption prices. To arrive at a general
description of the health financing constraints, we introduce two additional functions. The
first (B(mi,ri)) gives the out-of-pocket payments. These are dependent on the level (and
structure) of medical care consumption and on the degree of supplementary insurance
coverage ri. The form of the function B(.) is determined by the health care system in
which the individual lives. In a National Health Service-system where all expenditures are
taken care of by the government and there are no co-payments or deductibles, the value of
B(mi,ri) can be zero. If individuals take supplementary insurance, they will have to pay
a premium ρ(ri,ei): the premium amount will depend on the degree of insurance coverage
ri, and on a private insurance market with premium differentiation it will also depend
on the genetic health endowment ei. Buying supplementary insurance is an individual
decision, taken at an earlier stage.8
7This (ordinal) utility function is to be interpreted as the representation of a preference ordering <i
for individual i. In section 6 we will argue that we do not assume that subjective utility is cardinally
measurable or interpersonally comparable.
8This assumption of a two stage decision-making process is only made for convenience. However, it
In addition, while individuals have some freedom in their choice of health care con-
sumption, it is generally accepted that they are restricted by the decisions taken by health
care professionals. The behavior of the providers will be influenced by the characteristics
of the health care system, more specifically by the way in which they are remunerated.
Moreover, in many countries there is huge interregional variation in the availability of
health care services. This acts as a kind of quantity rationing constraint. We will summa-
rize these supply side influences by saying that an individual i can only choose his medical
consumption vector mifrom a restricted choice set M, the shape of which is determined
by supply side variables zi, by his health endowments eiand the stochastic shock εi, by
his level of supplementary insurance coverage and by his social background:
Note that eq. (6) captures restrictions on choice determined by the supply side, not the
choice behavior of the individuals themselves. The influence of social background and
supplementary insurance coverage in (6) refers to the situation in which providers differ-
entiate their behavior according to the social background of the individual or according
to whether they have supplementary insurance or not (e.g. in the situation where they
can raise additional supplementary fees from patients with a supplementary insurance).
In the extreme case where individual patients had no freedom of choice at all, the set M
reduces to a singleton, and medical care consumption is fully determined by the providers.
We can now summarize our stylized model of individual behavior as follows. In a
first stage, individuals choose to take supplementary insurance or not. This decision will
be influenced by their health and income prospects (affected by eiand airespectively)
and by their time and risk preferences Ri. Moreover, we know that the information about
insurance opportunities is unequally distributed over the population and that some social
groups might find it more difficult to buy insurance than others. Rather than modelling
this decision process explicitly, we summarize it by the following reduced form specifica-
seemed important to us to introduce supplementary insurance into the model, because it also plays an
important role in recent attempts to explain inequity in delivery (see e.g. Jones et al., 2006).
In a second stage individuals decide about (mi,oi,ci) by maximizing individual utility
Ui(mi,ci,oi,hi) under the budget constraint (5), the information constraint (4), and the
supply-side constraint (6). The resulting behavior can be expressed as a function of the
exogenous individual characteristics as follows:
The values of health, of income and of achieved welfare are endogenously determined.
Introducing the decision variables in the utility function, in eq. (2) and in eq. (3) we get
the following reduced form expressions:
Hidden behind these reduced form expressions (8)-(13) are market characteristics
(defining p and the shape of the functions ρ(.) in (5) and Y (.) in (3)) and policy variables
(the shape of the functions B(.) and T(.) in the budget constraint (5)). The supply effects
on medical care consumption in (6) can be seen as resulting from a mixture of market
forces and policy decisions. Evaluating the inequality in medical care consumption (8), in
health (11) and in welfare (13) then indeed boils down to an evaluation of the whole social
structure. The advantage of the reduced form expressions is that they neatly distinguish
different exogenously given characteristics of the individuals. At the same time, consid-
ering the whole structural model clearly shows where and how these characteristics enter
the analysis. This is of crucial importance to decide whether these characteristics should
be treated as legitimate or illegitimate sources of interpersonal differences in health and