Second Conference On Measuring Human
Progress
Going Beyond Income: Measuring Inequality
March 4, 2013
Conchita D’Ambrosio, University of Milan
Alan Fuchs, Human Development Report Office
Incorporating Equality when measuring
Human Development
 Equality is at the core of the human
development approach which intrinsically
pursues the value of social justice
Inequality-Adjusted HDI
•
Adjusts HDI for inequalities in distribution of each
component
•
Discounts average value according to inequality level
•
Inequality measured by Atkinson-Kolm-Sen method:
•
•
•
Allows use of different inequality aversion parameters
Requires micro-data (household survey data)
Difference between IHDI and HDI represents loss
due to inequalities in distribution of achievements in
each dimension
Inequality-Adjusted HDI
Presumed policy relevance:
• Inform
policies
towards
reduction in each dimension
inequality
• HDI could be viewed as index
“potential” human development
• IHDI is index
development
of
“actual”
of
human
Issues related to IHDI
• Loss in HDI due to inequality needs better
justification and interpretation
• Applying welfare-based Atkinson-Kolm-Sen
measure to distributions of life expectancy and
years of schooling is questionable
• Income index (log transformed) is adjusted by
inequality from untransformed income data
assuming that the percentage loss due to
inequality in income distribution is the same for
both average income and its log
Issues related to IHDI
• Combining inequalities that pertain to different
years across dimensions may be misleading and
misinterpreted
• IHDI is not association sensitive: it does not
account for overlapping inequalities
• Values of indicators at the micro level need to be
adjusted to non-negative/non-zero values
uniformly across countries so that the geometric
mean can be computed
Comments and suggestions on the IHDI
by Walter Bossert, Conchita D’Ambrosio and Louise Grenier
IHDI is a good idea.
The disadvantages we see are, to a large extent,
due to complexities regarding transformations
that are applied to the data and to the lack of
satisfactory data availability.
We argue that the most promising way forward in
order to provide a meaningful index is to collect
better data at the individual level.
Data available at the individual level
Natural way to proceed:
1) Obtain first an individual development index: di (hi, ei, xi).
2) Then aggregate across the population.
We do not see any advantage from path independence
(which holds if mean of same order is applied in both
stages).
h
h
…
h
e
e
…
e
x
x
…
x
2
1
di is not known:
A promising way to deal with the lack of exact
knowledge regarding individual aggregation
methods may be to assume that di are within a
parameterized
class
and
calculate
an
expectation over the range of possible
parameter values.
An alternative method has been proposed by Seth
(2009) where the individual development index
is assumed to be a weighted mean of order ß,
where ß reflects the degree of association
among attributes.
The use of measures additively decomposable
among population groups would allow issues
such as disparities between different subgroups
of the population to be addressed in a consistent
manner.
It is desirable to have one single method which
allows us to understand not only how much of
total inequality in human development is due to
differences between gender groups but also how
much inequality exists within each group, an
issue which is neglected by the GII.
For the time being
Until more comprehensive data are available,
temporary improvements can be realized by
computing for the countries where a possibility
already exists the IHDI directly from the available
datasets without modifying the HDI for the
presence of inequality.
We recommend a direct estimation of total
inequality in the distribution of the three dimensions
across the population.
Disconnect the IHDI from the HDI
Estimation of total inequality
By having such an estimate we avoid at least three weaknesses
of the current IHDI:
(a) The assumption that the percentage loss due to inequality in
income distribution is the same for both average income and
its logarithm.
(b) Adjusting the HDI components that refer to one year with the
inequalities that refer to different years.
(c) The IHDI will be completely independent from the HDI. This
will possibly allow an easier explanation of the advantages
generated from the fight against inequalities and offer an
incentive for policy makers to reach this objective.
Estimation of total inequality
For the EU countries individual data of good quality are
available.
We provide an application using EU-SILC from 2005 to
2009 of the IHDI as the general mean of general
means and discuss some of the decisions that should
be taken if this method were accepted.
Estimation of total inequality
For the three basic dimensions—a decent standard of
living, access to knowledge and a long and healthy life—
the following variables are in the dataset:
• disposable household income (per capita vs. equivalent),
• the highest International Standard Classification of
Education (ISCED) level attained (seven categories),
• self-reported health status (five categories).
Interpretation of loss
Following our proposal of the direct estimation of total
inequality in the distribution of the three dimensions, we
could estimate directly the general means and compare
these values to the corresponding arithmetic means.
This gain would be expressed as a percentage as
follows:
This will provide incentives to cut inequality, since it will
sound like “We achieved the level of the HDI of 0.8 but if
distributions were more equal, the HDI would be 0.9”
Interpretation of loss
year
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
country
AT
BE
BG
CY
CZ
DE
DK
EE
ES
FI
FR
GR
HU
IE
IS
Gain
8.938
9.977
10.224
11.683
7.289
8.553
8.298
8.702
12.207
8.073
11.008
13.928
8.167
10.496
10.690
Ranking
7
11
28
16
18
6
3
19
17
4
9
21
26
12
8
year
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
2009
country
IT
LT
LU
LV
MT
NL
NO
PL
PT
RO
SE
SI
SK
UK
Gain
11.005
11.000
11.338
10.731
9.115
9.004
8.554
10.864
12.161
11.792
9.575
7.246
7.779
10.814
Ranking
14
25
2
23
20
5
1
27
22
29
10
15
24
13
Non-negative/non-zero values
These modifications do have a strong impact on the value
of the inequality measure.
The method reduces inequality by squeezing the range of
the income distribution and also modifies inequality since
the index is scale invariant (the transformation would be
irrelevant had a translation-invariant measure been
used).
For these reasons we believe that it would be preferable to
use another specification of the Atkinson-Kolm-Sen
inequality index which would behave differently when the
value of an observation is zero.
Non-negative/non-zero values
We drop all observations with missing values in any of the
dimensions and use sample weights in the estimation of
the indices.
We do not normalize the data and we compare the rankings of
the countries for three cases:
Case A) uses the income data as they appear in the dataset,
hence the inclusion of zero and negative values in the
measure;
Case B) replaces zero and negative values by the minimum
value of the bottom 0.5 percentile of the distribution of
positive incomes;
Case C) includes only positive incomes by dropping zero and
negative values.
Of course in Case A the geometric mean is not considered.
Non-negative/non-zero values
Rankings
Effects of Case A/B/C in 2006, r=0.5, income per capita
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Case B
Case C
Case A
NO LU
IS
DK
DE
UK
SE
FI
AT
BE
FR
IE
IT
CY
SI
ES
PT
GR
CZ
EE
HU
SK
LV
LT
PL
Non-negative/non-zero values
It seems to us that, once the functional form is chosen, then
it has to be applied accepting all its consequences, and
modifying the data to produce a more appealing situation
somehow lacks legitimacy.
If the functional form has to be maintained, dropping zero
and negative incomes seems preferable to us since we
do not know what is behind these unusual observations
which would indicate a non-survival level for the
individual.
However, the same does not necessarily apply to education
and health where a zero value represents exactly what is
intended.
Means of different orders: alternative values
of the inequality aversion parameter
A possible improvement that reflects inequality
aversion and imperfect substitutability across
dimensions may be achieved by using an alternative
member of the Atkinson-Kolm-Sen family that is
based on the sum of means of an order strictly
between 0 and 1 (this parameter restriction
guarantees inequality aversion), such as a mean of
order ½.
We believe that this choice is preferable to modifying
the data in order to avoid the exclusion of zero
values.
Means of different orders: alternative values
of the inequality aversion parameter
Rankings
Effects of r in 2009
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
r=1
r=0.5
r=0
NO LU DK
FI
NL DE AT
IS
FR SE BE
IE
UK
IT
SI
CY ES CZ EE MT GR PT LV SK
LT HU PL BG RO
Income: per capita vs equivalent, log vs level
We are in full agreement with Alkire and Foster (2010) that
incomes rather than their logarithms should be used.
Each dimension index is a proxy for capabilities in the
corresponding dimension, the transformation function
from income to capabilities is likely to be concave
(Anand and Sen, 2000).
The typical distribution of income has a long right tail, which
renders this transformation inappropriate when
computing the equality component for income.
Computing inequality on the distribution of the log of
income would imply a consistent reduction of the actual
level of inequality.
Income: per capita vs equivalent, log vs level
The standard practice within the IHDI is to divide household
income by the number of household members to obtain
per capita income.
We expand this tradition and generate the results also for
equivalent income, that is, for disposable household
income divided by a smaller number in order to take into
account economies of scale generated by cohabitation.
The latter is more standard in the income distribution
literature and preferred to the first as a proxy for material
well-being. The equivalent scale we use is the modified
OECD scale which assigns a coefficient of 1 to the first
adult, 0.5 to any additional individual aged 14 and above
and 0.3 if the additional individual is younger.
Income: per capita vs equivalent, log vs level
Rankings
Effects of r and Ye in 2009
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
r=1, Ye
r=0.5, Ye
r=0, Ye
r=0, Ypc
NO LU DK FI
NL DE AT
IS
FR SE BE
IE UK IT
SI
CY ES CZ EE MT GR PT LV SK LT HU PL BG RO
Conclusion
We have proposed to compute the IHDI directly from
the available data at the individual level, without
going through the modification of the HDI.
With an application to EU countries we have offered a
sensitivity analysis of three main issues:
1) the transformation of the data in order to deal with
negative and zero values;
2) income per capita as opposed to equivalent
income;
3) alternative values of the inequality aversion
parameter.
Conclusion
Our preferred choice, for the various reasons we
have highlighted, is a general mean of order r
strictly between 0 and 1 (such as r=½) of
general means of the same order applied to the
unmodified distributions of equivalent incomes.
We hope that the sensitivity analysis we have
provided will be of help to the relevant parties in
the decision on the type of IHDI for the next few
years.
Conclusion
Once individual data from a unique source will
become available for many countries, more
analysis is needed to test the effects of the
individual-first aggregation procedure and
alternative inequality indices such as those that
are additively decomposable among population
subgroups.