Second Conference On Measuring Human Progress

Going Beyond Income: Measuring Inequality

March 4, 2013

Conchita D’Ambrosio, University of MilanAlan 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 inequality reduction in each dimension

• HDI could be viewed as index of “potential” human development

• IHDI is index of “actual” human development

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 IHDIby 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

1

2

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.

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

For the time being

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).

Estimation of total inequality

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 lossyear country Gain Ranking year country Gain Ranking2009 AT 8.938 7 2009 IT 11.005 142009 BE 9.977 11 2009 LT 11.000 252009 BG 10.224 28 2009 LU 11.338 22009 CY 11.683 16 2009 LV 10.731 232009 CZ 7.289 18 2009 MT 9.115 202009 DE 8.553 6 2009 NL 9.004 52009 DK 8.298 3 2009 NO 8.554 12009 EE 8.702 19 2009 PL 10.864 272009 ES 12.207 17 2009 PT 12.161 222009 FI 8.073 4 2009 RO 11.792 292009 FR 11.008 9 2009 SE 9.575 102009 GR 13.928 21 2009 SI 7.246 152009 HU 8.167 26 2009 SK 7.779 242009 IE 10.496 12 2009 UK 10.814 132009 IS 10.690 8

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

NO LU IS DK DE UK SE FI AT BE FR IE IT CY SI ES PT GR CZ EE HU SK LV LT PL123456789

10111213141516171819202122232425

Effects of Case A/B/C in 2006, r=0.5, income per capita

Case BCase CCase A

Rank

ings

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

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 RO123456789

1011121314151617181920212223242526272829

Effects of r in 2009

r=1r=0.5r=0

Rank

ings

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

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 RO123456789

1011121314151617181920212223242526272829

Effects of r and Ye in 2009

r=1, Yer=0.5, Yer=0, Yer=0, Ypc

Rank

ings

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.