DISCUSSION PAPER SERIESIZA DP No. 1219

Inequalities and Their Measurement
Almas Heshmati

July 2004

Forschungsinstitut
zur Zukunft der Arbeit
Institute for the Studyof LaborInequalities and Their Measurement

Almas Heshmati
MTT Economic Researchand IZA Bonn

Discussion Paper No. 1219
July 2004

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IZA Discussion Paper No. 1219
July 2004

ABSTRACT
Inequalities and Their Measurement
This paper is a review of the recent advances in the measurement of inequality. Inequality
can have several dimensions. Economists are mostly concerned with the income andconsumption dimensions of inequality. Several inequality indices including the most widelyused index of inequality namely the Gini coefficient is discussed. Non-income inequality
includes inequality in skills, education, opportunities, happiness, health, wealth, and others.
The direct and indirect effects of inequality in non-income factors on earnings and health are
discussed. Results from review of the literature suggest relationship between inequality inincome and non-income dimensions. This indicates that one should account for theinterrelationship between the different dimensions in the measurement and analyses ofinequalities.

JEL Classification:
Keywords:

D31, I30, N30

income inequality, inequality indices, income distribution

Almas Heshmati
MTT Economic Research
Luutnantintie 1300410 Helsinki
Finland
Email: Almas.Heshmati@mtt.fi

1. INTRODUCTION
There is ongoing and increasing interest in measuring and understanding the level,causes and development of inequality during the 1990s. This period signified a shift inresearch previously focused on economic growth, the identification of the determinantsof economic growth and convergence in GDP per capita across countries to analysis of
distribution of income, its development over time and identification of factors
determining the distribution of income. This shift in focus is specifically from the issuesof convergence or divergence of per capita incomes to the long-term equalisation orpolarisation of incomes across regions and countries of the world. This shift is not onlya reflection of technological change and raised human capacity to create growth, wealthand in the effective use of resources, but also due to awareness of the growing disparity
and importance of redistribution and poverty reduction. The growing disparity calls foranalysis of possible trends in global income inequality.
Inequality can have many dimensions. Economists are concerned specifically with theeconomics or monetarily-measurable dimension related to individual or householdincome and consumption. However, this is just one perspective and inequality can belinked to inequality in skills, education, opportunities, happiness, health, life
expectancy, welfare, assets and social mobility. This paper will, in reviewing theliterature, give attention to the relationship between income inequality and the nonincome inequality dimensions.
Remaining parts of the paper is organised as follows. In Section 2 distribution andinequality of income is illustrated in the Lorenz diagram. Section 3 introduces several
inequality indices. Generalizations of Gini index is discussed in Section 4. Section 5 and6 discuss income and non-income inequalities. The final Section concludes.
2. THE LORENZ CURVE
Income inequality refers to the inequality of the distribution of individuals, household orsome per capita measure of income among the population of a country.1 In illustrations
we follow the notation found in Anand (1997). An income distribution is a vector ofincomes, x = ( x1 , x 2 ,....., xn ) , where xi indicate the income of the ith individual in asociety consisting of n individuals. The mean of the distribution of x and its
dimensionality are written as µ (x) and n(x) . Here income is a continuous randomvariable bounded in the interval x0 (≥ 0) and x . The density, distribution and the firstx

moment functions are f (x) , F (x) , and Φ (x) . Where f (x) , F ( x) = ∫x0 f ( y )dy , andx

Φ( x) = 1 / µ ∫x yf ( y )dy are the proportion of the population with income x , cumulative0

proportion of the population with income x , and cumulative share in total income,∞respectively. The mean of the distribution is µ = ∫0 yf ( y )dy .

1

For a review of the notion of inequality and alternative ethical theories see Subramanian (1997). Cowell(2000) provides a comprehensive survey where analysis of inequality is placed in the context of recent
developments in economics and statistics. The focus is on inequality measurement to give meaning tocomparisons of income distributions. The natural limitations of the subject and answers to a number ofquestions raised are discussed.

1

The graph of F (x) against Φ (x) is the Lorenz (1905) curve representing the inequalityof income distribution. The divergence of a Lorenz curve for perfect equality and theLorenz curve for a given income distribution is measured by some index of inequality.
The most widely used index of inequality is the Gini coefficient. The distribution andinequality of income is illustrated in the Lorenz diagram, Figure 1.
Figure 1 about here
The Lorenz curve plots the cumulative share of total income against the cumulative
proportion of income receiving units. It is used for analysing the size distribution ofincome and wealth, to estimate the Gini index and other measures of inequality andpoverty. However, an important drawback of the traditional models of the Lorenz curve
is a lack of satisfactory fit over the entire range of a given income distribution. There
are two parametric approaches to estimate the Lorenz curve (Ryu and Slottje, 1999). In
the first approach one assumes a hypothetical statistical distribution for income
distribution on which to base the estimate of the Lorenz curve (McDonald and Xu,
1995). In the second approach, a specific functional form is fit to the Lorenz curve
directly to estimate the empirical Lorenz curves (Ryu and Slottje 1996; andChotikapanich and Griffiths 2002).
The estimated Lorenz curve is sensitive to errors in survey data. The robustness
properties of inequality and poverty measures assuming contaminated data and usingparametric and non-parametric methods with illustrations are considered in Cowell andVictoroa-Feser (1996a and 1996b). Hasegawa and Kozumi (2003) propose analternative approach to Lorenz curve estimation with contaminated data using Bayesiannon-parametric analysis and present a method for removing the contaminatedobservations. Results obtained using both simulated and real data suggest that thisapproach estimated the Lorenz curve and Gini indices adequately.
A further drawback of the traditional models of the Lorenz curve is that they lacksatisfactory fit over the entire range of a given income distribution. Ogwang and Rao(2000) propose two hybrid Lorenz curve, namely the additive models and themultiplicative models by combination of traditional models written as:(1)

y = f ( p ) = δ f1 ( p ) + (1 − δ ) f 2 ( p ) andy = f ( p) = f1 ( p ) γ f 2 ( p ) λwhere 0 ≤ δ ≤ 1, γ ≥ 1, λ ≥ 1 , and the subscripts 1 and 2 denote the two additive andmultiplicative descriptions of a Lorenz curve. A comparison of the performance of thehybrid and traditional curves shows that the hybrid models are flexible and performbetter in fitting different portion of the observed income distribution well. This is
illustrated using US income data for 1977.
3. INEQUALITY INDICES

Several inequality indices can be derived from the Lorenz diagram. The Lorenz Curve
construction also gives us a rough measure of the amount of inequality in the income
distribution. The measure is called the Gini Coefficient. Computation of the Gini
Coefficient is illustrated by Figure 2. The Gini coefficient is a standard measure ofinequality defined as the area between the Lorenz curve and the line of perfect equality
divided by the area below the perfect equality line expressed as:

2

(2)

n −1

Gini = 1 − ∑ ( Fi +1 − Fi )(Φ i +1 + Φ i )
i =0

where F and Φ are as previously defined (see Figure 2). The index lies in the interval 0(perfect equality) and 1 (perfect inequality). Among the other notable measures ofinequality are: the range, the variance, the squared coefficient of variation, the varianceof log incomes, the absolute and relative mean deviations, and Theil’s two inequality
indices (see Anand 1997).
Figure 2 about here
The range and the variance are the two common statistical measures of dispersion for a
distribution in general. These are useful measures in the context of income. The range isdefined as the absolute difference between the highest and the lowest income levels
divided by the mean income:(3)

RGE = ( xmax − xmin ) / µ

where the arithmetic mean income is µ = 1 / n∑in=1 yi . The method is very sensitive toextreme observations. The variance of income is written as:(4)

VAR = var( y ) =1 n( yi − µ ) 2 .
∑n i =1The squared coefficient of variation is obtained by dividing the variance with squared
mean:
(5)

SCV = VAR / µ 2 .

In similarity with the range, the variance and squared coefficient of variation are
sensitive to extreme observations. The variance of logarithm of income can be writtenas:(6)

VLI = var(log y ) =1 n(log yi − log µ~ ) 2∑
n i =1where(7)log µ~ =1 n∑ log yin i =1is the geometric mean income of the distribution. Finally, the first Theil’s entropy index
of inequality is defined as:
(8)

T1 =

y
1 n yi
log i .
∑µ
n i =1 µThis can be directly computed from the Lorenz curve of income distribution. The
second measure can be written as:(9)n

T 2 = ∑ (1 / n) log
i =1µ(1 / n)
1 n= ∑ logyi( y i / Y ) n i =13

where Y = nµ is the total income. The T 2 is analogous to T 1 except that it reverses therole of income shares ( y i / Y ) and population shares (1 / n) . Both Theil’s indicesmeasure the divergence between income shares and population shares, but using
different distance functions.
Anand (1997) discuss indices based on the Lorenz diagram and also several otherindices. The Absolute Mean Difference index is among the indices based on the Lorenz
diagram as an alternative definition to the Gini coefficient ( AGC ) is specified as:(10)

AGC = 1 / 2( AMDiff / µ )∞ ∞where AMDiff = ∫0 ∫0 x − y f ( x) f ( y )dxdy is the absolute mean difference of two
income distributions of x and y. AGC can also be defined as one-half of the relative
mean difference:(11)

AGC = 1 / 2( AMDev / µ )∞where AMDev = ∫0 y − µ f ( y )dy is the absolute mean deviation. These absolute andrelative definitions are equivalent. Another measure of inequality based on the Lorenz
diagram is the value of the maximum discrepancy ( p * ) between the line of perfectequality and the Lorenz curve written as:(12)

MD = [P * − L( p * )] = 1 / 2( AMDev / µ ) = RMDev / 2

where RMDev is the relative mean deviation. Another divergence measure proposed isbased on the area of the largest triangle between the Lorenz curve and the line ofequality and the area below the line of perfect equality. This measure reduces to thevalue of MD.
We have listed several inequality indices and showed how these are measured. The
indices have different properties that can be used in their ranking, relevance andperformance evaluation. There are three basic properties that one would expect that theabove indices of inequality to satisfy: mean or scale independence, population size
independence and the Pigou-Dalton condition. According to the first two properties theindex remains invariant if everyone’s income or if the number of people at each income
level is changed by the same proportion, respectively. The third condition states that thevalue of an index is reduced if the transfer from richer to the poorer does not result in achanged ranking.
The Gini coefficient and the squared coefficient of variation satisfy all three conditions,while the relative and absolute mean difference and the range measures satisfy only the
first two conditions but violate the Pigou-Dalton condition by ignoring the distribution
inside the range. The variance measure violates the mean independence property.
Unlike the variance of income, the variance of log income is a mean independentmeasure. The two Theil’s inequality measures also satisfy each of the three desirable
properties.2

2

For more details on the properties of the different indices of inequality see Anand (1997).

44. GENERALIZATIONS OF THE GINI COEFFICIENT

A generalization of the Gini coefficient, called the extended Gini coefficient, wasintroduced by Yitzhaki (1983). The new index accommodates differing aversions toinequality. Empirical estimation of the extended index has been limited to thecovariance formula suggested by Lerman and Yitzhaki (1989):

[

M

(13)

v
Gˆ 1 (v) = −pi ( xi − x ) (1 − πˆ i ) v −1 − m
x i =1∑]

where πˆ i = (π i + π i −1 ) / 2 , pi = 1 / M is the proportion of observation in each of the M
income groups, π i = p1 + p 2 + ... + pi is the cumulative proportion of observations inincome groups, m = ∑i pi (1 − πˆ i ) v −1 , and ν > 1 is an inequality aversion factor. The
extended Gini is equal to the original Gini coefficient when the aversion factor v = 2 .
Chotikapanich and Griffiths (2001) suggest an alternative estimator, obtained byapproximating the Lorenz curve by a series of linear segments:(14)

M φ 
Gˆ 2 (v) = 1 + ∑  i  (1 − π i ) v − (1 − π i −1 ) v
i =1  p i []

where π i = p1 + p 2 + ... + pi is the cumulative proportion of observations, and
φ i = pi xi / ∑ j p j x j is the proportion of income. The covariance and the linear segment
estimators are identical for the original Gini coefficient ( Gˆ (v) = Gˆ (v) if v = 2 ) but
12

differ for the extended Gini coefficient where v > 1 . In a Monte Carlo experiment
designed to assess the relative bias and efficiency (relative variance and mean-squarederror) of the two estimator Chotikapanich and Griffiths show that the two estimators
have similar properties when calculated from individual observations or from groupeddata where the number of groups is 30 or more. The dimensions over which sensitivity
was assessed were: (i) the distribution function, (ii) value of aversion parameter(v = 1.33,1.67, 2, 3, 5) , (iii) number of income groups ( M = 10, 20, 30) , and (iv) drawing
5000 samples each of size 2000. However, when calculated from grouped data with 20
or fewer groups, the linear segment estimator outperforms the covariance estimator interms of both bias and mean-squared-error. The log-normal where log(x) is normally
distributed with mean µ = 5 and standard deviation σ = 1.5 , and Singh and Maddata(1976) distributions:(15)

π = F ( x) = 1 −

1(1 + a x )
1

a2 a3

are used as hypothetical income distributions, where a1 = 1 / b , a 2 = aα , a3 = 1 / a , andb = 1 / e c1 , where c1 is a constant of integration in the three parameters of the
distribution. Empirical results in Singh and Maddala (1976) based on US income data
show that the function suggested above give a better fit than the log-normal and gamma
distributions.

55. INCOME INEQUALITY

Traditional measures of inequality, such as the Gini coefficient computed for a single
year, do not capture much about what is happening over time and/or within particularsocieties’ income distribution. Two societies with exactly the same Gini coefficient,could be extremely different in terms of mobility, individual opportunity andvulnerability and their intergenerational differences over time (see Graham, 2002).
In reviewing the literature on income inequality it is important to distinguish between
inequality measured at different levels, its decomposition into different components andto identify their determinants. Pyatt (1976) introduced a decomposition where theoverall Gini is broken into three components(16)

Gini = (m' p ) −1 p ' E p

where p and m are the k-element column vectors of population proportions ( pi ) andaverage income of individuals in population group i (mi ) , and E is a k × k matrix with(i, j ) elements. An empirical illustration of the disaggregation based on a 1973
household survey of income distribution in Sri Lanka in which the total population ofincome receivers is classified geographically by location in urban, rural or estate areas.
The Gini is sum of three non-negative parts. The components are between-groups due todifferences in mean incomes between groups, the within-group due to variations inincome within groups, and overlapping component due to overlaps between the income
ranges in different groups. It is also suggested that the method may have relevance tostudies of migration from one group to another and discrimination.
The above decomposition is applicable to aggregate levels of data where inequality isdecomposed into three components. At the country level these are within country,
between country and overlapping components. The first component reflects inequality
due to the differences in income between the recipients in individual countries. The
second component accounts for differences in mean incomes among the countries, while
the third component reflects the homogeneity of the population (Yitzhaki, 1994) andappears because the Gini coefficient is not exactly decomposable by recipients. Using asimilar Pyatt-type decomposition technique the index of world inequality can be
decomposed into international, national and overlapping or residual inequality
components. At the disaggregate level the overall inequality is decomposed into withinsubgroup, between-subgroup, and overlapping components. Here the subgroup refers to
sub-groups of a population.
International inequality refers to inequality across countries due to differences in percapita income among them. Here the unit of analysis is country and the intra-country
income differences among its citizens ignored. Among important methodologicalconsiderations in studies of inter-national inequality are the exchange rates used, thesource of income data, the reference unit, data coverage and how to weight countries by
their population. In the measurement of world inequality the unit of analysis ispreferably the citizens of the world rather than countries (Milanovic, 2002). Here the
distribution of income is the outcome of all three (within country, between country andoverlapping) components. The decomposition formula is:

6

(17)

n
n n  y − y ji
π i p j + L
Gini = ∑ Gi piπ i + ∑∑ yi ii j >i n
1 n n= ∑ Gi piπ i + ∑∑ ( y j − yi ) pi p j + Liµ i j >iwhere yi is mean income of country i, Gi is Gini coefficient of country i, π i is income
share of country i in total income of the region, pi is country’s population share, µ is
the mean income of the region, and L is the overlapping component. The national
inequality component refers to the disparity of the distribution of income within acountry. It serves as an informative complement to the two extreme cases of international and aggregate world income inequalities.
6. NON-INCOME INEQUALITY

Income inequality is just one dimension of inequality. Other dimensions include
inequality in skills, education, opportunities, happiness, health, life-years, welfare,
assets and social mobility. A selection of studies analyzing different non-income
inequalities, their interrelationship and their relations with income inequality found in
the economic and sociology literatures are briefly given.
6.1 Relationship between inequality in income and education

Education has positive effects on earnings. Differences in opportunities to invest in
human capital, its levels and quality, together with poor redistributive policies may
result in increased inequality. Higher educational attainment and more equal distributionof education should enhance economic growth and more equal income distribution.
Castello and Domenech (2002) provide new measures of human capital inequality for apanel of countries. Taking school attainment levels they compute Gini coefficients andthe distribution of education by quintiles for 108 countries over five-year intervals from1960 to 2000. The human capital Gini coefficient is computed as:(18)

Gini h =n1 x2 (n2 + n3 ) + n3 x3 (n1 + n2 )1 3 3xˆi − xˆ j ni n j = n0 +∑∑2 H i = 0 j =1
n1 x2 + n2 ( x1 + x2 ) + n3 ( x1 + x2 + x3 )where H is the average schooling years of the population aged above 15 years, i and jdenote different levels of education (no schooling (0), primary (1), secondary (2), andhigher education (3)), ni and n j are the shares of population with a given level of
education, xi and x j are average schooling years of each educational level andxˆ i and xˆ j are their cumulative averages, xˆ 0 ≡ x0 = 0 , xˆ1 ≡ x1 , xˆ 2 ≡ x1 + x 2 , andxˆ 3 ≡ x1 + x2 + x3 . The results show that most countries have tended to reduce theinequality in human capital distribution. Moreover, human capital inequality measuresprovide more robust results than income inequality in the estimation of growth andinvestment equations. Yemen and the US are found to be at the extremes of the
distribution. In a regression of human capital inequality accounting for country specificeffects Castello and Domenech estimate the following simple linear trend model:

7

(19)

Giniith = α i + β Trend t + ν it

where they test for stability of within country and between country variability. The test
results show that differences in the distribution of education across countries(α i ≠ α , ∀i ) are substantial, and countries have tended to reduce the inequality in humancapital over time ( β < 0) . A process of convergence in human capital equality hastaken place. Inequality in education is associated with lower investment rate and lower
income growth rates. They conclude that, it is desirable that policies aimed to promote
growth take both the level and distribution of education into account.
The effects of inequality in skills on inequality in earnings across advanced major
English-speaking and a number of continental European Union countries wasinvestigated by Devroye and Freeman (2001). Using standard adult literacy test scores
the results indicate that skill inequality explains only about 7 per cent of the crosscountry differences in earnings inequality. Aghion (2002) argues that wage inequality
between educational groups in developed economies has increased. The within
educational groups inequality is larger, but unlike the between group it affects the
temporary component of income. The persistence of increased inequality in transition
countries is expected by Aghion and Commander (1999) to depend on the pace at which
the acquisition of skills takes place and on the evolution of the educational system in thetransition economies. Education policies can dampen the increase in wage inequality.
The relationship between inequality in education and inequality in income isinvestigated by Cornia and Kiiski (2001) using aggregate country level data.
Empirically, inequality in education (see references cited therein) rises until the average
number of years of schooling reaches 6.3 and declines thereafter. However, thethreshold increases with economic development and adoption of skill-intensive
technologies. Differences in educational achievement in Latin America and sub-SaharanAfrica are identified to be important sources of income inequality in the two regions.
Empirical evidence shows that increased educational attainment increased inequality inother geographical regions as well (see Cameron, 2000). At the international level De
Gregorio and Lee (2002) using cross-section and time-series of countries present
evidence on how higher educational attainment and more equal distribution of education
make income distribution more equal.
Eicher and Garcia-Penalosa (2001) examine how human capital accumulationinfluences both economic growth and income inequality. They argue that the stock of
educated workers determines both the rate of growth and income inequality. Parametersof the demand and supply of labour are crucial determinants of direction and changes ininequality as an economy accumulates human capital. Empirical evidence from Latin
America show that educational attainment in addition to its impacts on inequality
affects the future prospects of mobility, opportunity and vulnerability by increasing theprobability of moving out of poverty or reducing the probability of not falling intopoverty (Graham, 2002). At the micro-level based on data from Holland Hartog andOosterbeek (1998) show that the group with non-vocational intermediate level of
education score highest on health, wealth and happiness. Clark and Oswald (1996) intesting the hypothesis that utility depend on income relative to a comparison orreference level. Results based on British workers data presented in Clark and Oswald

8

suggest that satisfaction levels being inversely related to their comparison wage rates,and satisfaction declining in levels of education.
6.2 Relationship between income inequality, (un)employment and (un)happiness

Employment is not only a source of income; it also provides individuals with social
relationships and identity. Unemployment thus has both economic and social costs toindividuals and societies; it affects income, inequality and happiness. Joblessness is
expected to be negatively correlated with individual wellbeing and health.
The extent of joblessness in advanced countries has caused concern about the direct
monetary costs to both the employers and employees, social costs and the costs of an
economy operating below its production potential among others. Concerning the social
cost, it is suspected that unemployment imposes additional burdens on the individual, aburden referred to as the non-pecuniary cost3 of unemployment. Winkelmann andWinkelmann (1998) test for the importance of non-pecuniary costs of unemployment
using the longitudinal German Socio-economic Panel Study data-set on life-satisfactionof about 10000 working age men in Germany for 1984-89. The results from a logit
analysis show that unemployment has a larger detrimental effect on satisfaction. The
non-pecuniary effect is much larger than the pecuniary direct effect that stems from theloss of income; for instance, adverse psychological wellbeing affects job searchstrategies and lowers productivity.
The relationships between unemployment and unhappiness is investigated by Clark and
Oswald (1994) using mental wellbeing scores. The British Household Panel Study forthe 1991 touched upon various questions like presence of differences in concerns about
being unemployed by different characteristics. These characteristics include age,location, unemployment rate, duration of unemployment, gender, and level of
education. Results from an ordered probit regression of individual wellbeing on a set of
personal characteristics, as expected, show that the effect of being jobless is negatively
correlated with wellbeing.4 Clark and Oswald reject the hypothesis that unemployment
is voluntary. There is a U-shape in mental wellbeing with respect to age. On averagehappiness is lowest in a person’s mid-thirties. The high-educated individuals show more
distress while married people have the lowest degree of mental distress. Wellbeing ishigher among healthy persons. Hartog and Oosterbeek (1998) show that the Dutchgroup with a non-vocational intermediate level of education score highest on health,wealth and happiness. Fathers working independently and women are healthier andhappier.
The relationship between inequality and happiness5 is analysed by Alesina, DiTella and
MacCulloch (2001). The issue is whether Europeans and Americans are different with3

Among the non-pecuniary effects of employment are direct costs of decreased psychological wellbeing
and its adverse individual outcomes are increased mortality, suicide risk, crime rates, decreased maritalstability, etc.
4

Wellbeing is measured based on the General Health Questionnaire (GHQ) survey containing several
indicators of psychological distress or ‘disutility’. Here ‘Caseness scores’ are calculated based on answers
to 12 indicators. The highest level of wellbeing (0) corresponds to a caseness level of ‘feeling (fairly or
highly) stressed’, to the lowest level category of 12. The former would benefit from psychiatric treatment.
5

For reviews of research on the index measures of happiness and mental health see Fordyce (1998), andNg (1996).

9

respect to inequality and happiness. Inequality is measured as a Gini coefficient of grossfamily income in the US but is calculated using expenditure, gross or net income for theEuropean countries. Using a large random sample survey of 128106 answers they find alarge, negative and significant effect of inequality on happiness in Europe but not in the
US. The period of study covers 1972-94 for the US and 1975-92 for Europe. In an
ordered logit model happiness is regressed against inequality, macro and micro
variables and personal and subgroup characteristics. The differences in happiness arepotentially explained by European preference for more equal societies and higher social
mobility in the US. They test these hypotheses by partitioning the sample across income
and ideological lines. Low social mobility in Europe is found to be a source of
unhappiness among the subgroups of poor and socialist with preference for more equal
societies.
6.3 Relationship between income inequality and (ill) health

The connection between income inequality and health is explored by Deaton (2001).6
The empirical analysis is based on both rich and poor countries. Here ill health isdefined as the rate of mortality. In exploring the theoretical basis for such a relationship
Deaton discusses a range of mechanism including education, economic growth, landholdings, politics, crime, non-linear income effects, credit restrictions, nutritional traps,
public goods provision and relative deprivation. Given the poor data quality underlying
inequality, the conclusion is that there is no direct link from income inequality to illhealth. However, in the design of redistributive policies the importance of income andother inequalities, and the social environment, should not be neglected. Income
inequality is an indicator of the quality of social arrangements, of stress in richcountries, and of mortality in poor countries. Deaton and Lubotsky (2002) argue that thecorrelation between mortality rates and income inequality across the cities and states of
the US is confounded by the effects of racial composition. For instance, conditional on
the percentage of blacks neither city nor state mortality rates are correlated with income
inequality. White mortality and incomes are lower in places where the fraction of blacks
is higher. This result is present within geographical regions of the country and for all
age groups (except boys aged 1-9), and for both sexes and is robust to conditioning on
income, education and unobserved state fixed effects. However, it remains unclear why
white mortality is related to racial composition.
Pradhan, Sahn and Younger (2003) explore global inequality in health status anddecompose it into within- and between-country inequality components. The data used intheir analysis are representative from the demographic and health surveys on childhealth, fertility, contraceptive use and related demographic. It covers 55 developing
6

The literature on the relationship between health and economic development begin with the Preston
curve (Preston, 1975), that shows the cross-country relationship between life-expectancy and income perhead. Life-expectancy increase with income for poor countries, but at a decreasing rate, and it is weaker
or absent for rich countries. For a selection of other (cross-country) studies on economic and social
correlates of suicide rates see Chuang and Huang (1997) and Rodriguez-Andres (2003), on income
distribution and life expectancy see Wilkinson (1992) and Mellor and Milyo (2001), and on income
inequality and population health see Judge, Mulligan and Benzeval (1997). An excellent example of therelationship between inequality in health and economic development based on individual data including
income information using Swedish data is by Gerdham and Johannesson (2000). In examining theexistence of a negative association between income and mortality they find that inequalities in healthfavour higher income groups.

10countries and OECD countries since 1989. Health is an important indicator of
wellbeing; there is extensive literature on the measurement of health differences acrosssocioeconomic dimensions and linking inequality in health to income andsocioeconomic status. Morbidity, mortality and life expectancy are traditionally used ashealth indicators and income and expenditure as welfare indicators. However Pradhan,
Sahn and Younger use standardized height of pre-school children to examine healthinequality; an abundance of medical and public health research shows that height is agood objective indicator of the general health status of children determined by nutrient
intake, disease and deprivation. Results indicate that in contrast with income inequality
research, within-country variation is the source of most inequality, rather than betweencountry differences. The relationship between income and health when measured bynutrition indicators, is a strongly concave function.
Kakwani, Wagstaff and van Doorslaer (1997) clarify the relationship between two
widely used indices of socioeconomic inequality in health, namely the relative index ofinequality and the concentration index, and explain their superiority to other indices. On
individual-level data the concentration index (C) is calculated as:
(20)

C=

2 n
∑ xi Ri − 1
nµ i =1

where xi is ill health score of the ith individual, n is the number of individuals,µ = 1 / n∑i =1 xi is the mean level of ill health, and Ri is the relative rank of the ithnperson. As indicators of ill health the authors used chronic illness (dummy variable) anda self-assessed health variable (categorical). They also develop distribution-free
asymptotic estimators of the standard errors of both the relative index of inequality andconcentration index. The role that demographic standardization by gender and age
interval plays in the analysis of socioeconomic inequality in health is clarified. Healthinterview survey data from Holland covering 10232 individuals for 1980 and 1981 isused in the empirical illustration. The result of their study suggests that extra precision
allowed for by individual-level data is to be retained but the gain may not always be thatlarge.
Income-related inequality in self-assessed health in nine industrialized countries7 wasestimated by van Doorslaer et al. (1997). Here the concentration index is used as ameasure of inequality, and the results show that inequality in heath significantly
favoured the higher income groups in all countries. Gerdtham and Johannesson (2000)
find the concentration index to be an incomplete measure of health since it ignores thelength of life. They investigate income-related inequalities with respect to life years andquality-adjusted life-years. In the health literature there is evidence of the existence of anegative association between income and mortality. Results based on 40000 Swedish
individuals followed up for 10-16 years, show that inequalities in health favour higher
income groups. A Dutch study (Hartog and Oosterbeek, 1998) also indicates thepresence of gender effects in the wealth–health–happiness relationship. Women incomparison with men are less wealthy, equally healthy but are happier.

7

East Germany, Finland, Spain, Sweden, Switzerland, the Netherlands, UK, USA, and West Germany.

11

6.4 Relationship between inequality in wealth and growth

The growth and inequality literature has recognized that it may be the distribution ofassets, rather than income, that underlies effects of inequality on growth by restricting
access to credit markets (Stiglitz and Weiss, 1981). In testing the robustness of theinequality–growth relationship using country level data for 108 countries during 196092 on income and land distribution Deininger and Squire (1998) show that there is astrong negative relationship between initial inequality in asset distribution and longterm growth. Inequality reduces income growth for the poor, but not for the rich.
Growth and inequality are affected by the redistribution of assets and increased
aggregate investment. Distribution of land is characterized by more cross-country
variation than that of income. Distribution of income, assets and government
redistributive policies are among important factors determining the level of income
inequality.
Available evidence on the distribution of personal wealth,8 referring to material assetsthat can be sold in the market, and its evolution over time for a number of countries issummarized by Davies and Shorrocks (2000). The results, despite deficiencies of survey
data on wealth, reconfirm the known fact that wealth is more unequally distributed thanincome and points to a downward trend in wealth inequality in several European
countries over most of the twentieth century. In addition to lifecycle accumulation andinheritance which plays a major role in the explanation of wealth differences, they also
give attention to several factors: the reasons for holding wealth, individual differencesin wealth holdings, an examination of the causes of these differences, the link between
wealth status across generations, and motives for leaving bequests. Inheritance is foundto account for about 35-40 per cent of aggregate wealth in the US. Contributions fromdemographic trends, and changes in assets and housing prices are found to affect the
distribution of wealth.
Static analysis of distributions does not provide information about changes in therelative positions of different units over time. Measures of mobility are constructedwhen data are provided in the form of a transition matrix illustrating the dynamic
movements of different units over time. Shorrocks (1978) explores some of the issues
involved in the construction of mobility measures, presenting a number of properties
required of an index of mobility, a proposed set of axioms and discussion of the
problems of comparing matrices defined over different time intervals. Shorrocks
discusses an index that is incompatible with an objective notion of perfect mobility butable to compensate for differing time periods important to the observed mobility.
King (1983) discusses horizontal equity and social mobility, proposing an alternativeindex of overall inequality which is possible to be decomposed into vertical andhorizontal equity components. King derives a functional form for the social welfare
function and presents results from an application of the index to UK households to amodel of optimum lump-sum taxation. The proposed index is expected to supplement
analysis of tax reform effects on the level and distribution of welfare by explicitly
accounting for horizontal equity or social mobility. Maasoumi (1996) surveys the twomain welfare theoretic approaches to the measurement of mobility. One is based on
8

Total wealth consists of human plus non-human capital. Here the human capital component is excluded
and the focus is on material assets in the form of real property and financial claims. Less attention is paid
to private pensions, social security wealth and its link to demographic factors.

12transition matrices (Shorrocks, 1978) and their reduction to a scalar measure, and theother is a generalization of the index initiated by Shorrocks (1978) labelled the
Maasoumi–Shorrocks–Zandvakili ‘inequality reducing’ measure applied to long-run
incomes and describes statistical methods for their implementations. Some popularmobility indices are also analyzed.
7. SUMMARY

Inequality can have different dimensions. Economists are mostly concerned with theincome and consumption dimensions of inequality. Among other non-income inequality
dimensions we can include inequality in skills, education, opportunities, happiness,health, life-years, welfare and assets.
Several inequality indices can be derived from the Lorenz diagram. The divergence of aLorenz curve for perfect equality and the Lorenz curve for a given distribution ismeasured by some index of inequality. Several inequality indices follow along withsome basic properties that one would expect the indices to satisfy. These properties areto be used in their ranking, relevance and performance evaluation. The most widelyused index of inequality is the Gini coefficient. Gini is generalized to accommodate
differing aversions to inequality.
Income inequality can be decomposed at different levels of aggregation. At the national
level it can be decomposed into within-subgroup, between subgroup, and overlapping
components. In a similar way at the international level it can be decomposed into
within-country, between-country, and overlapping components. In the measurement ofworld income inequality it is desirable that the unit of analysis is the citizens of theworld rather than countries. Representative individual based micro data is preferable.
The effects of inequality in non-income factors on earnings can be summarized
variously. Inequality in education explains a minor fraction of differences in crosscountry earnings inequality. The impact decreases by the level of education and depends
on the economic development and skill-intensive nature of production technologies. It
also negatively affects the investment rate and growth rate of income. There is no direct
link from income inequality to ill health measured as mortality, but a range of
mechanism and social arrangements indicate the presence of an indirect link. Unlike inthe case of income inequality, within country health inequality is a dominating source of
inequality. Regions differ with respect to the effects of inequality on happiness; thedifferences in happiness are associated with preferences for equal societies and higher
social mobility.
Employment in addition of being a source of income is also is a provider of social
relationships and individual social identity. Joblessness has a direct cost to the employee
and employers, social costs and a cost in in-optimal operation of an economy. The
additional burden of unemployment on individual wellbeing, the non-pecuniary cost, is
an important non-monetary cost of joblessness and much larger than the pecuniary
effect that stems from the loss of income, though the negative effect varies by personal
characteristics. Inequality in the distribution of assets is found to affect long-term
growth. In sum the results suggests that one should account for the interrelationshipbetween the different dimensions in the measurement and analyses of inequalities.

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Figure 1. The Lorenz diagram.
1

Cumuative percentage of income

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Cumulative percentage of population
cummulative income share

14Line of perfect equality

1

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