Inequality and Human Development, Maria Ana Lugo

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Inequality and

HumanDevelopment

Maria Ana Lugo

University of Oxford

20th Sept 2004

[email protected]



2

Purpose

To present key issues (debates) aroundinequality

To explore methodologies to comparedistributions

To analyse how much HDI incorporates(or can incorporate) inequality



3

Outline

1. Initial Remarks – definitions

2. Issues on Inequality

3. Why does inequality matter?

4. Methods

5. Inequality and HDI

6. Example (Arg)



4

1. Initial Remarks

“Inequality is like an elephant: Youcan’t define it, but you know it when

you see it” (Fields 2001, 14)

The meaning of inequality: encapsulating ethical concepts

vs. statistical dispersion (distribution rather than inequality)

Inequality, poverty and welfare. Related but distinct

broader than poverty – defined over the whole distribution, notonly below a certain poverty line

narrower than welfare – if indep of mean, only concerned withthe second moment (relative vs absolute measures)

But 3 closely related, sometimes used in composite measures

(e.g. Sen’s measure contains the Gini among the poor)



5

2. Issues on Inequality

WHY should we care about inequality?

HOW do we compare distributions? (we alwayscompare!) Empirical issues (dimensions, variables, unit of

analysis, methods -indices and orderings-,between/within inequality)

WHY is there inequality? [ineq as ‘output] Theories to explain determinants: factor share and

market imperfections theories – especially LM i.e. infoasymmetries, efficiency wages, selection models

Tools: decompositions, vertical vs. horizontal inequality

WHAT are the effects of inequality? [ineq as‘input’] On growth, HD, poverty, conflict, democracy, etc



6

“Because it is high and increasing!” - Magnitude of the problem

Maps World inequality … increasing?

International: between countries

National: Within country-inequality

World: between + within

“Because it is fair” - Theories of justice Sense of justice and self-worth

“Because it affects dev/growth/HD/ democracy /social cohesion”

Mechanisms from inequality to variables

.matter?

“.. every normative theory of socialarrangement that has at all stood the test of

time seems to demand equality of something – something that is regarded asparticularly important on that theory”

(Sen 1992, 12)

‘equality of what?’ [space of equality:Utilitarians, Rawlsians, Nozicksean, and

Senians]egalitarian in some space, anti-egalitarian insome other space.

Inequality good or bad for

(income) growth?INEQ-Levels: Kuznets inverted ‘U’ hypINEQ to Growth: HK Loss (-), Access to K mkt(+/-), Efficiency wages (-), Savings (+),political instability (-)

Human Development: effects on levels

(of edu, health, others) achieved, politicalparticipation, etc.

Poverty: sensitivity of poverty to growth,effect of specific policies

Social cohesion (Stewart):

Horizontal Ineq (vs vertical) culturallydefined groups => social stability,instrumental and direct welfare reasons

International unw International w World

Source National accounts National accounts Household surveys

Unit of analysis Country Country Individuals

Welfare concept GDPpc GDPpc Mean pc income

National currency Market ER or PPP ER

Within -country Ignored Ignored IncludedMeasure: relative or absolute

4 H

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4. How o we compare twodistributions?

“It is generally agreed that, other things being equal, a considerablereduction in inequality of incomes found in most modern communities

would be desirable. But it is not generally agreed how this inequality should be measured”

Hugh Dalton (1920) “The measurement of the inequality of incomes”

Economic Journal , 1920, Vol. 30, p. 348

Ineq of what and among whom?

Variable/Indicator : one or many? Which one(s)? If income,pre/post taxes; includes profits of capital and land or not.

Unit of analysis: individuals, households, regions, countries(≠ recipient unit)

Adjustments/corrections: e.g. adult equivalent (eq scales),economies of scales, cost-of-living differentials (rural-urban,diff regions)



8

. ow o we compare wodistributions?

One ‘x’or

many ‘xs’?

UNI-DIMENSIONAL MULTI-DIMENSIONAL

1. Indices(real #)

2. Orderings(CDFs, LC)

Item-by-Item Aggregative Non-aggreg

2 step MD Indices

4 H t



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UNIDIMENSIONAL

1. Indices

E.g. Gini coefficient, Theil index, Atkinson Index, 90-10 Ratio

Which one shall we use?How do we choose between indices?

Axiomatic approach: desirable properties

Anonymity, Scale Independence, Population Independence,Transfer Principle (Pigou-Dalton) => M of Relative Inequality

Others: Decomposability, Transfer Sensitivity

‘Ad hoc’: mathematical appeal (GE)

neat statistical or graphical interpretation (Gini)

4 H t



10


Some measuresGini Coefficient: most widely use inequality measure.

- Function of differences between every pair of inds’ income

- Ranges from 0 to 1

- It is a relative measure

- Has a close relation to Lorenz Curves => clear representation

- Can be easily computed from normally available data (%pop/%income)

But

- Not decomposable (between- and within-groups)

21 1

1

2 ( )

n n

i ji j

Gini y y n y µ = =

= −∑∑

4 H t



11


Other two relative measuresGE measures: from Theory of Information

α weight to changes at different parts of the distribution. The lower the α,the more sensitive to the lower part.

- When α=0 Theil’s mean log; When α=1 Theil index (equal weight);

Atkinson index: includes subjective elements

ε : parameter of inequality aversion, explicit choice of weights to changesat different parts of the distribution. The higher the ε , the more weight to

the lower part

1/ (1 )1

11

( )

i x I

n x

ε ε

ε µ

−− = −

∑

1 11

(1 ) ( )

i x GE

n x

α

α α α µ

= − −

∑



12

.distributions?

Formula Mean

Indep

Pop indep Pigou-

Dalton

Decomposability Transfer sensitivity. Others

RangeR =

µ

ii Y MinY Max −

• • X Ignores inside the extremes

Variance

V =n

Y i

∑− 2

)( µ X

• •

Relative Mean DeviationM =

1iY

n µ

µ −∑

• • X

Not sensitive to transfers among same

side of the mean income.

Gini CoefficientG =

2

1

2i j j i

Y Y n µ

−∑ ∑ • • •

X Sensitive to centre of distrib –depends

on # people between. Not incomes.

Standard deviation of logs

H =

2/12

loglog

−

∑ n

Y µ

• • X (might

violate for very

high income)

• More sensitive for transfer in the lower

end. Not defined for zero income

earnings

GE measuresGE

?= ∑

−

−

α

α α iY

Y

n1

1

)1(

1

• • • • Depending on α

Theil second α = 0

L = ∑iY

Y

nlog

1

• • • • Very sensitive to lower end. Not

defined for zero income values

Theil indexα = 1

T = ∑Y

Y

Y

Y

n

ii log1 • • • • Sensitive to lower end

Coefficient of Variation α = 2

GE2= ( ) 2

2

1CV ;CV =

µ

V

• • • • Transfer neutrality, equally sensitive to

all income transfers

Atkinson(ε)

A?=

ε ε

/1

11

− ∑

Y

Y

n

i

• • • X

Depending on ε

4 H t



13


2.Orderings (C»D)

Lorenz Curves (1905)

Atkinson (1970): LC if do not cross, then any measuresatisfying above axioms would rank distributions equally

=> we do not have to worry about which one to use

Percentage of Population

Φ(y)

Percentage

of Income

Line of Perfect

Equality (LPE)

Lorenz Curve

L(y) - LC

0 1

1

F (y)

B

A

AGini

A B=

+

4 H t



14


But if they cross? => We cannot conclude anythingunambiguously (incomplete ordering)

- Either we choose some measure of inequality

=> different measures might give us different answers, in

fact, we are always able to find 2 measure that disagree!!

- Or we leave the analysis at this point

Is this bad? Sen argues instead of this being a drawback of LDcriterion, it is in fact its greatest advantage, as it captures the

essential ambiguity of the concept of inequality

“Ambiguity of inequality should be preserved rather thantrying to remove it through some arbitrary completed ordering” (Sen 1997, p. 121)

NB: LC for continuous (‘distributable’) unbounded variables

4 H t



15


MULTIDIMENSIONAL

1. Item-by-item: each vle examined separately

UD methods (indices/orderings) + covariance/correlation analyses

2. Aggregative strategies: Collapsing dimensions Two-step procedure: (1) well-being index (2) UD methods

Multidimensional measures of inequality

=> Complete ordering of distributions.

Decisions over: weighting (w), degree of substitution bt dimensions ( β),

and degree of inequality aversion.

HDI: chooses w: [1/3, 1/3, 1/3] and β: 1 for all pair of attributes

3. Non-aggregative strategies:

Tests comparing MD distributions, as in UD ordering: Kolmogorov-Smirnov and Pearson’s tests. Not easy to implement, few studies

4 H t



16

Advantages Disadvantages

ITEM-BY-ITEM No problem of aggregation

(commensurability, choice of w, β)

Not easy to compare if

#dimensions increase

No account of MD aspectat unit level (only corr)

AGGREGATIVE Summarises info, easy tocompare bt units

Gives complete ordering

Have to imposeassumptions (values) onw, β, α

Commensurability

(units), types of vles

NON-AGGREG Deals with MD of unit

Not many assumptions of parameters required

Difficult to implement

Problem of high # obsrequired

Most probable, leads to

ambiguous conclusions




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5. HDI and Inequality Between-country inequality: HDI as a 1st step,

then apply UD indices

Within-country inequality: HDI components are

national averages => not included

“An intrinsic concern for inequality in human development requires

adjustment of average achievements in each of the three dimensions

(by the extent of measured inequality in each) – as well as an

accounting of the covariances in achievements along the differentdimensions” (Anand 2000: 99)

Only GDI – including gender differentials

1991-94 HDR include Yadj=Y(1 – G)



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5. HDI and InequalityShould we include w-c inequality?

Efficiency arguments: variables as means to other

ends, in a diminishing way. That’s why income in logs

Equity arguments: intrinsically valuable

Basic problem: type of indicators in HDI

- LE is probability-based group measure, not individual

- Literacy: group measure (%) or individual (0-1) then noefficiency argument for a 0-1 variable

⇒ Change indicators (for a continuous unbounded)

⇒ Sub-group inequality (gender, location, race) – municipalities[though same for 3 attributes!]



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5. HDI and InequalityHow shall we include inequality?

Hicks (1997): Extending HDR91-93 income (Sen Index)

Each x dimension

G x : Gini coefficient for component x

Edu: years of schooling / Health: life-span attainment (age-at-death)

BUT:

- It is not group-consistent/decomposable, bc. Gini is not

- It depends on the ordering of aggregation across people anddimensions

-

Also, Anand-Sen’s critique: interpretation of reductions

[ ]( )* 1 x x x IA x G µ λ = −



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5. HDI and Inequality Foster (2003): ‘General Mean of Means’ (Atkinson Index)

Each x dimension

Aggregate components

- Choose ε according to concern for inequality –higher ε more weightto lower part of distribution (more aversion to inequality)

- Group-decomposable and sequencing-free

- Sensitive to inequality across dimensions (penalising uneven

development, there is some substitutability but it’s not infinite)

[ ]

11 1

1( ) ( ) 1 ( )

i

i

x

x x I x n

ε ε

ε ε µ µ

− −

−

= − =

∑

[ ]1 1 1 1( ) ( ), ( ), ( )H D x y z ε ε ε ε ε µ µ µ µ − − − −=



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5. HDI and Inequality

Related questions

- Should ε be the same for all dimensions? (seeAnand 2003) – bc of nature of the dimension and

of the indicator used

- How should be choose ε?

- Substitutability between inequality across

dimensions, but not between levels of components (valid ? also for HDI).

i i



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6. Exercise – Argentineprovinces Objective: Do multivariate distribution analyses contribute to

the study of Argentine welfare inequality?

ExercisePeriod: 1991 vs. 2001

Dimensions:

Units of analysis: provinces

Weights: one province one observation (as in HDI!)

Dimension Indicator SourceIncome Per capita household income

(w regional cost-of-living adj)PHS(ENGH)

Health Life expectancy at birth Vital StatisticsPopulation Census

Education % adult population with at

least Complete primary

Population Census



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6. Results

Income µ 1991 f µ 2001 Stoch dom and measures 1991f 2001

Health (LE) µ 2001 f µ 1991 Stoch dom and measures 2001f 1991

Education µ 2001 f µ 1991

Stoch dom and measures 2001f

1991

Item- by-item

Income distr worsen Health and educ distr improved

NB: Low values of ineq (not sign different). Between-ineq is relevant

Stoch dom and measures 2001f 1991Maasoumi(1 w, 4 β, 2 α )

Different result from income distributionAggregativeStrategies

Bourguignon(1 w, 4 , range0 β -1α )

Depends on values of andα β if ? ½ =>β 2001f 1991if < ½ =>β 1991 f 2001

Two opposite results



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Conclusions There are enough reasons to include distribution (inequality)

issues in the analysis. But not consensus on how, even withinUD.

Be specific, demand specificity! “Definitional issues are tooserious to be left to footnotes or ignore altogether” (AB 2000:

14) Inequality OF WHAT (vle) AMONG WHOM (unit)?

Atkinson’s 1st result: All measures imply assumptions(embedded SWF) – important to make them explicit andunderstand them

Different measures might give different orderings of distributions =>

Atkinson’s 2nd result: Use LC criterion when possible Test robustness of results (diff measures/parameters) Or use one and give reason for choosing it over the others



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Conclusions Multidimensional inequality: three strategies with adv and

disadv.

Also they imply taking many decisions

“There is an inescapably arbitrariness in the choice of [β]. The right

way to deal with the issue is to explain clearly what is being assumed… so that public criticism of the assumption is possible” (Anand 2003:218)

Better than neglecting the issue altogether, as generally done,and focus solely on income distribution

⇒ Again, use sensitivity analysis, results under differentassumptions

Statistical Inference: for data derived from surveys,meaningful comparisons between estimates need includestandard errors of the measures (not usually done)



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ReferenceAtkinson (1970)

"On the Measurement of Inequality", Journal of Economic Theory , 2 (3): 244-263.

Fields, G. S. (2001), Distribution and development : a new look at thedeveloping world, New York, London: Russell Sage Foundation; MIT Press.Chapter 2 "The Meaning and Measurement of Income Inequality"

Sen, A. K. (1992), Inequality reexamined, New York and Oxford: RussellSage Foundation;Clarendon Press. Chapter 1 "Inequality of what?"

Sen, A. K., and J. E. Foster (1997), On economic inequality (Enl. / ed.),

Oxford: Clarendon Press. Chapter 2 "Measures of inequality"Sen, A. (2000), "Social Justice and the Distribution of Income" in Handbook

of Income Distribution (Vol. 1), A. B. Atkinson and F. Bourguignon (eds),Oxford: Elsevier Science, pp. 59-85.

Stewart, F. (2001), "Horizontal Inequalities: A Neglected Dimension of Development", CRISE Working Paper 1, Centre for Research on Inequality,Human Security and Ethnicity (CRISE) and Queen Elizabeth House (QEH),University of Oxford, Oxford

ON INEQ GLOBAL/WORLDAtkinson, A. B., and A. Brandolini. (2004), "Global World Inequality:

Absolute, relative or Intermediate?" presented at the 28th General Conference of The International Association for Research in Income and Wealth, August 22-28, Cork, Ireland.

Bourguignon, F., and C. Morrisson. (2002), "Inequality among World

Citizens: 1820-1992", American Economic Review , 92 (4), 727-744



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ReferenceON WHY INEQ Gral Theories of social justice and INEQAtkinson, A. B., and F. Bourguignon. (2000), "Introduction: Income Distribution

and Economics" in Handbook of income distribution (Vol. 1), eds. A. B. Atkinsonand F. Bourguignon, Oxford: Elsevier Science, pp. 1-58.

Milanovic, B. (2003), "Why we all do care about inequality (but are loath to admitit)", EconWPA /0404002, UNPUBLISHED.

Sen, A. (2000), "Social Justice and the Distribution of Income" in Handbook of income distribution (Vol. 1), eds. A.-B. Atkinson and F. Bourguignon, Oxford:Elsevier Science, pp. 59-85.

ON INEQUALITY AND GROWTH, HD, POVERTYKanbur (2004) “Growth, inequality, and Poverty: some hard questions” at

www.people.cornell.eduy/pages/sk145Kanbur, R. (2000), "Income Distribution and Development" in Handbook of income

distribution (Vol. 1), eds. A. B. Atkinson and F. Bourguignon, Amsterdam; NewYork and Oxford: Elsevier Science, North-Holland, pp. 791-841.

Fields, G. S. (2001), Distribution and development : a new look at the developingworld, New York, London: Russell Sage Foundation; MIT Press. Chapter 3 and10.

Stewart, F. (2000), "Income Distribution and Development", QEH Working PapersSeries 37, University of Oxford, Oxford

Stewart, F. (2001), "Horizontal Inequalities: A Neglected Dimension of Development", CRISE Working Paper 1, Centre for Research on Inequality, CRISEand QEH, University of Oxford, Oxford

Subramanian, S. V., and I. Kawachi. (2004), "Income Inequality and Health:What Have We Learned So Far?" Epidemiologic Reviews, 26: 78-91.

http://www.people.cornell.eduy/pages/sk145

http://www.people.cornell.eduy/pages/sk145



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ReferenceON INEQ IN HDI

Anand, S., and A. K. Sen (1995), Gender inequality in human development :theories and measurement, New York: United Nations Development Programme.

Anand, S., and A. K. Sen. (2000), "The income component of the humandevelopment index", Journal of Human Development , 1 (1): 83-106. Also,printed in (1999) mimeo, New York: UNDP Human Development Report Office.

Anand, S., and A. K. Sen. (2003), "Concepts of human development and

poverty : a multidimensional perspective" in Readings in human development :concepts, measures and policies for a development paradigm, eds. S. Fukuda-Parr and A. K. Shiva Kumar, New Delhi: Oxford University Press, pp. 204-220.

Foster, J. E., L. Lopez-Calva, and M. Szekely. (2003), "Measuring theDistribution of Human Development: Methodology and an Application to Mexico"presented at the WIDER Conference on Inequality, Poverty and Human Well-Being, 30-31 May, Helsinki, Finland: WIDER.

Hicks, D. A. (1997), "The Inequality-Adjusted Human Development Index: A

Constructive Proposal", World Development , 25 (8), 1283-1298.Anand, S. (2002), "The concern for equity in health", Journal of Epidemiology and

Community Health, 56 (7): 485-487.Sen, A. K. (2002), “Why health equity?”, Health Economics, 11: 659-666.

Inequality and Human Development, Maria Ana Lugo

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