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8/2/2019 Inequality and Human Development, Maria Ana Lugo
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Inequality and
HumanDevelopment
Maria Ana Lugo
University of Oxford
20th Sept 2004
maria.lugo@economics.ox.ac.uk
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Purpose
To present key issues (debates) aroundinequality
To explore methodologies to comparedistributions
To analyse how much HDI incorporates(or can incorporate) inequality
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Outline
1. Initial Remarks – definitions
2. Issues on Inequality
3. Why does inequality matter?
4. Methods
5. Inequality and HDI
6. Example (Arg)
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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)
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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
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“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)
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. 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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4. How o we compare twodistributions?
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
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4. How o we compare twodistributions?
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
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4. How o we compare twodistributions?
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
= − −
∑
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.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
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4. How o we compare twodistributions?
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
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4. How o we compare twodistributions?
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
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4. How o we compare twodistributions?
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
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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
4. How o we compare twodistributions?
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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.
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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.
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