Transcript No Slide Title

Cornell 2009
Lateral Thinking:
Promising Path or
Deceptive Deviation?
A B Atkinson, Nuffield College, Oxford
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Introduction: On lateral thinking
1. Indices covering different dimensions:
income and health inequality
2. Keeping dimensions separate and radar
diagrams
3. Interdependence and copulas
Conclusions: Directions for future research
2
Lateral thinking
“My interest in the question of measuring inequality was
originally stimulated by reading an early version of the
paper by Rothschild and Stiglitz [“Increasing risk: A
definition and its economic consequences”], to which I owe
a great deal” (Journal of Economic Theory, 1970, p 244).
CLEAR PARALLEL: Risk and Inequality
1. Mean preserving spread and principle of transfers (Pigou
and Dalton).
2. Expected utility and additive social welfare function.
3. Risk aversion and inequality aversion.
4. Stochastic dominance.
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Diagram on country rankings for different values of ε was
based on the diagrams used to show the results of college
rowing races (bumps).
Ranking for different values of epsilon
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Rank (least unequal top)
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Great Britain 1951
Italy 1948
US 1950
Puerto Rico 1953
Netherlands 1950
Denmark 1952
India 1955
West Germany 1950
Sweden 1948
Ceylon 1952
Barbados 1951
Mexico 1957
8
6
4
2
0
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
Value of epsilon
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Different views!
“The e parameter, which is bound by the limits of 0 and 1,
determines the level of inequality aversion” (US Census Bureau,
2000, p 11).
LIS Key Figures uses values of epsilon of 0.5 and 1.0.
“A system of weighting that appeals to me is the inverse square
law, according to which the welfare weight is the inverse of the
square of the individual’s income” (Mirrlees, 1978, p 134).
A Sen, The Idea of Justice, allow “the possibility that even in
the original position different people could [take] very different
principles as appropriate for justice, because of the plurality of
their reasoned political norms and values” (2009, p 90).
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ECONOMICS HAS BENEFITED FROM BORROWING
FROM OTHER DISCIPLINES (examples)
• Physics (Samuelson’s Foundations).
• Psychology (behavioural economics).
• Ecology (“Ecology for bankers”, Nature, 2009).
WITHIN ECONOMICS (examples)
• Offer curves from international trade.
• Duality applying cost function to consumer theory.
• Harberger model in public finance (“This paper … was
inspired by a long tradition of writings in the field of
international trade” (JPE, 1962, page 215).
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BUT
• Need for care in drawing parallels
• Illustrate by issues raised by move to other dimensions:
• New dimensions and aggregation of sub-indices
• Portraying sub-indices: different dimensions of inequality
• Multi-dimensionality at individual level.
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Introduction: On lateral thinking
1. Indices covering different dimensions:
income and health inequality
2. Keeping dimensions separate and radar
diagrams
3. Interdependence and copulas
Conclusions: Directions for Future Research
8
CAN WE APPLY THE SAME MEASURES TO HEALTH?
“It is surprising in view of … the sheer amount of literature on
inequalities in health that so little attention has been paid to
the question of how health inequality is best measured”
(Wagstaff, Paci and van Doorslaer, 1991).
First need to distinguish
• inequality of health status, h
• covariance of h with income or socio-economic status,y
Much of the health literature is concerned with second
question. Reserve term “health inequity” to refer to positive
covariance.
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Strategic Review of Health Inequalities in England post 2010
Health inequality: distribution of h
Self perception of general health during last 12 months
Great Britain
100
90
percentage of all persons 16+
80
GOOD
70
60
50
40
FAIRLY GOOD
30
20
10
NOT GOOD
0
1998
2000
2001
2002
2003
2004
2005
2006
2007
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Health inequity: covariance of h and y
Reported restricted activity due to sickness in previous
14 days Great Britain 2007
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males 45-64
20
females 45-64
15
10
5
0
Professional
Intermediate
Lower
supervisory
Semi routine
Routine
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Inequalities in health status
Some authors apply same measures as income to health status or age at
death: Lorenz curve and Gini coefficient.
BUT important questions
• is health status purely ordinal (Allison and Foster, 2004): “not good”, “fairly
good”, …
• Where cardinal (as with achieved life, ℓ), should we use the Gini or
constant aversion measure?
• Absolute Gini seems more appropriate than usual relative Gini (compare
achieved life spans of 50,70 and 90 with 55, 77 and 99).
• Kolm index more appropriate for same reason, but if use epsilon, then “we
should be more averse to inequalities in health than to inequalities of
income” (Anand, 2004, page 16).
• If we are combining W[Iy,Ih] should W be homothetic?
• Does marginal value of extra year decline with ℓ? WDR 1993 shows value of
extra year rising up to around age 10.
• For these reasons, may be limited to first order comparisons.
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CONCLUSIONS
For health
• Need to distinguish health inequality and health
inequity
• Health may be ordinal variable, and limit to first
order dominance.
• Cardinal variables absolute rather than relative
In general
• Need to treat each dimension on its own terms:
(Trannoy and Muller).
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Introduction: On lateral thinking
1. Indices covering different dimensions:
health inequality
2. Keeping dimensions separate and radar
diagrams
3. Interdependence and copulas
Conclusions: Directions for Future Research
14
How portray different dimensions?
“It would always be desirable to have a snapshot
view of the status of human development in various
States while analysing their respective strengths
and weaknesses on some relevant human
development indicators. … To meet this objective
the National Human Development Report introduces
Development Radars” (Indian Planning Commission,
2002, page 12).
Radar diagram, also known as web chart, spider
chart or star plot.
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Or as “Wind rose” (Crothers, Field Studies, 1981)
Wind direction at St Ann’s Head, Pembrokeshire
North
16
14
NW
12
NE
10
8
6
4
2
West
East
0
SW
SE
South
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How do we interpret these charts?
“The Development Radars give a snapshot view. … They capture the relative
contribution of different dimensions in overall human development. The
greater the shaded area of any indicator the better is the attainment on that
indicator. … the more is the shaded area corresponding to the 1990s vis a vis
the area corresponding to the 1980s, the faster is the pace of human
development.” (Indian Planning Commission, 2002, pages 15-16).
Human development in India
Per capita expenditure
5
IMR
4
Poverty
1980s
3
2
1990s
1
Life expectancy
0
Formal education
Safe water
Pucca house
Literacy
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Problems:
• Effect of improvement in indicator i depends on sum of
indicators h and j.
• Area depends on ordering of indicators: “the order of
assigning variables to features in a symbol (to the rays in a
star, for example) is usually rather arbitrary, yet the shape of
the symbol, and to some extent the effectiveness of the
whole display, can depend critically on the assignment”
(Chambers, Cleveland, Kleiner and Tukey, 1983, page 164) .
• Area is visually misleading (Tufte).
Advantages over histogram:
• Could allow weighting (?)
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First set of ten EU
Social Indicators
Income
2.5
Health
2
Income
1.5
1
Health
Income
0.5
0
Education
Income
Employment
Employment
Employment
Income
X
Health
X
Employment
Education
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CONCLUSIONS
• Need to be careful in use of radar diagrams.
• May introduce unplanned interactions.
• Positive message: when moving to higher level of
evaluation with multiple dimensions, need to
consider the full range of domains, including those
not represented by indicators.
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Introduction: On lateral thinking
1. Indices covering different dimensions:
income and health inequality
2. Keeping dimensions separate and radar
diagrams
3. Interdependence and copulas
Conclusions: Directions for Future Research
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Interdependence at level of individual: that health
status positively correlated with income. If
individual’s circumstances evaluated by v(y,h), then
aversion to correlation implies that vy h ≤ 0. Positive
transformations of h leave the sign unchanged. This
property is assumed here.
Let the joint cumulative distribution be H(y,h), with
marginal cumulative distributions F(y) and G(h).
Where the marginal distributions are identical, the
first order dominance condition is that H(y,h) be less
(or identical) for all y and h.
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Thinking laterally, how does this relate to copulas?
Sklar’s theorem: given a joint distribution function H
and respective marginal distribution functions, there
exists a copula C that binds the margins to give the
joint distribution: H(y,h) = C{F(y),G(h)}. Where the
marginal distributions are identical, the first order
dominance condition is that H(y,h) be less (or
identical) for all y and h.
Separates differences in marginal distributions from
differences in interdependence.
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G(h)
C{F,G}
h
Only
ranks
matter
F(y)
y
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Health inequity in European Union
100
90
80
70
60
50
40
30
20
10
VERY GOOD
GOOD
FAIR
BAD
0
Q1
Q2
Income quintile group
Q3
VERY BAD
Q4
Self-reported health status
Q5
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Difference from independence
3.5
3
2.5
2
1.5
1
Q1
Q2
0.5
Q3
Q4
0
Q5
VERY
BAD
BAD
FAIR
GOOD
VERY
GOOD
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Difference between UK (adjusted to have EU marginal)
and E25
1
0.8
0.6
0.4
per cent
0.2
0
VERY GOOD
GOOD
FAIR
BAD
VERY BAD
-0.2
-0.4
Q1
Q2
Q3
Q4
Q5
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Digression: Understanding total income
G(h)
Non-earned
income
C{F,G}
F(y)
Rise in top income shares:
Earned income
• Marginal distribution of earnings
• Marginal distribution of non-earned
income
• Change in correlation
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Conclusions: Directions for
Future Research
• Lateral thinking can be highly productive; good
reason for reading widely.
• Inequality measurement benefited.
• BUT need care when extending to new dimensions:
treat each dimension on its own terms.
• Need care when using analytical tools developed
for other purposes (e.g. radar diagrams); have to
ask what they bring to the party.
• There are promising paths to pursue (e.g. copulas).
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