The World Distribution of Income

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The World Distribution of Income
A B Atkinson Nuffield College, Oxford based on
research with Andrea Brandolini Bank of Italy,
Economic Research Department
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• Sources of disagreement
• International versus world inequality
• Review of recent results
• Absolute versus relative approaches
• 2. Social welfare based measures of world
  inequality
• Constant relative, absolute, and intermediate
  measures
• Application to cost of world income inequality
• Towards a new approach
• Elasticity of the social marginal valuation of
  income
• Increasing, then decreasing sensitivity to
  transfers
• Applications of new measure

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Grounds for disagreements

• International versus World inequality
• Counting countries versus weighting by population
• Use of survey (Ya) versus national accounts (µa)
  mean incomes

yia versus yia µa/Ya
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• Global income inequality
• Data from Bourguignon and Morrisson (2002)
• ? evidence on distributions for a country (or a
  grouping of countries) about income shares of
  decile groups and top 5 per cent
• ? groups treated as homogeneous, which means
  that overall inequality under-stated
• Distributional data combined with estimates of
  national GDP per head, expressed in constant
  purchasing power parity dollars (at 1990 prices)
  from historical time series by Maddison (1995)
• Data taken here at face value!

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Distribution among World Citizens 1820-1992
Ratio of top decile to bottom decile
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world income inequality worsened dramatically
over the past two centuries. due mainly to a
dramatic inequality across countries. The burst
of world income inequality now appears to be
over. (Bourguignon and Morrisson, page 742).
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A Kuznets curve for the world as a whole?
Inequality
OECD countries industrialise
Developing countries industrialise, OECD
countries continue to grow
?
Time
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after remaining constant during the 1970s,
global income inequality declined substantially
during the last two decades. Global poverty
rates declined significantly over the last three
decades. when the MDG was established in 2000,
the world was already 60 percent of the way
toward achieving it. The world might just be
in better shape than many of our leaders
believe! (Sala-i-Martin, 2006, pages 389 and
392-3).
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• Contrast
• MDG 1 a day threshold absolute
• World inequality measured by Gini coefficient
  (unchanged if all incomes doubled)
• relative

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• Motivation
• 2. Rethinking social welfare based measures of
  world inequality
• Constant relative measures
• Leaky bucket experiment
• Towards a new approach

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• Social welfare function assumed to be
• Symmetric
• Additively separable
• Function defined over incomes,
• y1, y2, , yn.
• W FV(y1) V(y2)

Note not U, not necessarily utilitarian
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• Constant elasticity, ?, of social marginal
  valuation corresponds to
• W1-? (1/n) ? Yi 1-?
• Or equally distributed income, Yede, equal to W,
  which leads to the constant relative aversion
  index of inequality (Atkinson, 1970), where µ is
  the mean
• I 1 - Yede / µ
• This measure is scale invariant
• income inequality remains unchanged when all
  incomes are increased/decreased by the same
  proportion

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• Leaky Bucket Experiment (Okun)
• 1 from person with income Y
• (1 - l) to person with income Y/z
• Denote social marginal valuation of income by
  f(Y)
• Transfer desirable where f(Y/z) gt f(Y) / ( 1 - l)
• Depends on elasticity of f(Y). If constant at ?,
  then require
• l lt 1 z -?
• elasticity 1 implies accept transfer from US
  P25 to US P10 where loss less than 50, and from
  P50 to P10 where loss less than 75
• elasticity ½ implies accept transfer from P25
  to P10 where loss is less than 1 1/?2 29,
  but accept transfer from P50 to P10 where loss
  less than 50
• NB US approximately P90 2 x P50 P50 2 x P25
  P25 2 x P10

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If elasticity ½, accept transfer from US P90 to
World P10 if loss less than 88 cents
Divide by 2
Divide by 2
Divide by 2
If elasticity ?, accept transfer from US P90 to
World P10 if loss less than 41 cents, BUT reject
transfer from US P25 to US P10 if loss greater
than 8 cents.
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• Little and Mirrlees, there is no particular
  reason why the social marginal valuation should
  fall at the same proportional rate at all
  consumption levels. Why should twice as much
  consumption deserve a quarter of the weight,
  whether consumption is low or high?
• On the other hand, the Gini coefficient by
  revealed preference points way to go.
• Increasing, then Decreasing Sensitivity to
  Transfers

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• Two motivations
• Variation in social marginal valuation of
  income the Gini coefficient by revealed
  preference points way to go Increasing, then
  Decreasing Sensitivity to Transfers
• Incorporate views of those concerned with
  poverty but not inequality Charitable
  Conservatism

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Social marginal valuation of income
Gini SMV 21-F(y)
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Social marginal valuation of income
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• New measure
• W (1/n) ? yi ? 1/ß loge (1 exp(ß(yi -d)))
  (yi -d)
• Social marginal valuation of income
• f(yi) 1 ? / 1 exp ß(yi -d)
• Second derivative
• - ß? / 1exp(ß(y-d)) 1exp(-ß(y-d))
• which has its minimum value (i.e. the steepest
  downward slope) at y d. Both before and after y
  d the slope is less.
• Special cases
• ? 0 distributional indifference
• ? gt 0, ß ? 8 charitable conservatism

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Social marginal valuation of income
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Cost of world inequality (µ yede )
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Cost of world inequality (µ yede )/µ
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Delta proportionate to mean income
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• Sum Up Three Issues
• Shape of SMV curve (increasing then decreasing
  sensitivity to transfers)
• How far SMV anchored over time (1 a day poverty
  line versus 50 mean income)
• Measuring the total cost of inequality in terms
  of billion rather than as a percentage of total
  world income Matter of choice