Outline ...
• What to measure?
• Role of Value Judgements
• Two inequality measures
Inequality in New Zealand
How Should We Measure It?
John Creedy and Norman Gemmell
Has inequality been increasing in New Zealand?
Dichotomy between Theory and Measurement
Empty economic boxes?
Ministry of Social Development ...
Measurement without
theory?
Basic Problems ...
• What?
• ‘welfare metric’: Income, expenditure, leisure
• 0 and negative values?
• Whose?
• Individual, household (sharing), unit of analysis
• When?
• Annual, lifetime – link with mobility
Perry, B. (2014) Household incomes in NZ: Trends in indicators of
inequality and hardship 1982 to 2013. MSD.
1
The Central Role of Value
Judgements
• Robbins
• The Nature and Significance of
Economic Science (1932)
An Important Contribution …
Atkinson (1970)
• Clarified role of principle of
transfers
• Inequality measure based on
clearly stated Value Judgements
of disinterested judge (SWF)
• Stimulated search for values
implicit in other measures (eg,
Gini)
Tony Atkinson
The Lorenz Curve …
A basic Value Judgement
• ‘A transfer of income from a richer person to a
poorer person, which leaves their relative
positions unchanged, represents a reduction in
inequality’.
Proportion of Income
1
• Share 60 among 3
people …
• 10, 20, 30
• 10, 25, 25
• 15, 15, 30
Max Otto Lorenz
0
Proportion of people
1
One distribution (A) is unambiguously more
equal than another (B) if …
The Pigou-Dalton Principle of Transfers
• Lorenz Curve of A lies
closer to line of equality
than that of B.
• A ‘Lorenz Dominates’ B
• ‘Lorenz Dominance’ and
the ‘Principle of Transfers’
are equivalent
• But … they often intersect
2
A particular form for U(y)
Value Judgements and Social Welfare Function
U  y 
• Explicit expression of a judge’s values …
• Social Welfare Function (SWF)
1 1
y
1 
for   1,   0
1
W W
1 n
1
yE    yi1 
 n i1

 y 1 , y 2 , ..., y n 
yE is the ‘power mean’
Ɛ is ‘relative inequality aversion’
A class of measures …
Choice of Ɛ: ‘Leaky bucket’ experiment
• Suppose ‘rich’ has twice
as much as ‘poor’. Take
$1 from ‘rich’:
• For Ɛ=1: give 50 cents
• For Ɛ=2: give 25 cents
• If ‘rich’ has three times
‘poor’.
• For Ɛ=1: give 33 cents
• For Ɛ=2: give 11 cents
• Equally Distributed Equivalent Income, yE
• The income which, if equally distributed, gives
same Social Welfare as actual distribution.
W  yE , yE,..., yE  W  y1, y2,..., yn 
yE
y
I  1
Atkinson Inequality Measure: Uses
SWF of form:
U(y )
i 1
•
•
•
•
•
1
n
i
U reflects weight given by judge (not ‘utility’)
Individualistic; Additive; Paretian
Concave U: principle of transfers
When A and B have equal arithmetic means …
If A Lorenz-dominates B, ALL forms of U give W
higher for A compared with B
Proportion of Income
W 
The Gini Measure
0
Gini = Twice the area
between L curve and
line of equality
Proportion of people
1
3
Gini, Atkinson and Value Judgements
• Atkinson:
yE
n

i 1
1
y 1 
1  i
‘power mean’ with exponent 1-Ɛ
• Gini:
yE
W 
W 
n
 n  1  i  y
i 1
i
Reverse-rank weighted mean
Atkinson, Gini and Top Incomes
•
•
•
•
•
•
•
•
Nine incomes of:
5, 6, 7, 7, 8, 8, 9, 10, 12
plus a top income of:
100
1,000
10,000
100,000
1,000,000
Allowing for Household size and composition
Conclusions
• Avoid nihilism: strong need for policy
evaluation …
• … of policies designed to influence
distribution, and others (‘unintended
consequences’)
• Avoid Separation of Theory and Practice
• Remember the message of Lionel Robbins
The End
• ‘Welfare metric’: income per adult equivalent
person
• No scales are Value-Free …
• Need for sensitivity analysis
4
Some references ...
• Atkinson, A.B. (1970) On the measurement of inequality. Journal of
Public Economics, 2, 244-266
• Ball, C. & Creedy, J. (2015) Inequality in NZ 1983/84 to 2013/14. NZ
Treasury WP 15/06
• Creedy, J. and Eedrah, J. (2015) Income redistribution and changes in
inequality in NZ from 2007 to 2011: alternative distributions and value
judgements. NZEP (online)
• Creedy, J. (2015) Interpreting inequality measures and changes in
inequality. NZEP (online)
• Creedy, J. and Sleeman, C. (2005) Adult equivalent scales: inequality
and poverty in NZ. NZEP, 39, 51-83.
• Lambert, P. (2001) The Distribution and Redistribution of Income.
Manchester University Press
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