ELITISM AND STOCHASTIC DOMINANCE
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ELITISM AND STOCHASTIC DOMINANCE Stephen BAZEN (GREQAM, Université d’Aix- Marseille II) Patrick MOYES (GREThA, Université de Bordeaux IV) Presentation at the Tenth SSCW International Meeting, Moscow, 21-24 July 2010
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ELITISM AND STOCHASTIC DOMINANCE. Stephen BAZEN (GREQAM, Université d’Aix-Marseille II) Patrick MOYES (GREThA, Université de Bordeaux IV). Presentation at the Tenth SSCW International Meeting, Moscow, 21-24 July 2010. Comparison of distributions. Risk : distribution of returns. - PowerPoint PPT Presentation
Transcript of ELITISM AND STOCHASTIC DOMINANCE
ELITISM AND STOCHASTIC DOMINANCE
Stephen BAZEN (GREQAM, Université d’Aix-Marseille II)
Patrick MOYES (GREThA, Université de Bordeaux IV)
Presentation at the Tenth SSCW International Meeting, Moscow, 21-24 July 2010
Comparison of distributions
Risk : distribution of returns
Inequality: distribution of income (earnings, wealth,…)
In general, emphasis on progressive transfers
Elitism
8,5,4,1x
7,5,4,2z
x is obtained from z by a regressive transfer
8,5,4,1x
8,5,3,2 y
Progressive transfer
- Academic performance
- Affluence
Welfare function for distribution h(.): dxxhxuW
0
GF WW
Comparison of two distributions in terms of social welfare
dxxfxuWF
0
dxxgxuWG
0
00
dxxgxfxuWW GF
Stochastic dominance
00
dxxgxfxuWW GF
0
'0
0
dxxGxFxuxGxFxu
Stochastic dominance – standard application
xxGxFdxxGxFxuxu
0if0'0'0
First order stochastic dominance
GF
x
WWxdttFtG 00
0",0' xuxuSecond order stochastic dominance
)(xG)(xF
x
dttGx
)(0
x
dttFx
)(0
First order stochastic dominance(F dominates G)
Second order stochastic dominance(F dominates G)
1
Elitism and stochastic dominance
dxxhxvW
0
Performance :
xh density of individuals’ publication scores
xv value function
Assumption 1 :
An additional publication increases performance 0' xv
)(1 xF
1
x
)(1 xG
xxGxFdxxgxfxvxvb
011if00'0
xxFxG 0)(or
Assumption 2 :
A regressive transfer of publication scores increases performance 0" xv
Convexity of the value function rather than concavity in the standard case
Criterion for ranking departments by performance :
xdttGdttF
dxxgxfxvxvxv
b
x
b
x
b
11if
00"0'
0
x
dttFb
x 1
dttGb
x 1
b
F
G
x~0
)max()max()( GxFxi
xExEii GF )(
If distribution F stochastically dominates G in terms of the survival function then
Assumption 3 :
A regressive transfer of publication scores of given size increases perfomance more at the higher end of the scale than at the lower end
0"' xv
Criterion for ranking departments by performance :
xdudttGdudttF
dxxgxfxvxv
xvxv
b
x
b
t
b
x
b
t
b
11(b) and
(a) if
00'"
0"0'
GF
0
Tilburg
EssexToulouse dominates all departments except
Louvain
dominate: LSEStockholm U. Nottingham
Second order stochastic dominance
UCL No dominance over :Essex, Cantab, Erasmus
dominates: LSEStockholm U. Amsterdam
Stockholm School of Economics
dominates:
WarwickYorkMaastrichtAutonoma BarcelonaBonnLondon Business School
Amsterdam
dominates:
OxonStockholm School of Economics
dominates:
Free University of Amsterdam
Amsterdam
Nottingham
Tilburg and UCL
dominate:Nottingham
Louvain
dominates:
Free University of Amsterdam
Amsterdam
Does more affluence mean less poverty ?
Ranked by both criteria - an example
3,2,1y 5.3,5.1,5.1x
(i) Generalised Lorenz dominance :
5.0,5.0,5.0 yx
progressive transfer increment
(ii) Reverse Generalised Lorenz dominance :
5.0,5.0,5.0 yx
regressive transferincrement
