determinants of inequality and intergenerational mobility chicago, hceo working group april 18, 2014
DESCRIPTION
Standard BT ModelTRANSCRIPT
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Determinants of inequality and intergenerational mobility
Chicago, HCEO working GroupApril 18, 2014
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Motivations
1. Relation between inequality and mobility (Great Gatsby curve)
2. Size of the intergenerational persistence, eg Clark’s recent book. In contrast, in a study of surnames in the Catalonia census, 2001, Guell, Rodriguez Mora and Telmer find:
• In a calibration exercise estimating (Informational Content of surnames, Gini (of surnames), number of persons per surname) an intergenerational coefficient for education of 0.6
• Assortative mating is large, and has increased in the 20th century
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Standard BT Model
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Standard Model
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Model
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Mating rules
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Predictions
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First intuition: Single gene model
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Assortative mating on phenotype
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INCOME DISTRIBUTION
Small number of genes (5), 20 thousand individuals, 100 periodsas variance of income increases
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INTERGENERATIONAL IMMOBILITY
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0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1.2
0.20.4
0.60.8
1
Intergenerational immobility (rho)medium income variance
gamma
rho
beta
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0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1.2
0.20.4
0.60.8
1
Intergenerational Immobility (rho)small income variance
gamma
rho
beta
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Small variance
Higher variance in income shock
beta
gam
ma
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INEQUALITY
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0.1
.2.3
.4.5
Den
sity
0 5 10Income
beta = 0.8, gamma = 1
0.2
.4.6
Den
sity
-1 0 1 2 3Income
beta = 0.8, gamma = 0.2
0.2
.4.6
.8D
ensi
ty
-1 0 1 2 3Income
beta = 0.2, gamma = 10
.51
1.5
2D
ensi
ty
-.5 0 .5 1Income
beta = 0.2, gamma = 0.2
Gini 0.14 Gini 0.33
Gini 0.18 Gini 0.41
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0.2
.4.6
.8Lo
renz
Inco
me
0 .2 .4 .6 .8 1Cumulative population proportion
beta = 0.2, gamma = 0.2
0.5
11.
52
Lore
nz In
com
e
0 .2 .4 .6 .8 1Cumulative population proportion
beta = 0.2, gamma = 1
0.5
11.
52
Lore
nz In
com
e
0 .2 .4 .6 .8 1Cumulative population proportion
beta = 0.8, gamma = 0.2
0.5
11.
52
Lore
nz In
com
e
0 .2 .4 .6 .8 1Cumulative population proportion
beta = 0.2, gamma = 1
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GammaBeta
0.2 1
0.2 0.30 0.97
0.8 0.94 1.000
Immobility
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0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.2, gamma = 0.2
0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.2, gamma = 1
0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.8, gamma = 0.2
0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.8, gamma = 1
Gene frequency, 5 genes, high variance
Deviations from HW
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0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.2, gamma = 0.2
0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.2, gamma = 1
0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.8, gamma = 0.2
0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.8, gamma = 1
Gene frequency, 5 genes, low variance
Deviations from HW
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LARGER NUMBER OF GENES
Larger number of genes (20), 10 thousand individuals, 100 periodsas variance of income increases
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0.5
11.
52
Den
sity
-.5 0 .5 1Income
beta = 0.2, gamma = 0.2
0.2
.4.6
.8D
ensi
ty
0 1 2 3Income
beta = 0.2, gamma = 10
.2.4
.6.8
1D
ensi
ty
-1 0 1 2 3Income
beta = 0.8, gamma = 0.2
0.0
5.1
.15
Den
sity
0 2 4 6 8 10Income
beta = 0.8, gamma = 1
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0.2
.4.6
.8Lo
renz
Inco
me
0 .2 .4 .6 .8 1Cumulative population proportion
beta = 0.2, gamma = 0.2
0.5
11.
5Lo
renz
Inco
me
0 .2 .4 .6 .8 1Cumulative population proportion
beta = 0.2, gamma = 10
.51
1.5
Lore
nz In
com
e
0 .2 .4 .6 .8 1Cumulative population proportion
beta = 0.8, gamma = 0.2
02
46
Lore
nz In
com
e
0 .2 .4 .6 .8 1Cumulative population proportion
beta = 0.8, gamma = 1
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GammaBeta
0.2 1
0.2 0.224 0.867
0.8 0.839 1.002
Immobility
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0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.2, gamma = 0.2
0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.2, gamma = 1
0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.8, gamma = 0.2
0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.8, gamma = 1
Gene frequency, 20 genes, high variance
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0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.2, gamma = 0.2
0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.2, gamma = 1
0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.8, gamma = 0.2
0.1
.2.3
.4.5
.6Fr
actio
n
0 1 2Gene
beta = 0.8, gamma = 1
Gene frequency, 20 genes, low variance
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Predictions on the genetic similarity among spouses
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Notation
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Similarity among individuals
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Beta=0.2, gamma=0.2, v = 0.2
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Beta=0.4, gamma=0.4, v = 0.2
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ASSORTATIVE ON WHAT?
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IQ: r = 0.37
8010
012
014
016
0IQ
_MO
M
60 80 100 120 140 160IQ_DAD
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Traditionalism (MPQ) r = 0.43
3040
5060
70TR
_M
30 40 50 60 70TR_D
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Control (MQP derived) r = 0.20
100
120
140
160
180
200
CN
_M
80 100 120 140 160 180CN_D
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Education: polychoric r = 0.777
02
46
810
ED
_MO
M
0 2 4 6 8 10ED_DAD