determinants of inequality and intergenerational mobility chicago, hceo working group april 18, 2014
DESCRIPTION
Standard BT ModelTRANSCRIPT
Determinants of inequality and intergenerational mobility
Chicago, HCEO working GroupApril 18, 2014
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
Standard BT Model
Standard Model
Model
Mating rules
Predictions
First intuition: Single gene model
Assortative mating on phenotype
INCOME DISTRIBUTION
Small number of genes (5), 20 thousand individuals, 100 periodsas variance of income increases
INTERGENERATIONAL IMMOBILITY
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
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
Small variance
Higher variance in income shock
beta
gam
ma
INEQUALITY
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
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
GammaBeta
0.2 1
0.2 0.30 0.97
0.8 0.94 1.000
Immobility
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
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
LARGER NUMBER OF GENES
Larger number of genes (20), 10 thousand individuals, 100 periodsas variance of income increases
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
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
GammaBeta
0.2 1
0.2 0.224 0.867
0.8 0.839 1.002
Immobility
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
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
Predictions on the genetic similarity among spouses
Notation
Similarity among individuals
Beta=0.2, gamma=0.2, v = 0.2
Beta=0.4, gamma=0.4, v = 0.2
ASSORTATIVE ON WHAT?
IQ: r = 0.37
8010
012
014
016
0IQ
_MO
M
60 80 100 120 140 160IQ_DAD
Traditionalism (MPQ) r = 0.43
3040
5060
70TR
_M
30 40 50 60 70TR_D
Control (MQP derived) r = 0.20
100
120
140
160
180
200
CN
_M
80 100 120 140 160 180CN_D
Education: polychoric r = 0.777
02
46
810
ED
_MO
M
0 2 4 6 8 10ED_DAD