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