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“Cheap Children and the Persistence of Poverty” “Cheap Children and the Persistence of Poverty”

Omer Moav

The Economic Journal, 115 (January 2005)

Omer Moav

The Economic Journal, 115 (January 2005)

INTRODUCTION INTRODUCTION

Theory of fertility and child educational choice To explain persistence of poverty within and across countries

Evidence: high fertility rates

• Poor households

low invest. education

• High-income

low fertility rates families high invest. education

• ffspring are

also poor

• ffspring

with high income

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INTRODUCTION INTRODUCTION

Key assumption: Individual’s productivity as teachers increases with their

• wn human capital.

Minimum time cost of raising a child regardless of the child’s quality is not affected by parental education. Result: ' price of child quantity with individuals wage price of child quality ↑

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INTRODUCTION: Value Added

• Simple model: dynasties within a country can converge to
• ne of two equilibria.

– Low education – high fertility – High education – low fertility

• Extended model: amplifies effect of quality choice on

income per-capita capturing diluting effect of fertility on the accumulation of physical capital.

• Countries can converge to two different levels of income

per capita.

– Negative cross-country relationship between fertility-growth – Positive cross-country relationship between education- growth

INTRODUCTION: Value Added

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INTRODUCTION: Value Added

Becker et.al.(1990)

• Representative agent model
• Trade-off between quantity and quality of their offspring
• Multiple steady states

return to education is lower in poor countries.

• Theoretical and empirical limitations:

– Poverty trap equ. is a result of a market failure. – Fertility choices may amplify the negative impact of low education investment on income per capita, but they are not the source of multiple equilibria. – In poor economies all families eventually converge to a low- educational equilibrium.

INTRODUCTION: Value Added

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INTRODUCTION: Value Added

In this paper

• OLG model
• Multiple steady states

comparative advantage of educated workers in the production of educated children

• No restrictive assumptions.
• Correlation of education-income within a dynasty is testable.
• Educated individuals would invest highly in their offspring’s

education, even in poor countries.

• Poverty can persist in rich countries, and educated individuals

can exist in the long run in poor countries.

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INTRODUCTION: Value Added

Importance

• From the model we can have an explanation of a fact that we
• bserve in many countries around the world: persistence of

poverty with high fertility rates.

• Evaluation of policies.

Importance

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Simple Model

• OLG model over infinite discrete time
• Single homogeneous good produced in the economy

under CRS technology and using human capital.

• Individuals live 2 periods:

– First: acquire human capital – Second: endowed with 1 unit time Child rearing

• Part. labor force

Simple Model

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Simple Model

• Preferences:

( )

( )

1

1 log log log

i i i i t t t t

u c n wh β β θ

+

= − + +

where: : relative weight given to children (quantity and quality) : relative weight given to child quality : number of children in a household : wage rate per efficiency unit of labor : level of human capital of each child; : level of investment in education of individual i at t. : consumption level

i t

n w

1 i t

h + θ β

( )

1 1 i i t t

h h e

+ +

=

1 i t

e +

i t

c

Simple Model

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Simple Model

• Budget constraint:

( )

1 i i i i i t t t t t

n w h e c wh τ

+

+ + ≤

where: : min. time cost required for raising a child : full income : real cost of investment in education (quality) : opp. cost of raising a child (cost of child quantity)

i t

wh τ

1 i t

we +

i t

w h τ

The cost of child quantity increases with h.

Simple Model

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Simple Model

( )

( ) ( )

1 1 1 1

1 log log log . ( )

i i i t t t i i i i i t t t t t i t t

Max c n wh n w h e c wh s t h h e β β θ τ

+ + + +

− + +  + + ≤   =  

• Problem:

Choice variables: number and quality of children, and consumption.

• Solution:

[ ] ( ) ( )

( )

[ ]

( ) ( ) ( )

[ ]

( ) ( ) ( ) ( )

$ $

1 1 1 1 1 1

: 1 1 ' 1 : :

i i i t t t t i i t t t i i i i t t t t i t i i i t t t i t t i i t t

c c wh wh e h e if e e if e h e h e e if e e n n n e h e if e e h e e β β θ τ β τ β τ φ

+ + + + + +

= − = − ≤ =  − = > +     ≤  = =  >    +     ( )

$ $

1 i t i i t t i t

if e e e e if e e φ

+

= ≤  =  > >  

where:

Simple Model

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Dynamic System Simple Model

1 t

e +

Dynamic System Simple Model

$

e

T

e e

( )

t

e φ

t

e

convergence to high-education, high-income, and low fertility SS

i T

e e > ⇒

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Main Results Simple Model

• Lower parent’s education

cheaper the children parent’s choice shifts to higher fertility rates lower investment in offspring’s human capital

• (quantity cost)

relative cost of quantity

τ ↑

move to child quality

Main Results Simple Model

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Extended Model

• Introduce endogenous physical capital accumulation

capture effect of fertility on capital per worker amplify effect of quality choice on econ. growth

• Explain cross-country income differences and club

convergence.

• Allow bequeath capital to offspring
• 2 inputs: physical and human capital

( ) ( )

,

t t t t t t t

Y F K H H f k H Ak α = = =

( ) ( ) ( )

1

1

t t

w k Ak r k Ak

α α

α α

−

= − =

Extended Model

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Extended Model

( )

( )

( )

( )

1 1 1 1 1 1 1 1

1 log log log . ( )

t t t t t t t t t t t t t t t t t t t

Max c n w h r s n w h w e s c w h r s s t h h e β β τ

+ + + + + + + +

− + + +  + + + ≤ +   =  

• Problem:

Choice variables: number and quality of children, consumption, and quantity of physical capital transferred to each child.

• Solution:

[ ] ( )(

)

[ ]

( ) ( )

[ ) [ ]

( )

( )

1 1 1 1 1 1 1 1 1 1 1 1 1 1

: 1 0, : : '

t t t t t t t t t t t t t t t t t t t t t t t

c c w h r s if s h e w if s s r h e w if s h e if e e h e h e if e β τ τ

+ + + + + + + + + + + + + +

= − + > = = ∈ ∞ −  + < → ∞  ≥ =  −  + = >  

Extended Model

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Dynamic System Extended Model

t

k kk ee ee

( )

1 1

,

T t t t T t t t t

e e e e e e e e e and e e

+ +

> ∀ ∈ < ∀ < >

( ) ( )

1 1 SS t t t t SS t t t t

k k k k e k k k k e

+ +

> ∀ < < ∀ >

t

e

$

e

T

e e = e e = e =

Dynamic System Extended Model

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Main Results Extended Model

• Lower parent’s education

cheaper the children parent’s choice shifts to higher fertility rates amplified reallocation from child quality to quantity

• (quantity cost)

relative cost of quantity move to child quality (amplified by the diluting effect on physical capital.

τ ↑

Main Results Extended Model

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Conclusions and Implications

• Model offers explanation for the persistence of poverty

consistent with the relationship fertility-education, and the cross-country relationship fertility-education-economic growth.

• Generation of multiple steady states based on the trade-
• ff between child quality and quantity without imposing

restrictive assumptions.

• Poor countries fail to catch up with the rich because of

insufficient progress in education due to high fertility rates.

Conclusions and Implications

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Conclusions and Implications

• Dynamic system generates a poverty trap along with a

high-income equilibrium. poor (rich) dynasties with income below (above) a threshold level converge to the low-income (high-income) steady state. if initial average income in society is above the threshold, then in a more equal society, more individuals are above the threshold and more dynasties converge to the high SS

• Inequality affects economic growth negatively via its

interaction with fertility choice.

Conclusions and Implications

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Conclusions and Implications

• An increase in the cost of quantity induces a reallocation
• f resources to child quality.

this would positively affect economic growth and could release an economy from the poverty-trap. it can be achieve through canceling or reversing policies that reduce child quantity cost (i.e. tax discount for large families, child allowances, subsidized day care and meals, and unregulated child labor) and reallocate them to the financing of schools.

Conclusions and Implications

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