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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion The Child is Father of the Man: Implications for the Demographic Transition David de la Croix 1 and Omar Licandro 2 1 IRES, Dept. of economics & CORE,

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

‘The Child is Father of the Man:’ Implications for the Demographic Transition

David de la Croix1 and Omar Licandro2

1IRES, Dept. of economics & CORE, Univ. cath. Louvain 2European University Institute

Taiwan, April 2009

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Introduction

  • New theory of the demographic transition
  • Evidence (natural sciences): Body development during

childhood is an important determinant of life expectancy

  • Continuous time OLG model where fertility, longevity and

education result all from individual decisions

  • Main result: The model dynamics displays the key features of

the demographic transition

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

The demographic transition

  • From a world of low population growth with high fertility and

mortality

  • To a world of low population growth with low mortality and

fertility

  • In the transition, a hump in the population growth rate

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Childhood development

  • Positive relation between early body development and adult

mortality

  • Body height a proxy of body development is a good predictor
  • f adult mortality
  • Good nutrition and low exposition to infections (hygienic

habits) favor early body development

  • Wordsworth’s aphorism: ‘The Child is Father of the Man’
  • The way a child is brought up determines what he will be
  • The new mechanism: Trade-off between the number of

children and their body development

  • Nature vs nurture

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Height and Life Expectancy in Sweden

40 45 50 55 60 65 1 7 6 1 7 7 1 7 8 1 7 9 1 8 1 8 1 1 8 2 1 8 3 1 8 4 1 8 5 1 8 6 1 8 7 1 8 8 1 8 9 1 9 1 9 1 1 9 2 1 9 3 1 9 4 1 9 5 1 9 6 generations years 164 166 168 170 172 174 176 178 180 cm life expectancy at age 10 height of conscripts

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Fertility and Education in Sweden

0.5 1 1.5 2 2.5 3 3.5 4 1 2 3 4 5 6 7 8 9 10 11 children per woman years of schooling generations

years of primary schooling years of primary+secondary schooling net fertility rate

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

The Timing of the Demographic Transition

  • (Net) Fertility is hump shaped, reducing in the modern era
  • Years of secondary schooling increase during the modern era
  • Reductions in adult mortality arrive well before

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Continuous time OLG model

  • The economy is composed by a continuum of dynasties
  • Each dynasty is a sequence of generations i ∈ {1, 2, 3, ...}
  • Individuals take their life expectancy A as given
  • Optimally decide on its own schooling time T
  • Number of children ˆ

n and children’ life expectancy ˆ A

  • At equilibrium, dynasty life expectancy follows: Ai+1 = fA(Ai)
  • Aggregates are then computed and the dynamics solved

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Individuals life

birth puberty work starts death z − B z + T(z) + φˆ n(z) z + A(z) z

  • Cohorts are index by the time of puberty, z
  • Birth date is z − B, were B is puberty age, B > 0
  • Life expectancy at age B is A
  • The survival law is rectangular
  • Seniority is reached at z + T + φn
  • The schooling time is θ + T, 0 < θ < B and T > 0
  • An individual has n children at z + T(z)
  • Raising a children takes φ, φ > 0

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Individual Problem

max A c (z) dz +

  • β ln ˆ

n + δ ln ˆ A

  • s.t.

A c (z) dz = g(T) (A − T − φˆ n) − ˆ n Ψ(ˆ A) T ≥ 0, A c (z) dz ≥ 0

  • Preferences satisfy δ < 2β
  • Human capital technology g(T) = µ (θ + T)α
  • productivity, µ > 0
  • child schooling time, θ > 0
  • returns to schooling time, α ∈ (0, 1)
  • Quadratic childhood development costs Ψ(ˆ

A) =

  • κ

2 ˆ A2 A

  • cost parameter, κ > 0

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Individual Problem (2)

max

c,T,ˆ A,ˆ n

c +

  • β ln ˆ

n + δ ln ˆ A

  • s.t. c = µ (θ + T)α
  • human capital

(A − T − φˆ n)

  • working life

− ˆ n

  • κ

2 ˆ A2 A

  • child cost

T ≥ 0, c ≥ 0

  • Quasilinear preferences and subsistence consumption
  • Trade-off between number and survival of descendants

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Solution to the individual problem

There exist A and ¯ A, 0 < A < ¯ A, s.t.

  • Malthusian Regime: For 0 < A < A, corner solution with

T = 0 and zero consumption

  • Intermediary Regime: For A ≤ A < ¯

A, corner solution with T = 0 but positive consumption

  • Modern Regime: For A ≥ ¯

A, interior solution

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Mechanics: Modern Regime (A ≥ ¯ A)

  • Childhood development
  • Parents like to have children,

but care about their longevity

  • Trade-off: Negative relation

between fertility and longevity

  • The Ben-Porath mechanism
  • The return to education

depends on life expectancy

  • Larger life expectancy makes

schooling more profitable

  • Trade-off education vs fertility
  • Individuals allocating more

time to education have less children

ˆ A2 = δA κˆ n T = α 1 + α (A − φˆ n) − θ 1 + α ˆ n = β − δ/2 µφ (θ + T)−α

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Malthusian Regime (0 < A < A)

  • Consumption and schooling are

both at a corner

  • Parents living longer can afford

more and healthier children ˆ A2 = δ κ µθαφ β − δ/2A, T = 0, ˆ n = β − δ/2 βφ A.

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Intermediary Regime (A ≤ A < ¯ A)

  • Schooling is at a corner and

fertility is time invariant

  • Parents living longer consume

more and invest more in childhood development ˆ A2 = δ κˆ nA, T = 0, ˆ n = β − δ/2 µφθα .

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Dynamics of life expectancy

A dynasty is a sequence of generations i = 1, 2, 3, ..., such that Ai+1 = fA(Ai)

  • A stationary solution A = fA(A) exists, is unique and globally

stable

  • It may belong to any of the three regimes above
  • Then, a solution path for n and T exists and is unique

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Dynamics of life expectancy

A ˆ A A A fA(A) ˆ n

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

The interior regime in the long-run

The steady state is in the interior regime if κ < 4αδθ2αµ2φ (2β − δ) (α[2β − δ] + 2θ1+αµ) ≡ κ (1) if childhood development technology is cheap enough, there is an interior steady state with positive education

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Total population

N (t) = t+B

t−¯ A(t)

P (z) dz ¯ A(t) = A

  • t − ¯

A (t)

  • Cohort size P(z) follows

P (z + T (z) + B) = ˆ n (z) P (z)

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Population at time t

v + T(v) + φˆ n(v) z + A(z) t t − ¯ A(t)

  • ldest alive

t − ¯ T(t) − φ¯ n(t) z v t yougest worker

  • ¯

A(t) is the age of the oldest cohort still alive at t

  • ¯

T(t) is schooling time of the youngest active cohort at t

  • ¯

n(t) is the number of kids of the youngest active cohort at t

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Balanced growth path

The growth rate of population converges to η = ln (n) T + B

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Demographic Transition

  • The economy is initially on the Malthusian regime
  • B = 13.5, φ = 1, θ = 6, α = 1/6
  • µ, κ, β, δ are set to reproduce basic facts before the 18th C

A = 27 (B + A = 40.5), T = 0, η = .005, A = 28 → ¯ A = 37

  • A slow reduction in childhood development costs makes

investing in life expectancy more profitable

  • Logistic function: 95% of the change between 1700 and 2050
  • The economy converges to the modern regime
  • Life expectancy increases from 40.5 to 90
  • Mortality and fertility shape the demographic transition

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Rise in medical knowledge?

Common view: The period 1500-1870 does not contain major technology changes in health that could have increased life expectancy But

  • 1500-1800: medicine showed an increasingly experimental

attitude: no improvement on theory but advances on practice and empirical observations. (new drugs coming from the New World)

  • As early as 1829, Dr.F.B. Hawkins wrote a book entitled

Elements of Medical Statistics, in which he described a set of diseases which were leading causes of death but can now (in 1829) be treated effectively: leprosy, plague, sweating sickness, ague, typhus, smallpox, syphilis and scurvy.

  • Number of books containing lifestyle advice increasing

significantly over the period 1750-1800.

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Number of books on health published in England, 1600-1800

Period Number of books 1600-24 9 1625-49 16 1650-74 17 1675-99 25 1700-24 28 1725-49 34 1750-74 53 1775-1800 81

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

The demographic transition

1700 1750 1800 1850 1900 1950 20 30 40 50 60 70

Cohorts' life expectancy at puberty

1700 1750 1800 1850 1900 1950 1.02 1.04 1.06 1.08 1.10 1.12 1.14

Total cohort fertility rate

1750 1800 1850 1900 1950 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Cohorts' education

1750 1800 1850 1900 1950 0.002 0.004 0.006 0.008 0.010

Population growth rate 25 / 34

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Unified Growth Theory

Unified explanation of: Transition from Malthusian stagnation to sustained growth Demographic transition (↓ fertility-mortality, popul. growth) Parents’ trade-off between number of children and education Industrial Revolution → Increasing demand for skilled workers→ Households increase education of offspring → Demographic transition and take-off (Galor) Validation: rise in the skill premium ?

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Validation

Clark (2005) measures over 1220-1990 the relative wage of skilled building workers relative to all laborers. “The market premium for skills does not explain the increased investment in human skills evident after 1600.”

Doubts

Can the fertility transition in the 19th century be explained through greater demand for educated children?

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Modeling Growth

Assumptions:

  • Human capital as an engine of growth

h(z) = µ (θ + T(z))α ¯ H(z) ¯ H is human capital per worker

  • Preferences and childhood technology face the same

externality, then the individual problem does not change

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Human Capital

H (t) = t− ¯

T(t)−φ¯ n(t) t−¯ A(t)

P (z) µ (θ + T (z))α ¯ H (z)

  • h(z)

dz Human capital per worker is ¯ H (t) = H (t) E (t) The technology producing the final good is linear in H with productivity one Output per capita is then H(t)

N(t).

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Active population

E (t) = t− ¯

T(t)−φ¯ n(t) t−¯ A(t)

P (z) dz ¯ T(t) = T(t − ¯ T(t) − φ¯ n(t)) ¯ n(t) = ˆ n(t − ¯ T(t) − φ¯ n(t))

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Balanced Growth Path

  • Population grows at rate

η = ln (n) T + B

  • Human capital grows at rate

γ = P⋆ E ⋆ µ(θ + T)α e−γ(T+φn) − e−γA

  • Human capital per worker
  • All cohorts share the same human capital technology
  • But, growing externality
  • Per capita output grows at γ − η

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

From Malthus to Modern Growth

1750 1800 1850 1900 1950 3.65 3.60 3.55 3.50 3.45

log GDP per capita

  • There is no growth in the Malthusian regime
  • In the intermediary regime, per capita growth rates increase

slowly due to the reduction in the dependency ratio

  • In the modern regime, human capital accumulation

accelerates per capita growth

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Conclusion

A new theory of the demographic transition Fertility, longevity and education are decided by individuals Based on the evidence that adult life expectancy depends on body development during childhood (natural sciences) Replicate the main characteristics of the demographic transition Adding human capital as a growth engine replicates the transition from the Malthusian era to Modern growth

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Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion

Further test of our theory

Look at the relation between family size and to childhood development (height) on historical micro-data?

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