The Child is Father of the Man: Implications for the Demographic - PowerPoint PPT Presentation

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, Univ. cath. Louvain 2 European University Institute Taiwan, April 2009 1 / 34

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 2 / 34

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 3 / 34

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 of 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 4 / 34

Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion Height and Life Expectancy in Sweden 180 life expectancy at age 10 65 height of conscripts 178 176 60 174 55 years 172 cm 170 50 168 45 166 40 164 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 generations 5 / 34

Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion Fertility and Education in Sweden 11 4 10 3.5 9 3 8 2.5 children per woman 7 years of schooling 6 2 years of primary schooling 5 years of primary+secondary 1.5 schooling net fertility rate 4 1 3 0.5 2 1 0 generations 6 / 34

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 7 / 34

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 n and children’ life expectancy ˆ • Number of children ˆ A • At equilibrium, dynasty life expectancy follows: A i +1 = f A ( A i ) • Aggregates are then computed and the dynamics solved 8 / 34

Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion Individuals life z + T ( z ) + φ ˆ n ( z ) z + A ( z ) z − B z birth puberty work starts death • 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 + φ n • 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 9 / 34

Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion Individual Problem � A � � n + δ ln ˆ max c ( z ) d z + β ln ˆ A 0 � A n Ψ(ˆ s.t. c ( z ) d z = g ( T ) ( A − T − φ ˆ n ) − ˆ A ) 0 � A T ≥ 0 , c ( z ) d z ≥ 0 0 • Preferences satisfy δ < 2 β • Human capital technology g ( T ) = µ ( θ + T ) α • productivity, µ > 0 • child schooling time, θ > 0 • returns to schooling time, α ∈ (0 , 1) � � ˆ A 2 • Quadratic childhood development costs Ψ(ˆ κ A ) = 2 A • cost parameter, κ > 0 10 / 34

Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion Individual Problem (2) � � n + δ ln ˆ max c + β ln ˆ A c , T , ˆ A , ˆ n � � ˆ A 2 κ s.t. c = µ ( θ + T ) α ( A − T − φ ˆ n ) − ˆ n 2 A � �� � � �� � human capital working life � �� � child cost T ≥ 0 , c ≥ 0 • Quasilinear preferences and subsistence consumption • Trade-off between number and survival of descendants 11 / 34

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 12 / 34

Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion Mechanics: Modern Regime ( A ≥ ¯ A ) • Childhood development • Parents like to have children, A 2 = δ A ˆ but care about their longevity κ ˆ n • Trade-off: Negative relation between fertility and longevity • The Ben-Porath mechanism α θ • The return to education T = 1 + α ( A − φ ˆ n ) − 1 + α depends on life expectancy • Larger life expectancy makes schooling more profitable • Trade-off education vs fertility n = β − δ/ 2 ( θ + T ) − α ˆ • Individuals allocating more µφ time to education have less children 13 / 34

Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion Malthusian Regime (0 < A < A ) µθ α φ A 2 = δ ˆ β − δ/ 2 A , • Consumption and schooling are κ both at a corner T = 0 , • Parents living longer can afford n = β − δ/ 2 more and healthier children ˆ A . βφ 14 / 34

Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion Intermediary Regime ( A ≤ A < ¯ A ) • Schooling is at a corner and A 2 = δ ˆ nA , fertility is time invariant κ ˆ T = 0 , • Parents living longer consume more and invest more in n = β − δ/ 2 ˆ µφθ α . childhood development 15 / 34

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 A i +1 = f A ( A i ) • A stationary solution A = f A ( 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 16 / 34

Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion Dynamics of life expectancy ˆ n ˆ A f A ( A ) A A A 17 / 34

Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion The interior regime in the long-run The steady state is in the interior regime if 4 αδθ 2 α µ 2 φ κ < (2 β − δ ) ( α [2 β − δ ] + 2 θ 1+ α µ ) ≡ κ (1) if childhood development technology is cheap enough, there is an interior steady state with positive education 18 / 34

Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion Total population � t + B N ( t ) = P ( z ) d z t − ¯ A ( t ) � � ¯ t − ¯ A ( t ) = A A ( t ) Cohort size P ( z ) follows P ( z + T ( z ) + B ) = ˆ n ( z ) P ( z ) 19 / 34

Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion Population at time t oldest alive t − ¯ t A ( t ) z z + A ( z ) yougest worker t − ¯ T ( t ) − φ ¯ n ( t ) t v v + T ( v ) + φ ˆ n ( v ) • ¯ 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 20 / 34

Introduction Individuals Dynasties Aggregates Dem Transition Growth Conclusion Balanced growth path The growth rate of population converges to η = ln ( n ) T + B 21 / 34

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 22 / 34