Structural Change, Demographic Transition and Fertility Di erence

Transcription

1 Structural Change, Demographic Transition and Fertility Di erence T. Terry Cheung February 14, 2017 T. Terry Cheung () Structural Change and Fertility February 14, / 35

2 Question Question: The force that drives demographic transition and makes poor countries have higher fertility the same one? T. Terry Cheung () Structural Change and Fertility February 14, / 35

3 Question Question: The force that drives demographic transition and makes poor countries have higher fertility the same one? Answer: 1 Agricultural productivity and subsistence level together made agricultural sector in less developed areas larger. 2 Agricultural sectors usually associated with higher fertility rate. T. Terry Cheung () Structural Change and Fertility February 14, / 35

4 Motivations US time series T. Terry Cheung () Structural Change and Fertility February 14, / 35

5 Motivations Cross-Country Total Fertility Rate T. Terry Cheung () Structural Change and Fertility February 14, / 35

6 Why is Agricultural Sector Important? Children Ever Born by Sector T. Terry Cheung () Structural Change and Fertility February 14, / 35

7 Why is Agricultural Sector Important? Simple Decomposition Exercise T. Terry Cheung () Structural Change and Fertility February 14, / 35

8 Why is Agricultural Sector Important? Simple Decomposition Exercise fertility t0!t 1 = α it1 F it1 i = α it1 F it1 i α it0 F it0 i i = (α it1 α it0 ) F it1 i {z } between α it0 F it1 + α it0 F it1 i + α it0 (F it1 F it0 ) i {z } within α it0 F it0 i T. Terry Cheung () Structural Change and Fertility February 14, / 35

9 Why is Agricultural Sector Important? A Decomposition Example T. Terry Cheung () Structural Change and Fertility February 14, / 35

10 Why does Agricultural Sector have more birth? Demand Agricultural Labor Share negatively correlated with agricultural productivity and income T. Terry Cheung () Structural Change and Fertility February 14, / 35

11 Why does Agricultural Sector have more birth? Demand In areas that are less developed, farmers used more physical labors than other inputs; Restuccia et al. (2008) T. Terry Cheung () Structural Change and Fertility February 14, / 35

12 Why does Agricultural Sector have more birth? Demand In areas that are less developed, there are more farmers (as a fraction of labor force) More farmers in agricultural sector who use extensively physical labor T. Terry Cheung () Structural Change and Fertility February 14, / 35

13 Why does Agricultural Sector have more birth? Demand Fertility rate is associated with child labor prevalence T. Terry Cheung () Structural Change and Fertility February 14, / 35

14 Why does Agricultural Sector have more birth? Supply Distance; quality of schooling; return to schooling T. Terry Cheung () Structural Change and Fertility February 14, / 35

15 Sectorial di erences in fertility T. Terry Cheung () Structural Change and Fertility February 14, / 35

16 Model to explain the di erences in trend Greenwood and Seshadri (2002) cannot explain: V = max... + (1 + β) χ q ζ (1 ζ e) w 0 + ev 0 ξ s.t. w =... + q [e (τ + t) + (1 e) τ] w Note that both (1 e) w 0 + ev 0 and e (τ + t) + (1 e) τ are linear so that there should be a threshold τ+t τ, such that both agents will give birth to skilled children if w 0 v > τ+t 0 τ. Co-movement of sectorial fertility in their model T. Terry Cheung () Structural Change and Fertility February 14, / 35

17 Literature Mortality Decline(Kalemli-Ozcan, 2002) Cannot be the sole reason as it cannot match the magnitude (~30% infant mortality) (e.g. Doepke, 2005) Unless taken into account its e ect on (human) capital accumulation (e.g. Manuelli & Seshadri, 2007) Contraceptive Methods Introduced after transition taken place in e.g. France and USA (Guinnane, 2011) Social Insurance and Old-Age Support (Jones & Boldrin 2002) Varies from country to country (e.g. US popular after WWII; Germany in 1880s before transition; GB in 1900 after transition) Increase in the direct cost Only relevant one is urban housing/rural land (Guinnane, 2011) Increase in the Opportunity Costs of Childbearing Can explain the decline not the sectoral di erence T. Terry Cheung () Structural Change and Fertility February 14, / 35

18 Production (Labor Demand) Two sectors (i): agricultural and non-agricultural (or manufacturing) sectors (i = A, M) N d working (adult) individuals and, among them, N s are skilled workers Endogenous share of unskilled labor being allocated to the agricultural sector be ξ a η s = N s N d η a = ξ a (1 η s ) η m = (1 ξ a ) (1 η s ) T. Terry Cheung () Structural Change and Fertility February 14, / 35

19 Production (Labor Demand) Two types of agents (j) in the economy: skilled (s) and unskilled (u) Agricultural Sector: unskilled labor (L a,u ) Non-agricultural Sector: nskilled labor (L m,u ) and skilled labor (L m,s ) Production function for agricultural (Y a ) and non-agricultural products (Y m ) are given as: Y a = A a L a,u Y m = A m Lm,uL α 1 m,s α T. Terry Cheung () Structural Change and Fertility February 14, / 35

20 Production (Labor Demand) Firm s Problem: max py a w a,u L a,u (1) max Y m w m,u L m,u w m,s L m,s (2) Gives w a,u = pa a w m,u = αa m lm,s l m,u 1 w m,s = (1 α)a m lm,u l m,s w s w u = 1 α α lm,u l m,s α α T. Terry Cheung () Structural Change and Fertility February 14, / 35

21 Household (Labor Supply) Each adult can give birth to both types of children (k): skilled (s) and unskilled (u) Children, if they are not to be endowed skills, only consume their parents time endowment If the agent chooses to endow their children with skills, they have to pay goods cost in terms of non-agricultural goods. The adults make the following decisions: 1 Consumption (both agricultural and non-agricultural) 2 Number of children to have and whether to educate them 8 < V (w j, i) = max c i,j a,c i,j m,n s,n u : + ν[(ca i,j c)] 1 σ i,j (1 ν)(cm ) 1 σ 1 σ + 1 σ ψ (n i,js +n i,ju ) n i,js V (w 0s, i 0 ) + n i,ju V (w 0u, i 0 ) ε (3) 9 = ; T. Terry Cheung () Structural Change and Fertility February 14, / 35

22 Household (Labor Supply) The income I i,j of the agents are given as: I i,j w u = The e ective cost to raise children (eτ i,jk ) is di erent for di erent k: w s ( h i eτ i,js = τ s w j + γ s Γ i=a + γ s (1 Γ i=a ) eτ i,ju = τ u w j Γ i=a is an indicator function to determine if the agent is working in agricultural sector (γ s > γ s ) Assumption: Child labors works in the same sector as their parents (Edmonds, 2005) Budget Constraint is then: pc i,j a + cm i,j = w j eτ i,jk n k (4) k=u,s T. Terry Cheung () Structural Change and Fertility February 14, / 35

23 Analytical Result Optimality Lemma The problem can be rewritten as: 8 >< V (w j, i) = max C i,j,f i,j ψ >: s.t. w j = C i,j + E i,j Ω(p; ν) (C i,j pc) 1 σ 1 σ + E i,j 1 ε h f i,j bτ s V (w 0s, i 0 ) + 1 ( f i,j bτ s + 1 f i,j bτ u ) ε f i,j bτ u V (w 0u, i 0 ) i 9 >= >; C i,j pca i,j + cm i,j Ω(p; ν) ν σ 1 1 σ 1 σ p + (1 ν) 1 σ σ E i,j k=u,s eτ i,jk n k f i,j being the share of child-rearing expenditure (E i,j ) spent on skill endowed children. T. Terry Cheung () Structural Change and Fertility February 14, / 35

24 Analytical Result Optimality Proposition In optimality, one agent will give birth to only one type of child, but not both. That is, either k = u or k = s but not both for an agent. 8 >< V (w j, i) = max C i,j,f i,j >: Ω(p; ν) (C i,j pc) 1 σ 1 σ + E i,j 1 ε h f i,j bτ s V (w 0s, i 0 ) + 1 ψ ( f i,j bτ s + 1 f i,j bτ u ) ε f i,j bτ u V (w 0u, i 0 ) i 9 >= >; T. Terry Cheung () Structural Change and Fertility February 14, / 35

25 Analytical Result Optimality w s > w u and γ s > γ s Then the cost structure will be: τ s w s + γ s τ u w s < τs w u + γ s τ u w u < τs w u + γ s τ u w u Indi ernce: V (w 0s, i 0 ) eτ i,js 1 ε = V (w 0u, i 0 ) eτ i,ju 1 ε T. Terry Cheung () Structural Change and Fertility February 14, / 35

26 Analytical Result Equilibrium The steadyn state equilibrium is o a vector of price fp, w u, w s g, an allocation ca i,j, cm i,j, n i,jk, λ i,jk, an aggregate allocation fl i,j, ξ a, y a, y m g and value function V (w u, a), V (w u, m) V (w s, m) and migration cost B such that given the productivity A a, A m and skilled endowment ratio η s 1 η s 1 Given the price vector, the rm maximizes its pro t according to (1) and (2) 2 Given the price vector, the households maximize their value according to (3) subject to (4) 3 All ve markets (3 labor markets and 2 goods markets) clear 4 The skilled ratio η s 1 η is time invariant s 5 The value for both unskilled agents are the same 6 V (w 0j ) = V (w j ) V (w u, a) = V (w u, m) B = V (w u ) T. Terry Cheung () Structural Change and Fertility February 14, / 35

27 Analytical Result Equilibrium Proposition Along the steady state equilibrium, the following are true 1 There can only be one type of agents indi erent between the type of child; 2 At least a fraction of skilled workers would give birth to skilled child while at least a fraction of agricultural workers would give birth to unskilled child. If σ > ε then the value of (E ms ) and (E au ) are uniquely de ned. T. Terry Cheung () Structural Change and Fertility February 14, / 35

28 Analytical Result Characterization T. Terry Cheung () Structural Change and Fertility February 14, / 35

29 Analytical Result Characterization Take τ u = τ s = 0 for a moment: w s = 1 α w u α = 1 α α lm,u l m,s (1 η s ) η s (1 ξ a ) As agricultural productivity increases, ξ a decreased and the economy can sustain a higher η s without driving the skilled wage too low. T. Terry Cheung () Structural Change and Fertility February 14, / 35

30 Calibration Pre-set Value Calibrated Jointly to data in 1870 T. Terry Cheung () Structural Change and Fertility February 14, / 35

31 Result Some Prediction T. Terry Cheung () Structural Change and Fertility February 14, / 35

32 Calibrate two ends Parameter Value changed T. Terry Cheung () Structural Change and Fertility February 14, / 35

33 Result Some Prediction T. Terry Cheung () Structural Change and Fertility February 14, / 35

34 Trend Comparative Statics Exercise: 1 Interpolate (and extrapolate) τ s throughout the time period by using value from 1870 and Varying τ u and η s to target Jointly average total fertility and the declined trend in non-agricultural wage premium by Caselli and Coleman (2001) for di erent regimes 3 De ne a loss function (depends on total fertility and agricultural employment share) 4 Choose the regime with the smallest loss T. Terry Cheung () Structural Change and Fertility February 14, / 35

35 Exercise T. Terry Cheung () Structural Change and Fertility February 14, / 35

36 Exercise T. Terry Cheung () Structural Change and Fertility February 14, / 35