French Fertility and Education Transition: Rational Choice vs Cultural Diffusion David de la Croix 1 Faustine Perrin 2 1 Univ. cath. Louvain 2 Lund University May 30, 2017
Introduction Model Data Estimation the Unexplained Conclusion The French fertility and education transition 36 0.9 0.8 34 0.7 32 0.6 30 0.5 28 0.4 26 0.3 24 crude birth rate (left axis, ‰) 0.2 boys' enrolment rate (right axis, %) 22 0.1 girls' enrolment rate (right axis, %) 20 0 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 years 2 / 36
Introduction Model Data Estimation the Unexplained Conclusion Question Incentives or norms ? socioeconomic theories vs diffusionist/cultural views Becker vs Princeton project Matters for policy design. If fertility is a question of culture and norms instead of incentives, policy playing on incentives (family allowances, tax break for families, ...) have little impact. 3 / 36
Introduction Model Data Estimation the Unexplained Conclusion Why France France often seen as the best case for diffusionist/cultural view, as fertility transition leads take-off to modern growth (Weir, 1984) 45 40 Annual births per 1000 population 35 30 25 Crude Birth Rates France 20 Crude Birth Rates England 15 1740 1790 1840 1890 4 / 36 Years
Introduction Model Data Estimation the Unexplained Conclusion What we do Evaluate (i) How much one can explain by relying strictly on a parsimonious economic set-up modelling a few incentives; and (ii) which additional factors (cultural, geographic, institutional, etc.) correlate with the part that remained unexplained at step (i). Data: French counties ( d´ epartements ) over the nineteenth century. The continuity of the State allows to benefit from census data over a long period of time, as well as detailed education data. 5 / 36
Introduction Model Data Estimation the Unexplained Conclusion Advantages of our approach compared to existing literature Structural model → impose additional discipline to the exercise. For example, by considering the joint decision about fertility and education, we identify the mechanisms using both birth rate and school enrollment data. Use gendered education data. Use three generations of households (one household = one county): born around 1800, born in 1821-31, born in 1846-56. 6 / 36
Introduction Model Data Estimation the Unexplained Conclusion Preview of the results The parsimonious rational-choice model explains 38% of the variation of fertility over time and across counties, and 71% and 83% of school enrollment of boys and girls respectively. In this model, two variables are important to explain fertility: child mortality, and mothers’ education. What remains unexplained is correlated with family structures (Todd 1985) and with language barriers (Oil vs Oc) Neglecting cultural variables does not bias the estimates of the structural parameters 7 / 36
Introduction Model Data Estimation the Unexplained Conclusion Endowment and Technology Unitary Couple. Labor income: t ) + ω h g t ( 1 − a g y t = h b t ( 1 − a b t ) , (1) Child mortality: n t = ( 1 − m t ) N t . (2) Sex ratio: n g t = n b t = 1 2 n t . (3) Production function of children: � t a g a b φ n t + ψ ( N t − n t ) = (4) t . 8 / 36
Introduction Model Data Estimation the Unexplained Conclusion Objective and constraints Utility: t + 1 + n g t ω h g ln ( c t ) + γ ln ( n b t h b t + 1 ) . (5) Budget: t + e g t n g c t + p t ( e b t n b t ) = y t + b t , (6) Education: t ) η j t + ε ℓ j h j t + 1 = ( e j (7) t + 1 . 9 / 36
Introduction Model Data Estimation the Unexplained Conclusion Summary of the problem � { a g t , e g t , a b t , e b t , n t } = arg max ln ( c t ) � � � g ) η g t + ε ℓ g t ) η b t + ε ℓ b t + 1 + ω ( e j n t 2 (( e b + γ ln t + 1 ) subject to � m t � � t a g a b φ + ψ n t = t 1 − m t t ) + ω h g t ( 1 − a g h b t ( 1 − a b c t = t ) + b t t + e g − p t ( e b t ) n t 2 10 / 36
Introduction Model Data Estimation the Unexplained Conclusion Properties of the solution Share of child-rearing supported by mother inversely related to her human capital Cost of having children increases with human capital of parents Boys and girls educated so as to equalize the return of education across genders Rise in child expected lifetime labor endowment ℓ j t + 1 increases education spending and decreases fertility [Ben-Porath effect]. Rise in non labor income increases fertility and education [income effect]. 11 / 36
Generations Introduction G e n e r a t i o n s G0 Y e a r s 1 7 9 0 b o r n 1 8 0 0 b g s c h o o l : g e t h , h Model 0 0 e n d o w e d w i t h ℓ 0 1 8 1 0 G 1 m a r r i a g e ( 1 8 1 6 - 2 0 ) Data 1 8 2 0 N b i r t h s c h i l d r e n s u r v i v e n 0 0 ( 1 8 2 1 - 2 6 - 3 1 ) e n d o w e d w i t h ℓ 1 1 8 3 0 b g d e c i d e e , e 0 0 b g e d u c a t i o n s c h o o l : g e t h , h 1 1 G2 ( 1 8 3 7 ) Estimation 1 8 4 0 m a r r i a g e ( 1 8 5 4 - 5 5 ) 1 8 5 0 N b i r t h s 1 c h i l d r e n s u r v i v e n 1 ( 1 8 4 6 - 5 1 - 5 6 ) e n d o w e d w i t h ℓ 2 1 8 6 0 b g d e c i d e e , e 1 1 b g e d u c a t i o n s c h o o l : g e t h , h 2 2 ( 1 8 6 3 ) the Unexplained 1 8 7 0 n 2 N b i r t h s 2 c h i l d r e n ( 1 8 7 2 - 7 6 - 8 1 ) s u r v i v e 1 8 8 0 e n d o w e d w i t h ℓ 3 b g d e c i d e e , e 2 2 e d u c a t i o n s c h o o l ( 1 8 8 6 - 8 7 ) 1 8 9 0 Conclusion 12 / 36
Introduction Model Data Estimation the Unexplained Conclusion Generations − 1 , e g e b − 1 predicted by marriage 1800 0 , h g school: get h b signature 1816-1820 0 endowed with ℓ 0 ℓ 0 : Life Table 1806-11 1810 marriage % brides and grooms signing (1816-20) with marks, 1816-1820 1820 N 0 births n 0 children survive N 0 : Crude birth rates, 1821,6 & 31 (1821-26-31) m 0 : Mortality rates 0-5, 1821,6 & 31 endowed with ℓ 1 ℓ 1 : Life Table 1821, 6 & 31 1830 0 , e g decide e b 0 1 , h g school: get h b education e b 0 : School enrollment, prim., boys, 1837 1 (1837) e g 0 : School enrollment, prim., girls, 1837 1840 marriage % brides and grooms signing (1854-55) with marks, 1854-1855 1850 13 / 36
Introduction Model Data Estimation the Unexplained Conclusion Links 36 0.9 0.8 34 0.7 32 0.6 30 0.5 28 0.4 26 0.3 24 0.2 crude birth rate (left axis, ‰) boys' enrolment rate (right axis, %) 22 0.1 girls' enrolment rate (right axis, %) 20 0 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 years 14 / 36
Introduction Model Data Estimation the Unexplained Conclusion Crude birth rate 15 / 36
Introduction Model Data Estimation the Unexplained Conclusion Boy’s enrollment 16 / 36
Introduction Model Data Estimation the Unexplained Conclusion Girl’s enrollment 17 / 36
Introduction Model Data Estimation the Unexplained Conclusion Structural model First order conditions imply 9 equations ( G = 0 , 1 , 2 ) for i = 1 . . . 81: f ⋆ n G , i = n [ π G , ρ G , i ] e b f ⋆ (8) = eb [ π G , ρ G , i ] G , i e g f ⋆ = eg [ π G , ρ G , i ] G , i G , η g π G = { φ , ψ , γ , η b G , b G , p G , ω , ǫ } : parameters of generation G , same across counties. G , i , h g ρ G , i = { ℓ G , i , ℓ G + 1 , i , h b G , i , m G , i } : exogenous variables relevant for generation G in county i . 18 / 36
Introduction Model Data Estimation the Unexplained Conclusion Minimum distance estimator The set of parameters to identify is Π = π 0 ∪ π 1 ∪ π 2 . The parameter φ is set a priori at 0.075. The remaining parameters are estimated by minimizing the distance between predicted and observed data. The estimation problem writes: � 2 � 2 � 81 2 1 − f ⋆ 1 − f ⋆ n [ π G , ρ G , i ] eb [ π G , ρ G , i ] � �� ∑ ∑ Ω ( Π ) = arg min + e b n G , i ˆ ˆ Π i = 1 G = 0 G , i 2 � � 2 � 0 , i ) η b 0 + ǫ ℓ 1 � f ⋆ e b ( ˆ eg [ π G , ρ G , i ] 1 + 1 − + 1 − ω e g 0 , i ) η g e g ˆ ˆ 0 + ǫ ℓ 1 δ i ( ˆ G , i 19 / 36
Introduction Model Data Estimation the Unexplained Conclusion Estimation results Elasticity of human capital to Parameter Estimation S.E. education is larger for girls than γ 0.407 0.029 for boys. η b 0.338 0.091 η g 0.482 0.095 Cost of education p G highest for the initial generation, when ǫ 0.111 0.102 fewer schools were available. p 0 0.182 0.013 p 1 0.106 0.009 Non labor income negligible for p 2 0.128 0.012 generations 0 and 1, while it is ω 0.739 0.012 positive for generation 2. b 0 0.012 0.012 Effect of longevity on the return b 1 0.000 0.001 to schooling, ǫ not significantly b 2 0.098 0.021 different from 0. 20 / 36
Introduction Model Data Estimation the Unexplained Conclusion Goodness of Fit. G0: light gray. G1: gray. G2: black 5.5 5.0 4.5 4.0 Fitted 3.5 3.0 2.5 2.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 Observed Fertility 21 / 36
Recommend
More recommend
