French Fertility and Education Transition: Rational Choice vs - - PowerPoint PPT Presentation

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French Fertility and Education Transition: Rational Choice vs Cultural Diffusion

David de la Croix1 Faustine Perrin2

• 1Univ. cath. Louvain

2Lund University

May 30, 2017

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Introduction Model Data Estimation the Unexplained Conclusion

The French fertility and education transition

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 20 22 24 26 28 30 32 34 36 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 years crude birth rate (left axis, ‰) boys' enrolment rate (right axis, %) girls' enrolment rate (right axis, %)

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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.

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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)

15 20 25 30 35 40 45 1740 1790 1840 1890 Annual births per 1000 population Years Crude Birth Rates France Crude Birth Rates England 4 / 36

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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.

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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.

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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

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Introduction Model Data Estimation the Unexplained Conclusion

Endowment and Technology

Unitary Couple. Labor income: yt = hb

t (1 − ab t ) + ωhg t (1 − ag t ),

(1) Child mortality: nt = (1 − mt)Nt. (2) Sex ratio: ng

t = nb t = 1 2nt.

(3) Production function of children: φnt + ψ(Nt − nt) =

• ab

t ag t .

(4)

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Introduction Model Data Estimation the Unexplained Conclusion

Objective and constraints

Utility: ln(ct) + γ ln(nb

t hb t+1 + ng t ωhg t+1).

(5) Budget: ct + pt(eb

t nb t + eg t ng t ) = yt + bt,

(6) Education: hj

t+1 = (ej t)ηj

t+εℓj t+1.

(7)

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Introduction Model Data Estimation the Unexplained Conclusion

Summary of the problem

{ag

t , ab t , eg t , eb t , nt} = arg max

• ln(ct)

+ γ ln

• nt

2 ((eb t )ηb

t +εℓb t+1 + ω(ej

g)ηg

t +εℓg t+1)

subject to

• φ + ψ

mt 1 − mt

• nt

=

• ab

t ag t

ct = hb

t (1 − ab t ) + ωhg t (1 − ag t ) + bt

−pt(eb

t + eg t ) nt 2

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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 ℓj

t+1 increases

education spending and decreases fertility [Ben-Porath effect]. Rise in non labor income increases fertility and education [income effect].

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Introduction Model Data Estimation the Unexplained Conclusion

Generations

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

G0 G 1 G2

b

• r

n s c h

• l

: g e t h

b

, h

g

m a r r i a g e ( 1 8 1 6

• 2

) N b i r t h s ( 1 8 2 1

• 2

6

• 3

1 ) d e c i d e e

b

, e

g

e d u c a t i

• n

( 1 8 3 7 ) n c h i l d r e n s u r v i v e s c h

• l

: g e t h

b 1

, h

g 1

N

1

b i r t h s ( 1 8 4 6

• 5

1

• 5

6 ) d e c i d e e

b 1

, e

g 1

e d u c a t i

• n

( 1 8 6 3 ) s c h

• l

: g e t h

b 2

, h

g 2

n

1

c h i l d r e n s u r v i v e N

2

b i r t h s ( 1 8 7 2

• 7

6

• 8

1 ) d e c i d e e

b 2

, e

g 2

e d u c a t i

• n

( 1 8 8 6

• 8

7 ) Y e a r s G e n e r a t i

• n

s n

2

c h i l d r e n s u r v i v e s c h

• l

e n d

• w

e d w i t h ℓ e n d

• w

e d w i t h ℓ

1

e n d

• w

e d w i t h ℓ

2

m a r r i a g e ( 1 8 5 4

• 5

5 ) e n d

• w

e d w i t h ℓ

3

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Introduction Model Data Estimation the Unexplained Conclusion

Generations

1800 1810 1820 1830 1840 1850 school: get hb

0, hg

marriage (1816-20) N0 births (1821-26-31) decide eb

0, eg

education (1837) n0 children survive school: get hb

1, hg 1

eb

−1, eg −1 predicted by marriage

signature 1816-1820 % brides and grooms signing with marks, 1816-1820 N0: Crude birth rates, 1821,6 & 31 m0: Mortality rates 0-5, 1821,6 & 31 eb

0: School enrollment, prim., boys, 1837

eg

0: School enrollment, prim., girls, 1837

endowed with ℓ0 ℓ0: Life Table 1806-11 endowed with ℓ1 ℓ1: Life Table 1821, 6 & 31 % brides and grooms signing with marks, 1854-1855 marriage (1854-55) 13 / 36

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Introduction Model Data Estimation the Unexplained Conclusion

Links

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 20 22 24 26 28 30 32 34 36 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 years crude birth rate (left axis, ‰) boys' enrolment rate (right axis, %) girls' enrolment rate (right axis, %)

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Introduction Model Data Estimation the Unexplained Conclusion

Crude birth rate

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Introduction Model Data Estimation the Unexplained Conclusion

Boy’s enrollment

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Introduction Model Data Estimation the Unexplained Conclusion

Girl’s enrollment

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Introduction Model Data Estimation the Unexplained Conclusion

Structural model

First order conditions imply 9 equations (G = 0, 1, 2) for i = 1 . . . 81:        nG,i = f ⋆

n [πG, ρG,i]

eb

G,i

= f ⋆

eb[πG, ρG,i]

eg

G,i

= f ⋆

eg[πG, ρG,i]

(8) πG = {φ, ψ, γ, ηb

G, ηg G, bG, pG, ω, ǫ}: parameters of generation

G, same across counties. ρG,i = {ℓG,i, ℓG+1,i, hb

G,i, hg G,i, mG,i}: exogenous variables

relevant for generation G in county i.

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Introduction Model Data Estimation the Unexplained Conclusion

Minimum distance estimator

The set of parameters to identify is Π = π0 ∪ π1 ∪ π2. 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:

Ω(Π) = arg min

Π 81

∑

i=1

• 2

∑

G=0

• 1 − f ⋆

n [πG, ρG,i]

ˆ nG,i 2 +

• 1 − f ⋆

eb[πG, ρG,i]

ˆ eb

G,i

2 +

• 1 −

f ⋆

eg[πG, ρG,i]

ˆ eg

G,i

2 +  1 − ω (ˆ eb

0,i)ηb

0+ǫℓ1

(ˆ eg

0,i)ηg

0 +ǫℓ1

1 ˆ δi  

2

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Introduction Model Data Estimation the Unexplained Conclusion

Estimation results

Elasticity of human capital to education is larger for girls than for boys. Cost of education pG highest for the initial generation, when fewer schools were available. Non labor income negligible for generations 0 and 1, while it is positive for generation 2. Effect of longevity on the return to schooling, ǫ not significantly different from 0.

Parameter Estimation S.E. γ 0.407 0.029 ηb 0.338 0.091 ηg 0.482 0.095 ǫ 0.111 0.102 p0 0.182 0.013 p1 0.106 0.009 p2 0.128 0.012 ω 0.739 0.012 b0 0.012 0.012 b1 0.000 0.001 b2 0.098 0.021

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Introduction Model Data Estimation the Unexplained Conclusion

Goodness of Fit. G0: light gray. G1: gray. G2: black

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 Observed Fertility Fitted

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Introduction Model Data Estimation the Unexplained Conclusion

Goodness of Fit. G0: light gray. G1: gray. G2: black

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Observed Boys Enrollment Fitted

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Introduction Model Data Estimation the Unexplained Conclusion

Goodness of Fit. G0: light gray. G1: gray. G2: black

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Observed Girls Enrollment Fitted

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Introduction Model Data Estimation the Unexplained Conclusion

Goodness of Fit (R2) under Different Scenarii

Removing heterogeneity in. . . Equation benchmark inf. future mothers’ fathers’ mortality longevity education education Fertility 37.9 14.6 37.6 21.1 35.9 Boys’ enrollment 70.8 70.7 70.7 58.7 65.1 Girls’ enrollment 82.9 82.9 83.0 65.7 80.5

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Introduction Model Data Estimation the Unexplained Conclusion

Time devoted to children - mothers’ share

20 40 60 80 Counties 0.60 0.65 0.70 0.75 0.80 0.85 0.90 % supported by mother

G0: light gray. G1: gray. G2: black

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Introduction Model Data Estimation the Unexplained Conclusion

Effect of Parents’ Education Level on Fertility

ef n0 n1 n2 0.1 2.41 2.47 0.2 2.20 2.22 0.3 2.11 2.12 2.38 0.4 2.08 2.07 2.29 0.5 2.05 2.03 2.23 0.6 2.04 2.02 2.20 0.7 2.00 2.17 0.8 2.00 2.15 0.9 1.99 2.13 1. 2.12 em n0 n1 n2 0.1 2.25 0.2 2.34 2.28 0.3 2.42 2.36 0.4 2.48 2.43 2.69 0.5 2.54 2.48 2.73 0.6 2.59 2.54 2.77 0.7 2.58 2.81 0.8 2.62 2.85 0.9 2.66 2.88 1. 2.91

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Introduction Model Data Estimation the Unexplained Conclusion

Closing the gender education gap

marginal return - boys marginal return - girls marginal cost education

• beg. 19th C

marginal cost education end 19th C gender education gap beg. 19th C gender education gap end 19th C School enrolment rate

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Introduction Model Data Estimation the Unexplained Conclusion

Explaining the Unexplained

Objective:

– assess importance of other factors in explaining family decisions. – indicate in which direction should economic theory be developed.

The “unexplained” is represented by the nine residuals: εn

G = ˆ

nG,i − f ⋆

n [ ˆ

πG, ρG,i] εeb

G = ˆ

eb

G,i − f ⋆ eb[ ˆ

πG, ρG,i] εeg

G = ˆ

eg

G,i − f ⋆ eg[ ˆ

πG, ρG,i]

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Introduction Model Data Estimation the Unexplained Conclusion

Candidates

Family structure Religion Cultural barriers Elites (upper tail knowledge)

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Introduction Model Data Estimation the Unexplained Conclusion

Family structure

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Introduction Model Data Estimation the Unexplained Conclusion

Dialects

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Introduction Model Data Estimation the Unexplained Conclusion

Correlations

εn εeb εeg εn

1

εeb

1

εeg

1

εn

2

εeb

2

εeg

2

FAMILY TYPES (VS NUCLEAR): extended 0.542∗∗∗ 0.089∗ 0.114∗∗∗ 0.427∗∗∗ −0.059∗ −0.022 −0.166 −0.123∗∗∗ −0.121∗∗∗ stem 0.181 0.022 0.032 0.156 −0.086∗∗ −0.046 −0.024 −0.043 −0.046∗ RELIGION: % catho 0.176∗ 0.067∗∗ 0.061∗∗ 0.017 0.009 −0.037∗ 0.101 −0.016 −0.043∗∗ % protest 0.171∗ 0.067∗∗ 0.063∗∗ −0.014 0.005 −0.040∗ 0.088 −0.017 −0.044∗∗ secularization −0.011 −0.020 0.002 0.040 0.002 0.003 0.100∗∗ 0.016∗ −0.004 GEOGRAPHICAL & CULTURAL DISTANCE : dist. 0.004 0.001 0.002∗∗ 0.004 −0.0001 −0.0002 0.002 −0.001∗∗ −0.001∗∗

• dist. by road

−0.003 −0.001 −0.001∗ −0.003 −0.00004 0.0002 −0.002 0.001∗ 0.001∗∗

• il lang.

−0.358∗∗∗ −0.082∗ −0.071∗ −0.198 −0.041 −0.005 0.123 0.007 0.036

• cc. lang.

−0.124 0.002 −0.036 −0.023 0.054 0.004 0.156 −0.021 0.005 UPPER TAIL KNOWLEDGE :

• s. Encyclop´

edie −0.014 −0.009 −0.011∗∗ 0.006 −0.0005 0.001 0.011 0.003 0.005∗ # infrast. 0.013∗ −0.002 −0.003 0.007 −0.003∗∗ −0.001 0.001 0.0003 0.0001 area infrast. −0.003∗∗ 0.0003 0.0003 −0.004∗∗ 0.0004 −0.00004 −0.001 0.0002 0.0001 Observations 81 81 81 81 81 81 81 81 81 Adjusted R2 0.520 0.139 0.286 0.206 0.176 0.018 0.016 0.415 0.469 32 / 36

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Introduction Model Data Estimation the Unexplained Conclusion

Residuals εn

0 and εn 2

O¨ ıl Oc Extended family

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Introduction Model Data Estimation the Unexplained Conclusion

Omitted variable bias

Family structure and language matter for demogr. transition → “omitted variable bias” in structural parameter estimates ? We propose to estimate:

arg min

Π,Z 81

∑

i=1

• 2

∑

G=0

• 1 − f ⋆

n [πG, ρG,i] + ζn,GOili + ξn,GExti

ˆ nG,i 2 +

• 1 − f ⋆

eb[πG, ρG,i] + ζeb,GOili + ξeb,GExti

ˆ eb

G,i

2 +

• 1 −

f ⋆

eg[πG, ρG,i] + ζeg,GOili + ξeg,GExti

ˆ eg

G,i

2 +  1 − ω (ˆ eb

0,i)ηb

0+ǫℓ1

(ˆ eg

0,i)ηg

0 +ǫℓ1

1 ˆ δi  

2

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Introduction Model Data Estimation the Unexplained Conclusion

Estimation of the extended model

Parameter 95% conf. interval benchmark new estimate γ [0.349, 0.465] 0.356 ηb [0.160, 0.516] 0.212 ηg [0.296, 0.669] 0.342 ǫ [−0.088, 0.311] 0.237 p0 [0.157, 0.208] 0.166 p1 [0.089, 0.124] 0.095 p2 [0.104, 0.151] 0.110 ω [0.716, 0.762] 0.726 b0 [−0.012, 0.036] 0.036 b1 [−0.001, 0.001] 0.000 b2 [0.056, 0.140] 0.127

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Introduction Model Data Estimation the Unexplained Conclusion

A parsimonious rational choice model has some power in explaining the variation of fertility and education across time and space Child mortality and mothers’ education are important factors Still there remain 65% of variation in fertility to explain. Family structure and cultural barriers are correlated with residuals → direction for future research.

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More

FOCs

Childrearing: ag

t =

• hb

t

ωhg

t

• φ + ψ

mt 1 − mt

• nt,

ab

t =

• ωhg

t

hb

t

• φ + ψ

mt 1 − mt

• nt.

Fertility: γ nt = 1 ct

• eb

t + eg t

2

• pt + 1

ct 2

• hb

t hg t

• φ +

mt 1 − mt ψ

• Education:

pt ct nt 2 = γ(ηb

t + ǫℓt+1)(eb t )ηb

t +ǫℓt+1−1

hb

t+1 + ωhg t+1

= γ(ηg

t + ǫℓt+1)(eg t )ηg

t +ǫℓt+1−1ω

hb

t+1 + ωhg t+1

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More

Goodness of Fit (R2)

All sample G0 G1 G2 Fertility 37.9 32.0 29.4 48.0 Boys’ enrollment 70.8 55.1 71.3 19.9 Girls’ enrollment 82.9 67.1 85.2 37.6

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More

Robustness

benchmark varying η φnt = 1

2 (ab t + ag t )

γ 0.407 0.335 0.180 ηb 0.338 0.070 ηg 0.482 0.171 ǫ 0.111 0.203 0.261 p0 0.182 0.181 0.080 p1 0.106 0.082 0.043 p2 0.128 0.078 0.051 ω 0.739 0.709 0.678 b0 0.012 0.130 0.000 b1 0.000 0.000 0.000 b2 0.098 0.000 0.290 ηb 0.302 ηg 0.443 ηb

1

0.192 ηg

1

0.325 ηb

2

0.278 ηg

2

0.142 Ω( ˆ Π) 38.512 33.900 44.715 3 / 3