Fertility and Childlessness in the US Thomas Baudin 1 David de la - - PowerPoint PPT Presentation

▶

Feb 20, 2023 259 likes •618 views

Fertility and Childlessness in the US Thomas Baudin 1 David de la Croix 1 Paula Gobbi 3 1 Universit e catholique de Louvain 3 Paris School of Economics March 22, 2014 Introduction Theory Moments Identification Comparative Statics

SLIDE 1

Fertility and Childlessness in the US

Thomas Baudin1 David de la Croix1 Paula Gobbi3

1Universit´

e catholique de Louvain

3Paris School of Economics

March 22, 2014

SLIDE 2

Introduction Theory Moments Identification Comparative Statics Conclusion

Various family types

New types of families. Q: Childlessness is no longer necessarily a fate, it can also be a

choice. By whom?

2 / 35

SLIDE 3

Introduction Theory Moments Identification Comparative Statics Conclusion

Childlessness

voluntary: “child-free” (our estimation for US: 8.1%) involuntary

“natural sterility” (our estimation for US: 2.3%) “social sterility” (our estimation for US: 2.5%)

Understanding the incentives can: predict population trends enhance welfare (fighting poverty driven childlessness)

3 / 35

SLIDE 4

Introduction Theory Moments Identification Comparative Statics Conclusion

Childlessness, more than a special case of fertility (=0)

1871 1876 1881 1886 1891 1896 1901 1906 1911 1916 1921 1926 1931 1936 1941 1946 1954 1956 1958 1960 1962 1964 2.0 2.5 3.0 3.5 4.0 4.5 0.04 0.09 0.14 0.19 no school e Ph.D 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 0.00 0.05 0.10 0.15 0.20 brazil usa mex

Completed Fertility of Mothers vs. Childlessness By Cohort in the USA (left panel), By Education levels in Brazil, Mexico and the USA (right panel)

4 / 35

SLIDE 5

Introduction Theory Moments Identification Comparative Statics Conclusion

Research Question

What is the share of childlessness that is voluntary ? What is the share of childlessness that is poverty driven ? How do economic changes affect the different family types? In particular, how can we reduce the involuntary part of childlessness? → one needs a theory to measure the types of childlessness

5 / 35

SLIDE 6

Introduction Theory Moments Identification Comparative Statics Conclusion

Methodology

A theory to explain jointly marriage and parenthood decisions Identification of the parameters using moments from Census Show that co-existence of involuntary and voluntary causes of childlessness is key to explain facts (US, 1990) Predictions: How better education did affect both types of childlessness and fertility over time. Policy experiment: How inequality does affect both types of childlessness.

6 / 35

SLIDE 7

Introduction Theory Moments Identification Comparative Statics Conclusion

Main features of the model

1 agents are matched randomly, once in life 2 they decide to marry or not 3 they discover their natural fertility status 4 Cooperative decision on consumption and fertility

Women can have children, married or not = Men should marry to have children Exogenous potential income (education): wi + heterogeneity in non labor income ai ⊥wi

7 / 35

SLIDE 8

Introduction Theory Moments Identification Comparative Statics Conclusion

Preferences

Individuals: u

ci, n
= ln ci + ln (n + ν)

No gender differences in preferences ν > 0: Services from children are superior good Couples: θ u(cf , n) + (1 − θ) u(cm, n) with θ ≡ 1 2 θ + (1 − θ) wf wf + wm , θ ∈ (0, 1) ⇒ although ∃ marriage surplus, one spouse may refuse marriage

8 / 35

SLIDE 9

Introduction Theory Moments Identification Comparative Statics Conclusion

Sterility

Natural: χ and ζ: % of female and male who are naturally sterile Social: Minimal consumption to be able to procreate: cmin n > 0 ⇒ cf ≥ cmin Why ? Mc Fall, (1979):

1 Malnutrition 2 Poor use more drugs 3 Poor have less access to medical services: if they want to

abort, they may be sterile after a medical mistake + no access to IVF

4 Poor live in more polluted areas: ց fecundity 9 / 35

SLIDE 10

Introduction Theory Moments Identification Comparative Statics Conclusion

Time constraints

Endowment per person: 1 if married; 1 − δf , 1 − δm if not First child costs φ(1 + η) units of time Additional children cost φ units of time Singles: mothers support the time cost of children alone Married’s: α ∈ ( 1

2, 1) mother’s share of child support (exogenous)

Upper bound on number of children one can have: 0 ≤ n ≤ 1 − δf − φη φ ≡ ¯ nM(singles) 0 ≤ n ≤ 1 − αφη αφ ≡ nM(couples)

10 / 35

SLIDE 11

Introduction Theory Moments Identification Comparative Statics Conclusion

Budget constraints

Single men: bm(cm) = cm − (1 − δm)wm − am + µ ≤ 0. µ: cost of running a household Single women: bf (cf , n) = cf + φ (1 + η(n)) wf n − (1 − δf )wf − af + µ ≤ 0 Couples: b(cf , cm, n) = cf + cm + φ (1 + η(n))

αwf + (1 − α)wm

n − wm − wf − am − af + µ ≤ 0.

11 / 35

SLIDE 12

Introduction Theory Moments Identification Comparative Statics Conclusion

Value functions

V s,m = max{u(cm, 0); bm(cm) ≤ 0} [single male] V s,f = max{u(cf , n); bf (cf , n) ≤ 0, 0 ≤ n ≤ ¯ nM, cf < cmin ⇒ n = 0.} [single female] ˜ V s,f = max{u(cf , 0); bf (cf , 0) ≤ 0} [single sterile female] V ω,i = u(ci, n) where {cf , cm, n} = arg max{U(cf , cm, n); b(cf , cm, n) ≤ 0, 0 ≤ n ≤ nM, cf < cmin ⇒ n = 0. [married] ˜ V ω,i = u(ci, 0) where {cf , cm} = arg max{U(cf , cm, 0); b(cf , cm, 0) ≤ 0} [sterile married]

12 / 35

SLIDE 13

Introduction Theory Moments Identification Comparative Statics Conclusion

Marriage if

(χ + (1 − χ)ζ) ˜ V ω,f + (1 − χ)(1 − ζ)V ω,f ≥ χ ˜ V s,f + (1 − χ)V s,f (χ + (1 − χ)ζ) ˜ V ω,m + (1 − χ)(1 − ζ)V ω,m ≥ V s,m

13 / 35

SLIDE 14

Introduction Theory Moments Identification Comparative Statics Conclusion

Regimes given Marriage Decision

Depending on which constraint binds, people can be in six different situations: [N] Natural sterility, [S] social sterility when n > 0 ⇒ cf ≥ cmin binds and n = 0, [M] maximum fertility when the time constraint, n ≤ ¯ nM or n ≤ nM, binds, [C] constrained fertility when n > 0 ⇒ cf ≥ cmin binds and n > 0, [V] voluntary childlessness when the constraint n ≥ 0 binds, and, finally, [U] unconstrained fertility. Conditionally on being married or not, ∃ thresholds for wages and non-labor income separating different regimes.

14 / 35

SLIDE 15

Introduction Theory Moments Identification Comparative Statics Conclusion

Fertility conditionally on being married when af ∈ [A0, A1[

wf n

[S] [C] [U] [V] [V]

Wf

10

Wf

11

Wf

8

Wf

9

15 / 35

SLIDE 16

Introduction Theory Moments Identification Comparative Statics Conclusion

Fertility conditionally on being married when af ∈ [A1, A2[

wf n

[M] [C] [U] [V]

Wf

10

Wf

11

Wf

13

16 / 35

SLIDE 17

Introduction Theory Moments Identification Comparative Statics Conclusion

Moments used for identification

Data: US Census, 45-70 year old married and never married women in 1990. Completed fertility Drop Separated, Widowed and Divorced (≈ 30%), concentrate on Married and Single Potential income - 12 education categories - 1127080 obs

Nb Category

N. obs.

Nb Category

N. obs.

1 No school 12122 7 Grade 12 479703 2 Grade 1-4 14050 8 1 year of college 178274 3 Grade 5-8 84243 9 2 years of college 53428 4 Grade 9 38121 10 Bachelor degree 99046 5 Grade 10 57213 11 Master degree 56855 6 Grade 11 49413 12 Doctoral degree 4612

17 / 35

SLIDE 18

Introduction Theory Moments Identification Comparative Statics Conclusion

Facts used for identification

Fact 1: fertility Fertility of mothers decreases with education, for both married and single women.

1.5 2 2.5 3 3.5 4 4.5 5 1 2 3 4 5 6 7 8 9 10 11 12

18 / 35

SLIDE 19

Introduction Theory Moments Identification Comparative Statics Conclusion

Facts used for identification

Fact 2: childlessness Childlessness exhibits an U-Shaped relationship with education for both singles and married

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.4 0.5 0.6 0.7 0.8 0.9 1 1 2 3 4 5 6 7 8 9 10 11 12 singles married

19 / 35

SLIDE 20

Introduction Theory Moments Identification Comparative Statics Conclusion

Facts used for identification

Fact 3: marriage There is a hump-shaped relationship between marriage rates and education levels for women. Marriage rates (weakly) increase with education for men.

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1 2 3 4 5 6 7 8 9 10 11 12

20 / 35

SLIDE 21

Introduction Theory Moments Identification Comparative Statics Conclusion

Identification of the Parameters

Fix some parameters a priori For the others: We minimize [d − s(p)] [W ] [d − s(p)]′ d: vector of 72 moments from Census p: vector of 11 parameters s(p): vector of simulated moments W : weighting matrix.

21 / 35

SLIDE 22

Introduction Theory Moments Identification Comparative Statics Conclusion

Some parameters are fixed a priori

Wages Potential labor income depending on education we = γ exp{ρe}, γ = 0.869, ρ = 0.092 (estimated on census data) Sterility χ + (1 − χ)ζ = 0.024 (childlessness rate of Hutterites) χ = ζ = 0.0121

22 / 35

SLIDE 23

Introduction Theory Moments Identification Comparative Statics Conclusion

How the simulated moments are computed

For each woman we draw a non labor income from a log-normal distribution (mean and variance are parameters to be identified) a potential husband, with random education level and non-labor income We compute whether each potential couple will marry, and what will be the optimal fertility of the woman Simulated moments obtained by aggregating all individual choices

23 / 35

SLIDE 24

Introduction Theory Moments Identification Comparative Statics Conclusion

Identified parameters

Description Value S.E. Variance of the log-normal distribution σa 0.247 0.012 Average ratio of non-labor income to labor income ¯ ma 1.001 0.012 Preference parameter ν 9.362 0.146 Minimum consumption level to be able to procreate cmin 0.399 0.009 Good cost to be supported by a household µ 0.272 0.013 Bargaining parameter θ 0.864 0.014 Fraction of childrearing to be supported by women α 0.524 0.005 Time cost of having children φ 0.206 0.003 Fixed cost of children η 0.114 0.006 Time cost of being single (men) δm 0.256 0.015 Time cost of being single (women) δf 0.077 0.013

24 / 35

SLIDE 25

Introduction Theory Moments Identification Comparative Statics Conclusion

Childlessness and Completed Fertility of Mothers, Married Women

1 2 3 4 5 6 7 8 9 10 11 12 0.02 0.07 0.12 0.17 0.22 5 10 15 20 1 2 3 4 5 6 7 8 9 10 11 12 1.5 2.5 3.5 4.5 5 10 15 20

25 / 35

SLIDE 26

Introduction Theory Moments Identification Comparative Statics Conclusion

Childlessness and Completed Fertility of Mothers, Single Women

1 2 3 4 5 6 7 8 9 10 11 12 0.4 0.5 0.6 0.7 0.8 0.9 1 5 10 15 20 1 2 3 4 5 6 7 8 9 10 11 12 1.5 2.5 3.5 4.5 5 10 15 20

26 / 35

SLIDE 27

Introduction Theory Moments Identification Comparative Statics Conclusion

Marriage Rates of Women and Men

1 2 3 4 5 6 7 8 9 10 11 12 0.5 0.6 0.7 0.8 0.9 1 5 10 15 20 1 2 3 4 5 6 7 8 9 10 11 12 0.5 0.6 0.7 0.8 0.9 1 5 10 15 20

27 / 35

SLIDE 28

Introduction Theory Moments Identification Comparative Statics Conclusion

Overidentification check

1 2 3 4 5 6 7 8 9 10 11 12 2 3 4 5 5 10 15 20 1 2 3 4 5 6 7 8 9 10 11 12 0.04 5 10 15 20

Completed Fertility of Married Fathers (left), Childlessness rates of Married Men (right), by Years of Schooling. Data (black), Simulation (grey), Education Categories (labels)

28 / 35

SLIDE 29

Introduction Theory Moments Identification Comparative Statics Conclusion

% of women in each regime by education category

1 2 3 4 5 6 [N] 2.3 2.3 2.3 2.3 2.3 2.3 [S] 14.2 10.3 5.5 3.9 3.2 2.6 [M] 11.6 9.2 5.5 3.8 3.0 2.3 [C] 29.6 22.8 9.4 4.0 2.5 1.3 [V] 0.5 0.7 2.0 3.1 4.0 5.1 [U] 41.9 54.6 75.3 82.9 85.0 86.5 7 8 9 10 11 12 tot 2.3 2.3 2.3 2.3 2.2 2.1 2.3 2.1 1.8 1.4 0.8 0.5 0.0 2.5 1.7 1.2 0.9 0.4 0.3 0.0 2.0 0.5 0.1 0.0 0.0 0.0 0.0 1.8 6.5 8.3 10.7 17.2 21.5 39.5 8.1 86.8 86.3 84.7 79.4 75.5 58.4 83.3

29 / 35

SLIDE 30

Introduction Theory Moments Identification Comparative Statics Conclusion

Causes of childlessness

1 2 3 4 5 6 7 8 9 10 11 12 5 10 15 20 25 30 35 40 45 5 10 15 20 Involuntary childlessness (biological) Voluntary childlessness Involuntary childlessness (social)

30 / 35

SLIDE 31

Introduction Theory Moments Identification Comparative Statics Conclusion

Historical experiment

1.5 2.5 3.5 4.5 5.5 1870 1890 1910 1930 1950 data edu tech edu+tech edu+tech+a 0.05 0.10 0.15 0.20 1870 1890 1910 1930 1950 data edu tech edu+tech edu+tech+a

Fertility and childlessness rate of married women General trend in captured. Non linear interaction between education and TFP. Two events are not captured: baby boom, super high childlesness in 1900

31 / 35

SLIDE 32

Introduction Theory Moments Identification Comparative Statics Conclusion

Historical experiment

Simulated Childlessness by Cohort, Married (left) and Singles (right)

5 10 15 20 1870 1890 1910 1930 1950 Involuntary Childlessness (social) Involuntary childlessness (biological) Voluntary childlessness !! married women only 10 20 30 40 50 60 70 80 90 100 1870 1890 1910 1930 1950 Involuntary Childlessness (social) Involuntary childlessness (biological) Voluntary childlessness

Social sterility has disappeared for married, but not for singles

32 / 35

SLIDE 33

Introduction Theory Moments Identification Comparative Statics Conclusion

Childlessness Rate for Different Levels of Inequality (Mincer Coefficient)

0.05 0.1 0.15 0.2 0.25 5 10 15 20

Grey Line is the Benchmark ρ = 0.092 and Dotted Line is the Historical Maximal ρ = 0.126.

33 / 35

SLIDE 34

Introduction Theory Moments Identification Comparative Statics Conclusion

Childlessness Rate & gender wage gap γ

0.05 0.1 0.15 0.2 5 10 15 20

γ = 0.755 (dashed), γ = 0.869 (solid), and γ = 1 (dotted) Usual opportunity cost effect on fertility Drop in Involuntary Childlessness and rise in Voluntary Childlessness

34 / 35

SLIDE 35

Introduction Theory Moments Identification Comparative Statics Conclusion

Conclusion

Distinguish decision to have children from choice of their number New “regimes” of fertility, relevant in the data:

4.8% of American women are involuntarily childless in 1990
8.1% are voluntarily childless

Co-existence of regimes explains U-shaped relationship between childlessness and education (for both married and single women) Marriage interacts with childlessness:

for low skilled woman ⇒ marriage gives more resources to be able to

have children ⇒ reduces involuntary childlessness.

for high skilled women, marriage reduces opportunity cost of having

children ⇒ reduces voluntary childlessness.

Reducing inequality helps fighting social sterility

35 / 35