Introduction Background Theory Empirical strategy Results Robustness Conclusion

Sex-Ratio Imbalance and Premarital Investments:

The Implications of Imperfect Commitment

V. Bhaskar Wenchao Li Junjian Yi

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Premarital investments in children

Imperfect commitment within marriage

• Bargaining power before/after marriage• Before: high power of women due to abundance of men in China• After: low power of women due to prohibitively costly divorce

• Control over different capital• Future labor income: by ex post bargaining• Public goods (property rights can be easily allocated, e.g., a

house): consuming without bargaining

Implications for families with boys when sex ratio is high

1. Total level of premarital investments ↑2. Composition

• Bequeathed physical capital ↑• Human capital ↓

in order to signal a credible commitment

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Theoretical predictions borne out in empirical analysis

For son families relative to daughter families, a 0.1 increase in sexratio associated with

1. a 24.1% higher probability of having a migrant father2. a 4.1% larger increase in house construction area3. a 11.0% larger decline in annual education expenditure per child

Mean increase in sex ratio in China from 2002 to 2010 is 0.1

Literature

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Sex ratio in China rises drastically in recent decadesamong second- and higher-order births

.5.6

.7.8

Mal

e fr

actio

n

1970-1974 1975-1979 1980-1984 1985-1989 1990-1994 1995-2000Year of birth

1st Birth 2nd Birth 3rd Birth

Figure: Male Fraction of Births by Birth Order in China

Source: Ebenstein (2010)3 / 21

Introduction Background Theory Empirical strategy Results Robustness Conclusion

Background

1. Sex-ratio imbalance and marriage market competition

• Sex ratio at birth increased from 1.12 in 1990 to 1.2 in 2000

• Higher sex ratio, larger marriage expenditure Evidence

• Grooms’ families spending more on marriage over time Evidence

2. Premarital physical capital investment: housing

• The largest purchase of bequeathed physical capital for groomfamilies as a prerequisite for marriage

• Dominant role in household wealth composition

• Marriage premium of housing is higher than education for menHousing, education, and marital status of males

3. Imperfect commitment within marriageLow divorce rates

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Baseline model

W = U(zj , `j) + θjV (xj , yj), j ∈ {S,D} (1)

subject to budget constraint

zj ≤ w`j − c(xj)− yj (2)

• Parents’ utility U ; child utility V (j = S for son, D for daughter)

• Human capital investment (private good) xj ; physical capitalinvestment (public good) yj ; parental consumption zj ; labor supply `j

• Labor earning of man xS + ε, ε ∼ F ; that of woman xD + η, η ∼ G

Payoffs of husband and wife when (xS + ε, yS) marries (xD + η, yD)

λS(xS + ε) + (1− λD)(xD + η) + v(yS + yD) (3)

λD(xD + η) + (1− λS)(xS + ε) + v(yS + yD) (4)

• Public goods of (yS + yD), valued by each at v(yS + yD)

• Private goods based on asymmetric Nash bargaining

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

First-order conditions

• Quasi-symmetric equilibrium: (x∗j , y∗j ), z∗j , and `∗j

• Matching function φ(ε) : F (ε) = G(φ(ε)), f = g

• U is Cobb-Douglas,

U(zj , `j) = α ln zj + β ln(T − `j) (5)

where T is total parental time endowment

FOC for investments in public and private goods

θjv′(y∗S + y∗D)

[

1 +(1− λ−j)(1− λj)

]

=α

z∗j=

β

w(T − `∗j

) = µj (6)

θj [λj + (1− λ−j)] = µjc′(x∗j ) (7)

where µj is Lagrange multiplier on parental budget constraint

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

When sex ratio is biased towards males

Measure of women is r < 1, measure of men is 1

• Matching function φ(ε, r) : 1− F (ε) = r [1−G(φ(ε, r))]

• f and g are uniform and equal, k is common value of densities

Prediction

A male-biased sex ratio induces parents of boys, relative to those ofgirls, to

1. Supply more labor

2. Invest more in physical capital

3. Invest less in child’s human capital

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

First-order conditions• Investments in public and private goods for son families

θS

{

rv′(y∗S + y∗D)

[

1 +(1− λD)

(1− λS)

]

+ (1− r)v′(y∗S)

+k

1− λS

[v(y∗S + y∗D)− v(y∗S) + (1− λD) (η + x∗D)− (u+ x∗S)

]}

= µS

(8)

θS{

(1− r) + rλS + (1− λD)r

+k[v(y∗S + y∗D)− v(y∗S) + (1− λD) (η + x∗D)− (u+ x∗S)

] }= µSc

′(x∗S)(9)

where u is a payoff received by an unmarried man

• Investments in public and private goods for daughter families

θD

{

v′(y∗S + y∗D)

[

1 +(1− λS)

(1− λD)r

]}

= µD (10)

θD [λD + (1− λS)r] = µDc′(x∗D) (11)

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Data source: China Family Panel Studies (CFPS)

2010 baseline survey

• Nationally representative of Chinese individuals, households, andcommunities

• 25 provinces, 95% of total population

Sample

• Cross section: persistency of local sex-ratio imbalances

• First-born children: 0–15 years old

Main outcome variables

1. Parental migration (`) Migration increases income

2. Housing investment (y)

3. Child educational investment (x)Summary statistics

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Regression specification

kic = β0 + β1first sonic + β3first sonic ∗ sex ratioc +XicΓ + λc + εic

• County-specific sex ratio for premarital-age cohort 10–24

Hypotheses

1. β3 > 0 for parental migration

2. β3 > 0 for housing investment

3. β3 < 0 for child educational investment

Estimation method: OLS

• Randomness of first-child genderSex ratio of first-born children is normal A balance test

• Sex ratioPotential endogeneity

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Parental migration

0.1

.2.3

.4.5

Pat

erna

l mig

ratio

n fr

ac.

1 1.1 1.2 1.3 1.4 1.5Sex ratio

First-son families

0.2

.4.6

Pat

erna

l mig

ratio

n fr

ac.

1 1.1 1.2 1.3 1.4 1.5Sex ratio

First-daughter families

Figure: County-Level Sex Ratio and Paternal Migration in China

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Parental migration

Table: Parental Migration

Intended purpose of migration remittances

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Premarital investments

78

910

1112

Hou

sing

mor

tgag

e

1 1.1 1.2 1.3 1.4 1.5Sex ratio

First-son families

89

1011

1213

Hou

sing

mor

tgag

e

1 1.1 1.2 1.3 1.4 1.5Sex ratio

First-daughter families

Figure: County-Level Sex Ratio and Housing Mortgage in China

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Premarital investments

020

0040

0060

0080

00E

duca

tion

expe

nditu

re

1 1.1 1.2 1.3 1.4 1.5Sex ratio

First-son families

050

0010

000

1500

020

000

Edu

catio

n ex

pend

iture

1 1.1 1.2 1.3 1.4 1.5Sex ratio

First-daughter families

Figure: County-Level Sex Ratio and Education Expenditure in China

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Premarital investments

Table: Premarital Investments

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Children’s human capital outcomes

Human capital development of boys undermined due to

• Parents working outside hometown Migration hampers child development

• Underinvestment in education

Trends in high school enrollment rate

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Robustness: son-preferring fertility stopping rulesChinese families more likely to stop childbearing if they have a son

1. Family-size effect

2. Child gender composition

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Robustness: potential endogeneity of sex ratio

1. Unobservable cross-county heterogeneity

2. Son preferences

3. Family planning policy

4. Gender-screening technology

5. IV estimations

6. Sex ratios for alternative age cohorts

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Table: Robustness Checks: Instrumental Variable Estimations

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Robustness: mechanism of marriage market competitionand imperfect commitment

Alternative mechanisms

1. Return to housing investment

2. Wealth effect

3. Grandparental coresidence

4. Status seeking

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Table: Robustness Checks: Potential Endogeneity of Sex Ratio andAlternative Mechanisms

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Conclusion

• Imperfect commitment combines with sex-ratio imbalance toaffect magnitude and composition of parental investments

• Distinction between physical vs. human capital investment

• Empirical evidence from CFPS

Implications for study of marriage

• Marriage matching along multiple dimensions

Potential limitations

• Implicit modelling of after-marriage bargaining process

• Quasi-experimental variations in sex ratios not fully isolated

• Alternative explanations

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Introduction Background Theory Empirical strategy Results Robustness Conclusion

Thank you!

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Literature

• Premarital investments1. Full commitment : Becker (1973), Cole et al. (2001), Iyigun and

Walsh (2007), Lafortune (2013), Chiappori et al. (2009)2. Imperfect commitment : Lundberg and Pollak (1993, 1996), Pollak

(1985), Peters and Siow (2002), Bhaskar and Hopkins (2016)

• Marriage payments as a commitment device (theory)• Nunn (2005), Anderson and Bidner (2015)

• Effects of imperfect commitment on householdintertemporal decisions (empirics)• Mazzocco (2007), Voena (2015)

• Imbalance of sex ratio and its implications• Wei and Zhang (2011)

Back

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05

1015

Mar

riage

exp

endi

ture

(lo

g)

.9 1 1.1 1.2 1.3Sex ratio

Figure: County-Level Sex Ratio and Marriage Expenditure in China

Back

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1000

3000

5000

7000

9000

1100

0M

arria

ge e

xpen

ditu

re

11.

051.

11.

15S

ex r

atio

1996 1998 2000 2002 2004 2006Year

Sex ratio Grooms Brides

Figure: Trends in Sex Ratio and Marriage Expenditure in China

Back

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-.05

-.03

-.01

.01

.03

.05

Diff

. in

high

sch

ool e

nrol

lmen

t rat

e, M

-F

1.05

1.1

1.15

1.2

Sex

rat

io

2000 2002 2004 2006 2008 2010Year

Sex ratio Gender difference in education

Figure: Trends in Sex Ratio and Gender Difference in Education in China

Back

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Table: Summary Statistics of Outcome Variables

Back26 / 21

Table: Balance Test: First-Son versus Fist-Daughter Families

Back 27 / 21

Table: Marriage Status by Age, Gender, and Education Level

Back

28 / 21

Table: Housing, Education, and Marital Status of Males

Back

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Table: Parental Migration and Gross Family Income

Back

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Table: Intended Purpose of Migration Remittances

Back

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Table: Parental Migration and Child Development

Back32 / 21