E ects of Family Composition on Human Capital Formation

Introduction The Problem Identification Data Results Conclude

Effects of Family Composition on Human CapitalFormation: Extensive and Intensive Margins

Stacey H. Chen (Academia Sinica)Yen-Chien Chen (Chinan U.)

with data support fromJin-Tan Liu (National Taiwan U.)

March 27, 2013

Stacey H. Chen (Academia Sinica) Yen-Chien Chen (Chinan U.) with data support from Jin-Tan Liu (National Taiwan U.)

Effects of Family Composition on Human Capital Formation: Extensive and Intensive Margins


MotivationI The ratio of boys to girls at birth in China, India, Taiwan and

South Korea continuously rise even with rapid economicgrowth.

I Domestic inequality between boys and girls remains a relevantissue particularly in regions with cultural preference for boys.

I Social scientists have long been interested in how familycomposition affects human capital formation, but most of theprevious studies focus on one channel – either total number ofchildren (sibsize) or sibling sex composition – taking the otherchannel as absent or fixed.

I Quality and quality trade-off: Rosenzweig and Wolpin(1980), Black, Devereux and Salvanes (2005), Angrist, Lavyand Schlosser (2010)

I Sibling rivalry/spillover: Garg and Moduch (1998), Butcherand Case (1994), Dahl and Moretti (2008),




Motivation

I But these two channels cannot be truly separated in effect,because sibling sex composition affects sibsize if parents prefera specific sibling-sex composition.

I American parents of same-sex siblings tend to have anadditional child (Angrist and Evans 1998).

I Taiwanese parents of two girls have an average of 0.53additional children over those of two boys.

I In this paper we use a decomposition method to distinguishextensive from intensive margins.

I Extensive margin or indirect effect: sibling sex compositionaffects children’s human capital formation, by changing fertilitychoice.

I Intensive margin or direct effect: sibling sex compositionaffects children’s human capital formation, not by changingfertility choice.




The Research Question

I We estimate the effects of family composition on formation ofhuman capital.

I As starter we study only the first child with one or moresiblings. We can extend the model to other parities.

I Human capital formation of the first child (Y ) is measured bythe child’s university attainment or SAT scores.

I Given the firstborn’s gender, family composition is described bythe gender of the next sibling (Boy2nd or B) and the numberof children (or Sibsize or N):

Y = f(B,N,X) + ε

where ε is the error term, and X are covariates.




The Identification Problem

If sibsize (N) and sibling gender (B) are both exogenous and Bdoes not affect N , then an ordinary least squares (OLS)analysis would have worked.

Boy2nd (B)

Sibsize(N)

Education(Y)




The Existing LiteratureSibling rivalry

I Sibling rivalry is conditional on sibsize. Having a son (versus adaughter) may lower parental investment in the other childrenif parents have resource constraints and a preference for sons(Parish-Willis 1993; Garg-Morduch 1998).

Sibling feedback/spilloverI Sibling feedback/spillover is conditional on sibsize. Their

having a brother rather than a sister may increase parents’investment in the sibling because of externalities.

I Gender roles and reference groups: Koch (1955), Butcher-Case(1994), Kaestner’s (1997) reanalysis of the Butcher-Case study

I “Intellectual environment”: Zajonc (1976)

In all of the previous studies, sibling sex composition is taken as anintervention variable, and sibsize an exogenous control variable.




The Existing Literature

Conventional methods require the following assumptions:

(1) The number of children is predetermined, independent ofsibling sex composition.

I But parents with no son are more likely to go on to have anadditional child.

(2) The number of children is exogenousI But sibsize and children’s human capital formation are related

to unobserved parental backgrounds.

(3) There is no sex selective abortion; sibling gender composition isassigned randomly.

I But in regions with strong demand for sons, this assumption istoo strong if ultrasound is widely available.

These limitations have not been resolved in the previous literature.




In this paper

(1) We clarify parameters of interest:I Observed sibsize cannot be fixed, but potential sibsize can be

fixed conceptually.I Pearl’s (2001) and VanderWeele’s (2013) conceptual models

(2) We further apply instrumental-variable methods to correct forthe endogenous mediator or post-intervention variable.

(3) We use a unique administrative data set that coverspre-ultrasound periods and exhibits normal sex ratios.

The key finding: After correcting for endogenous sibsize, we findthe previous estimates are not robust.




Notations

Let Y denote the observed educational outcomes and let N denoteobserved sibsize, N ∈ N ≡ {2, 3, ..., n̄}. We use capital letters todenote random variables, and use lower-case letters to denote theirrealized values.Using Rubin’s (1974) counterfactual notations, we define:

I N0, N1: potential sibsize of the firstborn given the gender ofthe next child b = 0, 1.

I Y0, Y1: potential outcome of the firstborn given the gender ofthe next child b = 0, 1.

I Y0n, Y1n: potential outcome of the firstborn given sibsize nand sibling gender b = 0, 1.




Notations

The relationship between potential and observed outcomes satisfiesthe “consistency” condition (Robins 1987).

Assumption (Consistency)

I N = BN1 + (1−B)N0 and Y = BY1 + (1−B)Y0.

I Y0 = Y0N0 , Y1 = Y1N1 .

Notably, we never observe (Y0N1 , Y1N0).




Notations

The previous literature relies on the condition of randomizedintervention, which we maintain in this paper. For ease ofexposition, we suppress the notation of covariates exogenous Xthroughout the paper although our entire analysis is conditional onX.

Assumption (Randomized Intervention)

Conditional covariates X, we assume:

(a) (Y0, Y1) ⊥ B,

(b) 0 < Pr{B = 1} < 1.




Conventional MeasuresConventional measures for the effect of the gender of the nextchild or the intensive margins (CIM) take observed sibsize N asan exogenous and predetermined covariate. Given N = n, define

CIM(n) ≡ E[Y1 − Y0|N = n]

= E[Y1|B = 1, N = n]− E[Y0|B = 0, N = n]

= E[Y1|B = 1, N1 = n]− E[Y0|B = 0, N0 = n]

= E[Y |B = 1, N = n]− E[Y |B = 0, N = n]

whereI the second equality is because B is a randomized experiment;I the third equality requires consistency and assumes no

extensive margin (N0 = N1 = n), which implicitly assumesthat sibsize is exogenous and predetermined;

I the fourth equation is from consistency.




Problems with the Conventional Measure

The mediator variable Nb cannot be taken as a predeterminedcontrol, because its potential value depends on intervention.

I Angrist and Pischke (2008) call it a “bad-control problem,”

I while Heckman and Vytlacil (2007) a “feedback” issue.

I Griliches and Mason (1972)

I Chamberlain (1977, 1978)




Problems with the Conventional MeasureThe causal-inference literature has noted the problem with theconventional methods:

I Judd (1981) and Robins and Greenland (1992):In the absence of additional assumptions, direct and indirecteffects are not identified even in randomized experiments.

I Pearl (2001):An indirect effect, driven by a change in an intervention, istypically ill-defined in the conventional framework.

I Omission of interactions between the effect of potentialsibsize and the effect of sibling gender while fixing potentialsibsize leads to biased results.

I VanderWeele and Vansteelandt (2009): Conventional methodsthat assume linear models with no interactions are biased.

I VanderWeele (2013) propose decomposition methods usingnon-parametric models.




Initial Assumptions

In this paper we consider a model with a post-treatment variable(N) and a randomized intervention (B), satisfying the followingconditions, in addition to consistency and randomized intervention:

Assumption (Additional Conditions for RandomizedIntervention)

Conditional covariates X, we assume:

(a) (N0, N1) ⊥ B,

(b) (Y0n, Y1n) ⊥ B|(N0, N1),




Redefining Parameters of Interest

We redefine the parameters using the conditional expectationfunction of counter-factual outcomes, given potential sibsize:

I Given sibling gender b = 0 or 1, the intensive margin (orcalled ”direct effect”) is conditional on the potential sibsize n.

IMb(nb) ≡ Y1nb− Y0nb

.

The average intensive margin is averaging over all possiblevalues of potential sibsize n ∈ N , given the probability massfunction of potential sibsize p(n|b) ≡ Pr{Nb = n|b}, given b.

AIMb ≡∑n∈N

(Y1n − Y0n)p(n|b).




Redefining Parameters of InterestI Given sibling gender b = 0 or 1, the extensive margin (or

called ”indirect effect”) is measured by varying the potentialsibsize across sibling genders.

EMb(n0, n1) ≡ Ybn1 − Ybn0 .

The average extensive margin is

AEMb ≡∑n∈N

Ybn[p(n|1)− p(n|0)].

I Notably, unlike the extensive margins, the quality-quantitytrade-off is measured by the effect of an increment in observedsibsize, instead of comparing potential sibsize.

QQb = Yb,n+1 − Ybn,




DecompositionI The total effect is

TE(n0, n1) ≡ Y1n1 − Y0n0 = (Y1n1 − Y0n1) + (Y0n1 − Y0n0)

= IM1(n1) + EM0(n0, n1)

= IM1(n0) + EM1(n0, n1)−∆(n0, n1), (1)

where the adjustment term is the difference in the extensivemargin across sibling genders; that is, an interaction betweensibsize and sibling gender.

∆(n0, n1) ≡ EM1(n0, n1)− EM0(n0, n1).

I Likewise, we can write

TE(n0, n1) = IM0(n0) + EM1(n0, n1)

= IM0(n0) + EM0(n0, n1) + ∆(n0, n1). (2)




Decomposition

I From equations (1) and (2), the decomposition of total effectcan be rewritten as follows, given b = 0 or 1:

TE(n0, n1) = IMb(n0) + EMb(n0, n1) + (1− 2b)∆(n0, n1).

I The average total effect and the average adjustment are

ATE ≡ E[Y1 − Y0] =∑n∈N

[Y1np(n|1)− Y0np(n|0)]

∆̄ ≡ AEM1 −AEM0 =∑n∈N

(Y1n − Y0n)[p(n|1)− p(n|0)]




Bias in Conventional Measure for Intensive Margin

Conventional methods ignore the fact that the mediator variableNb is affected by the intervention variable b. Its definition is givenby observed sibsize and by presuming N1 = N0 = n.

CIM(n) = TE(n, n) = IMb(n) + EMb(n, n) + (1− 2b)∆(n, n)︸︷︷︸Bias

Both equalities are derived by construction.

I The conventional measure CIM is unbiased only if N is notaffected by sibling gender, EM0 = EM1 = 0 = ∆.




Modelling Counterfactuals Given a Binary Mediator

I For purposes of exposition, we focus on the case of a binarymediator, N = MoreThan2 = 0 or 1.

I The method is ready to be extended to cases of a multi- valuedmediator (e.g., Sibsize).

I We can identify AIM and AEM if we can identify Ybn andp(n|b), both of which can be linked to the expecated values ofobservables, by the condition of consistency.

E[Ybn|b, n] = E[Y |b, n]

E[Nb|b] = E[N |b] = Pr{N = 1|b} = p(n|b) ≡ n̄b.




Parameters of interest if no interactionI We first consider a simple model of the counterfactuals Ybn,

where we temporarily assume no interaction between thetreatment and the mediator. Again, we suppress the notationof covariates for ease of exposition.

E[Ybn|b, n] = E[Y |b, n] = β0 + β1n+ β2b.

Greek letters are coefficients.I Given this model, the parameters of interest can be spelled out:

I Average intensive margin AIM0 = AIM1 = CIM = β2.I Average extensive margin AEM0 = AEM1 = β1(n̄1 − n̄0).I If n̄1 = n̄0), then ATE = β1(n̄1 − n̄0) + β2 = β2.I Average adjustment term ∆̄ = 0.

I In this case CIM is an unbiased measure for AIM0 andAIM1.




Adding an interaction between sibsize and sibling gender

Now we consider a model with an interaction term:

E[Ybn|b, n] = E[Y |b, n] = β0 + β1n+ β2b+ β3nb.

The parameters of interest now become the following:

I Conventional measure CIM(n) = β2 + β3n.

I Average intensive margin AIMb = β2 + β3n̄b.

I Average extensive margin AEMb = (β1 + β3b)(n̄1 − n̄0).I Average adjustment term ∆̄ = β3(n̄1 − n̄0).I Average total effect ATE = β1(n̄1 − n̄0) + β2 + β3n̄1.

I Effect of a one-unit change in the mediator on outcomes isβ1 + β3b, not necessarily equal to AEMb, unless n̄1 − n̄0 = 1.




Endogeneity of the Mediator

Identification strategies

When the mediator N (that is, fertility choice) is endogenous,conventional estimation methods are biased. To address this, weuse conventional 2SLS methods to characterize thecounterfacturals:

Ybn = β0 + β1n+ β2b+ β3nb+ V

Nb(z) = α0 + α1z + α2b+ α3zb+ U

where V and U are error terms. Greek letters are coefficients.





Identification strategies

Assume there exists a valid instrument Z = z for the mediatorvariable, satisfying the following assumptions (conditional on X inthe background):

Assumption (Validity of the Instrument)

(a) Independence: ({Ybn}n∈N , {Nb(z)}z∈Z) ⊥ Z, given B = b;

(b) Relevance: E(N |B,Z) = P (B,Z) is a non-degeneratefunction Z, given B.





Identification strategiesI To identify AIM and AEM, we need to derive n̄1,n̄0 andn̄1 − n̄0 from the first-stage estimates:

n̄b = α0 + α1z̄ + α3z̄b

n̄1 − n̄0 = α2 + α3z̄

I Let Nb(z) denote the potential fertility choice, given siblinggender b and instrument z. By a simple extension from Imbensand Angrist’s (1994) results, the average effect of sibsize onoutcome can be identified, given B = b:

E[Yb1 − Yb0|Nb(0) = 0, Nb(1) = 1]

=E[Y |Z = 1, B = b]− E[Y |Z = 0, B = b]

E[N |Z = 1, B = b]− E[N |Z = 0, B = b]




Examples

ExamplesI One important example is the model by Butcher and Case

(1994) and Kaestner (1997), who estimate the effect of siblingsex composition on children’s education.

I This requires an imposition that sibling gender has no effect onsibsize; that is, AEM=0.

I Thus CIM(n̄) = β2 + β3n̄ = TE = AIM.

Anysister

Sibsize

Education




Examples

ExamplesI Another important example is Angrist and Evans (1998). To

identify the effect of fertility choice on parents’ labor supply,they use the Samesex indicator for the first two births toinstrument fertility choice.

I This requires an assumption that Samesex does not affectparental labor supply; that is, AIM=0.

SameSex

MoreThan2

Mother's laborSupply




Examples

ExamplesAngrist & Evans (1998) impose two assumptions:

I β2 = 0: Sibling sex composition does not directly affectparents’ labor supply.

I β3 = 0: The effect of family size on parents’ labor supply doesnot change with sibling sex composition.

But as Angrist & Evans have noted, if parents change the familyenvironment in response to child gender, then exogeneity of thesame-sex instrument is violated. For example, if there is a soninstead of a daughter,

I the mother tends to work less (Rose 2000), the father more(Rose 2000; Lundberg & Rose 2003);

I and the father are less likely to divorce or leave home (Dahl &Moretti 2008; Ananat & Michales 2008).




Examples

Examples

I So SameSex might affect parental labor supply via causalpathways other than MoreThan2. If so, Samesex would bean invalid instrument and the interaction between Samesexand Morethan2 should be taken into account.

I The pathways not through changing fertility choice are the“intensive margins.”

I We estimate the intensive margins using the 5% PUMS sampleof all women from Angrist’s Data Archive, as a test forexogeneity of SameSex. N = 394, 840

I We also test for significance of the interaction betweenSamesex and Morethan2.




Examples

1) Effects of Sex Composition on Fertility Choice

Angrist-Evans (1998)

(1) (2) (3) (4)

2SLS ModelIV for Morethan2 Samesex Twin2nd Twin2nd Twin2nd,

Twin2nd×SamsexControls Boy1st, Boy1st,

Boy2nd Boy2nd Samesex Samesex

1) First stageFertility choice = Morethan2Twin2nd - 0.621 0.622 0.647

(0.008) (0.008) (0.011)Samesex 0.059 - 0.059 0.060

(0.001) (0.001) (0.001)Twin2nd × Samesex - - - -0.051

(0.015)




Examples

2) Effects of Fertility Choice on Mothers’ Weeks Worked


(1) (2) (3) (4)

2SLS ModelIV for Morethan2 Samesex Twin2nd Twin2nd Twin2nd,

Twin2nd×SamsexControls Boy1st, Boy1st,

Boy2nd Boy2nd Samesex Samesex

2) Second StageOutcome= Weeks WorkedMorethan2 -5.711 -3.663 -3.664 -4.138

(1.155) (0.599) (0.598) (0.806)Samesex - - -0.126 2.15

(0.077) (0.283)Morethan2×Samesex - - - -5.213

(0.746)




Examples

Decompose the Sibling-Gender Effect on Mothers’ WeeksWorked


(1) (2) (3) (4)

3)Decompose the same-sex effectExtensive margin, given Samesex=0 -0.338 -0.338 -0.216 -0.245

(0.069) (0.069) (0.036) (0.048)Extensive margin, given Samesex=1 -0.338 -0.338 -0.216 -0.553

(0.069) (0.069) (0.036) (0.015)Intensive margin, fixing n0 - - -0.126 0.211

(0.077) (0.069)Intensive margin, fixing n1 - - -0.126 -0.100

(0.077) (0.083)Adjust for interaction - - - -0.308

(0.045)Total effect, given covariates -0.338 -0.338 -0.342 -0.346

(0.069) (0.069) (0.069) (0.069)




Data

I Large and detailed data is a prerequisite for identifying thecausal effects of sibling gender and family size.

I We use 2 national administrative data sets covering all ofTaiwan:

I Birth Registry (1978-1999)I University Entrance Test records (1996-2003)

I The Birth Registry was linked to University Entrance Testrecords by using children’s unique ID numbers.

I Education Outcomes:I admitted to university at age 18,I high school completion, which we use ”taking SAT tests” as a

proxy for since most of graduating seniors take the tests.




Data

I Analysis sample:I First-borns with at least one sibling⇒ We control for birth order

I Born prior to 1985, when access to ultrasound was limited.⇒ We addressed the issue of endogenous child gender

I Sex ratio of first-borns = 1.039 - 1.042.I Sex ratio of second-borns = 1.064 - 1.065.I The F-statistic for the regression of the sex of second-born on

family backgrounds was small and insignificant.

I Complete family size: We trace each mother who had the firstbaby between 1978 and 1984 for 15 to 22 years. No baby wasborn to the mothers in our sample in 1997-1998.




Characteristics of the Firstborn Sample

Mean of firstborn singletons who have at least one sibling (part 1)

Born in 1978-1984 Born in 1978-1979

Next siblingborn by 1985

Sample size 833,371 358,177 336,828Sex-ratio of boys to girls 1.045 1.047 1.046Sex-ratio of the next sibling 1.070 1.069 1.068Birth years of the next siblings 1984 1981 1981Complete family size 2.696 2.784 2.814Twins at 2nd birth 0.007 0.006 0.006Subject’s birth weight (kg) 3.212 3.223 3.223Urban (place of birth) 0.337 0.340 0.333Mother’s age at first birth 23.5 23.2 23.2Mother’s year of birth 1958 1956 1956Father’s year of birth 1954 1952 1952




Characteristics of the Firstborn SampleMean of firstborn singletons who have at least one sibling (part 2)

Born in 1978-1984 Born in 1978-1979

Next siblingAll born by 1985

5-yrs avg taxable income per 728,791 726,922 723,397capita in village

Mother’s highest degreeCollege/professional deg. or + 0.069 0.064 0.061HS diploma 0.061 0.053 0.052Vocational HS 0.187 0.161 0.158Junior HS 0.261 0.214 0.214Father’s highest degreeCollege degree or above 0.063 0.061 0.058Professional degree 0.073 0.067 0.066HS diploma 0.092 0.088 0.086Vocational HS 0.181 0.160 0.160Junior HS 0.237 0.187 0.187

Other covariates: dummies for the subject’s age, parental ages, and themother’s age at first birth.




Strong Demand for SonsEffect of Sibling Sex Composition on Sibsize

All firstborns Mother finished

(1) (2) (3) junior HS or above

Two girls 0.5376 0.5375 0.5363 0.4098(0.0024) (0.0024) (0.0024) (0.0035)

Mixed gender 0.1007 0.1008 0.1 000 0.0613(0.0018) (0.0018) (0.0018) (0.0025)

Born in urban -0.1782 -0.0757 -0.0913 -0.0714(0.0017) (0.0021) (0.0020) (0.0029)

Ln(taxable income per -0.3717 -0.2441 -0.1574capital in village) (0.0044) (0.0044) (0.0059)

Parental education Yes Yes

Sample size 833,371 833,371 833,371 264,105R-squared adjusted 0.15 0.16 0.18 0.13

Sample size = 833,371. Other covariates: dummies for urban, parentalages and maternal age at first birth.




Instrument for Sibsize

Robins and Greenland (1992), Cole and Hernan (2002) andVanderWeele (2010) have noted that with an endogenousmediator, identification of extensive and intensive margins cannotbe achieved by using data on the triplet (Y,B,N) alone. In thispaper we introduce conventional Instrumental-Variable methods tothe causal-inference literature by bring in a “fourth” variable,which is the instrument for the mediator.




Instrument for Sibsize

Twins at the second birth (Rozensweig and Wolpin, 1980)

I Potential issues: Compared to singletons, twins are lighter andlive shorter on average.

I After controlling for birth weight, college enrolment rates oftwins and singletons are about the same (see figures 2a and2b).

I We include birthweight in X, as Rosenzweig and Zhang (2009)have suggested, to tackle the concern on the endowmentdeficit of twins.

I Black, Devereux and Salvanes (2007) find similar results usingdata from Norway.




Figure 2a: Firstborn Girls’ College Enrolment Rate, GivenBirth Weight

0.0

5.1

.15

.2 P

roba

bilit

y of

ent

erin

g a

colle

ge

1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 4.75 5Birth weight

Twin Singleton

College outcome by birth weights(kg) for first−born girls

Data: Taiwanese Birth Registry 1978-1984, firstborn girlsStacey H. Chen (Academia Sinica) Yen-Chien Chen (Chinan U.) with data support from Jin-Tan Liu (National Taiwan U.)



Figure 2b: Firstborn Boys’ College Enrolment Rate, GivenBirth Weight

0.0

5.1

.15

.2 P

roba

bilit

y of

ent

erin

g a

colle

ge

1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 4.75 5Birth weight

Twins Singleton

College outcome by birth weights(kg) for first−born boys

Data: Taiwanese Birth Registry 1978-1984, firstborn boysStacey H. Chen (Academia Sinica) Yen-Chien Chen (Chinan U.) with data support from Jin-Tan Liu (National Taiwan U.)



Sample Mean by Firstborn Gender (part 1)

Firstborn girls Firstborn boys

Sample size 407,467 425,904

Random TreatmentNext sibling is male (Boy2nd=1) 0.52 0.52

Endogenous post-treatmentMore than 2 children (Morethan2=1) 0.60 0.46Sibsize 2.83 2.57

Instrument for fertilityTwinning at 2nd birth 0.007 0.006

Outcome variables:Admitted to univ. 0.17 0.15High school completion .24 .23




Sample Mean by Firstborn Gender (part 2)Control variables: Firstborn girls Firstborn boys

Birth weight 3.16 3.26Born in urban 0.34 0.34Mother’s year of birth 1957 1958Mother’s age at first birth 23.49 23.46Father’s year of birth 1954 1954Taxable income per capita (1000) 729.33 728.28Mother’s highest degreeCollege/professional degree or + 0.07 0.07HS diploma 0.06 0.06Vocational HS 0.19 0.19Junior HS 0.26 0.26Father’s highest degreeCollege degree of above 0.06 0.06Professional degree 0.07 0.07HS diploma 0.09 0.09Vocational HS 0.18 0.18Junior HS 0.24 0.24




Outline of the main results

Sample = Families with at least two children

(1) First Stage (for endogenous fertility choice):I Dependent variable =Morethan2 or SibsizeI Relevance of the instrument, Twinning at 2nd birth (Twin2nd)I Key covariate = having a 2nd-born brother (Boy2nd)

(2) Second Stage (effects of fertility choice on child outcomes):I Education variables = Admitted to university, HS completionI Effect of fertility choice on the fristborn’s educationI Effect of having Boy2nd on the firstborn’s education

(3) Decompose the effect of sibling gender on educationI Total effectI Extensive and intensive marginI Adjustment for interaction between potential sibsize and sibling

gender.




(1) First-Stage Estimates (Fertility Choice)

More than two kids Sibsize

(1) (2) (3) (4) (5)

Firstborn girlsTwinning at 2nd (Twin2nd) 0.444 0.306 0.306 0.652 0.671

(0.008) (0.013) (0.013) (0.015) (0.023)Next sibling is male (Boy2nd) -0.220 -0.222 -0.222 -0.438 -0.438

(0.001) (0.001) (0.001) (0.002) (0.002)Twin2nd× Boy2nd 0.234 0.234 -0.031

(0.017) (0.017) (0.030)Birthweight -0.015 -0.032

(0.002) (0.003)

N=407,467. Standard errors in (.). Other covariates include parental age,mother’s age at first birth, subject’s age, birthplace, urban dummy, andlogarithm of taxable income per capita of birth village.




(1) First-Stage Estimates (Fertility Choice)

More than two kids Sibsize

(1) (2) (3) (4) (5)

Firstborn boysTwinning at 2nd (Twin2nd) 0.566 0.530 0.530 0.723 0.721

(0.009) (0.014) (0.014) (0.013) (0.020)Next sibling is male (Boy2nd) -0.064 -0.064 -0.064 -0.102 -0.102

(0.001) (0.001) (0.001) (0.002) (0.002)Twin2nd× Boy2nd 0.065 0.065 0.005

(0.018) (0.018) (0.026)Birthweight -0.023 -0.039

(0.002) (0.002)

N=425,904. Standard errors in (.). Other covariates include parental age,mother’s age at first birth, subject’s age, birthplace, urban dummy, andlogarithm of taxable income per capita of birth village.




(2) Outcome equation (Admitted to University)OLS 2SLS

Interact Interact Birthweight

Firstborn girlsMore than 2 kids (Morethan2) -0.0140 -0.0101 -0.0322 -0.0837 -0.0855

(0.0013) (0.0018) (0.0152) (0.0348) (0.0348)Next sibling is male (Boy2nd) -0.0011 0.0031 -0.0051 -0.0470 -0.0484

(0.0012) (0.0019) (0.0035) (0.0238) (0.0238)Morethan2×Boy2nd -0.0068 0.0626 0.0646

(0.0024) (0.0329) (0.0329)Birthweight 0.0185

(0.0013)Firstborn boysMore than 2 kids (Morethan2) -0.0181 -0.0153 -0.0126 -0.0194 -0.0197

(0.0011) (0.0016) (0.0115) (0.0190) (0.0190)Next sibling is male (Boy2nd) -0.0007 0.0019 -0.0003 0.0000 -0.0003

(0.0010) (0.0014) (0.0013) (0.0090) (0.0090)Morethan2×Boy2nd -0.0056 -0.0017 -0.0011

(0.0021) (0.0179) (0.0179)Birthweight 0.0171

(0.0012)




(3) Decompose the effect on college education

OLS 2SLS

Firstborn girls Interact Interact Birthweight

If next sibling is female:fertility channel AEM0 0.0031 0.0022 0.0071 0.0184 0.0188

(0.0003) (0.0004) (0.0033) (0.0077) (0.0077)non-fertility channel AIM0 -0.0011 -0.0017 -0.0051 -0.0026 -0.0026

(0.0012) (0.0012) (0.0035) (0.0012) (0.0012)If next sibling is male:fertility channel AEM1 0.0031 0.0037 0.0071 0.0046 0.0046


(0.0012) (0.0012) (0.0035) (0.0078) (0.0077)Adjust for interaction 0.0015 -0.0138 -0.0142

(0.0005) (0.0072) (0.0072)Total effect 0.0020 0.0020 0.0020 0.0022 0.0021

(0.0011) (0.0011) (0.0011) (0.0011) (0.0011)




(3) Decompose the effect on college education

OLS 2SLS

Firstborn boys Interact. Interact. Birthweight

If next sibling is female:fertility channel AEM0 0.0012 0.0010 0.0008 0.0012 0.0013


(0.0010) (0.0011) (0.0013) (0.0011) (0.0011)If next sibling is male:fertility channel AEM1 0.0012 0.0013 0.0008 0.0013 0.0013


(0.0010) (0.0011) (0.0013) (0.0016) (0.0016)Adjust for interaction 0.0004 0.0001 0.0001

(0.0001) (0.0011) (0.0011)Total effect 0.0005 0.0005 0.0005 0.0005 0.0005

(0.0010) (0.0010) (0.0010) (0.0010) (0.0010)




2SLS Estimates of the Effects on Education

Mother has JHS diploma

Firstborn girls Admitted HS Admitted HSto univ. completion to univ. completion

Outcome mean 0.173 0.241 0.306 0.414

More than 2 kids (Morethan2) -0.0855 -0.1084 -0.1327 -0.1998(0.0348) (0.0386) (0.0493) (0.0523)

Next sibling is male (Boy2nd) -0.0484 -0.0621 -0.0645 -0.0990(0.0238) (0.0264) (0.0269) (0.0285)

Morethan2×Boy2nd 0.0646 0.0810 0.1037 0.1638(0.0329) (0.0365) (0.0474) (0.0503)

Sample size 407,467 407,467 129,287 129,287




DecompositionMother has JHS diploma

Admitted HS Admitted HSFirstborn girls to univ. completion to univ. completion

If next sibling is female:fertility channel AEM0 0.0188 0.0239 0.0320 0.0481

(0.0077) (0.0085) (0.0119) (0.0126)non-fertility channel AIM0 -0.0026 -0.0047 -0.0068 -0.0079

(0.0012) (0.0014) (0.0027) (0.0029)If next sibling is male:fertility channel AEM1 0.0046 0.0060 0.0070 0.0087

(0.0006) (0.0006) (0.0010) (0.0011)non-fertility channel AIM1 -0.0169 -0.0225 -0.0318 -0.0474

(0.0077) (0.0086) (0.0121) (0.0128)Adjust for interaction -0.0142 -0.0178 -0.0250 -0.0395

(0.0072) (0.0080) (0.0114) (0.0121)Total effect 0.0020 0.0013 0.0002 0.0007

(0.0011) (0.0013) (0.0025) (0.0027)




Summary of the Main Results (1/2)

I The total effects of having a brother on firstborn girls’/boys’university entry are marginal and insignificant, because theextensive and intensive margins typically have opposite signscancelling each other.

I Results are very sensitive to inclusion of the interactionbetween sibsize and sibling gender.




Summary of the Main Results (2/2)

I For firstborn boys, all margins are nearly zero.I For firstborn girls:

I Extensive margins (via reduced sibsize) are significantlypositive, while intensive margins are negatively small throughmarginally significant.

I If the interaction is ignored, we understand the extensivemargins.

I If the second born is female, it’s likely to be a larger family.The effect of having a brother via changing the sibsize is large.

I If the second born is male, it’s likely to be a smaller family. Theeffect of having a brother via changing the sibsize is small.

I But in smaller families, the direct effect of having a brother(i.e., intensive margin) is larger for girls.




Concluding remarks

I We clarified the parameters of interest, pointing out thepost-intervention bias in the previous estimators.

I We used instrumental-variable methods to address theendogenous post-treatment variable (family size).

I We applied the new method to examine the identificationassumption of Angrist and Evans (1998).

I We constructed a unique administrative database minimallyaffected by sex-selective abortion.

I We introduced new outcomes variables – university attainmentand high school completion – to measure the long-term impactof having a brother on human capital formation.




Concluding remarksI We pointed to alternative pathways - intensive margin, less

emphasized in the previous literature, for sibling gender to havean impact, namely, parental behavioural changes that alterfamily environments.

I We examined Goodkind’s (1996) hypothesis in a carefulempirical design.

I Goodkind hypothesized that pre-natal sex-selective abortionsubstitutes post-natal sex discrimination.

I Although pre-natal sex-selective abortion was not legallypermitted during the sample period, parents in Taiwan havefreely implemented their pro-male biased fertility-stopping rulebecause of no One-Child policy.

I The total effect of having a brother relative to a sister is closeto zero because the positive effect due to the extensive margincancel out a negative effect due to the intensive margin and anegative effect due to a decrease in the extensive margin.



Documents

E ects of Family Composition on Human Capital Formation