Introduction
The Problem
Identification
Data
Results
Conclude
Effects of Family Composition on Human Capital
Formation: Extensive and Intensive Margins
Stacey H. Chen (Academia Sinica)
Yen-Chien Chen (Chinan U.)
with data support from
Jin-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
Introduction
The Problem
Identification
Data
Results
Conclude
Motivation
I
I
I
The ratio of boys to girls at birth in China, India, Taiwan and
South Korea continuously rise even with rapid economic
growth.
Domestic inequality between boys and girls remains a relevant
issue particularly in regions with cultural preference for boys.
Social scientists have long been interested in how family
composition affects human capital formation, but most of the
previous studies focus on one channel – either total number of
children (sibsize) or sibling sex composition – taking the other
channel as absent or fixed.
I
I
Quality and quality trade-off: Rosenzweig and Wolpin
(1980), Black, Devereux and Salvanes (2005), Angrist, Lavy
and Schlosser (2010)
Sibling rivalry/spillover: Garg and Moduch (1998), Butcher
and Case (1994), Dahl and Moretti (2008),
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
Introduction
The Problem
Identification
Data
Results
Conclude
Motivation
I
But these two channels cannot be truly separated in effect,
because sibling sex composition affects sibsize if parents prefer
a specific sibling-sex composition.
I
I
I
American parents of same-sex siblings tend to have an
additional child (Angrist and Evans 1998).
Taiwanese parents of two girls have an average of 0.53
additional children over those of two boys.
In this paper we use a decomposition method to distinguish
extensive from intensive margins.
I
I
Extensive margin or indirect effect: sibling sex composition
affects children’s human capital formation, by changing fertility
choice.
Intensive margin or direct effect: sibling sex composition
affects children’s human capital formation, not by changing
fertility choice.
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
Introduction
The Problem
Identification
Data
Results
Conclude
The Research Question
I
I
I
I
We estimate the effects of family composition on formation of
human capital.
As starter we study only the first child with one or more
siblings. We can extend the model to other parities.
Human capital formation of the first child (Y ) is measured by
the child’s university attainment or SAT scores.
Given the firstborn’s gender, family composition is described by
the gender of the next sibling (Boy2nd or B) and the number
of children (or Sibsize or N ):
Y = f (B, N, X) + where is the error term, and X are covariates.
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
Introduction
The Problem
Identification
Data
Results
Conclude
The Identification Problem
If sibsize (N) and sibling gender (B) are both exogenous and B
does not affect N , then an ordinary least squares (OLS)
analysis would have worked.
Boy2nd
(B)
Education
(Y)
Sibsize
(N)
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
Introduction
The Problem
Identification
Data
Results
Conclude
The Existing Literature
Sibling rivalry
I Sibling rivalry is conditional on sibsize. Having a son (versus a
daughter) may lower parental investment in the other children
if parents have resource constraints and a preference for sons
(Parish-Willis 1993; Garg-Morduch 1998).
Sibling feedback/spillover
I 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
I
Gender roles and reference groups: Koch (1955), Butcher-Case
(1994), Kaestner’s (1997) reanalysis of the Butcher-Case study
“Intellectual environment”: Zajonc (1976)
In all of the previous studies, sibling sex composition is taken as an
intervention variable, and sibsize an exogenous control variable.
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
Introduction
The Problem
Identification
Data
Results
Conclude
The Existing Literature
Conventional methods require the following assumptions:
(1) The number of children is predetermined, independent of
sibling sex composition.
I
But parents with no son are more likely to go on to have an
additional child.
(2) The number of children is exogenous
I
But sibsize and children’s human capital formation are related
to unobserved parental backgrounds.
(3) There is no sex selective abortion; sibling gender composition is
assigned randomly.
I
But in regions with strong demand for sons, this assumption is
too strong if ultrasound is widely available.
These limitations have not been resolved in the previous literature.
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
Introduction
The Problem
Identification
Data
Results
Conclude
In this paper
(1) We clarify parameters of interest:
I
I
Observed sibsize cannot be fixed, but potential sibsize can be
fixed conceptually.
Pearl’s (2001) and VanderWeele’s (2013) conceptual models
(2) We further apply instrumental-variable methods to correct for
the endogenous mediator or post-intervention variable.
(3) We use a unique administrative data set that covers
pre-ultrasound periods and exhibits normal sex ratios.
The key finding: After correcting for endogenous sibsize, we find
the previous estimates are not robust.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Notations
Let Y denote the observed educational outcomes and let N denote
observed sibsize, N ∈ N ≡ {2, 3, ..., n̄}. We use capital letters to
denote random variables, and use lower-case letters to denote their
realized values.
Using Rubin’s (1974) counterfactual notations, we define:
I N0 , N1 : potential sibsize of the firstborn given the gender of
the next child b = 0, 1.
I Y0 , Y1 : potential outcome of the firstborn given the gender of
the next child b = 0, 1.
I Y0n , Y1n : potential outcome of the firstborn given sibsize n
and sibling gender b = 0, 1.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Notations
The relationship between potential and observed outcomes satisfies
the “consistency” condition (Robins 1987).
Assumption (Consistency)
I
I
N = BN1 + (1 − B)N0 and Y = BY1 + (1 − B)Y0 .
Y0 = Y0N0 , Y1 = Y1N1 .
Notably, we never observe (Y0N1 , Y1N0 ).
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
Introduction
The Problem
Identification
Data
Results
Conclude
Notations
The previous literature relies on the condition of randomized
intervention, which we maintain in this paper. For ease of
exposition, we suppress the notation of covariates exogenous X
throughout the paper although our entire analysis is conditional on
X.
Assumption (Randomized Intervention)
Conditional covariates X, we assume:
(a) (Y0 , Y1 ) ⊥ B,
(b) 0 < P r{B = 1} < 1.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Conventional Measures
Conventional measures for the effect of the gender of the next
child or the intensive margins (CIM) take observed sibsize N as
an 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]
where
I 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 assumes
that sibsize is exogenous and predetermined;
I the fourth equation is from consistency.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Problems with the Conventional Measure
The mediator variable Nb cannot be taken as a predetermined
control, 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)
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
Introduction
The Problem
Identification
Data
Results
Conclude
Problems with the Conventional Measure
The causal-inference literature has noted the problem with the
conventional methods:
I Judd (1981) and Robins and Greenland (1992):
In the absence of additional assumptions, direct and indirect
effects are not identified even in randomized experiments.
I Pearl (2001):
An indirect effect, driven by a change in an intervention, is
typically ill-defined in the conventional framework.
I Omission of interactions between the effect of potential
sibsize and the effect of sibling gender while fixing potential
sibsize leads to biased results.
I
I
VanderWeele and Vansteelandt (2009): Conventional methods
that assume linear models with no interactions are biased.
VanderWeele (2013) propose decomposition methods using
non-parametric models.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Initial Assumptions
In this paper we consider a model with a post-treatment variable
(N ) and a randomized intervention (B), satisfying the following
conditions, in addition to consistency and randomized intervention:
Assumption (Additional Conditions for Randomized
Intervention)
Conditional covariates X, we assume:
(a) (N0 , N1 ) ⊥ B,
(b) (Y0n , Y1n ) ⊥ B|(N0 , N1 ),
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
Introduction
The Problem
Identification
Data
Results
Conclude
Redefining Parameters of Interest
We redefine the parameters using the conditional expectation
function of counter-factual outcomes, given potential sibsize:
I Given sibling gender b = 0 or 1, the intensive margin (or
called ”direct effect”) is conditional on the potential sibsize n.
IMb (nb ) ≡ Y1nb − Y0nb .
The average intensive margin is averaging over all possible
values of potential sibsize n ∈ N , given the probability mass
function of potential sibsize p(n|b) ≡ P r{Nb = n|b}, given b.
X
AIMb ≡
(Y1n − Y0n )p(n|b).
n∈N
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
Introduction
The Problem
Identification
Data
Results
Conclude
Redefining Parameters of Interest
I
Given sibling gender b = 0 or 1, the extensive margin (or
called ”indirect effect”) is measured by varying the potential
sibsize across sibling genders.
EMb (n0 , n1 ) ≡ Ybn1 − Ybn0 .
The average extensive margin is
X
AEMb ≡
Ybn [p(n|1) − p(n|0)].
n∈N
I
Notably, unlike the extensive margins, the quality-quantity
trade-off is measured by the effect of an increment in observed
sibsize, instead of comparing potential sibsize.
QQb = Yb,n+1 − Ybn ,
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
Introduction
The Problem
Identification
Data
Results
Conclude
Decomposition
I
The total effect is
T E(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 extensive
margin across sibling genders; that is, an interaction between
sibsize and sibling gender.
∆(n0 , n1 ) ≡ EM1 (n0 , n1 ) − EM0 (n0 , n1 ).
I
Likewise, we can write
T E(n0 , n1 ) = IM0 (n0 ) + EM1 (n0 , n1 )
= IM0 (n0 ) + EM0 (n0 , n1 ) + ∆(n0 , n1 ). (2)
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
Introduction
The Problem
Identification
Data
Results
Conclude
Decomposition
I
From equations (1) and (2), the decomposition of total effect
can be rewritten as follows, given b = 0 or 1:
T E(n0 , n1 ) = IMb (n0 ) + EMb (n0 , n1 ) + (1 − 2b)∆(n0 , n1 ).
I
The average total effect and the average adjustment are
X
AT E ≡ E[Y1 − Y0 ] =
[Y1n p(n|1) − Y0n p(n|0)]
n∈N
¯ ≡ AEM1 − AEM0 =
∆
X
(Y1n − Y0n )[p(n|1) − p(n|0)]
n∈N
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
Introduction
The Problem
Identification
Data
Results
Conclude
Bias in Conventional Measure for Intensive Margin
Conventional methods ignore the fact that the mediator variable
Nb is affected by the intervention variable b. Its definition is given
by observed sibsize and by presuming N1 = N0 = n.
CIM (n) = T E(n, n) = IMb (n) + EMb (n, n) + (1 − 2b)∆(n, n)
{z
}
|
Bias
Both equalities are derived by construction.
I The conventional measure CIM is unbiased only if N is not
affected by sibling gender, EM0 = EM1 = 0 = ∆.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Modelling Counterfactuals Given a Binary Mediator
I
I
I
For purposes of exposition, we focus on the case of a binary
mediator, N = M oreT han2 = 0 or 1.
The method is ready to be extended to cases of a multi- valued
mediator (e.g., Sibsize).
We can identify AIM and AEM if we can identify Ybn and
p(n|b), both of which can be linked to the expecated values of
observables, by the condition of consistency.
E[Ybn |b, n] = E[Y |b, n]
E[Nb |b] = E[N |b] = P r{N = 1|b} = p(n|b) ≡ n̄b .
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
Introduction
The Problem
Identification
Data
Results
Conclude
Parameters of interest if no interaction
I
We first consider a simple model of the counterfactuals Ybn ,
where we temporarily assume no interaction between the
treatment and the mediator. Again, we suppress the notation
of covariates for ease of exposition.
E[Ybn |b, n] = E[Y |b, n] = β0 + β1 n + β2 b.
I
Greek letters are coefficients.
Given this model, the parameters of interest can be spelled out:
I
I
I
I
I
Average intensive margin AIM0 = AIM1 = CIM = β2 .
Average extensive margin AEM0 = AEM1 = β1 (n̄1 − n̄0 ).
If n̄1 = n̄0 ), then AT E = β1 (n̄1 − n̄0 ) + β2 = β2 .
¯ = 0.
Average adjustment term ∆
In this case CIM is an unbiased measure for AIM0 and
AIM1 .
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
Introduction
The Problem
Identification
Data
Results
Conclude
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 + β1 n + β2 b + β3 nb.
The parameters of interest now become the following:
I Conventional measure CIM (n) = β2 + β3 n.
I Average intensive margin AIMb = β2 + β3 n̄b .
I Average extensive margin AEMb = (β1 + β3 b)(n̄1 − n̄0 ).
¯ = β3 (n̄1 − n̄0 ).
I Average adjustment term ∆
I Average total effect AT E = β1 (n̄1 − n̄0 ) + β2 + β3 n̄1 .
I Effect of a one-unit change in the mediator on outcomes is
β1 + β3 b, not necessarily equal to AEMb , unless n̄1 − n̄0 = 1.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Endogeneity of the Mediator
Identification strategies
When the mediator N (that is, fertility choice) is endogenous,
conventional estimation methods are biased. To address this, we
use conventional 2SLS methods to characterize the
counterfacturals:
Ybn = β0 + β1 n + β2 b + β3 nb + V
Nb (z) = α0 + α1 z + α2 b + α3 zb + U
where V and U are error terms. Greek letters are coefficients.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Endogeneity of the Mediator
Identification strategies
Assume there exists a valid instrument Z = z for the mediator
variable, satisfying the following assumptions (conditional on X in
the 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-degenerate
function Z, given B.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Endogeneity of the Mediator
Identification strategies
I
To identify AIM and AEM, we need to derive n̄1 ,n̄0 and
n̄1 − n̄0 from the first-stage estimates:
n̄b = α0 + α1 z̄ + α3 z̄b
n̄1 − n̄0 = α2 + α3 z̄
I
Let Nb (z) denote the potential fertility choice, given sibling
gender b and instrument z. By a simple extension from Imbens
and Angrist’s (1994) results, the average effect of sibsize on
outcome 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]
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
Introduction
The Problem
Identification
Data
Results
Conclude
Examples
Examples
I
I
I
One important example is the model by Butcher and Case
(1994) and Kaestner (1997), who estimate the effect of sibling
sex composition on children’s education.
This requires an imposition that sibling gender has no effect on
sibsize; that is, AEM=0.
Thus CIM (n̄) = β2 + β3 n̄ = T E = AIM.
Anysister
Education
Sibsize
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
Introduction
The Problem
Identification
Data
Results
Conclude
Examples
Examples
I
I
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 to
instrument fertility choice.
This requires an assumption that Samesex does not affect
parental labor supply; that is, AIM=0.
Mother's labor
Supply
SameSex
MoreThan2
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
Introduction
The Problem
Identification
Data
Results
Conclude
Examples
Examples
Angrist & Evans (1998) impose two assumptions:
I β2 = 0: Sibling sex composition does not directly affect
parents’ labor supply.
I β3 = 0: The effect of family size on parents’ labor supply does
not change with sibling sex composition.
But as Angrist & Evans have noted, if parents change the family
environment in response to child gender, then exogeneity of the
same-sex instrument is violated. For example, if there is a son
instead 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).
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
Introduction
The Problem
Identification
Data
Results
Conclude
Examples
Examples
I
I
I
I
So SameSex might affect parental labor supply via causal
pathways other than M oreT han2. If so, Samesex would be
an invalid instrument and the interaction between Samesex
and M orethan2 should be taken into account.
The pathways not through changing fertility choice are the
“intensive margins.”
We estimate the intensive margins using the 5% PUMS sample
of all women from Angrist’s Data Archive, as a test for
exogeneity of SameSex. N = 394, 840
We also test for significance of the interaction between
Samesex and M orethan2.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Examples
1) Effects of Sex Composition on Fertility Choice
Angrist-Evans (1998)
2SLS Model
IV for Morethan2
Controls
1) First stage
Fertility choice = Morethan2
Twin2nd
Samesex
Twin2nd × Samesex
(1)
(2)
(3)
(4)
Samesex
Twin2nd
Twin2nd
Twin2nd,
Twin2nd×Samsex
Boy1st,
Boy2nd
Boy1st,
Boy2nd
Samesex
Samesex
-
0.621
(0.008)
-
0.622
(0.008)
0.059
(0.001)
-
0.647
(0.011)
0.060
(0.001)
-0.051
(0.015)
0.059
(0.001)
-
-
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
Introduction
The Problem
Identification
Data
Results
Conclude
Examples
2) Effects of Fertility Choice on Mothers’ Weeks Worked
Angrist-Evans (1998)
2SLS Model
IV for Morethan2
Controls
2) Second Stage
Outcome= Weeks Worked
Morethan2
Samesex
Morethan2×Samesex
(1)
(2)
(3)
(4)
Samesex
Twin2nd
Twin2nd
Twin2nd,
Twin2nd×Samsex
Boy1st,
Boy2nd
Boy1st,
Boy2nd
Samesex
Samesex
-5.711
(1.155)
-
-3.663
(0.599)
-
-
-
-3.664
(0.598)
-0.126
(0.077)
-
-4.138
(0.806)
2.15
(0.283)
-5.213
(0.746)
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
Introduction
The Problem
Identification
Data
Results
Conclude
Examples
Decompose the Sibling-Gender Effect on Mothers’ Weeks
Worked
Angrist-Evans (1998)
(1)
(2)
(3)
(4)
Intensive margin, fixing n0
-0.338
(0.069)
-0.338
(0.069)
-
-0.338
(0.069)
-0.338
(0.069)
-
Intensive margin, fixing n1
-
-
Adjust for interaction
-
-
-0.216
(0.036)
-0.216
(0.036)
-0.126
(0.077)
-0.126
(0.077)
-
-0.338
(0.069)
-0.338
(0.069)
-0.342
(0.069)
-0.245
(0.048)
-0.553
(0.015)
0.211
(0.069)
-0.100
(0.083)
-0.308
(0.045)
-0.346
(0.069)
3)Decompose the same-sex effect
Extensive margin, given Samesex=0
Extensive margin, given Samesex=1
Total effect, given covariates
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
Introduction
The Problem
Identification
Data
Results
Conclude
Data
I
I
Large and detailed data is a prerequisite for identifying the
causal effects of sibling gender and family size.
We use 2 national administrative data sets covering all of
Taiwan:
I
I
I
I
Birth Registry (1978-1999)
University Entrance Test records (1996-2003)
The Birth Registry was linked to University Entrance Test
records by using children’s unique ID numbers.
Education Outcomes:
I
I
admitted to university at age 18,
high school completion, which we use ”taking SAT tests” as a
proxy for since most of graduating seniors take the tests.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Data
I
Analysis sample:
I
I
First-borns with at least one sibling
⇒ We control for birth order
Born prior to 1985, when access to ultrasound was limited.
⇒ We addressed the issue of endogenous child gender
I
I
I
I
Sex ratio of first-borns = 1.039 - 1.042.
Sex ratio of second-borns = 1.064 - 1.065.
The F-statistic for the regression of the sex of second-born on
family backgrounds was small and insignificant.
Complete family size: We trace each mother who had the first
baby between 1978 and 1984 for 15 to 22 years. No baby was
born to the mothers in our sample in 1997-1998.
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
Introduction
The Problem
Identification
Data
Results
Conclude
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 sibling
born by 1985
Sample size
Sex-ratio of boys to girls
Sex-ratio of the next sibling
Birth years of the next siblings
Complete family size
Twins at 2nd birth
Subject’s birth weight (kg)
Urban (place of birth)
Mother’s age at first birth
Mother’s year of birth
Father’s year of birth
833,371
1.045
1.070
1984
2.696
0.007
3.212
0.337
23.5
1958
1954
358,177
1.047
1.069
1981
2.784
0.006
3.223
0.340
23.2
1956
1952
336,828
1.046
1.068
1981
2.814
0.006
3.223
0.333
23.2
1956
1952
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
Introduction
The Problem
Identification
Data
Results
Conclude
Characteristics of the Firstborn Sample
Mean of firstborn singletons who have at least one sibling (part 2)
Born in 1978-1984
5-yrs avg taxable income per
capita in village
Mother’s highest degree
College/professional deg. or +
HS diploma
Vocational HS
Junior HS
Father’s highest degree
College degree or above
Professional degree
HS diploma
Vocational HS
Junior HS
Born in 1978-1979
All
Next sibling
born by 1985
728,791
726,922
723,397
0.069
0.061
0.187
0.261
0.064
0.053
0.161
0.214
0.061
0.052
0.158
0.214
0.063
0.073
0.092
0.181
0.237
0.061
0.067
0.088
0.160
0.187
0.058
0.066
0.086
0.160
0.187
Stacey H. Chen
(Academia
Sinica) Yen-Chien
Chen for
(Chinan
with data support
from Jin-Tan
Liu (National
Taiwan U.)
Other
covariates:
dummies
theU.)subject’s
age, parental
ages,
and the
Effects of Family
Composition
mother’s
ageonatHuman
firstCapital
birth.Formation: Extensive and Intensive Margins
Introduction
The Problem
Identification
Data
Results
Conclude
Strong Demand for Sons
Effect of Sibling Sex Composition on Sibsize
All firstborns
Two girls
Mixed gender
Born in urban
Ln(taxable income per
capital in village)
Parental education
Mother finished
(1)
(2)
(3)
junior HS or above
0.5376
(0.0024)
0.1007
(0.0018)
-0.1782
(0.0017)
0.5375
(0.0024)
0.1008
(0.0018)
-0.0757
(0.0021)
-0.3717
(0.0044)
0.5363
(0.0024)
0.1 000
(0.0018)
-0.0913
(0.0020)
-0.2441
(0.0044)
Yes
0.4098
(0.0035)
0.0613
(0.0025)
-0.0714
(0.0029)
-0.1574
(0.0059)
Yes
Sample size
833,371
833,371
833,371
264,105
R-squared adjusted
0.15
0.16
0.18
0.13
Sample size = 833,371. Other covariates: dummies for urban, parental
ages and maternal age at first birth.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Instrument for Sibsize
Robins and Greenland (1992), Cole and Hernan (2002) and
VanderWeele (2010) have noted that with an endogenous
mediator, identification of extensive and intensive margins cannot
be achieved by using data on the triplet (Y, B, N ) alone. In this
paper we introduce conventional Instrumental-Variable methods to
the causal-inference literature by bring in a “fourth” variable,
which is the instrument for the mediator.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Instrument for Sibsize
Twins at the second birth (Rozensweig and Wolpin, 1980)
I Potential issues: Compared to singletons, twins are lighter and
live shorter on average.
I After controlling for birth weight, college enrolment rates of
twins and singletons are about the same (see figures 2a and
2b).
I We include birthweight in X, as Rosenzweig and Zhang (2009)
have suggested, to tackle the concern on the endowment
deficit of twins.
I Black, Devereux and Salvanes (2007) find similar results using
data from Norway.
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
Introduction
The Problem
Identification
Data
Results
Conclude
0
Probability of entering a college
.05
.1
.15
.2
Figure 2a: Firstborn Girls’ College Enrolment Rate, Given
Birth Weight
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 5
Birth weight
Twin
Singleton
College outcome by birth weights(kg) for first−born girls
Data: Taiwanese Birth Registry 1978-1984, firstborn girls
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
Introduction
The Problem
Identification
Data
Results
Conclude
0
Probability of entering a college
.05
.1
.15
.2
Figure 2b: Firstborn Boys’ College Enrolment Rate, Given
Birth Weight
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 5
Birth weight
Twins
Singleton
College outcome by birth weights(kg) for first−born boys
Data: Taiwanese Birth Registry 1978-1984, firstborn boys
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
Introduction
The Problem
Identification
Data
Results
Conclude
Sample Mean by Firstborn Gender (part 1)
Firstborn girls
Firstborn boys
407,467
425,904
Random Treatment
Next sibling is male (Boy2nd=1)
0.52
0.52
Endogenous post-treatment
More than 2 children (Morethan2=1)
Sibsize
0.60
2.83
0.46
2.57
Instrument for fertility
Twinning at 2nd birth
0.007
0.006
Outcome variables:
Admitted to univ.
High school completion
0.17
.24
0.15
.23
Sample size
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
Introduction
The Problem
Identification
Data
Results
Conclude
Sample Mean by Firstborn Gender (part 2)
Control variables:
Birth weight
Born in urban
Mother’s year of birth
Mother’s age at first birth
Father’s year of birth
Taxable income per capita (1000)
Mother’s highest degree
College/professional degree or +
HS diploma
Vocational HS
Junior HS
Father’s highest degree
College degree of above
Professional degree
HS diploma
Vocational HS
Junior HS
Firstborn girls
Firstborn boys
3.16
0.34
1957
23.49
1954
729.33
3.26
0.34
1958
23.46
1954
728.28
0.07
0.06
0.19
0.26
0.07
0.06
0.19
0.26
0.06
0.07
0.09
0.18
0.24
0.06
0.07
0.09
0.18
0.24
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
Introduction
The Problem
Identification
Data
Results
Conclude
Outline of the main results
Sample = Families with at least two children
(1) First Stage (for endogenous fertility choice):
I
I
I
Dependent variable =M orethan2 or Sibsize
Relevance of the instrument, Twinning at 2nd birth (T win2nd)
Key covariate = having a 2nd-born brother (Boy2nd)
(2) Second Stage (effects of fertility choice on child outcomes):
I
I
I
Education variables = Admitted to university, HS completion
Effect of fertility choice on the fristborn’s education
Effect of having Boy2nd on the firstborn’s education
(3) Decompose the effect of sibling gender on education
I
I
I
Total effect
Extensive and intensive margin
Adjustment for interaction between potential sibsize and sibling
gender.
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
Introduction
The Problem
Identification
Data
Results
Conclude
(1) First-Stage Estimates (Fertility Choice)
More than two kids
Firstborn girls
Twinning at 2nd (Twin2nd)
Next sibling is male (Boy2nd)
Twin2nd× Boy2nd
Birthweight
Sibsize
(1)
(2)
(3)
(4)
(5)
0.444
(0.008)
-0.220
(0.001)
0.306
(0.013)
-0.222
(0.001)
0.234
(0.017)
0.306
(0.013)
-0.222
(0.001)
0.234
(0.017)
-0.015
(0.002)
0.652
(0.015)
-0.438
(0.002)
0.671
(0.023)
-0.438
(0.002)
-0.031
(0.030)
-0.032
(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, and
logarithm of taxable income per capita of birth village.
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
Introduction
The Problem
Identification
Data
Results
Conclude
(1) First-Stage Estimates (Fertility Choice)
More than two kids
Firstborn boys
Twinning at 2nd (Twin2nd)
Next sibling is male (Boy2nd)
Twin2nd× Boy2nd
Birthweight
Sibsize
(1)
(2)
(3)
(4)
(5)
0.566
(0.009)
-0.064
(0.001)
0.530
(0.014)
-0.064
(0.001)
0.065
(0.018)
0.530
(0.014)
-0.064
(0.001)
0.065
(0.018)
-0.023
(0.002)
0.723
(0.013)
-0.102
(0.002)
0.721
(0.020)
-0.102
(0.002)
0.005
(0.026)
-0.039
(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, and
logarithm of taxable income per capita of birth village.
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
Introduction
The Problem
Identification
Data
Results
Conclude
(2) Outcome equation (Admitted to University)
OLS
2SLS
Interact
Firstborn girls
More than 2 kids (Morethan2)
Next sibling is male (Boy2nd)
Interact
Birthweight
-0.0140
(0.0013)
-0.0011
(0.0012)
-0.0101
(0.0018)
0.0031
(0.0019)
-0.0068
(0.0024)
-0.0322
(0.0152)
-0.0051
(0.0035)
-0.0837
(0.0348)
-0.0470
(0.0238)
0.0626
(0.0329)
-0.0855
(0.0348)
-0.0484
(0.0238)
0.0646
(0.0329)
0.0185
(0.0013)
-0.0181
(0.0011)
-0.0007
(0.0010)
-0.0153
(0.0016)
0.0019
(0.0014)
-0.0056
(0.0021)
-0.0126
(0.0115)
-0.0003
(0.0013)
-0.0194
(0.0190)
0.0000
(0.0090)
-0.0017
(0.0179)
-0.0197
(0.0190)
-0.0003
(0.0090)
-0.0011
(0.0179)
0.0171
(0.0012)
Morethan2×Boy2nd
Birthweight
Firstborn boys
More than 2 kids (Morethan2)
Next sibling is male (Boy2nd)
Morethan2×Boy2nd
Birthweight
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
Introduction
The Problem
Identification
Data
Results
Conclude
(3) Decompose the effect on college education
OLS
Firstborn girls
If next sibling is female:
fertility channel AEM0
non-fertility channel AIM0
If next sibling is male:
fertility channel AEM1
non-fertility channel AIM1
Interact
Birthweight
0.0031
(0.0003)
-0.0011
(0.0012)
0.0022
(0.0004)
-0.0017
(0.0012)
0.0071
(0.0033)
-0.0051
(0.0035)
0.0184
(0.0077)
-0.0026
(0.0012)
0.0188
(0.0077)
-0.0026
(0.0012)
0.0031
(0.0003)
-0.0011
(0.0012)
0.0037
(0.0004)
-0.0002
(0.0012)
0.0015
(0.0005)
0.0020
(0.0011)
0.0071
(0.0033)
-0.0051
(0.0035)
0.0046
(0.0006)
-0.0164
(0.0078)
-0.0138
(0.0072)
0.0022
(0.0011)
0.0046
(0.0006)
-0.0169
(0.0077)
-0.0142
(0.0072)
0.0021
(0.0011)
Adjust for interaction
Total effect
2SLS
Interact
0.0020
(0.0011)
0.0020
(0.0011)
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
Introduction
The Problem
Identification
Data
Results
Conclude
(3) Decompose the effect on college education
OLS
Firstborn boys
If next sibling is female:
fertility channel AEM0
non-fertility channel AIM0
If next sibling is male:
fertility channel AEM1
non-fertility channel AIM1
Interact.
Birthweight
0.0012
(0.0001)
-0.0007
(0.0010)
0.0010
(0.0001)
-0.0009
(0.0011)
0.0008
(0.0007)
-0.0003
(0.0013)
0.0012
(0.0012)
-0.0009
(0.0011)
0.0013
(0.0012)
-0.0009
(0.0011)
0.0012
(0.0001)
-0.0007
(0.0010)
0.0013
(0.0001)
-0.0005
(0.0011)
0.0004
(0.0001)
0.0005
(0.0010)
0.0008
(0.0007)
-0.0003
(0.0013)
0.0013
(0.0001)
-0.0008
(0.0016)
0.0001
(0.0011)
0.0005
(0.0010)
0.0013
(0.0001)
-0.0008
(0.0016)
0.0001
(0.0011)
0.0005
(0.0010)
Adjust for interaction
Total effect
2SLS
Interact.
0.0005
(0.0010)
0.0005
(0.0010)
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
Introduction
The Problem
Identification
Data
Results
Conclude
2SLS Estimates of the Effects on Education
Mother has JHS diploma
Firstborn girls
Admitted
to univ.
HS
completion
Admitted
to univ.
HS
completion
Outcome mean
0.173
0.241
0.306
0.414
-0.0855
(0.0348)
-0.0484
(0.0238)
0.0646
(0.0329)
-0.1084
(0.0386)
-0.0621
(0.0264)
0.0810
(0.0365)
-0.1327
(0.0493)
-0.0645
(0.0269)
0.1037
(0.0474)
-0.1998
(0.0523)
-0.0990
(0.0285)
0.1638
(0.0503)
407,467
407,467
129,287
129,287
More than 2 kids (Morethan2)
Next sibling is male (Boy2nd)
Morethan2×Boy2nd
Sample size
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
Introduction
The Problem
Identification
Data
Results
Conclude
Decomposition
Mother has JHS diploma
Firstborn girls
If next sibling is female:
fertility channel AEM0
non-fertility channel AIM0
If next sibling is male:
fertility channel AEM1
non-fertility channel AIM1
Adjust for interaction
Total effect
Admitted
to univ.
HS
completion
Admitted
to univ.
HS
completion
0.0188
(0.0077)
-0.0026
(0.0012)
0.0239
(0.0085)
-0.0047
(0.0014)
0.0320
(0.0119)
-0.0068
(0.0027)
0.0481
(0.0126)
-0.0079
(0.0029)
0.0046
(0.0006)
-0.0169
(0.0077)
-0.0142
(0.0072)
0.0020
(0.0011)
0.0060
(0.0006)
-0.0225
(0.0086)
-0.0178
(0.0080)
0.0013
(0.0013)
0.0070
(0.0010)
-0.0318
(0.0121)
-0.0250
(0.0114)
0.0002
(0.0025)
0.0087
(0.0011)
-0.0474
(0.0128)
-0.0395
(0.0121)
0.0007
(0.0027)
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
Introduction
The Problem
Identification
Data
Results
Conclude
Summary of the Main Results (1/2)
I
I
The total effects of having a brother on firstborn girls’/boys’
university entry are marginal and insignificant, because the
extensive and intensive margins typically have opposite signs
cancelling each other.
Results are very sensitive to inclusion of the interaction
between sibsize and sibling gender.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Summary of the Main Results (2/2)
I
I
For firstborn boys, all margins are nearly zero.
For firstborn girls:
I
I
I
I
I
Extensive margins (via reduced sibsize) are significantly
positive, while intensive margins are negatively small through
marginally significant.
If the interaction is ignored, we understand the extensive
margins.
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.
If the second born is male, it’s likely to be a smaller family. The
effect of having a brother via changing the sibsize is small.
But in smaller families, the direct effect of having a brother
(i.e., intensive margin) is larger for girls.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Concluding remarks
I
I
I
I
I
We clarified the parameters of interest, pointing out the
post-intervention bias in the previous estimators.
We used instrumental-variable methods to address the
endogenous post-treatment variable (family size).
We applied the new method to examine the identification
assumption of Angrist and Evans (1998).
We constructed a unique administrative database minimally
affected by sex-selective abortion.
We introduced new outcomes variables – university attainment
and high school completion – to measure the long-term impact
of having a brother on human capital formation.
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
Introduction
The Problem
Identification
Data
Results
Conclude
Concluding remarks
I
I
We pointed to alternative pathways - intensive margin, less
emphasized in the previous literature, for sibling gender to have
an impact, namely, parental behavioural changes that alter
family environments.
We examined Goodkind’s (1996) hypothesis in a careful
empirical design.
I
I
I
Goodkind hypothesized that pre-natal sex-selective abortion
substitutes post-natal sex discrimination.
Although pre-natal sex-selective abortion was not legally
permitted during the sample period, parents in Taiwan have
freely implemented their pro-male biased fertility-stopping rule
because of no One-Child policy.
The total effect of having a brother relative to a sister is close
to zero because the positive effect due to the extensive margin
cancel out a negative effect due to the intensive margin and a
negative effect due to a decrease in the extensive margin.
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