Intrafamily Resource Allocations: A Dynamic Model of Birth Weight

Intrafamily Resource Allocations: A Dynamic Model of Birth Weight

Emilia Del Bono, University of Essex John Ermisch, University of Essex

Marco Francesconi, University of Essex and IFS

May 2008

(Verona, 19 May 2008)

Background

• Socioeconomic gradient in cognitive ability opens up at a very early age (Feinstein 2003, Illsley 2002, Cunha & Heckman 2007)

• Cognitive development has been shown to be one of the most inheritable traits (Plomin 2004)

• Growing evidence that the magnitude of the genetic influence on cognitive development increases over the life course (McGue et al. 1993)

Pre-school investments

• Emphasis on pre-school investments (Carneiro and Heckman 2003) [Refer to literature on pre-market characteristics]

• Post-birth investments – Government intervention such as Head Start, Sure Start, etc.

(Currie and Thomas 1995)– Maternal employment (Ruhm 2004; Gregg et al. 2005)– Family structure (Brooks-Gunn, Waldfogel, McLanahan, Duncan

and many others)– Parenting styles (Ermisch 2007)

• Pre-birth investments– Infant mortality and birth weight

Roadmap of the talk

• Motivation• Production function • A dynamic model of parental behaviour• Data requirements• Datasets and descriptives• OLS and FE regressions• Dynamic model (GMM) estimates• Father’s smoking • Main findings and future work

Motivation: Why birthweight?

• Effects on infant and adult health (Black et al. 2007, Case et al. 2005)

• Effects on future labour market outcomes (Behrman and Rosenzweig 2004, Black et al. 2007, Oreopoulos et al. 2007)

• Broad consensus on the sign of these effects, although still some controversy on the magnitude (Almond et al. 2005, Royer 2006)

Most of the previous (medical/economic) literature has considered various “inputs”, including:– Age of mother at birth – Sex of child and parity – Education of the mother

We stress prenatal investment:• Smoking during pregnancy (Rosenzweig and Wolpin 1995) [but also

look at father]• Labour supply during pregnancy• Antenatal care (Rosenzweig and Wolpin 1995)

What’s in the birthweight? (or “birhtweight production function”)

Empirical specification

From the model the empirical specification of the birthweight (k) production function for a two child family (a,b) with one input x is:

ka = xa+ μ+ a

kb = xb+ μ+ b

where μ captures family-specific effects

Estimation (1): FE-IV (GMM estimation)

• Moments:

.σβσσ

,βσσβσσ

,σβσσ

,σβσσ

,σβσ)σβ(σσβσ

,σσβσσβσ

,σσβσσβσ

μx2xxk

εxμxxxxk

μxxxxk

μx2xxk

2μεxμxμxxx

2kk

2ε

2μμx

2x

22k

2ε

2μμx

2x

22k

bbbb

abababa

abaab

aaaa

abbababa

bbbb

aaaa

Estimation (2): FE (nested in FE-IV)

If no dynamic considerations in place.

Moments:

.σβσσ

,βσσβσσ

,σβσσ

,σβσσ

,σβσ)σβ(σσβσ

,σσβσσβσ

,σσβσσβσ

μx2xxk

εxμxxxxk

μxxxxk

μx2xxk

2μεxμxμxxx

2kk

2ε

2μμx

2x

22k

2ε

2μμx

2x

22k

bbbb

abababa

abaab

aaaa

abbababa

bbbb

aaaa

Estimation (3): OLS (nested in FE)

If no dynamic considerations in place and no family fixed-effects.

Moments:

.βσσ

,βσσ

,βσσ

,βσσ

,σβσ

,σσβσ

,σσβσ

2xxk

xxxk

xxxk

2xxk

xx2

kk

2ε

2x

22k

2ε

2x

22k

bbb

baba

baab

aaa

baba

bbb

aaa

• 2 child families (child a and child b)• 3 period model (time=1,2,3)• Each child requires prenatal and postnatal investments

(xa1, xa2, xb2, xb3) • Utility depends on children’s human capital (ka and kb), and a

public good (G)

Problem is to:

max Ut=U(Gt)+W(ka+kb)

s.t. the human capital (birthweight) production technology:

ka=f(xa1+εa, xa2)

kb=f(xb2+εb, xb3)

A dynamic model of parental investment (1)

Dynamic model (2)

and s.t. parental resource constraint at time t:

yt=Gt+xat+xbt

where εa and εb are birth endowments

Information & endowment correlation structure:• Parents do not know εa and εb before the child is born

• This implies that xa1 is independent of both εa and εb

• However, xb2 will depend on εa

After solving the parents’ utility maximization problem backward, we can write the resource allocation rule for prenatal investments in the second child:

xb2/a = gεb2= [UGGf1

a(Waaf2a−Wabf2

b) − Waf2bWabf1

af22a]/D

and xb2/a>0, when Wab>0 and when U, W and f are strictly concave.

Thus, mothers who have an unexpectedly better endowed first child devote more resources to prenatal investments in the second child. We call this the equity motive.

Dynamic model (3)

If the human capital production technology is not linear in the child’s endowment, but takes a more general specification:

ka=f(xa1,xa2, εa)

Then, the resource allocation rule becomes:

xb2/a = gεb2= [UGGf1

a(Waaf2a−Wabf2

b) − Waf2bWabf1

af22a+

+Waf2εa(UGG+Wabf2

af2b)]/D

This new term (in red) is negative, and the sign is now ambiguous. This is because there is now an efficiency motive for more postnatal investment in the first child when his/her birth endowment is higher.

Dynamic model (4)

A linear approximation to the parents’ resource allocation rule for prenatal investment in the second child is:

xb2= g0b2 +gε

b2 εa+ gy

b2y2

We are interested in the parameter gεb2:

• If positive, we conclude that equity considerations prevail

• If negative, efficiency motive dominates.

Dynamic model (5)

Data requirements

• Multiple births to the same mother (siblings)• Child-varying information on pre-birth parental inputs

– Mother’s age (Rosenzweig and Wolpin 1995, Royer 2006)

– Interval between births (Rosenzweig and Wolpin 1995)

– Maternal smoking during pregnancy (Abrevaya 2005, Evans and Ringel 1999, Lien and Evans 2001, Rosenzweig and Wolpin 1991, 1995)

– Mother’s time input (Rhum 1998, Rhum 2000, Tanaka 2005, Gregg et al. 2005)

– Antenatal care (Abrevaya and Dahl 2006, Abrevaya 2005, Rosenzweig and Wolpin 1995)

– Father’s smoking (Tominey 2007)

Data Sources

• Millennium Cohort Study 2000/01 (GB)– Many inputs, also from fathers

– Large sample size

– Cross-sectional (information only on one child)

• British Household Panel Study 1991-2005 (GB)– Longitudinal, and retrospective

– Information on fathers

– Small sample size

• National Survey of Family Growth 2002 (USA)– Longitudinal, but retrospective

– Large sample size

– No information on fathers

Dependent variable (kit) (in greater detail)

MCS BHPS NSFG

Birth weight (kg) 3.382

(0.564)

3.321

(0.560)

3.319

(0.618)

Fetal growth (gr/wk) 85.107

(12.827)

83.731

(12.590)

85.632

(14.774)

Time period (of child’s birth) 2000-01 1991-2006 1979-2003

Estimate: kit=α0+α1t+ α2qi+uit

where t is a time-dummy and q represents quarter of birth

Take the residuals ûit as the regression-adjusted measure of birth weight and fetal growth.

Birth weight and fetal growth0

.2.4

.6.8

Den

sity

-4 -2 0 2 4Birth weight in kg (regression adjusted)

0.0

1.0

2.0

3.0

4D

en

sity

-100 -50 0 50 100Fetal growth in gr/weeks (regression adjusted)

BHPS MSC NSFG

Mean birth weight by gestation-3

-2-1

01

Ave

rage

birth

we

ight in

kg

(re

gre

ssio

n a

dju

sted

)

25 30 35 40 45Weeks of gestation

BHPS MSC NSFG

Descriptive Statistics BHPS MCS NSFG

Birth weight in kg (reg adj) 0.000

(0.559)

0.000

(0.564)

0.000

(0.617)

Fetal growth in gr/wk (reg adj) 0.000

(12.531)

0.000

(12.827)

0.000

(14.752)

Sex of the child 0.495 0.514 0.505

First born 0.681 0.416 0.523

Mother’s age (in months) 28.013

(5.751)

29.272

(5.794)

24.675

(5.513)

Mother smoked during pg 0.225 0.259 0.127

Mother stops ~ birth (ref.) 0.158 0.082

Mother stops <3 months 0.134 0.503

Mother stops 4-9 months 0.099 0.086

Mother did not work during pg 0.397 0.328

Mother missing inf. on work 0.211 -

Mother no mat. leave (ref.) 0.324

Mother mat. leave <1 month 0.142

Mother mat. leave 1-3 months 0.075

Mother mat. leave 3+ months 0.053

Mother did not work during pg

Antenatal care 1st trimester n.a. 0.755

0.405

0.305

N 1,339 17,483 8,345

Birth weight MCS BHPS NSFG

(Table 2) OLS OLS OLS

Mother smoked -0.219** -0.205** -0.203**

Mother stops <3 months 0.324** 0.162*

Mother stops 4-9 months 0.277** 0.162*


0.249** 0.092

Mother no mat. leave (ref.) -

Mother mat. leave <1 month -0.011

Mother mat. leave 1-3 months

0.007


-0.020


-0.021

Antenatal care 1st trimester -0.005 n.a. 0.004

N 17,483 1,339 8,345

Birth weight MCS BHPS NSFG

(Table 2) OLS OLS FE OLS FE

Mother smoked -0.219** -0.205** -0.189 -0.203** -0.154**

Mother stops <3 months 0.324** 0.162* 0.187

Mother stops 4-9 months 0.277** 0.162* 0.241


0.249** 0.092 0.143

Mother no mat. leave (ref.) - -

Mother mat. leave <1 month -0.011 0.062


0.007 0.017


-0.020 -0.012


-0.021 -0.010

Antenatal care 1st trimester -0.005 n.a. 0.004 0.076**

N 17,483 1,339 804 8,345 6,791

Fetal growth MCS BHPS NSFG

(Table 2) OLS OLS FE OLS FE

Mother smoked -5.117** -4.512** -4.687* -2.635** -1.806**

Mother stops <3 months 5.240** 2.831** 3.730*

Mother stops 4-9 months 4.583** 3.108** 4.257**


3.866** 1.597** 2.645*

Mother no mat. leave (ref.) - -

Mother mat. leave <1 month -0.129 1.974**


0.511 0.652


-0.241 0.273


-0.341 -0.145

Antenatal care 1st trimester 0.037 n.a. n.a. -0.217 1.513*

N 17,483 1,339 804 8,345 6,791

Birth weight NSFG

(Table 3) OLS FE FE-IV FE-IV restricted

Mother smoked -0.203** -0.154** -0.205* -0.213*

Mother mat. leave <1 month -0.011 0.062 0.042 0.057

Mother mat. leave 1-3 months 0.007 0.017 0.098 0.046

Mother mat. leave 4-9 months -0.020 -0.012 0.054 0.010

Mother did not work during pg -0.021 -0.010 -0.013 -0.011

Antenatal care 1st trimester 0.004 0.076** 0.058 0.061

Correlations (selected): smoking & family endowment

σsmoke1,μ -0.029* -0.041**

σsmoke2,μ -0.004 -

σsmoke3,μ -0.007 -

Correlations (selected): smoking & idiosyncratic shock

σsmoke2,ε1-0.013* -0.015**

σsmoke3,ε2-0.009** -0.009**

σsmoke3,ε1 -0.004 -

N 8,345 6,791 6,791 6,791

Fetal growth NSFG

(Table 3) OLS FE FE-IV FE-IV restricted

Mother smoked -2.635** -1.806** -2.137* -2.184*

Mother mat. leave <1 month -0.129 1.974** 1.758* 1.773**


0.511 0.652 1.261 1.259


-0.241 0.273 1.298 1.057


-0.341 -0.145 0.177 0.068

Antenatal care 1st trimester -0.217 1.513* -0.085 0.147


σsmoke1,μ -0.611* -0.623*

σsmoke2,μ -0.230* -0.247*

σsmoke3,μ -0.379 -


σsmoke2,ε1-0.056** -0.063**

σsmoke3,ε2-0.035 -

σsmoke3,ε1 -0.021 -

N 8,345 6,791 6,791 6,791

Birth weight BHPS

(Table 4) OLS FE FE-IV

2-children only

FE-IV restricted

2-children only

Mother smoked -0.205** -0.189 -0.189 -0.191

Mother stops <3 months 0.162* 0.187 0.170 0.178

Mother stops 4-9 months 0.162* 0.241 0.250* 0.247**

Mother did not work during pg 0.092 0.143 0.136 0.140


σsmoke1,μ -0.049* -0.055*

σsmoke2,μ -0.091* -0.087*


σsmoke2,ε1-0.029* -0.027*

N 1,339 804 654 654

Fetal growth BHPS

(Table 4) OLS FE FE-IV

2-children only

FE-IV restricted

2-children only

Mother smoked -4.512** -4.687* -4.281* -4.319*

Mother stops <3 months 2.831** 3.730* 3.698 3.726*

Mother stops 4-9 months 3.108** 4.257** 4.232** 4.208**


1.597** 2.645* 2.269 2.316


σsmoke1,μ -0.108 -

σsmoke2,μ -0.326* -0.258*


σsmoke2,ε1-0.195* -0.184*

N 1,339 804 654 654

Father’s smoking (Table A2)

MCS BHPS

OLS OLS FE FE-IV

2 children

only

Birth weight

Mother smoked -0.209** -0.192** -0.0192** -0.180

Father smoked -0.043** -0.043 -0.004 -0.008

Fetal growth

Mother smoked -4.845** -4.173** -4.769** -4.276*

Father smoked -1.009** -0.975 0.320 -0.054

N 17,483 1,339 804 654

Fetal growth BHPS

(Table 5) OLS GLS-IV FE

2-children only

FE-IV†

2-children only

Mother smoked -4.038** -6.667 -4.740* -5.120*

Mother did not workor stopped working 1+ months before birth

2.942** -3.609 3.589** 4.570*

Correlations smoking & maternal endowment

σsmoke1,ε -0.155

σsmoke2,ε -0.280*

Correlations smoking & idiosyncratic shock

σsmoke2,ν1-0.191*

N 1,339 804 654 654

† GLS-IV and FE-IV use father’s smoking and partnership status as exogenous variables, i.e. additional instruments

Brief summary of results (1)

• FE-IV is statistically the preferred model specification

• Mother’s smoking (during pregnancy): negative effect – reduces birthweight by about 200 grams– reduces fetal growth by 2-4 grams/week

• Job stops (during pregnancy)/maternity leave: positive effect (mainly through gestation)– no significant effect on birthweight– increases fetal growth by 2-4 grams/week

Brief summary of results (2)

• Antenatal care: no robust effect (positive in FE but undone with FE-IV, suggesting that other correlations with time-varying endowments might be at work)

• Father’s smoking: – No direct effect (after accounting for family fixed

effects) – As instrument (for mother’s smoking) in FE-IV: both

effects of maternal smoking and labour supply get better measured, and both roughly offset each other (+/- 250 grams ; and +/- 5 grams/week)

Brief summary of results (3)• These results extend what we know since they have

been obtained:– using 3 different datasets (little about GB known before)– for 2 different countries – with a number of different econometric techniques

They can be taken quite seriously for “policy” purposes

• Beside this, from FE-IV: evidence that families have equity considerations in allocating resources across their children (“equal concern”)– This adds to our understanding of how families operate. It

contrasts with some of the results found by Heckman and colleagues (which emphasize efficiency considerations)

What next?• Post-natal investments

– Tricky: • Theory: ambiguous • Empirical specification: must account for all correlations, as

endowments are known• Data: Need to find child-specific investments (breastfeeding,

available in NSFG only)

• Direct survey evidence on equity vs efficiency (but cannot find information on this in the 3 datasets at hand)

• Use macro data (from birth registers) to gain efficiency with the GMM micro estimation in the BHPS (Imbens and Lancaster)

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