Intrafamily Resource Allocations: A Dynamic Model of Birth Weight

1. Intrafamily Resource Allocations: A Dynamic Model of Birth Weight Emilia Del Bono, University of Essex John Ermisch, University of Essex Marco Francesconi, University of EssexandIFS May 2008 (Verona, 19 May 2008)

2. 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)

3. 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

4. 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

5. Motivation: Why birthweight? • Effects on infant and adulthealth (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)

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

7. 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

8. Estimation (1): FE-IV (GMM estimation) • Moments:

9. Estimation (2): FE (nested in FE-IV) If no dynamic considerations in place. Moments:

10. Estimation (3): OLS (nested in FE) If no dynamic considerations in place and no family fixed-effects. Moments:

11. A dynamic modelof parental investment (1) • 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)

12. 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 knowεa and εbbefore the child is born • This implies that xa1 is independent of both εa and εb • However, xb2will depend on εa

13. Dynamic model (3) 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= [UGGf1a(Waaf2a−Wabf2b) − Waf2bWabf1af22a]/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.

14. Dynamic model (4) 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= [UGGf1a(Waaf2a−Wabf2b) − Waf2bWabf1af22a+ +Waf2εa(UGG+Wabf2af2b)]/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.

15. Dynamic model (5) A linear approximation to the parents’ resource allocation rule for prenatal investment in the second child is: xb2= g0b2 +gεb2 εa+gyb2y2 We are interested in the parameter gεb2: • If positive, we conclude that equity considerations prevail • If negative, efficiency motive dominates.

16. 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)

17. 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

18. Dependent variable (kit) (in greater detail) 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.

19. Birth weight and fetal growth

20. Mean birth weight by gestation

29. Father’s smoking (Table A2)

31. 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

32. 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)

33. 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)

34. 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)