Registration for elective courses Fall 2009

1. Registration for elective coursesFall 2009 Have you remembered to pre-registrer? If not! Please do so before the 30th of March at 12 o’clock through the webpage of the Study Board. At least 12 students need to sign up for a given course before it is required.

2. Empirical Fertility Models (plus some theory) Marianne Simonsen, AU

3. Fertility, n Income, wages Child quality, q

4. Outline • Becker’s QQ model • How do we think about quality? • Empirical observations, QQ • Policy relevance • Testing theory: Black, Devereux, and Salvanes (2005) • … with some limitations (Simonsen, Skipper, and Smith (2009))

5. Brush-up of Becker’s QQ model • Parents maximise welfare subject to their budget constraint • (Becker (1992): ”individuals can be selfish, altruistic, loyal, spiteful, or masochistic”) Keep in mind (for empirical analysis): • Becker’s QQ model is static • Quality assumed to be the same for all children within a family

6. Brush-up of Becker’s QQ model • The shadow price of children wrt. number, n, is positively related to quality, q • The shadow price of wrt. quality, q, is positively related to number, n Put differently: • An increase in quality is more expensive if there are more children because the increase has to apply to more units • An increase in the number of children is more expensive if the children are of higher quality, because higher-quality children cost more

7. How do we measure quality?? • ”Quality” in Becker’s model is an abstraction • Some people were (and still are) wildly provoked by the characterisation of children by their ”quality” • But quality could just as well be thought of as well-being of the child! • When taking the model to the data we need a (quantitative) measure of quality • Often: - education - labor market outcomes

8. How do we measure quality?? • Though (most) economists believe that an individual will be better off with, say, higher income, everything else being equal (think about the typical utility function)… • … it is still only a pragmatic solution… (adopted by both economists and quantitative sociologists) • Sufficient? • Are you necessarily a better child (in the eyes of your parents) if you have high income and high level of education? • Need to keep this in mind when interpreting our empirical results!

9. Empirical observations - Denmark Source: Simonsen, Skipper, and Smith (2009)

10. Fertility and child schooling -developed and developing countries Source: World Bank Development Indicators

11. Policy relevance • If smaller family size causes a higher average quality then it may be a good idea for policy makers to try to reduce fertility • Why? (Or maybe why not?) - what happens to child utility? Child productivity? - what happens to female labor supply? - does a smaller population with (slightly?) higher average skills necessarily lead to higher aggregate production? • World Bank strategy to reduce fertility in developing countries for the last 25 years • Can we test the relationship empirically?

12. From theory to empirical question • How does number of children born within a family affect child outcomes? • Is the negative correlation observed in the data a result of a causal effect of family size on quality – or are children born in larger families just different from children born in smaller families? • (put differently, is the quantity-quality trade-off real or not?) • Why might children born in large families ”just be different”? • What are the policy implications if this latter point is true?

13. The More the Merrier? The Effect of Family Size on Children’s Education Black, Devereux, and Salvanes (2005) Quarterly Journal of Economics

14. Data • 100% of the Norwegian population aged 16-74 at some point during 1986-2000 • Links parents and children (and their siblings) • Knowledge about both outcomes for children (quality) as well as characteristics of the parents • Sample of children at least 25 in 2000 with parents appearing in the main dataset

17. Identification strategy • Would like to estimate the following relation • where α is the parameter of interest, y is child outcome, and x are characteristics of the parents • Can we estimate α consistently using OLS? • Suggested solution: use exogenous variation such as twin births (and gender composition) as instrument for n

18. Other empirical examples • Leibowitz (1977), Rosenzweig and Wolpin (1980), Blake (1985), Hanushek (1992), Downey (1995) and many others • General finding: Negative estimated effect of family size on child outcomes • Common to these studies: - Small and non-representative samples and/or - do not handle endogeneity of family size

19. Birth order effects? • Introduce birth order into the model • If child quality (educational outcomes) decrease with birth order then, Black et al argue, we may confuse the effect of n with that of birth order! • Introduce birth order into the empirical model

20. Birth order literature Huge and colorful non-academic literature: • K. Leman: The New Birth Order Book: Why You Are the Way You Are (!!) • C. Isaacson: The Birth Order Effect for Couples: How Birth Order Affects Your Relationships and What You Can Do About it • Martensen-Larsen: Forstå dit Ophav og Bliv Fri (Understand Your Background and Set Yourself Free) Academic literature within soc and psych but also economics: • e.g. Hanushek (1992)

21. Findings

23. Conclusion • Little, if any, family size effect on child education when controlling for birth order or instrument with twin births • Large and robust effects of birth order on child education • Argue that existing fertility models – including the work by Becker – ought to be revised

24. The Model has been Mislaid: Birth order and the Quantity-Quality Trade-off Simonsen, Skipper, and Smith (2009)

25. Outline • A dynamic model of fertility and child investments • Predictions about the quantity-quality trade-off and birth order differences • Framework for interpretating the IV estimates from the empirical literature • Data in support of the model: testable predictions

26. A dynamic model • Assume for simplicity T=3 • Parents forward looking, maximize utility s.t. money and time budget constraints

27. A dynamic model • Assume • Assume investments in young children more productive (sensitive period) • Assume that quality in one period increases quality in the next period (self-productivity)

28. A dynamic model

29. Comparative statics Proposition 1: Birth order differences • (Given regularity conditions,) in the absence of credit and time constraints, parents will always invest more in lower parity children • Intuitively, this is because parents have more time to enjoy utility from lower parity children, will invest more in early, sensitive period • See also Price (2007) on quality time investments

30. Comparative statics Proposition 2: Quantity-quality trade-off • Given the same net present value of resources, families with more children will have fewer resources to spend in each child and will thus have lower quality children. • Intuitively, this follows from Proposition 1 and

31. I.e. • Model explains both family size effects and birth order differences • Birth order differences and family size effects are intimately related! • It does not make sense to try to distinguish the two from each other

32. Interpreting (twin) IV estimates? • Want: estimate of the effect of an extra child on child outcomes • Show formally: estimates of the effect of an extra child via a twin birth are downwards biased • Intuitively, this is because the parents expect to have n (plus epsilon) children and invest early in their lower parity children accordingly. Thus a late born unexpected twin will have little effect on outcomes of early born children!

33. Empirical analyses Data: • Register data from Statistics Denmark that resemble those from Black et al. (2005) • Danish Longitudinal Survey of Children with behavioral outcomes at age seven

34. Empirical analyses • Investigate investments (fx spacing and length of parental leave depending on birth order) like Price (2007) • Consider conditional correlations between family size and child outcomes depending on birth order • Model predicts that this should be smaller for lower parity children • Show that IV estimates are small as in Black et al. (2005)

35. Investments: spacing (time)

36. Outcomes: cognitive and non-cognitive

37. Q: How do we then investigate the effects of reducing family size? A: Estimate structural, dynamic model!