Fertility too The Child Perspective Marianne Simonsen Economics of the Family March 7, 2007

1. Fertility too The Child Perspective Marianne Simonsen Economics of the Family March 7, 2007 U N I V E R S I T Y O F A A R H U S School of Economics and Management

2. Fertility, n Income, wages Child quality, q U N I V E R S I T Y O F A A R H U S School of Economics and Management

3. Outline • Becker’s QQ model • How do we think about quality? • Empirical observations, QQ • Policy relevance • Testing theory: Black, Devereux, and Salvanes (2005) – a first-class example of an empirical paper… • … with some limitations (Simonsen, Skipper, and Smith (2007)) U N I V E R S I T Y O F A A R H U S School of Economics and Management

4. 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 U N I V E R S I T Y O F A A R H U S School of Economics and Management

5. Brush-up of Becker’s QQ model As you saw on Monday, this model leads to two important points: • 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 This quantity-quality trade-off is what we will be concerned with today! U N I V E R S I T Y O F A A R H U S School of Economics and Management

6. 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 U N I V E R S I T Y O F A A R H U S School of Economics and Management

7. 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! U N I V E R S I T Y O F A A R H U S School of Economics and Management

8. Empirical observations - Denmark Source: Simonsen, Skipper, and Smith (2007) U N I V E R S I T Y O F A A R H U S School of Economics and Management

9. Fertility and child schooling -developed and developing countries Source: World Bank Development Indicators U N I V E R S I T Y O F A A R H U S School of Economics and Management

10. 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 • => first thing we need to do to is to investigate the quantity-quality trade-off empirically U N I V E R S I T Y O F A A R H U S School of Economics and Management

11. 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? U N I V E R S I T Y O F A A R H U S School of Economics and Management

12. The More the Merrier? The Effect of Family Size and Children’s Education Black, Devereux, and Salvanes (2005) Quarterly Journal of Economics U N I V E R S I T Y O F A A R H U S School of Economics and Management

13. Black et al (2005) - data • What data would you need to investigate the question in mind? Black et al: • 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 U N I V E R S I T Y O F A A R H U S School of Economics and Management

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16. Black et al (2005) – identification strategy • Would like to estimate the following relation • where is the parameter of interest, y is child outcome, and x are characteristics of the parents • Can we estimate consistently using OLS? • Solution: Use exogenous variation such as twin births (and gender composition) as instrument for n U N I V E R S I T Y O F A A R H U S School of Economics and Management

17. Black et al (2005) – other examples in the literature • 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 • Black et al strategy superior U N I V E R S I T Y O F A A R H U S School of Economics and Management

18. Black et al (2005) – birth order • 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! • Need to introduce birth order into the empirical model U N I V E R S I T Y O F A A R H U S School of Economics and Management

19. Black et al (2005) – birth order 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) U N I V E R S I T Y O F A A R H U S School of Economics and Management

20. Black et al (2005) – findings U N I V E R S I T Y O F A A R H U S School of Economics and Management

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22. Black et al (2005) – 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 • Extremely provocative conclusion! U N I V E R S I T Y O F A A R H U S School of Economics and Management

23. Black et al – discussion • What is cool about the paper? • - the data set! (Which is similar to the Danish, btw) • - the rigorousness of the analysis (several instruments, discussion of instruments, heterogeneity of effects) • - the writing (every time I feel a point a criticism arise, it seems to be addressed just below what I am reading) • => convincing! U N I V E R S I T Y O F A A R H U S School of Economics and Management

24. Limitations – Simonsen, Skipper, and Smith (2007) What is not so cool about Black et al (2005)? • - the lack of connection to an economic model! • (Inclusion of an economic model in economic papers is a great improvement of the lack thereof…) This implies (as we will see): • - quantity and birth order effects not opposing explanations for quality! One may be evidence of the other… • - instrument based estimates not necessarily as informative as Black et al would like them to! You always estimate something! - Interpret within a dynamic version of the quantity-quality model U N I V E R S I T Y O F A A R H U S School of Economics and Management

25. Ad. 1 – birth order and quantity? • Birth order and quantity, n, are intimately related and both likely determined by parents optimal decision making – it is impossible to observe high birth order if n is small!  • Further, imagine a case where the quality of children, for some behavioral reason, is decreasing with birth order (for example because of limited private time with parents) • This will automatically generate a negative correlation between the number of siblings and the average quality • Yet if one holds birth order fixed and investigates the relationship between outcome and sibship size, the correlation may disappear! • (For a more rigorous analysis and discussion, see Simonsen, Skipper, and Smith (2007)) U N I V E R S I T Y O F A A R H U S School of Economics and Management

26. Ad. 2 – interpreting the IV estimates • Assume that investment in offspring can take place in two periods – baby and child • Imagine a three-period model • In period one and two, parents must decide whether to have a (n) (additional) child and in all periods they must decide how many resources to invest in their existing pool of children (s.t. dynamic budget constraints) • Essentially, parents decide on quantity n and the quality of each child • Assume that parental investments are more important early in the child’s life (this is backed by literature in medicine and psychology) • Allow for a small probability of twin births (parents can have a max of four children in this set-up) • The parents solve this problem via backward induction U N I V E R S I T Y O F A A R H U S School of Economics and Management

27. Ad. 2 – interpreting the IV estimates U N I V E R S I T Y O F A A R H U S School of Economics and Management

28. Ad. 2 – interpreting IV estimates • Consider parents who solve their dynamic decision problem and find that it is optimal to have two children • Birth number one realised as a single child • Parents acknowledge that birth number two may result in twins • However, when the twins arrive, parents have already invested in the first child in the crucial first period and he is therefore only slightly affected by this • Thus it seems that an increase in n does not affect this first child – but this is just because the third child was unexpected and parents were pushed off of their equilibrium path! U N I V E R S I T Y O F A A R H U S School of Economics and Management