U N I V E R S I T Y O F A A R H U S School of Economics and Management 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 Fertility, nIncome, 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 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 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): 1.Becker’s QQ model is static 2.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 Brush-up of Becker’s QQ model As you saw on Monday, this model leads to two important points: 1.The shadow price of children wrt. number, n, is positively related to quality, q 2.The shadow price of wrt. quality, q, is positively related to number, n Put differently: 1.An increase in quality is more expensive if there are more children because the increase has to apply to more units 2.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 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 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 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 Fertility and child schooling - developed and developing countries Countries, 2000Births per woman Primary school completion rates Heavily indebted poor countries % European Monetary Union % 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 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 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 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 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 at some point during 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

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

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

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