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If not! Please do so before the 30th of March at 12 o’clock through the webpage of the Study Board.

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Empirical Fertility Models(plus some theory)

Marianne Simonsen, AU

Fertility, n Income, wages

Child quality, q

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))

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

ssnqItssqnUU ..,,max

Brush-up of Becker’s QQ model

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

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

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!

Empirical observations - Denmark

Mothers' Fathers' Fraction Fraction FractionAverage Average Average with <12 with 12 with >12

Education Education Education years years years

1 12.7 10.7 11.7 0.24 0.13 0.632 13.0 10.8 11.9 0.19 0.11 0.703 12.8 9.9 11.1 0.24 0.08 0.684 12.5 9.0 10.2 0.30 0.06 0.645 12.0 8.2 9.5 0.40 0.04 0.566 11.5 7.6 9.0 0.48 0.04 0.497+ 11.1 7.5 8.3 0.55 0.03 0.42

Family Size

AVERAGE EDUCATION BY NUMBER OF CHILDREN IN FAMILY

Source: Simonsen, Skipper, and Smith (2009)

Fertility and child schooling -developed and developing countries

Countries, 2000 Births per woman

Primary school completion rates

Heavily indebted poor countries

5.58 46%

European Monetary Union

1.47 101%

Source: World Bank Development Indicators

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?

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?

The More the Merrier?The Effect of Family Size on Children’s Education

Black, Devereux, and Salvanes (2005)Quarterly Journal of Economics

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

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

uxny

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

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

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)

Findings

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

The Model has been Mislaid:Birth order and the Quantity-Quality Trade-off

Simonsen, Skipper, and Smith (2009)

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

A dynamic model

• Assume for simplicity T=3

• Parents forward looking, maximize utility

s.t. money and time budget constraints

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,,

1,

21

it

tiitititit

tttt

age

qageDq

nqqUU

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)

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A dynamic model

Offspring 1:

Offspring 2:

Baby

Baby

Child

Child

Educational attainment / Final quality of offspring 1

t

t

Period 1 Period 2 Period 3

Period 2 Period 3

Educational attainment / Final quality of offspring 2

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

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

0,0 itit

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

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!

Empirical analyses

Data:1. Register data from Statistics Denmark that

resemble those from Black et al. (2005)

2. Danish Longitudinal Survey of Children with behavioral outcomes at age seven

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)

Investments: spacing (time)

N Mean S.D. MedianChild 1 - Child 2 229,046 43 27 37Child 2 - Child 3 91,788 51 33 44Child 3 - Child 4 25,755 47 34 39Child 4 - Child 5 6,826 43 32 34

Two child families Child 1 - Child 2 137,258 48 28 41

Three child families Child 1 - Child 2 66,033 37 22 32 Child 2 - Child 3 66,033 56 35 50

Four child families Child 1 - Child 2 18,929 31 19 26 Child 2 - Child 3 18,929 41 27 35 Child 3 - Child 4 18,929 51 36 44aCompleted families are defined as families where the youngest is at least 16 in 2002.

Conditional on Completed Familiesa

Outcomes: cognitive and non-cognitive

Dependent Dependentvariable: Child's variable: Child's

education SDQ scoreAll children -0.136 (0.009) All children -0.083 (0.087)First child 0.028 (0.012) First child 0.083 (0.186)Second child -0.122 (0.017) Second child 0.379 (0.197)Third child -0.257 (0.030) Third child 0.921 (0.358)

controlsWith demographic

controlsWith demographic

Q: How do we then investigate the effects of reducing family size?

A: Estimate structural, dynamic model!