Life Cycle Effects of Fertility on Parents’ Labor Supply

1. Life Cycle Effects of Fertility on Parents’ Labor Supply James P. Vere University of Hong Kong January 16, 2007

2. Introduction • Overarching problem: what is the relationship between fertility and female labor supply? • Strong negative correlation established since the 1960s • Causal link much more difficult to extract • Researchers started to take this seriously in the 1980s

3. Introduction • Why do we care about the causal link between fertility and labor supply? • Policy implications • Many government policies have pronatalist or antinatalist side effects (welfare reform, family leave) • Sometimes fertility is treated as a policy objective in its own right (e.g, Singapore’s “Stop at Two” policy)

4. Introduction • Theoretical implications • Many, many models link labor markets and family structure • Desirable to put them to empirical tests • There may be feedback to other aspects of the household (e.g., marital stability, husband’s labor supply)

5. Introduction • Empirical contribution of this paper: what are the age-specific causal effects of second and higher children on female labor supply? • Instruments used in earlier research: • The incidence of twin births (2nd and higher children) • Sex composition of the first two children (3rd children) • I use a twins-based estimation strategy • Method allows characterizing the age distribution of parity-specific effects

6. Introduction • Object of the empirical work: to find out how the causal effects of fertility on household labor supply have been changing over time. • Why might they be changing? • Work incentives are changing, esp. for low-income people (e.g., welfare reform, expansion of the EITC) • Household structures are also changing (e.g., increased assortative matching in marriage)

7. Introduction • Key findings: • For single women, the causal effects of second and third children on labor supply have declined significantly over time • This may be because of policy reforms designed to increase their incentives to work • For married couples, specialization in response to fertility has increased, despite declines in men’s comparative advantage in market work • It is unclear why this has occurred

8. Introduction • Outline of points I will cover: • Data • Instruments and First-Stage Relationships • Fertility and Female Labor Supply • Fertility and Household Labor Supply • Conclusions

9. Data • Data are from the 1980, 1990 and 2000 U.S. Census Public Use Micro Samples (PUMS). • Sample limited to women with these characteristics: • Ages 21-35 • Reported as head of household, spouse of head of household, or parent/spouse in married couple subfamily • Angrist and Evans (1998) do the same – idea is to impute fertility history from household composition

10. Data • Covariates in the model: • Age, age squared • Years of education • If black • If married • Measures of labor supply: • Labor force participation / Employment • Hours worked per week (usual & last week) • Weeks worked last year • Wage or Salary income last year • Women’s birth histories are imputed from data on household composition

11. Data • Does this method introduce selection bias (table 1)? • Differences are statistically but not economically significant

12. Instruments and First-Stage Relationships • The instruments are indicators for multiple births • TWINS2 – 1st and 2nd child born in same year • TWINS3 – 2nd and 3rd child born in same year • For 1980, they are also imputed from quarter-of-birth data (TWINS2Q, TWINS3Q) • For 1990 and 2000, they are imputed from year-of-birth data only

13. Instruments and First-Stage Relationships Means and (standard errors) of the instruments x1000 (table 2):

14. Instruments and First-Stage Relationships • Why have twinning rates increased over time? • Women having children later • Increased use of fertility drugs • Bovine growth hormone • Age, education covariates control for these factors • Is not having quarter of birth data a problem? • Only if measurement error is correlated with the error term in the second stage • Overidentification tests with 1980 data and TWINS2Q, TWINS3Q as benchmarks suggest not

15. Instruments and First-Stage Relationships • First stage – initially of the form • Where Z is the binary instrument (=1 if child n-1 & n are part of the same multiple birth set) • Sample consists of women with at least n-1 children. • C is an indicator equal to one if a woman has at least n children, zero otherwise (Angrist & Evans 1998).

16. Instruments and First-Stage Relationships • In a model without covariates, p2 can be calculated • Thus, if you believe the instrument is randomly assigned, p2 tells you the number of “extra” children induced by the instrument. • Since some women would have had second or third children anyway, p2 will not be equal to one.

17. Instruments and First-Stage Relationships • First-stage estimates of p2 (table 3; with covariates included):

18. Instruments and First-Stage Relationships • Observations from first stage • p2 increasing over time – because more and more women would not otherwise have had a 2nd (or 3rd) child by the time of the survey • For 1980, using TWINS2Q and TWINS3Q does not make much difference (at most 0.01-0.02) • Including the covariates in the first stage also does not make much difference

19. Fertility and Female Labor Supply • Angrist and Imbens (1995) show that 2SLS estimates of d in the labor supply equation • can be interpreted as average, per-unit causal effects of C on Y • A “unit” here is simply a second or third child • For now we will not worry about age-specific causal effects

20. Fertility and Female Labor Supply • In a model without covariates, d can be calculated • The denominator is where the “per-unit” interpretation comes from • Where comparable, estimates of d are quite similar to others found in the literature (e.g. Angrist and Evans (1998), Carrasco (2001)).

21. Fertility and Female Labor Supply • Estimates of d (table 4):

22. Fertility and Female Labor Supply • For 1980, using quarter-of-birth data to construct the instruments, or not, makes no statistical difference • However, we might be concerned by the assumption that d is invariant to children’s ages • It is more realistic to interpret the preceding results as weighted averages of age-specific causal effects • The weights are proportional to • where C(a)=1 if there is an nth child of age a in the household

23. Fertility and Female Labor Supply

24. Fertility and Female Labor Supply • Notes on preceding figure: • Third children are drawn from a younger age distribution than second children • Age distributions have become younger over time (1980, 1990, 2000) • Why? • Twins of second children are always younger than twins of first children • Twin first children are more likely to replace planned births (i.e., which replaces a young child with an older one) • This could explain why causal effects have increased over time

25. Fertility and Female Labor Supply • How can age-specific causal effects be estimated? • Intuition – Census microdata contain snapshots of many different “twins” experiments, all initiated at different points in time • Hence, multiple births have varying effects on a set of age-specific fertility indicators depending on how long ago the birth occurred • For instance, if the birth was five years ago – positive effect on C(5), negative effects on C(0) through C(4)

26. Fertility and Female Labor Supply • Formally, the first stage is • Z is a vector created by interacting the multiple birth indicator (TWINS2 or TWINS3) with a set of k time dummy variables, T0, T1, ..., Tk−1, where Ti is equal to one if the multiple birth occurred i years ago and zero otherwise • This specification permits identifying k separate age-specific effects

27. Fertility and Female Labor Supply • The second stage is • Where Y is a labor supply outcome and C is a vector of age-specific fertility indicators (the C(a)’s). • The covariates in X are age, age squared, years of education, and dummy variables for being black and being married.

28. Fertility and Female Labor Supply

29. Fertility and Female Labor Supply • Q: Why stop at age 13? • A: This is when junior high school starts (so it is a natural cut point in the data). It is also when the age-specific effects are no longer significantly different from zero (both here and in Angrist and Evans (1998). • Other observations: • Causal effects decline with age and parity of the child • The difference by parity is especially pronounced at age 6, suggesting that it is easier to realize economies of scale when children start school

30. Fertility and Female Labor Supply • When these age-specific effects are summed together, the result is a synthetic-cohort life cycle effect. • These are useful for year-to-year comparisons because the underlying age distribution is fixed. • They are analogous to life expectancy statistics.

31. Fertility and Female Labor Supply • Synthetic-Cohort Life Cycle Effects of 2nd Children on • Female Labor Supply (table 5)

32. Fertility and Female Labor Supply • Synthetic-Cohort Life Cycle Effects of 3rd Children on • Female Labor Supply (table 5)

33. Fertility and Female Labor Supply • Observations from table 5: • Effects of 2nd children on female labor supply have fallen over time, esp between 1980 and 1990 • This was not clear when we did not control for age-specific effects • For 3rd children the effects decline most strongly between 1990 and 2000

34. Conclusions • Innovation in the paper – identification of age-specific causal effects. • This is done by interacting the multiple birth indicator with the time since the multiple birth occurred. • This is important because different instruments identify the effects of children drawn from different age distributions. • It also permits estimation of synthetic-cohort life cycle effects.

35. Conclusions • Main findings: • The causal effect of fertility has declined significantly for single women, but remained stable for married women • Specialization within married couples in response to fertility has increased, with men tending to respond with income rather than time spent on child care • The latter finding is surprising because marriages have increasingly become between men and women with similar market earning power.