25-10-2016, 04:27 PM
Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size
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Research on the labor-supply consequences of childbearing is complicated by
the endogeneity of fertility. This study uses parental preferences for a mixed
sibling-sex composition to construct instrumental variables (IV) estimates of the
effect of childbearing on labor supply. IV estimates for women are significant but
smaller than ordinary least-squares estimates. The IV are also smaller for more
educated women and show no impact offamily size on husbands' labor supply.
A comparison of estimates using sibling-sex composition and twins instruments
implies that the impact of a third child disappears when the child reaches age
An understanding of the relationship between
fertility and labor supply is important for a num-
ber of theoretical and practical reasons. First,
economists and demographers have developed a
variety of models linking the family and the la-
bor market. Empirical studies of childbearing
and labor supply are sometimes seen as tests of
these models (e.g., Reuben Gronau, 1973; Mark
R. Rosenzweig and Kenneth I. Wolpin, 1980b;
T. Paul Schultz, 1990). Second, the link be-
tween fertility and labor supply might partly ex-
plain the postwar increase in women's
labor-force participation rates if having fewer
children causes an increase in labor-force attach-
ment (Mary T. Coleman and John Pencavel,
1993). Evidence for this thesis includes Claudia
Goldin's (1995) study, which shows that few
women in the 1940's and 1950's birth cohorts were able to combine childbearing with strong
labor-force attachment. Other researchers have
also drawn a link between fertility-induced with-
drawals from the labor force and lower wages
of women (e.g., Gronau, 1988; Sanders
Korenman and David Neumark, 1992). So per-
haps childbearing keeps women from develop-
ing their careers.
Any success in disentangling the causal
mechanisms linking fertility and labor supply
should shed light on other substantive issues as
well. For example, reductions in female labor
supply could increase the total time parents de-
vote to child care, making at least some children
better off (see, e.g., Frank P. Stafford, 1987;
Francine Blau and Adam J. Grossberg, 1992).
Some theories of family behavior also suggest
that changes in wives' earnings affect marital
stability (Becker et al., 1977; Becker, 1985).
Not surprisingly, given the wide and long-
standing interest in the connection between
childbearing and labor supply, hundreds of
empirical studies report estimates of this re
lationship. The vast majority of these studies
find a negative correlation between fertility (or
family size) and female labor supply.1 As noted in two recent literature surveys, how-
ever, the interpretation of these correlations re-
mains unclear. In his assessment of the
"economics of the family," Robert J. Willis
(1987 p. 74) writes, "... it has proven difficult
to find enough well-measured exogenous vari-
ables to permit cause and effect relationships
to be extracted from correlations among fac-
tors such as the delay of marriage, decline of
childbearing, growth of divorce, and increased
female labor force participation ... ." Martin
Browning (1992 p. 1435) expresses similar
views: "... although we have a number of ro-
bust correlations, there are very few credible
inferences that can be drawn from them." 2
Skepticism regarding the causal interpreta-
tion of associations between fertility and labor
supply arises in part from the fact that there
are strong theoretical reasons to believe that
fertility and labor supply are jointly deter-
mined (see, e.g., Schultz, 1981, or Goldin,
1990). In fact, this endogeneity is reflected in
the academic research agenda. On one hand,
papers on labor supply often treat child-status
variables as regressors in hours of work equa-
tions, while on the other hand, economic
demographers and others discuss regressions
and models that are meant to characterize the
impact of wages or measures of labor-force
attachment on fertility. Since fertility variables
cannot be both dependent and exogenous at
the same time, it seems unlikely that either sort
of regression has a causal interpretation.:
This paper focuses on the causal link run-
ning from fertility to the work effort of both
men and women. Our main contribution is the
use of a new instrumental variables (IV) strat-
egy based on the sibling sex mix in families
with two or more children. This instrument ex-
ploits the widely observed phenomenon of pa-
rental preferences for a mixed sibling-sex
composition. In particular, parents of same-sex
siblings are significantly and substantially
more likely to go on to have an additional
child.4 Because sex mix is virtually randomly
assigned, a dummy for whether the sex of the
second child matches the sex of the first child
provides a plausible instrument for further
childbearing among women with at least two
children. Moreover, in spite of the fact that the
sibling sex mix is obviously a function of the
sex of both children, we present a range of
evidence which suggests that there is little pos-
sibility that any secular impact of the sex of
offspring contaminates the IV estimates.
We also compare results generated using sex
mix as an instrument to results generated using
twins to construct instruments. Twinning at
first birth has been used in a inumber of previous
studies to estimate the relationship between