S. Lundberg,
E. Rose
r Labour
Economics 7
2000 689
– 710
697 Table 2
Ž .
Dependent variable: log of real wage rate. Random effects estimates p-values for hypothesis tests in bold and t–statistics in parentheses
Ž . Ž .
Ž . Ž .
Ž . Ž .
1 Wives 2 Wives
3 Wives 4 Husbands
5 Husbands 6 Husbands
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
Sample All 11 134
Contin. 8058 All 11 134
All 15 106 Contin. 7777
All 15 106 Ž
. Ž
. Ž
. Ž
. Ž
. Ž
. Before
y0.09 2.8 y0.10 3.0
y0.06 1.7 y0.09 3.1
y0.10 3.0 y0.07 2.0
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
After y0.15 5.1
y0.10 3.3 y0.32 10.4
y0.01 0.3 y0.03 1.1
0.02 0.7 Ž
. Ž
. C Before
0.02 0.6 y0.05 1.8
Ž .
Ž .
C After 0.28 13.1
y0.06 3.2
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
p b s b
0.00 0.99
0.00 0.00
0.00 0.00
Be fore After
[ ]
[ ]
p b s b
0.00 0.61
C Before
C After
[ ]
[ ]
p b H b
0.83 0.00
Be fore C
Before
s b H b
Af ter C After
S. Lundberg,
E. Rose
r Labour
Economics 7
2000 689
– 710
698
Table 3 Ž
. Dependent variable: hours worked. Random effects estimates
p-values for hypothesis tests in bold and t–statistics in parentheses Ž .
Ž . Ž .
Ž . Ž .
Ž . 1 Wives
2 Wives 3 Wives
4 Husbands 5 Husbands
6 Husbands Ž
. Ž
. Ž
. Ž
. Ž
. Ž
. Sample
All 17 334 Contin. 8814
All 17 334 All 17 403
Contin. 8840 All 17 403
Ž .
Ž .
Ž .
Ž .
Ž .
Ž .
Before 243 4.7
104 2.4 80 1.6
41 1.0 71 1.5
y38 0.8 Ž
. Ž
. Ž
. Ž
. Ž
. Ž
. After
y577 12.4 y367 9.9
y1073 28.3 66 1.8
13 0.3 87 2.2
Ž .
Ž .
C Before 345 7.3
122 2.7 Ž
. Ž
. C After
991 39.2 y45 1.7
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
p b s b
0.00 0.00
0.00 0.24
0.03 0.00
Be fore After
[ ]
[ ]
p b s b
0.00 0.00
C Before
C After
[ ]
[ ]
p b H b
0.00 0.12
Be fore C
Before
s b H b
Af ter C After
region. In most of the models estimated, the child effects are assumed to be the same for the entire sample; in others, interaction terms allow the coefficients on
ABeforeB and AAfterB to differ between the continuous and non-continuous Ž
samples. For each of the non-interacted specifications i.e., columns 1, 2, 4, and .
5 , the p-value associated with the test of a significant difference between the coefficients on ABeforeB and AAfterB for that subsample is reported in bold. The
Ž interpretation of the tests is different for interacted specifications columns 3 and
. 6 . The first p-value in each column is associated with the test that there is a
significant difference in the coefficients on ABeforeB and AAfterB for the Anon- continuousB subsample. The second p-value for columns 3 and 6 is associated
with the test for a significant difference between the AcontinuousB and Anon-con- tinuousB samples in the coefficients on ABeforeB and AAfter.B For the last row of
columns 3 and 6, the test is for a significant difference in the ABeforeB and AAfterB coefficients for the AcontinuousB subsample.
Ž . Ž
Table 2 reports the estimates of Eq. 1 for the outcomes wife’s wage columns .
Ž .
1 through 3 and husband’s wage columns 4 through 6 . For the entire sample of Ž
. wives column 1 , there is evidence of negative heterogeneity: Women who have
children earn nine percentage points less than non-childbearers even prior to the Ž
. birth of the child controlling for age, education, region, and race . There is also
evidence that earnings fall in response to the birth of the child. The coefficient on AAfterB is six percentage points lower than the coefficient on ABefore,B and the
Ž .
difference between the two coefficients is statistically significant p - 0.01 .
Column 2 reports the same specification estimated for our AcontinuousB subsam- ple. There is evidence of negative heterogeneity for this subsample as well, but the
coefficients on ABeforeB and AAfterB are not different, indicating that the birth of the child has not resulted in wage losses for this group of women. This is
Ž .
consistent with Waldfogel’s 1998b findings for the United States and Britain, that women who have maternity leave coverage and return to work earn more than
women who return but do not have job-protected maternity leave. In column 3, we report the results for the full sample in a specification, which includes interactions
of AcontinuousB with ABefore,B ABorn,B and AAfter.B This allows us to test for a difference in the responses of women’s wages to the birth of the child for the
AcontinuousB group and its complement, and we find that the difference is
Ž .
statistically significant p - 0.01 . Results for the same set of specifications are reported for the husbands in
Ž . columns 4 through 6. According to the random effects estimates of Eq. 1 , which
are reported in column 4, men earn 8 more per hour after the birth of the first child. There is substantial negative heterogeneity in the wages of fathers relative to
non-fathers. The AcontinuousB subsample for husbands consists of the husbands of women who participate in every year of the window except the year in which a
child was born. The effect of the birth of a child on the wage rates of these AcontinuousB husbands is somewhat smaller than for the sample of husbands
whose wives experience substantial spells of non-employment, but the difference between the effects is not significant.
11
Table 3 reports the same set of specifications as in Table 2, but the dependent variable is the number of hours worked by wives in columns 1 through 3 and
hours worked by husbands in columns 4 through 6. For women, not surprisingly, hours worked are substantially lower after the birth of a child and the difference is
smaller for women in the AcontinuousB subsample. There is also positive hetero- geneity: Women who have children work more hours prior to the birth of the first
child than women who have not had children within the sample.
The results for men are reported in columns 4 through 6. Men work more after the birth of the first child. However, the results reported in the interacted
specifications in column 6 indicates that this increase in hours worked occurs only for the Anon-continuousB husbands. Hours worked by husbands whose wives work
Ž .
continuously are significantly lower p s 0.03 after the birth of the child relative to before.
To better capture the differences in the profiles for parents and non-parents, we consider a specification in which we break the ABeforeB and AAfterB variables into
a series of dummy variables corresponding to the number of years before and after the birth, i.e.:
Y s b q b Before11 q b
Before10 q . . . qb Before1
i t m11
i t m10
i t m1
i t
q b Born q b After1 q b
After2 q . . . b After29
m 0 i t
p1 i t
p 2 i t
p 29 i t
q b Age q b X q m q h 2
Ž .
4 i t
5 i t
i i t
Ž . Ž .
where Before s is a dummy variable corresponding to s years before the birth Ž .
Ž . of the first child, and After s is a dummy variable corresponding to s years
subsequent to the birth of the first child. Simulated age–wage and age–hours profiles for both husbands and wives are
Ž . presented in Figs. 1–8. To obtain these profiles, we estimate Eq. 2 for the
relevant outcome using random effects, evaluate the variables in X at their sample means, and plot two profiles for ages ranging from 24 to 45. The solid line in each
11
In specifications not reported here, we allowed the age dummies to vary by AcontinuousB vs. Anon-continuousB husbands and wives and for parents vs. non-parents. In every case except one — the
effects of having a child on the wages of men who were fathers and those who were not fathers — we rejected the hypothesis of heterogeneity in the effects of the age dummies and the qualitative results
Ž .
were similar although the magnitudes of the key coefficients were smaller . In the case in which heterogeneity could not be rejected, the qualitative results were similar except that the significance
level of the test that difference between b and b
is smaller for AcontinuousB husbands relative to
3 1
Ž .
Ž .
Anon-continuousB husbands for the outcome hourly wages was 0.13 borderline significant .
Fig. 1. Simulated wage of wife — all working wives.
figure is the simulated profile when the wife does not have a child prior to the end Ž
Ž . Ž .
of the sample period i.e., when Born s Before s
s After s s 0 for all
i t i t
i t
Ž ..
12
s . For wives, the crossed line is the simulated profile for a woman who has
her first child at age 30; for husbands, the crossed line is the profile for a man whose wife gives birth at age 30.
13
Fig. 1 contrasts the wage profiles for mothers and non-mothers. The crossed line is always below the solid line, suggesting that there is negative selection into
motherhood. Mothers earn less than non-mothers even prior to the birth of the first child. The profiles diverge over time: A first birth reduces women’s wages still
further. There is a particularly distinct fall in wages in the fifth year after the first child’s birth. This may be attributed to entry into the labor force of mothers of
school-age children for part-time work.
Fig. 2 shows the same profiles for the subset of women who work continuously during our sample window with the exception of the year in which a child is born
Ž .
the AcontinuousB subsample . There is evidence of selection between mothers and non-mothers in this subsample as well, but there appears to be less divergence
between the two profiles after the birth.
12
Since we do not observe couples during the entire course of their potential childbearing years, some individuals classified as parents may become parents at some point beyond our sample and
therefore should appropriately be classified as ABefore.B So the comparison of ABeforeB vs. ANoneB is really a comparison of ABefore the end of the sampleB vs. ANone.B
13
The coefficients and t-statistics for the coefficients used to generate these profiles are reported in Appendix A.
Fig. 2. Simulated wage of wife — wives who participate every year.
Fig. 3 contains simulated wage profiles for the husbands. Fathers earn less than non-fathers initially, although this relationship reverses at the time the first child is
born. Fathers appear to earn more than non-fathers until the child is about 10 years Ž .
old. For the husbands of wives who work continuously . , the fathers earn less than the non-fathers over the entire range. The gap narrows about 4 years after the
birth of the first child and then widens. In general, the profiles suggest negative selection into fatherhood, but a positive effect on wages of the birth of the first
child.
Fig. 3. Simulated wage of husband — all working husbands.
Fig. 4. Simulated wage of husband — whose wives participate every year.
Fig. 5. Simulated hours worked by wife — all working wives.
Fig. 6. Simulated hours worked by wife — wives who participate every year.
Fig. 7. Simulated hours worked by husbands — all working husbands.
Hours profiles are reported in Figs. 5–8. Fig. 5 indicates that average hours worked by wives falls from about 1700 to about 1000 hours per year upon the
birth of the first child, and then begin to increase about 5–10 years after the child’s birth. The simulation in Fig. 6 indicates that hours fall for women who are
continuous participants as well. As expected, the effect of the birth on hours worked by the husbands is less dramatic, but hours worked for the entire sample
Ž .
appear to increase following the birth Fig. 7 , while the effect for the husbands of Ž
. the continuous participants is very small but negative, at least initially Fig. 8 .
Examining these profiles is useful for gaining a broad view of the labor market experiences of first-time parents. However, there are some reasons to interpret
these profiles with caution. Many of the individual year ABeforeB and AAfterB
Fig. 8. Simulated hours worked by husbands — whose wives participate every year.
dummies are imprecisely estimated, especially far away from the birth. While random effects estimates are required in order to identify profiles of parents
relative to non-parents, the random effects estimates assume that the error term is uncorrelated with the regressors. Estimates of the AeffectB of a birth on hours and
wages can be consistently estimated under fixed effects under a less restrictive set of circumstances than estimates obtained under random effects. We therefore turn
to these fixed effects estimates in the next section.
5. Fixed effects estimates of the effects of parenthood on wage rates and hours
