is presented for all known children and three subsamples: 1 children continuously in the sample, 2 children for whom supplemental information is sometimes col-
lected, and 3 children for whom supplemental information is never collected. The comparisons are done separately for the full and cross-sectional samples. Although
the mothers of children in the continuous sample score higher on the AFQT than the mothers of children who are either sometimes or never in the NLSY-C, along most
other dimensions they look similar to the mothers of the children for whom supple- mental information is sometimes collected. The mothers of the children for whom
supplemental information is never collected look different in that they are the most likely to have had a child and the least likely to have never been married at the 1979
interview.
Overall, children who are surveyed in some of the child supplement years in which they are eligible are similar to those who are surveyed in all eligible years. The
mothers of these two groups of children also appear similar. However, the children who are not interviewed in any of the mother-child supplement years and their moth-
ers are different. These mothers more often experienced an early marriage or birth. Attrition from the NLSY79 prior to the start of the child supplement appears nonran-
dom with respect to women’s fertility through 1979 and marital status at that time. Evaluating the effects that this attrition has on the sample of children is made difcult
because there is no information on children whose mothers attrite before their births, but the fact that there are not many of these children minimizes the chance that their
absence will have large consequences.
III. Nature of Attrition
This section further examines how attritors are different from nonat- tritors by estimating two types of equations. The samples for these equations are
restricted to children who have been born in 1994 or earlier and have not attrited prior to having been assessed for the rst time on the PPVT eligible at age three
or the BPI eligible at age four depending on the assessment of interest. The rst of these equations is a probit that estimates the probability that an individual is an
attritor at a future NLSY79-C interview.
1 P
[A
i 2000
5 1] 5 FX
i
b
l
1X
it
b
2
where A
i2000
indicates that the individual attrites by the year 2000 interview, X is the general notation for the covariates included in the analysis, some of which are perma-
nent characteristics of the child or her mother and others are measured at age t in the survey where the child is rst age-eligible for the assessment, and b are the
parameters estimated to gauge the extent to which attritors come from certain seg- ments of the population. The equation is estimated for the full and cross-sectional
samples of the children in the NLSY79-C. Four specications are estimated; they focus on family income early in the child’s life measured by average income over
the child’s rst three years in 1984 or maternal employment in the child’s rst year measured by hours worked during the child’s rst year and a dummy variable
indicating the mother worked at all in the child’s rst year and contain either BPI or PPVT standard scores at the rst survey in which the child was age-eligible for
the assessment. By including individual characteristics, one can test whether children who attrite come from particular backgrounds.
7
Table 6 presents coefcient estimates and marginal effects for Equation 1. The full sample results indicate that Black and Hispanic children are more likely than
other children to attrite. The children whose mothers have never married are less likely to attrite compared to those whose mothers are married, separated, or divorced.
The probability of attrition increases in average family income during the child’s rst three years. In the specications that include family income, the probability of
future attrition is decreasing in the educational attainment of one’s maternal grand- father by 0.6 of a percentage point for each additional grade completed by one’s
grandfather. Moreover, in the specication that includes early maternal employment and BPI scores, attrition appears nonrandom with respect to BPI scores.
As was the case in the full sample, in the cross-section a child from higher-income family or whose mother is divorced or separated or married is more likely to attrite,
and the effects remain small. However, attrition appears less connected to character- istics of the children when the cross-section is examined separately, implying that
the process of attrition for the cross-section may be different than that in the Black and Hispanic supplements.
Although attrition is related to some of the characteristics included in the probit equations on attrition, the psuedo-R
2
for these equations is quite low, ranging from 0.012 to 0.034 which indicates that much of the attrition is not associated with the
variables controlled for in these specications. Attrition appears random with respect to maternal employment in the child’s rst year of life, but is related to family income
early in the child’s life.
The second type of equation examines the effect of attrition on the estimates of the effect of family characteristics measured early in the child’s life on his BPI and
PPVT standard scores. 2
AS
it
5 a 1 rFC
iE
1 b
1
Z
i
1 b
2
Z
it
1 e
it
where AS
it
is child i’s assessment standard score on either the PPVT or BPI and t is the rst interview at which the child is age-eligible for that assessment, FC
iE
is a characteristic of the child’s parent or family measured early in the child’s life at
time E, Z are the additional covariates controlled for, e
it
is a random error, and r is the coefcient on the family characteristics of interest. These equations are esti-
mated using the same samples that are used in the attrition probits above, as well as, the subsample of nonattritors. The differences in the estimates of r for the sample
with and without the attritors are then compared to see how attrition impacts the estimated relationship. Four models are estimated for each sample and subsample:
1 Model 1 contains no additional covariates, 2 Model 2 includes a dummy vari- able for race, a dummy variable for ethnicity, child’s gender, child’s age in months,
and highest grade completed by each of the child’s maternal grandparents in the Vector Z, 3 Model 3 adds a set of dummy variables indicating child’s year of birth
7. This analysis is similar to Mott 1998 where the probability of having a valid PIAT-math or BPI score at the next child-supplement interview is examined conditional on having a valid score at the current
interview.
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Table 6a Attrition Probit, Child Ever Out: Full Sample
Coefcient Marginal Coefcient Marginal Coefcient Marginal Coefcient Marginal Estimate
Effect Estimate
Effect Estimate
Effect Estimate
Effect Black
0.348 0.119
0.379 0.132
0.312 0.107
0.338 0.118
0.061 0.062
0.071 0.073
Hispanic 0.497
0.175 0.520
0.186 0.468
0.167 0.520
0.188 0.072
0.074 0.080
0.082 Mother’s age 1979
20.013 20.004
20.012 20.004
20.023 20.008
20.015 20.005
0.018 0.019
0.021 0.021
Mother’s highest grade 1979 0.001
0.000 0.006
0.002 0.013
0.004 0.010
0.003 0.019
0.020 0.022
0.023 Number of children 1979
20.093 20.030
20.106 20.035
20.053 20.018
20.038 20.013
0.060 0.062
0.066 0.066
Mother’s marital status Married
0.177 0.061
0.213 0.074
0.194 0.067
0.192 0.068
0.081 0.083
0.089 0.093
Divorcedseparated 0.417
0.151 0.493
0.183 0.404
0.148 0.432
0.160 0.194
0.210 0.213
0.218 Male child
0.083 0.027
0.070 0.023
0.079 0.026
0.056 0.019
0.038 0.040
0.044 0.046
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Table 6a continued
Coefcient Marginal Coefcient Marginal Coefcient Marginal Coefcient Marginal Estimate
Effect Estimate
Effect Estimate
Effect Estimate
Effect Grandmother’s highest grade
0.005 0.002
0.004 0.001
0.002 0.001
0.005 0.002
0.011 0.011
0.012 0.012
Grandfather’s highest grade 20.018
20.006 20.017
20.006 20.019
20.006 20.018
20.006 0.009
0.009 0.009
0.010 PPVT score
20.000 20.000
0.000 0.000
0.001 0.001
BPI score 20.003
20.001 20.003
20.001 0.002
0.002 Average income in rst three years
0.012 0.004
0.016 0.005
10,000 0.006
0.006 Maternal hours worked
0.053 0.018
0.069 0.023
In rst year 1,000 hours 0.042
0.045 Work rst year
20.084 20.028
20.044 20.015
0.073 0.080
Number of observations 5,080
4,582 3,872
3,493 Psuedo R-squared
0.030 0.034
0.031 0.034
Notes: Samples are composed of children born in 1994 or earlier and who do not attrite prior to rst assessment on either the BPI or PPVT. PPVT and BPI scores are standardized for age of the child. indicates signicance at the 1 percent level and at the 5 percent level. Standard errors are clustered by mother id and are presented
in parentheses. Regressions also include two dummy variables indicating grandfather’s education and grandmother’s education are missing.
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Table 6b Attrition Probit, Child Ever Out: Cross-Section
Coefcient Marginal Coefcient Marginal Coefcient Marginal Coefcient Marginal Estimate
Effect Estimate
Effect Estimate
Effect Estimate
Effect Black
0.008 0.002
0.068 0.020
0.018 0.005
0.036 0.011
0.103 0.104
0.116 0.119
Hispanic 20.002
20.001 0.059
0.017 0.073
0.022 0.145
0.045 0.129
0.134 0.136
0.139 Mother’s age 1979
0.007 0.002
0.005 0.001
0.009 0.003
0.014 0.004
0.027 0.028
0.029 0.030
Mother’s highest grade 1979 20.029
20.008 20.016
20.005 20.032
20.009 20.023
20.007 0.030
0.031 0.032
0.034 Number of children 1979
20.074 20.021
20.086 20.025
20.081 20.024
20.037 20.011
0.086 0.091
0.092 0.092
Mother’s marital status Married
0.157 0.046
0.213 0.065
0.209 0.065
0.207 0.065
0.104 0.107
0.113 0.117
Divorcedseparated 0.635
0.218 0.642
0.222 0.685
0.243 0.667
0.237 0.224
0.244 0.243
0.249 Male child
0.059 0.017
0.069 0.020
0.014 0.004
20.000 20.000
0.053 0.055
0.057 0.061
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Table 6b continued
Coefcient Marginal Coefcient Marginal Coefcient Marginal Coefcient Marginal Estimate
Effect Estimate
Effect Estimate
Effect Estimate
Effect Grandmother’s highest grade
20.010 20.003
20.010 20.003
20.022 20.007
20.017 20.005
0.017 0.017
0.018 0.019
Grandfather’s highest grade 20.008
20.002 20.005
20.001 20.003
20.001 20.004
20.001 0.012
0.013 0.013
0.013 PPVT
20.002 20.001
20.001 20.000
0.002 0.002
BPI 20.001
20.000 20.002
20.001 0.002
0.002 Average income in rst three years
0.014 0.004
0.018 0.005
10,000 0.007
0.008 Maternal hours worked
20.004 20.001
20.024 20.007
In rst year 1,000 hours 0.055
0.061 Work rst year
20.067 20.019
20.015 20.005
0.095 0.103
Number of observations 3,139
2,820 2,417
2,155 Pseudo R-squared
0.012 0.014
0.019 0.020
Notes: Samples are composed of children born in 1994 or earlier and who do not attrite prior to rst assessment on either the BPI or PPVT. PPVT and BPI scores are standardized for age of the child. indicates signicance at the 1 percent level and at the 5 percent level. Standard errors are clustered by mother id and are presented
in parentheses. Regressions also include two dummy variables indicating grandfather’s education and grandmother’s education are missing.
to the variables included in Model 2, and 4 Model 4 adds mother’s AFQT score to those variables in Model 3.
As Fitzgerald, Gottschalk, and Moftt 1998 note, some attrition will have oc- curred before the child reaches age t and consequently the estimates may already
be biased. To test whether further attrition is biasing, Fitzgerald, Gottschalk, and Moftt assume that attrition pre- and post- age t biases the coefcient estimates in
the same direction. This assumption is sufcient to permit inference that there is attrition bias in the sample if attrition bias is found in the post-period. I also make
this assumption.
Table 7 examines how attrition impacts estimation of the effect of average income during the child’s rst three years measured in units of 10,000 1984 on PPVT
and BPI standard scores. The top half presents coefcient estimates for the full sam- ple while the bottom half present the estimates for the cross-section.
As in past literature that has examined the effect of family income on child devel- opment Blau 1999, Mayer 1997, income tends to improve test scores by a small,
but statistically signicant amount. In general, the magnitude of the family income effect is slightly larger among the nonattritors; however, in no case is the difference
between the coefcient estimates using all observations and using the nonattritors signicantly different from zero.
8
Table 8 examines the impact of attrition on estimates of the effect of maternal employment on children’s PPVT and BPI scores. Hours of work in units of 1,000
hours during the child’s rst year and a dummy variable indicating whether the mother worked during the child’s rst year are used to measure maternal employ-
ment.
9
In Panel A, the coefcient estimates for the maternal employment variables are presented for the full sample for both all children and for the nonattritors. Panel
B presents this same information for the cross-sectional sample. The estimates pre- sented here are in accord with a large number of studies that use the NLSY79-C
and nd small effects of maternal employment on early PPVT and BPI scores for example, James-Burdumy 1999 and Harvey 1999.
10
Although in the full sample hours worked in the child’s rst year do not have a signicant impact on PPVT scores, the dummy variable indicating that the mother
worked implies that it is benecial for the child to have a mother who works during his rst year of life. These benets decline as controls are added, which seems to
imply positive selection of women into the labor force during their children’s rst year. In Models 1 and 2, additional hours of work by the mother appear to reduce
behavioral problems and the dummy variable for working in the child’s rst year has
8. The standard errors are calculated using the fact that the variance of the difference in the coefcients for the total sample and the nonattriting subsample is equal to the difference in the variances. See Fitzgerald,
Gottschalk, and Moftt 1998 and reference therein for more detail. 9. In much of the literature on the impact of maternal employment on child development, maternal employ-
ment is measured by hours worked in the child’s rst three years measured with three variables, one for each year. Owing to the high correlation between hours worked in these years, changes in either the sample
used for estimation or the specication can have large effects on all three of the coefcients estimates on hours worked that may balance each other out. Consequently, to study the impact of attrition, I measure
early maternal employment using only employment in the child’s rst year. 10. A larger detrimental effect from early maternal employment is found when either the outcomes of
white children Han and Waldfogel 2001 or achievement test scores for 5- and 6- year-olds Ruhm 2001 are examined.
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Table 7 Estimates of Effect of Average Family Income in First 3 Years on Child Assessments
PPVT BPI
Full Sample Nonattritors
All Nonattritors
All n 5 3,872 n 5 2,782
Difference n 5 5,080
n 5 3,695 Difference
Model 1 0.957
1.012 0.055
20.440 20.487
0.047 0.160
0.218 0.148
0.064 0.075
0.039 [0.030]
[0.030] [0.014]
[0.015] Model 2
0.247 0.236
0.011 20.320
20.345 0.025
0.095 0.120
0.073 0.058
0.067 0.034
[0.321] [0.342]
[0.033] [0.037]
Model 3 0.228
0.235 0.007
20.221 20.237
0.016 0.097
0.124 0.077
0.054 0.062
0.030 [0.325]
[0.345] [0.060]
[0.068] Model 4
0.061 0.027
0.034 20.175
20.182 0.007
0.089 0.114
0.071 0.052
0.062 0.034
[0.357] [0.379]
[0.064] [0.072]
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All n 5 2,417 n 5 1,883
Difference n 5 3139
n 5 2,496 Difference
Model 1 0.663
0.762 0.099
20.400 20.440
0.040 0.152
0.203 0.135
0.073 0.084
0.042 [0.020]
[0.021] [0.014]
[0.014] Model 2
0.144 0.202
0.058 20.274
20.302 0.028
0.093 0.114
0.066 0.064
0.074 0.037
[0.291] [0.295]
[0.041] [0.038]
Model 3 0.135
0.193 0.058
20.194 20.203
0.009 0.097
0.121 0.072
0.061 0.069
0.032 [0.296]
[0.301] [0.071]
[0.074] Model 4
0.007 0.022
0.015 20.165
20.165 0.000
0.091 0.114
0.069 0.060
0.070 0.036
[0.327] [0.333]
[0.074] [0.077]
Notes: Samples are composed of children born in 1994 or earlier and who do not attrite prior to rst assessment on either the BPI or the PPVT. PPVT and BPI scores are standardized for age of the child. Income is measured in units of 10,000 1984 . Model 1 includes no additional controls, Model 2 includes a dummy variable for
race, a dummy variable for ethnicity, child’s gender, child’s age in months, highest grade completed by each of the child’s maternal grandparents, and dummy variables indicating grandparents’ highest grade is missing in the Vector X, Model 3 includes a set of dummy variables indicating child’s year of birth and the variables included
in Model 2, and Model 4 includes mother’s AFQT score and those variables in Model 3. indicates signicance at the 1 percent level and at the 5 percent level. Standard errors are clustered by mother id and are presented in parentheses. R-squared’s are presented in square brackets.
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Table 8a Estimates of Effect of Maternal Employment in First Year on Child Assessments: Full Sample
PPVT BPI
Nonattritors All
Nonattritors All n 5 3,493
n 5 2,478 Difference
n 5 4,582 n 5 3,289
Difference Model 1
Hours 21.055
21.270 0.215
21.009 21.402
0.393 0.649
0.764 0.403
0.416 0.471
0.221 Any work
8.909 9.007
0.098 20.651
20.179 0.472
1.195 1.359
0.647 0.725
0.828 0.400
[0.029] [0.028]
[0.006] [0.008]
Model 2 Hours
0.128 20.497
0.625 21.139
21.489 0.350
0.543 0.622
0.303 0.411
0.466 0.220
Any work 3.540
3.632 0.092
0.441 0.933
0.492 0.976
1.086 0.476
0.726 0.830
0.402 [0.331]
[0.347] [0.033]
[0.038]
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All n 5 3,493 n 5 2,478
Difference n 5 4,582
n 5 3,289 Difference
Model 3 Hours
0.130 20.401
0.531 20.467
20.785 0.318
0.577 0.641
0.279 0.412
0.469 0.224
Any work 3.536
3.702 0.166
0.151 0.591
0.440 0.986
1.098 0.483
0.718 0.825
0.406 [0.335]
[0.352] [0.061]
[0.069] Model 4
Hours 20.169
20.630 0.461
20.384 20.725
0.341 0.543
0.620 0.299
0.413 0.471
0.226 Any work
2.294 2.225
0.069 0.458
0.959 0.501
0.986 1.078
0.436 0.717
0.827 0.412
[0.363] [0.383]
[0.066] [0.075]
Notes: Samples are composed of children born in 1994 or earlier and who do not attrite prior to rst assessment on either the BPI or the PPVT. PPVT and BPI scores are standardized for age of the child. Hours are measured in units of 1,000. Model 1 includes no additional controls, Model 2 includes a dummy variable for race, a
dummy variable for ethnicity, child’s gender, child’s age in months, highest grade completed by each of the child’s maternal grandparents, and dummy variables indicating grandparents’ highest grade is missing in the Vector X, Model 3 includes a set of dummy variables indicating child’s year of birth and the variables included
in Model 2, and Model 4 includes mother’s AFQT score and those variables in Model 3. indicates signicance at the 1 percent level and at the 5 percent level. Standard errors are clustered by mother id and are presented in parentheses. R-squared’s are presented in square brackets.
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Table 8b Estimates of Effect of Maternal Employment in First Year on Child Assessments: Cross-Section
PPVT BPI
All Nonattritors
All Nonattritors
n 5 2,155 n 5 1,670
Difference n 5 2,820
n 5 2,225 Difference
Model 1 Hours
20.773 20.965
0.192 20.483
20.991 0.508
0.762 0.849
0.374 0.521
0.554 0.188
Any work 6.407
6.110 0.297
20.850 20.227
0.623 1.366
1.538 0.707
0.890 0.967
0.378 [0.018]
[0.015] [0.003]
[0.004] Model 2
Hours 0.002
0.041 0.039
20.551 21.057
0.506 0.648
0.712 0.295
0.511 0.548
0.198 Any work
2.332 1.913
0.419 0.033
0.540 0.507
1.126 1.240
0.519 0.892
0.972 0.386
[0.288] [0.282]
[0.039] [0.038]
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n 5 2,155 n 5 1,670
Difference n 5 2,820
n 5 2,225 Difference
Model 3 Hours
0.135 0.200
0.065 0.166
20.313 0.479
0.666 0.739
0.320 0.516
0.554 0.202
Any work 2.198
1.859 0.339
20.226 0.266
0.492 1.130
1.246 0.525
0.884 0.967
0.392 [0.294]
[0.291] [0.071]
[0.072] Model 4
Hours 20.156
20.024 0.132
0.221 20.267
0.488 0.647
0.716 0.307
0.516 0.555
0.204 Any work
1.170 0.766
0.404 20.008
0.509 0.517
1.106 1.227
0.531 0.882
0.967 0.396
[0.322] [0.322]
[0.075] [0.076]
Notes: Samples are composed of children born in 1994 or earlier and who do not attrite prior to rst assessment on either the BPI or the PPVT. PPVT and BPI scores are standardized for age of the child. Hours are measured in units of 1,000. Model 1 includes no additional controls, Model 2 includes a dummy variable for race, a
dummy variable for ethnicity, child’s gender, child’s age in months, highest grade completed by each of the child’s maternal grandparents, and dummy variables indicating grandparents’ highest grade is missing in the Vector X, Model 3 includes a set of dummy variables indicating child’s year of birth and the variables included in Model
2, and Model 4 includes mother’s AFQT score and those variables in Model 3. indicates signicance at the 1 percent level and at the 5 percent level. Standard errors are clustered by mother id and are presented in parentheses. R-squared’s are presented in square brackets.
no effect. In both the PPVT and BPI equations, the differences between the coefcient estimates on the maternal employment variables when the attritors are included in
the estimation and when they are not included are small and never signicant. When these equations are estimated using the cross-sectional sample, the coef-
cient estimates on the maternal employment variables are rarely signicant. For all four specications of BPI standard scores, the differences in the coefcient estimates
on hours worked in the child’s rst year are signicant. Though the coefcient esti- mates themselves are not signicantly different from zero in three of the four speci-
cations, exclusion of the attritors makes it appear that hours worked by the mother in the child’s rst year are more effective in decreasing behavioral problems com-
pared to those estimates that include the attritors. This may imply that the intensity of work during a child’s rst year varies systematically by future attrition with char-
acteristics that are not controlled for here.
I also estimate Equations 1 and 2 using an older sample that employs the assess- ment scores from two years later and requires children not to have attrited up to that
point. The sample sizes are much smaller and hence it is not surprising that almost none of the regressors in the attrition probits are signicant. However, family income
remains signicantly negative in the probit that includes PPVT. In the estimates of Equation 2 that use the older children, the differences in the estimates of r between
samples that include and exclude the attritors are never signicant. Compared with the results presented in Tables 7 and 8, the computed differences and their standard
errors are approximately an order of magnitude larger.
IV. Conclusion
