Table 2 Summary Statistics for Children in Sample
Older Sibling Younger Sibling
Birth year 1985.39
1988.54 5.75
5.60 Female
0.4867 0.4841
0.4999 0.4998
Hispanic 0.0871
0.0817 0.2820
0.2739 Black
0.1916 0.1824
0.3936 0.3862
Ideal family size in 1979 2.98
2.98 1.28
1.29 Total number of children, by 2006
3.16 3.17
1.19 1.19
Age of mother at first birth 23.16
22.98 5.04
4.84 PIAT Score, reading
23.26 20.53
12.99 11.15
PIAT Score, math 20.94
19.03 11.73
10.19 Gap between Child 2 and Child 3
0.2704 0.2705
Gap between Child 3 and Child 4 0.1028
0.0988 Gap between Child 4 and Child 5
0.0288 0.0290
Observations 5,010
4,868 Mean years between
3.40 1.97
Median years between 2.84
Fraction less than two years apart 0.2598
0.4386 Miscarriage between siblings
0.0635 0.2438
Data are from the NLSY79 and the NLSY79 Child and Young Adult Survey. Each observation is a sibling pair. Standard deviations are in parentheses. Child weights are used, and the sample is restricted to intervals
smaller than ten years.
IV. Estimation: OLS
We begin by estimating the effects of birth spacing on sibling out- comes using OLS. The model to be estimated is:
Score = β + gap β + X β + Z β + u
1
is i
1 s
2 i
3 is
where the subscript i indexes a sibling pair and s indicates whether the variable describes the older or younger sibling of the pair. In all regressions, the effect of
the gap is estimated separately for older and younger siblings. The dependent vari- able is the standardized, age-adjusted PIAT score in math or reading recognition.
The variable gap
i
is either a the spacing between the births of the two siblings, in years;
14
b the log of spacing, in years; or c a dummy variable indicating that the spacing was shorter than two years.
15
We also consider specifications with a qua- dratic in spacing. The vector X
s
is a set of characteristics specific to child s of the pair, including gender, race, birth order, and a set of year- and month-of-birth dum-
mies. Z
i
is a vector of characteristics common to both children in the pair, and includes the mother’s age at first birth, ideal number of children in 1979, and marital
history, highest degree obtained, and adjusted AFQT score; u
is
is error. Estimates are weighted by NLSY child sampling weights. Because a mother with more than
two children will have more than one sibling pair in the data set, standard errors are clustered by mother.
OLS results for older siblings are presented in Table 3, with results for reading in Panel A and for math in Panel B. In the first column, the coefficient is from a
simple regression of test score on the gap in years. The correlation is positive but small and statistically insignificant for both reading and math. However, in Speci-
fication 2 with the above controls included, there is a small statistically significant relationship between spacing and math scores. A one-year increase in spacing is
associated with an increase in scores of 0.0248 SD. The regressions with log or quadratic functional forms have slightly higher R-squared values, suggesting that the
relationship might be non-linear; the level of spacing that maximizes predicted test scores is around six years. The coefficient on the dummy indicating spacing of
shorter than two years is −0.07 for reading and −0.14 for math, indicating that especially close spacing has a strong negative association with academic achieve-
ment.
For the younger siblings, however, there is little association between spacing from the older sibling and test scores Table 4. The raw correlation is negative for math,
but the coefficient is smaller and statistically insignificant when controls are added. It does appear that spacing of shorter than two years is associated with lower math
scores, but the effect is smaller than the effect for older children.
The results in this section show that longer spacing between siblings is associated with higher test scores, though primarily for older siblings. However, our results
may be biased if spacing between siblings is correlated with unobservable charac- teristics of the mother or children. Rosenzweig 1986 and Rosenzweig and Wolpin
1988 show that unobserved heterogeneity across- and within-families biases OLS
14. We measure spacing as days between births, and convert it to years by dividing by 365 for ease in interpretation.
15. We choose a point of two years because it is interesting from a policy perspective; programs like those mentioned in the introduction typically advocate spacing of greater than two years. Also, as seen in Figure
1, the mode of the spacing distribution is about two years. We have produced both OLS and IV results using other measures, and results generally accord with intuition. For example, estimates of the effect of
spacing shorter than three years on test scores for older children are still negative but are smaller in magnitude and less precisely estimated.
Table 3 OLS Estimates of Effect of Spacing on Test Scores of OLDER Siblings
Panel A: PIAT-Reading Spacing Measure
1 2
3 4
5 Gap in years
0.0023 0.0136
0.0672 0.0096
0.0086 0.0327
Gap in years
2
−0.0060 0.0034
lngap in years 0.0615
0.0304 Gap less than two years
−0.0712 0.0408
R -squared
0.0000 0.1932
0.1939 0.1936
0.1934 Controls
x x
x x
Panel B: PIAT-Math Spacing Measure
1 2
3 4
5 Gap in years
0.0075 0.0087
0.0248 0.0077
0.1029 0.0320
Gap in years
2
−0.0087 0.0033
lngap in years 0.1074
0.0279 Gap less than two years
−0.1375 0.0388
R -squared
0.0002 0.2117
0.2132 0.2129
0.2129 Controls
x x
x x
Each column is from a separate regression and gives the coefficient on the spacing measure for the indicated specification where gaps in years are calculated as days365. Each observation is a sibling pair, and child
weights are used. The dependent variable is the age-adjusted, standardized test score in math or reading, for the older sibling in the pair. Additional controls include child gender and mother’s race, age at first
birth, education, ideal family size in 1979, marital status, AFQT score, and child month-and year-of-birth dummies. Standard errors are clustered by mother in parentheses. Sample is restricted to intervals smaller
than ten years; there are 4,398 observations in each regression.
estimates of the effects of birth spacing on child outcomes. Rosenzweig 1986 finds that when parents have a child with a better endowment, they have the next birth
sooner. In this case, OLS estimates of the effect of spacing on the outcomes of the older child would be negatively biased, and may also be negatively biased for the
Table 4 OLS Estimates of Effect of Spacing on Test Scores of YOUNGER Siblings
Panel A: PIAT-Reading Spacing Measure
1 2
3 4
5 Gap in years
0.0006 −0.0079
−0.0445 0.0092
0.0102 0.0328
Gap in years
2
0.0041 0.0034
lngap in years −0.0339
0.0350 Gap less than two years
0.0125 0.0436
R -squared
0.0000 0.2024
0.2028 0.2025
0.2022 Controls
x x
x x
Panel B: PIAT-Math Spacing Measure
1 2
3 4
5 Gap in years
−0.0172 −0.0066
0.0265 0.0086
0.0105 0.0325
Gap in years
2
−0.0037 0.0035
lngap in years 0.0025
0.0351 Gap less than two years
−0.0884 0.0404
R -squared
0.0012 0.2254
0.2257 0.2253
0.2267 Controls
x x
x x
Each column is from a separate regression and gives the coefficient on the spacing measure for the indicated specification where gaps in years are calculated as days365. Each observation is a sibling pair, and child
weights are used. The dependent variable is the age-adjusted, standardized test score in math or reading, for the younger sibling in the pair. Additional controls include child gender and mother’s race, age at first
birth, education, ideal family size in 1979, marital status, AFQT score, and child month-and year-of-birth dummies. Standard errors are clustered by mother in parentheses. Sample is restricted to intervals smaller
than ten years; there are 4,074 observations in each regression.
younger child if outcomes are positively correlated across children. However, if families with larger gaps between children are more likely to have planned their
births, and planning is correlated with better outcomes, OLS results would have a positive bias. These are just two plausible stories of omitted variable bias; there are
likely others. In order to address this problem, we employ an identification strategy that uses miscarriages as exogenous factors that affect birth spacing.
V. Miscarriages as an Instrumental Variable
