New Approach Using Danish Register Data
5. Empirical Strategy
29 in a family fixed effect model.
Table 1 - Summary Statistics by Sample and Childbearing Timing
Sample 1 Sample 2 Sample 3
1NEC 1EC Diff (1)-(2) 2NEC 2EC Diff (5)-(6) 3NEC 3EC Diff (9)-(10)
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Log(Adult earnings) 14.80 14.59 0.21*** 14.67 14.54 0.12*** 14.50 14.46 0.04
(0.82) (1.02) (0.97) (1.08) (1.08) (1.10)
Education Length 13.12 12.39 0.72*** 13.01 12.25 0.76*** 12.37 11.99 0.38***
(2.13) (2.18) (2.23) (2.17) (2.24) (2.27)
Primary and Secondary
Education 0.20 0.29 -0.09*** 0.22 0.32 -0.10*** 0.28 0.36 -0.08***
(0.40) (0.45) (0.41) (0.47) (0.45) (0.48)
Vocational Education 0.45 0.48 -0.03*** 0.45 0.48 -0.03*** 0.48 0.44 0.03
(0.50) (0.50) (0.50) (0.50) (0.50) (0.50)
Tertiary Education 0.35 0.23 0.12*** 0.33 0.21 0.12*** 0.25 0.20 0.05**
(0.48) (0.42) (0.47) (0.41) (0.43) (0.40)
Yearly Earnings 269,761.6 249,410.0 20,351.6*** 261,192.2 242,132.8 19,059.4*** 234,725.3 229,975.1 4,750.2 (155,496.3) (153,075.1) (161,809.8) (151,677.4) (157,00.0) (168,454.3)
Wage Rate (#) 186.39 172.82 13.58*** 184.48 172.79 11.68*** 171.07 167.39 3.68
(62.44) (55.27) (63.56) (54.93) (56.75) (49.90)
Labor Participation 0.90 0.87 0.02*** 0.87 0.86 0.01** 0.85 0.85 0.00
(0.30) (0.33) (0.34) (0.35) (0.36) (0.36)
Age at first Birth 28.92 22.02 6.91** 27.42 21.91 5.51*** 27.17 21.55 5.62***
(3.65) (1.82) (3.23) (1.85) (2.94) (1.95)
Birth Year 1967.74 1966.77 0.97*** 1967.53 1967.15 0.38*** 1967.05 1966.59 0.46***
(4.48) (4.42) (4.64) (4.73) (4.40) (4.43)
Diagnoses 0.25 0.26 -0.005*** 0.30 0.27 0.03*** 0.31 0.27 0.04**
(0.48) (0.51) (0.54) (0.53) (0.52) (0.54)
Mother's Education 10.08 9.39 0.69***
(3.16) (2.90)
Father's Education (##) 10.56 10.48 0.07*** 11.01 10.39 0.61*** 10.03 9.98 0.05
(3.34) (3.32) (3.40) (3.28) (3.27) (3.24)
Observations 37,042 36,093 4,880 123,825 938 1,076
Note. 1EC and 1NEC are the early and non-early childbearing sisters in sample 1. 2EC and 2NEC are the early and non-early childbearing mothers in sample 2. 3EC and 3NEC are the early and non-early childbearing sisters in sample 3. Log(Adult Earnings) is the natural logarithm of the labor earnings from ages 25 to 40. Education Length is the years of the education from entering elementary school to finishing the highest ranked education. Primary and Secondary Education is a dummy indicating if the highest obtained education is either elementary or high school. Vocational Education is a dummy indicating if the highest obtained education is vocational training. Tertiary Education is a dummy indicating if the highest obtained education is any tertiary education, such as short cycle, medium cycle, bachelor, master or doctoral degrees. These three categories are mutually exclusive. Yearly Earnings consists of all labor earnings at age 40. Wage Rate is the hourly wage at age 40. (#) The observation numbers for this variable is lower since wage rates are only recorded for a subsample of the working population: 27,543; 25,919; 3,504; 86,449; 636; and 731 observations for 1NEC, 1EC, 2NEC, 2EC, 3NEC, and 3EC, respectively.
Labor Participation is a dummy taking the value 1 if the women have any labor earnings in the given year. Diagnoses is the average number of diagnoses per year excluding all pregnancy related diagnoses. Mother’s and Father’s Education is the educational length of the sample women’s parents – the small differences in the fathers’ education length between the sisters in sample 1 and 3 are due to the few sisters with different fathers. (##)The observation number for the father’s education is also lower since some of the fathers’ education length are not available:
34,271; 33074; 842; and 968 observations for 1NEC, 1EC, 3NEC and 3EC. There are none-missing for S2, since it is a control variable used in the regressions on this sample are women with missing information on their father’s education excluded. Monetary values are translated into year-2014 DKK using the Consumer Price Index from the Danish National Accounts. 1DKK≈0.13€. T-test for the difference in means between the early and non-early childbearing within the sample are shown at significant levels: p*<0.10, **0.05,
***p<0.01.
30 estimate the parameters in the following equation:
(1) ,
where yijt is the outcome variable of interest for individual i in family j at time t, whether it is the natural logarithm of adult earnings, yearly earnings, or educational length. EC is a dummy indicating early childbearing. γ is the coefficient of interest, estimating the effect of early childbearing. X is a vector of observable family- and individual-variant variables, such as the woman’s age, number of diagnoses, and birth order. Fj is a vector of observable family-invariant variables: immigration status and parental education level. Year is a year dummy included to absorb time effects common to all women. Let δ be the individual unobservable heterogeneity and α be the unobserved family heterogeneity, which is the same for all members of the same family – for example, parental involvement and social background.19 Cross-sectional models produce biased estimates if EC is correlated with the error term ε, as a result of omitted variables or reverse causality. Women may have differing priorities for family and career that lead some of them to both invest less effort in work and begin childbearing sooner. Further bias arises if women’s fertility timing is responsive to actual or anticipated career outcomes. If women with higher earnings potential postpone motherhood in order to reduce the financial penalty, the cross-sectional estimates will overestimate the benefits of postponing childbearing.
For my first approach, I follow Geronimus and Korenman (1992) and apply a within-family estimator to remove any within-family heterogeneity. This method compares sisters, one of whom is early childbearing and the other not. By taking the family averages, (2), and then subtracting it from the individual levels, (3), both the observed, F, and unobserved, α, family characteristics are removed from the model, (4). The idea is that after the heterogeneity that comes from the women’s social background is removed, the remaining differences between the
19 Some studies have proposed that parental involvement actually differs between their children. Hence, the parents are more involved in their first born than in the rest of their children. This phenomenon will be discussed in details later.
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sisters’ outcomes should be due to the difference in their age at first childbirth. The equations below show the within-family transformation of the family fixed effects estimator:
(2) (3) (4)
The family fixed effects model requires strict exogeneity within each family to be unbiased, which implies that early childbearing should be random among sisters, conditionally on X.
Individual heterogeneities between the sisters certainly still exist and may be correlated both with likelihood of early childbearing and with labor market outcomes. This problem can be partially resolved by controlling for pre-childbearing observables. Unobserved individual heterogeneities between the sisters, such as abilities and priorities for family and career, may still bias the estimator if no further measures are taken.
For my second approach, I follow Hotz et al. (1997) and exploit miscarriages as exogenous variation in timing of childbearing. There should not be any pre-pregnancy life-planning differences between the miscarrying and the non-miscarrying women, because all of them were pregnant with no evident intention of terminating the pregnancy. This addresses the selection problems between the early and non-early childbearing women.
Although miscarriages are perceived as highly random, three concerns must be raised: (i) Miscarriages may adversely affect the women psychologically. This could lead to later labor market effects if the miscarrying women suffer from longer spells of depression. Regan (2001) found that severe psychological effects of miscarrying predominantly affect women who experience recurrent miscarriages, which he estimates to be less than 1% of women. It is therefore doubtful that this effect will bias the results. (ii) Women with poor health and risky behavior during pregnancy may be more likely to miscarry. Both of these factors are also correlated with women’s labor market outcomes. Individuals with health problems generally
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perform worse in the labor market (Smith, 2009). This makes it difficult to separate differences in labor market performance due to miscarriage from those due to poor health. Although I cannot observe the pregnant women’s behavior, medical evidence does not support a strong impact of behavioral factors on risk of miscarriage (Merck, 1999).20 To address the health concern, I apply a control variable that captures the systematic health differences between the sisters, explained in detail in section 3. (iii) Ashcraft et al. (2013) and Fletcher and Wolfe (2009) found that even if miscarriages are biologically random, they are not socially random. Women from more disadvantaged backgrounds have a higher probability of miscarrying even after health differences are controlled for.
Finally, I combine the two approaches and estimate the effect of early childbearing on women’s adult earnings, yearly earnings and educational attainment by applying a within-family estimator and using sisters who postponed childbearing due to miscarriage.21 This strategy has the advantages of both strategies and also exhibits significant synergistic effects when the two are applied together. While miscarriages serve as an exogenous variation in timing of childbearing, addressing most of the selection issues, the within-family estimator addresses the bias due to family and social heterogeneities, which might affect both childbearing timing and the social bias in miscarriages. Lastly, I use controls for the sisters’ health and birth orders to address possible biases due to biological heterogeneities in miscarriages and intra-family biases, respectively.22
To implement the three identification strategies, I construct three samples, described in detail in section 3. I apply the standard family fixed-effects model on sample 1, with additional controls for health, birth order, and year dummies. On sample 2, I apply an OLS regression in which members of the control group were all pregnant before age 25 but miscarried and thus postponed childbearing until after turning 25, while also controlling for health, birth order, and
20 Chatenoud et al. (1998), George et al. (2006), and Venners et al. (2004) found mixed results on the impact of smoking on pregnancy losses.
21 This strategy is an extension of my previous work presented in my Master Thesis (Rosenbaum, 2014).
22 Some literature find evidence for birth order effects on economic outcomes, see Berhman & Taubman (1986), Ejrnæs & Portner (2004), Black (2005), Sulloway (1996), Price (2008) and Ladner (1971).
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year dummies. For this sample, I also control for the observed time-invariant family variables such as parental education level and being immigrants.23 On sample 3, I apply the family fixed effects model, conditioning it so that the control sister was pregnant before 25 but miscarried and thus postponed childbearing until after turning 25, while also controlling for health, birth order, and year dummies.
Visual Evidence
To evaluate the common trend assumption and the strength of treating miscarriages as exogenous variation, I reorganize the panel as an event study to show the exact timing of the labor market divergence between early and non-early childbearing mothers. I define the event t0
as the age at first birth for the early childbearing mother and as the age at miscarriage for the non-early childbearing mother.24 Since the non-early childbearing sisters in sample 1 do not have a natural event benchmark, the early childbearing sister’s age at first birth is defined as the event, t0, for all sisters in the family. I follow the women from t0-5 to t0+16.
The panels in figure 2 show a high degree of common trend up until t0-1 for the early and non-early childbearing women in sample 2 and 3, indicating similar labor, educational, and marital trajectories. The figure shows that there are bigger pre-event differences within sample 1, where fewer non-early childbearing sisters are married and more are undertaking an education. Panel A shows that the trajectories in yearly earnings are similar before the event but diverge at that time:
the early childbearing mother falls behind just after the event for all samples. The gap between the early childbearing and non-early childbearing mothers then persists through the time series for sample 1 and 2, but it narrows and almost disappears for sample 3. The trajectories are similar for labor participation, shown in Panel C.
The trends are in fact also similar when looking at panel C, where the ratio of women who
23 Immigrant is defined as a dummy equal to 1 if the mother is a first- or second-generation immigrant.
24 If the non-early childbearing woman had multiple miscarriages, I use the last one before age 25 as the event.
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are either married or in cohabiting relationships is depicted. The pre-event gap in married women is much larger in sample 1 compared to sample 2 and 3. Lastly, panel D shows the ratio of women under education, defined as not having completed their highest educational attainment.
This panel shows similar trends for all women and does not indicate any drastic change in pursuing education due to having or expecting to have a child.25 One small difference remains, the panel shows that the non-early childbearing women in sample 1 are pursuing education for a bit longer than the rest of the women. Altogether, this is in line with the prediction that there would be less pre-pregnancy differences between the miscarrying and the non-miscarrying women, because all of them were pregnant with no evident intention of terminating the pregnancy. This suggests that treating miscarriage as exogenous variation addresses the possible pre-birth heterogeneities between the mothers.
25 This may be due to Danish institutional settings, where education is free and students are subsidized with a monthly transfer from the government of around DKK 6,000 while undertaking any tertiary education. The consequences of the specific Danish institutional settings will be discussed in the next section.
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Figure 2 – Time Trends, Crude Means by Sample and Early Childbearing Panel A. Yearly Earnings Panel B. Labor Participation
Panel C. Marriage Panel D. Under Education
Note. The figures show the crude means around the event from t-5 to t+16 of the early and non-early childbearing women in Yearly Earnings (panel A), Labor Participation (panel B), Marital Status (panel C), and being in Education (panel D). The event is defined as the age of first birth for the early childbearing mother and as the age of the miscarriage for the non-early childbearing mother. For Sample 1 the early childbearing sister’s age at first birth is defined as the event for all sisters in the family. Labor Participation is a dummy taking the value 1 if the women have any labor earnings in the given year. Marriage is defined as either marriage by law or being in a cohabiting relationship. Under Education is defined as not having completed their highest educational attainment. Monetary values are translated into year-2014 DKK using the Consumer Price Index from the Danish National Accounts. 1DKK≈0.13€.
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Amenability to Generalization: Global or Local Treatment Effect?
Ideally, the sample selection process of this study provides a universe in which the only systematic difference between the sisters is the timing of their first births. This is done by imposing strict inclusion criteria and thus focusing on the few specific women who are very much alike. Murphy (2005) argued that the number of early pregnancies in a family is correlated with poor socioeconomic status, indicating that the estimates obtained on the basis of the samples might be interpreted as a local treatment effect that does not account for the entire population of early childbearing mothers. On the other hand, the majority of early childbearing mothers come from economically disadvantaged backgrounds in the first place, which suggests that this study is relevant for most of the cases.