4.1.1. First-stage equation

We exploit exogenous variation in coresidence status by legal marriageability defined by marriageable age legislation and the reform of the legislation. We use two dummy variables as IVs, one indicating eligibility to marry without parental consent (NoConsent) and the other eligibility to marry with parental consent (Consent). The first-stage equation is as follows:

(1)$$CRB_{it} = \alpha_1{Consent}_{it} + \alpha_2{NoConsent}_{it} + \kappa_1{Age}_{it} + \kappa_2{Age}^2_{it} + X_{it}\gamma_1 + \tau_{1t} + \epsilon_{1it}$$

where subscripts represent individual birth i at year t and X _it is other control variables.Footnote ¹² CRB _it is the indicator for CRB mothers, which can be formally written as the following:

(2)$$CRB_{it} = 1[ \tau^C_{it} < \tau^R_{it}] $$

where $\tau ^C_{it}$ is the time of conception and $\tau ^R_{it}$ is the start time of coresidence. The indicator variable represents that conception is ahead of coresidence.

Alternatively, as the dependent variable in equation (1), we use a continuous variable, which is the proportion of pregnancy period with a coresiding partner:

(3)$$CRRatio_{it} = {{\tau^B_{it} - \tau^R_{it}\over \tau^B_{it} -\tau^C_{it}}}$$

where $\tau ^B_{it}$ is the time of birth. The denominator, $( \tau ^B_{it} - \tau ^C_{it})$, is the length of gestation. Thus, this is a measure of the intensity of coresidence treatment, the ratio of co-residing pregnancy out of the whole gestation weeks [which we call as the CR (Conception–Coresidence) ratio]. For noR mothers, $\tau ^B_{it}$ is equal to $\tau ^R_{it}$ and the variable is 0 because they never coreside during pregnancy. Likewise, for RCB mothers the ratio is equal to 1 by definition because these are the mothers who coreside during the entire duration of pregnancy. For robustness, we use both CRB _it and CRRatio _it but, for expositional simplicity, explain the estimation models using the first.

The first two variables on the right-hand side in equation (1) are our IVs. Consent _it is the indicator of whether the mother must have parental consent to marry. Specifically, the variable indicates whether she was between the ages of 16 and 19 before 2008 or between 18 and 19 since 2008 when the cutoff age for marriageability with parental consent was changed. NoConsent _it is the indicator of whether the mother can marry without parental consent—whether she is 20 years of age or older. It is reasonable to assume that the pure age effect on coresidence is smooth and continuous at around age 20 without any arbitrary restriction. It seems reasonable to specify the age profile of coresidence given the relatively narrow range of age in our sample. Thus, after controlling for age and age squared, α₂ is likely to be the effect of the age cutoff. Since legal marriageability should increase the probability of coresidence because coresidence is more likely among marriageable couples and future marriage is often a condition for coresidence, we expect both α₁ and α₂ to be positive.

Note that our second IV is valid only if the quadratic specification can fully capture the pure age effect of coresidence. Although this assumption is not unreasonable in our sample, we still check the robustness of our results to this assumption in two ways. First, we only use the first IV by restricting the sample to those under the age of 20 and see the robustness of our findings. Second, we specify the age effect in a fully non-parametric way, that is, by controlling for all age dummies, as in the following equation and, again, use the first instrument only. The non-parametric specification actually allows us to test whether the age cutoff for marriageability without parental consent indeed affects the likelihood of coresidence.

(4)$$CRB_{it} = \alpha \cdot Consent_{it} + \sum^{22}_{\,p = 17} \theta_p Age_{ip} + X_{it}\gamma_1 + \tau_1 t + \epsilon_{1it}$$

where Age _ip is the indicator variable for age p, which takes values between 17 and 22. We can check the validity of our second IV by testing whether θ₂₀ differs so much from θ₁₉ that there is a discrete jump in the coresidence rate, which is large enough for us to argue that it should be caused by the cutoff age for marriageability. In this sense, this strategy somewhat resembles the regression discontinuity approach.

In both equations (1) and (4), vector X _it includes control variables such as the mother's demographic characteristics—education level (two dummy variables, one for high school graduation, and the other for college or more), the baby's sex, multiple births (twins, triples, or more), month of birth, and province of birth. Lastly, τ_1t represents the birth year fixed effect, which is expected to subsume any macro-level impact on infant health. The results for equations (1) and (4) are summarized in Table 2 (See section 4.2.1).

Table 2.

Impacts of legal marriageability on coresidence status: first-stage and reduced-form results

Notes: Robust standard errors are reported in parentheses.

*** indicates significance at the 1% level, **indicates significance at the 5% level, and * indicates significance at the 10% level.

4.1.2. Reduced-form equation

We estimate the following reduced form analysis:

(5)$$Y_{it} = \gamma_1{Consent}_{it} + \gamma_2{NoConsent}_{it} + \kappa_1{Age}_{it} + \kappa_2{Age}^2_{it} + X_{it}\gamma_1 + \tau_{1t} + \epsilon_{1it}$$

where the dependent variable is one of the following birth outcomes: birth weight, LBW (birthweight < 2500 grams), and preterm birth (gestation weeks < 38) and all other variables are similarly defined as equation (1). The results show how the marrying age restrictions directly affect birth outcomes.The results for reduced-form equation (5) is summarized in Table 2 (See section 4.2.1).

4.1.3. Second-stage equation

The second-stage equation is as follows:

(6)$$Y_{it} = \beta \cdot CRB_{it} + \rho_{1} Age_{it} + \rho_{2} Age^{2}_{it} + X_{it} \gamma + \tau_{t} + \epsilon_{it}$$

where the dependent variable is one of the following birth outcomes: birth weight (in kilograms), low birth weight (LBW, defined as birth weight under 2,500 grams), and preterm birth (defined as the gestation weeks of less than 37 weeks). For LBW and preterm birth, we estimate the equation using bivariate-probit since the dependent variables and the endogenous variable (CRB _it) are both dummy variables. When the endogenous variable is CRRatio _it, which is continuous, we use IV-probit to estimate the equation.Footnote ¹³ The second-stage equation corresponding to the first-stage estimation described in equation (2) is as follows:

(7)$$Y_{it} = \beta \cdot CRB_{it} + \sum^{22}_{\,p = 17} \theta_p Age_{ip} + X_{it}\gamma + \tau_{t} + \epsilon_{it}$$

where all other variables are identically defined as in equation (4). The second-stage estimation results for equations (6) and (7) are reported in Tables 3–5 (See section 4.2.2).Footnote ¹⁴

Table 3.

Impacts of coresidence on birth weight

Notes: Robust standard errors are reported in parentheses. CRB refers to the mothers who first conceive (C), then start coresidence (R), then give births (B). The control group consists of the mothers who give birth without ever starting coresidence (noR mothers). CR ratio refers to the duration between conception (C) and co-residence (R) out of total gestation weeks, formally defined in equation (3).

***p < 0.01, **p < 0.05, *p < 0.1.

Table 4.

Impacts of coresidence on low birth weight (LBW)

Notes: This table shows the results of equation (5). Marginal effects, evaluated at sample means, are presented. For bivariate probit, birth month fixed effects are excluded from the estimation equation for coresidence. Robust standard errors are reported in parentheses.

***p < 0.01, **p < 0.05, *p < 0.1.

Table 5.

Impacts of coresidence on preterm birth incidence

Notes: Marginal effects, evaluated at sample means, are presented. For bivariate probit, birth month fixed effects are excluded from the estimation equation for coresidence. Robust standard errors are reported in parentheses.

***p < 0.01, **p < 0.05, *p < 0.1.

For comparison with previous studies that have examined the effect of legal marriage at birth rather than coresidence, we also estimate the effect of marital status at time of birth by using equation (6), with the CRB indicator replaced with legal-marriage-at-birth indicator. Mothers who are not eligible for marriage without parental consent (aged 16–17 after 2008) should not be legally married. However, we observe that out of 1,285 young mothers, 221 mothers were reported to be married at the time of birth. Therefore, we take this as an indication of greater commitment and stronger union for legally non-marriageable mothers. The proportion of pregnancy period without a partner does not change with marital status; hence, the analysis using the continuous explanatory variable is to be repeated.

Lastly, we examine if RCB mothers differ from CRB mothers and noR mothers:

(8)$$Y_{it} = \beta_1 \cdot CRB_{it} + \beta_{2} \cdot RCB_{it} + \rho_{1} Age_{it} + \rho_{2} Age^{2}_{it} + X_{it}\gamma + \tau_{t} + \epsilon_{it}$$

where RCB _it is the RCB mother indicator. This analysis compares the birth outcomes of RCB and CRB mothers to noR mothers. β ₁ should capture any benefits from post-conception coresidence, whereas β ₂ should capture any benefits from coresiding for the full period of pregnancy. We also replace the indicator variables for RCB and CRB mothers with the proportion of pregnancy with a partner. The results for equation (8) are summarized in panel B of Table 6. In the table footnote, we report Angrist-Pischke multivariate F test statistics to test the weakness of our instruments separately.

Table 6.

Marital status and early start of coresidence

Notes: Sample size is 246,378 in all panels. Only the key variables are reported. Robust standard deviations are reported in parentheses. Angrist-Pischke multivariate F test statistics for CRB is 22.61, while it is 90.48 for RCB.

***p < 0.01, **p < 0.05, *p < 0.10.

4.2.1. First-stage results

In Table 2, we present the results of the first-stage equations (1) and (4). Columns (1) and (2) use the CRB mother indicator as the dependent variable, and columns (3) and (4) use the CR ratio as the dependent variable. Columns (1) and (3) present the results of equation (1), using both IVs under the assumption that the age profile is quadratic. Columns (2) and (4) present the results of equation (4), taking only the time-varying IV while controlling for all age dummies. The analysis takes the age of 16 as the baseline age.

The results show that our IVs have significant and positive effects on both the CRB status and the CR ratio. Specifically, in column (1), those mothers who are eligible to marry with parental consent are 28 percentage points more likely to start coresidence during pregnancy than those who are not. Somewhat surprisingly, the effect of marriageability without parental consent is similar in magnitude. Column (3) shows that marriageability with parental consent significantly increases the proportion of pregnancy period with a partner by 17 percentage points, which is approximately 6.7 weeks, out of average gestation week of 39.4 weeks. The effect of marriageability without parental consent is again similar in magnitude. The first-stage F statistic and Hansen's J test statistic support the relevance and validity of our IVs, as reported in the bottom of Tables 3–5.

The results in columns (2) and (4) are similar to those in columns (1) and (3), respectively. Mothers who are eligible to marry with parental consent were 30% more likely to initiate coresidence during pregnancy. The CR ratio is 18 percentage point greater than mothers who are not eligible to marry. The results suggest that couples who are not eligible to legally marry may fail to receive parental consent. This may be indicative of South Korean culture, where coresidence without legal marriage, especially for teenage girls, largely brings disapproval.

In Figure 2, we plot the estimates in Table 2 to visualize the effect of the cutoff age for legal marriageability without parental consent. Panel A presents two age profiles, one based on the estimates in column (1) of Table 2 (left) and the other based on the estimates in column (2) of Table 2 (right). Both graphs are normalized by setting the effect at age 16 to be zero. When marriageability with and without partner are both exclusively estimated, as in column (1), the age profile clearly shows a discrete jump in the likelihood of coresidence at age 20. Panel A shows that even when all ages are non-parametrically controlled as dummy variables and only marriageability with parental consent is controlled, there is a discrete change in the coresidence rate at the cutoff age. Similarly, using the estimates from column (3) of Table 2 (left) and column (4) of Table 2 (right), Panel B also shows that the change in the coresidence rate is visible at the cutoff age under both specifications. This relieves the concern about our second IV. In columns (5)–(7) of Table 2, we present the reduced form results of equation (5). For all three birth outcomes, the estimated coefficients are negligible and statistically insignificant, except for the marriageability without consent for preterm birth.Footnote ¹⁵

Figure 2.

Estimated age Profiles for coresidence and CR ratio. Panel A: coresidence by age. Panel B: CR ratio by age.

Notes: Panel A is based on the estimates in columns (1) and (2) of table 2. Panel B is based on the estimates in columns (3) and (4) of table 2 The estimate at age 16 is normalized to zero. The dotted line is the fitted linear regression line before and after age 20. The vertical bar around the estimate for each age represents the 95% confidence interval.

4.2.2. Second-stage results

Results for birth weight. Table 3 shows the results from the second-stage equation using birth weight as the dependent variable. In columns (1) and (2), we use the indicator variable for CRB mothers and in columns (3) and (4) we use the CR ratio, the continuous treatment intensity variable. Columns (1) and (3) present OLS estimates, and columns (2) and (4) show IV estimates. The OLS results in column (1) show that coresidence during pregnancy correlates with about 91 gram increase of birth weight. The results in column (3) show that one standard deviation increase in the CR ratio (0.26 from Table 1) is associated with an increase in birth weight of 19 grams (=0.073*0.26).

However the IV results indicate little effect of coresidence on birth weight. In both columns (2) and (4), the estimates are statistically insignificant. One might think that the standard errors of IV estimates are inflated. However, the results show that the estimates are not only statistically insignificant but also their magnitudes are close to zero and economically insignificant.

The results for other control variables are overall consistent with the intuition. For example, we find that boys are approximately 90 grams heavier than girls. Babies born to mothers with high-school education or college or higher education are approximately 30 grams heavier than those born to mothers with less than high-school education. Unsurprisingly, birth weight for multiple births is substantially lower than for single births (by approximately 870 grams). The estimates for these variables are almost identical between OLS and IV estimations.

Results for LBW. Table 4 presents the results for LBW. Columns (1) and (3) present the simple probit results, and columns (2) and (4) present the bivariate-probit and IV-probit estimates, respectively. In the table, we present marginal effects evaluated at sample means. The results in column (1) show that coresidence is associated with a reduction in LBW by 2.6 percentage points. In column (3), one standard deviation increase in the CR ratio is correlated with a 0.6 percentage point increase in the rate of LBW incidence. The effect is substantial, compared to the average incidence of LBW is 7.1% for noR mothers.

However, consistent with the birth weight, the benefit of coresidence mostly disappears after the selection issue is addressed, as shown in columns (2) and (4). The IV estimates are not only statistically insignificant but also very close to zero. Some other results are worth noting. We find that boys are approximately 6% less likely to be born with low birth weight, and higher-educated mothers are significantly less likely to have LBW babies. Multiple births significantly increase the probability of LBW. These results are consistent with the previous literature.

Results for preterm birth. Preterm birth indicates a birth with a gestational period of less than 37 weeks and it is another key birth outcome with significant implications for infant health as well as long-term economic outcomes. Table 5 presents the results, the marginal effects evaluated at sample means. We find that coresidence is correlated with a reduction in the incidence of preterm birth by 4 percentage points, and a one standard deviation increase in the CR ratio is correlated with an increase in the incidence of preterm birth by 1 percentage point, as illustrated in columns (1) and (3). Unlike birth weight and LBW, coresidence seems to have a causal and favorable effect on preterm birth. In column (2), we find that coresidence reduces the probability of preterm birth by 2.9 percentage points. However, notice that the effect is much smaller than the estimate in column (1) and statistically only marginally significant. Also, when the CR ratio is used in column (4), the coefficient becomes statistically insignificant and the magnitude of coefficient substantially decreases. Therefore, we conclude that there is a causal but limited effect of coresidence on the likelihood of preterm birth.

Marriage premium. One might think that we failed to find any positive effect of coresidence because coresidence is a less binding relationship than marriage. Thus, we examine the effect of legal marriage at birth by using the same specifications that we have used so far for coresidence. Also the results utilizing marriage are more comparable to the findings in the literature than the results using coresidence status since previous studies are focused on the effect of parents’ marital status on offsprings. In Table 6, we present only the estimates of our main interest. Panel A presents the results of the analysis comparing married and unmarried mothers. In columns (1), (3), and (5) where we do not resolve the endogeneity of marriage, we find that birth weight for married mothers is on average 62 grams heavier, the LBW probability is 1.8 percentage points smaller, and the preterm birth probability is 2.7 percentage points smaller than for unmarried mothers. However, similar to what we found about coresidence, we find no causal effect of marriage on birth weight and LBW. On the other hand, consistent with the results presented in column (2) of Table 5, we find that marriage reduces the probability of preterm birth by 1.6 percentage point. But the estimate is only marginally significant and smaller than that in column (5).

Coresidence prior to conception. So far we have excluded RCB mothers, those who started coresidence before conception, from our analysis. One might be curious about whether starting coresidence before conception makes any difference. Panel B1 in Table 6 presents the results of the analysis that compares CRB and RCB mothers, separately, with noR mothers. Again, the results without addressing the endogeneity of coresidence show that both CRB and RCB mothers have more favorable birth outcomes compared to noR mothers. However the IV estimates show that there is actually no significant difference in terms of birth weight and LBW between RCB and noR mothers. But we find that RCB mothers are 2 percentage point less likely to have preterm birth than noR mothers. Lastly, for the sample including RCB mothers with the CR ratio set to be one, the results in panel B2 show that all IV estimates for the CR ratio are statistically insignificant for all three birth outcomes.

4.2.3. Possible explanations

Our findings show that while coresidence and infant health at birth are positively correlated, there is no causal relationship. This suggests that the young mothers who select into coresidence should have unobservable characteristics that are favorable for infant health, but coresidence per se has no exclusive additional benefit. We should interpret our findings cautiously because our estimates are local average treatment effects (LATE). That is, we do not identify the effect on a general group of young mothers but on a restricted group where their coresidence and marriage decision is affected by the change in the marriageable age. This indicates that they are at the margin of marriage and no marriage (or coresidence and no coresidence), so the return to marriage (coresidence) is likely to be minimal. Therefore, we should not generalize our findings too far, but we want to point out that these mothers whom we identify the marriage effect off are those we could influence by a policy like the reform of the marriageable age.

There might be various explanations for why the coresidence has little impact on infant health from economic, social, and cultural perspectives. One possible explanation is related with the degree of the contribution to be made by the potential partner to improve infant health. For young mothers like those in our sample, their partners may be more likely to have low socioeconomic status, and consequently less capable of financially helping their pregnant partner. Even worse, they might have some behavioral problems, such as drinking and smoking, that may have a negative effect on pregnant women and their fetus. Then, they might be unable to provide enough support, either financial or emotional, to make any meaningful contribution to infant health. This possibility was also pointed out in Finlay and Neumark (Reference Finlay and Neumark2010). Using state-by-year variation in the male incarceration rate as the IV for the marriage rate, they found that the impact of marriage on children's educational outcomes is actually negative for Hispanic mothers. To explain this puzzling finding, they suggested the possibility that potential spouses available to those Hispanic mothers are likely to be of low socioeconomic status and the mothers might be better off without spouse.

Another possible interpretation for our findings is related to the quality of non-spousal support available to these young mothers. For the young pregnant women, alternatives to the support of their potential partner are public assistance from government or private support from parents, and/or friends. It is likely that those mothers between the ages of 16 and 22 are living together with their parents, especially in Korea where it is conventional for adult offspring to live with their parents until marriage. Therefore, if they opt not to coreside with their partner, they could receive some compensatory support from their parents, which might be better than what they would receive from their potential partner. Then, those whose parents are more willing and able to help their pregnant young daughters would choose not to coreside with their partner. In this case, even if there may be a positive contribution made by the partner, it may not be superior to what those alternative caregivers or the different levels of governments can provide for those young mothers.

Lastly, it is worth noting that our finding of the lack of the marriage premium is in contrast with the finding of Buckles and Price (Reference Buckles and Price2013). They found a sizable positive impact of marriage on birth outcomes. Of course, it is difficult to explain different results in two studies for some obvious reasons, such as differences in population of the study, data, and estimation method. For example, they excluded mothers under the age of 18 whereas we only included young mothers. Also, they estimated the fixed-effect model to control for time-invariant maternal characteristics, while we took the IV approach. Also, the differences in the degree of social and family care for single mothers between Korea and the United States may account for the differences in the results between two countries.