To assess our theoretical predictions empirically, we draw data from the Korea Labor and Income Panel Study (KLIPS) 1998-2008 (Nam et al., 2010). KLIPS is an ongoing panel study that has traced respondents annually beginning in 1998 with nationally representative samples of more than 13,000 respondents in 5,000 households. KLIPS registered a 74.2% retention rate of original samples in the 11th wave, which is quite comparable with the Panel Study of Income Dynamics (PSID) of the United States.

Because we focus on fertility differentials according to women’s wage, we select all women aged 15 through 49. To obtain our analytical samples, we apply the listwise deletion method, which excludes observations with at least one missing value in the variables that will be described soon. We are concerned with this method because our estimates would be biased if our set of covariates were not sufficient for explaining the longitudinal attrition and survey nonresponse and because there were differential response rates based on a combination of our main causal variables and propensity to childbirth (Allison, 2002). To consider an empirical perspective, our positive estimates for women’s high wages would be upwardly biased if those who received low wages and were eager to give birth to a baby were more likely to exit the surveys than those who received low wages but were not eager to give birth. To ameliorate this problem, we use the longitudinal weight “w11_pl” in all analyses reported in this paper (Nam et al., 2010).

The outcome variable, time to childbirth, is retrieved from individual-level records that contain information on respondents and household-level records that enclose the date of birth of every household member. Using information on average monthly wages, we classify women’s wages into four categories: 1) up to 1 million Korean Won (KRW) (baseline category), 2) more than 1 to 2 million KRW, 3) more than 2 million KRW, and 4) out of the labor force. In this coding scheme, women with the values 1, 2, and 3 were in the labor force. Throughout this paper, we use Korean Won (KRW) as a unit of monetary values. In addition, monetary values are inflated to the 2008 level, such that a ten thousand KRW in 1998 is the same amount as in 2008. Ten thousand KRW in 2008 is equivalent to approximately 10 US dollars. For instance, 200 ten thousand KRW may be equivalent to 2,000 USD. To assess the effects of the percentage of women’s wages in household income, we create a categorical variable with four levels: 1) up to 30% (baseline category), 2) 30% to 70%, 3) more than 70%, and 4) out of the labor force.

Some readers may wonder why monthly wage is considered instead of some other measures such as hourly wage. First and foremost, we think that levels of monthly wage are more appropriate for our theoretical formulations than hourly wage. For instance, income effect has much stronger bearing on monthly wage than hourly wage. In this respect a totally different set of theoretical perspectives should be formulated if we want to evaluate effects of hourly wage. We also think that people tend to choose a job after considering monthly wage rather than hourly wage, particularly because, in Korea, working overtime is the rule rather than the exception (Bae, 2012), and only one quarter of women workers receive extra pay for their overtime work (Shin, Y. Kim, J. Kim, Nam, & O, 2013). Finally, working hour variables in the raw data had many missing values, putting us in risk of losing a large portion of our observations if we used it.

Concerns with omitted variable bias in an observational study urge us to control for a wide array of confounding variables (e.g., Wooldridge, 2002). Using the question regarding household income for the last year (Do & Choi, 2013), we employ a monthly household income variable with four categories: 1) up to 2 million KRW (baseline category), 2) 2 to 4 million KRW, 3) 4 to 6 million KRW, and 4) more than 6 million KRW. Home ownership, a proxy for family wealth that does not fluctuate in the short term, is included as a categorical variable with four values: own home (baseline category), reclaimable down payment, monthly rent, and others (D. Kim, 2009; Kim et al., 2006). A reclaimable down payment refers to a type of rent in which renters deposit an appreciable amount of money at approximately 60% to 70% of the house price and claim this money when they vacate the house. There is no monthly rent in this arrangement. The last category may include a house provided by an institution to which a family member belongs or a house owned by a relative.

Household structure should be adjusted for because it may affect women’s labor force participation and women’s wages as well as childbirth decisions (e.g., H. Kim & J. Kim, 2012). In particular, percentage of wage in household income may have different implications on childbearing behaviors depending on household structure. For instance, married women who live with dependent parents may be reluctant to give birth to a child even though they earn high wages and contribute high proportion to the household income. However, those who live with high-income parents are likely to show prenatal tendencies in spite of a trivial contribution. Because we do not have fine-tuned measurements in these respects, we hope that two variables―the total number of household members and co-residence with at least one parent―capture the skeletons of highly divergent household structures. The total number of household members is categorized into four levels (1-2 [baseline category], 3, 4, and 5 or more) for the first childbirth and three levels (1-3 [baseline category], 4, and 5 or more). Co-residence with a parent is a binary variable with 0 indicating not living together and 1 otherwise.

The individual characteristics of the respondents consist of their marital status, birth cohort, and educational attainment. The most critical proximate determinant of childbearing has been shown to be marital status (e.g., J. C. Caldwell & B. K. Caldwell, 2005). We have two categories indexing marital status: married and the others. The first category may include women who have been married more than once, and the latter category consists of several types, such as never married, divorced, separated, and widowed. One of the few established facts in the transition of fertility in Korea is a fertility decline in recent cohorts; thus, we consider birth cohort to be a categorical variable (e.g., Eun, 2001). Birth cohort has three categories: up to 1970 (baseline category), 1971 through 1980, and 1981 and later.

Educated women with careers are more empowered by the knowledge of their reproductive rights and the benefits of fewer children, which leads to low childbirth hazards for them compared to women with low levels of education (e.g., Kravdal & Rindfuss, 2008). Hence, we include education as a control variable. Education is broken down into three categories: up to high school graduation (baseline category), attending college or graduate schools, and college graduation or more. Finally, urbanicity of residence is included as a categorical variable because it is widely known that women in rural areas tend to receive lower wages but give birth to more children (White et al., 2008). This variable is measured with three levels: city (baseline category), rural, and metropolitan area.

We fit our data to the Cox proportional hazards model (Cleves, Gould, & Gutierrez, 2004). We choose the Cox model for hazard patterns over analytical time periods since the descriptive results indicate the adequacy of the model, as we will describe shortly. We fit three analytical models by parity. The first model predicts fertility hazard using women’s wage variables and other control variables. Here women’s wage variables represent women’s wage levels and a category indicating that a woman chooses to stay out of labor force. Hence, we can examine the effects of labor force participation compared with the baseline category (Lehrer & Nerlove, 1986).

However, the estimates on women’s wages are likely to be biased under the framework of the first model, as there were considerably distinguishable effects of the confounding variables between subpopulations divided by labor force participation status (Allison, 2002). In the second model, we omit women who are out of labor force to assess the women’s wage effect among women in the labor force. Finally, it is of particular interest from the gender equity perspective to determine whether there are differential fertility hazards according to the percentage of wife’s wages in household income. To investigate this possibility, we replaced women’s wages in the second model with categories embodying the percentages of female wages in household income.

Finally, we are concerned with the fact that there were households from which more than one woman was drawn. In this case, there may be an unobserved correlation among women within households, which could lead to bias in the variance estimation. We address this concern by specifying the option [cluster] in our data analysis, which is designed to account for correlation among women within households (Cleves et al., 2004).

Table 1 summarizes the descriptive statistics according to variables included in our analyses. We compute person-years at risk of first (or second childbirth), numbers of a first (or second) childbirth and incidence rates. Incidence rates can be interpreted as “the ratio of new children in a particular period divided by the person-years lived in a population (Preston, Heuveline, & Guillot, 2001).” We multiply the original rate by 1,000 to simulate incidence rates for 1,000 women. This measure can be interpreted as indicating how many children a woman would give birth to for one year of duration of 1,000 females at risk of a first (or second) childbirth (Kim, 2014). Additionally, note that fertilities are displayed according to variables and parity for complete information.

The first row shows that, on average, approximately 40.45 first children and 127.51 second children per 1,000 women would be born if women were under the same fertility risk for one year. We present incidence rates by age intervals in the second row block, although age serves as the analytical time. We observe the highest fertility levels for the first childbirth in 25-34. We find that the age intervals of 20 through 34 are the prime time for the second childbirth. Sharply enhanced incidence rates for the second childbirth appear to indicate that young women who gave birth to their first child tended to rush into the second childbirth. However, the dramatic fall in incidence rates after age 35 reflects the previous finding that those who did not give birth to a baby before age 36 were likely to forgo childbirth, whether a first or second childbirth (Park & Kim, 2003).

Across two parities, fertility statistics on women’s wages reveal a tendency for women with high wages to have experienced a high risk of childbirth. For instance, women who earned up to 1 million KRW would give birth to 36.59 first children, whereas those who received more than 2 million KRW would deliver 103.09 first children. This gap by wage levels appears to be similar for the second childbirth, although the difference is less pronounced. One interesting finding in the row block is that women out of the labor force registered the lowest fertility for the first childbirth, but those women were the most fertile for the second childbirth. This result clearly demonstrates the M-shaped women’s labor force participation in Korea, in which young women leave the labor force when they marry or become pregnant and do not return until they give birth to the desired number of children or raise children to an age when they do not need mothers’ intensive care (Lee & Cho, 2005).

The fourth row block displays differential fertility according to the percentage of women’s wages in household income. With respect to the first childbirth, we can observe that the higher percentages of women’s contributions to household income are correlated with greater fertility risks. More interestingly, the fertility gaps feature a well-spaced gradient in which a jump to the higher category appears to have raised a similar amount of fertility risk across categories. However, the tendency is reversed for the second childbirth. In other words, incidence rates decreased remarkably as the percentage increased for the second childbirth.

Because graphical representation would substantially refine our understanding of the previous observations, Figures 1 and 2 are presented below. Figure 1 describes fertility hazard schedules for first childbirths over the reproductive ages by our main causal variables, women’s wages and their percentages (Cleves et al., 2004). In the graphs, the x-axis refers to age in years, and the y-axis marks the hazard rates for the first childbirth.

Figure 1. 
Hazard rates of the first childbirth by women’s wages and their percentages

Notes. Unit of women’s wages is 10,000 KRW. Out of LF refers to women out of the labor force.

First, we observe that hazard rates increased as women aged until approximately 30, but they decreased thereafter, forming a sort of normal distributions. The hazard curves on the left panel show remarkable proportionalities by categories of women’s wages with arresting hazard gaps at the peak but decreasing gaps toward tails, which increases our confidence in choosing the Cox model. However, the hazard curve for women out of the labor force shows the highest level across all ages, which appears to contradict our previous findings that those women did not register the highest fertility rates in Table 1>. This finding was observed simply because a dominant portion of risk exposure for those women occurred when they were in school, which inflated the denominator in the fertility rate that led to the low fertility rate. As they graduated from schools and entered the labor force, the denominator of the hazard curve displayed in Figure 1 became considerably small, unraveling the true trajectory of the hazard rate. We also find that women earning more than 2 million KRW experienced higher hazards than women receiving up to 1 million KRW. Women in the wage category between 1 million KRW and 2 million KRW exhibited the lowest fertility level.

The graph in the right panel shows the hazard curves according to the percentage of women’s wages in household income, which appears to support the proportional hazard assumption once again. The hazard curve for women out of the labor force is the same as we observed in the left panel, as expected. The difference between women with percentages of up to 30 and those with percentages of 31 to 70 appears negligible, whereas women with percentages greater than 70 exhibited somewhat higher fertility hazards compared with the other two groups.

Figure 2 above provides hazard schedules for the second childbirth according to women’s wages and their percentages. Note that the x-axis in Figure 2 indexes months after the first childbirth because the risk of second childbirth begins from the birth of the first child. Hazard curves for the second childbirth are distinguished from those for the first childbirth in that the former did not form normal distributions but left truncated normal distributions. Namely, hazard rates began at high levels from the number of months after the first childbirth and then increased until approximately 42 months to decline along the steep curves. These patterns are likely to have emerged because women who preferred to have a second child must have made this decision one or two years after the first childbirth, feeling rushed to obtain the desired number of children.

Figure 2. 
Hazard rates of the second childbirth by women’s wages and their percentages

Notes. Unit of women’s wages is 10,000 KRW. Out of LF refers to women out of the labor force.

The hazard rates according to women’s wages appear to deviate from the proportional hazard assumption. The main force behind the non-proportionality is the atypical hazard function of women who enjoyed more than 2 million KRW in wages. These women did not show an increase but a constant decrease from the initial level. This finding is consistent with the argument that only selective women with high wages were willing to have a second child and that these women hastened to complete their fertility schedules to return to their careers as soon as possible (Park & Kim, 2003). It is worth noting that women out of the labor force were not matched with the other wage groups in their enhanced hazard rates for the second childbirth (Kim, 2014). Nevertheless, it is evident that women earning between 1 million KRW and 2 million KRW traced along a higher hazard curve than women receiving up to 1 million KRW. By contrast, it is notable to recognize that as the percentage of women’s wages in household income increased, the levels of fertility hazards decreased in the right panel.

Table 2 below exhibits the coefficients in three Cox regression models for the first childbirth. The model number refers to the models introduced in the statistical method section.

In modern causal inference literature, confounding variables are supposed to influence women’s wages and fertility levels such that those coefficients on confounding variables do not recover marginal or total effects (Wooldridge, 2002). Those coefficients instead represent conditional effects not mediated through women’s wages because we add women’s wages to the models. For instance, we should exclude women’s wages from the models if we wish to estimate the effect of educational attainment on fertility because one of the critical theoretical mechanisms is mediated through the wage effect. If we included educational attainment and women’s wage, then we would be in a grey area when we interpret the coefficients on educational attainment. Thus, we focus on interpreting coefficients on the main variables of interest in this paper, although the other coefficients are listed in the result tables.

Several interesting patterns emerge from Table 2. First, we discover that high women’s wages were likely to enhance fertility hazards, although the effect had categorical rather than linear effects. To illustrate, women in the category of the 1-to-2 million KRW exhibited exp(0.038)=1.039 times the hazard rates as women in the category of 1 million KRW or less. However, the hazard rates steeply increased as exp(0.618)=1.855 times for women in the category above 2 million KRW. In addition, the hazard rates sustained as exp(0.551)=1.735 times for the out-of-labor-force category. The first coefficient is not statistically significant at the conventional α-0.05 level, whereas the last two coefficients are, suggesting that the first difference may stem from mere chance. We also test the difference of the coefficients on the 1-2 million KRW and more than 2 million KRW categories to obtain a statistically significant difference at the α-0.05 level.

The results in the second are still consistent with the previous findings, although the effect parameters exhibit slight changes in size. In other words, we detect a minor difference between women earning up to 1 million KRW and women earning 1 to 2 million KRW but a vast difference between the former women and women with wages above 2 million KRW. Regarding differential fertility according to the percentage of women’s wages in household income (Model 3), we observe that the differences are negligible in both effect size and statistical significance.

Table 3 below delivers estimates in various Cox models for the second childbirth.

From Table 3 we find that women with high wages were more likely to give birth to a second child than women with low wages. However, these estimates are not statistically significant, particularly because of the small number of childbirths for women in the labor force, as Table 1 demonstrated. Women out of the labor force were strikingly more likely to give birth to a second child than any other groups in the labor force (all differences are statistically significant). This finding appears to reflect the social milieu in which a dominant portion of women does not return to the labor force until they complete their fertility schedules (Park & Kim, 2003). The coefficients from Model 2 do not deliver distinguishably different results from those of Model 1.

Finally, it is somewhat surprising to find that women whose wages contributed to 30% to 70% of household income were likely to exhibit lower fertility hazards than women whose contribution was less than 30%. Although this estimate is not statistically significant at the conventional α-0.05 level, its p-value is 0.068. The effect size is exp(-0.427)=0.652, meaning that the fertility hazard of the former group was less than two-thirds of the fertility hazard of the latter group. We argue that this finding indicates a substantively significant effect because 1) the effect size is not negligible, 2) the numbers of events in these groups are too small to properly evaluate their statistical significance as Table 1 documented, and 3) its p-value is 0.068.