Intergenerational effects of shifts in women's educational distribution in South Korea: Transmission, differential fertility, and assortative mating

Abstract

This study examines the intergenerational effects of changes in women's education in South Korea. We define intergenerational effects as changes in the distribution of educational attainment in an offspring generation associated with the changes in a parental generation. Departing from the previous approach in research on social mobility that has focused on intergenerational association, we examine the changes in the distribution of educational attainment across generations. Using a simulation method based on Mare and Maralani's recursive population renewal model, we examine how intergenerational transmission, assortative mating, and differential fertility influence intergenerational effects. The results point to the following conclusions. First, we find a positive intergenerational effect: improvement in women's education leads to improvement in daughter's education. Second, we find that the magnitude of intergenerational effects substantially depends on assortative marriage and differential fertility: assortative mating amplifies and differential fertility dampens the intergenerational effects. Third, intergenerational effects become bigger for the less educated and smaller for the better educated over time, which is a consequence of educational expansion. We compare our results with Mare and Maralani's original Indonesian study to illustrate how the model of intergenerational effects works in different socioeconomic circumstances.

1. Intergenerational effects of education

This study examines how the changes in distribution of educational attainment in one generation lead to changes in the next generation in South Korea. Changes in education affect intermediate demographic processes (e.g., marriage and childbearing) as well as offspring's educational attainment. Therefore, we need to account for differential population renewal processes to examine the changes in the distribution of education across generations. Following Mare and Maralani (2006), we define intergenerational effect as the expected change in distribution of the offspring's educational attainment caused by the change in distribution of educational attainment in the parental generation. The estimates of intergenerational association (e.g., Mare, 1981) could be directly converted to intergenerational effects if there were no socioeconomic differentials in reproduction rates. These differentials, however, do exist. Our approach accounts for educational differentials in reproduction rates that determine distribution of family background in the next generation. Because groups with higher reproduction rates (usually less-educated groups) will be more represented in the next generation, accounting for such educational differentials is necessary in examining changes in the distribution of educational attainment across generations. Our approach also allows for decomposing total intergenerational effect into three different pieces: assortative marriage, differential fertility, and intergenerational transmission.

Research in social mobility has not studied differential population renewal processes extensively until recently.¹ Most previous studies on social mobility have focused on the relationship between parental and offspring's socioeconomic outcomes (e.g., education, occupation, and income). This is common for the status attainment model (Blau and Duncan, 1967; Sewell et al., 1969; Hauser et al., 1983), occupational mobility studies (Erikson and Goldthorpe, 1992; Hout, 1988), and educational mobility studies (Mare, 1981; Shavit and Blossfeld, 1993). Estimating the net intergenerational association in socioeconomic outcomes has been a central task in this line of research. Crucial methodological innovations have also been achieved to tackle this issue, including: handling measurement errors (Hauser et al., 1983), controlling for the influence of structural or distributional change (Erikson and Goldthorpe, 1992; Mare, 1981), and purging out unmeasured individual-specific heterogeneity (Mare, 1993). The estimates of the net association tell us the expected changes in the offspring's socioeconomic outcomes associated with the changes in family backgrounds after controlling for other covariates. In other words, such estimates aim at quantifying the differences in the socioeconomic outcomes between individuals who, except for their parents' socioeconomic status, are identical. As sociological research becomes keener to estimate causal effects from the counterfactual perspective (e.g., Morgan and Win-ship, 2007), we may expect that more efforts will be devoted to getting more refined estimates of the effects of family background on children's socioeconomic outcomes. Such estimates, although sophisticated, cannot be directly used to assess how the changes in distribution of socioeconomic traits in one generation lead to changes in the next generation. To address this question appropriately, we should account for differential population renewal processes.

Examining intergenerational effect is important in two respects. First, this provides a complete description of the intergenerational transmission of family backgrounds, which is a marked improvement over most previous mobility research that does not address the question of differential population renewal. Second, the estimates of intergenerational effects will provide a tool for evaluating long-term socioeconomic consequences of current education policies. For example, postsecondary education expanded substantially throughout the world after World War II (Shavit et al., 2007). Such an expansion should have long-term implications beyond improving the level of educational attainment in the current population. Sociological literature has consistently shown that offspring's educational attainment is positively associated with parental education (Mare, 1981; Shavit and Blossfeld, 1993) and that parents attempt to provide their offspring with at least the same level of educational attainment as they have (Breen and Goldthorpe, 1997). Given such a strong intergenerational association in educational attainment, educational expansion at a certain time point should have trickle-down effects on future educational distribution in a population. This issue is particularly relevant to policy makers in developing countries who would plan to expand educational opportunity as a crucial strategy of socioeconomic development. However, the estimates of net intergenerational association from most previous research in social mobility cannot address such a policy issue because differential population reproduction is difficult to account for in such approaches. Hence, the estimates of intergenerational effects would provide better guidance to policy makers in developing countries with regard to the long-term implications of current educational policies.

2. Goals and research questions

The first goal of the current study is to see how Mare and Maralani's (2006) recursive population renewal model works in an institutional setting other than Indonesia. South Korea is suited for this purpose for several reasons. Substantively, South Korea experienced fast and fundamental socioeconomic and demographic changes over the past 50 years, making it particularly relevant to apply a recursive population renewal model. First, educational opportunity expanded dramatically. While almost none of the women over the age 25 in 1960 had ever attended college, nearly 60% of women of the same age in 2005 received at least some college education (Korea Statistical Office, 2010). Such a rapid educational expansion yielded enormous upward educational mobility. For example, 45% of Korean people born between 1970 and 1985 whose father had not attended high school received at least some postsecondary education (Phang and Kim, 2002, p. 208). This rapid educational expansion would yield small intergenerational effects because children are likely to attain high level of educational attainment regardless of their parental education level. While upward mobility has been prominent, intergenerational association in educational attainment decreased just modestly (Park, 2004, 2007). This is consistent with findings in other industrialized countries (Mare, 1981; Shavit and Blossfeld, 1993), which document invariant intergenerational association over time and across countries. This persistent intergenerational association suggests that cohort changes in intergenerational effects be modest. Second, spousal resemblance in educational attainment is strong from the comparative perspective (Park and Smits, 2005). Such strong assortative mating should consolidate the rigidity of social inequality, strengthening intergenerational effects. Third, South Korea transited from a high fertility country to a ‘lowest-low’ fertility county (Kohler et al., 2002) in less than a half century. During such rapid fertility transition, fertility differentials by education remained quite stable (Jun, 2004). The persistent fertility differentials by education would dampen the intergenerational effects because better-educated women tend to produce fewer children than their less-educated counterparts. The contributions of assortative mating and differential fertility, however, would not be substantial because children are likely to attain high level of educational attainment regardless of parental education due to the rapid educational expansion in South Korea. In this sense, we can see if accounting for differential demographic behaviors makes a substantial difference in our understanding of educational mobility when educational opportunity expanded rapidly. In the results section, we will discuss the implications of rapid educational expansion for intergenerational effects in more detail in comparison with Mare and Maralani's (2006) original case, Indonesia.

Schooling and family formation patterns in South Korea also facilitate estimating Mare and Maralani's model, which is another reason to use the Korean data. Mare and Maralani's model assumes that education affects the intermediate demographic processes such as marriage and fertility. If women commonly get married or become a mother before finishing school, such an assumption is difficult to hold. The schooling and family transition patterns among the Korean women, however, were neatly ordered: marriage is almost universal in Korea despite the delay in marriage (Byun, 2004), the prevalence of cohabitation is still very low despite the rising trend (Lee, 2008), non-marital fertility is still negligible (Korea Statistical Office, 2010), and the majority of marriage and childbearing occurs after leaving school (Kye, 2008). Transition patterns in other industrialized countries are much less ordered (Cohen et al., 2011), making it difficult to apply this type of recursive population renewal model. These unordered transition patterns necessitate examining the causal direction in the opposite way in the United States–the effect of timing of fertility on schooling (Lee, 2010; Stange, 2011). Of course, the ordered transition patterns do not rule out a possible endogenous relationship in South Korea, because observed and unobserved confounders would exist. The Korean case, however, is much better suited for applying Mare and Maralani's recursive demographic model than other industrialized countries.

Another goal is to elaborate Mare and Maralani's model by using the bootstrap method to estimate standard errors of intergenerational effects. Mare and Maralani (2006) used a recursive population renewal model that is based on several regression models. Because the estimates of intergenerational effects are functions of parameter estimates in each regression, it is challenging to compute the standard errors of intergenerational effects analytically. Because Mare and Maralani (2006) did not present standard error estimates, they cannot assess statistical significance of contributions of demographic elements to intergenerational effects. In this study, we address this problem by estimating bootstrap standard errors, which allows for statistical tests. Having these goals in mind, we examine the following research questions.

1. How do changes in women's educational distribution in one generation affect the educational distribution of the daughter's generation in South Korea? In other words, how strong are the intergenerational effects in South Korea?

2. How strong is the impact of assortative mating and differential fertility on the intergenerational effects in South Korea?

3. How do the intergenerational effects change over time in South Korea?

3. Method: A recursive population renewal model

3.1. Baseline model

This study examines intergenerational effects, which must be assessed at the aggregate level because we are interested in the expected change of the education distribution in the next generation associated with a change in the previous one. Inferring intergenerational effects based on standard regression analyses would be valid if reproduction rates are equal across socioeconomic groups. This is hardly the case; demographic research has consistently shown socioeconomic differentials in fertility (Bongaarts, 2003; Jejeebhoy, 1995; Skirbekk, 2008), which yield differential reproduction rates. Hence, an alternative method is necessary to address the research questions asked.

We use a one-sex recursive ‘population renewal model’ (Mare and Maralani, 2006) to address this issue. In this model, the distribution of offspring's education is jointly determined by intergenerational transmission, differential fertility, and assortative mating. The intergenerational transmission rate of women's educational attainment is expressed in the following equation:

$$r_{\mathit{\text{jk}}|i}=p_{k|i}^H{f}_{\mathit{\text{ik}}}{d}_{\mathit{\text{ik}}}{p}_{j|\mathit{\text{iks}}}^D$$ (1)

(where i: woman's education, k: husband's education, j: daughter's education, i = 1, …, 4, k = 1, …, 4, and j = 1, …, 4). Here, we classify woman's, husband's, and daughter's education into four categories: 0–8,9–11,12, and 13+ years. Students spend 6 years in primary school, 3 years in junior high school, and 3 years in high school under the Korean educational system. Hence, each category represents less than junior high school graduate (0–8 years), less than high school graduate (9– 11 years), high school graduate (12 years), and some tertiary education (13+ years). The r_jk|i represents the joint distribution of husband's (k) and daughter's (j) educational attainment given women's educational attainment (i). The $p_{k|i}^H$ represents the probability distribution of husband's educational attainment conditional on wife's educational attainment. The f_ik is the expected number of children born to women in education group i and husbands in education group k. The d_ik is the proportion of daughters of children born to women in education category i and husbands in education category k. Finally, the $p_{j|\mathit{\text{iks}}}^D$ is the probability distribution of daughter's educational attainment (j) conditional on women's education (i), husband's education (k), and the number of siblings (s). Following Mare and Maralani (2006), we estimate the three equations separately: ordinal logistic regression models are used for husband's education ( $p_{k|i}^H$) and daughter's education ( $p_{j|\mathit{\text{iks}}}^D$), and Poisson regression for the number of children (f_ik). The estimated parameters are used to compute each component, conditional probability distribution in Eq. (1). Using the estimated r_jk|i and observed marginal distribution of women's educational attainment, the marginal distribution of daughter's educational attainment is computed in the following way:

$$D_j=\sum _{i=1}^4\sum _{k=1}^4{r}_{\mathit{\text{jk}}|i}{W}_i$$ (2)

(where D_j and W_i are marginal distributions of daughter's and women's educational attainment respectively).²

This model explicitly takes into account assortative mating and fertility differentials, which is distinctive from most prior social mobility research. First, we expect that assortative mating will amplify the intergenerational effects to some extent. Spousal resemblance in socioeconomic status has been studied extensively (Kalmijn, 1991; Mare, 1991; Schwartz and Mare, 2005) because this shapes family backgrounds in the next generation (Mare and Schwartz, 2006). The degree of spousal resemblance should affect the distribution of children's socioeconomic outcomes, but empirical studies show that this impact is not substantial. Mare (2000) showed that increasing spousal resemblance in educational attainment over time does not increase educational inequality substantially because intergenerational mobility is large enough to offset educational assortative mating effects. Preston and Campbell (1993) also showed that equilibrium IQ distributions do not depend heavily on mating patterns because of substantial intergenerational mobility. This evidence suggests a modest influence of assortative mating on intergenerational effects. Second, differential fertility has two implications for the distribution of offspring's education. Because better-educated women tend to produce fewer children, differential fertility should reduce the intergenerational effects of changes in women's education. However, lower reproduction rates among better-educated women lead to a smaller sibship size among their offspring, which offsets the reduction of intergenerational effects to some extent. In other words, although lower reproduction rates among better-educated women may lower the overall level of children's educational attainment, their own children should benefit from the smaller family size, which may contribute to improvement in educational attainment in the next generation. Hence, whether or not differential fertility exerts a downward pressure on the education distribution in the next generation should be answered empirically and not a priori. This study will show which forces are stronger in the Korean context.

3.2. Simulation

When we improve women's educational attainment, daughter's educational distribution may change in three different ways. First, improvement of women's educational attainment directly enhances daughter's educational attainment. Second, better-educated women are likely to marry better-educated husbands, and this improvement in husband's education should positively influence daughter's educational attainment in addition to the direct impact of improvement of women's educational attainment. Finally, better-educated women tend to produce fewer daughters, which might dampen the benefits of enhanced women's educational attainment to the education distribution of daughters. The smaller family size among them, however, would reduce this dampening effect because family size is negatively associated with children's educational outcomes (Guo and VanWey, 1999).

Here, we assess the intergenerational effect of changes in women's educational distribution in six different scenarios: (1) “Transmission only” (T only), (2) “Transmission + Fertility” (TF), (3) “Transmission + Marriage in an unconstrained marriage market” (TM), (4) “Transmission + Marriage in a constrained marriage market” (TMC), (5) “Transmission + Fertility + Marriage” in an unconstrained marriage market (TFM), and (6) “Transmission + Fertility + Marriage in a constrained marriage market” (TFMC). In each scenario, we redistribute the educational attainment of 5% of women in the sample from the lower education category to the higher education category in four different ways and examine how daughter's educational attainment changes after these redistributions.³ In the (1) T only model, a change in women's educational distribution does not entail any change in marriage and fertility behaviors at all. In other words, women who experience improvement of education still marry the same kind of husbands and produce the same number of children. In this model, improvements in women's educational attainment only directly affect daughter's educational distribution. In the (2) TF and (3) TM models, either fertility or marriage behaviors respectively adjust to the change in the distribution of women's education. In the (5) TFM model, both marriage and fertility behaviors alter according to the change in women's education.⁴ Formally, we modify $p_{k|i}^H$ (assortative marriage) and f_ikd_ik (differential fertility) in Eq. (1) to capture these hypothetical conditions. Let us illustrate how the simulation works by considering the scenario in which we redistribute 5% of women in the sample from 0–8 to 13+ years of schooling. This change leads to changes in $p_{k|i}^H$ and f_ikd_ik among those with 13+ years of schooling, leaving $p_{k|i}^H$ and f_ikd_ik unchanged for other education categories.

$$p_{k|4}^{H\_\mathit{\text{NM}}}=W_4\times p_{k|4}^H+.05\times p_{k|1}^H$$ (3)

$$f_{4k}{d}_{4k}^{\mathit{\text{NF}}}=W_4\times f_{4k}{d}_{4k}+.05\times f_{1k}{d}_{1k}$$ (4)

Eq. (3) shows the distribution of husband's education if women's education equals 13+ years when assortative mating is absent after redistributing women's education. This states that distribution of husband's education of women with 13+ years of schooling is a weighted average of $p_{k|4}^H$ and $p_{k|1}^H$ where weights are given by the observed proportion of college-educated women (W4) and the simulated proportion of women who change their education from 0–8 to 13+ years, which is .05. Eq. (4) shows the expected number of children among college-educated women given husband's education k when differential fertility is absent. This states that the expected number of children among college-educated women given husband's education equals the weighted average of f_4kd_4k and f_1kd_1k where weights are given in the same way as in Eq. (3). The expected daughter's educational attainment after simulation in each scenario is computed in following ways:

$$\mathrm{T}\text{only}:D_j=\sum _{i=1}^4\sum _{k=1}^4{p}_{k|i}^{H\_\mathit{\text{NM}}}{f}_{\mathit{\text{ik}}}{d}_{\mathit{\text{ik}}}^{\mathit{\text{NF}}}{p}_{j|\mathit{\text{iks}}}^D{W}_i^{\text{'}}$$ (5)

$$\text{TF}:D_j=\sum _{i=1}^4\sum _{k=1}^4{p}_{k|i}^H{f}_{\mathit{\text{ik}}}{d}_{\mathit{\text{ik}}}^{\mathit{\text{NF}}}{p}_{j|\mathit{\text{iks}}}^D{W}_i^{\text{'}}$$ (6)

$$\text{TM}:D_j=\sum _{i=1}^4\sum _{k=1}^4{p}_{k|i}^{H\_\mathit{\text{NM}}}{f}_{\mathit{\text{ik}}}{d}_{\mathit{\text{ik}}}{p}_{j|\mathit{\text{iks}}}^D{W}_i^{\text{'}}$$ (7)

$$\text{TFM}:D_j=\sum _{i=1}^4\sum _{k=1}^4{p}_{k|i}^H{f}_{\mathit{\text{ik}}}{d}_{\mathit{\text{ik}}}{p}_{j|\mathit{\text{iks}}}^D{W}_i^{\text{'}}$$ (8)

(W′_i is simulated marginal distribution of women's education).

After simulations, we measure the intergenerational effects by the ratios of the simulated proportions to the baseline proportions. If the ratio is equal to one, no intergenerational effect exists. If the ratio is greater than one, this means that a positive intergenerational effect exists in a given category. If the ratio is smaller than one, this means that a negative intergenerational effect exists. The greater the deviation from one, the larger the intergenerational effect. By comparing the size of intergenerational effects in each scenario, we can assess how intergenerational effects depend on demographic and mobility components.

In the (3) TM and (5) TFM model, husband's education is assumed to change following the improvement in women's educational attainment. This change is assumed to alter the marginal distribution of husband's education automatically. However, husband's marginal education distribution may change differently; the change could be larger or smaller. Historically, improvement in women's education has been more rapid than in men's education in South Korea (Phang and Kim, 2002), so we may expect smaller improvement in husband's education. This gendered pattern of improvement of educational attainment may have important implications for our analyses. This could cause a lack of marriageable men among the highly educated women (Raymo and Iwasawa, 2005), which may lead to delayed marriage, increasing never-married women, and increasing childless women. These issues, however, are difficult to handle for a couple of reasons. First, our model does not account for the timing of marriage and childbearing. Second, we assume that every woman gets married. Because marriage is almost universal and childlessness is rare for the cohort of women considered in the present study (Byun, 2004; Jun, 2004), the results may not change substantially if we account for them. In addition, it is difficult to predict the magnitude of change a priori. Hence, we experiment with two extreme scenarios: (1) marginal distribution of women's education changes according to scenario without any restriction in the marginal distribution of husband's education, and (2) husband's marginal distribution does not change at all and the association between women's education and husband's education, measured by odds ratios, remains the same. Using the given marginal distribution and the set of odds ratios, we can compute a hypothetical distribution of husband's education conditional on the changed marginal distribution of women's education (see Agresti, 2002, pp. 345–346).⁵ In this scenario, the marriage market is constrained in that the marginal distribution of husband's education is fixed regardless of changes in women's educational distribution. However, the association between women's and husband's education remains the same. We do this simulation both without differential fertility (TMC) and with differential fertility (TFMC). We may interpret the estimates from the unconstrained marriage market models as upper bounds and those from the constrained marriage market models as lower bounds because realistic husband's educational attainment will be between the unconstrained and the constrained models.

The intergenerational effect is determined by the parameter estimates in each regression model. As long as the parameter estimates are consistent, the estimates of intergenerational effects should be consistent. The sampling variability of intergenerational effects, however, is difficult to assess analytically because it is not clear how sampling variability of parameter estimates in each regression model is translated into the sampling variability of the estimates of intergenerational effects. Bootstrapping is an option to assess sampling variability in this situation (e.g., Osberg and Xu, 2000). Because the sample used in this study, the Korean Longitudinal Study of Aging (KLoSA), is a stratified multi-stage probability sample, a bootstrap method that assumes simple random sampling will yield biased estimates of standard errors (Lee and Forthofer, 2006). We implement the following steps to estimate bootstrap standard errors of intergenerational effects by accounting for sampling design of the data. First, we resample 1000 independent bootstrap samples from the original data set because 1000 replications are sufficient to yield reliable bootstrap confidence intervals (Efron and Tibshirani, 1993). For each stratum defined by region, type of areas, and type of housing (see the next section for description of data), we re-sample the same number of primary sampling units in the original data. By pulling the sample from each stratum together, we construct each bootstrap sample. Second, we compute intergenerational effects in each replication. That is, we go through the processes described in previous paragraphs for each replication. Finally, we estimate standard errors by the standard deviation of intergenerational effects from the 1000 replications. In the results section, we report the estimates of intergenerational effects and bootstrap standard errors.

3.3. Exogeneity of education

The assumption of exogeneity of education to marriage, fertility, and offspring's education in the Mare and Maralani's model, which is necessary in estimation and decomposition of intergenerational effects, is likely to deviate from the reality. First, Mare and Maralani's model assumes that women's educational attainment determines husband's educational attainment. However, the relationship between women's and husband's education should be reciprocal rather than causal. Second, the statistical association between women's education and level of fertility may not be causal. There may be other factors affecting women's education and demographic behaviors. For example, risk-taking tendency may explain variations in education and the timing of first marriage and first childbearing (Schmidt, 2008). Third, some unobservable genetic factors could affect both mothers' and daughters' education. Hence, assuming exogeneity of women's education is not ideal.

Nevertheless, we make this assumption for two reasons. First, this is useful to illustrate demographic pathways through which intergenerational effects are accrued while avoiding too much complication. Without making such a simplifying assumption, estimation of intergenerational effects will be formidably difficult. Second, endogeneity of education does not threaten the validity of analysis too greatly in the South Korean context where most women finish schooling before marriage and childbirth. Furthermore, non-marital childbearing is very unusual (Kye, 2008). In a society where non-marital childbearing is not rare and marriage and childbearing among school enrollees are not extraordinary, assuming exogeneity of women's education would be more problematic. The orderly pattern in South Korea does not rule out the possibility of the endogeneity of education, but makes the endogeneity issue less problematic.

4. Data

We use the first wave of the Korean Longitudinal Study of Aging (KLoSA), a biannual longitudinal survey of the non-institutionalized Korean population aged 45 and older in 2006 (Korea Labor Institute, 2007). The survey interviewed all the individuals aged 45 or over in the household. The data include information on broad socioeconomic circumstances of adults in South Korea. The KLoSA is a multistage probability sample, which stratified geographic areas by region, urbanicity, and type of housing. First, it stratified 15 cities and provinces. Each city and province is first stratified by type of area (urban and rural), and then type of housing (apartment and ordinary housing). Out of 52 strata,⁶ 1000 enumeration districts were selected, and 1–12 households were interviewed in each enumeration district. This sampling design is accounted for when assessing the sampling variability of intergenerational effects.

This study constructs two analytic samples: a marriage-fertility sample and an intergenerational transmission sample. The marriage-fertility sample includes 4894 ever-married women aged 45–79 whose husband's educational attainment is not missing. When weighted, the married-fertility sample represents ever-married Korean women who were born between 1927 and 1961 and still alive in 2006. The data do not include information on marital history. So we do not know for sure if women and their husbands listed are the biological parents of the children. How serious the first problem is depends on the prevalence of marital disruptions and the educational resemblances among multiple partners for those who have remarried. If marital disruptions (divorce, separation, and widowhood) are prevalent, lack of information on biological fathers would be problematic. In South Korea, divorce rates have been low. Fewer than 5 divorces per 1000 married women occurred until the early 1990s when most women in the sample were already married (Korea Statistical Office, 2010).⁷ Adult mortality, leading to widowhood, is also fairly low (Kim, 2004). No study has studied educational resemblances among the sequential spouses in South Korea, and a study shows that educational assortative mating patterns are similar for first marriage and remarriage in the Netherlands (Gelissen, 2004, p. 370). This evidence, though not perfect, lessens the seriousness of this data issue to some extent.⁸ The transmission sample includes 6902 daughters aged 20 and older of 3625 women aged 45–79 who have at least one adult daughter with valid information on educational attainment. Among the 4894 women in the marriage-fertility sample, 101 women are childless and 1168 women do not have an adult daughter. When weighted, the transmission sample represents all daughters who are 20 and older of ever-married surviving Korean women born between 1927 and 1961.

Because we rely on retrospective information from respondents aged 45 and older, we cannot address differential mortality appropriately: women who survived to age 45 and older are likely to differ from their original birth cohorts. In particular, we speculate that better-educated women are overrepresented in the sample because of educational differentials in mortality. Table A.1 confirms this speculation, showing higher mortality for the less-educated women. So, we should be cautious in making inferences to the broader population from the analysis reported here. In addition, we can see that mortality differentials decrease as women age. Actually, the existence of mortality differentials is more problematic for older women because they have been exposed to differential mortality for a longer period of time. If mortality differentials grew over ages, our inferences for the older cohorts would be even more limited. The decreasing mortality differentials over ages at least do not worsen the sample selection problem. We can also see that mortality differentials by education increase over time, with larger mortality differentials for the younger cohorts than the older. This suggests that ignoring mortality differentials is more problematic for the younger cohorts. However, we should note that South Korea experienced rapid educational expansion and the share of less educated individuals decreased quickly over time (See Table 1). For example, while 86.5% of women in the oldest cohort in the sample, born between 1927 and 1941, received 0–8 years of schooling, this figure amounts to only 23.3% in the youngest cohort in the sample, born between 1951 and 1961. Although increasing differential mortality contributes to this reduction to some extent, the trends cannot be fully explained by differential mortality alone. Thus, the distortion due to differential mortality is not particularly problematic for the younger cohorts. Although the existence of mortality differentials makes inferences to the entire birth cohort difficult, this limitation does not seriously impair the external validity of this study.

Table 1.

Descriptive statistics for marriage-fertility sample, by birth cohort.

Women's education	Husband's education (%)					Number of children (s.d)		Women's marginal (N)
	0–8	9–11	12	13+	Total
Cohort 1 (1927–1941)
0–8	74.6	12.4	9.8	3.2	100.0	4.09	(1.73)	86.5	(1622)
9–11	10.4	22.7	45.6	21.3	100.0	3.53	(1.61)	6.6	(137)
12	4.9	5.5	40.6	49.1	100.0	3.37	(1.19)	5.5	(108)
13+	0.0	3.3	6.7	90.0	100.0	3.09	(0.94)	1.4	(30)
Total	65.4	12.6	13.8	8.2	100.0	4.00	(1.70)	100.0	(1897)
Cohort 2 (1942–1951)
0–8	61.3	20.8	16.3	1.7	100.0	3.10	(1.27)	60.6	(842)
9–11	9.6	29.4	52.1	9.0	100.0	2.85	(1.07)	20.2	(279)
12	2.3	6.8	52.0	38.9	100.0	2.37	(0.91)	14.8	(199)
13+	0.0	0.0	10.8	89.2	100.0	2.19	(0.70)	4.4	(56)
Total	39.4	19.5	28.6	12.5	100.0	2.90	(1.20)	100.0	(1376)
Cohort 3 (1952–1961)
0–8	53.7	26.8	18.1	1.5	100.0	2.41	(0.93)	23.3	(371)
9–11	7.9	39.7	47.7	4.7	100.0	2.21	(0.79)	23.2	(383)
12	0.9	5.7	60.7	32.8	100.0	2.06	(0.77)	43.8	(706)
13+	1.1	1.1	8.7	89.1	100.0	1.97	(0.64)	9.7	(161)
Total	14.9	18.0	42.7	24.4	100.0	2.16	(0.82)	100.0	(1621)
Entire sample
0–8	66.4	17.8	13.5	2.3	100.0	3.46	(1.60)	54.4	(2835)
9–11	8.8	33.8	49.2	8.2	100.0	2.61	(1.12)	17.3	(799)
12	1.5	5.9	57.4	35.2	100.0	2.22	(0.91)	22.9	(1013)
13+	0.7	1.0	9.1	89.2	100.0	2.11	(0.74)	5.5	(247)
Total	38.0	16.9	29.5	15.7	100.0	2.95	(1.46)	100.0	(4894)

In addition, the survey collected information only on the total number of surviving children, and not on the number of total births. Given the negative association between maternal education and child mortality in South Korea (Choe, 1987; Kim, 1988), using the number of surviving children would underestimate the educational differentials in fertility. This underestimation has two implications for the present analysis. First, differential child mortality by mother's education is not problematic for the fertility model as long as we are interested in differential reproduction rates where reproduction should mean the survival until adult ages and the completion of a certain level of schooling. This suggests that the number of surviving children would be an even more appropriate measure than the number of total births in this analysis. However, we should consider adult mortality too because some daughters of the women in this sample survived until a certain adult age (e.g., age 20) but died before the survey. If this mortality rate depends on maternal education, our daughter's sample may not be representative of the population of interest. We speculate that there is a modest association between maternal education and young adult mortality because of (1) the intergenerational association in educational attainment, and (2) educational differentials in mortality. However, we do not find any empirical evidence for or against this conjecture. In addition, mortality rates among young adults are quite low (Kim, 2004), making the influences of differential mortality by maternal education small. Second, differential child mortality by mother's education has implications for the transmission model because sibship size is underestimated, particularly for the less educated. Resource competition is claimed as a primary reason for the negative association between socioeconomic outcomes and sibship size (Guo and VanWey, 1999). From this standpoint, early deaths (e.g., infant mortality) may not pose a significant problem for the transmission model. However, later deaths (e.g., in teenage and young adult years) would be problematic, particularly if maternal education is strongly associated with the chance of these deaths. We speculate modest association between these, but do not have empirical evidence for or against this conjecture.

The above discussion suggests that ignoring mortality differentials by education reduces the external validity of the present analysis to some extent. However, Kye (2011) found that the implication of differential mortality for the intergenerational transmission of women's educational attainment is not great because of substantial intergenerational educational mobility. This suggests that ignoring mortality differentials by education should not seriously distort the results.

5. Results

5.1. Descriptive results

Table 1 shows descriptive statistics for the marriage-fertility sample by women's birth cohorts. First, we see strong educational homogamy and hypergamy. For all cohorts, a significant percentage of women married husbands whose educational attainments are the same as theirs. This is particularly true for college-educated women; about 90% of women with a college education married men with the same level of education. We can also see that women tend to marry up: upper diagonal cells tend to be bigger than lower diagonal cells. For example, more than one third of women with 12 years of schooling married men with more than 13 years of schooling, but less than 10% of these women married down. Second, women's education is negatively associated with the number of children for all cohorts. While the mean number of children decreased across cohorts, educational differentials in the number of children are persistently observed for all cohorts. The existence of educational differentials in fertility may dampen the intergenerational effects of increasing women's educational attainment to some extent. Finally, we can see that younger cohorts are better educated than older cohorts. For example, while less than 7% of women in the oldest cohort (born in 1927–1941) attained a high school diploma, more than half of the women in the youngest cohort (born in 1952–1961) did so.

Table 2 shows descriptive statistics for the transmission sample by birth cohorts. First, we can see that upward educational mobility is prominent. While only about 20% of mothers and 40% of fathers finished high school, more than 80% of daughters attain at least a high school diploma. This strong upward mobility is observed for all birth cohorts. Secondly, a positive association between mother's and daughter's education is observed: better educated mothers tend to have daughters with more schooling.

Table 2.

Descriptive statistics for transmission sample, by birth cohort.

Women's education	Daughter's education (%)					Daughter's marginal (N)		Father's marginal (N)		Mother's marginal (N)
	0–8	9–11	12	13+	Total
Cohort 1 (1927–1941)
0–8	17.9	16.8	47.5	17.8	100.0	15.9	(531)	65.3	(1020)	86.6	(1366)
9–11	1.9	1.8	49.2	47.0	100.0	15.0	(509)	12.8	(214)	6.6	(114)
12	0.8	1.5	26.7	71.0	100.0	46.2	(1686)	14.1	(224)	5.6	(93)
13+	0.0	0.0	6.3	93.7	100.0	22.9	(868)	7.9	(137)	1.3	(22)
Total	15.9	15.0	46.2	22.9	100.0	100.0	(3594)	100.0	(1595)	100.0	(1595)
Cohort 2 (1942–1951)
0–8	3.6	8.3	54.1	34.1	100.0	2.4	(46)	41.3	(453)	62.6	(676)
9–11	0.2	1.2	33.6	65.0	100.0	5.7	(101)	19.6	(215)	19.7	(211)
12	0.0	0.0	11.7	88.3	100.0	43.3	(841)	27.3	(282)	13.6	(146)
13+	1.5	0.0	3.1	95.4	100.0	48.6	(951)	11.8	(123)	4.2	(40)
Total	2.4	5.7	43.3	48.6	100.0	100.0	(1939)	100.0	(1073)	100.0	(1073)
Cohort 3 (1952–1961)
0–8	1.7	1.8	41.0	55.4	100.0	0.5	(6)	17.7	(169)	27.8	(259)
9–11	0.0	0.3	29.6	70.1	100.0	0.7	(11)	19.9	(191)	26.6	(256)
12	0.0	0.0	13.9	86.1	100.0	26.0	(349)	43.7	(414)	38.9	(375)
13+	0.0	1.8	7.1	91.1	100.0	72.7	(1003)	18.7	(183)	6.7	(67)
Total	0.5	0.7	26.0	72.7	100.0	100.0	(1369)	100.0	(957)	100.0	(957)
Entire sample
0–8	11.4	12.4	49.0	27.2	100.0	7.7	(583)	42.4	(1642)	60.3	(2301)
9–11	0.4	0.9	34.7	63.9	100.0	8.5	(621)	17.3	(620)	17.2	(581)
12	0.1	0.2	14.9	84.8	100.0	40.5	(2876)	27.7	(920)	18.5	(614)
13+	0.6	0.7	5.3	93.3	100.0	43.3	(2822)	12.6	(443)	4.0	(129)
Total	7.7	8.5	40.5	43.3	100.0	100.0	(6902)	100.0	(3625)	100.0	(3625)

5.2. Parameter estimates

Table 3 reports parameter estimates of models for husband's education, number of children, and daughter's schooling. Weights and clustering within the primary sampling unit are taken into account in estimating each model. First, we see strong educational assortative mating as expected from the descriptive analysis in Table 1: highly educated women are likely to marry highly educated men.⁹ Second, there is a monotonic negative association between women's educational attainment and fertility. However, we also see a curvilinear relationship between husband's educational attainment and fertility. The least-educated men (0–8 years) have the most children. Once finishing junior high school (9 years+), more-educated men tend to have more children. This result is consistent with findings in most demographic research which show that women's socioeconomic status is negatively associated with fertility (Bongaarts, 2003; Jejeebhoy, 1995; Skirbekk, 2008) because it increases direct and opportunity costs of childbearing, but high status men are able to have more offspring because of their higher purchasing power (Blake, 1968). Finally, we see that parental education is positively associated with daughter's education and that daughters growing up in larger families are worse off. Father's education has a bigger impact on daughter's education than does mother's education. Combined with the results for husband's schooling, this confirms previous research showing that women's educational attainment is a strong predictor of husband's socioeconomic status but is not influential for family's socioeconomic status, net of husband's status in South Korea (Lee, 1998).

Table 3.

Parameter estimates for models of marriage, fertility, and intergenerational transmission.^a

	Husband's schooling (ordered logit)		Number of children (poisson)		Daughter's schooling (ordered logit)
	β	z	β	z	β	z
Women's education 0–8 (reference)
9–11	2.291	29.66	−0.215	−9.95	0.699	6.68
12	4.076	35.00	−0.401	−17.01	1.189	9.28
13+	6.709	27.26	−0.479	−14.14	1.253	3.51
Husband's education 0–8 (reference)
9–11	–	–	−0.170	−7.94	0.821	8.61
12	–	–	–0.102	–4.81	1.288	12.61
13+	–	–	–0.050	–1.70	2.347	12.18
# of Siblings	–	–			–0.394	–14.41
Intercept	–	–	1.283	97.45	–	–
Cut point 1	0.628	–	–	–	–3.381	–
Cut point 2	1.863	–	–	–	–2.402	–
Cut point 3	4.607	–	–	–	0.194	–
Observations (N)	4894		4894		6902
Pseudo log likelihood	–4659.38		–12,421,922.00		–6364.16

^aWeights and clusters are taken into account in estimating each model.

From the coefficient estimates, we can speculate the magnitude of the intergenerational effects in each simulation. First, we expect bigger intergenerational effects in simulations with a corresponding change in marriage behavior (TM and TFM) than those without it (T and TF) because the effect of change in women's educational attainment will be amplified via improved husband's educational attainment in the TM and TFM model. Second, the inclusion of a fertility component in the simulation may reduce or increase the magnitude of intergenerational effects. On one hand, this may reduce the intergenerational effects because of higher reproduction rates of less-educated women compared to their better-educated counterparts. On the other hand, the curvilinear relationship between husband's education and fertility may offset the reduction in intergenerational effects in the TMF simulation because improvement in women's education also increases the number of highly-educated husbands who have higher reproduction rates than the less educated. However, coefficient estimates from the Poisson regression suggest that women's education matters more for reproduction rates than does husband's education, indicating that the reduction in intergenerational effects due to this curvilinear relationship is not great. In addition, a negative association between sibship size and educational attainment should reduce the negative impact of fertility differentials on the offspring's educational attainment to some degree. Hence, the implications of differential fertility for intergenerational effects depend on the strength of fertility differentials by women's education and the magnitude of the penalty that large family sizes pose on daughter's educational attainment.

5.3. Simulations

Tables 4 and 5 summarize the simulation results. Table 4 reports the ratios of simulated distributions to baseline distributions along with bootstrap standard errors. In the “Transmission only” (T only) simulation, we redistribute 5% of women's years of schooling according to four scenarios, but their marriage and fertility behaviors are assumed to remain the same. For example, the first scenario in the T only model (0–8 to 9–11) assumes that 5% of women change their years of schooling from 0–8 to 9–11 years, but the characteristics of their husbands do not change accordingly and they produce the same number of children as before. If the ratio is equal to one, this implies that the simulated change in women's education distribution does not affect daughter's education distribution (no intergenerational effect). The larger the deviation from one, the larger the intergenerational effects. Table 5 presents statistical tests of differences in intergenerational effects across models when we redistribute 5% of women's schooling from 0–8 to 13+ years. The “Diff.” columns show the differences in intergenerational effects between models, and “s.e.” columns present bootstrap standard errors associated with these differences. For example, the difference in the proportion of daughters with 13+ years of schooling is 2.5% between T only model and the “Transmission, Fertility, and Marriage” (TFM) model, with bootstrap standard error of .7%. In both Tables 4 and 5, we can see that bootstrap standard errors are not substantial. None of the bootstrap standard errors are greater than 1%, suggesting that the estimates of intergenerational effects are fairly precise.

Table 4.

Intergenerational effects, ratios of the simulated proportions to the baseline predicted proportions of daughter's educational attainments.

	Daughter's education
	0–8		9–11		12		13+
	Ratio	s.ea	Ratio	s.ea	Ratio	s.ea	Ratio	s.ea
Simulationb
Transmission only, T
0–8 to 9–11	0.939	0.007	0.946	0.012	0.990	0.003	1.029	0.003
9–11 to 12	0.995	0.006	0.999	0.009	1.011	0.005	0.991	0.006
12 to 13+	1.002	0.004	1.001	0.004	0.998	0.004	1.001	0.005
0–8 to 13+	0.951	0.007	0.954	0.007	0.972	0.005	1.042	0.007
Transmission + Fertility, TF
0–8 to 9–11	0.944	0.006	0.951	0.010	0.988	0.002	1.029	0.003
9–11 to 12	1.011	0.006	1.014	0.009	1.020	0.005	0.978	0.005
12 to 13+	1.005	0.004	1.003	0.004	1.000	0.004	0.999	0.004
0–8 to 13+	0.959	0.003	0.961	0.004	0.977	0.002	1.035	0.003
Transmission + Marriage, TM (Unconstrained marriage market)
0–8 to 9–11	0.923	0.003	0.934	0.005	0.972	0.002	1.050	0.003
9–11 to 12	0.995	0.002	0.990	0.004	0.981	0.002	1.020	0.003
12 to 13+	0.996	0.003	0.995	0.003	0.990	0.003	1.010	0.003
0–8 to 13+	0.912	0.004	0.915	0.004	0.934	0.004	1.089	0.005
Transmission + Marriage, TMC (Constrained marriage market)
0–8 to 9–11	0.955	0.004	0.960	0.006	0.983	0.002	1.030	0.003
9–11 to 12	1.005	0.002	0.999	0.003	0.987	0.002	1.011	0.003
12 to 13+	0.999	0.003	0.999	0.003	0.997	0.003	1.003	0.004
0–8 to 13+	0.956	0.005	0.953	0.005	0.957	0.005	1.054	0.006
Transmission + Fertility + Marriage, TFM (Unconstrained marriage market)
0–8 to 9–11	0.931	0.003	0.941	0.004	0.974	0.002	1.045	0.002
9–11 to 12	1.002	0.002	0.997	0.003	0.985	0.002	1.013	0.002
12 to 13+	0.999	0.003	0.998	0.003	0.993	0.003	1.007	0.003
0–8 to 13+	0.932	0.003	0.935	0.003	0.952	0.003	1.066	0.004
Transmission + Fertility + Marriage, TFMC (Constrained marriage market)
0–8 to 9–11	0.964	0.004	0.967	0.005	0.985	0.002	1.026	0.003
9–11 to 12	1.012	0.002	1.006	0.003	0.992	0.002	1.004	0.003
12 to 13+	1.002	0.003	1.002	0.003	0.999	0.003	1.000	0.004
0–8 to 13+	0.977	0.004	0.974	0.005	0.976	0.004	1.030	0.004
Observed distribution (%)	7.7		8.5		40.5		43.3
Baseline distribution (%)	4.6		6.3		39.8		49.3

^aBootstrap standard errors are reported (1000 replications).

^bRedistribution of 5% of women from lower to higher categories in each simulation.

Table 5.

Differences in intergenerational effects across models (redistribution of 5% of women from 0–8 to 13+ years of schooling).

Models compared			Daughter's education
			0–8		9–11		12		13+
			Diff.	s.ea	Diff.	s.ea	Diff.	s.ea	Diff.	s.ea
T only	vs.	TF	0.007	0.005	0.008	0.005	0.005	0.004	−0.007	0.005
		TM	−0.039	0.008	−0.039	0.008	−0.038	0.006	0.048	0.008
		TMC	0.005	0.008	−0.001	0.008	−0.015	0.006	0.013	0.008
		TFM	−0.019	0.007	−0.019	0.007	−0.020	0.005	0.025	0.007
		TFMC	0.026	0.007	0.020	0.008	0.004	0.005	−0.011	0.007
TF	vs.	TFM	−0.026	0.003	−0.026	0.003	−0.025	0.003	0.032	0.003
		TFMC	0.018	0.004	0.012	0.004	−0.001	0.003	−0.004	0.004
TM	vs.	TMC	0.020	0.002	0.020	0.002	0.018	0.002	−0.023	0.003
		TFM	0.044	0.003	0.038	0.003	0.023	0.002	−0.035	0.003
TMC	vs.	TFMC	0.021	0.002	0.021	0.002	0.018	0.002	−0.024	0.003
TFM	vs.	TFMC	0.045	0.003	0.039	0.003	0.024	0.002	−0.036	0.003

T only: Transmission only.

TF: Transmission + Fertility.

TM: Transmission + Marriage in an unconstrained marriage market.

TMC: Transmission + Marriage in a constrained marriage market.

TFM: Transmission + Fertility + Marriage in an unconstrained marriage market.

TFMC: Transmission + Fertility + Marriage in a constrained marriage market.

^aBootstrap standard errors are reported.

The results summarized in Tables 4 and 5 point to the following conclusions. First, we can confirm positive intergenerational effects. The intergenerational effects are largest when redistributing women's education from 0–8 to 13+ years. In addition, the intergenerational effects are larger when redistributing the least-educated women: intergenerational effects are greater when we redistribute 5% of women from 0–8 to 9–11 years than from 9–11 to 12 years, or from 12 to 13+ years of schooling. This is the case regardless of presence or absence of demographic elements. This suggests that providing more opportunities for schooling for the least-educated group would have been most beneficial to the next generation. Finishing junior high school (i.e., 9 years of schooling) makes more difference than do transitions in more advanced levels. Given that more than half of Korean middle-aged and elderly women (age 45 and above) in the sample belong to the least-educated category (54.4%, see Table 1), we may conclude that finishing junior high school was very important for women's socioeconomic and family-related outcomes that are associated with children's educational successes.

Next, demographic factors are important in intergenerational effects: assortative mating makes a significant positive contribution to intergenerational effects whereas differential fertility operates in the opposite direction. For simplicity, we focus on the changes in the highest educated category, 13+ years of schooling. First, a change in marriage behavior makes an important positive contribution to intergenerational effects. For example, intergenerational effects in the “Transmission and Marriage” (TM) and TFM simulations are much greater than in the T only and “Transmission and Fertility” (TF) simulations. Whereas a 5% change in women's educational attainment from less than a junior high graduate (0–8) to tertiary education (13+) would increase tertiary education (13+) by 4.2% in the T only simulation, this increases to 8.9% in the TM simulation (Table 4). This 4.8% difference is statistically significant with bootstrap standard error of .08% (Table 5). This confirms that the improvement in offspring's educational attainment is due partly to the corresponding improvement of husband's education in addition to the net effect of improvement in mother's own educational attainment. However, in the “Transmission and Marriage in a constrained marriage market” (TMC) simulation, where the marginal distribution of husband's education remains the same, the size of the intergenerational effect is only 5.4% (Table 4), which is not much greater than the effect found in the T only simulation (4.2%) and the difference is not statistically significant (Table 5). The same pattern is observed for the comparison between TF and “Transmission, Fertility and Marriage in a constrained marriage market” (TFMC) simulation. This suggests that the change in the marginal distribution of husband's education corresponding to the change in women's education is crucial for explaining the importance of assortative mating in the intergenerational transmission process in South Korea. The significant impact of demographic elements is interesting because we expected that the influences of demographic elements may not be substantial due to the massive increase of educational attainment over time. In terms of tertiary education among offspring, the difference in intergenerational effects between T only and TFM simulation is 2.5%, which is statistically significant (Table 5). Hence, we can conclude that accounting for differential demographic behaviors is still important for educational mobility even when educational opportunity expands dramatically.

Finally, the implications of differential fertility depend on the presence of assortative mating. For example, the comparison between T only and TF simulation shows no significant difference (Table 5). The insignificant difference between them suggests that differential fertility is not large enough to offset the positive influence of smaller family size on daughter's education when assortative mating is absent. Inclusion of the fertility component, however, becomes significant when assortative marriage is present. Whereas a 5% change in women's educational attainment from less than a junior high graduate (0– 8) to tertiary education (13+) would increase the share of those with a tertiary education (13+) by 8.9% in the TM simulation (5.4% in TMC simulation), this amounts to 6.6% in the TFM simulation (3.0% in TFMC simulation). These differences are statistically significant (Table 5). In sum, a change in marriage behaviors amplifies the intergenerational effect and changes in fertility dampen the intergenerational effect when assortative mating is present.

Fig. 1 visually summarizes the results discussed above. It shows the size and the variability of intergenerational effects in the most extreme scenarios examined: simulations in which 5% of women change their education from 0–8 to 13+. From this graph, we can see the maximum, 75 percentile, median, 25 percentile, and minimum for the ratios of the simulated to the baseline proportion of each education category.¹⁰ We see that sampling variability of estimates is not great and that ranges do not include 1 in any simulations. This means that the estimates for intergenerational effects are precise and that the shift in women's education in each simulation has a statistically significant effect on daughter's educational distribution. Substantively, this graph illustrates the implications of assortative mating and differential fertility for intergenerational effects discussed above. Again, we see that a change in marriage behaviors corresponding to educational upgrading is important. In the TM simulation, the proportion with the highest education increased the most and the proportions of other education categories decreased the most. The strong impact of assortative mating on the size of intergenerational effects has two important implications for intergenerational transmission of women's educational attainment in South Korea. First, this suggests that marriage is an institution that consolidates educational inequality in South Korea. Without assortative mating, educational inequality in the next generation is not strongly influenced by the educational inequality in previous one. Second, this also confirms husband's primacy in determining family's socioeconomic status (Lee, 1998). Without a change in husband's education, the increase in women's education has a weaker impact on the distribution of daughter's education. This is also evident from the substantially smaller inter-generational effects found in the simulation that impose marriage market constraints. Second, differential fertility dampens the intergenerational effect to some extent, as reproduction rates are higher among the less-educated women than the better-educated women. The negative influence of large family size on daughter's educational attainment does not fully offset differential reproduction rates. The influences of differential fertility are insignificant when assortative mating is absent.

Fig. 1.

Intergenerational effects, proportional changes in daughter's educational attainment when 5% of women change schooling from 0–8 to 13+ years.

The intergenerational effects in South Korea show different patterns than Mare and Maralani's (2006) Indonesian case, where the recursive demographic model for intergenerational effects was first applied. The comparison not only illustrates the uniqueness of the Korean experience, but also improves our understanding of the process of distributional changes in education across generations. We can see two noticeable differences. First, the magnitude of intergenerational effects is much larger in Indonesia than in South Korea, although direct comparison between these two countries is not feasible because of a different categorization of educational attainment. For example, whereas redistributing 5% of women from 0– 8 years to 13+ years of schooling in South Korea leads to a 5.4% increase in percent of college-educated daughters (see Table 4), much less drastic change in Indonesia (e.g., redistribution of 5% of women from 10–12 years to 13+ years of schooling) leads to a slightly larger change, a 5.9% increase (see Table A.1 in Mare and Maralani (2006, p. 562)). The smaller intergenerational effects in South Korea are consistent with our expectation that rapid educational expansion yields small intergenerational effects because children are likely to attain the high level of educational attainment regardless of their parents' education level. While Indonesia also experienced substantial change in the marginal distribution of education attainment across generations, the change is much more drastic in South Korea.¹¹ The huge upward educational mobility driven by educational expansion in South Korea is largely responsible for the smaller intergenerational effects.

Second, the implications of assortative mating and differential fertility are weaker in South Korea than in Indonesia. The difference in percentage of college-educated daughters between T only and TFM simulation in Indonesia is 17.8% when redistributing 5% of women's education from no schooling to 13+ years (see Table A.1 in Mare and Maralani (2006, p. 561)). The difference in percentage of college-educated daughters between T only and TFM simulation in South Korea is 2.4% when redistributing 5% of women's education from 0–8 to 13+ years of schooling. Such a big difference suggests much smaller implications of demographic processes for intergenerational effects in South Korea than in Indonesia. This is interesting because substantial educational differentials in marriage and fertility also exist in South Korea. We also find that these elements make a statistically significant difference in intergenerational effects in South Korea. This pattern is also related to the rapid educational expansion in South Korea. As we have discussed, daughters in South Korea are likely to attain high levels of education due to the huge expansion of educational opportunity. Hence, demographic reproduction has only modest, while statistically significant, implications for intergenerational effects. In sum, the comparison with the Indonesian case highlights the importance of educational expansion in determining the intergenerational effects in South Korea.

5.4. Cohort comparison

As discussed above, South Korea experienced rapid socioeconomic and demographic change in the past half-century. This leads us to expect sizeable transformation of intergenerational transmission, differential reproduction, and assortative mating processes over time, which also influence the size of intergenerational effects. To test this idea, we separately estimate the marriage, fertility, and transmission model by cohorts, and do the simulations for each cohort using the parameter estimates. The results for each cohort are reported in Tables A.2–A.4. The bootstrap standard errors from 1000 replications are reported. Bootstrap standard errors tend to be larger in cohort-specific simulations than simulations using an entire sample due to smaller sample size. Here, we focus on the intergenerational effects for the least-educated and the most-educated group from the most extreme simulations in which we change 5% of women's education attainment from 0–8 to 13+.

Two general patterns are observed for all the cohorts. First, we see similar patterns observed in Table 4 and Fig. 1: substantial intergenerational effects with a corresponding change in marriage behavior and weaker influences of differential fertility on intergenerational effects than assortative mating. This suggests persistent patterns of intergenerational effects of changing women's educational attainment over time despite the changing magnitude. Second, the estimates of intergenerational effects are less reliable for the least-educated youngest cohort (0–8, 1952–1961) and the most-educated oldest cohort (13+, 1927–1941) than others. This is the case because the sample sizes for these groups are quite small.

We can also see cohort changes in intergenerational effects. First, the upper panel in Fig. 2 shows that intergenerational effects increase across cohorts for the group of least-educated daughters. While a less than 10% decrease in the least-educated daughters is expected from the simulation for the cohort born between 1927 and 1941, this amounts to 10–20% for the youngest cohort (born in the 1950s). Second, intergenerational effects decrease across cohorts for the most-educated group (lower panel in Fig. 2). For example, let us consider the TMF simulation. Whereas a 5% change in women's educational attainment from less than a junior high graduate (0–8) to having at least some tertiary education (13+) would increase the percent tertiary (13+) by about 15% for the oldest cohort, this amounts to much less than 5% for the youngest cohort. The changing intergenerational effects across cohorts are interesting because the intergenerational association in education does not change much across cohorts. The persistent intergenerational association over time is also observed in previous studies (e.g., Park, 2007). Hence, the cohort changes in intergenerational effects largely reflect the rapid educational expansion in South Korea. The increasing intergenerational effect for the least educated suggests the disappearance of the least-educated category over time. Among the youngest cohort, only 0.5% of women belong to this category. Because the least educated are composed of such a small portion of population, the small or modest decrease in this group leads to large proportional change. Hence, further improvement of women's educational attainment and subsequent enhancement in daughter's education attainment will lead to the disappearance of the least-educated group in the future. In addition, the decreasing intergenerational effects for highly educated women reflect a saturation of women's educational attainment for the younger cohort. Whereas only 23% of daughters of the oldest cohort received a tertiary education, 73% of daughters of the youngest cohort attended college (see Table 2). Therefore, there is not much room for improvement in women's educational attainment in the youngest cohort. The compositional constraints make intergenerational effects for highly educated women smaller over time. In sum, changing intergenerational effects suggests the disappearance of the least-educated group and a saturation of women's educational attainment in South Korea. This change also illustrates the importance of distributional changes for educational mobility.

Fig. 2.

Cohort comparison of intergenerational effects, proportional changes in daughter's educational attainment when 5% of women change schooling from 0–8 to 13+ years.

Third, the impact of marriage on intergenerational effects decreased substantially. For example, the difference between TF and TFM is about 10% for the oldest cohort (1927–1941), about 5% for the middle cohort (1942–1951), and almost negligible for the youngest cohort (1952–1961). This suggests that the indirect benefits of increasing women's educational attainment via a parallel upgrading of husband's education have been decreasing over time in South Korea. As mentioned earlier, Lee (1998) showed that women's educational attainment is a strong predictor of husband's socioeconomic status but is not influential for family's socioeconomic status net of husband's status in South Korea. The analysis of the entire sample in the current study also confirms the strong impact of assortative mating on intergenerational effects. Cohort comparison, however, suggests weakening of the impact of assortative mating on the intergenerational effects. We speculate a couple of explanations for this change: improvement in women's socioeconomic status during the socioeconomic development (Mason, 1985) and changing labor markets conditions for men and women (Oppenheimer, 1988). We need more systematic investigation on this topic to test these ideas rigorously, which is beyond the scope of the current study.

6. Summary and discussion

The present study examines the intergenerational effects of women's education by replicating Mare and Maralani's (2006) model to South Korea, a nation that experienced rapid socioeconomic and demographic transformation over the last half century. Examining intergenerational effects is important because this provides a complete description of the intergenerational transmission of family backgrounds, which is a marked improvement over most previous mobility studies. The current study also improves Mare and Maralani's (2006) original study by estimating bootstrap standard errors that allow for testing statistical significance. The results point to the following conclusions. First, differential demographic behaviors are important intervening mechanisms in South Korea, similar to Mare and Maralani's (2006) Indonesian case. When improvement in women's education leads to the improvement in husband's education, the intergenerational effects are amplified substantially. By contrast, differential fertility reduces intergenerational effects significantly. Second, the magnitude of intergenerational effects, however, is smaller in South Korea than in Indonesia. More drastic change in the distribution of educational attainment in South Korea leads to weaker dependence of daughter's education on mother's education, which yields smaller intergenerational effects. Third, the contribution of assortative marriage and differential fertility to intergenerational effects is also weaker in South Korea than in Indonesia. The rapid educational expansion is also responsible for this weaker contribution. The level of daughter's education in South Korea is so high that there is not enough room for differential demographic behaviors to be influential for intergenerational effects. Finally, intergenerational effects change across cohorts, reflecting South Korea's educational expansion over several decades. In particular, the size of intergenerational effects shows a decreasing trend for the highly educated daughters although the cohort difference is not statistically significant due to large sampling variability among the highly educated women in the older cohorts and the less-educated women in the younger cohorts.

Research on social mobility has found that industrialized countries exhibit common patterns of intergenerational association but specific parameters that vary by time and place (Erikson and Goldthorpe, 1992; Shavit and Blossfeld, 1993). Positive intergenerational association exists almost universally, but the size of this association varies. One source of this cross-national difference is structural mobility, defined as changes in marginal distribution of socioeconomic status across generations (Hout, 2004).¹² This claim, however, cannot be assessed appropriately, in part because most mobility studies rely on data from existing parent-offspring dyads. These data cannot address the issue of differential reproduction, which affects a key element of structural mobility, the marginal distribution of socioeconomic status in the parental generation (Duncan, 1966). The findings of the current study, including the comparison between South Korea and Indonesia, suggest that the patterns of intergenerational effects are consistent with intergenerational association: positive intergenerational effects are confirmed with the Korean and Indonesian data. However, the intergenerational effects are smaller in South Korea than in Indonesia. Because our model accounts for differential demographic reproduction, we can link the varying intergenerational effects to structural mobility more confidently. This is arguably an important advantage of the new model of intergenerational effects over previous approaches in social mobility. Hence, we attribute the cross-national differences in intergenerational effects to the difference in structural mobility in educational attainment and find that greater improvement in educational attainment in South Korea than Indonesia is responsible for this difference. In other words, the difference in distributional changes explains the cross-national differences in the magnitude of intergenerational effects. Further applications of this model to other countries will be necessary to advance this claim further.

This study leaves a couple of issues unanswered. First, models for husband's schooling, fertility, and daughter's schooling are not necessarily the best models for each process. In particular, we ignore cultural factors prevalent in Korea that influence the family reproduction process. Some of these factors include strong son preference and more sex-discriminative educational investment practices in Korean families than in Western ones (Choe and Park, 2006), although these have been weakening over time. Taking into account these elements in fertility and transmission models will provide a better description of the intergenerational transmission of educational attainment and will enhance our ability to assess intergenerational effects. However, such improvement will be achieved at the cost of much more complication in data analysis. Another point is the constraints in the marriage market. The present study simply assumes that husband's education distribution also changes according to the change in women's education distribution (TM and TFM model), or that the association (e.g., odds ratios) is the same but the marginal education distribution of husbands does not change at all (TMC and TFMC model). Yet actual matching mechanisms in marriage markets may differ from this. Using matching models that account for the opportunity and constraints of both sexes (e.g., Logan et al., 2008) will improve the understanding of marriage markets, which will help us better assess the intergenerational effects of increasing women's education.

This article, however, provides much richer description of educational mobility in South Korea than most previous studies. Whereas earlier efforts focused on the intergenerational association based on existing parent-offspring dyads in South Korea (e.g., Park, 2004; Phang and Kim, 2002), we show how intermediate demographic processes contribute to the changing distribution of educational attainment across generations. Hence, this study provides a better understanding of the rapid demographic and socioeconomic changes in South Korea over the past half century than do previous studies.

Appendix A

Table A.1.

Mortality differentials by cohort and education.^a

Cohort	Age
	25–34	35–44	45–54	55–64
1926–1935
No schooling	–	1.15	1.17	0.95
Primary	–	1.09	1.02	1.15
Secondary	–	0.50	0.62	0.72
Tertiary	–	0.37	0.55	0.64
1936–1945
No schooling	2.20	2.41	1.28	1.09
Primary	1.12	1.07	1.19	1.13
Secondary	0.44	0.51	0.20	0.77
Tertiary	0.29	0.33	0.49	0.52
1946–1955
No schooling	8.55	4.06	2.07	–
Primary	1.49	1.64	1.39	–
Secondary	0.46	0.67	0.79	–
Tertiary	0.38	0.44	0.54	–
1956–1965
No schooling	14.77	4.59	–	–
Primary	3.03	2.86	–	–
Secondary	0.74	0.89	–	–
Tertiary	0.50	0.45	–	–
1966–1975
No schooling	15.58	–	–	–
Primary	8.54	–	–	–
Secondary	1.11	–	–	–
Tertiary	0.57	–	–	–

^aAge-education-specific mortality ratios to overall age-cohort mortality assuming the same differential mortality in 10-year period. Sources: Kim (2004).

Table A.2.

Intergenerational effects, ratios of the simulated proportions to the baseline predicted proportions of daughter's educational attainments (1927–1941).

	Daughter's education
	0–8		9–11		12		13+
	Ratio	s.ea	Ratio	s.ea	Ratio	s.ea	Ratio	s.ea
Simulationb
Transmission only, T
0–8 to 9–11	0.972	0.012	0.945	0.005	1.012	0.003	1.030	0.008
9–11 to 12	0.989	0.005	0.998	0.007	0.991	0.005	1.026	0.015
12 to 13+	0.994	0.012	0.991	0.012	0.977	0.012	1.056	0.040
0–8 to 13+	0.965	0.009	0.965	0.009	0.976	0.006	1.097	0.024
Transmission + Fertility, TF
0–8 to 9–11	0.974	0.011	0.949	0.005	1.011	0.003	1.029	0.008
9–11 to 12	0.996	0.005	1.004	0.006	0.993	0.004	1.014	0.013
12 to 13+	0.996	0.012	0.993	0.012	0.979	0.011	1.051	0.039
0–8 to 13+	0.982	0.006	0.982	0.006	0.988	0.005	1.049	0.017
Transmission + Marriage, TM (Unconstrained marriage market)
0–8 to 9–11	0.954	0.004	0.952	0.004	0.993	0.003	1.079	0.009
9–11 to 12	0.994	0.005	0.999	0.005	0.984	0.004	1.037	0.013
12 to 13+	0.992	0.008	0.990	0.008	0.977	0.008	1.059	0.025
0–8 to 13+	0.939	0.008	0.939	0.008	0.948	0.008	1.188	0.027
Transmission + Marriage, TMC (Constrained marriage market)
0–8 to 9–11	0.981	0.006	0.971	0.005	0.999	0.003	1.035	0.010
9–11 to 12	1.000	0.005	1.005	0.006	0.989	0.005	1.019	0.014
12 to 13+	0.995	0.011	0.994	0.011	0.982	0.009	1.043	0.031
0–8 to 13+	0.972	0.012	0.965	0.011	0.961	0.010	1.121	0.035
Transmission + Fertility + Marriage, TFM (Unconstrained marriage market)
0–8 to 9–11	0.958	0.004	0.956	0.004	0.993	0.003	1.073	0.008
9–11 to 12	0.996	0.005	1.001	0.005	0.985	0.004	1.032	0.012
12 to 13+	0.996	0.008	0.993	0.008	0.980	0.008	1.049	0.027
0–8 to 13+	0.950	0.007	0.950	0.008	0.958	0.008	1.155	0.025
Transmission + Fertility + Marriage, TFMC (Constrained marriage market)
0–8 to 9–11	0.985	0.005	0.975	0.005	0.999	0.002	1.029	0.009
9–11 to 12	1.002	0.005	1.007	0.006	0.990	0.004	1.015	0.013
12 to 13+	0.998	0.010	0.997	0.011	0.985	0.009	1.033	0.030
0–8 to 13+	0.982	0.011	0.976	0.011	0.971	0.010	1.088	0.032
Observed distribution (%)	15.9		15.0		46.2		22.9
Baseline distribution (%)	12.5		13.6		48.6		25.3

^aBootstrapping standard errors are reported (1000 replications).

^bRedistribution of 5% of women from lower to higher categories in each simulation.

Table A.3.

Intergenerational effects, ratios of the simulated proportions to the baseline predicted proportions of daughter's education attainments (1942–1951).

	Daughter's education
	0–8		9–11		12		13+
	Ratio	s.eb	Ratio	s.eb	Ratio	s.eb	Ratio	s.eb
Simulationa
Transmission only, T
0–8 to 9–11	0.942	0.016	0.945	0.015	0.986	0.004	1.021	0.004
9–11 to 12	1.002	0.008	0.995	0.009	0.989	0.008	1.011	0.009
12 to 13+	1.014	0.008	1.014	0.008	1.005	0.008	0.993	0.008
0–8 to 13+	0.959	0.007	0.961	0.007	0.972	0.006	1.031	0.007
Transmission + Fertility, TF
0–8 to 9–11	0.943	0.016	0.946	0.015	0.986	0.004	1.021	0.004
9–11 to 12	1.013	0.008	1.006	0.008	0.996	0.008	1.002	0.008
12 to 13+	1.014	0.008	1.014	0.008	1.005	0.008	0.993	0.008
0–8 to 13+	0.968	0.003	0.970	0.003	0.981	0.003	1.022	0.003
Transmission + Marriage, TM (Unconstrained marriage market)
0–8 to 9–11	0.928	0.006	0.937	0.006	0.972	0.003	1.035	0.004
9–11 to 12	0.992	0.005	0.985	0.005	0.975	0.004	1.025	0.005
12 to 13+	0.997	0.005	0.996	0.005	0.990	0.006	1.009	0.006
0–8 to 13+	0.917	0.006	0.918	0.006	0.933	0.006	1.073	0.008
Transmission + Marriage, TMC (Constrained marriage market)
0–8 to 9–11	0.960	0.011	0.959	0.008	0.984	0.004	1.021	0.004
9–11 to 12	1.002	0.005	0.994	0.005	0.982	0.005	1.017	0.005
12 to 13+	1.002	0.006	1.002	0.006	0.998	0.007	1.002	0.007
0–8 to 13+	0.963	0.012	0.953	0.009	0.959	0.008	1.043	0.009
Transmission + Fertility + Marriage, TFM (Unconstrained marriage market)
0–8 to 9–11	0.930	0.006	0.939	0.006	0.973	0.003	1.034	0.003
9–11 to 12	1.001	0.005	0.995	0.005	0.981	0.004	1.017	0.004
12 to 13+	0.999	0.006	0.998	0.006	0.992	0.006	1.008	0.006
0–8 to 13+	0.930	0.005	0.931	0.005	0.946	0.006	1.059	0.006
Transmission + Fertility + Marriage, TFMC (Constrained marriage market)
0–8 to 9–11	0.962	0.011	0.961	0.008	0.984	0.003	1.020	0.004
9–11 to 12	1.011	0.005	1.003	0.005	0.989	0.004	1.009	0.004
12 to 13+	1.004	0.006	1.004	0.006	0.999	0.007	1.000	0.007
0–8 to 13+	0.977	0.012	0.967	0.008	0.972	0.007	1.030	0.007
Observed distribution (%)	2.4		5.7		43.3		48.6
Baseline distribution (%)	1.9		4.7		41.5		52.0

^aRedistribution of 5% of women from lower to higher categories in each simulation.

^bBootstrapping standard errors are reported (1000 replications).

Table A.4.

Intergenerational effects, ratios of the simulated proportions to the baseline predicted proportions of daughter's education attainments (1952–1961).

	Daughter's education
	0–8		9–11		12		13+
	Ratio	s.ea	Ratio	s.ea	Ratio	s.ea	Ratio	s.ea
Simulationb
Transmission only, T
0–8 to 9–11	0.787	0.011	0.863	0.072	0.979	0.011	1.008	0.004
9–11 to 12	1.037	0.021	1.023	0.025	1.029	0.023	0.990	0.007
12 to 13+	1.008	0.007	1.012	0.009	1.020	0.016	0.993	0.005
0–8 to 13+	0.821	0.012	0.839	0.019	0.950	0.011	1.017	0.004
Transmission + Fertility, TF
0–8 to 9–11	0.791	0.011	0.862	0.067	0.977	0.011	1.009	0.004
9–11 to 12	1.046	0.021	1.032	0.025	1.032	0.022	0.989	0.007
12 to 13+	1.009	0.007	1.013	0.009	1.021	0.016	0.993	0.005
0–8 to 13+	0.823	0.012	0.842	0.019	0.951	0.009	1.017	0.003
Transmission + Marriage, TM (Unconstrained marriage market)
0–8 to 9–11	0.785	0.011	0.817	0.030	0.967	0.010	1.012	0.004
9–11 to 12	1.002	0.003	0.989	0.013	0.966	0.007	1.011	0.002
12 to 13+	1.000	0.003	1.011	0.014	0.993	0.008	1.002	0.003
0–8 to 13+	0.786	0.011	0.817	0.028	0.921	0.012	1.027	0.004
Transmission + Marriage, TMC (Constrained marriage market)
0–8 to 9–11	0.814	0.031	0.866	0.047	0.978	0.011	1.008	0.004
9–11 to 12	1.015	0.013	1.001	0.014	0.977	0.008	1.007	0.003
12 to 13+	1.000	0.004	1.010	0.013	1.011	0.009	0.996	0.003
0–8 to 13+	0.826	0.036	0.877	0.044	0.960	0.014	1.014	0.005
Transmission + Fertility + Marriage, TFM (Unconstrained marriage market)
0–8 to 9–11	0.789	0.011	0.820	0.029	0.966	0.010	1.012	0.003
9–11 to 12	1.006	0.003	0.993	0.014	0.968	0.007	1.010	0.002
12 to 13+	1.002	0.003	1.012	0.013	0.994	0.008	1.002	0.003
0–8 to 13+	0.795	0.011	0.823	0.026	0.927	0.010	1.025	0.003
Transmission + Fertility + Marriage, TFMC (Constrained marriage market)
0–8 to 9–11	0.819	0.031	0.869	0.046	0.977	0.011	1.009	0.004
9–11 to 12	1.019	0.013	1.005	0.014	0.979	0.008	1.007	0.003
12 to 13+	1.001	0.004	1.011	0.012	1.012	0.009	0.996	0.003
0–8 to 13+	0.836	0.037	0.884	0.042	0.967	0.013	1.012	0.004
Observed distribution (%)	0.5	0.7			26.0		72.7
Baseline distribution (%)	0.4	0.6			22.4		76.6

^aBootstrapping standard errors are reported (1000 replications).

^bRedistribution of 5% of women from lower to higher categories in each simulation.