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Housewife, “gold miss,” and equal: the evolution of educated women’s role in Asia and the U.S.

Abstract

The fraction of U.S. college graduate women who ever marry has increased relative to less educated women since the mid-1970s. In contrast, college graduate women in developed Asian countries have had decreased rates of marriage, so much so that the term “Gold Misses” has been coined to describe them. This paper argues that the interaction of rapid economic growth in Asia combined with the intergenerational transmission of gender attitudes causes the “Gold Miss” phenomenon. I present a simple dynamic model then test its implications using U.S. and Asian data on marriage and time use.

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Notes

  1. The Economist, “The flight from marriage,” August 20th 2011.

  2. Terms have been coined in each region to refer to this group—in Korean Gold Miss (because they are “old misses” but highly educated and financially independent), in Japanese Hanako-zoku (literally “Hanako tribe,” named after the readers of the consumer magazine Hanako, which targets young single women) or Wagamama (translated as “single parasites” because most unmarried adults live with their parents), and in Chinese Sheng-nu (translated as “leftover women”). Among these, I choose to use the term Gold Miss throughout this paper.

  3. Korea and Japan are ranked the two lowest among OECD countries in out-of-wedlock childbirths. Thirty-eight percent of births are out-of-wedlock in the U.S. (OECD Family Database, 2011)

  4. For references on the trends of U.S. college graduate women’s marriage and fertility, see for example, Kalmijn (1991), Goldin (2004), and Schwartz and Mare (2005), and Stevenson and Wolfers (2007).

  5. Feyrer et al. (2008) share similar intuitions, although they do not present a formal model. Looking at cross-country differences in fertility rates, they argue that countries where women’s household status lags behind their labor market opportunities experience the lowest fertility rates.

  6. See for example, Giuliano (2007), Fernández and Fogli (2009), Alesina and Giuliano (2010), and Alesina et al. (2011), and Hwang (2013) for discussions on the persistence of family culture. Regarding assimilation profiles, Blau et al. (2013) study immigrants in the U.S. and find second generation women’s fertility, education, and labor supply converging to native levels.

  7. Age 35 is young enough to capture recent developments and old enough to distinguish between “marriage delayed” and “marriage forgone” among women in Asia. Despite the rise in women’s age at first marriage—29 in Japan and Korea, 28 in Taiwan, 30 in Hong Kong, and 28 in Singapore (Jones and Gubhaju 2009)—marriage rates fall starkly once women reach their late 30s. The age-specific marriage rate for brides in age group 35–39 is only 12.2 (per thousand) in Korea and 9.2 (per thousand) in Japan (Statistics Korea, 2010 and Vital Statistics of Japan, 2009). This is not unrelated to the fact that female fertility drops sharply after age 35.

  8. The increase was 5 percentage points in the U.S. during the same period.

  9. Among those above age 35, however, there are still more male college graduates than female. Hence, the increase in female college enrollment rates alone cannot explain the Gold Miss phenomenon; there is no “excess” supply of college graduate women in the Asian marriage market.

  10. See Kawaguchi and Lee (2012) for a discussion about female migration from developing Asian countries to developed East Asian countries. They find that foreign brides currently comprise 4 to 35 percent of newlyweds in Japan, Korea, Singapore, and Taiwan although there is no raw sex ratio imbalance in these countries. Men with low socioeconomic statuses marry foreign women.

  11. Singapore and Taiwan do not provide Census micro-data. Including all individuals over age 35 may overstate the marriage rates of earlier cohorts since they are being observed at later ages than recent cohorts. The bias is expected to be relatively unimportant, however, since first marriages are rare once women reach their late 30s. (See footnote 7 for more detail.)

  12. Japanese data are from the Statistics and Information Department of the Ministry of Health, Labour, and Welfare. Korean data are from the 1975–2009 Occupational Wage Survey. See Goldin (1990) Table 3.2 for U.S. data.

  13. ryōsai kenbo in Japanese, hyun mo yang ch’o in Korean, and xián qī liáng mù in Chinese.

  14. Possible answers are (1) Agree, (2) Disagree, and (3) Neither. (Don’t know and missing are excluded.) The sample size for each country is U.S. 1238, Hong Kong 1225, Japan 1042, Korea 1197, and Taiwan 1226. No statistics are available for Singapore on this question.

  15. Possible answers are (1) Strongly agree, (2) Agree, (3) Disagree, and (4) Strongly disagree in the GSS and (1) Strongly agree, (2) Fairly agree, (3) Somewhat agree, (4) Neither agree or disagree, (5) Somewhat disagree, and (6) Strongly disagree in the EASS. (Don’t know and missing are excluded.) The sample size for each country is U.S. 13,748, Japan 2130, Korea 1605, and Taiwan 2102. Singapore and Hong Kong are not included.

  16. See Appendix A for information on these datasets.

  17. Hong Kong has a foreign domestic worker (FDW) program and the government sets the minimum wage for these workers. According to Cortes and Pan (2013), the minimum wage is more than four times lower than high skilled women’s wage. Though limited, Taiwan and Singapore have similar programs; the FDW’s wage is about 30–40 % of native college graduate women’s. Japan and Korea have stricter immigration policies. The relative price of live-in domestic workers is nearly half of native college graduate women’s wage, as in the U.S. (See Huang et al. (2005) for more information on foreign domestic workers.)

  18. Standard models of household production can also show that growth in women’s earning power reduces the gain from marriage or that positive assortative mating becomes optimal as technology advances (Becker 1991). However, they cannot explain why marriage patterns would evolve differently across similarly developed countries. Intra-household models also face this limitation if bargaining power is a function of only wages. (See Chiappori and Donni (2011) for a survey of this literature.) Assuming that the sharing rule is affected by other “distribution factors,” in which gender attitudes can be a component, is an option. The difference with my model would then be that the husband’s type affects the wife’s utility via consumption.

  19. If men also differed in their educational attainment and wages, there would be four categories of men, with the modern and educated being the most attractive husband and the traditional and uneducated being the least attractive. Figure 1a and Kawaguchi and Lee (2012) address this outcome. Since my paper’s focus is on the Gold Misses, I do not add the education dimension to men. But the traditional and uneducated men not being able to marry is a by-product of the Gold Miss phenomenon, and can thus be explained by the same mechanisms addressed here.

  20. p E t is defined in Eq. 6 below. How λ E t is endogenously determined is discussed in Section 3.4.

  21. Similar effects may exist for girls as well: girls who grew up in male-breadwinner households may be more traditional than those who grew up in dual-earner households. For example, Olivetti et al. (2013) study how women’s working behavior is influenced by the working status of their mothers and their childhood friends’ mothers using the National Longitudinal Survey of Adolescent Health. However, when economic growth creates opportunities for girls that did not exist for their mothers, girls are no longer constrained to traditional roles. Thus, given the time frame of my model—the past century during which women’s wages increased greatly—the intergenerational transmission plays a much smaller role (on net) for girls than for boys. Section 4.1 presents supportive evidence (see footnote 33).

  22. See Appendix B.1.1 for a discussion on how the model changes when the disutility term is in the men’s utility function.

  23. Refer to Section 2 to see cross-country variation in responses to stylized gender role questions. Research on the relationship between husbands’ gender attitudes and the quality of marital relations provide further evidence. See for example, Hochschild and Machung (1989) and Rubin (1983). Empirical evidence also suggests that the current setup depicts reality in that even “modern” men do not spend substantial amounts of time on domestic chores. Rather, the more important difference between the two types of men seem to arise through how much they are willing to substitute wife’s housework time with market goods and services. Section 4.2 of my paper and the small variation in men’s non-market work time across groups documented in previous studies support this view (see for, e.g., Aguiaran and Hurst 2007; Guryan et al. 2008; Cortes and Tessada 2011).

  24. The first order conditions of Eqs. 2 and 3 when j = M:

    $$\left\{\begin{array}{l} \frac{1}{2}w_{m}-\frac{\beta}{2-t_{m}-t_{f}}-\mu_{m} \leq 0, t_{m} \geq 0\\ 1-t_{m}\geq 0,\mu_{m}\geq 0\\ \frac{1}{2}w_{f}-\frac{\beta}{2-t_{m}-t_{f}}-\mu_{f} \leq 0, t_{f} \geq 0\\ 1-t_{f}\geq 0,\mu_{f}\geq 0 \end{array}\right. $$

    where μ m and μ f are the Lagrangian multipliers. Given w m > w f and w m ≥ 2β, there are only two possible (corner) solutions.

  25. Allowing individuals who are unmarried after the first round to redraw does not make any difference in the fraction and type of men and women who remain single, because only educated women and traditional men would remain. A directed search model would yield a higher fraction of married agents in the population, because modern men prefer educated women to uneducated women (V m increases in w f ). However, a directed search model would require all women to correctly anticipate ex-ante what fraction of her contemporaries would choose to become educated.

  26. The proof for this and all other propositions can be found in Appendix B.2.

  27. See Appendix B.1.2 for a discussion on how wages may instead be proportionate to the effort exerted such that a greater e generates a better wage distribution.

  28. λ E = 1 (and therefore λ M = 1) is ruled out, because e can be unboundedly large. Because wages are exogenous, \(\widehat {e}(\lambda _{M})\) is independent of the fraction of women who decide to become educated. That is, I abstract from general equilibrium effects on wages.

  29. See Appendix A for description of each dataset.

  30. 2000, 2001, 2002, 2003, 2005, 2006, and 2008. The sample size is about 3500 per year.

  31. Responses to these five statements differ by sex and cohort. I find that women always respond less traditionally than men and the gap is larger in recent cohorts. Also, there has been a significant evolution of beliefs for both men and women over time. Those who were born after 1960 responded less traditionally to at least one or two more statements compared with those born in the 1920s.

  32. The JGSS asks “When you were about 15 years old, did your mother have any paying job? If so, what did she do?” M o m L F P i s t is zero for those who answered “She was not working.” Respondents who “Don’t know” or did not have a mother at that time are excluded. M o m C o l l i s t equals 1 for 4-year colleges (not junior college or college of technology).

  33. When I replicate this analysis for female respondents, I find that both mother’s LFP and mother being a college graduate do not have statistically significant effects on women’s gender attitudes. Consistent with the model’s assumption, the intergenerational transmission of gender attitudes matters more for men than women.

  34. These findings are consistent with those in Kawaguchi and Miyazaki (2009), where they use 2000–2003 JGSS.

  35. All foreign born immigrants are categorized as foreign born regardless of their age at migration. There are no respondents who are foreign born yet with a U.S. born father in the sample, reducing the possibility of bias from adoptees. I also do not exclude those who have migrated to the U.S. as adults because unlike education and marriage decisions in Section 4.3 below, time use at home within married couples is an everyday practice, and thus is not contingent on the decisions made before coming to the U.S. Second generation are U.S. born respondents whose fathers are foreign born.

  36. Usual work hours are only available for individuals who are employed. I recode the variable to zero for those currently unemployed. Individuals who responded “hours vary” are excluded from the analyses.

  37. Hwang (2013) obtains similar results for men from countries with low female labor force participation (FLFP) rates in general. The U.S. born effect is not statistically significant when the sample is restricted to men from countries with FLFP rates as high as that of the U.S

  38. I can alternatively use mother’s birthplace and the results are similar (95 % of respondents have parents born in the same country). FLFP is commonly used in the political economy literature as an indicator of a country’s family culture and women’s economic status. See for example, Alesina and Giuliano (2010) and Fernández and Fogli (2009). For my purposes, married women’s LFP rates would be ideal, but they are not available in cross-country datasets.

  39. I obtain similar results when I use the actual FLFP rate in the husband’s father’s birthplace instead of the dichotomous distinction of high and low FLFP origins.

  40. See footnote 6 for references on U.S. immigrants’ cultural and economic assimilation.

  41. The Census and ACS collect parent’s birthplace only for respondents who live with their parents at the time of the survey (less than 5 % of the adult population). Single race is assigned according to respondent’s self-reported race in the survey and is comparable across all years and is available for all respondents (including those with multiple-race). Individuals with multiple-race are assigned to the single race category deemed most likely. However, multiple-race is extremely rare among Koreans and Japanese: 99 % of Koreans and 98 % of Japanese self-reported themselves as “Korean” or “Japanese” in the detailed race question (and not “Korean and White” or “Japanese and White,” for instance).

  42. See Appendix A.5 for how age at migration is calculated. Adoptees may be identified as Korean or Japanese in the Census despite having been brought up by American parents and not having any cultural connections to Korea or Japan. According to the Intercountry Adoption statistics from the U.S. Department of State, 99 % of adoptees from Korea and Japan in 1999–2011 arrived in the U.S. when they were younger than 3 years old. The Holt International Children’s Services data in Sacerdote (2007) also shows similar figures for Korean adoptees placed during 1964–1985: 91.4 % of children arrived under the age of three.

  43. It is impossible to distinguish between second and higher generations without information on parent’s birthplace. Since the immigration wave from East Asia began in the 1960s (after the Immigration and Nationality Act Amendments of 1965), however, third or higher generations are expected to comprise a small fraction of my sample. Naturalized citizens are categorized as foreign born.

  44. The overall development across time is similar for the foreign born and the U.S. born. The fraction college graduate is larger among Koreans and Japanese in the U.S. than among white Americans (less than 40 %).

  45. The differential marriage patterns by respondent’s sex and U.S. nativity are robust to including respondent’s age, education, ethnicity, and state and cohort fixed effects.

  46. Pooling all state-cohort cells, the fraction foreign born among Korean and Japanese men ranges from 0 to 1 and has mean of 0.51 and standard deviation of 0.29. Hawaii and Idaho have low fraction foreign born, whereas New Jersey and New York have high fraction foreign born among Korean and Japanese men.

  47. State here refers to the state of current residence. Note that state of birth cannot be used because of the foreign born group.

  48. Repeating the analysis for Korean and Japanese men shows that the fraction foreign born among the Korean and Japanese women in respondent’s state and cohort does not have a statistically significant effect. That is, Korean and Japanese men’s preference for Asian wives do not respond sensitively to the composition of the female population.

  49. Using alternative definitions of work status, such as usual hours worked per week, yields similar results.

  50. Using the National Latino and Asian American Survey, Chen and Takeuchi (2011) similarly find that Asian women in the U.S. who marry non-Asians are not marrying-up in terms of education or occupation status.

  51. I abstract from the trivial case where the disutility is so small that everybody marries.

  52. Note that this does not imply that individuals enjoy working per se.

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Acknowledgements

I am grateful to Alberto Alesina, Raj Chetty, Claudia Goldin, and Lawrence Katz for their guidance and feedback throughout this project. I would also like to thank Wenxin Du, John Friedman, Paola Giuliano, Edward Glaeser, Seok Ki Kim, Joana Naritomi, Claudia Olivetti, Amanda Pallais, Dana Rotz, László Sándor, Anitha Sivasankaran, two anonymous referees, and seminar participants at Harvard University, IZA/CEPR European Summer Symposium in Labour Economics, Korea Labor Institute, Korea University, Korean Labor Economic Association, the Bank of Korea, and University of Hong Kong for helpful comments and discussions. This project received financial support from Hankuk University of Foreign Studies and the Lab for Economic Applications and Policy at Harvard University.

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Correspondence to Jisoo Hwang.

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Appendices

Appendix A: Data Appendix

A.1 Korean data

The Korean Population Census is collected by the National Statistical Office every 5 years and are 2 % samples of the population, excluding the institutionalized. Micro-data is available for years 1995, 2000, and 2005. The 2005 data does not distinguish between 4-year colleges and less than 4-year colleges, however, and hence I only use the 1995 and 2000 samples (N = 1, 756, 493). For the most recent cohorts, I use the Korean Economically Active Population Survey instead. It is collected monthly and covers individuals age 15 and older (both in and out of labor force) in Korea. I pool all months of 2012 (N = 327, 865).

Korea’s Time Use Survey is collected by the National Statistical Office and covers household members older than age 10 in 8100 households nationwide. “Household Activities” corresponds to the same category in the Bureau of Labor Statistics time use data. Activities such as housework, food and drink preparation and clean-up, interior maintenance, exterior maintenance, vehicle maintenance, and household management are included. It does not include time spent on caring for children or other family members.

A.2 Hong Kong data

The 2006 Hong Kong Population By-Census is collected by the Hong Kong Census and Statistics Department and is a 5 % sample of the population (N = 460, 197). Educational attainment is defined using the variable EDUCNH (highest level completed). The four groups corresponding to high school, junior college, college, and graduate school are senior secondary, post-secondry (non-degree), post-secondary (degree), and graduate school. More specifically, senior secondary includes secondary forms 4 to 7; post-secondary (non-degree) includes various diploma courses and vocational training schools; post-secondary (degree) includes degree institutions; and graduate level includes master degree, PhD, and other postgraduate courses.

A.3 Japanese data

The JGSS has a variable WEIGHT to weight data for population estimates based on the Japanese Population Census. In the 2000–2005 datasets, this is produced by calculating the number of people which one respondent represents by taking into account sex (two categories), 10–year age group (six categories), region (six categories), and city or not (two categories). From 2006, the variable is produced by sex (two categories) and 10–year age groups (seven categories). In order to attach weights across survey years, I harmonize this variable so that weight is constructed from sex (two categories) and 10–year age group (six categories) for all years in my sample.

There are 47 prefectures in Japan, which are governmental bodies larger than cities, towns, and villages. The prefectures are grouped into six regions (BLOCK) in the JGSS. Urban is a set of three dummies for the size of municipality—largest cities, other cities, and town/village. Largest cities are the “Cabinet-Order designated cities” that have more than 500,000 people.

Income (SZINCOMX, SSSZINCM) reports the total annual income during the previous year (before taxes and other deductions) from main job. This is converted into 1999 yen using the Consumer Price Index adjustment factors. All top-coded values in each year are multiplied by 1.45.

In the 2008 survey, age is reported in intervals. I construct respondents’ exact age by subtracting birth year (which is available across all years) from the year of the survey. Respondents under age 25 are excluded from the sample. However, birth year for spouse is not provided. Hence, I take the midpoint of each 10–year age group for the spouse. The intervals range from age group 20–29 to 90–99. Hence, spouses who are actually under age 25 may be included in the analyses.

To control for the number of children when analyzing married women’s labor force participation, we need to know the number of children (under a certain age) who are currently living with the respondent. Total number of children (CCNUMTTL) variable in the JGSS, however, counts both those who left home or are deceased. Hence, I construct a variable that counts the number of children under 19 living with the respondent by compiling the age of each child (CC01AGE, CC02AGE, etc.) as reported by the respondent. Because child’s age is categorical data in 10–year age groups, I use 19 as the cut-off (instead of 18, as in other datasets).

The Japanese Time Use Survey is conducted by the Bureau of Statistics and covers household members older than age 10 in 99,000 households nationwide. “Housework” is a separate category from “Child care” and “Nursing” and includes activities such as food preparation, cleaning, caring for family members other than children, keeping the family account, and visits to the public office on personal or family matters.

A.4 ATUS

I weigh all observations using the person weight (WT06) to make the sample representative. Family income (FAMINCOME) includes the income of all members of the household who are 15 years of age or older. Income includes money from jobs, net income from business, pensions, dividends, interest, Social Security payments, and any other monetary income received by family members. This is the only earnings information available on the self-employed as well. It is based on categorical data; I calculate the midpoint of the categorical variable. When top-coded ($75,000 from January to September in 2003 and $150,000 thereafter), it is multiplied by a factor of 1.45.

Individuals whose father’s birthplace (FBPL) is indicated as regions or continents, such as “Central America n.s.” and “Africa n.s.” are excluded from the analyses. For the countries that are named or grouped differently in the ATUS from the United Nations dataset, the following adjustments have been made (FBPL are assigned the LFP rate of the country in parenthesis): Czechoslovakia and Czech Republic (Czech Republic); Korea and South Korea (Republic of Korea); England, Scotland, Wales, United Kingdom, and United Kingdom n.s. (United Kingdom); Ireland and Northern Ireland (Ireland); Other USSR/Russia and USSR n.s. (Russian Federation).

A.5 U.S. Census and ACS

I weigh all observations using the IPUMS person weight (PERWT) to make the sample representative. Age at migration is calculated by subtracting the respondent’s birthyear from the year of immigration variable. For cases when the year of immigration is given as intervals, I take the most conservative approach by using the last year in the bracket (to ensure that I do not include any immigrants who came to the U.S. when older than 17).

Appendix B:Technical Appendix

B.1 Discussions

B.1.1 Disutility term and joint maximization

Other things equal, assume that the disutility term is in men’s utility function instead of women’s. Then the utility of a married man of type M and T are:

$$\left\{\begin{array}{ll} V_{M}(w_{m}, w_{f})=\max_{0\leq t_{m}\leq 1}&\frac{1}{2}(t_{m}w_{m}+t_{f}w_{f})+\beta log((1-t_{m})+(1-t_{f}))\\ V_{T}(w_{m}, w_{f})=\max_{0\leq t_{m}\leq 1}&\frac{1}{2}(t_{m}w_{m}+t_{f}w_{f})+\beta log((1-t_{m})+(1-t_{f})) \\ &-(\alpha_{0}+\alpha_{1}(t_{f})) \end{array}\right. $$

whereas a married woman’s utility function is invariant to the type of husband:

$$V_{f}(w_{m}, w_{f})=\max_{0\leq t_{f}\leq 1}\frac{1}{2}(t_{m}w_{m}+t_{f}w_{f})+\beta log((1-t_{m})+(1-t_{f})) $$

Unlike in Section 3.2, a woman’s optimal time allocation, \(t^{\ast }_{f}\), now does not depend on the type of husband: if w f > 2β, she spends \(1-\frac {2\beta }{w_{f}}\) of her time on market activities and if w f ≤ 2β, she stays at home.

Since \(t^{\ast }_{f}\) is increasing in w f , and men’s disutility is also increasing in \(t^{\ast }_{f}\), there is a threshold wage w f where V T drops below ν m .Footnote 51 Hence, Gold Misses arise when traditional men reject educated women with wages above this threshold. (This contrasts with the model where educated women are choosing to remain single.) The expected utility from becoming educated (V E (λ M )) and the fraction of educated women (λ E ) thus decrease as women’s wages rise over time.

Therefore, the model is not isomorphic to the case with the disutility term in men’s utility function. In papers that study only married couples (and not whether to marry or not) or that do not focus on changes in women’s wages over time (e.g., Fernández et al. 2004) both setups may yield similar results.

Alternatively, the two cases may be isomorphic in a joint maximization framework. For example, let each married household maximize the following weighted average of husband’s and wife’s utility:

$$ \max_{0\leq t_{m}, t_{f}\leq 1}\theta U_{m}(c_{m}, h, t_{m}, t_{f})+(1-\theta)U_{f}(c_{f}, h, t_{m}, t_{f}) $$
(14)

where 0 < θ < 1, c i is consumption, h is household public goods, and t i is defined as before. (Unmarried agent’s utility function is defined analogously.)

Assume that time spent on market activity enters directly into the utility function because the disutility from working is smaller than the disutility from doing household chores. That is, in addition to earning market wage w i , self-fulfillment, working conditions, and other fringe benefits from a job are higher than from staying at home.Footnote 52

Hence, some function of t i and t j enters in the utility of agent i married to agent j, where the marginal utility from t i , \(MU_{t_{i}}\), is positive. For simplicity, assume \(MU_{t_{j}}=0\) for all women and modern men. That is, apart from the utility gain from increase in household income, there need not be any additional utility gain from one’s spouse working versus staying at home.

Traditional men, however, are characterized by \(MU_{t_{j}}\ll 0\). They get disutility from wife working. Thus, solving Eq. 14 given wages, a woman is more likely to be a housewife when her husband is traditional.

Furthermore, since the disutility from working is smaller than that from housework, a woman with a sufficiently high wage would choose to remain single when matched to a traditional man. When single, she can optimally outsource housework, whereas when married to a traditional man, she has to do the less enjoyable housework due to her husband’s disutility. Men always prefer to marry since with w m > w f , they always work in equilibrium.

B.1.2 Effort and wage distributions

Wages may be proportionate to the effort exerted such that a greater e generates a better wage distribution (in the sense of first-order stochastic dominance). That is, W(w f ;e) would be a continuous cumulative distribution function with support [0, w m ) where W(w f ;e 2) ≤ W(w f ;e 1)∀w f if e 2 > e 1.

Women differ in their costs of investing in education, C(e). Each woman chooses e to maximize her expected utility:

$$\max_{e\geq 0} W(2\beta;e)V_{U}(\lambda_{M})+(1-W(2\beta;e))V_{E}(\lambda_{M})-C(e) $$

where V U (λ M ) and V E (λ M ) are defined as in Eq. 7. Once a woman chooses her optimal e , she draws her wage from W(w f ;e ). If her wage is higher than 2β, she works in equilibrium. If her wage is lower, she becomes a full-time housewife.

The difference with my model is that by choosing e, each woman can directly affect the wage distribution from which she draws from. Since the support of W(w f ; e) is [0, w m ), there is a probability that even an educated woman draws a wage lower than 2β. Thus, women would be distinguished by their revealed wages instead of their education investment per se. Consequently, Eq. 9 would also be redefined, such that λ E equals the fraction of women who draw wages above 2β. Marriage and household time allocation decisions are unaffected since they are functions of w f , and not e.

This alternative setup would require one to define how e translates into different wage distributions and how that also interacts with the wage distribution exogenously changing over time.

B.2 Proofs of Propositions

Proposition 1

When α 0 and α 1 satisfy Eq. 5, \(\underline {w}_{E}<\widetilde {w}_{E}<w_{m}\) . When they are larger, \(\widetilde {w}_{E}<\underline {w}_{E}<w_{m}\) . When they are smaller, \(\underline {w}_{E}<w_{m}<\widetilde {w}_{E}\).

Proof

\(\underline {w}_{E}<\widetilde {w}_{E}\) holds if ν f < V E T at \(w_{f}=\underline {w}_{E}\). \(\underline {w}_{E}\) can be found from equating V U T with V E T . Plug in the expression for \(\underline {w}_{E}\) to Eqs. 3 and 4. The inequality with regards to α is: \(\alpha _{0}+\alpha _{1}<\frac {1}{2}(w_{m}-\underline {w}_{E})+\beta log2\)

\(\widetilde {w}_{E}<w_{m}\) holds if ν f > V E T at w f = w m . Plug in w m to Eqs. 3 and 4. The inequality with regards to α is: α 0+α 1 > β l o g2.

When both inequalities above are satisfied, \(\underline {w}_{E}<\widetilde {w}_{E}<w_{m}\). □

Proposition 2

\(\widehat {e}(\lambda _{M})\) is an increasing function of λ M , and \(\widehat {e}(\lambda _{M})\geq 0\) always holds.

Proof

Since \(\widehat {e}(\lambda _{M})\) is defined as in Eq. 8 and V U (λ M )=α 0, we just need to show that V E (λ M ) > α 0 holds.

$$V_{E}{\prime}(\lambda_{M})={\int}_{2\beta}^{\underline{w}_{E}}(V_{EM}-V_{ET})dW+{\int}_{\underline{w}_{E}}^{\widetilde{w}_{E}}\alpha_{0}dW+{\int}_{\widetilde{w}_{E}}^{w_{m}}(V_{EM}-\nu_{f})dW $$

Plugging in the equations for V E M , V E T , and ν f from Eqs. 3 and 4, the expression becomes:

$$\begin{array}{@{}rcl@{}} V_{E}{\prime}(\lambda_{M})=&\alpha_{0}+{\int}_{2\beta}^{\underline{w}_{E}}\left(\frac{1}{2}w_{E}-\beta+\beta log(\frac{2\beta}{w_{E}})\right)dW \\ &+{\int}_{\widetilde{w}_{E}}^{w_{m}}\left(\frac{1}{2}(w_{m}-w_{E})+\beta log2-\alpha_{0}\right)dW \end{array} $$

The first integral is non-negative when w E ≥ 2β. (It equals zero if w E are all higher than \(\underline {w}_{E}\).) By assumption (5) and that α 0β l o g2, the second integral is positive. It would equal zero if and only if α 0 = β l o g2 and there is a discrete jump at w E = w m such that \(prob(\widetilde {w}_{E}\leq w_{E}<w_{m})=0\). Since W(w E ) is a continuous cumulative function over (2β, w m ), the latter condition cannot hold. Hence V E (λ M ) > α 0 and therefore V E (λ M )−V U (λ M ) > 0.

Since \(\widehat {e}(\lambda _{M})\) is an increasing function of λ M , it is sufficient to show that \(\widehat {e}(0)>0\). \(\widehat {e}(0)={\int }_{2\beta }^{\widetilde {w}_{E}}V_{ET}dW+{\int }_{\widetilde {w}_{E}}^{w_{m}}\nu _{f}dW-V_{UT}\). We know that V E T = V U T when \(2\beta <w_{E}\leq \underline {w}_{E}\), V E T > V U T when \(\underline {w}_{E}<w_{E}\leq \widetilde {w}_{E}\), and ν f > V E T when \(w_{E}>\widetilde {w}_{E}\). Thus \(\widehat {e}(0)\geq 0\) always holds. □

Proposition 3

Given W t−1 (.) and λ Mt−1 , if the distribution W t1 (.) first-order stochastically dominates W t2 (.), F Et1F Et2.

Proof

Given W t − 1(.) and λ M t − 1, λ M t is determined regardless of W t (.) (see Eq. 1). \(\widehat {e}(\lambda _{Mt})=V_{E}(\lambda _{Mt})-V_{U}(\lambda _{Mt})\). V U (λ M t ) is invariant to changes in w E . So we just need to show that

$$\begin{array}{@{}rcl@{}} V_{E}(\lambda_{Mt})=&{\int}_{2\beta}^{\widetilde{w}_{E}}(\lambda_{Mt}V_{EM}+(1-\lambda_{Mt})V_{ET})dW_{t} \\ &+{\int}_{\widetilde{w}_{E}}^{w_{m}}(\lambda_{Mt}V_{EM}+(1-\lambda_{Mt})\nu_{f})dW_{t} \end{array} $$

is larger under W t1(.) than under W t2(.).

By definition of first-order stochastic dominance, \(W_{t1}(\widetilde {w}_{E})\leq W_{t2}(\widetilde {w}_{E})\) and hence the probability weight on the second integral is relatively larger under W t1(.) than under W t2(.). Since V E M is an increasing function of w E and V E T < ν f when \(w_{E}>\widetilde {w}_{E}\) (by definition of \(\widetilde {w}_{E}\)), (λ M V E M + (1 − λ M )ν f ) is larger than (λ M V E M + (1 − λ M )V E T ). Hence the probability weight on the larger term is larger under W t1(.) than under W t2(.).

The comparative statics follows directly from Eqs. 9 and 10. □

Proposition 4

Given W t−1(.) and λ Mt−1, educated women’s marriage probability is an increasing function of \(W_{t}(\widetilde {w}_{E})\). Hence if the distribution W t1 (.) first-order stochastically dominates W t2(.), p Et1p Et2.

Proof

We need to show that p E (λ M t ) (as defined in Eq. 6) is smaller under W t1(.) than under W t2(.). Given W t − 1(.) and λ M t − 1, λ M t does not change with regards to W t (.) (see Eq. 1). p E (λ M t ) can be rewritten as \(W_{t}(\widetilde {w}_{E})(1-\lambda _{Mt})+\lambda _{Mt}\). Since λ M t < 1, p E t is an increasing function of \(W_{t}(\widetilde {w}_{E})\). □

Proposition 5

Suppose W t (.) first-order stochastically dominates W t−1 (.) at all t. The decrease in p E from t−1 to t is larger when (i) the drop in \(W(\widetilde {w}_{E})\) from t−1 to t is larger and (ii) the drop in \(W(\widetilde {w}_{E})\) from t−2 to t−1 is smaller.

Proof

  1. Condition (i):

    From Proposition 4, we know that p E (λ M t ) decreases in \(W_{t}(\widetilde {w}_{E})\) given λ M t . Hence a drop in \(W(\widetilde {w}_{E})\) from t − 1 to t helps decrease educated women’s marriage probability.

  2. Condition (ii):

    By Proposition 3 and Eq. 1, we know that the increase in λ M from t − 1 to t is larger when the (first-order stochastically dominating) change in W(.) from t − 2 to t − 1 is larger. Hence, if there is a large positive shift in the wage distribution from t − 2 to t − 1, λ M t would be much larger than λ M t − 1. This helps increase educated women’s marriage probability since p E (λ M t ) increases in λ M t (see Eq. 6) given W t (.).

Both (i) and (ii) are needed for the Gold Miss phenomenon to arise. If only condition (i) holds and there was a significant wage growth from t − 2 to t − 1, then even if there is a large drop in \(W(\widetilde {w}_{E})\) at t, p E may not fall because there is now a larger fraction of modern type in the marriage market than at t − 1. Conversely, if only condition (ii) holds and there is only a trivial change in \(W(\widetilde {w}_{E})\), p E would not fall since a woman (matched to a traditional type) does not forgo marriage unless her wage is higher than \(\widetilde {w}_{E}\). □

Fig. 4
figure 4

GDP per capita trends of developed asian countries. Notes. Data are taken from Angus Maddison’s Historical Statistics of the World Economy. GDP per capita is measured in 1990 international (Geary-Khamis) dollar units

Fig. 5
figure 5

Female college enrollment rates. Notes. Data are from the Basic School Survey collected by the Japanese Ministry of Education, Culture, Sports, Science and Technology, the Statistical Yearbook of Education collected by the Korean Educational Development Institute and the Korean Ministry of Education, Science, and Technology, and the Current Population Survey collected by the U.S. Census Bureau. Enrollment rate is measured as the number of entrants to colleges divided by the number of graduates from middle school 3 years before (Japan), or by the number of graduates from high school that year (Korea), or by the number of 18–24 year olds in the population that year (U.S.). Primary and secondary education (until 9th grade) is compulsory in both Japan and Korea: enrollment in middle school is higher than 99 % throughout the period. In Korea, more than 95 % of middle school graduates go on to high school throughout this period. College does not include junior colleges

Fig. 6
figure 6

Countries by female labor force participation rates in 1985. Notes. Female labor force participation (FLFP) data are from the United Nations (UN) and are matched to father’s birthplace in the ATUS sample (see Appendix A for details). Father’s birthplace is defined as high (low) FLFP if labor force participation rates of women in age group 25–34 were higher (lower) than that of the U.S. in 1985. Total of 121 countries in the UN data are matched to the ATUS sample—42 high FLFP (light gray) and 79 low FLFP (dark gray). Unmatched countries (either because they do not have data on FLFP or because they are not available as father’s birthplace in the ATUS) are in white

Table 6 Descriptive statistics, JGSS sample
Table 7 Effects of mother’s LFP and education, college graduate men in Japan
Table 8 Descriptive statistics of married respondents from gold miss countries, ATU.S. sample
Table 9 Descriptive statistics of Koreans and Japanese in the U.S., census and ACS sample
Table 10 Effect of husband’s ethnicity and U.S. nativity on LFP of Korean and Japanese women in the U.S.
Table 11 Marrying-up?, Korean and Japanese women in the U.S.

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Hwang, J. Housewife, “gold miss,” and equal: the evolution of educated women’s role in Asia and the U.S.. J Popul Econ 29, 529–570 (2016). https://doi.org/10.1007/s00148-015-0571-y

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Keywords

  • Marriage
  • Education
  • Female labor force participation
  • Cultural transmission

JEL Classification

  • J12
  • D10
  • Z10