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.

Appendices

Appendix A: Data Appendix

1.1 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.

1.2 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.

1.3 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.

1.4 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).

1.5 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

1.1 B.1 Discussions

1.1.1 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 .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.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.

1.1.2 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.

1.2 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 ₀ ≤ β 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 _Et1 ≥ F _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 _Et1 ≤ p _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

• 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.

• 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

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

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

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.