An Empirical Study of the Chinese Marriage Market: “Leftover” or Not?

Using census data from 1990 to 2010, this paper describes the trend of the Chinese marriage market focusing on “leftover men” and “leftover women”. In general, it was identified that there was an increasing share of being single for young and more educated population. The share of single population for less educated men after age 35 was higher than other age groups across the years, providing consistent evidence for leftover men. Meanwhile, more educated women showed no clear difference in marriage rate than others in their late 30s. This study further found that increasing comparative supply of men and more educated women due to demographic change and education reform explains the phenomena observed. In addition, women who get married later were found to have husbands showing disadvantages in age and education level, while men displayed no similar pattern, suggesting that Chinese women might lower their selecting standard as their age increases.


Introduction
Recently, researchers, policy makers and social media in China have discussed widely about the "leftover women" and "leftover men" phenomena. The discussion on leftover men is mainly based on the skewed sex ratio in China. The one-child policy provoked the traditional son preference, leading to soaring sex ratio at birth since 1970s (Li, 2007, [1]; Loh et al., 2015, [2]), Tuljapurkar, et al. (1995) [3] forecasted that China would have one million excess men in the mar-the effect of college expansion on marriage market and reported that college graduates' marriage rate dropped after the expansion, while the decline was greater for women. Existing literature has discussed Chinese marriage market from different angles concentrated on the gender difference in the changes (Wu et al., 2014, [10]; Zhang et al., 2015, [11]); however, the trend of the market and the existence of leftover women remain in question.
Experiencing continuous drop in the fertility rate and aging society, the discussion on leftover women and leftover men has become heated but there still lacks critical evidence to support this assertion. Whether to get married or not?
When to get married? Who to marry with? The answers to these questions are still in vague. Using National Bureau of Statistics (NBS) Population Census datasets from 1990 to 2010, we display the trend of Chinese marriage market and empirically test the existence and mechanism of leftover men and leftover women. This paper found that the share of being single for low educated men was higher than counterparts because of excess supply in the market, or to say low educated men are leftover after age 35. Meanwhile, highly educated women postpone their marriage choice for increasing competence, but show no significant difference after age 35, providing no evidence as leftover women. However, women who get married late in life might suffer from decline in quality of marriage considering husband's age and education.
The remainder of the paper proceeds as follows. Section 2 describes the data- Another result variable we explored was the age at first marriage, which is available in 2000 and 2005 census. Individuals reporting first marriage age younger than 15 were excluded from the sample according to NBS rules.
To explore the matching pattern in Chinese marriage market, this paper further constructed a matched couple data using 1990, 2000 and 2005 censuses. The methodology employed is as follows. Using the "relationship with household head" variable in the data, we matched married individuals with the opposite gendered one reporting as married and the corresponding category in the relationship variable, specifically matching "household head" with "spouse of household head", "son/daughter" with "son/daughter in law". For 1990 census, the survey did not differentiate "son/daughter" from "son/daughter in law", so the sample was further restricted requiring that the age gap between the couple should be less than 10 years in order to exclude possible mismatch between 3 The incentive and mechanism of re-marriage market might be entirely different from first marriage decisions, which we would like to explore in further studies if possible. We showed the trend of single rates in Chinese marriage market by hukou, gender, age and education level as presented in Table 1 and Table 2, and also we categorized the full sample to three education levels: middle school and below, high school, college and above so as to discuss the difference across groups. The The Chinese Census is practiced as household level under hukou system. For Chinese family with multiple children, it is most likely for the children to move out the household (get a new hukou) at the time of marriage and have one child (with his/her spouse) stay and take the responsibility of taking care of aging parents, so it is unlikely to have two or more close-aged grown-up married siblings in the same household.  Table 1 and Table 2 was set at 60, the common limit for the labour age in China.
From Table 1 and Table 2, we observed that single rates of all population groups dropped significantly after age 40 to a level which is not of primary interest (all less than 5% excepted for men with middle school or below education). Hence, we concentrated mainly on the population younger than 40 and might try to explore the full picture in further studies. Generally, urban residents naturally they postpone their entering into the marriage market. Better developed parts of China have lower percentage of early marriage. As we are primarily discussing the difference of marriage choice across gender and education levels, we further restricted the sample to age 23 and above, which allows the population to have the chance to finish higher education.
For urban residents of all education levels aged 23 to 29, the single rates increase throughout the years. In urban population also, the gap between college group and above and high school group increased from 10.7% in 2000 to 17.9% in 2010 for women and from 7.2% to 12.8% for men. Meanwhile, the gap for rural population slightly decreased. One possible reason is that college and university education is one of the few channels to change hukou in China, so people with college education might just enter the urban marriage market instead. We show the education composition of the sample by year and hukou in Figure 1 and it can be seen that the education distribution is significantly different across hukou types. For clearer comparison, we further grouped the individuals by assigning urban individuals with college education and above and rural individuals with high school education and above as high education group, the rest as low education group 5 .
Gender difference in single rate of individuals with same education is important when discussing leftover women or leftover men in the marriage market.
For urban population aged 23 to 29, we observed that the gender gap in college education and above group decreased from 16.6% in 2000 to 11.9% in 2010. This means that there are comparatively more single young women than men middle and below high school college and above 5 The criteria allow at least 10% of the population in high education group while the rest as low education group for each year and hukou type.  Table 1 and Table 2 show the trend of single rates through census year. Using the data across two decades (1990 to 2010), we were able to describe the marriage choice of the 1960-1970 cohort from age 20 to 45. Figure 2 shows the trend of single rates of the cohort by gender, education and hukou. From the graph we observed that people in the high education group had higher single rate during their 20s in general. The age for 50% of the population to get married for urban high educated women was approximately two years later than low educated ones, while the difference was about one year for men. However, the gap be-

Empirical Analysis
In this section we empirically examined the trend of Chinese marriage market using the census data of 1990, 2000, and 2005. We employed the Linear Possibility Model (LPM) to determine marriage trend as follow: The dependent variable is the marriage status of individual i, assigned as 1 for being single and 0 as with marriage experience; group i describes the individual's type categorized by gender and education, including dummy variables for low educated women, low educated men, high educated women and high educated men 6 ; as we were mainly discussing the trend in marriage market, T i implies  6 Similar to Section 2, the criteria categorizing education group is different across hukou type. Rural: high education group = high school and above, low education group = middle school and below; Urban: high education group = college and above, low education group = high school and below. interested in the phenomena of leftover women and leftover men, we chose the low educated women as the control group for a clearer comparison. From Table   1 and Table 2 we observed that population's single rate dropped to very low level after age 40, we chose the sample age 23 to 39 as the group for empirical study and age 40 to 44 for additional information. Regression results by hukou and age group are shown in Table 3 and Table 4.
Column 1 in Table 3 shows the regression result of urban population aged 23 to 29. It is clear that the high educated group had higher single rate than low   Table 4 shows the regression results using rural population. We observed significantly higher single rate for low educated men in all age groups. The gender gap in 1990 was 9.2% for age 30 -34 and 6.7% for age 40 -44, supporting leftover men. However, we found that the gender gap in rural low education group was decreasing as the year passes. This is probably due to the increasing labor migration, allowing more opportunities for rural individuals to get in touch with peers. Meanwhile, the urban low education group showed an increasing gender gap in single rate. That is, from 3.9% in 1990 to 7.9% in 2005 for age 30 -34, from 1.1% to 2.8% for age 35 -39 and from 0.7% to 1.8% for age 40 -44. The findings indicate that leftover men might not be just for rural market, as the single rate of urban low educated men was also increasing comparatively.
From the former results, we found that high educated women postponed marriage but showed no significant difference in single rate than other subgroups after age 35, while low educated men showed significantly higher single rate than counterparts for all age groups considered. To study the possible reason of leftover women and leftover men, we further explored the trend of comparative supply in marriage market introduced by Becker (1973) [13].
The demographic structure and education composition of Chinese population have shifted dramatically since 1990s. On one hand, the widely discussed soaring sex ratio at birth of China leads to increasing comparative supply of men in the marriage market (Figure 4), especially for rural areas (Yuan X, et al., 2005, [14]).
On the other hand, the average education level of Chinese population has increased substantially since the education reform started in 1980s. The reform affects men and women differently. From Figure 5 we can see that the percentage of female in college graduates increased from less than 30% in late 1980s to more than 50% in 2010s, showing that the comparative supply of high educated women increased throughout the years.
Before considering the impact of shifting comparative supply in marriage market on individual marriage decisions, we need to explore the matching pattern of Chinese couples. Using matched couple data from 1990, 2000 and 2005 census, we show the matching pattern considering education level for all couples of which wife's age ranged between 20 and 40 in Table 5. We observed that Chinese women tend to marry-up, and men tend to marry-down considering education.
The percentage of urban women married to high educated men increased    while the percentage of rural low educated men married to high educated women dropped through the years. We also explored the matching pattern considering hukou type and found that the percentage of cross-hukou-type marriage is extremely low and decreasing through years, possibly because the hukou type could be changed through marriage. So we considered urban and rural as two separate marriage markets in following discussions. The matching pattern considering age is more straightforward, husbands are at average about 2 years older than their wives 7 .
The ladder-type matching pattern considering education could lead to structural matching failure of high educated women and low educated men. The situation could be worse as the comparative supply of these two groups increased through the years as we discussed earlier. We will try to explore whether the change in comparative supply could explain the trend we observed in following discussions.
To measure the comparative supply each individual faces in actual marriage market, we employed the sex ratio of the group with same province, hukou, and the corresponding education and age group.     Table 6 are the basic regression on gender interacted 8 Regression results considering urban low educated male and rural high educated female are available on request.  Similarly for Table 7 being leftover. Besides whether to get married or not and when to get married, who to get married with is also an important consideration. Using the matched couple data, we attempted to explore whether there was difference in the age gap between the couple and the spouse's education level between people who get married earlier in life and later for urban population 9 , which may give us some hint on the marriage choice of high educated women. Figure 6 displays the percentage of individuals whose spouses were more than 3 years older/younger (for women/men) at the time of marriage. It is clear that men who got married early tend to marry with women of the similar age range.
But as their age increases, more men tend to marry with younger women, with the percentage stayed comparatively steady after age 30. For women the trend was totally different; young wives were more likely to be married with older husbands. Women who got married between 25 to 30 tend to marry with men of the similar age range, with the percentage being lower for high educated; while for women who got married after age 30, the percentage of getting married with an older husband increased with marriage age. Figure 7 shows the percentage of individuals whose spouse are high educated by the age of marriage. For men, the possibility of marrying high educated women is increasing with age, however for women, it is dropping for all education group after age 26.  To summarize, women who get married later in life have higher possibility to match with older spouse and lower possibility to match with high educated men, and the effect tend to be more severe for high educated women, while men showed no such trend. That is to say, although high educated women might not show significant difference in lifetime single rate than other sub-group population, they may have to sacrifice the quality of marriage for postponing their marriage. High educated women who were unable to make a fulfilling match in earlier years in the market, could lower their standard in order to avoid becoming leftover women.

Conclusions and Discussion
Using the NBS census datasets from 1990 to 2010, we showed the trend of single rates in the Chinese marriage market. Overall, the single rate of population aged 23 to 29 increased throughout the years, as well as the differences across education levels. Empirically, we found that urban high educated women tended to postpone their marriage but showed no significant difference than other subgroups in single rate after age 35, providing no evidence for leftover women.
Meanwhile, low educated men, in both urban and rural areas, showed consistently higher single rates than other population groups, supporting the view of leftover men. Further exploring the issue of marriage decision, we conclude that shifting comparative supply caused by demographic change and education reform could partially or wholly explain the phenomenon observed above.
High single rate for low educated men is not only a loss in welfare of the group, but it could also have negative effect on the stability of society. High marriage rate for low educated women along with the loosening of birth control policies could lead to a cluster in low income population and increasing inequality. The decrease in marriage quality of high educated women who get married later in life is also of interest for people concerning the welfare level of the whole society. Policies designed to encourage marriage should take all perspectives into consideration, while one key element should be eliminating discrimination and protecting free choice of marriage. As the Chinese population is becoming more educated and more skewed in sex ratio and age structure, facing continuously shifts in comparative supply in marriage market, there is the need to obtain more recent data to support future discussion on single rates and marriage choices.