Impacts of sibling and gender on supplementary education opportunities in China

Abstract Supplementary education, which is different from the formal education system, is more likely to reflect the other form of inequality in educational opportunities through the process of education. In China, supplementary education is generally divided into two sorts: academic-oriented classes and hobby-oriented classes. Using the dataset of China Family Panel Studies 2018 and analysing with the Logit Regression models (LR), this study analyses how gender and sibling structure impact the students’ supplementary education participation opportunities. Applying the “resource dilution theory” and “budget constraint theory” in Chinese modern families, siblings might have a competitive relationship with each other in obtaining limited family resources, while parents would assess the lifetime cost of raising a child when deciding the investment in supplementary education. According to the results, an increase in sibling numbers and density dilutes the family resources of supplementary education for each child on average. Females have more opportunities to participate in supplementary education than males, especially in hobby-oriented supplementary education. The “female advantage” is significant in the supplementary education opportunity of the first-born child and the “gender minority” child. This study claims that the family allocation of supplementary educational resources is influenced by economic motives. This study supports both the “resource dilution theory” and the “budget constraint theory” in supplementary education in contemporary China, while the issues of gender inequality regarding family resources allocation seem still remain.


Introduction
Since the population control policy was implemented in 1971, the total fertility rate of the Chinese has dropped sharply. Between 1970 and1990, Chinese total fertility rate (TFR) declined ABOUT THE AUTHORS Chen Xinyue is a PhD candidate in the School of Sociology and Anthropology at Sun Yat-sen University, China. Her research interests are in the field of population sociology, demographic dividend, and human capital. Jinghui Huang is a PhD candidate in the Department of Educational Administration and Policy at The Chinese University of Hong Kong, HKSAR, China. Her research interest is in the field of sociology of parenting, shadow education and educational inequalities. Yuying Huang is a PhD student in the Department of Management, Marketing and Entrepreneurship, UC Business School at the University of Canterbury (UC), New Zealand. Her research interests are in educational service scape, tourism and place attachment. from 5.8 to 2.3. Since 1995, TFR has remained below 1.5 in China (Z. Guo, 2016). Children born in the one-child policy era have relatively less competition with their siblings during their growth. Children in one-child families could enjoy all the family education resources (Forsythe et al., 2000). This family transition also changed Chinese family educational strategies. Family educational resources could be classified into "necessary resources" and "developmental resources" (Ye, 2013). The former refers to the necessary family resources required to cover the tuition, accommodation and living expenses to support their children for participating in the formal education system from compulsory education to tertiary education recognized by the official systems. The latter refers to the family resources allocated for supplementary education, which is informal paid tutoring outside the formal school system, such as cram school (Fung, 2003;Zhang, 2014). The allocation of developmental resources could further indicate parents' perceptions of the extra-curriculum and the commercialized tutoring service that would profoundly impact children's future overall development (Zhang, 2020;Zhang & Bray, 2020).
Many studies in formal education have examined the allocation of Chinese family educational resources, "years of schooling" is frequently used as an indicator to measure educational attainment (Lei et al., 2017;Xiong et al., 2020;Ye & Wu, 2011). These studies also identified gender and sibling structures as two important factors in the family's education resources allocation. For children's gender, some studies claimed that the phenomenon of "male advantage" in family educational resource allocation is obvious in China (Das Gupta et al., 2003;Wang, 2005;Wang et al., 2020). For sibling structure, within the perspective of resource dilution theory, previous studies found that sibling size was negatively correlated with the resources allocated to each child in a family (Lei et al., 2017;Lu & Treiman, 2008). In addition, Mechoulan and Wolff (2015) contended that family educational strategies might display a "seniority effect", indicating that the first-born child, who is regarded as the chief heir of the family blood, would receive more family resources. The sibling gender composition would also affect children's educational attainment. For example, Lei et al. (2017) claimed that the son(s) could obtain more educational resources than their sisters in traditional Chinese families. In these families, gender structure and sibling structure might have dual double effects on children's educational attainment (Xiong et al., 2020). However, the influences of gender and sibling structure on the allocation of family education resources are more likely to be discussed within the formal education system in previous studies (Chang, 2007), while limited study examined their impacts on the families' education resources allocated for supplementary education.
Supplementary education has become prevalent as supplementary educational activities beyond formal education to improve K12 students' achievement (Bray, 2010;Mori & Baker, 2010). Driven by the economic boom, high-stakes examinations, the value of education of traditional Confucian culture at the macro-level, and increase family income at the microlevel, this phenomenon is also significant in China (Zhang, 2014). The participation of supplementary education usually occurs in the process of individual education. Considering the factors about children's gender and sibling structure, even though existing research have identified the "female advantage" in supplementary education, which is quite different from family strategies for formal education (Y. Liu et al., 2020;Park & Lim, 2020;G. Wei & Zhang, 2021), this study claims that the dual effect of gender and sibling structure on family resource allocation for supplementary education is also important to be investigated, especially in the context of Chinese traditional families. Therefore, this study aims to examine influence of gender and sibling structure on the participation of supplementary education. This study could thereby imply how sibling gender composition affects family educational strategies in a developing country under unique demographic and social transitions and further provide insight into educational equality, which plays an important role in social equality (Brown et al., 2013).

Literature review and research hypotheses
Supplementary Education and Supplementary Education Opportunities Stevenson andBaker (1992, p. 1640) defined "shadow education, a set of educational activities outside formal schooling that are designed to improve a student's chances of successfully moving through the allocation process." Shadow education is usually interchangeably employed with the term of private tutoring, which focuses on privateness and academic achievement (Bray, 1999). However, in the context of Chinese societies, the hobby/leisure orientation of private tutoring is also included in the classic "private tutoring" with ambiguous boundaries. The private tutoring market of Mainland China blurs the distinctions between academic-oriented and hobby-oriented private tutoring for children, as the related education providers usually marketing the hobby/ leisure-oriented tutoring by embedding academic elements (Wang & Song, 2013). Within this perspective, supplementary education and shadow education seem to be intertwined in Mainland China. This study employs the term of "supplementary education (Aurini et al., 2013)" to depict and examine the social facts of families' investment in children's outside-schooling education in Mainland China, which could encompass the diversity of private tutoring or extraclass of students' learning that benefits multi-dimensionally children's development.
Supplementary education in China could be defined with two major types: (1) academic-oriented supplementary education that aims for academic achievements in formal educational institutions, which is close to the classic definition of "shadow education" by Stevenson and Baker (1992); (2) hobby-oriented supplementary education that aims for accumulation of highbrow culture capitals, such as hobby-oriented classes of riding, dancing, and Chinese calligraphy. The concept of supplementary education goes beyond the "shadow" side of private tutoring and emphasises the independent effect of private tutoring compared to mainline education in sense of official discourses (Aurini et al., 2013). Recently, supplementary education systems are becoming private and market-oriented in Mainland China, providing both various academic-oriented classes for formal education courses and a large number of hobby-oriented classes (Wang & song, 2013). The academic-oriented supplementary education dominates the education market, especially among K12 students (Aurini et al., 2013); the hobby-oriented supplementary education is more likely in a subordinate position (Wang & Song, 2013). In other words, when choosing supplementary education with limited family resources, parents would prefer the former because it is perceived to have direct positive impacts on children's academic achievement in entrance examination (Zhang, 2020). Compared to formal education institutions, supplementary education usually has higher the hourly tuition fee, which need to be fully paid by student's family (Lin, 2018).
Regarding educational opportunities, supplementary education is more likely to have issues of the unequal distribution of resources in the process of education than formal education (Ho, 2009). Family educational resources for children include both monetary and non-monetary resources (e.g., educational philosophy, parenting time and energy; B. Liu, 2020), which are necessary for a family to support their children to participate Despite supplementary education requires extra family resources, considering China's highly competitive National College Entrance Examination and high-selective educational system, many families still have strong willingness to spend both monetary and non-monetary resources on supplementary education to improve their student's academic performance and competitiveness. With appropriate supplementary education, students would obtain more cultural capital (e.g., excellent scores, talents, skills), which could further transform into the economic capital of the family aspect for students.

Unequal Allocation in Family Educational Resource
Educational opportunities involve the issues of educational inequality. The factors leading to educational inequality could be summarized into two perspectives, including the family's social class 1 and sibling composition. The relatively limited educational resources and opportunities in the huge population country increase the educational resources competition from different social classes (Lin, 2018). Compared to the disadvantaged class and rural household registration, the middle-/affluent-class and urban household registration families have more economic and cultural capital, these families could provide their children with more educational resources (J. Li & Ho, 2019). Also, the families with higher economical capital are able to spend more educational resources on supporting their children, such as attending better schools for compulsory education and obtaining better supplementary education resources (B. Liu, 2020; W. Liu et al., 2021). In addition, parents' educational attainment would influence children's formal education performance and outcome (J. Guo, 2011;Z. Li & Qiu, 2018). Parents with higher educational attainment would have higher educational expectations and spend more resources on children's education (Li, 2010;Wang & Song, 2013;Wu, 2016). In general, the fierce competition on educational resources among families in Mainland China is essentially a competition for upward social mobility and of social reproduction. Considering gender in social reproduction, the preference for males in families' educational investment brings profound impacts on the unequal distributions between sons and daughters in traditional Chinese families (Ye & Wu, 2011). However, whether the supplementary education promotes the social reproduction by gender still awaits to be examined (Entrich & Lauterbach, 2020).

Dilution effect of siblings
Sibling size (numbers) is another factor of educational inequality in households. Resource dilution theory suggests that siblings might compete with each other in obtaining limited family resources (Blake, 1981). The more children a family has, the fewer resources each child can get on average. Thus, family resources for education would be diluted by the increase of siblings. Additionally, in families with multiple children, the small difference of ages among siblings also has a dilution effect on the children's family resources. More children at similar ages within a family means their demands for family resources are homogenous. They would thus face more intense sibling competition for limited family resources.
Based on the resource dilution theory, the following hypotheses are proposed in this study: Hypothesis 1a: Siblings' size negatively influences children's opportunity to participate in supplementary education. The more siblings within a family, the fewer opportunities for each child to participate in supplementary education.
Hypothesis 1b: Sibling density difference negatively influences children's opportunity to participate in supplementary education. The bigger age difference among siblings within a family, the greater opportunity for each child to participate in supplementary education.
Gender inequality would result in education inequality within a family. Considering the differences between supplementary education and formal education, whether gender influences education inequality in supplementary education or not remains uncertain and requires further research (Hannum, 2005). Previous research has concluded that formal education shows a male advantage based on parental gender advantages at the sibling level (Hannum, 2005;G. Wei & Zhang, 2021). Budget constraint theory suggests that parents would assess the lifetime cost of raising a child when allocating an appropriate proportion of family resources for supplementary education (Strauss & Thomas, 1995). As a result, the resources used for the sons to participate in supplementary education might be squeezed with the limited family resource.

Gender difference
Different genders of children might also lead to the inequality of educational resources allocated within a family. The male preference for supplementary education investment is a significant global phenomenon (Entrich & Lauterbach, 2020;Nath, 2008;Tansel, 2013). In Germany, boys from low-income families are more likely to obtain supplementary education, potentially counteracting a widening of the SES-and gender-achievement gap (Entrich & Lauterbach, 2020). Some studies have pointed out the tendency of "son advantage" in the allocation of formal educational resources (Lee, 2012;Wang et al., 2020). Some traditional Chinese families are more likely to provide boys with formal educational resources to promote intergenerational mobility and to meet the family's expectations of success. Supplementary education transforms family investment into economic and/or cultural capital differently compared to formal education. It could be categorized into two types: extra-curricular hobby-oriented classes and academic-oriented classes. The hobby-oriented class tends to meet the requirements of a student's highbrow "cultural capital" (Bourdieu et al., 1977;DiMaggio, 2019) to have access to high status in the society. Academic-oriented classes aim to improve students' academic performance and increase their opportunities for obtaining higher education, which is viewed as a supplement to formal education. Due to the ideology of gender and the popular domestic decision of children's education investment, many families would reduce the other resources for their sons, especially in the non-academic development resources, while, meanwhile, balancing the overall cost of raising all the children (S. J. Wei & Zhang, 2011;Zhou & Yuan, 2014). Compared to male children, they are more likely to get a certain amount of family investment to participate in supplementary education to discover their interests. Regarding children's education as a type of family investment, the different decision-making bodies would have various impacts on the allocation of family investment.
Therefore, the hypotheses are proposed based on the gender inequality:

Hypothesis 2a: Females have more opportunities to participate in supplementary education than males.
Hypothesis 2b: The gender difference is mainly due to the hobby-oriented classes which have a weaker relationship with formal education.

The role of sibling's order
As the Confucian culture values the sibling order in traditional Chinese family, sibling order could affect the allocation of educational resources within a family. In traditional society, the first-born child would enjoy more educational advantages than the later-born child.
In modern society, some studies have found that the first-born child still has higher educational expectations and actual educational gains than younger siblings (Bu, 2016;Susanne, 2020), which might bring two possible explanations. Firstly, in terms of emotional resources invested by the parents, the eldest child enjoys a longer parental time, while the younger children need to compete for more attention from parents, thus the firstborn usually has more "time endowment" (time considerable; Blake, 1981;Hanushek, 1992). Another explanation is that parents would have relatively high expectations of the firstborn child due to the aim of setting an example for younger children in families with multiple children (Joseph & Pantano, 2015). The parents are thus more likely to allocate resources to the firstborn child. Similar to the eldest child effect, the youngest child within a family would also have advantages of obtaining educational resources. Booth and Kee (2009) concluded several reasons for the "youngest child advantage" in the allocation of family educational resources: (1) Children born later are more likely to grow up in a wealthier environment with higher family income than their brothers and/or sisters; (2) Parents have more experience in educating their later-born children; (3) Younger children could receive resources not only from their parents but also from their elder siblings, benefiting younger children development. Based on the hypothesis of "eldest child advantage" and "youngest child advantage", the following hypotheses are thus proposed:

Hypothesis 3 The Inequality Impact of Siblings Orders
Hypothesis 3a: The eldest children have more opportunities to participate in supplementary education than later-born children.
Hypothesis 3b: The middle children have fewer opportunities to participate in supplementary education than both the eldest children and the youngest children within a family.

The influence of gender minority on siblings
The one-child policy since in the early of 1980s brings revolutions of family structure in mainland China albeit it has been gradually abolished during 2010s. The family size is sharply minimized into the structure of 4-2-1 model ("Four Grandparents-Two Parents-One Child") in urban areas; in rural areas, the families also transform into small families (2 or 3 Children) with looser fertility size control than the urban areas (W. Feng et al., 2013;X. T. Feng et al., 2014). The sibship size of both urban and rural families in mainland China are declined (X. T. Feng et al., 2014). The different combinations of children's gender and sibling structure might have various impacts on the distribution of family educational resources. Many scholars have found that elder boys have the advantage of sharing more formal education resources within a traditional Chinese family, while elder girls are usually at a disadvantaged status (Chang, 2007;Chu et al., 2007;Lei et al., 2017). This phenomenon might be induced by the intra-generational transfer of family education resources (Chang & Li, 2016). They examined a phenomenon that some elderly sisters in poor families dropped out of school to save or earn monetary resources for their younger brothers to receive an education. However, gender inequality in supplementary education is different from formal education as mentioned before. According to budget constraint theory, although parents might have a stronger willingness to invest in their firstborn's education, supplementary education is not perceived to bring a direct economic return (Zhou & Yuan, 2014). Therefore, parents will consider the problem of limited resource allocation for the resource in their firstborn's supplementary education. In traditional Chinese society, the eldest son plays the role of heir to the family blood, which encourages parents to allocate more resources to them.
Other scholars have proposed the "gender minority hypothesis" in the allocation of educational resources within a family (Rosenberg, 1965). For example, females who only have brothers would receive better educational resources than females who only have sisters, while the education level of males who only have sisters is not influenced by the gender minority of children structure within their family (Butcher & Case, 1994;Chang & Li, 2016). According to the seniority of the eldest child and gender minority, the hypotheses are thus proposed: Hypothesis 4a: The eldest daughter would have a higher possibility of attending supplementary education, but for the eldest son, it would not be significant.

Hypothesis 4b: Females who only have brothers have more opportunities to participate in supplementary education, and the siblings' gender has an insignificant influence on the males' opportunities to participate in supplementary education.
Hypothesis 1a-4b are listed in Table 1.

Data
This study employed the dataset of the China Family Panel Studies (CFPS) . CFPS is a householdbased panel study, conducted by the Institute of Social Science Survey at Peking University, which was conducted biennially from 2010 (wave 1) to 2018 (wave 5) on a nationally representative sample. The sample of CFPS2010 covers 25 provinces, covering 95% of the Chinese population (Xie & Hu, 2014). CFPS uses a multistage stratification with a probability proportional to size (PPS) sampling method. All members of each household are interviewed.
The individual questionnaire covers detailed demographic, socioeconomic, and education information about all members of the household, and the household questionnaire collects demographic and socioeconomic information of families, providing a good dataset to study sibling structure and gender composition impacts on supplementary education. Our study focuses on K-12 students' supplementary education. The original dataset has 4952 K-12 students, after deleting samples missing sibling information, this study employed 4529 valid responses from the dataset, including 3507 responses from families with more than one child. Table 2 and Table 3 provide summary statistics for CFPS2018 in all samples and multi-child samples respectively. The dependent variable is "whether to participate in supplementary education", which set two answers of "yes" and "no." The questionnaire covers six detailed questions about supplementary education: Have you ever participated or are you currently participating in (1) any tutoring for class at school (such as Chinese, math, English, physics, chemistry, geography and other subjects); (2) any tutoring for academic competition (such as the International Math Olympiad, China Cup competition, and Hope Cup competition); (3) any tutoring for talent (such as musical instrument, chess, calligraphy, painting, sports, and so on); (4) any tutoring for intelligence development (such reckoning by the abacus, mental arithmetic, magic cube, right brain development, and so on); (5) in any other tutoring; (6) ever had a private tutor. In this study, we set supplementary education as "yes" if a student participates in any form of supplementary education. The academic-oriented supplementary education is set as "yes" if a student participates in any form of (1)/(2)/(6), and the hobby-oriented supplementary education is set as "yes" if a student participates in any type of (3)/(4)/(5). (In China, the academic-oriented supplementary education is apparent to identify. But the hobby-oriented class has much more various forms, hence it is reasonable to regard "any other tutoring" as a category of hobby-oriented class). In total, 34% of respondent students participated supplementary education. Only 28% of respondent students in multiple-child families participated in supplementary education, which is obviously less than former.
The gender distribution of the students in the sample is relatively balanced, male students are slightly more than female students. Sibling structure is composed of four dimensions: number, density, order, and gender minority. The average number of siblings of the respondents in all samples and multiple-child samples are 1.08 and 1.38 respectively. The mean age gap between siblings used for the density of siblings is 2.75 years, which means the average interval between children within the families was about 3 years. Sibling order is divided into three types: eldest child, middle-born, and youngest child, accounting for 44%, 11%, and 45%, respectively. The middleborn account for the least, indicating that the proportion of families with three children or more is low.
In China, urban families and rural families have obvious differences in supplementary education. The mean of per capita household income of the children attending the supplementary education is CNY 35163.37 in urban areas, while in rural areas is only CNY 16416.54, which is less than half of the former. As the former research shows, the urban-rural regional disparity is an important impact factor (Y. Xie, 2013).
Parents' educational attainment and family socioeconomic status also matters (Hu, 2015;W. Liu et al., 2021). This study set these factors as control variables, which are indicated in Table 4. As seen in Table 4, missing data occurs on parental education, occupational prestige of parents and the logarithm of per capita annual family income. The missing values are addressed using multiple imputations (Schafer & Graham, 2002). Further analyses are based on the imputed datasets.

Research Methods
The dependent variable in this study is "whether to participate in supplementary education", which is a dichotomous variable, it is more appropriate to use the binary Logit regression model to conduct data analysis. The binary Logit regression model used in this study is as follows: Where P represents the occurrence probability of whether the dependent variable participates in supplementary education; gender i and sibship i represent gender and sibling structure respectively of the core independent variable, control i refers to a set of control variables, including individual characteristics and family circumstances.

Result analysis
Dilution Effect on Siblings Table 5 reports the results of the Siblings Dilution Effect of supplementary education participation. According to Model 1, several siblings are negative to a student's probability of participating in supplementary education (−0.38). In Model 2, this study measures each kind of sibling. It shows that regardless of the gender and birth order of siblings, siblings significantly decrease students' probability of supplementary education participation. Hypothesis 1a mentioned above is thus supported. Previous studies indicated that the number of elder sisters is positive to the student's educational attainment, especially for male students, while the number of brothers is negative to Siblings' size negatively influences children's opportunity to participate in supplementary education. The more siblings within a family, the fewer opportunities for each child to participate in supplementary education.

H1b
Sibling density difference negatively influences children's opportunity to participate in supplementary education. The bigger the sibling age difference within a family, the greater opportunity for each child to participate in supplementary education.
Gender Advantage

H2a
Females have more opportunities to participate in supplementary education than males.

H2b
The gender difference is mainly due to the hobby classes which have a weaker relationship with formal education.
The Role of Sibling's Order

H3a
The eldest children have more opportunities to participate in supplementary education than laterborn children.

H3b
The middle children have fewer opportunities to participate in supplementary education than both the eldest children and the youngest children within a family.

H4a
The eldest daughter would have a higher possibility of attending supplementary education, but for the eldest son, it would not be significant.

H4b
Females who only have brothers have more opportunities to participate in supplementary education, and the siblings' gender has an insignificant influence on the males' opportunities to participate in supplementary education.
the students' educational attainment (Chang & Li, 2016;Zheng, 2013). The empirical results of this study show sisters and brothers both decrease the possibility to attend supplementary education.
In Model 3, this study analysed the sibling density by the mean age gap of siblings in a family with more than one child. The result shows that the mean age differences of siblings positively impact on students participating in supplementary education opportunities (0.08). The sibling density is negative to the student's probability of participating in supplementary education. Hypothesis 1b is supported. Table 6 reports the result of gender advantage in supplementary education. All samples are divided into two groups: (a) born in a family with one child and (b) born in a family with more than one child. Model 4a and Model 4b show that female student has a significantly higher probability to participate in supplementary education both in a family with one child (−0.32) and in a family with more than one child (−0.34). Hypothesis 2a is supported.

Gender Advantage in Supplementary Education
To figure out which kind of supplementary education has gender difference; we divide supplementary education into academic-oriented supplementary education and hobby-oriented supplementary education. Academic-oriented supplementary education, including tutoring classes both within and outside the school, proposes to improve student academic performance. Hobbyoriented supplementary education propose to develop student hobbies and interests. Model 5a and Model 5b show that the attendance of academic-oriented supplementary education has no significant gender difference. While the Model 6a and Model 6b show that the female student has a significantly higher possibility to attend to hobby-oriented supplementary education (−0.26, −0.52). Hypothesis 2b is supported.
The Role of Sibling's Order In Table 7, this study analysed sibling order in a family with more than one child. Model 7 reports the eldest child has a higher probability to attend supplementary education than a middle child and youngest child (−0.41, −0.29) and the middle child has the lowest probability to participate in supplementary education. Hypothesis 3a and 3b are supported.
Since the eldest child has the most opportunity to participate in supplementary education, this study further explored the gender difference in the oldest child. In Model8, the eldest daughter has a higher probability to participate in supplementary education than her other siblings (0.44). While in Model 9 the eldest son has no significant difference from his other siblings in attending supplementary education. Hypothesis 4a is supported.
The Influence of Gender Minority on Siblings Table 8 reports the effect of gender minority of siblings. Model 10 suggests that a student whose gender is different from all siblings has no significantly higher probability to participate in supplementary education. In Model 11, after adding the interaction item of gender and gender minority, the gender minority has a significant positive impact, and the coefficient of the interaction item is negative and significant. The result proves that the gender minority of siblings indeed has gender differences.
We estimate the gender minority or sibling's impact on female and male student supplementary education participation respectively. In Model 12, the gender minority of siblings has a positive Note: All the models include control variables. Coefficients for these control variables are not reported here. *** p < 0.01, ** p < 0.05, * p < 0.1 impact on the female students attending supplementary education (0.35). While Model 13 reports male students whose gender is different from all siblings do not have a significant impact on supplementary education participation. Hypothesis 4b is supported.
Robust Test Note: All the models include control variables. Coefficients for these control variables are not reported here. *** p < 0.01, ** p < 0.05, * p < 0.1  Note: All the models include control variables. Coefficients for these control variables are not reported here. *** p < 0.01, ** p < 0.05, * p < 0.1 As the Chinese one-child policy impacts the family sibling structure, whether the student is in a one-child family is not random. The sibling structure is affected by the fertility behaviours of parents, the result might have "selection bias". And we use PSM (Propensity Score Matching) to test.
We use the binary logit model to estimate the propensity score of whether the student is the only child, the control variable is family income, parents' educational attainment and occupational reputation, student's gender, ethnicity and the household registration. In Table 9, the result shows the family income, and parents' educational level both have a significantly positive correlation to the probability of students in a one-child family (0.39,0.26). Male students with non-agricultural household registration would be more likely in a one-child family (0.41,-1.24).
The Table 10 shows the result of PSM in two ways. The K-nearest neighbour matching(K = 4) has a slightly better covariate imbalance (mean bias = 1.3, p-value of LR chi2 = 4.61%). Two matching methods both have significant ATT (0.36), which means student in a one-child family has a significantly positive correlation to supplementary education attendance even if "selection bias" is taken into account.

Discussion and conclusions
Based on the findings and implications of the analyses above, a student's supplementary education attendance is affected by the following factors. First, the number of siblings significantly decreases the opportunity to participate in supplementary education. And the density of siblings, or the number of siblings at the same age, also lowers the chance of attending supplementary Note: All the models include control variables. Coefficients for these control variables are not reported here. *** p < 0.01, ** p < 0.05, * p < 0.1 education. The result supports that the resource dilution theory is suitable for supplementary education. Third, female students have more opportunities to participate in supplementary education, which is contrary to the "male advantage" in formal education. G. Wei and Zhang (2021) explained that the "female advantage" in supplementary education is caused by a change in the Chinese old-age support pattern. Daughters, instead of sons, play the most important role in supporting the elderly in urban areas. As a result, parents are more likely to invest money in their daughters' supplementary education. Another possible explanation is the budget constraint theory, suggesting parents would consider the lifetime cost of raising a child before deciding to invest in the child's education (Strauss & Thomas, 1995). Chinese parents attach importance to their sons' formal education attainment and marriage (Zhou & Yuan, 2014). This would decrease costs in other aspects.
To figure out which one is the reason cause different gender advantage in formal education and supplementary education, this study further analysed gender impact in a different type of supplementary education. Supplementary education in this study is composed of academic-oriented and hobby-oriented. The former is proved to be beneficial to formal education attainment (Y. Liu et al.,  Note: Untreated are students in a family with more than one child, treated are students in the one-child family; *** p < 0.01, ** p < 0.05, * p < 0.1. 2020), and the latter is not. According to the analysis above, female students have a significantly higher probability of attending hobby-oriented supplementary education. While in academicoriented, gender differences are not significant, which means there is no "female preference" in formal education. The results could imply that female status has improved in contemporary China. However, the gender advantage is driven by traditionalism still exists, though in a different way for men and women (Fuse, 2013). Formal education and marriage would cost much more, and sons would inherit much more family resources for their inborn gender (S. J. Wei & Zhang, 2011;Zhou & Yuan, 2014). And parents just spend their limited family resources on their daughter's supplementary education. It could be regarded as a persistent divergence in gender differences in China.
Third, birth order significantly affects the students' supplementary education participation. In a family with more than one child, the eldest child has the highest probability of attending supplementary education, the youngest child has a second higher probability, and the middle child has the least opportunity. According to existing research, the most educational resources allocated for the eldest child could be explained by the highest parental expectations (Hotz & Pantano, 2015;Kim, 2019).
Furthermore, this study examined the birth order and gender composition. The advantage of the eldest child in supplementary education participation also has a gender difference, the probability of attending supplementary education of the eldest daughter is significantly higher, while the eldest son is not. In traditional Chinese society, parents favour the eldest sons at the expense of others, especially in rural areas, because male children could provide labour for the family farm. Besides, Confucius's norms value the importance of first sons to carry on the family line (Oliveira, 2019). While in modern Chinese families, parents tend to spend equal resources on each child (Price, 2008). According to budget constraint theory, parents would like to spend more on the eldest daughter attending supplementary education, while the eldest son would not gain more resources in supplementary education.
Last, the gender minority of siblings is a significant factor affecting students' supplementary attendance, which also has a gender difference. Female students with different gender siblings would have a higher possibility of attending supplementary education, while it is not significant in male students. The results are the same as the gender difference of sibling gender minority in formal education indicated by previous studies (Butcher & Case, 1994;Conley, 2000;Lei et al., 2017).
In nutshell, our empirical results indicate that students of different genders and sibling structures have a different opportunity for supplementary education. Our findings support the sibling dilution hypothesis, and the budget constraint hypothesis in Chinese family resources allocation for their children's supplementary education. The gender advantage and sibling composition effect of supplementary education could still reflect the continued divergence of gender roles, which could further imply that traditional Confucius norms still work in Chinese families.
This study provides some avenues for future research. First, this study applies the budget constraint theory to explain the phenomenon of "female advantage" in supplementary education, which is only significant in hobby-oriented supplementary education and finds that the eldest female has higher probability to attending supplementary education. The study only employs the cross-sectional data, which is limited to provided further explanations of the results. Future research could use qualitative methods to explain the findings of this study. Second, this study focuses on how gender and sibling structure impact Chinese K12 students' supplementary education opportunities when the cram-school developed rapidly. In the past, the ministry of education prohibited home tutoring by teachers in public schools, while the regulation of private cram-school was laissez-faire (Kwok, 2010). Since 2010s, the development of supplementary tutoring of mainland China have experienced two stages hitherto: (1)2011-2018: In this deepening institutionalization, specialization and capitalization stage, face-to-face home tutoring gradually lose the market of the tutoring with technological innovations; (2) 2018-2021: In the massification, digitalization and integration stage, the integrations of three learning spaces (schools, families and private tutoring) in students' homes (Zhang & Bray, 2021, p. 51). Since 2021, the Double Reduction Policy (DRP) has been implemented to reduce the homework and after-school private tutoring for students from kindergarten to 9 th grade.
The central government has deeply taken governance on supplementary education, especially implementing strict control on academic-oriented supplementary education which is called "Offcampus Tutoring (Xiao Wai Pei Xun)" (Xue & Diao, 2020). The DRP banned private business from offering "subject-based" off-campus tutoring and encouraged freer academic and extra-curricular activities to be available to all students in schools (Ministry of Education in China, 2021). As the existing private tutoring institutions are under strict control by governments or transformed into non-profit organizations collaborating with schools, supplementary education would be more attached to schools, and the family non-economic resource would be more important to schooling students' supplementary education opportunities. Discussed by this study, the two types of supplementary tutoring with diverse opportunities distributions between genders. Thus, further research about how sibling structure and gender impact student education resource allocation would focus on home-school cooperation. When the family decisions and school provisions have been complementary with each other, it is worth inquiring the new reproduction or production of gender differences in educational opportunities distributions. Note 1. The narrations of social class since the establishment of PRC have experienced the change, which is from "Class (Jie ji)" to "Stratum (Jie ceng)" (Anagnost, 2008). The notion of "Stratum (Jie ceng)" has replaced the notion of "Class (Jie ji)" since 1990s, under the background of the boom of private market and within the blueprint of "relatively well off (Xiao kang)"in Reform era, referring to the new social inequality without the social antagonism, different from what the notion of "Class" does in Mao era (Anagnost, 2008). The notion of "Stratum (Jie ceng)" referred in Lu's studies and employed by the other contemporary Chinese mainland scholars is an indigenous conception rather than an indigenous theoretical concept substantively. The notion of "Stratum (Jie ceng)" is regarded as the equivalent of social class in common concept from academic community of class analysis and social stratifications (L.Z. Xie, 2016;Lu, 2005). Thus, to avoid confusion, when discussing social classes or social strata in this paper, the term "social class" is used consistently, with the only exception of "strata/stratum" in the discussion of Lu Xueyi's work.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Data Availability Statement
The data that support the findings of this study are openly available in Institute of Social Science Survey, Peking University, 2015, "China Family Panel Studies (CFPS)", https://doi.org/10.18170/DVN/45LCSO, Peking University Open Research Data Platform, V42.