Spillover effects from the divorce of peer parents: Evidence from student academic achievements in China

Spillover effects from the divorce of peer parents: Evidence from student academic achievements in China | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Spillover effects from the divorce of peer parents: Evidence from student academic achievements in China Boou Chen, Chunkai Zhao, Xiaoyu Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5797362/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 21 You are reading this latest preprint version Abstract Although the impact of parental divorce on children’s human capital development has received sufficient attention from scholars, little has been paid to the potential spillovers. Based on a quasi-natural experiment with random student-classroom assignment in secondary schools in China, we aimed to explore whether the peer parental divorce (PPD) can have a negative spillover effect on students’ academic achievements in a class. The results show that the PPD negatively impacted students’ test scores and cognitive abilities, but this adverse effect is not reflected in non-cognitive abilities. Mechanism analyses suggested that this spillover effect may be explained by the decline in parental expectations, development of students’ negative expectations and learning behaviors, and drop in teachers’ efforts and enthusiasm. Moreover, we found that the negative spillovers of PPD are more pronounced for urban children, only children, and non-poor children. Furthermore, supports from teachers, parents, and friends is expected to mitigate this adverse spillover effects. Our study reveals the spillovers from parental divorce, suggesting that the negative effects of divorce on human capital are not confined within the family. These findings further provide some insights into mitigating the human capital loss from divorce. Business and commerce/Economics Social science/Economics Social science/Education Parental divorce Student academic achievements Spillover effects Random student-classroom assignment China Figures Figure 1 Figure 2 1. Introduction In recent years, the persistently high divorce rate has attracted widespread attention throughout society. In China, the divorce rate has continued to rise since 1978. As shown in Fig. 1 , China’s divorce rate at 3.36‰ in 2019, which is 3.5 times higher than in 2000 and 18.7 times higher than in 1978. According to the 2019 Statistical Bulletin on the Development of Civil Administration, the number of marriages fell by 8.5% year-on-year, while divorces increased by 5.4% over the previous year. 1 Divorce is not only a break in the relationship between husband and wife, but also implies a change in the family relations constituted by the blood parent-child relationship (Bernardi & Radl, 2014 ; Zhuang et al., 2025 ), especially in the context of a traditional family culture like China (Sun & Li, 2009 ; Zhang, 2020 ). As more and more children live in non-intact families, such changes have profound impacts, with multiple consequences for children (Amato & Anthony, 2014 ; Corak, 2001 ; Kim, 2011 ). [Insert Fig. 1 about here] The negative effect of parental divorce on children development has received considerable scholarly attention. From the perspective of marital functioning and resource deprivation, prior research emphasized the adverse effect of parental divorce on children’s upbringing. Scholars provided evidence that divorce leads to the deterioration of the family’s economic situation (e.g., Albert, 2018 ; Hoffman & Duncan, 1988 ; Sun & Li, 2009 ), the destruction of the family structure (e.g., Conway & Li, 2012 ; McLanahan, 1985 ; Park, 2007 ), and the intensification of emotional conflicts (Amato & Cheadle, 2008 ; Kalmijn, 2013 ), which further negatively affects the children. Specifically, scholars concluded that parental divorce led to poor psychological development, deviant behaviors, moodiness, and weakened interpersonal skills (e.g., Anthony et al., 2014 ; Cáceres-Delpiano & Giolito, 2012 ; Kim, 2011 ; Hu, 2020 ; Park, 2008 ). More seriously, a number of studies pointed out compared to children from intact families, those from divorced families had worse school performance (Frimmel et al., 2024 ; Havermans et al., 2014 ; Park, 2008 ; Sun & Li, 2009 ), lower cognitive and non-cognitive skills (Amato & Anthony, 2014 ; Kim, 2011 ), and poorer self-control and learning habits (Anthony et al., 2014 ; Sigle-Rushton et al., 2005 ). In this paper, we were more concerned about whether this negative impact would have further spillover effects along the children’s peers in the classroom? To our knowledge, this spillover has not yet received the theoretical and empirical attentions. We explored the causal effect of marital stability on human capital accumulation in the Chinese social context by taking the spillover effect of peer parental divorce (PPD) as an example. Specifically, we considered that students in classes with a higher proportion of divorced parents are subject to more negative spillover effects, which then translate into significant disadvantages in academic achievement and cognitive ability. However, PPD and the class in which a student is enrolled may not be random, which may lead to serious endogeneity problems in our estimates. For example, if students with lower initial academic performance are assigned to the same class, these students are more likely to come from homes where parents are divorced, due to the negative effect of parental divorce on students’ achievement (Havermans et al., 2014 ; Sun & Li, 2009 ). In this context, even in the absence of spillovers from PPD, the empirical results would exhibit a negative correlation between the proportion of divorced parents and student performance in the classroom. Fortunately, the China Education Panel Survey (CEPS) provides us with a good quasi-experiment, the random student-classroom assignment (RSCA). In recent years, to maintain equity in education, many local governments in China have required that classes in compulsory education be randomly assigned by computer and that transfers be strictly limited after the classes have been determined. Also, this approach has been widely used in causal inference studies to confirm the peer effects (e.g., Chen & Zhao, 2024 ; Gong et al., 2018 ; Hu, 2018 ; Huang & Zhu, 2010; Xu et al., 2022 ). Based on the sample of RSCA in CEPS database, we found that in the classes with a high percentage of divorced parents, students from non-divorced families performed worse academically. which confirms the negative peer effect of parental divorce. Specifically, for each percentage point increase in the proportion of divorced parents in a class, students’ average test scores and cognitive ability scores decreased by an average of 0.2998 and 0.0087 points, equivalent to 0.0790 and 0.0543 standard deviations, respectively. To ensure that our findings are reliable, a series of robustness checks are conducted in this study. First, the generation process of the core explanatory variable from the RSCA is not systematically disturbed by omitted variables, which is the key to the validity of our causal identifications (Chen & Zhao, 2024 ; Gong et al., 2021 ; Hu, 2018 ). We overcame this bias by using balancing tests (Chen & Zhao, 2022 ; Gong et al., 2018 ; Xu et al., 2022 ), which showed that given a school with the RSCA, PPD is insignificantly correlated with a range of predetermined variables related to class characteristics, family characteristics, and student characteristics. These results suggest that the RSCA process is unlikely to be subject to human intervention and can be viewed as a quasi-experiment. Second, divorced parents may have negative spillover effects on children through multiple channels. To separate the spillover effects of parental divorce from those of other parental characteristics, in addition to controlling for parental education and parental occupational FE, we further considered a series of other spillover effects, such as parental human capital, unemployment, political capital, and migration, which have been mentioned in the previous literature (e.g., Chen et al., 2023 ; Dickson et al, 2016 ; Fruehwirth & Gagete-Miranda, 2019 ; Salas García & Rentería, 2024 ; Yin et al., 2020 ; Zheng & Zhou, 2024 ). Third, other robustness tests such as placebo tests, tighter controls, and exclusion of special observations similarly support our main results. We were also quite interested in the mechanisms by which negative spillovers from parental divorce arise. First, at the family and parental level, divorce may worsen the family economic situation and reduce parental attention to their children’s learning (Albert, 2018 ; Smock et al., 1999 ). This may lead to a decline in the family educational expenditures and lower educational expectations (Astone & McLanahan, 1991 ; Park, 2007 ). These trends may also affect other parents in the same class. Second, in terms of children, parental divorce may be detrimental to the shaping of positive attitudes and learning behaviors (Hu, 2020 ; Sun & Li, 2009 ), due to the psychological shock of parental divorce and the reduction of parental supervision. Other students in the class may also be affected by this negative peer effect. Third, from the perspective teachers, divorced parents may reduce teachers’ enthusiasm for teaching and are less likely to provide public goods to the class (Conway & Li, 2012 ), which may also have a negative effect on students’ school performance. Thus, the mechanisms of spillover effects of PPD should be understood at three levels: families and parents, students, and teachers. Our study contributes to the existing literature in at least three ways. First, while a considerable body of literature recognized the negative short- and long-term effects of parental divorce on children human capital accumulation, some scholars argued that the impact of parental divorce on children development is limited (Brand et al., 2019 ; Francesconi et al., 2010 ; Manski et al., 1992 ). They argued that since parental divorce implies a reduction in parental arguments and conflicts, this in turn may reduce negative psychological shocks on children (Amato & Anthony, 2014 ; Zhang, 2020 ). This research conflict may stem from differences in research perspectives and identification strategies. Unlike western countries, China is deeply influenced by traditional family values and the family plays a rather important role in child human capital development (Wen & Lin, 2012 ; Tang & Zhao, 2023 ). Moreover, using the special quasi-natural experiment of RSCA, we highlighted the negative effect of parental divorce on academic performance in China. Thus, we provided new evidence for the view that parental divorce is detrimental to children’s human capital. Additionally, we offered a potential measure for mitigating this negative peer effect from the particular perspectives of teacher, parent, and friend supports. Second, from the particular perspective of parental divorce, we provided additional supportive evidence for classroom peer effects. Peer effects have been a hot topic since the seminal study from Manski ( 1993 ). Subsequently, a considerable number of studies found that individual human capital development is greatly influenced by peer behaviors, characteristics, and family background (e.g., Dahl et al., 2014 ; Falk & Ichino, 2006 ; Hanushek et al., 2003 ; Gong et al., 2018 ; Zimmerman, 2003 ). Based on the Chinese context, some attention was also paid to the positive or negative spillover effects of classmates’ gender (Gong et al., 2021 ; Luo & Yang, 2023 ), cognitive ability (Huang & Zhu, 2020 ; Xu et al., 2022 ), migration (Hu, 2018 ; Min et al., 2019 ; Wang et al., 2018 ), disability (Huang et al., 2022), and family expenditure on education (Chen et al., 2023 ; Pan et al., 2022 ) on students’ academic performance. Although scholars noted how family background affects other students in the same class through their children’s social networks, a key element of parental divorce has not yet been mentioned in the literature. Importantly, we further aimed to uncover the mechanisms of parental divorce peer effects, which are not only manifested in both families and children, but may also have a negative impact on teachers’ efforts. Thus, our exploration provides insights for subsequent related studies. Third, we further strengthened the academic understanding of the intergenerational effects of human capital. Prior literature on how parents affect their children’s human capital accumulation has been framed primarily in terms of parental resources (e.g., human, social, physical, and political capital), recognizing that resources possessed by parents are likely to be passed on intergenerationally to their children (Amato & Anthony, 2014 ; Chen et al., 2023 ; Dickson et al, 2016 ; Sun & Li, 2009 ), which further contributes to the accumulation of human capital in their children (e.g., Behrman & Rosenzweig, 2002 ; Black et al., 2005 ; Guryan et al., 2008 ; Giannola, 2024 ; Taubman, 1989 ; Wang et al., 2020 ). We offered evidence from the perspective of parental marital stability and family structure. Importantly, we revealed that this negative effect on human capital may also have a spillover effect through the children’s social networks, leading to a shock in the academic performance of their classmates. This means that the adverse effects of parental divorce extend beyond the intra-family transmission characteristic and have the potential for further winder social impacts. 2. Data and variables 2.1. Data The data for this study is from the CEPS in the 2014–2015 academic year, a nationally representative micro-survey of middle school students in China. Based on a multistage stratified probability-proportional-to-size (PPS) sampling, the CEPS randomly selected about 20,000 secondary school students in 7th and 9th grades from 112 schools and 438 classes in the 2013–2014 academic year (baseline wave), and the follow-up survey in 2014–2015 academic year (the second wave) tracked the 10,750 students in the 8th grade (original 7th grade in the baseline wave). It is is a high-quality survey on secondary education, and its questionnaire contains a great deal of information on the characteristics of schools, students and their parents and family, and teachers and classes. Currently, the CEPS has been widely used in research on the economics of education, education, and adolescent development (e.g., Chen & Zhao, 2022 ; Gong et al., 2018 ; Hu, 2018 ; Huang & Zhu, 2020 ; Huang et al., 2023 ; Luo & Yang, 2023 ; Zhao et al., 2024 ). More importantly, the CEPS contains the variables and information needed for our study. Specifically, information about whether the parents of the students interviewed were divorced was collected in the CEPS for the 2014–2015 academic year, which allowed us to identify the spillover effects of PPD in the class. Meanwhile, the survey also collected students’ scores on mid-term exams, including the three main subjects of Chinese, Math, and English, which can be used to measure students’ academic achievement. Moreover, the CEPS contains students’ cognitive ability scores, 2 as well as a series of questions that measure non-cognitive abilities (Chen & Zhao, 2024 ; Zhao & Chen, 2022 ), helping us to examine the spillover effects of PPD from multiple perspectives. It is important to highlight that CEPS also investigated class assignment rules in different schools, i.e., whether students were randomly assigned to classes or whether they were assigned based on student scores or some other rules. 3 Reference to existing studies (Chen & Zhao, 2022 ; Gong et al., 2018 ; Huang & Zhu, 2020 ; Huang et al., 2023 ), we retained only the sample of students in schools with RSCA, and used it as a quasi-experiment to identify causal relationships between PPD and student outcomes. Finally, the sample used in the analysis consisted of 5,274 students from 204 classes in 79 middle schools, including 354 students whose parents were divorced and 4,920 students from intact families. It should be emphasized that we use the sample of students from intact families (4,920) in the baseline regressions, as we aimed to examine the spillover effects of PPD (Angrist, 2014 ). 2.2. Variables and summary statistics Table 1 and Table A1 in the appendix report the definitions and summary statistics of the variables in the econometric models. In Table 1 , Panel A shows a series of variables describing students’ academic achievements, mainly including students’ scores on the midterm exams of the three main courses, Chinese, Math, and English, the average score of the three main courses, and their cognitive ability scores (Gong et al., 2018 ; Huang et al., 2021 ; Salas García & Rentería, 2024 ; Zhao & Chen, 2023 ; Zhao et al., 2024 ). For comparative analysis, the scores for the three main courses were standardized on a scale ranging from 0-100 points. Among the students surveyed, the mean of the average score in the three main courses was 63.68, and the mean of the standardized cognitive ability scores was 0.277. Panel B reports descriptive statistics of the core explanatory variables. First, according to the information related to parents’ marital status in the questionnaire, we constructed a dummy Parental divorce , which was assigned to 1 if students’ parents were divorced, and 0 otherwise. According to the statistical results, the percentage of students in the sample whose parents are divorced is about 6.7%. Second, in line with previous studies (e.g., Gong et al., 2021 ; Guo et al., 2022 ; Hu, 2018 ; Huang & Zhu, 2020 ; Huang et al., 2021 ; Luo & Yang, 2023 ), we further calculated the percentage of students in the class whose parents are divorced, the core explanatory variable PPD , to examine the spillover effects of peer parental divorce. In terms of baseline control variables, we controlled for a range of characteristics of students, families and parents, and teachers. Specifically, see Panel C in Table 1 , where we considered students’ gender, age, hukou status, and only child. We also controlled for various characteristics of families and parents that may influence student performance in Panel D, including family economic status (self-rated), parents’ education, and government education subsidies (Gong et al., 2018 ; Hu, 2018 ). It is important to highlight that parental occupation may also have an impact on their marital status child academic performance (Hill, 1979), so we simultaneously include fixed effects (FEs) for father’s and mother’s occupation in our main specification based on the CEPS questionnaire. 4 More importantly, teacher characteristics and teacher quality are also important factors in students’ school performance (Chen & Zhao, 2022 ; Huang et al., 2023 ), so we controlled for the gender, education, and years of teaching experience of the homeroom teacher. Additionally, we controlled for the characteristics of the curriculum teacher, when examining students’ performance in a particular course. Teacher characteristics are detailed in Panel E. Table 1 Summary statistics Full sample Students with divorced parents Students from intact families (Sample for baseline regression) Variable N Mean S.D. N Mean S.D. N Mean S.D. Panel A. Student performances Average score 5274 63.68 19.24 354 59.20 20.23 4920 64.00 19.13 Chinese score 5274 68.40 15.13 354 65.19 17.33 4920 68.63 14.94 Math score 5274 62.62 25.94 354 55.85 26.50 4920 63.11 25.83 English score 5274 60.03 23.66 354 56.57 23.95 4920 60.28 23.62 Cognitive ability 5274 0.277 0.816 354 0.142 0.905 4920 0.286 0.808 Panel B. Parental divorce and divorce rate Parental divorce 5274 0.067 0.250 354 -- -- 4920 -- -- PPD 5274 7.364 5.140 354 -- -- 4920 7.106 5.044 Panel C. Student characteristics Gender of student 5274 0.510 0.500 354 0.438 0.497 4920 0.515 0.500 Age of student 5274 14.54 0.699 354 14.60 0.717 4920 14.54 0.697 Hukou 5274 0.526 0.499 354 0.449 0.498 4920 0.532 0.499 Only child 5274 0.410 0.492 354 0.551 0.498 4920 0.400 0.490 Panel D. Family and parental characteristics Self-rated wealth 5274 0.055 0.228 354 0.042 0.202 4920 0.0559 0.230 Education of father 5274 10.00 2.861 354 10.19 2.906 4920 9.987 2.857 Education of mother 5274 9.437 3.217 354 9.774 3.231 4920 9.413 3.215 Government subsidy 5274 0.684 0.465 354 0.684 0.466 4920 0.684 0.465 Panel E. Teacher characteristics Gender of homeroom teacher 5274 0.307 0.461 354 0.285 0.452 4920 0.308 0.462 Gender of Chinese teacher 5021 0.280 0.449 339 0.221 0.416 4682 0.284 0.451 Gender of Math teacher 4989 0.397 0.489 335 0.409 0.492 4654 0.396 0.489 Gender of English teacher 4952 0.167 0.373 331 0.169 0.376 4621 0.167 0.373 Education of homeroom teacher 5274 15.68 0.444 354 15.69 0.486 4920 15.68 0.441 Education of Chinese teacher 5021 15.72 0.657 339 15.83 0.811 4682 15.72 0.644 Education of Math teacher 5015 15.68 0.566 337 15.63 0.497 4678 15.68 0.571 Education of English teacher 4952 15.70 0.561 331 15.73 0.640 4621 15.70 0.555 Teaching experience of homeroom teacher 5274 16.83 8.277 354 17.09 8.522 4920 16.81 8.259 Teaching experience of Chinese teacher 5012 17.33 8.214 339 16.49 8.227 4673 17.39 8.211 Teaching experience of Math teacher 4983 18.14 8.806 336 19.27 8.228 4647 18.06 8.841 Teaching experience of English teacher 4819 17.03 9.772 319 17.38 10.24 4500 17.01 9.739 [Insert Table 1 about here] 3. Empirical strategy 3.1. Empirical model Base on the framework of a quasi-experiment with RSCA, we constructed the following econometric model to identify the causal effects of PPD on student academic performance: $$\:{SP}_{ics}=\alpha\:+\beta\:{PPD}_{cs}+{Z}_{ics}^{{\prime\:}}\gamma\:+{\delta\:}_{s}+{\epsilon\:}_{ics}$$ 1 where \(\:{SP}_{ics}\) measures the academic achievements for student i in class c of school s , which is examined across multiple dimensions, including test scores, cognitive ability, and non-cognitive abilities. 5 \(\:{PPD}_{cs}\) denotes the percentage of students whose parents are divorced (%) in class c of school s , the core explanatory variable to reflect the spillover effects of peer parental divorce. \(\:{Z}_{ics}^{{\prime\:}}\) is a set of covariates composed of three vectors as mentioned above. \(\:{\delta\:}_{s}\) is the school FE. Since our identification method relies on differences in PPD between schools, controlling for school FE helps to mitigate potential endogeneity problems posed by school characteristics (Chen & Zhao, 2022 ; Yin et al., 2020 ). \(\:{\epsilon\:}_{ics}\) is the error term. Moreover, to accommodate heteroskedasticity and arbitrary serial correlation across students in each class, we clustered the standard errors at the class level throughout the empirical study (Balestra et al., 2022 ; Huang et al., 2021 ). 3.2. Random student-classroom assignment Accurately identifying the causal relationship between PPD and student performance is usually difficult because students’ peers are not randomly determined. This selectivity results in some potential correlations between PPD and other class, student, and family characteristics. In addition, if the process of assigning classes and students is not randomized, for example, by students’ scores on entrance exams, it will also lead to biased estimates. Thus, to mitigate this potential endogeneity issues, referring to the empirical strategy commonly employed in previous literature (e.g., Chen & Zhao, 2022 ; Gong et al., 2018 ; Guo et al., 2022 ; Hu, 2018 ; Huang et al., 2021 ; Huang & Zhu, 2020 ; Huang et al., 2023 ; Luo et al., 2021; Wang et al., 2018 ; Xu & Li, 2018 ), we resorted to the quasi-experiment of RSCA on the basis of Eq. 1 for causal identification. Specifically, with the RSCA, students are matched to their classmates randomly, which means that whether a student matches a classmate whose parents are divorced is also randomized. In other words, for each student, PPD as a class characteristic was randomized and exogenously given. Of course, before employing this quasi-experiment, we need to verify that the process of RSCA is sufficiently random. There are two potential concerns that could interfere with the RSCA. The first threat comes from the effectiveness of identification. Ideally, if class sizes are large enough, differences in the proportion of parental divorce between classes in the same school should tend to zero after the RSCA. As shown in Table 1 , we found that the standard deviation of the proportion of divorced parents is only 0.0514. 6 Especially within a school, PPD should not vary much from class to class. As mentioned above, in fact, our identification relies on differences in PPD between schools. The next question is whether there is enough variation in our data to effectively identify PPD spillovers after adding school FE. Moreover, we plotted the distribution of the PPD for RSCA sample in Fig. 2 . Specifically, we found that this variable is more widely distributed in the sample with a larger standard deviation. Then, after controlling for school FE, we further plotted the distribution of the residuals of PPD in Fig. 2 (b), found that the residuals largely follow a normal distribution with a smaller standard deviation, which reflects the fact that after fixing the schools, the variable PPD were relatively random and independent in the sample. This suggests that there is still enough variability in the data to support the empirical strategy in our study. Compared to the previous literature (Chen & Zhao, 2022 ; Yin et al., 2020 ), we considered this variability (standard deviation 5.5870) that we utilized for identification. [Insert Fig. 2 about here] The second threat is from the verification of randomness. We performed the balancing tests to verify whether the variation in PPD random conditional on school FE. That means, whether the variable PPD is expected to be uncorrelated with any predetermined background characteristics of students, parents and families, and classes. More specifically, we regress a series of predetermined variables related to student, family, and class characteristics (including number of students, percentage of girls, percentage of fathers/mothers with higher education, average of education expenditures, gender of homeroom teacher, etc.) on the variable PPD . Descriptive statistics for these class-level predetermined variables are shown in Tables A2 and A3 in the Appendix . The results of the balancing tests are shown in Appendix Table A4, which indicate that PPD is not correlated with all the predetermined variables after controlling for school FE. The results further support the randomness of PPD in our sample, and suggests that the process of RSCA is real and effective in the CEPS (e.g. Chen & Zhao, 2024 ; Gong et al., 2018 ; Hu, 2018 ; Wang et al., 2018 ). Based on the above evidence, we are confident that the quasi-experiment of RSCA is valid, and have sufficient confidence in the randomness and exogeneity of the core variable PPD . Furthermore, we used a non-RSCA sample for further balancing tests in Table A5 in the Appendix . Clearly, the estimated coefficients on PPD are also insignificant in all columns. Thus, it is reasonable to conjecture that parental divorce is not a factor that interferes with the RSCA, which further implies the rationalization and reliability of using the RSCA as a causal identification method. Taken together, we provided evidence that the process of SRCA is sufficiently efficient and randomized, which excludes the potential confounding factors and endogeneity issues as much as possible. In the empirical analysis above, OLS estimates adequately capture the negative spillover effects of PPD on children’s academic achievements. 4. Results 4.1. Prior evidence: Effects of parental divorce on children’s performances This study is concerned with the spillover effects of PPD on student academic achievements. However, this spillover effect arises from the premise that parental divorce is indeed detrimental to children’s performances. As mentioned above, despite the considerable literature identifying this negative effect, there are still some scholars who found that the effect of parental divorce on children’s school performance is very limited (Brand et al., 2019 ; Francesconi et al., 2010 ). Thus, in this subsection, we provided an a priori evidence about whether parental divorce negatively affects family educational involvement and their children’s educational achievement. According to Table A6 in the Appendix , we found a significant negative relationship between parental divorce and children’s test scores, cognitive ability, educational expectations, and parental educational involvement, which implies that parental divorce is likely to inhibit students’ educational achievement and various types of performance in school. Clearly, these results are similar to previous studies that emphasized that parental divorce is detrimental to children’s human capital accumulation in China (e.g., Frimmel et al., 2024 ; Hu, 2020 ; Sun & Li, 2009 ; Zhang, 2020 ). It is important to emphasize that results in Table A6 only focused on the correlation between parental divorce and children’s performances, not causation, and served as a supportive test prior to the baseline regressions. It needs to be explained that the direct effect of parental divorce on children’s performances is not the goal of this paper, so we only examined their correlations as some supporting evidence. 4.2. Main results: Spillover effects of peer parental divorce In Table 2 , we examined the causal effect of PPD on student academic achievements by using a sample of students from intact families. The results in columns (1) to (4) show that PPD has a negative effect on students’ academic achievement. More specifically, a one-percentage-point increase in PPD leads to an approximate 0.2998-point decrease in students’ average scores, along with decreases in Chinese, Math, and English scores of approximately 0.1698, 0.5243, and 0.5108 points, respectively. 7 By converting to standard deviations, a one standard deviation increase in PPD (a 5.044% increase in the percentage of divorced parents) results in a 0.0790 standard deviation decrease in average score, as well as a decrease in Chinese, Math, and English scores and cognitive ability scores by 0.0573, 0.1024, and 0.1091 standard deviations, respectively. Furthermore, in column (5), as expected, PPD similarly significantly reduced students’ cognitive abilities, indicating that for every percentage increase in PPD in the class, students’ cognitive ability scores decreased by 0.0087 points, which equates to a 0.0543 standard deviation change in cognitive ability for each PPD standard deviation. Meanwhile, in the Tables A7 and A8 in the Appendix , we further explored the effect of PPD on students’ non-cognitive abilities, and found that the effect was not significant. Overall, it is clear that the high rate of parental divorce in the class had a very significant negative impact on all students in the class, especially in terms of their test scores and cognitive development. Our results are similar to some previous literature emphasizing the potential negative effects of parental divorce (e.g., Albert, 2018 ; Conway & Li, 2012 ; Hu, 2020 ; Kalmijn, 2013 ; Sun & Li, 2009 ). Moreover, we confirmed that this negative impact is likely to spillover to other students through the peer effects. In sum, our baseline results indicate the existence of spillovers from parental divorce, suggesting that the adverse impact of parental divorce on children’s human capital development extends beyond the intra-family context. Table 2 Baseline regressions: Spillover effects of PPD on student scores and cognitive ability (1) (2) (3) (4) (5) Average score Chinese score Math score English score Cognitive ability PPD -0.2998** -0.1698* -0.5243*** -0.5108*** -0.0087* (0.1188) (0.0879) (0.1916) (0.1759) (0.0050) Gender of student -8.3903*** -7.5705*** -5.3174*** -12.3211*** -0.0334 (0.5336) (0.4193) (0.7625) (0.7547) (0.0231) Age of student -3.1848*** -1.5789*** -4.1198*** -3.8593*** -0.1800*** (0.3184) (0.2570) (0.4558) (0.4001) (0.0174) Rural 0.5255 -0.0522 1.6504** 0.6825 -0.0069 (0.5201) (0.4048) (0.7814) (0.6689) (0.0235) Only child 0.7743 0.6701 0.7066 1.1446* -0.0095 (0.5626) (0.4425) (0.8445) (0.6466) (0.0257) Self-rated wealth -2.8237*** -1.3756* -4.4243*** -2.8792** -0.0375 (0.9087) (0.7215) (1.2554) (1.2157) (0.0456) Education of father 0.4262*** 0.1731** 0.4306*** 0.6632*** 0.0139*** (0.0994) (0.0820) (0.1513) (0.1235) (0.0049) Education of mother 0.0522 -0.0079 0.0854 0.0930 -0.0010 (0.0940) (0.0812) (0.1385) (0.1199) (0.0039) Government subsidy 2.6701*** 2.0682*** 3.2757*** 2.4924*** 0.0996*** (0.5851) (0.4209) (0.8289) (0.8010) (0.0272) Gender of homeroom teacher -4.4997*** -2.2900** -4.7963*** -4.9712*** -0.1735*** (1.2213) (0.8859) (1.7954) (1.7192) (0.0634) Education of homeroom teacher 0.6226 2.1635** -0.1051 2.6181 -0.0438 (1.3406) (0.8844) (2.1085) (2.2172) (0.0476) Teaching experience of homeroom teacher 0.0827 0.0880 0.1084 0.0926 0.0052 (0.0823) (0.0619) (0.0987) (0.1211) (0.0032) Curriculum teacher characteristics No Yes Yes Yes No Father’s occupation FE Yes Yes Yes Yes Yes Mother’s occupation FE Yes Yes Yes Yes Yes School FE Yes Yes Yes Yes Yes Constant 110.7322*** 94.3715*** 165.2870*** 112.6970** 3.9344*** (22.7935) (15.2808) (39.1941) (45.4057) (0.8307) R 2 0.4116 0.4828 0.3404 0.4167 0.2844 N 4920 4673 4623 4500 4920 Notes: ***, **, * indicate significance at the levels of 1%, 5%, and 10%, respectively. Standard errors clustered at the class level are reported in parentheses. As reported in the summary statistics, Curriculum teacher characteristics, i.e., Chinese, Math and English teachers’ characteristics, including their gender, education, and teaching experience. [Insert Table 2 about here] 4.3. Robustness checks We conducted a series of robustness checks to ensure the reliability of the baseline results, including controlling for other spillover effects, the exclusion of special observations, adding control variables, and placebo tests. First, given that spillover effects from other characteristics of peers’ parents may interfere with the results of the baseline regressions, such as parents’ education, unemployment, political capital, and parental migration etc., which have already been explored in the previous literature (e.g. Hu, 2018 ; Huang & Zhu, 2020 ; Zhao & Zhao, 2021 ; Zhou & Hill, 2023 ). Thus, in Table A9 , we controlled for additional spillover effects for robustness tests, including the spillover effects from parental education, unemployment, political capital, migration, households with frequent drinkers, interparental verbal conflict and households with sick or mobility-impaired members referred to in the previous literature (Chen et al., 2023 ; Dickson et al, 2016 ; Fruehwirth & Gagete-Miranda, 2019 ; Yin et al., 2020 ; Zheng & Zhou, 2024 ). The results show that after controlling for these additional spillover effects, the results are still largely consistent with the main estimates in Table 2 , further verifying that our findings are reliable. Second, in Appendix Table A10, we excluded some special observations to ensure the generality of the sample, such as unhealthy students, students with high educated parents, the best and worst schools in the county, students attending evening classes, and classes with experienced teachers. On the one hand, in columns (1) and (2), we excluded the sample of students with poor health and with highly educated parents, considering that these characteristics of the samples may interfere with the results of the baseline regressions (Chen & Zhao, 2022 ). On the other hand, the factors of best and worst schools in the county, fuller school schedules, and high-quality teachers in classroom allocations could also potentially cause bias in the total sample estimates (Huang et al., 2023 ; Zhao & Chen, 2023 ), so we also excluded samples with these factors in columns (3) to (7). Clearly, when we excluded the samples with the special factors mentioned above respectively, the estimation results obtained are basically very close to the baseline regression results. Third, we included more control variables in the baseline model that may affect student performance, including school, class, family, and student characteristics. It is important to highlight that our identification strategy is primarily based on a quasi-experiment of RSCA, and that the results of the balancing tests have demonstrated that the core explanatory variable PPD is not directly correlated with most of the class-level predetermined variables, i.e., PPD is random and independent. Thus, in the main specifications, we controlled for some variables at the classroom and teacher, student, and household levels, with school FE and standard errors clustered at the class level. To capture the causal effect more accurately, we still employed the approach of adding more control variables at the school, class, family, and student levels to further assess the robustness of our findings (Chen & Zhao, 2024 ; Gong et al., 2018 ; Hu, 2018 ). The descriptive statistics of these control variables are represented in Table A11 in the Appendix . In Table A12 , on the basis of the main specification, we added these additional control variables at the school, and class, family, and student levels in columns (1) to (3), respectively, and controlled all these variables in column (4). The results in each column are generally consistent with the baseline regression in terms of estimated coefficients and significance of PPD , confirming that our previous findings are reliable. Third, we conducted placebo tests using the observed students’ academic performance in sixth grade in primary school (Hu, 2018 ; Huang et al., 2021 ). The CEPS questionnaire investigated students’ subjective perceived difficulty in learning Chinese, Math, and English when they were in sixth grade, which can be used to measure students’ academic performance prior to RSCA (Chen & Zhao, 2022 ). As reported in Appendix Table A13, the placebo tests showed no association between PPD in students’ current classes and their academic performance in 6th grade, which indirectly indicates the robustness of our baseline estimation results. 4.4. Mechanisms The main results confirm the negative spillover effect of PPD on student academic achievements. In this subsection, we explored the potential mechanisms of this undesirable spillover effects at the student, teacher, and parent levels as highlighted earlier, specifically encompassing: (i) Parental responses; (ii) Students’ expectations, attitudes and behaviors in learning; (iii) Teachers’ teaching efforts and enthusiasm. 4.4.1. Parental responses Divorced parents may have a spillover effect in the class by influencing other parents’ expectations of educational achievement and decisions related to family educational expenditure. According to the view of resource deprivation, parental divorce may be a deprivation of resources for children’s education and reduce the family human capital investment (Hoffman & Duncan, 1988 ; Sun & Li, 2009 ). Moreover, the decline in income after divorce makes it more difficult for families to weigh their children’s education expenditures against other expenditures (Conway & Li, 2012 ; Park, 2007 ). In addition, existing studies showed that parents’ educational and career expectations, and active involvement in their children’s education are important factors in influencing student academic achievements (Hao & Yeung, 2015 ; Li et al., 2020 ; Luo & Yang, 2023 ). Inevitably, parents’ attitudes toward their children’s education and their motivation to family educational expenditure influence each other in the classroom. As parental divorce becomes more prevalent among the students in the classroom, it is likely to consciously or unconsciously lower their education involvement and educational expenditure of their children. Especially in China, where many families are motivated by intra-class competition, and the amount of attention and actual investment in their children’s education depends on that of the parents of their classmates (Guo & Qu, 2022 ; Zhao & Zhao, 2022 ). Thus, high PPD may reduce the family educational expenditure and parental expectations and their involvement in children’s education, resulting in a potential negative impact on students’ academic achievements. Based on the above analysis, according to CEPS and related previous research (Wang et al., 2020 ; Wen & Lin, 2012 ; Zhao & Chen, 2022 ), a series of variables on family educational expenditure, parental expectations and educational involvement were selected, as listed in Panel A of Table A14 in the Appendix . In columns (1)-(3) of Table 3 , we can see that the coefficients on PPD is significantly positive in the latter two columns. That is, the PPD did have a negative spillover effect on parents’ career and migration expectations for their children in the future. As prior studies have already demonstrated, declining parental expectations further lead to poorer student performance (Hao & Yeung, 2015 ; Zhao & Chen, 2023 ). Thus, these results suggest that the PPD may diminish parents’ positive expectations for their children’s future, which in turn is detrimental to academic performance. Instead, in columns (4) and (5) of Table 3 , we found that the estimated coefficients on PPD are all insignificant, which means that increase in PPD did not dampen the family educational expenditure or involvement in the class, such as controlling Internet access. The potential cause is that influenced by Confucian culture, Chinese parents always emphasize their children’s investment in human capital and academic performance (Chi & Qian, 2016 ; Chen et al., 2021 ). The effect of PPD may not be sufficient to change parents’ educational expenditure decisions and educational involvement towards their children. Taken together, our results imply that from the parental responses, the negative spillover effects of PPD are mainly reflected in the psychological dimension of educational expectations. Table 3 Parental responses (1) (2) (3) (4) (5) Parental education expectations Parental career expectations Parental migration expectations Education expenditure Parental control of Internet PPD -0.0001 -0.0036** -0.0037** 0.0195 -0.0004 (0.0015) (0.0018) (0.0016) (0.0202) (0.0010) Baseline control variables Yes Yes Yes Yes Yes Father’s occupation FE Yes Yes Yes Yes Yes Mother’s occupation FE Yes Yes Yes Yes Yes School FE Yes Yes Yes Yes Yes N 4716 4888 4896 4920 4800 Notes: ***, **, * indicate significance at the levels of 1%, 5%, and 10%, respectively. Standard errors clustered at the class level are reported in parentheses. Marginal effects of Probit estimates are reported in columns (1), (2), (3) and (5). [Insert Table 3 about here] 4.4.2. Students’ expectations, attitudes, and behaviors in learning We then examined the effects of PPD on students’ expectations, attitudes, and behaviors in their learning process, as students are clearly most directly influenced by their peers. As mentioned in previous studies, parental divorce may have a direct negative impact on their children’s school performance, such as grades and cognitive and non-cognitive skills (e.g., Amato & Anthony, 2014 ; Havermans et al., 2014 ; Kim, 2011 ; Park, 2008 ; Sun & Li, 2009 ). Meanwhile, students with divorced parents show poorer performance in learning habits, self-control, and emotions (Anthony et al., 2014 ; Sands et al., 2017 ; Sigle-Rushton et al., 2005 ; Strohschein, 2005 ). These students’ poorer school performance, behaviors, and psychological states have potential peer effects other students in the classroom (e.g., Chen et al., 2023 ; Dahl et al., 2014 ; Gong et al., 2021 ; Hanushek et al., 2003 ; Salas García & Rentería, 2024 ; Zimmerman, 2003 ). Specifically, high parental divorce rate in the class is likely to imply that there are more students with poorer performance and learning habits, which in turn may have a negative modelling effect on the behaviour and psychology of other students in the class, or even directly interfere with their learning. Thus, the PPD is likely to ultimately have an adverse effect on the academic achievements of students in the class. To further validate the above mechanism, based on the CEPS questionnaire and previous literature (Huang et al., 2023 ; Wang et al., 2018 ; Zhao & Chen, 2023 ), we selected a series of variables about students’ learning attitudes, psychological expectations and learning behavior for analysis, as shown in Panel B of Table A14 . From the results in Table 4 , it is easy to see that the PPD has a combined hindering effect on student’ expectations, attitudes and behaviors in their learning. Specifically, as shown in columns (2) and (3), increased PPD significantly dampens students’ career and migration expectations, i.e., students’ desire for high-skilled occupations decreases, and aspirations to relocate to a major city in the future decrease. The decline in positive expectations inevitably leads to a lack of motivation for students to study, which is manifested in a rapid decline in academic performance in the short term (Luo & Yang, 2023 ). In addition, results in columns (4) to (6) show that an increase in PPD also increases the frequency of undesirable behaviors such as skipping classes and copying homework, as well as a decrease in students’ attitudes toward learning, all of which directly contribute to poorer academic performance (Anthony et al., 2014 ; Kalmijn, 2013 ; Zhuang et al., 2025 ). According to above results, the PPD has a negative effect on the expectations, learning attitudes and behaviors of students, which is one of the important mechanisms by which it may hinder students’ academic achievements. Table 4 Students’ expectations, attitudes and behaviors in learning (1) (2) (3) (4) (5) (6) (7) (8) Education expectations Career expectations Migration expectations Frequency of skipping classes Frequency of copying classmates’ homework Studying hard Time spent on the Internet on weekends Time for homework on weekends PPD -0.0013 -0.0026* -0.0034*** 0.0021* 0.0042* -0.0039** 0.0033 -0.0065 (0.0199) (0.0016) (0.0011) (0.0012) (0.0021) (0.0020) (0.0056) (0.0050) Baseline control variables Yes Yes Yes Yes Yes Yes Yes Yes Father’s occupation FE Yes Yes Yes Yes Yes Yes Yes Yes Mother’s occupation FE Yes Yes Yes Yes Yes Yes Yes Yes School FE Yes Yes Yes Yes Yes Yes Yes Yes N 4920 4914 4886 4876 4859 4920 4894 4911 Notes: ***, **, * indicate significance at the levels of 1%, 5%, and 10%, respectively. Standard errors clustered at the class level are reported in parentheses. Marginal effects of probit estimates are reported in columns (2), (3) and (6). [Insert Table 4 about here] 4.4.3. Teachers’ teaching efforts and enthusiasm The divorce of peers’ parents may also affect the performance of the students in the classroom by influencing the teachers’ teaching efforts and enthusiasm. A large body of literature has previously demonstrated that teachers investing more time and enthusiasm in teaching and classroom management will inevitably have a positive impact on student performance (e.g., Chen & Zhao, 2022 ; Gong et al., 2018 ; Huang et al., 2023 ; Xu & Li, 2018 ). Meanwhile, some studies have also shown that the attitudes and characteristics of students’ parents are likely to affect teachers’ work effort and enthusiasm in China (Chen et al., 2023 ; Zheng & Zhou, 2024 ). Therefore, high parental divorce rate in the classroom may also inhibit teachers’ attitudes and efforts invested in their work. For example, parental divorce leads to a decrease in parental interest in their children’s schooling 8 ; if the percentage of divorced parents is too high it may inadvertently send a signal to teachers that “the parents of many students in the class do not care enough about their students”. In this case, teachers are likely to experience less pressure from parents even if they are not performing well in their work. For these reasons, some teachers may reduce their efforts and enthusiasm in teaching and class management because the cost of underperformance is lower for classes with high parental divorce rate (Conway & Li, 2012 ). Ultimately, decreased teachers’ effort and enthusiasm leads to poorer student performance. In Table 5 , we tested the effect of PPD on teaching effects and enthusiasm, including teachers’ working time, hours for preparing lessons, hours for homework correction, teacher-student communication, sense of responsibility, and patience. These variables have been emphasized in the previous studies (Chen & Zhao, 2022 ; Gong et al., 2018 ; Zhao & Chen, 2023 ), and they are described in Panel C of Table A14 in the Appendix . The results in Table 5 indicate that although the PPD does not have a significant effect on teachers’ time spent on preparing lessons, and on their responsibility and patience with students, it has a highly significant negative effect on teachers’ working time and hours for homework correction, which is basically consistent with our previous speculation. These results suggest that the negative spillover effects of parental divorce affect teachers’ teaching efforts, which may further reduce the teaching quality. Considering that teacher efforts are closely related to student human capital accumulation (e.g., Chen & Zhao, 2024 ; Hung et al., 2023; Xu & Li, 2018 ), we further identify the third mechanism for the negative impact of PPD on students’ academic achievements at the teacher level. Table 5 Teachers’ teaching efforts and enthusiasm (1) (2) (3) (4) (5) (6) Working time Hours for preparing lessons Hours for homework correction Percentage of total working time spent on homework correction Sense of responsibility Patience PPD -0.5075*** 0.0203 -0.1648** -0.0023*** 0.0042 0.0062 (0.1663) (0.0949) (0.0789) (0.0004) (0.0038) (0.0039) Baseline control variables Yes Yes Yes Yes Yes Yes Father’s occupation FE Yes Yes Yes Yes Yes Yes Mother’s occupation FE Yes Yes Yes Yes Yes Yes School FE Yes Yes Yes Yes Yes Yes N 4828 4916 4853 4717 4877 4871 Notes: ***, **, * indicate significance at the levels of 1%, 5%, and 10%, respectively. Standard errors clustered at the class level are reported in parentheses. [Insert Table 5 about here] 4.5. Heterogeneity Considering the growing evidence that spillover effects in the classroom vary across students, families, and teachers with different characteristics (e.g., Huang et al., 2021 ; Min et al., 2019 ; Pan et al., 2022 ; Xu et al., 2022 ; Zheng & Zhou, 2024 ), we further explored the heterogeneous effects of PPD on students’ academic achievements from several perspectives: students’ place of origin, gender, only child, household economic condition, finding the spillover of PPD differ by these characteristics. First, we analyzed the spillover effect of PPD on students with different characteristics. Specifically, in columns (1) and (2) of Table 6 , we found that the negative impacts of PPD on both achievement and cognitive ability are more significant for urban students compared to rural students, and may be greater in terms of the coefficients. This result is unexpected, and we speculated that the reason for this is that the better living conditions and favourable upbringing of urban students make them more susceptible to negative external influences (Crouch et al., 2021 ). 9 In addition, the results in columns (3) and (4), we found that estimated coefficients on PPD do not differ significantly for the two groups of boys and girls in the two Panels, suggesting that gender differences in the spillover effects of parental divorce are unnoticeable. Furthermore, results in columns (5) and (6) show a more significant impact of PPD on the cognitive ability of only children. The main reason for this is also likely to be that these two groups are more vulnerable to negative influences of PPD because of their biological characteristics and family structure. Some studies have shown that only children are relatively more emotionally vulnerable and more susceptible to the negative emotions of their classmates than non-only children (Chen & Zhao, 2022 ; Kim, 2011 ). Consequently, when class PPD is high, they may be also more prone to negative emotions, hindering their performance in school. Then, in columns (7)-(9) in Table 6 , we found that the negative effects of PPD on students’ test scores and cognitive ability were significant mainly among students from ordinary and relatively wealthy families, but not for students in relative poverty. Similar to the above results, the negative spillover effects of parental divorce are more pronounced for non-vulnerable groups. Moreover, these results suggest that the impact of disadvantaged groups’ own disadvantages on students’ human capital development may be more noticeable compared to the spillover effects of their classmates. Table 6 Heterogeneity (1) (2) (3) (4) (5) (6) (7) (8) (9) Rural Urban Girl Boy Only child Non-only child Relative poverty Ordinary Relatively wealthy Panel A. Average score PPD -0.1647 -0.5139*** -0.2411** -0.3198** -0.3735** -0.2657** -0.0063 -0.3745*** -0.4080 (0.1196) (0.1577) (0.1036) (0.1536) (0.1466) (0.1331) (0.1788) (0.1259) (0.2774) Panel B. Cognitive ability PPD -0.0045 -0.0132** -0.0089** -0.0085 -0.0142*** -0.0075 0.0098 -0.0137*** -0.0321*** (0.0056) (0.0059) (0.0042) (0.0062) (0.0051) (0.0062) (0.0078) (0.0052) (0.0096) Baseline control variables Yes Yes Yes Yes Yes Yes Yes Yes Yes Father’s occupation FE Yes Yes Yes Yes Yes Yes Yes Yes Yes Mother’s occupation FE Yes Yes Yes Yes Yes Yes Yes Yes Yes School FE Yes Yes Yes Yes Yes Yes Yes Yes Yes N 2616 2304 2387 2533 1966 2954 1092 3475 353 Notes: ***, **, * indicate significance at the levels of 1%, 5%, and 10%, respectively. Standard errors clustered at the class level are reported in parentheses. [Insert Table 6 about here] 5. Further exploration 5.1. Mitigating effects of supports from teachers, parents, and friends In above results, we confirmed that parental divorce has a negative spillover effect on other students in the classroom. Therefore, how to mitigate the effects of PPD should be emphasized by education authorities and parents. In this subsection, we explored feasible measures to mitigate the negative effects of PPD, focusing on supports from teachers, parents, and friends. As highlighted in the prior literature, supports from school and parents may increase students’ self-confidence and focus, which help improve students’ academic achievements (Dietrich et al., 2015 ; Hu & Wu, 2020 ). Specifically, we examined whether their supports could mitigate the negative spillovers of PPD by constructing some interaction terms. The definitions and descriptive statistics of these variables are detailed in Appendix Table A15 and the results are shown in Table A16 in the Appendix . In terms of teachers’ supports, we found that homeroom teachers who also serve in an administrative position do a much better job of mitigating the negative spillover effects of PPD in their classes in column (1). This may be attributed to the fact that these teachers have stronger managerial and non-cognitive abilities to provide more psychological support to their students, and that the administrative roles reinforce their effectiveness in the classroom management. For instance, students may respect and follow their guidance and management more (Chen & Zhao, 2024 ). Moreover, in columns (2) and (3), we found that after school, teachers spending more time communicating with students and parents could also be effective in mitigating negative spillovers from PPD. Furthermore, in columns (4) to (9), we examined the effectiveness of parents’ supports can provide to their children in mitigating the negative effects of PPD. First, according to the results in columns (4) to (5), we found that only parental concern for students’ friendships is effective in attenuating the negative effects of excessive PPD in the class, whereas parental concern for students’ learning has a very limited effect. Meanwhile, the results in columns (6)-(9) suggest differences in the role parents may play in mitigating the negative spillover effects of PPD. For fathers, being more attentive to their children’s worries and difficulties can effectively attenuate the negative impacts from PPD, but spending more time caring about their children’s relationships with classmates is not. Differently, mothers who were more concerned about their children’s relationships with classmates were effective in mitigating the negative effects of PPD (Chen et al., 2023 ), but less effective by caring about their students’ worries and difficulties (Flouri, 2006 ). This difference may be attributed mainly to the different roles in the family. Particularly in China, fathers tend to play a decision-making and problem-solving role in the family, while mothers are usually more concerned about their children’s emotional problems and social relationships (Francesconi et al., 2010 ; Sun & Li, 2009 ). Last, the result in column (10) shows that the coefficient of the interaction term is significantly positive, indicating thathaving a larger number of friends similarly helps to mitigate the negative spillovers from PPD, which implies the importance of good friendships in mitigating these negative spillovers. In conclusion, some supports from teachers, parents and friends may be effective in mitigating the negative spillover effects from PPD. 5.2. Reverse spillovers on students with divorced parents In addition to the spillover effect of PPD on student academic achievements, we are also interested in whether students from intact families have reverse spillover effects on students with divorced parents. As discussed in previous studies, peer spillover effects are often not one-dimensional (Yin et al., 2020 ; Zheng & Zhou, 2024 ). We constructed a variable to measure this reverse spillover effect, measured by the proportion of parents not divorced in the class. As reported in Appendix Table A17, we observed that the estimated coefficients are positive in all columns and significant in columns (1), (3), and (5). Despite the large drop in sample size, we still obtained the conclusion that students whose parents are not divorced may have a positive spillover effect on the academic achievements of students with divorced parents, especially in math scores and cognitive skills. Thus, we further confirmed the bidirectional spillover effects of parental divorce from the level of student academic performances and reinforced the idea of negative spillovers from PPD. 5.3. Effects on some special disadvantaged students In this subsection, we further focused on the spillover effects of PPD on two special disadvantaged groups of children in China, including migrant children and left-behind children. 10 In recent years, all sectors of society pay close attention to the status of the human capital of these special children (e.g., Hu & Wu. 2018; Zhang & Zhou, 2024; Zhao & Chen, 2022 ; Zhao et al., 2024 ). In Table A18 in the Appendix , we explored the spillover effects of PPD on migrant children and left-behind children, finding that PPD significantly inhibits the academic performance of left-behind children, but has a very limited impact on migrant children. An important reason for this may be that left-behind children are separated from their parents and are more emotionally vulnerable to negative spillovers such as parental divorce (Zhang & Zhou, 2024; Zhao & Chen, 2022 ). 6. Conclusions and discussion Although considerable attention was paid to the adverse effect of parental divorce on children human capital development, there is little literature on whether this negative impact extends beyond the inter-family and spills over to children’s peers. To determine the causal effect of PPD on students’ school performance in the class, we employed a quasi-natural experiment with SCRA as an identification strategy. Balanced tests and a series of robustness checks provide supportive evidence for our empirical framework. Our conclusions are summarized below. First, we found a negative causal effect of the PPD on students’ academic achievements, confirming the spillover effects of parental divorce. Specifically, for each standard deviation increase in PPD (%), students’ average score and cognitive ability decreased by 0.0790 and 0.0543 standard deviations, respectively. However, the PPD did not significantly affect students’ non-cognitive abilities. Second, the mechanism analysis showed that this negative spillover effect of divorced parents may be explained in three ways: parents, students, and teachers. Our estimates suggest that the PPD led to a decline in parental expectations, the development of negative expectations and learning behaviors among students, and a drop in teachers’ efforts and enthusiasm, which is further detrimental to students’ academic achievements. Third, heterogeneity effect results revealed negative spillovers of PPD mainly among some relatively advantaged students, such as urban students, only children, and students from non-poor families. Further studies indicated that supports from teachers, parents, and friends may mitigate the negative spillover effects of PPD. We revealed a reverse positive spillovers of parental non-divorced on students with divorced parents in the classroom. More seriously, the human capital of left-behind children may also be negatively shocked by this spillover effect. Our study has some theoretical insights. First, in the debate over whether parental divorce reduces children’s human capital accumulation, our results are more supportive of the idea of a negative effect based on the Chinese case. In the short run, parental divorce is not only significantly detrimental to children’s academic performance (Havermans et al., 2014 ; Park, 2008 ; Sun & Li, 2009 ), but also spills over this negative effect to other students in the same class. Thus, the negative effects of parental divorce are not limited to the intra-family level, but may have broader societal implications. Second, we provided new evidence on the classic research topic of educational peer effects from the special perspective of parental divorce. Starting from the dimensions of family background and parental characteristics, existing literature mainly explored peer effects from family education expenditures and parental resources (Chen et al., 2023 ; Pan et al., 2022 ). We offered additional insights in terms of parental marital stability and family structure. In terms of policy implications, this study reveals some measures to mitigate the negative spillover effects of PPD. Therefore, there is a great need to further strengthen the school, family, and peer supportive environments, especially at the school level. Potential measures include strengthening home-school ties, enhancing teacher-student interactions, and paying special attention to students with divorced parents. In addition, the negative spillover effects of PPD are detrimental to the human capital accumulation of some disadvantaged groups, such as the left-behind children. Thus, to further alleviate educational inequality, it is important to provide them with more support to easily reduce the negative effects of PPD, such as creating a good classroom culture and avoiding discrimination in schools. Currently, divorce has become commonplace in most countries. The impact of divorce on children’s human capital is not confined to the family, but the social cost of divorce requires the attention of society as a whole. How to minimize the negative impact of divorce on the accumulation of human capital requires the attention of the public sector, educational institutions and families in general. Some limitations remain to be addressed in future studies. First, since the CEPS only provides a cross-section of data on parental divorce, we are unable to explore the dynamic impact of the spillover effect of PPD. Also, we cannot capture the heterogeneous effects of PPD on students’ school performance at different school-age stages, such as primary or high school. Second, some mechanisms may not have been adequately tested. For example, at the teacher level, the PPD affect teachers’ classroom management effectiveness to the indirect detriment of student school performance, but there are no appropriate variables to capture this mechanism in the CEPS. In addition, mechanisms at the classroom and school levels need to be added in further studies. Third, owing to the lack of more information on parental divorce, such as parental arguments and negative behaviours, children’s residency status after parental divorce, and the length of the divorce. As a result, it is difficult to capture the differential impact of different types of PPD on student achievement. Last, variables on support of parents, teachers, and friends may not be exogenous, so these measures to mitigate the negative effects of peer parent divorce are merely suggestive. In the follow-up research, it would be interesting to further analyze the multifaceted spillover effects of PPD on human capital by designing a set of questionnaires specialized in information on divorced families and children. Declarations Author Contribution Chen and Zhao wrote the main manuscript text; Zhao prepared figures 1-2; Liu prepared the Appendix; Chen prepared the tables 1-6. All authors reviewed the manuscript. Data availability: The data that support the findings of this study are available from National Survey Research Center (NSRC) at Renmin University of China, but restrictions apply to the availability of these data, which were used under licence for the current study and so are not publicly available. The data are, however, available from the authors upon reasonable request and with the permission of National Survey Research Center (NSRC) at Renmin University of China. References Albert, A. (2018). Parental duties, labor market behavior, and single fatherhood in America. Review of Economics of the Household, 16 (4), 1063-1083. Amato, P. R., & Anthony, C. J. (2014). Estimating the effects of parental divorce and death with fixed effects models. Journal of Marriage and Family, 76 (2), 370-386. Amato, P. R., & Cheadle, J. E. (2008). Parental divorce, marital conflict and children’s behavior problems: A comparison of adopted and biological children. Social Forces, 86 (3), 1139-1161. 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School nutritious feeding and cognitive abilities of students in poverty: Evidence from the nutrition improvement program in China. Children and Youth Services Review, 159 , 107519. Zhao, L., & Zhao, Z. (2021). Disruptive peers in the classroom and students’ academic outcomes: Evidence and mechanisms. Labour Economics, 68 , 101954. Zhao, N., Liao, W., Xia, J., & Zhang, Z. (2023). The effect of intergenerational mobility on family education investment: Evidence from China. Humanities and Social Sciences Communications, 10 (1), 1-12. Zheng, X., & Zhou, Y. (2024). Are migrants a threat? Migrant children and human capital investments among local households in urban China. Humanities and Social Sciences Communications, 11 (1), 1-14. Zhou, W., & Hill, A. J. (2023). The spillover effects of parental verbal conflict on classmates’ cognitive and noncognitive outcomes. Economic Inquiry, 61 (2), 342-363. Zhuang, J., Ng, J. C., & Wu, Q. (2025). The role of parent-child communication on Chinese rural left-behind children’s educational expectation: A moderated mediation analysis. Humanities and Social Sciences Communications, 12 (1), 1-11. Zimmerman, D. J. (2003). Peer effects in academic outcomes: Evidence from a natural experiment. Review of Economics and Statistics, 85 (1), 9-23. Footnotes Data source: https://www.mca.gov.cn/images3/www2017/file/202009/1601261242921.pdf . CEPS examined the cognitive abilities of the interviewed students by organizing a uniform cognitive ability test and standardizing that score. In the CEPS, principals are asked about the school's rules for assigning students to classes in the following categories: (1) Placement exams prior to the beginning of students' first academic year; (2) Students’ residential status; (3) Random student-classroom assignment; (4) Others. CEPS classifies parental occupations into 14 categories, including: (1) Government officials; (2) Senior managers in institutions or enterprises; (3) Professional staff, e.g. scientists, engineers, university teachers; (4) Doctors, lawyers, primary and secondary school teachers; (5) Technical staff, e.g. accountants, nurses, software programmers, etc.; (6) Clerical staff, e.g. secretaries, bank tellers, librarians, etc.; (7) Commercial and service workers, e.g. salespersons, agents, cooks, barbers, beauticians, etc.; (8) Skilled workers, e.g. drivers, plumbers, electricians, mechanics, etc.; (9) General workers, e.g. porters, production line workers, etc.; (10) Farmers, herders, fishermen; (11) Elementary laborers, e.g. cleaning, security, nanny, sanitation, etc.; (12) Individual businessmen; (13) Retired, jobless, unemployed, laid off; (14) Others. In the baseline regression, we primarily tested the effects of PPD on students' academic performances and cognitive ability (significant). We also examined the effect on students' non-cognitive abilities (not significant), and the descriptive statistics and regression results are detailed in the Appendix . The variable PPD expands 100 times in the main specification, so the actual standard deviation for peer parental divorce in class should shrink 100 times to 0.0514. In Table 3 , we reported results only for the core variables in the baseline regression. The complete results containing the estimates for the control variables of the baseline regressions are presented in Table A5 in the Appendix . As previously verified in Table A3 in the Appendix , parental divorce is significantly and negatively associated with decreased parental educational expectations, parental guidance of student homework, and controlling for the time students spend online. Each standard deviation increase in PPD reduces the average score of rural students by 0.0556 standard deviations, and the average score of urban students by 0.1343 standard deviations. All analyses of heterogeneity will calculate and consider the change in standard deviation as a reference based on the statistical characteristics of the different groups. Migrant children are children who live and go to school with their parents in other cities (outside their home towns). Left-behind children are children whose parents have gone out to work for a long period of time and who stay in their hometown to attend school and live there. Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5797362","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":405151061,"identity":"5070738f-9ec8-4f1a-bfe4-865d5a5a39dd","order_by":0,"name":"Boou Chen","email":"","orcid":"","institution":"Nanjing University of Finance and Economics","correspondingAuthor":false,"prefix":"","firstName":"Boou","middleName":"","lastName":"Chen","suffix":""},{"id":405151062,"identity":"eeab2e5c-20cd-4321-a1c1-f326cf67cca2","order_by":1,"name":"Chunkai Zhao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvUlEQVRIiWNgGAWjYDACHiBmbGBg4GdmPvyANC2S7WxpBqRpMTjPoyBBlA7+nuMPGH/usJMzPszDYMBQYxNNUIvE2YYEBskzycZmh3kPPGA4lpbbQEiLAT/DAQbDNubEbYf5EgwYGw4TowXokcS2+sTNzTwGEsRp4W1mYDjYdjhxAzOxWiTOHGNgbGw7bixxGBjICcT4hb8nHRhibdVy/P2HDz/4UGNDWAsQsP+AMxOIUD4KRsEoGAWjgAgAACEqOglM6VZFAAAAAElFTkSuQmCC","orcid":"","institution":"South China Agricultural University","correspondingAuthor":true,"prefix":"","firstName":"Chunkai","middleName":"","lastName":"Zhao","suffix":""},{"id":405151063,"identity":"17be2636-35da-4f57-b8e7-2089c174fe92","order_by":2,"name":"Xiaoyu Liu","email":"","orcid":"","institution":"Shanghai University of Finance and Economics","correspondingAuthor":false,"prefix":"","firstName":"Xiaoyu","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2025-01-09 14:38:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5797362/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5797362/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":74587107,"identity":"b70dd125-fea9-455a-b8d9-bc2024370968","added_by":"auto","created_at":"2025-01-23 16:54:21","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":33240,"visible":true,"origin":"","legend":"\u003cp\u003eThe divorce rate in China 1978-2019 (‰)\u003c/p\u003e\n\u003cp\u003eData source: China Statistical Yearbooks\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5797362/v1/0d3abadd77639f156793bd9b.png"},{"id":74587108,"identity":"586912fd-e649-4fb7-abfc-4ca69be3799f","added_by":"auto","created_at":"2025-01-23 16:54:21","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":49977,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of PPD distributions for school FE with and without controls (classes with RSCA, N=204)\u003c/p\u003e\n\u003cp\u003e(a). Distribution of PPD\u003c/p\u003e\n\u003cp\u003eNote: The standard deviation of PPD is 6.8521.\u003c/p\u003e\n\u003cp\u003e(b). Distribution of the residuals of PPD controlling for the school FE\u003c/p\u003e\n\u003cp\u003eNote: The standard deviation of the residuals is 5.5870.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5797362/v1/9059de4646ec2acf8dd5f1c4.png"},{"id":74588214,"identity":"a56b54e5-fbfc-4f1a-8557-f74a4b32a1e0","added_by":"auto","created_at":"2025-01-23 17:10:23","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1612681,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5797362/v1/6eaa2cf0-812a-4cdd-af66-3e93c6c68555.pdf"},{"id":74585999,"identity":"8704667a-e44e-44fc-9f1b-dddb1a164b46","added_by":"auto","created_at":"2025-01-23 16:46:21","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":62008,"visible":true,"origin":"","legend":"","description":"","filename":"Appendix.docx","url":"https://assets-eu.researchsquare.com/files/rs-5797362/v1/294ea1e46a33b0bf2086f394.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Spillover effects from the divorce of peer parents: Evidence from student academic achievements in China","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIn recent years, the persistently high divorce rate has attracted widespread attention throughout society. In China, the divorce rate has continued to rise since 1978. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, China\u0026rsquo;s divorce rate at 3.36\u0026permil; in 2019, which is 3.5 times higher than in 2000 and 18.7 times higher than in 1978. According to the 2019 Statistical Bulletin on the Development of Civil Administration, the number of marriages fell by 8.5% year-on-year, while divorces increased by 5.4% over the previous year.\u003csup\u003e1\u003c/sup\u003e Divorce is not only a break in the relationship between husband and wife, but also implies a change in the family relations constituted by the blood parent-child relationship (Bernardi \u0026amp; Radl, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Zhuang et al., \u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), especially in the context of a traditional family culture like China (Sun \u0026amp; Li, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Zhang, \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). As more and more children live in non-intact families, such changes have profound impacts, with multiple consequences for children (Amato \u0026amp; Anthony, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Corak, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Kim, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e[Insert Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e about here]\u003c/p\u003e \u003cp\u003eThe negative effect of parental divorce on children development has received considerable scholarly attention. From the perspective of marital functioning and resource deprivation, prior research emphasized the adverse effect of parental divorce on children\u0026rsquo;s upbringing. Scholars provided evidence that divorce leads to the deterioration of the family\u0026rsquo;s economic situation (e.g., Albert, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Hoffman \u0026amp; Duncan, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e1988\u003c/span\u003e; Sun \u0026amp; Li, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2009\u003c/span\u003e), the destruction of the family structure (e.g., Conway \u0026amp; Li, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; McLanahan, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e1985\u003c/span\u003e; Park, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2007\u003c/span\u003e), and the intensification of emotional conflicts (Amato \u0026amp; Cheadle, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Kalmijn, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), which further negatively affects the children. Specifically, scholars concluded that parental divorce led to poor psychological development, deviant behaviors, moodiness, and weakened interpersonal skills (e.g., Anthony et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; C\u0026aacute;ceres-Delpiano \u0026amp; Giolito, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Kim, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Hu, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Park, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). More seriously, a number of studies pointed out compared to children from intact families, those from divorced families had worse school performance (Frimmel et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Havermans et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Park, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Sun \u0026amp; Li, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2009\u003c/span\u003e), lower cognitive and non-cognitive skills (Amato \u0026amp; Anthony, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Kim, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2011\u003c/span\u003e), and poorer self-control and learning habits (Anthony et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Sigle-Rushton et al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). In this paper, we were more concerned about whether this negative impact would have further spillover effects along the children\u0026rsquo;s peers in the classroom? To our knowledge, this spillover has not yet received the theoretical and empirical attentions.\u003c/p\u003e \u003cp\u003eWe explored the causal effect of marital stability on human capital accumulation in the Chinese social context by taking the spillover effect of peer parental divorce (PPD) as an example. Specifically, we considered that students in classes with a higher proportion of divorced parents are subject to more negative spillover effects, which then translate into significant disadvantages in academic achievement and cognitive ability. However, PPD and the class in which a student is enrolled may not be random, which may lead to serious endogeneity problems in our estimates. For example, if students with lower initial academic performance are assigned to the same class, these students are more likely to come from homes where parents are divorced, due to the negative effect of parental divorce on students\u0026rsquo; achievement (Havermans et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Sun \u0026amp; Li, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). In this context, even in the absence of spillovers from PPD, the empirical results would exhibit a negative correlation between the proportion of divorced parents and student performance in the classroom.\u003c/p\u003e \u003cp\u003eFortunately, the China Education Panel Survey (CEPS) provides us with a good quasi-experiment, the random student-classroom assignment (RSCA). In recent years, to maintain equity in education, many local governments in China have required that classes in compulsory education be randomly assigned by computer and that transfers be strictly limited after the classes have been determined. Also, this approach has been widely used in causal inference studies to confirm the peer effects (e.g., Chen \u0026amp; Zhao, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Gong et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Hu, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Huang \u0026amp; Zhu, 2010; Xu et al., \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Based on the sample of RSCA in CEPS database, we found that in the classes with a high percentage of divorced parents, students from non-divorced families performed worse academically. which confirms the negative peer effect of parental divorce. Specifically, for each percentage point increase in the proportion of divorced parents in a class, students\u0026rsquo; average test scores and cognitive ability scores decreased by an average of 0.2998 and 0.0087 points, equivalent to 0.0790 and 0.0543 standard deviations, respectively.\u003c/p\u003e \u003cp\u003eTo ensure that our findings are reliable, a series of robustness checks are conducted in this study. First, the generation process of the core explanatory variable from the RSCA is not systematically disturbed by omitted variables, which is the key to the validity of our causal identifications (Chen \u0026amp; Zhao, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Gong et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Hu, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). We overcame this bias by using balancing tests (Chen \u0026amp; Zhao, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Gong et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Xu et al., \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), which showed that given a school with the RSCA, PPD is insignificantly correlated with a range of predetermined variables related to class characteristics, family characteristics, and student characteristics. These results suggest that the RSCA process is unlikely to be subject to human intervention and can be viewed as a quasi-experiment. Second, divorced parents may have negative spillover effects on children through multiple channels. To separate the spillover effects of parental divorce from those of other parental characteristics, in addition to controlling for parental education and parental occupational FE, we further considered a series of other spillover effects, such as parental human capital, unemployment, political capital, and migration, which have been mentioned in the previous literature (e.g., Chen et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Dickson et al, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Fruehwirth \u0026amp; Gagete-Miranda, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Salas Garc\u0026iacute;a \u0026amp; Renter\u0026iacute;a, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Yin et al., \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Zheng \u0026amp; Zhou, \u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Third, other robustness tests such as placebo tests, tighter controls, and exclusion of special observations similarly support our main results.\u003c/p\u003e \u003cp\u003eWe were also quite interested in the mechanisms by which negative spillovers from parental divorce arise. First, at the family and parental level, divorce may worsen the family economic situation and reduce parental attention to their children\u0026rsquo;s learning (Albert, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Smock et al., \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). This may lead to a decline in the family educational expenditures and lower educational expectations (Astone \u0026amp; McLanahan, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1991\u003c/span\u003e; Park, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). These trends may also affect other parents in the same class. Second, in terms of children, parental divorce may be detrimental to the shaping of positive attitudes and learning behaviors (Hu, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Sun \u0026amp; Li, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2009\u003c/span\u003e), due to the psychological shock of parental divorce and the reduction of parental supervision. Other students in the class may also be affected by this negative peer effect. Third, from the perspective teachers, divorced parents may reduce teachers\u0026rsquo; enthusiasm for teaching and are less likely to provide public goods to the class (Conway \u0026amp; Li, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), which may also have a negative effect on students\u0026rsquo; school performance. Thus, the mechanisms of spillover effects of PPD should be understood at three levels: families and parents, students, and teachers.\u003c/p\u003e \u003cp\u003eOur study contributes to the existing literature in at least three ways. First, while a considerable body of literature recognized the negative short- and long-term effects of parental divorce on children human capital accumulation, some scholars argued that the impact of parental divorce on children development is limited (Brand et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Francesconi et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Manski et al., \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e1992\u003c/span\u003e). They argued that since parental divorce implies a reduction in parental arguments and conflicts, this in turn may reduce negative psychological shocks on children (Amato \u0026amp; Anthony, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Zhang, \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). This research conflict may stem from differences in research perspectives and identification strategies. Unlike western countries, China is deeply influenced by traditional family values and the family plays a rather important role in child human capital development (Wen \u0026amp; Lin, \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Tang \u0026amp; Zhao, \u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Moreover, using the special quasi-natural experiment of RSCA, we highlighted the negative effect of parental divorce on academic performance in China. Thus, we provided new evidence for the view that parental divorce is detrimental to children\u0026rsquo;s human capital. Additionally, we offered a potential measure for mitigating this negative peer effect from the particular perspectives of teacher, parent, and friend supports.\u003c/p\u003e \u003cp\u003eSecond, from the particular perspective of parental divorce, we provided additional supportive evidence for classroom peer effects. Peer effects have been a hot topic since the seminal study from Manski (\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e1993\u003c/span\u003e). Subsequently, a considerable number of studies found that individual human capital development is greatly influenced by peer behaviors, characteristics, and family background (e.g., Dahl et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Falk \u0026amp; Ichino, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Hanushek et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Gong et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Zimmerman, \u003cspan citationid=\"CR84\" class=\"CitationRef\"\u003e2003\u003c/span\u003e). Based on the Chinese context, some attention was also paid to the positive or negative spillover effects of classmates\u0026rsquo; gender (Gong et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Luo \u0026amp; Yang, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), cognitive ability (Huang \u0026amp; Zhu, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Xu et al., \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), migration (Hu, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Min et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), disability (Huang et al., 2022), and family expenditure on education (Chen et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Pan et al., \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) on students\u0026rsquo; academic performance. Although scholars noted how family background affects other students in the same class through their children\u0026rsquo;s social networks, a key element of parental divorce has not yet been mentioned in the literature. Importantly, we further aimed to uncover the mechanisms of parental divorce peer effects, which are not only manifested in both families and children, but may also have a negative impact on teachers\u0026rsquo; efforts. Thus, our exploration provides insights for subsequent related studies.\u003c/p\u003e \u003cp\u003eThird, we further strengthened the academic understanding of the intergenerational effects of human capital. Prior literature on how parents affect their children\u0026rsquo;s human capital accumulation has been framed primarily in terms of parental resources (e.g., human, social, physical, and political capital), recognizing that resources possessed by parents are likely to be passed on intergenerationally to their children (Amato \u0026amp; Anthony, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Chen et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Dickson et al, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Sun \u0026amp; Li, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2009\u003c/span\u003e), which further contributes to the accumulation of human capital in their children (e.g., Behrman \u0026amp; Rosenzweig, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Black et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Guryan et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Giannola, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Taubman, \u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e1989\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). We offered evidence from the perspective of parental marital stability and family structure. Importantly, we revealed that this negative effect on human capital may also have a spillover effect through the children\u0026rsquo;s social networks, leading to a shock in the academic performance of their classmates. This means that the adverse effects of parental divorce extend beyond the intra-family transmission characteristic and have the potential for further winder social impacts.\u003c/p\u003e"},{"header":"2. Data and variables","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Data\u003c/h2\u003e \u003cp\u003eThe data for this study is from the CEPS in the 2014\u0026ndash;2015 academic year, a nationally representative micro-survey of middle school students in China. Based on a multistage stratified probability-proportional-to-size (PPS) sampling, the CEPS randomly selected about 20,000 secondary school students in 7th and 9th grades from 112 schools and 438 classes in the 2013\u0026ndash;2014 academic year (baseline wave), and the follow-up survey in 2014\u0026ndash;2015 academic year (the second wave) tracked the 10,750 students in the 8th grade (original 7th grade in the baseline wave). It is is a high-quality survey on secondary education, and its questionnaire contains a great deal of information on the characteristics of schools, students and their parents and family, and teachers and classes. Currently, the CEPS has been widely used in research on the economics of education, education, and adolescent development (e.g., Chen \u0026amp; Zhao, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Gong et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Hu, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Huang \u0026amp; Zhu, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Luo \u0026amp; Yang, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zhao et al., \u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eMore importantly, the CEPS contains the variables and information needed for our study. Specifically, information about whether the parents of the students interviewed were divorced was collected in the CEPS for the 2014\u0026ndash;2015 academic year, which allowed us to identify the spillover effects of PPD in the class. Meanwhile, the survey also collected students\u0026rsquo; scores on mid-term exams, including the three main subjects of Chinese, Math, and English, which can be used to measure students\u0026rsquo; academic achievement. Moreover, the CEPS contains students\u0026rsquo; cognitive ability scores,\u003csup\u003e2\u003c/sup\u003e as well as a series of questions that measure non-cognitive abilities (Chen \u0026amp; Zhao, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Zhao \u0026amp; Chen, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), helping us to examine the spillover effects of PPD from multiple perspectives.\u003c/p\u003e \u003cp\u003eIt is important to highlight that CEPS also investigated class assignment rules in different schools, i.e., whether students were randomly assigned to classes or whether they were assigned based on student scores or some other rules.\u003csup\u003e3\u003c/sup\u003e Reference to existing studies (Chen \u0026amp; Zhao, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Gong et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Huang \u0026amp; Zhu, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), we retained only the sample of students in schools with RSCA, and used it as a quasi-experiment to identify causal relationships between PPD and student outcomes. Finally, the sample used in the analysis consisted of 5,274 students from 204 classes in 79 middle schools, including 354 students whose parents were divorced and 4,920 students from intact families. It should be emphasized that we use the sample of students from intact families (4,920) in the baseline regressions, as we aimed to examine the spillover effects of PPD (Angrist, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Variables and summary statistics\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Table \u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003eA1\u003c/span\u003e in the \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eappendix\u003c/span\u003e report the definitions and summary statistics of the variables in the econometric models. In Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, Panel A shows a series of variables describing students\u0026rsquo; academic achievements, mainly including students\u0026rsquo; scores on the midterm exams of the three main courses, Chinese, Math, and English, the average score of the three main courses, and their cognitive ability scores (Gong et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Salas Garc\u0026iacute;a \u0026amp; Renter\u0026iacute;a, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Zhao \u0026amp; Chen, \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zhao et al., \u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). For comparative analysis, the scores for the three main courses were standardized on a scale ranging from 0-100 points. Among the students surveyed, the mean of the average score in the three main courses was 63.68, and the mean of the standardized cognitive ability scores was 0.277. Panel B reports descriptive statistics of the core explanatory variables. First, according to the information related to parents\u0026rsquo; marital status in the questionnaire, we constructed a dummy \u003cem\u003eParental divorce\u003c/em\u003e, which was assigned to 1 if students\u0026rsquo; parents were divorced, and 0 otherwise. According to the statistical results, the percentage of students in the sample whose parents are divorced is about 6.7%. Second, in line with previous studies (e.g., Gong et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Guo et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Hu, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Huang \u0026amp; Zhu, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Luo \u0026amp; Yang, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), we further calculated the percentage of students in the class whose parents are divorced, the core explanatory variable \u003cem\u003ePPD\u003c/em\u003e, to examine the spillover effects of peer parental divorce.\u003c/p\u003e \u003cp\u003eIn terms of baseline control variables, we controlled for a range of characteristics of students, families and parents, and teachers. Specifically, see Panel C in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, where we considered students\u0026rsquo; gender, age, \u003cem\u003ehukou\u003c/em\u003e status, and only child. We also controlled for various characteristics of families and parents that may influence student performance in Panel D, including family economic status (self-rated), parents\u0026rsquo; education, and government education subsidies (Gong et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Hu, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). It is important to highlight that parental occupation may also have an impact on their marital status child academic performance (Hill, 1979), so we simultaneously include fixed effects (FEs) for father\u0026rsquo;s and mother\u0026rsquo;s occupation in our main specification based on the CEPS questionnaire.\u003csup\u003e4\u003c/sup\u003e More importantly, teacher characteristics and teacher quality are also important factors in students\u0026rsquo; school performance (Chen \u0026amp; Zhao, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), so we controlled for the gender, education, and years of teaching experience of the homeroom teacher. Additionally, we controlled for the characteristics of the curriculum teacher, when examining students\u0026rsquo; performance in a particular course. Teacher characteristics are detailed in Panel E.\u003c/p\u003e \n\u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary statistics\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eFull sample\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003eStudents with divorced parents\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003eStudents from intact families (Sample for baseline regression)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eS.D.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eS.D.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eS.D.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePanel A.\u003c/b\u003e Student performances\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage score\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e63.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e19.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e59.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e20.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e64.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e19.13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eChinese score\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e68.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e15.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e65.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e17.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e68.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e14.94\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMath score\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e62.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e25.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e55.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e26.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e63.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e25.83\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnglish score\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e60.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e23.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e56.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e23.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e60.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e23.62\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCognitive ability\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.277\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.816\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.142\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.905\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.808\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePanel B.\u003c/b\u003e Parental divorce and divorce rate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParental divorce\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.067\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.250\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e--\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e--\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e--\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e--\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePPD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.364\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e--\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e--\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e7.106\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e5.044\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePanel C.\u003c/b\u003e Student characteristics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGender of student\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.510\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.438\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.497\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.515\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge of student\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e14.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.699\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e14.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.717\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e14.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.697\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHukou\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.526\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.499\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.449\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.498\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.532\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.499\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOnly child\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.410\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.492\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.551\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.498\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.490\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePanel D.\u003c/b\u003e Family and parental characteristics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSelf-rated wealth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.055\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.228\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.202\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.0559\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.230\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEducation of father\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.861\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e10.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.906\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e9.987\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e2.857\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEducation of mother\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9.437\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.217\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e9.774\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.231\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e9.413\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e3.215\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGovernment subsidy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.684\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.465\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.684\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.466\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.684\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.465\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePanel E.\u003c/b\u003e Teacher characteristics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGender of homeroom teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.307\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.461\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.285\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.452\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.308\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.462\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGender of Chinese teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.280\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.449\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e339\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.221\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.416\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4682\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.284\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.451\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGender of Math teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4989\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.397\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.489\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e335\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.409\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.492\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4654\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.396\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.489\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGender of English teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4952\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.167\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.373\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e331\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.169\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.376\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4621\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.167\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.373\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEducation of homeroom teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e15.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.444\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e15.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.486\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e15.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.441\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEducation of Chinese teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e15.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.657\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e339\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e15.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.811\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4682\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e15.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.644\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEducation of Math teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e15.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.566\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e337\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e15.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.497\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4678\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e15.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.571\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEducation of English teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4952\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e15.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.561\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e331\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e15.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.640\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4621\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e15.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.555\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTeaching experience of homeroom teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e16.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.277\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e17.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e8.522\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e16.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e8.259\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTeaching experience of Chinese teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e17.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.214\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e339\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e16.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e8.227\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4673\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e17.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e8.211\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTeaching experience of Math teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4983\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e18.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.806\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e336\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e19.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e8.228\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4647\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e18.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e8.841\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTeaching experience of English teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4819\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e17.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e9.772\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e319\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e17.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e10.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e17.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e9.739\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e\n\u003cp\u003e[Insert Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e about here]\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Empirical strategy","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Empirical model\u003c/h2\u003e \u003cp\u003eBase on the framework of a quasi-experiment with RSCA, we constructed the following econometric model to identify the causal effects of PPD on student academic performance:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{SP}_{ics}=\\alpha\\:+\\beta\\:{PPD}_{cs}+{Z}_{ics}^{{\\prime\\:}}\\gamma\\:+{\\delta\\:}_{s}+{\\epsilon\\:}_{ics}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{SP}_{ics}\\)\u003c/span\u003e\u003c/span\u003e measures the academic achievements for student \u003cem\u003ei\u003c/em\u003e in class \u003cem\u003ec\u003c/em\u003e of school \u003cem\u003es\u003c/em\u003e, which is examined across multiple dimensions, including test scores, cognitive ability, and non-cognitive abilities.\u003csup\u003e5\u003c/sup\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{PPD}_{cs}\\)\u003c/span\u003e\u003c/span\u003e denotes the percentage of students whose parents are divorced (%) in class \u003cem\u003ec\u003c/em\u003e of school \u003cem\u003es\u003c/em\u003e, the core explanatory variable to reflect the spillover effects of peer parental divorce. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Z}_{ics}^{{\\prime\\:}}\\)\u003c/span\u003e\u003c/span\u003e is a set of covariates composed of three vectors as mentioned above. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\delta\\:}_{s}\\)\u003c/span\u003e\u003c/span\u003e is the school FE. Since our identification method relies on differences in PPD between schools, controlling for school FE helps to mitigate potential endogeneity problems posed by school characteristics (Chen \u0026amp; Zhao, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Yin et al., \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\epsilon\\:}_{ics}\\)\u003c/span\u003e\u003c/span\u003e is the error term. Moreover, to accommodate heteroskedasticity and arbitrary serial correlation across students in each class, we clustered the standard errors at the class level throughout the empirical study (Balestra et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Random student-classroom assignment\u003c/h2\u003e \u003cp\u003eAccurately identifying the causal relationship between PPD and student performance is usually difficult because students\u0026rsquo; peers are not randomly determined. This selectivity results in some potential correlations between PPD and other class, student, and family characteristics. In addition, if the process of assigning classes and students is not randomized, for example, by students\u0026rsquo; scores on entrance exams, it will also lead to biased estimates. Thus, to mitigate this potential endogeneity issues, referring to the empirical strategy commonly employed in previous literature (e.g., Chen \u0026amp; Zhao, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Gong et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Guo et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Hu, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Huang \u0026amp; Zhu, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Luo et al., 2021; Wang et al., \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Xu \u0026amp; Li, \u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), we resorted to the quasi-experiment of RSCA on the basis of Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e for causal identification. Specifically, with the RSCA, students are matched to their classmates randomly, which means that whether a student matches a classmate whose parents are divorced is also randomized. In other words, for each student, PPD as a class characteristic was randomized and exogenously given. Of course, before employing this quasi-experiment, we need to verify that the process of RSCA is sufficiently random.\u003c/p\u003e \u003cp\u003eThere are two potential concerns that could interfere with the RSCA. The first threat comes from the effectiveness of identification. Ideally, if class sizes are large enough, differences in the proportion of parental divorce between classes in the same school should tend to zero after the RSCA. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, we found that the standard deviation of the proportion of divorced parents is only 0.0514.\u003csup\u003e6\u003c/sup\u003e Especially within a school, PPD should not vary much from class to class. As mentioned above, in fact, our identification relies on differences in PPD between schools. The next question is whether there is enough variation in our data to effectively identify PPD spillovers after adding school FE. Moreover, we plotted the distribution of the PPD for RSCA sample in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Specifically, we found that this variable is more widely distributed in the sample with a larger standard deviation. Then, after controlling for school FE, we further plotted the distribution of the residuals of PPD in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b), found that the residuals largely follow a normal distribution with a smaller standard deviation, which reflects the fact that after fixing the schools, the variable \u003cem\u003ePPD\u003c/em\u003e were relatively random and independent in the sample. This suggests that there is still enough variability in the data to support the empirical strategy in our study. Compared to the previous literature (Chen \u0026amp; Zhao, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Yin et al., \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), we considered this variability (standard deviation 5.5870) that we utilized for identification.\u003c/p\u003e \u003cp\u003e[Insert Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e about here]\u003c/p\u003e \u003cp\u003eThe second threat is from the verification of randomness. We performed the balancing tests to verify whether the variation in \u003cem\u003ePPD\u003c/em\u003e random conditional on school FE. That means, whether the variable \u003cem\u003ePPD\u003c/em\u003e is expected to be uncorrelated with any predetermined background characteristics of students, parents and families, and classes. More specifically, we regress a series of predetermined variables related to student, family, and class characteristics (including number of students, percentage of girls, percentage of fathers/mothers with higher education, average of education expenditures, gender of homeroom teacher, etc.) on the variable \u003cem\u003ePPD\u003c/em\u003e. Descriptive statistics for these class-level predetermined variables are shown in Tables \u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003eA2\u003c/span\u003e and \u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003eA3\u003c/span\u003e in the \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e. The results of the balancing tests are shown in \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e Table A4, which indicate that PPD is not correlated with all the predetermined variables after controlling for school FE. The results further support the randomness of \u003cem\u003ePPD\u003c/em\u003e in our sample, and suggests that the process of RSCA is real and effective in the CEPS (e.g. Chen \u0026amp; Zhao, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Gong et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Hu, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Based on the above evidence, we are confident that the quasi-experiment of RSCA is valid, and have sufficient confidence in the randomness and exogeneity of the core variable \u003cem\u003ePPD\u003c/em\u003e.\u003c/p\u003e \u003cp\u003eFurthermore, we used a non-RSCA sample for further balancing tests in Table \u003cspan refid=\"Tab11\" class=\"InternalRef\"\u003eA5\u003c/span\u003e in the \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e. Clearly, the estimated coefficients on \u003cem\u003ePPD\u003c/em\u003e are also insignificant in all columns. Thus, it is reasonable to conjecture that parental divorce is not a factor that interferes with the RSCA, which further implies the rationalization and reliability of using the RSCA as a causal identification method. Taken together, we provided evidence that the process of SRCA is sufficiently efficient and randomized, which excludes the potential confounding factors and endogeneity issues as much as possible. In the empirical analysis above, OLS estimates adequately capture the negative spillover effects of PPD on children\u0026rsquo;s academic achievements.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Results","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Prior evidence: Effects of parental divorce on children\u0026rsquo;s performances\u003c/h2\u003e \u003cp\u003eThis study is concerned with the spillover effects of PPD on student academic achievements. However, this spillover effect arises from the premise that parental divorce is indeed detrimental to children\u0026rsquo;s performances. As mentioned above, despite the considerable literature identifying this negative effect, there are still some scholars who found that the effect of parental divorce on children\u0026rsquo;s school performance is very limited (Brand et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Francesconi et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Thus, in this subsection, we provided an a priori evidence about whether parental divorce negatively affects family educational involvement and their children\u0026rsquo;s educational achievement.\u003c/p\u003e \u003cp\u003eAccording to Table \u003cspan refid=\"Tab12\" class=\"InternalRef\"\u003eA6\u003c/span\u003e in the \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e, we found a significant negative relationship between parental divorce and children\u0026rsquo;s test scores, cognitive ability, educational expectations, and parental educational involvement, which implies that parental divorce is likely to inhibit students\u0026rsquo; educational achievement and various types of performance in school. Clearly, these results are similar to previous studies that emphasized that parental divorce is detrimental to children\u0026rsquo;s human capital accumulation in China (e.g., Frimmel et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Hu, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Sun \u0026amp; Li, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Zhang, \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). It is important to emphasize that results in Table \u003cspan refid=\"Tab12\" class=\"InternalRef\"\u003eA6\u003c/span\u003e only focused on the correlation between parental divorce and children\u0026rsquo;s performances, not causation, and served as a supportive test prior to the baseline regressions. It needs to be explained that the direct effect of parental divorce on children\u0026rsquo;s performances is not the goal of this paper, so we only examined their correlations as some supporting evidence.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Main results: Spillover effects of peer parental divorce\u003c/h2\u003e \u003cp\u003eIn Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, we examined the causal effect of PPD on student academic achievements by using a sample of students from intact families. The results in columns (1) to (4) show that PPD has a negative effect on students\u0026rsquo; academic achievement. More specifically, a one-percentage-point increase in PPD leads to an approximate 0.2998-point decrease in students\u0026rsquo; average scores, along with decreases in Chinese, Math, and English scores of approximately 0.1698, 0.5243, and 0.5108 points, respectively.\u003csup\u003e7\u003c/sup\u003e By converting to standard deviations, a one standard deviation increase in PPD (a 5.044% increase in the percentage of divorced parents) results in a 0.0790 standard deviation decrease in average score, as well as a decrease in Chinese, Math, and English scores and cognitive ability scores by 0.0573, 0.1024, and 0.1091 standard deviations, respectively.\u003c/p\u003e\u003cp\u003eFurthermore, in column (5), as expected, PPD similarly significantly reduced students\u0026rsquo; cognitive abilities, indicating that for every percentage increase in PPD in the class, students\u0026rsquo; cognitive ability scores decreased by 0.0087 points, which equates to a 0.0543 standard deviation change in cognitive ability for each PPD standard deviation. Meanwhile, in the Tables \u003cspan refid=\"Tab13\" class=\"InternalRef\"\u003eA7\u003c/span\u003e and \u003cspan refid=\"Tab14\" class=\"InternalRef\"\u003eA8\u003c/span\u003e in the \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e, we further explored the effect of PPD on students\u0026rsquo; non-cognitive abilities, and found that the effect was not significant.\u003c/p\u003e \u003cp\u003eOverall, it is clear that the high rate of parental divorce in the class had a very significant negative impact on all students in the class, especially in terms of their test scores and cognitive development. Our results are similar to some previous literature emphasizing the potential negative effects of parental divorce (e.g., Albert, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Conway \u0026amp; Li, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Hu, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Kalmijn, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Sun \u0026amp; Li, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Moreover, we confirmed that this negative impact is likely to spillover to other students through the peer effects. In sum, our baseline results indicate the existence of spillovers from parental divorce, suggesting that the adverse impact of parental divorce on children\u0026rsquo;s human capital development extends beyond the intra-family context.\u003c/p\u003e \n\u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBaseline regressions: Spillover effects of PPD on student scores and cognitive ability\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(4)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(5)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAverage score\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eChinese score\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMath score\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eEnglish score\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCognitive ability\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePPD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.2998**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.1698*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.5243***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.5108***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.0087*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.1188)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.0879)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.1916)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.1759)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0050)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGender of student\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-8.3903***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-7.5705***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-5.3174***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-12.3211***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.0334\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.5336)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.4193)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.7625)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.7547)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0231)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge of student\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-3.1848***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1.5789***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-4.1198***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-3.8593***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.1800***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.3184)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.2570)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.4558)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.4001)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0174)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRural\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.5255\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0522\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.6504**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6825\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.0069\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.5201)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.4048)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.7814)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.6689)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0235)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOnly child\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.7743\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.6701\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.7066\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.1446*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.0095\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.5626)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.4425)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.8445)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.6466)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0257)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSelf-rated wealth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-2.8237***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1.3756*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-4.4243***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-2.8792**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.0375\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.9087)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.7215)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(1.2554)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(1.2157)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0456)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEducation of father\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.4262***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1731**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.4306***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6632***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0139***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.0994)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.0820)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.1513)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.1235)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0049)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEducation of mother\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0522\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0079\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0854\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0930\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.0010\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.0940)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.0812)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.1385)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.1199)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0039)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGovernment subsidy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.6701***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.0682***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.2757***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.4924***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0996***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.5851)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.4209)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.8289)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.8010)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0272)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eGender of homeroom teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-4.4997***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-2.2900**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-4.7963***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-4.9712***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.1735***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1.2213)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.8859)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(1.7954)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(1.7192)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0634)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eEducation of homeroom teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.6226\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.1635**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.1051\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.6181\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.0438\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1.3406)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.8844)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(2.1085)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(2.2172)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0476)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTeaching experience of homeroom teacher\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0827\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0880\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1084\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0926\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0052\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.0823)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.0619)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.0987)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.1211)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0032)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCurriculum teacher characteristics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFather\u0026rsquo;s occupation FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMother\u0026rsquo;s occupation FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSchool FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConstant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e110.7322***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e94.3715***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e165.2870***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e112.6970**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.9344***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(22.7935)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(15.2808)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(39.1941)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(45.4057)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.8307)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.4116\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.4828\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.3404\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.4167\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.2844\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4673\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4623\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003eNotes: ***, **, * indicate significance at the levels of 1%, 5%, and 10%, respectively. Standard errors clustered at the class level are reported in parentheses. As reported in the summary statistics, Curriculum teacher characteristics, i.e., Chinese, Math and English teachers\u0026rsquo; characteristics, including their gender, education, and teaching experience.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \n\u003cp\u003e[Insert Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e about here]\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.3. Robustness checks\u003c/h2\u003e \u003cp\u003eWe conducted a series of robustness checks to ensure the reliability of the baseline results, including controlling for other spillover effects, the exclusion of special observations, adding control variables, and placebo tests.\u003c/p\u003e \u003cp\u003eFirst, given that spillover effects from other characteristics of peers\u0026rsquo; parents may interfere with the results of the baseline regressions, such as parents\u0026rsquo; education, unemployment, political capital, and parental migration etc., which have already been explored in the previous literature (e.g. Hu, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Huang \u0026amp; Zhu, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Zhao \u0026amp; Zhao, \u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Zhou \u0026amp; Hill, \u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Thus, in Table \u003cspan refid=\"Tab15\" class=\"InternalRef\"\u003eA9\u003c/span\u003e, we controlled for additional spillover effects for robustness tests, including the spillover effects from parental education, unemployment, political capital, migration, households with frequent drinkers, interparental verbal conflict and households with sick or mobility-impaired members referred to in the previous literature (Chen et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Dickson et al, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Fruehwirth \u0026amp; Gagete-Miranda, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Yin et al., \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Zheng \u0026amp; Zhou, \u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The results show that after controlling for these additional spillover effects, the results are still largely consistent with the main estimates in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, further verifying that our findings are reliable.\u003c/p\u003e \u003cp\u003eSecond, in \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e Table A10, we excluded some special observations to ensure the generality of the sample, such as unhealthy students, students with high educated parents, the best and worst schools in the county, students attending evening classes, and classes with experienced teachers. On the one hand, in columns (1) and (2), we excluded the sample of students with poor health and with highly educated parents, considering that these characteristics of the samples may interfere with the results of the baseline regressions (Chen \u0026amp; Zhao, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). On the other hand, the factors of best and worst schools in the county, fuller school schedules, and high-quality teachers in classroom allocations could also potentially cause bias in the total sample estimates (Huang et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zhao \u0026amp; Chen, \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), so we also excluded samples with these factors in columns (3) to (7). Clearly, when we excluded the samples with the special factors mentioned above respectively, the estimation results obtained are basically very close to the baseline regression results.\u003c/p\u003e \u003cp\u003eThird, we included more control variables in the baseline model that may affect student performance, including school, class, family, and student characteristics. It is important to highlight that our identification strategy is primarily based on a quasi-experiment of RSCA, and that the results of the balancing tests have demonstrated that the core explanatory variable \u003cem\u003ePPD\u003c/em\u003e is not directly correlated with most of the class-level predetermined variables, i.e., \u003cem\u003ePPD\u003c/em\u003e is random and independent. Thus, in the main specifications, we controlled for some variables at the classroom and teacher, student, and household levels, with school FE and standard errors clustered at the class level. To capture the causal effect more accurately, we still employed the approach of adding more control variables at the school, class, family, and student levels to further assess the robustness of our findings (Chen \u0026amp; Zhao, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Gong et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Hu, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). The descriptive statistics of these control variables are represented in Table \u003cspan refid=\"Tab17\" class=\"InternalRef\"\u003eA11\u003c/span\u003e in the \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e. In Table \u003cspan refid=\"Tab18\" class=\"InternalRef\"\u003eA12\u003c/span\u003e, on the basis of the main specification, we added these additional control variables at the school, and class, family, and student levels in columns (1) to (3), respectively, and controlled all these variables in column (4). The results in each column are generally consistent with the baseline regression in terms of estimated coefficients and significance of \u003cem\u003ePPD\u003c/em\u003e, confirming that our previous findings are reliable.\u003c/p\u003e \u003cp\u003eThird, we conducted placebo tests using the observed students\u0026rsquo; academic performance in sixth grade in primary school (Hu, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The CEPS questionnaire investigated students\u0026rsquo; subjective perceived difficulty in learning Chinese, Math, and English when they were in sixth grade, which can be used to measure students\u0026rsquo; academic performance prior to RSCA (Chen \u0026amp; Zhao, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). As reported in \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e Table A13, the placebo tests showed no association between PPD in students\u0026rsquo; current classes and their academic performance in 6th grade, which indirectly indicates the robustness of our baseline estimation results.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.4. Mechanisms\u003c/h2\u003e \u003cp\u003eThe main results confirm the negative spillover effect of PPD on student academic achievements. In this subsection, we explored the potential mechanisms of this undesirable spillover effects at the student, teacher, and parent levels as highlighted earlier, specifically encompassing: (i) Parental responses; (ii) Students\u0026rsquo; expectations, attitudes and behaviors in learning; (iii) Teachers\u0026rsquo; teaching efforts and enthusiasm.\u003c/p\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e4.4.1. Parental responses\u003c/h2\u003e \u003cp\u003eDivorced parents may have a spillover effect in the class by influencing other parents\u0026rsquo; expectations of educational achievement and decisions related to family educational expenditure. According to the view of resource deprivation, parental divorce may be a deprivation of resources for children\u0026rsquo;s education and reduce the family human capital investment (Hoffman \u0026amp; Duncan, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e1988\u003c/span\u003e; Sun \u0026amp; Li, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Moreover, the decline in income after divorce makes it more difficult for families to weigh their children\u0026rsquo;s education expenditures against other expenditures (Conway \u0026amp; Li, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Park, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). In addition, existing studies showed that parents\u0026rsquo; educational and career expectations, and active involvement in their children\u0026rsquo;s education are important factors in influencing student academic achievements (Hao \u0026amp; Yeung, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Li et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Luo \u0026amp; Yang, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Inevitably, parents\u0026rsquo; attitudes toward their children\u0026rsquo;s education and their motivation to family educational expenditure influence each other in the classroom. As parental divorce becomes more prevalent among the students in the classroom, it is likely to consciously or unconsciously lower their education involvement and educational expenditure of their children. Especially in China, where many families are motivated by intra-class competition, and the amount of attention and actual investment in their children\u0026rsquo;s education depends on that of the parents of their classmates (Guo \u0026amp; Qu, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Zhao \u0026amp; Zhao, \u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Thus, high PPD may reduce the family educational expenditure and parental expectations and their involvement in children\u0026rsquo;s education, resulting in a potential negative impact on students\u0026rsquo; academic achievements.\u003c/p\u003e \u003cp\u003eBased on the above analysis, according to CEPS and related previous research (Wang et al., \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Wen \u0026amp; Lin, \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Zhao \u0026amp; Chen, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), a series of variables on family educational expenditure, parental expectations and educational involvement were selected, as listed in Panel A of Table \u003cspan refid=\"Tab20\" class=\"InternalRef\"\u003eA14\u003c/span\u003e in the \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e. In columns (1)-(3) of Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, we can see that the coefficients on \u003cem\u003ePPD\u003c/em\u003e is significantly positive in the latter two columns. That is, the PPD did have a negative spillover effect on parents\u0026rsquo; career and migration expectations for their children in the future. As prior studies have already demonstrated, declining parental expectations further lead to poorer student performance (Hao \u0026amp; Yeung, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Zhao \u0026amp; Chen, \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Thus, these results suggest that the PPD may diminish parents\u0026rsquo; positive expectations for their children\u0026rsquo;s future, which in turn is detrimental to academic performance.\u003c/p\u003e \u003cp\u003eInstead, in columns (4) and (5) of Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, we found that the estimated coefficients on \u003cem\u003ePPD\u003c/em\u003e are all insignificant, which means that increase in PPD did not dampen the family educational expenditure or involvement in the class, such as controlling Internet access. The potential cause is that influenced by Confucian culture, Chinese parents always emphasize their children\u0026rsquo;s investment in human capital and academic performance (Chi \u0026amp; Qian, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Chen et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The effect of PPD may not be sufficient to change parents\u0026rsquo; educational expenditure decisions and educational involvement towards their children. Taken together, our results imply that from the parental responses, the negative spillover effects of PPD are mainly reflected in the psychological dimension of educational expectations.\u003c/p\u003e \n \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eParental responses\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(4)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(5)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParental education expectations\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eParental career expectations\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eParental migration expectations\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eEducation expenditure\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eParental control of Internet\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePPD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.0001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0036**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0037**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0195\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.0004\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.0015)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.0018)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.0016)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.0202)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0010)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBaseline control variables\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFather\u0026rsquo;s occupation FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMother\u0026rsquo;s occupation FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSchool FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4716\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4888\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4896\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4800\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003eNotes: ***, **, * indicate significance at the levels of 1%, 5%, and 10%, respectively. Standard errors clustered at the class level are reported in parentheses. Marginal effects of Probit estimates are reported in columns (1), (2), (3) and (5).\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \n\u003cp\u003e[Insert Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e about here]\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e4.4.2. Students\u0026rsquo; expectations, attitudes, and behaviors in learning\u003c/h2\u003e \u003cp\u003eWe then examined the effects of PPD on students\u0026rsquo; expectations, attitudes, and behaviors in their learning process, as students are clearly most directly influenced by their peers. As mentioned in previous studies, parental divorce may have a direct negative impact on their children\u0026rsquo;s school performance, such as grades and cognitive and non-cognitive skills (e.g., Amato \u0026amp; Anthony, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Havermans et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Kim, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Park, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Sun \u0026amp; Li, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Meanwhile, students with divorced parents show poorer performance in learning habits, self-control, and emotions (Anthony et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Sands et al., \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Sigle-Rushton et al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Strohschein, \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). These students\u0026rsquo; poorer school performance, behaviors, and psychological states have potential peer effects other students in the classroom (e.g., Chen et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Dahl et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Gong et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Hanushek et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Salas Garc\u0026iacute;a \u0026amp; Renter\u0026iacute;a, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Zimmerman, \u003cspan citationid=\"CR84\" class=\"CitationRef\"\u003e2003\u003c/span\u003e). Specifically, high parental divorce rate in the class is likely to imply that there are more students with poorer performance and learning habits, which in turn may have a negative modelling effect on the behaviour and psychology of other students in the class, or even directly interfere with their learning. Thus, the PPD is likely to ultimately have an adverse effect on the academic achievements of students in the class.\u003c/p\u003e \u003cp\u003eTo further validate the above mechanism, based on the CEPS questionnaire and previous literature (Huang et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Zhao \u0026amp; Chen, \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), we selected a series of variables about students\u0026rsquo; learning attitudes, psychological expectations and learning behavior for analysis, as shown in Panel B of Table \u003cspan refid=\"Tab20\" class=\"InternalRef\"\u003eA14\u003c/span\u003e. From the results in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, it is easy to see that the PPD has a combined hindering effect on student\u0026rsquo; expectations, attitudes and behaviors in their learning. Specifically, as shown in columns (2) and (3), increased PPD significantly dampens students\u0026rsquo; career and migration expectations, i.e., students\u0026rsquo; desire for high-skilled occupations decreases, and aspirations to relocate to a major city in the future decrease. The decline in positive expectations inevitably leads to a lack of motivation for students to study, which is manifested in a rapid decline in academic performance in the short term (Luo \u0026amp; Yang, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In addition, results in columns (4) to (6) show that an increase in PPD also increases the frequency of undesirable behaviors such as skipping classes and copying homework, as well as a decrease in students\u0026rsquo; attitudes toward learning, all of which directly contribute to poorer academic performance (Anthony et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Kalmijn, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Zhuang et al., \u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). According to above results, the PPD has a negative effect on the expectations, learning attitudes and behaviors of students, which is one of the important mechanisms by which it may hinder students\u0026rsquo; academic achievements.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStudents\u0026rsquo; expectations, attitudes and behaviors in learning\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(4)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(5)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(6)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e(7)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e(8)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEducation expectations\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCareer expectations\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMigration expectations\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eFrequency of skipping classes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFrequency of copying classmates\u0026rsquo; homework\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eStudying hard\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eTime spent on the Internet on weekends\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eTime for homework on weekends\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePPD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.0013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0026*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0034***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0021*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0042*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.0039**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.0033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.0065\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.0199)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.0016)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.0011)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.0012)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0021)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(0.0020)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e(0.0056)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e(0.0050)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBaseline control variables\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFather\u0026rsquo;s occupation FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMother\u0026rsquo;s occupation FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSchool FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4914\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4886\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4876\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4859\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4894\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e4911\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"9\"\u003eNotes: ***, **, * indicate significance at the levels of 1%, 5%, and 10%, respectively. Standard errors clustered at the class level are reported in parentheses. Marginal effects of probit estimates are reported in columns (2), (3) and (6).\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e[Insert Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e about here]\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e4.4.3. Teachers\u0026rsquo; teaching efforts and enthusiasm\u003c/h2\u003e \u003cp\u003eThe divorce of peers\u0026rsquo; parents may also affect the performance of the students in the classroom by influencing the teachers\u0026rsquo; teaching efforts and enthusiasm. A large body of literature has previously demonstrated that teachers investing more time and enthusiasm in teaching and classroom management will inevitably have a positive impact on student performance (e.g., Chen \u0026amp; Zhao, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Gong et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Huang et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Xu \u0026amp; Li, \u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Meanwhile, some studies have also shown that the attitudes and characteristics of students\u0026rsquo; parents are likely to affect teachers\u0026rsquo; work effort and enthusiasm in China (Chen et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zheng \u0026amp; Zhou, \u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Therefore, high parental divorce rate in the classroom may also inhibit teachers\u0026rsquo; attitudes and efforts invested in their work. For example, parental divorce leads to a decrease in parental interest in their children\u0026rsquo;s schooling\u003csup\u003e8\u003c/sup\u003e; if the percentage of divorced parents is too high it may inadvertently send a signal to teachers that \u0026ldquo;the parents of many students in the class do not care enough about their students\u0026rdquo;. In this case, teachers are likely to experience less pressure from parents even if they are not performing well in their work. For these reasons, some teachers may reduce their efforts and enthusiasm in teaching and class management because the cost of underperformance is lower for classes with high parental divorce rate (Conway \u0026amp; Li, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Ultimately, decreased teachers\u0026rsquo; effort and enthusiasm leads to poorer student performance.\u003c/p\u003e \u003cp\u003eIn Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, we tested the effect of PPD on teaching effects and enthusiasm, including teachers\u0026rsquo; working time, hours for preparing lessons, hours for homework correction, teacher-student communication, sense of responsibility, and patience. These variables have been emphasized in the previous studies (Chen \u0026amp; Zhao, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Gong et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Zhao \u0026amp; Chen, \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), and they are described in Panel C of Table \u003cspan refid=\"Tab20\" class=\"InternalRef\"\u003eA14\u003c/span\u003e in the \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e. The results in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e indicate that although the PPD does not have a significant effect on teachers\u0026rsquo; time spent on preparing lessons, and on their responsibility and patience with students, it has a highly significant negative effect on teachers\u0026rsquo; working time and hours for homework correction, which is basically consistent with our previous speculation. These results suggest that the negative spillover effects of parental divorce affect teachers\u0026rsquo; teaching efforts, which may further reduce the teaching quality. Considering that teacher efforts are closely related to student human capital accumulation (e.g., Chen \u0026amp; Zhao, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Hung et al., 2023; Xu \u0026amp; Li, \u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), we further identify the third mechanism for the negative impact of PPD on students\u0026rsquo; academic achievements at the teacher level.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTeachers\u0026rsquo; teaching efforts and enthusiasm\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(4)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(5)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(6)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWorking time\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHours for preparing lessons\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHours for homework correction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePercentage of total working time spent on homework correction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSense of responsibility\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003ePatience\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePPD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.5075***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0203\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.1648**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.0023***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.0062\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.1663)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.0949)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.0789)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.0004)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0038)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(0.0039)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBaseline control variables\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFather\u0026rsquo;s occupation FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMother\u0026rsquo;s occupation FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSchool FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4828\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4916\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4853\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4717\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4877\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4871\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003eNotes: ***, **, * indicate significance at the levels of 1%, 5%, and 10%, respectively. Standard errors clustered at the class level are reported in parentheses.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e[Insert Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e about here]\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e4.5. Heterogeneity\u003c/h2\u003e \u003cp\u003eConsidering the growing evidence that spillover effects in the classroom vary across students, families, and teachers with different characteristics (e.g., Huang et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Min et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Pan et al., \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Xu et al., \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Zheng \u0026amp; Zhou, \u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), we further explored the heterogeneous effects of PPD on students\u0026rsquo; academic achievements from several perspectives: students\u0026rsquo; place of origin, gender, only child, household economic condition, finding the spillover of PPD differ by these characteristics.\u003c/p\u003e \u003cp\u003eFirst, we analyzed the spillover effect of PPD on students with different characteristics. Specifically, in columns (1) and (2) of Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, we found that the negative impacts of PPD on both achievement and cognitive ability are more significant for urban students compared to rural students, and may be greater in terms of the coefficients. This result is unexpected, and we speculated that the reason for this is that the better living conditions and favourable upbringing of urban students make them more susceptible to negative external influences (Crouch et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003csup\u003e9\u003c/sup\u003e In addition, the results in columns (3) and (4), we found that estimated coefficients on \u003cem\u003ePPD\u003c/em\u003e do not differ significantly for the two groups of boys and girls in the two Panels, suggesting that gender differences in the spillover effects of parental divorce are unnoticeable. Furthermore, results in columns (5) and (6) show a more significant impact of PPD on the cognitive ability of only children. The main reason for this is also likely to be that these two groups are more vulnerable to negative influences of PPD because of their biological characteristics and family structure. Some studies have shown that only children are relatively more emotionally vulnerable and more susceptible to the negative emotions of their classmates than non-only children (Chen \u0026amp; Zhao, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Kim, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Consequently, when class PPD is high, they may be also more prone to negative emotions, hindering their performance in school.\u003c/p\u003e \u003cp\u003eThen, in columns (7)-(9) in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, we found that the negative effects of PPD on students\u0026rsquo; test scores and cognitive ability were significant mainly among students from ordinary and relatively wealthy families, but not for students in relative poverty. Similar to the above results, the negative spillover effects of parental divorce are more pronounced for non-vulnerable groups. Moreover, these results suggest that the impact of disadvantaged groups\u0026rsquo; own disadvantages on students\u0026rsquo; human capital development may be more noticeable compared to the spillover effects of their classmates.\u003c/p\u003e \n\u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eHeterogeneity\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(4)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(5)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(6)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e(7)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e(8)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003e(9)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRural\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGirl\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBoy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eOnly child\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNon-only child\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eRelative poverty\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eOrdinary\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eRelatively wealthy\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"10\" nameend=\"c10\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePanel A.\u003c/b\u003e Average score\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePPD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.1647\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.5139***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.2411**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.3198**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.3735**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.2657**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-0.0063\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.3745***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-0.4080\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.1196)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.1577)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.1036)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.1536)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.1466)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(0.1331)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e(0.1788)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e(0.1259)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e(0.2774)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"10\" nameend=\"c10\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePanel B.\u003c/b\u003e Cognitive ability\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePPD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.0045\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0132**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.0089**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.0085\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.0142***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.0075\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.0098\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.0137***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-0.0321***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(0.0056)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(0.0059)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(0.0042)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(0.0062)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(0.0051)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(0.0062)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e(0.0078)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e(0.0052)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e(0.0096)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBaseline control variables\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFather\u0026rsquo;s occupation FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMother\u0026rsquo;s occupation FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSchool FE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2616\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2304\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2387\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2533\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1966\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2954\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1092\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3475\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e353\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"10\"\u003eNotes: ***, **, * indicate significance at the levels of 1%, 5%, and 10%, respectively. Standard errors clustered at the class level are reported in parentheses.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \n\u003cp\u003e[Insert Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e about here]\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Further exploration","content":"\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e5.1. Mitigating effects of supports from teachers, parents, and friends\u003c/h2\u003e \u003cp\u003eIn above results, we confirmed that parental divorce has a negative spillover effect on other students in the classroom. Therefore, how to mitigate the effects of PPD should be emphasized by education authorities and parents. In this subsection, we explored feasible measures to mitigate the negative effects of PPD, focusing on supports from teachers, parents, and friends. As highlighted in the prior literature, supports from school and parents may increase students\u0026rsquo; self-confidence and focus, which help improve students\u0026rsquo; academic achievements (Dietrich et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Hu \u0026amp; Wu, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Specifically, we examined whether their supports could mitigate the negative spillovers of PPD by constructing some interaction terms. The definitions and descriptive statistics of these variables are detailed in \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e Table A15 and the results are shown in Table \u003cspan refid=\"Tab22\" class=\"InternalRef\"\u003eA16\u003c/span\u003e in the \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eIn terms of teachers\u0026rsquo; supports, we found that homeroom teachers who also serve in an administrative position do a much better job of mitigating the negative spillover effects of PPD in their classes in column (1). This may be attributed to the fact that these teachers have stronger managerial and non-cognitive abilities to provide more psychological support to their students, and that the administrative roles reinforce their effectiveness in the classroom management. For instance, students may respect and follow their guidance and management more (Chen \u0026amp; Zhao, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Moreover, in columns (2) and (3), we found that after school, teachers spending more time communicating with students and parents could also be effective in mitigating negative spillovers from PPD.\u003c/p\u003e \u003cp\u003eFurthermore, in columns (4) to (9), we examined the effectiveness of parents\u0026rsquo; supports can provide to their children in mitigating the negative effects of PPD. First, according to the results in columns (4) to (5), we found that only parental concern for students\u0026rsquo; friendships is effective in attenuating the negative effects of excessive PPD in the class, whereas parental concern for students\u0026rsquo; learning has a very limited effect. Meanwhile, the results in columns (6)-(9) suggest differences in the role parents may play in mitigating the negative spillover effects of PPD. For fathers, being more attentive to their children\u0026rsquo;s worries and difficulties can effectively attenuate the negative impacts from PPD, but spending more time caring about their children\u0026rsquo;s relationships with classmates is not. Differently, mothers who were more concerned about their children\u0026rsquo;s relationships with classmates were effective in mitigating the negative effects of PPD (Chen et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), but less effective by caring about their students\u0026rsquo; worries and difficulties (Flouri, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). This difference may be attributed mainly to the different roles in the family. Particularly in China, fathers tend to play a decision-making and problem-solving role in the family, while mothers are usually more concerned about their children\u0026rsquo;s emotional problems and social relationships (Francesconi et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Sun \u0026amp; Li, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2009\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eLast, the result in column (10) shows that the coefficient of the interaction term is significantly positive, indicating thathaving a larger number of friends similarly helps to mitigate the negative spillovers from PPD, which implies the importance of good friendships in mitigating these negative spillovers. In conclusion, some supports from teachers, parents and friends may be effective in mitigating the negative spillover effects from PPD.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e5.2. Reverse spillovers on students with divorced parents\u003c/h2\u003e \u003cp\u003eIn addition to the spillover effect of PPD on student academic achievements, we are also interested in whether students from intact families have reverse spillover effects on students with divorced parents. As discussed in previous studies, peer spillover effects are often not one-dimensional (Yin et al., \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Zheng \u0026amp; Zhou, \u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). We constructed a variable to measure this reverse spillover effect, measured by the proportion of parents not divorced in the class. As reported in \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e Table A17, we observed that the estimated coefficients are positive in all columns and significant in columns (1), (3), and (5). Despite the large drop in sample size, we still obtained the conclusion that students whose parents are not divorced may have a positive spillover effect on the academic achievements of students with divorced parents, especially in math scores and cognitive skills. Thus, we further confirmed the bidirectional spillover effects of parental divorce from the level of student academic performances and reinforced the idea of negative spillovers from PPD.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e5.3. Effects on some special disadvantaged students\u003c/h2\u003e \u003cp\u003eIn this subsection, we further focused on the spillover effects of PPD on two special disadvantaged groups of children in China, including migrant children and left-behind children.\u003csup\u003e10\u003c/sup\u003e In recent years, all sectors of society pay close attention to the status of the human capital of these special children (e.g., Hu \u0026amp; Wu. 2018; Zhang \u0026amp; Zhou, 2024; Zhao \u0026amp; Chen, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Zhao et al., \u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). In Table \u003cspan refid=\"Tab24\" class=\"InternalRef\"\u003eA18\u003c/span\u003e in the \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e, we explored the spillover effects of PPD on migrant children and left-behind children, finding that PPD significantly inhibits the academic performance of left-behind children, but has a very limited impact on migrant children. An important reason for this may be that left-behind children are separated from their parents and are more emotionally vulnerable to negative spillovers such as parental divorce (Zhang \u0026amp; Zhou, 2024; Zhao \u0026amp; Chen, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e"},{"header":"6. Conclusions and discussion","content":"\u003cp\u003eAlthough considerable attention was paid to the adverse effect of parental divorce on children human capital development, there is little literature on whether this negative impact extends beyond the inter-family and spills over to children\u0026rsquo;s peers. To determine the causal effect of PPD on students\u0026rsquo; school performance in the class, we employed a quasi-natural experiment with SCRA as an identification strategy. Balanced tests and a series of robustness checks provide supportive evidence for our empirical framework.\u003c/p\u003e \u003cp\u003eOur conclusions are summarized below. First, we found a negative causal effect of the PPD on students\u0026rsquo; academic achievements, confirming the spillover effects of parental divorce. Specifically, for each standard deviation increase in PPD (%), students\u0026rsquo; average score and cognitive ability decreased by 0.0790 and 0.0543 standard deviations, respectively. However, the PPD did not significantly affect students\u0026rsquo; non-cognitive abilities. Second, the mechanism analysis showed that this negative spillover effect of divorced parents may be explained in three ways: parents, students, and teachers. Our estimates suggest that the PPD led to a decline in parental expectations, the development of negative expectations and learning behaviors among students, and a drop in teachers\u0026rsquo; efforts and enthusiasm, which is further detrimental to students\u0026rsquo; academic achievements. Third, heterogeneity effect results revealed negative spillovers of PPD mainly among some relatively advantaged students, such as urban students, only children, and students from non-poor families. Further studies indicated that supports from teachers, parents, and friends may mitigate the negative spillover effects of PPD. We revealed a reverse positive spillovers of parental non-divorced on students with divorced parents in the classroom. More seriously, the human capital of left-behind children may also be negatively shocked by this spillover effect.\u003c/p\u003e \u003cp\u003eOur study has some theoretical insights. First, in the debate over whether parental divorce reduces children\u0026rsquo;s human capital accumulation, our results are more supportive of the idea of a negative effect based on the Chinese case. In the short run, parental divorce is not only significantly detrimental to children\u0026rsquo;s academic performance (Havermans et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Park, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Sun \u0026amp; Li, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2009\u003c/span\u003e), but also spills over this negative effect to other students in the same class. Thus, the negative effects of parental divorce are not limited to the intra-family level, but may have broader societal implications. Second, we provided new evidence on the classic research topic of educational peer effects from the special perspective of parental divorce. Starting from the dimensions of family background and parental characteristics, existing literature mainly explored peer effects from family education expenditures and parental resources (Chen et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Pan et al., \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). We offered additional insights in terms of parental marital stability and family structure.\u003c/p\u003e \u003cp\u003eIn terms of policy implications, this study reveals some measures to mitigate the negative spillover effects of PPD. Therefore, there is a great need to further strengthen the school, family, and peer supportive environments, especially at the school level. Potential measures include strengthening home-school ties, enhancing teacher-student interactions, and paying special attention to students with divorced parents. In addition, the negative spillover effects of PPD are detrimental to the human capital accumulation of some disadvantaged groups, such as the left-behind children. Thus, to further alleviate educational inequality, it is important to provide them with more support to easily reduce the negative effects of PPD, such as creating a good classroom culture and avoiding discrimination in schools. Currently, divorce has become commonplace in most countries. The impact of divorce on children\u0026rsquo;s human capital is not confined to the family, but the social cost of divorce requires the attention of society as a whole. How to minimize the negative impact of divorce on the accumulation of human capital requires the attention of the public sector, educational institutions and families in general.\u003c/p\u003e \u003cp\u003eSome limitations remain to be addressed in future studies. First, since the CEPS only provides a cross-section of data on parental divorce, we are unable to explore the dynamic impact of the spillover effect of PPD. Also, we cannot capture the heterogeneous effects of PPD on students\u0026rsquo; school performance at different school-age stages, such as primary or high school. Second, some mechanisms may not have been adequately tested. For example, at the teacher level, the PPD affect teachers\u0026rsquo; classroom management effectiveness to the indirect detriment of student school performance, but there are no appropriate variables to capture this mechanism in the CEPS. In addition, mechanisms at the classroom and school levels need to be added in further studies. Third, owing to the lack of more information on parental divorce, such as parental arguments and negative behaviours, children\u0026rsquo;s residency status after parental divorce, and the length of the divorce. As a result, it is difficult to capture the differential impact of different types of PPD on student achievement. Last, variables on support of parents, teachers, and friends may not be exogenous, so these measures to mitigate the negative effects of peer parent divorce are merely suggestive. In the follow-up research, it would be interesting to further analyze the multifaceted spillover effects of PPD on human capital by designing a set of questionnaires specialized in information on divorced families and children.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eChen and Zhao wrote the main manuscript text; Zhao prepared figures 1-2; Liu prepared the Appendix; Chen prepared the tables 1-6. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eData availability:\u003c/h2\u003e \u003cp\u003eThe data that support the findings of this study are available from National Survey Research Center (NSRC) at Renmin University of China, but restrictions apply to the availability of these data, which were used under licence for the current study and so are not publicly available. The data are, however, available from the authors upon reasonable request and with the permission of National Survey Research Center (NSRC) at Renmin University of China.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAlbert, A. (2018). Parental duties, labor market behavior, and single fatherhood in America. \u003cem\u003eReview of Economics of the Household, 16\u003c/em\u003e(4), 1063-1083.\u003c/li\u003e\n\u003cli\u003eAmato, P. R., \u0026amp; Anthony, C. J. (2014). 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Peer effects in academic outcomes: Evidence from a natural experiment. \u003cem\u003eReview of Economics and Statistics, 85\u003c/em\u003e(1), 9-23.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Footnotes","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003e Data source: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.mca.gov.cn/images3/www2017/file/202009/1601261242921.pdf\u003c/span\u003e\u003cspan address=\"https://www.mca.gov.cn/images3/www2017/file/202009/1601261242921.pdf\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e CEPS examined the cognitive abilities of the interviewed students by organizing a uniform cognitive ability test and standardizing that score.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e In the CEPS, principals are asked about the school's rules for assigning students to classes in the following categories: (1) Placement exams prior to the beginning of students' first academic year; (2) Students\u0026rsquo; residential status; (3) Random student-classroom assignment; (4) Others.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e CEPS classifies parental occupations into 14 categories, including: (1) Government officials; (2) Senior managers in institutions or enterprises; (3) Professional staff, e.g. scientists, engineers, university teachers; (4) Doctors, lawyers, primary and secondary school teachers; (5) Technical staff, e.g. accountants, nurses, software programmers, etc.; (6) Clerical staff, e.g. secretaries, bank tellers, librarians, etc.; (7) Commercial and service workers, e.g. salespersons, agents, cooks, barbers, beauticians, etc.; (8) Skilled workers, e.g. drivers, plumbers, electricians, mechanics, etc.; (9) General workers, e.g. porters, production line workers, etc.; (10) Farmers, herders, fishermen; (11) Elementary laborers, e.g. cleaning, security, nanny, sanitation, etc.; (12) Individual businessmen; (13) Retired, jobless, unemployed, laid off; (14) Others.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e In the baseline regression, we primarily tested the effects of PPD on students' academic performances and cognitive ability (significant). We also examined the effect on students' non-cognitive abilities (not significant), and the descriptive statistics and regression results are detailed in the \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e The variable \u003cem\u003ePPD\u003c/em\u003e expands 100 times in the main specification, so the actual standard deviation for peer parental divorce in class should shrink 100 times to 0.0514.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e In Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, we reported results only for the core variables in the baseline regression. The complete results containing the estimates for the control variables of the baseline regressions are presented in Table \u003cspan refid=\"Tab11\" class=\"InternalRef\"\u003eA5\u003c/span\u003e in the \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e As previously verified in Table \u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003eA3\u003c/span\u003e in the \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e, parental divorce is significantly and negatively associated with decreased parental educational expectations, parental guidance of student homework, and controlling for the time students spend online.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e Each standard deviation increase in PPD reduces the average score of rural students by 0.0556 standard deviations, and the average score of urban students by 0.1343 standard deviations. All analyses of heterogeneity will calculate and consider the change in standard deviation as a reference based on the statistical characteristics of the different groups.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e Migrant children are children who live and go to school with their parents in other cities (outside their home towns). Left-behind children are children whose parents have gone out to work for a long period of time and who stay in their hometown to attend school and live there.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"humanities-and-social-sciences-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"palcomms","sideBox":"Learn more about [Humanities \u0026 Social Sciences Communications](http://www.nature.com/palcomms/)","snPcode":"41599","submissionUrl":"https://submission.springernature.com/new-submission/41599/3","title":"Humanities and Social Sciences Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Parental divorce, Student academic achievements, Spillover effects, Random student-classroom assignment, China","lastPublishedDoi":"10.21203/rs.3.rs-5797362/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5797362/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAlthough the impact of parental divorce on children\u0026rsquo;s human capital development has received sufficient attention from scholars, little has been paid to the potential spillovers. Based on a quasi-natural experiment with random student-classroom assignment in secondary schools in China, we aimed to explore whether the peer parental divorce (PPD) can have a negative spillover effect on students\u0026rsquo; academic achievements in a class. The results show that the PPD negatively impacted students\u0026rsquo; test scores and cognitive abilities, but this adverse effect is not reflected in non-cognitive abilities. Mechanism analyses suggested that this spillover effect may be explained by the decline in parental expectations, development of students\u0026rsquo; negative expectations and learning behaviors, and drop in teachers\u0026rsquo; efforts and enthusiasm. Moreover, we found that the negative spillovers of PPD are more pronounced for urban children, only children, and non-poor children. Furthermore, supports from teachers, parents, and friends is expected to mitigate this adverse spillover effects. Our study reveals the spillovers from parental divorce, suggesting that the negative effects of divorce on human capital are not confined within the family. These findings further provide some insights into mitigating the human capital loss from divorce.\u003c/p\u003e","manuscriptTitle":"Spillover effects from the divorce of peer parents: Evidence from student academic achievements in China","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-23 16:46:17","doi":"10.21203/rs.3.rs-5797362/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-06-03T11:29:06+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-26T13:19:43+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-13T05:01:50+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"44122937045155820708229516654556514265","date":"2025-05-06T04:12:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"110458141800358236271554985881101459918","date":"2025-05-05T23:45:18+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-20T16:09:12+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-07T03:02:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"301490462894053697921233871104266180343","date":"2025-03-29T10:16:26+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"310309601037505686604438898536291013683","date":"2025-03-28T02:28:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"330575967033014714417818864412967763951","date":"2025-03-27T22:13:45+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"89611659163661293852213641701601081588","date":"2025-03-27T15:44:27+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"208391742826837623372131793568580810253","date":"2025-03-27T07:23:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"144986671687002871926536490442986082919","date":"2025-03-27T07:21:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"251966371006518097048600803527960127589","date":"2025-03-27T07:11:03+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"303300382743762708954942422569267912876","date":"2025-03-27T07:07:40+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"26273699394549032044631018250698594956","date":"2025-03-10T15:21:12+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-03-09T09:26:24+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-01-29T10:55:13+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-01-29T08:22:50+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-01-21T14:00:38+00:00","index":"","fulltext":""},{"type":"submitted","content":"Humanities and Social Sciences Communications","date":"2025-01-09T14:35:08+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"humanities-and-social-sciences-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"palcomms","sideBox":"Learn more about [Humanities \u0026 Social Sciences Communications](http://www.nature.com/palcomms/)","snPcode":"41599","submissionUrl":"https://submission.springernature.com/new-submission/41599/3","title":"Humanities and Social Sciences Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"216798e7-c0e4-4e50-a5c4-b9aff98af99e","owner":[],"postedDate":"January 23rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":43196834,"name":"Business and commerce/Economics"},{"id":43196835,"name":"Social science/Economics"},{"id":43196836,"name":"Social science/Education"}],"tags":[],"updatedAt":"2026-03-09T12:24:18+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-23 16:46:17","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5797362","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5797362","identity":"rs-5797362","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}