Abstract
This paper examines the causal effects of the proportion of low-ability students in the classroom on the academic performance of regular students, exploiting random assignment of students to classes within middle schools in China. We show that the share of students in a class who are low achievers has a significant negative impact on the academic achievement of regular students in the seventh grade. The peer effects are heterogeneous along their achievement distribution, with the strongest adverse impact at the bottom end but no discernable impact at the top end. In contrast, there is no evidence that low-ability students influence any part of the achievement distribution of regular students in the ninth grade. Therefore, peer effects in academic outcomes can vary with the length of regular students’ exposure to the same group of low-ability classmates. We further show that the differences in peer effects of low-ability students in seventh and ninth grades are driven by the adjustments of students’ friendship formation and learning environment when approaching the completion of middle school.
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Notes
For example, Burke and Sass (2013) find small to non-existent spillover effects from mean peer ability, while Sojourner (2013) finds substantial positive average effects of peer achievement. Antecol et al. (2016) show that the average classroom peer achievement negatively affects own student academic achievement. Using the same data as in Sojourner (2013) and Bietenbeck (2020) shows that the peer impact of low-ability classmates can be positive in the long run.
For example, if parents of high-ability students send their children to the same class, we cannot conclude that there is a causal linkage between high-ability students and their classmates’ learning outcomes.
Using rich data from middle schools in one county of China’s Jiangsu Province, Ding and Lehrer (2007) utilize extensive controls to capture the selection process and establish the link between peer performance and student achievement. Carman and Zhang (2012) share a similar limitation in the representativeness of data by using student records from only one middle school in a North China province. Students are not randomly assigned into classes in the data used in these two studies. Moreover, neither of the two investigates into the mechanisms through which their estimated peer impacts may operate.
Using data from the Tennessee Student/Teacher Achievement Ratio experiment (Project STAR), Bietenbeck (2020) shows that the short-term peer influence of exposure to repeaters in kindergarten on academic performance is negative. However, the long-term impact is positive, when peers at kindergarten are no longer in the same classroom anymore. The changes in peer effects estimated in Bietenbeck (2020) are different from ours because the classroom composition of repeaters and non-repeaters stays the same over time in middle schools in our sample. Other studies such as Bifulco et al. (2011) and Bifulco et al. (2014) analyze peer effects in high schools and their persistent influence in later years.
As discussed in Manski (1993) and Lin (2010), in the presence of endogenous effects, offering academic support to low achievers will have social multiplier effects. They benefit from the support and will subsequently affect the performance of their peers, which in turn will affect the achievement of the former, and so on. However, if only contextual effects exist, regular students are responding to socioeconomic composition of low-ability students, so offering learning support to repeaters will generate no multiplier influence.
Since 1986, China has implemented the policy of nine-year compulsory education that includes six years in primary school and three years in middle school. Students covered in the CEPS data were all receiving compulsory education at the time of the survey.
Exploiting the random assignment of students in the CEPS data, Hu (2018) and Wang et al. (2018) examine the academic peer effects of migrant students on urban students; Gong et al. (2018) and Gong et al. (2019) analyze the effects of teacher gender and classmates’ gender composition on academic and non-cognitive outcomes of students, respectively.
We begin with 19,487 students from 112 schools in our data, including (i) 3065 students from 16 schools that used non-random assignment; (ii) 2854 students from 15 schools that randomly assigned students in grade seven but rearranged classes for grades eight and nine; (iii) 13,046 students from 78 schools that randomly assigned students in grade seven and did not rearrange classes for grades eight and nine; and (iv) 522 students from 3 schools that did not report how they assigned students to classrooms.
As indicated in CEPS, none of these 78 middle schools requires students to repeat a grade if they fail the annual exam.
Results by subject are reported and discussed in Section 4.2.1.
For seventh graders, the correlation coefficients are 0.66 for Chinese and mathematics, 0.78 for Chinese and English, and 0.74 for mathematics and English. The three correlation coefficients for ninth graders are 0.74, 0.76, and 0.78, respectively.
We report the detailed PCA results in Appendix Table 13. For seventh graders, the eigenvalues for the transformed three components are 2.45, 0.34, and 0.21, respectively. The eigenvalues for ninth graders are 2.52, 0.26, and 0.21, respectively. Appendix Table 14 shows that the correlation coefficients between the first component and the original three test scores are between 0.56 and 0.60 for seventh graders. The correlation coefficients are between 0.57 and 0.59 for ninth graders. Therefore, our principle component is a good summary index of the three test scores for each grade.
From January 2014, the Ministry of Education of China requires students who finish elementary school education to be admitted to a middle school located close to the neighborhood of their residential address (see http://old.moe.gov.cn//publicfiles/business/htmlfiles/moe/s3321/201401/163246.html). Reshuffling of students into classes still happens in the transition to middle school. However, there may be a small chance that some students who were classmates at primary school will still be classmates in middle school because of this policy. In our sample, students were not affected by this policy. Ninth graders and seventh graders were admitted to their middle school in the autumn semester of the 2011 and 2013 academic year, respectively.
We also have checked whether class indicator predicts students’ predetermined repeater status within schools. Following the logic described in Chetty et al. (2011) and Bietenbeck (2020), if assignment to classes is indeed random, then the class to which students are assigned within a school should not be related to students’ repeater status. To test this empirically, we generate an indicator taking a value of 1 if a student is a repeater and 0 otherwise. For each grade in each school, as two classes are typically selected, we randomly select one class with a value of 1 assigned to it and a value of 0 assigned to the other class. Using the pooled sample of seventh and ninth graders, we regress the repeater indicator on the class indicator, controlling for grade-by-school fixed effects. The estimated coefficient on the class indicator represents the difference in the share of repeaters between two classes within the same grade of the same school. If the assignment of students to classes is random within schools, then the coefficient estimated for the class indicator should be small and statistically insignificant. The regression results show that this estimated coefficient is –0.001 with a standard error of 0.006 (p value= 0.893), suggesting that the class to which students are assigned cannot predict student predetermined repeater status within schools. We have also performed the same regressions for seventh graders and ninth graders separately. The coefficient estimates of the class indicator are both very small and statistically insignificant (0.010 and –0.014, with p values of 0.247 and 0.161, respectively). These results suggest that repeater status is indeed balanced across classes within the same grade of the same school.
The education system in China ranks teachers in primary and secondary schools by levels from intern teachers (the lowest) to third class, second-class, first-class, and superior-class teachers (the highest). Teachers’ salaries are largely determined by the ranking and years of working experience in the education sector.
In Section 4.1, we attempt to empirically separate endogenous peer effects from contextual peer effects.
As discussed in Footnote 8, 3065 students are from the 16 schools that use non-random assignment. After dropping 99 observations with missing information on variables used for panel B of Table 4, we are left with 2966 students, consisting of 2552 regular students and 414 low-ability students.
Lee (2007) considers the identification and estimation of structural interaction effects in a social interaction model, which shows that endogenous effects and contextual effects can be separately identified in the presence of sufficient variations in group sizes. Nakajima (2007) presents a peer effect model allowing different responses across different types of peers.
We thank one anonymous referee for this suggestion.
The sample sizes in Table 5 become smaller because some classes do not have any students who were a grade-repeater in primary school.
Table 5 shows some evidence of contextual peer effects of low-achieving students. The proportion of boys among low achievers has a significant negative impact on the academic performance of regular students in both grade seven and grade nine. The average paternal years of schooling of low achievers generates no peer influence, in either grade seven or grade nine. In contrast, the average maternal years of schooling of low-ability students exerts a significant positive effect in the ninth grade.
Hsieh and van Kippersluis (2018) have developed an extended spatial autoregressive (SAR) model to overcome the problem of disentangling endogenous peer effects from unobserved contextual effects. However, their approach requires detailed friendship nominations, which seems to be applicable only to the Add Health data.
Consequently, the negative mean academic impact of repeaters found in Xu et al. (2020) is mainly driven by the large adverse influence of repeaters on low-performing regular students in grade seven.
We also have included additionally the five characteristics of teachers for each subject in the regressions focusing on subject-level achievement. Results are similar to the estimates shown in Table 6.
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Acknowledgments
We are grateful to the Editors, Shuaizhang Feng and Madeline Zavodny, and two anonymous referees for helpful comments. Thanks also go to the Chinese National Survey Data Archive (http://cnsda.ruc.edu.cn) for providing access to the China Education Panel Survey data.
Funding
Bin Huang acknowledges financial support from China’s National Social Science Foundation in Education (Project Number: BFA190054). Rong Zhu acknowledges financial support from the Australian Research Council Linkage Project (Project Number: LP170100718).
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Huang, B., Zhu, R. Peer effects of low-ability students in the classroom: evidence from China’s middle schools. J Popul Econ 33, 1343–1380 (2020). https://doi.org/10.1007/s00148-020-00780-8
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DOI: https://doi.org/10.1007/s00148-020-00780-8