







































 

 

 

 

 

Peer Effect of Middle School Students: A 

Natural Experiment Based on Puberty 

Developmental Maturity

Yuhong Du, Yanbin Guo

Beijing Normal University, Beijing 100875, China 

 

Abstract. Peer is an important factor affecting the academic perfor-

mance of middle school students. Domestic research has discussed this 

issue, but there are still some shortcomings in solving endogeneity as-
pects. Therefore, this study used the random effect of natural changes in 

pubertal development and maturity of middle school students in two 
years adjacent to the same class to identify peer effects due to changes in 

pubertal development and maturity; at the same time, first-order differ-

ence and quantile regression are used to solve the endogeneity problems 
in general regression analysis. We found that girls’ developmental ma-

turity is significantly negatively related to their performance, and boys’ 

developmental maturity is significantly positively related to their per-
formance, which indicates that there is a gender difference in the impact 

of adolescent developmental maturity on academic performance of mid-
dle school students. In addition, the peer effect is also heterogeneous, 

that is, in overall, the lower the development maturity of girls in a class, 

the more conducive to the improvement of student performance; the 
higher the maturity of students in class, the more conducive to the im-

provement of student performance. The findings of this study have cer-
tain policy implications for adjusting the school age of school-age chil-

dren. 

Best Evid Chin Edu 2019; 4(1):425-442. 

Doi: 10.15354/bece.20.ar019. 

Keywords: Peer Effect; Natural Experiment; Developmental Maturity; Heteroge-

neity

 

 
 

Correspondence to: Yuhong Du, Professor, Director, Faculty of Education, Beijing Normal University, Beijing 

100875, China. E-mail: dyh@bnu.edu.cn. 



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 426 

Introduction 

N the framework of the educational production function, family, school, student 

personal characteristics and peers are all important factors affecting student aca-

demic performance. In the past few decades, a large number of studies have con-

ducted a lot of fruitful discussions on the factors of families, schools, and students, and 

can accurately estimate the role of each factor; however, there is no clear conclusion 

about the role of peers, especially in the mainland of China, and is particularly very rare 

on the peer effects in middle school students. Therefore, this study attempts to analyze 

the peer effect of middle school students in mainland of China.  

Literature Review 

Peer effect is also called peer effect. Research on the role of peers in education can be 

traced back to the Coleman report (1966). The study found that peers, families, teachers, 

schools and other factors affect students’ academic performance. Most of the early stud-

ies were limited to the discussion of the relationship between peers and academic per-

formance (Caldas & Bankston, 1997; Link & Mulligan, 1991), and did not overcome 

the endogeneity problem in estimation. In 2000, Hoxby (2000b) for the first time ana-

lyzed the peer effect in schools by using the random factors of the birth of the popula-

tion, and relatively accurately estimated the peer effect in education. Hoxby’s idea of 

using natural experiments to overcome endogeneity to estimate peer effects has gradual-

ly gained importance in subsequent related research. 

Concepts, Pathways, and Heterogeneity 

The definition of peer is the first step in the study of peer effects, and it is also a major 

challenge in the study of peer effects. Early studies often chose classmates (Sacerdote, 

2001; Zimmerman, 2003), class level (Ding & Lehrer, 2007), and grade level (Hoxby, 

2000b; Hanushek, et al., 2003) as individual student peers. In recent years, there have 

been an increasing number of researches using students’ self-reported friends 

(Ilmarinen, et al., 2017; Lavy & Sand, 2018) as peers for analysis. This social network-

based peer effect is obviously more real, but data acquisition is difficult and generally 

difficult to achieve. 

 

 

 

 
 

About the author: Yanbin Guo, Graduate Candidate, Beijing Normal University, Beijing 100875, China. E-mail: 

ybguo@mail.bnu.edu.cn 

Funding: This study was supported by the 2015 major research project of the Ministry of Education’s Philosophy 

and Social Science research project “Relationship and Contribution of Education and Economic Development” 

(Project #: 15JZD040). 

Conflict of Interests: None. 

 

I 



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 427 

In addition to defining peers, clarifying the concept of peer effects is also the 

basis for conducting related research. There has been no consensus on the concept of 

peer effects. At present, there are several representative views: Sacerdote (2011) be-

lieved that the peer effect includes almost all external factors that are not market- or 

price-driven, such as peer background, current behavior, or educational attainment. Lu 

& Zhang (2007) believed that the peer effect is the interaction between people, which 

directly affects the performance of relevant actors. Du & Yuan (2016) defined the peer 

effect in education as the influence of the background, behavior, and performance of 

peers in dormitories, classes, grades, or schools on student performance or behavior. 

There are various ways to influence this effect. Based on the above analysis, the author 

considers the effects of natural characteristics, background, behavior, performance, and 

non-cognitive characteristics of peers in schools on student performance, behavior, and 

non-cognitive skills as peer effects. 

There are many ways in which the peer effect can play a role, and peer perfor-

mance is not the only way to generate peer effects. Hoxby (2000b) believed that the 

ways of peer effect include: mutual help between students; students’ inherent ability to 

affect peers through the spillover effect of knowledge and the impact on class position-

ing; behaviors affected by the environment also affect peers; disability, race, gender, 

and family income also play a role; peer effects can also take a part through the atti-

tudes of teachers and administrators to students. 

Earlier studies on peer effects were mostly limited to the description of correla-

tions. Strategies such as ordinary least squares were often used, but these methods did 

not solve the problem of endogeneity well. One of the challenges in estimating peer 

effects is endogeneity. According to the theories of Manski (1993), Manski (1995), and 

Moffitt (2000), the endogeneity of the peer effect estimation mainly comes from Selec-

tion Bias and Reflection Problem. Parents often choose a school, class, or even a teach-

er for their children based on their family economic and social background, making it 

difficult to simply attribute changes in students’ academic performance to peers, which 

is the so-called self-selection bias. Individual students and their peers live in the same 

environment and receive the same education, and there will inevitably be mutual influ-

ences between each other. That is, students are not only affected by peers, but also stu-

dents themselves. Moreover, these two effects often occur at the same time, and it is 

often difficult to separate them, which causes the problem of simultaneous bias in the 

estimation of peer effects. 

Peer effects are also heterogeneous, meaning that students of different types or 

abilities may be affected to different degrees and directions by peers. Hoxby (2000b) 

found that the peer effect is asymmetric. Subsequent research has gradually verified this 

conclusion, but the existing researches on the direction of heterogeneity were not com-

pletely consistent. The conclusions mainly include two major categories: the smaller the 

differences in student abilities or types, the better the student’s development (Ding & 

Lehrer, 2007; Hoxby & Weingarth, 2005), and the larger the differences in student abil-

ities or types, the better the student’s development (Carman & Zhang, 2012; Vigdor & 

Nechyba, 2006). In addition, the identification of heterogeneity often uses two strate-



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 428 

gies: interaction (Hoxby & Weingarth, 2005) or quantile regression (Ding & Lehrer, 

2007; Hanushek, et al., 2003). 

Recognition Strategy 

In recent years, with the continuous improvement of causal inference technology, the 

identification of peer effects has become more accurate. Natural experiments (Angrist 

& Lang, 2004; Hoxby, 2000b) and quasi-experimental studies have gradually attracted 

attention. The key to natural experiments is to find the appropriate random factors. 

Since Hoxby (2000b), the research of natural experiments has been favored by the so-

cial sciences. When it comes to natural experiments, you first need to clarify the rela-

tionship among Random Control Experiment, Natural Experiment, and Conventional 

Observational Studies. 

Standard random experiments generally need to meet three conditions (Freed-

man et al, 2007). First, compare. Compare the differences between the experimental 

group and the control group after the experiment. Second, random assignment. The sub-

jects were randomly assigned to the control group and the experimental group. Third, 

manipulation or intervention by researcher. The researchers gave different experimental 

treatments to the experimental group and the control group. The ideal random experi-

ment needs to fully meet the three conditions mentioned above. Traditional observa-

tional research can often only meet the first condition, that is, “comparing” the differ-

ences between different research objects, and the conditions of “random allocation” and 

“human intervention / control” are often difficult to meet. Natural experiment is a re-

search method between random experiment and traditional observational research. 

Natural experiments are different from traditional observational studies. Be-

cause the former can meet the first condition of random experiments, that is, “compari-

son”, it can at least guarantee that the sample is random (Random) or approximately 

random (As Random), which is also a natural experiment closer to random experiments 

than traditional observational research. The reason is that it should be said that random-

ness is the key to natural experiments (Dunning, 2012). Therefore, finding enough ex-

ogenous and uncontrolled factors is a prerequisite for conducting natural experiments. 

“Nature” in natural experiments often comes from some phenomena in social life: for 

example: (1) exogenous shocks: disasters, climate, economic fluctuations; (2) individual 

biological factors: birth, aging, disease, death, etc. (3) geographical location: topogra-

phy, borders; (4) man-made purely random events: draw lots, test scores, government 

policies, etc. In addition, natural experiments are also observational studies, because 

natural experiments also cannot satisfy the condition of “control” in random experi-

ments, and the experimental process cannot be controlled by researchers. Natural exper-

iment, as a causal inference strategy closest to random experiment, provides us with a 

reliable identification strategy, which overcomes the disadvantages of traditional obser-

vational research to a certain extent. 

However, we must also admit that it is often difficult to provide the conditions 

for causal analysis of everything we want to evaluate in social life. The analysis of spe-

cific groups based on natural experiments can often only be regarded as a local average 



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 429 

treatment effect (LATE) (Dunning, 2012). The evaluation of natural experiments is 

generally carried out from three aspects, Plausibility, Credibility, and Relevance (Dun-

ning, 2012). Plausibility refers to the use of quantitative and qualitative methods to 

demonstrate that the allocation process of natural experiments is random; Credibility 

emphasizes that the causal relationship of the model is convincing, that is, the disposal 

variable is independent of other factors that affect the outcome variable; Relevance re-

fers to the problem and intervention to be studied Whether it is substantially related to 

the external validity of the experimental results. The excellent properties of natural ex-

periments in solving endogeneity make it an important choice for identifying peer ef-

fects. Hoxby (2000b) used the random factors of birth changes to identify the effect 

peer brought by gender and race. The key of this research is to cleverly find the natural 

changes in student gender and changes in student performance caused by natural chang-

es in race. It overcomes the corresponding endogenous problem, thus setting a prece-

dent for identifying the peer effect by natural experiments. 

Effective Natural Factors 

As a multi-disciplinary issue, the study of peer effects has been involved to varying de-

grees in economics, psychology (Ilmarinen, et al., 2017), and sociology (Cheng, 2017). 

In recent years, influenced by multidisciplinary, interdisciplinary, and transdisciplinary 

trends, different disciplines have learned from each other in terms of research content 

and research methods. Affected by psychology and sociology, a lot of researches have 

been done on the relationship between adolescent developmental maturity and students’ 

academic performance. The maturity of puberty is a natural phenomenon of life, and it 

is a normal physiological phenomenon that does not transfer by human will. Puberty 

refers to the physical development of people who were originally able to have children 

(McKechnie, 1979). Physiological research often uses the two indicators of Pubertal 

Status and Pubertal Timing to describe the physical development of adolescence. The 

former refers to changes in the body of an individual, including secondary sexual char-

acteristics, and the latter refers to the sooner or later of these changes compared to their 

peers. To characterize the differences in pubertal development in different individuals, 

the term “pubertal mature pubertal development” was introduced, and it is often meas-

ured as soon as puberty enters. 

Adolescent developmental maturity has a certain effect on individual cognitive 

skills and non-cognitive skills, and this effect is direct, that is, developmental maturity 

often depends on the sooner or later of puberty. A study by Beltz and Berenbaum (2013) 

found that the effects of adolescents entering puberty on their cognitive development 

and brain development differ by gender. They used the characteristics of male first 

spermatorrhea and female menarche as the proxy variables for puberty. The study found 

that boys who entered early adolescence performed better on cognitive tests than boys 

who entered later adolescence; for women, this effect was not significant. Cavanagh 

and Riegle-Crumb (2007) also used girls’ self-reported menarche as a proxy variable 

for early and late puberty. They found that girls who matured earlier had lower GPA in 

high school, were more likely to encounter failure in high school courses, and graduated 



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 430 

from high school is less likely. Research by Daniel et al. (1982) found that maturity at 

puberty affects both cognitive and non-cognitive performance of students. Compared 

with boys with normal developmental maturity, boys who have late maturity (secondary 

sexual development score below 80% of participants) have worse cognitive scores and 

lower expectations from their parents; they have earlier maturity of boys performed 

better on cognitive scores than boys of moderate maturity and later maturity. Kristian 

and Tuomas (2017) used the development of adolescent secondary sexual characteris-

tics as a proxy variable for early and late puberty. The study found that students who 

matured later (including boys and girls) have lower cognitive scores, worse academic 

performance, and Future income will be lower. This study believes that there is a differ-

ence between men and women entering puberty, but this is not the reason for the differ-

ences between men and women in cognitive ability and academic performance 

(Koerselman & Pekkarinen, 2017). 

In summary, adolescent developmental maturity is a natural factor that has a di-

rect impact on students’ academic performance, parental expectations, etc., and most 

studies support the conclusion that boys mature earlier and girls mature later are more 

favorable for student development. In this sense, the influence of peer development ma-

turity on student achievement can be regarded as a peer effect. Based on this, this study 

attempts to supplement and develop the existing research from the following three as-

pects: First, we have overcome the problems of self-selection bias and synchrony bias 

commonly encountered in the estimation of peer effects. This study uses natural exper-

iments on changes in adolescent developmental maturity to more accurately estimate 

the peer effect brought by adolescent developmental maturity. Second, it enriches the 

related theories of peer effects. This research combines the research results of psychol-

ogy and physiology, and focuses on the influence of the physiological characteristics of 

peers on students’ academic performance, which enriches the research content of peer 

effects to a certain extent. Of course, puberty developmental maturity is just one type of 

peer effect, and the overall analysis of all types of peer effect has yet to be explored. 

Third, the external validity of the study is higher. In the past, researches on peer effects 

mostly focused on a certain school, region, or project. The research on peer effects at 

the national level is still relatively limited. This study uses the tracking data of middle 

school students in mainland China to analyze this problem to a certain extent. This im-

proves the applicability of the conclusion. 

The following structural arrangement of this article is as follows: The third part 

introduces the model and data sources; the fourth part gives descriptive statistical re-

sults, the results of econometric analysis, and the robustness test; the fifth part gives 

research enlightenment and shortcomings. 

Research Design 

Empirical Strategy 

Natural Experiment 



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 431 

The recognition of peer effects is inseparable from the clever application of causal in-

ference technology. Therefore, finding suitable random factors is very important for the 

construction of the entire model. This factor must not only affect the academic perfor-

mance of peers, but also ensure that it is not affected by human factors. We use the ma-

turity of middle school students as a random factor to identify peer effects. In the pro-

cess of choosing a school and class, parents rarely consider the maturity of their class-

mates, and developmental maturity often has a significant impact on their academic 

performance. In addition, from the perspective of the educational production function, 

the factors affecting the average grade of the class include factors such as family char-

acteristics, school characteristics, and personal characteristics, but many factors will not 

change significantly in the short term. For example: the overall ability of class students, 

the family economic background of the class students as a whole, the school environ-

ment, the characteristics of teachers, etc., and other unobservable factors in the short-

term changes are random. Therefore, this article uses the number of students who en-

tered puberty (that is, the first male nocturnal emission or female menarche) in the same 

class as the proxy variable for student development and maturity, and then eliminates 

other factors that affect the average grade of the class through a first order difference. 

The effect of changes in the developmental maturity of middle school students on the 

change in the average grade of a class during the year can be regarded as a peer effect. 

This design for identifying peer effects can be regarded as a natural experiment. The 

basic model established in this article is as follows: 

 

               
                               (1) 

 

                     
                                       (2) 

 

     represents the average score of the academic performance (cognitive ability test) of 

grade c in class g of school j,     
    represents the maturity of the students in the class, 

and the corresponding coefficient α1 is the size of the companion effect concerned in 

this article;      represents the share of students in the same class School characteristics; 

     represents the average true ability of students in the same class;      is an unobserv-

able error term. 

We can obtain the following equation by first difference. 

 

                
             (3) 

 

Where the unobservable factor      is random, then       in Equation (3) has a 

normal distribution with a mean value of 0. Equation (3) gives the relationship model 

between the development maturity of the students in the class and the average perfor-

mance of all students in the class.       includes the results of students who have en-

tered adolescence. Therefore, in order to further overcome the problem of possible sim-

ultaneous errors, we replace the student’s grade       in formulas (1) and (2) with the 



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 432 

average grade     
  of students who have not yet entered adolescence in the same class, 

that is,      
  means that those in class c of class g of school j have not entered adoles-

cence. The average score of the students’ academic performance, so through the differ-

ence, we can get a model similar to (3): 

 

     
            

             (4) 

 

and the corresponding coefficient δ1 is the size of the peer effect concerned in this arti-

cle. 

Heterogeneity Model 

Studies (Ding & Lehrer, 2007; Hoxby & Weingarth, 2005) show that the peer effect is 

heterogeneous, that is, the direction and magnitude of peer influence on students at dif-

ferent levels may be different. We use the strategy of conditional quantile regression 

(Koenker & Bassett, 1978) proposed by Koenker and Bassett to identify the heterogene-

ity of peer effects. Combined with the research object of this article, we set the quantile 

regression model as follows: 

 

        
       

               
           (5) 

 

     
  represents the value of θ quantile given      

   . Quantile regression can estimate 

any percent and minimize the MSE function to obtain the estimator, which is equation 

(6). 

 

  
  

              
            

         
             

               
            

   

   cjg′  0+ 1  cjgmat   (6) 

 

Data Sources 

The data used in this article are micro-data from China Education Panel Survey (CEPS). 

CEPS uses PPS sampling to design a sampling frame based on the “six population” in 

four stages, covering 28 county-level units (counties, districts, and cities) randomly se-

lected across the country with the average education level and population ratio as strati-

fied variables. The sample is a good representation of mainland China. During the sam-

pling process, 1-2 classes were sampled in each grade of each school, and all students in 

the selected classes were sampled. The survey took the 2013-2014 school year as a 

baseline and surveyed 10,279 seventh-grade students. In the 2014-2015 school year 

follow-up survey, a total of 9,449 seventh-grade students were successfully followed up 

with a follow-up rate of 91.9%, and this is the representative of the situation in the 



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 433 

country. The survey also surveyed the backgrounds of student parents, classroom teach-

ers, class teachers, and school leaders. The relevant data can well meet the research 

needs of this article. 

Each round of the CEPS survey will test the students’ cognitive ability. The 

content of this test question does not involve the specific memorizing knowledge taught 

in the school curriculum, but measures the students’ logical thinking and problem solv-

ing ability. Finally, the three-parameter project reflection theory (IRT) is used to con-

vert the standard points into international standards and characteristics of national 

standardization. This study focuses on peer-level peer effects in schools and requires 

peer composition to remain stable for a certain period of time. As a result, we only kept 

data on 7,826 students from 184 classes in 96 schools that did not reclassify or merge 

during the two surveys. At the same time, 213 students who did not meet the study de-

sign
1
 were deleted, and the remaining valid sample was 7,613

2 
students in 184 classes of 

96 schools. 

Results 

Describe Statistical Results 

In combination with the literature review, this article summarizes the main factors that 

may affect the average grade of the class. Table 1 gives descriptive statistics of the 

main variables. From Table 1, we can find that from the core variables, the scores of 

the 8th grade students’ academic performance have decreased compared with the 7th 

grade; in the same class, the students’ average maturity, girls’ and boys’ maturity during 

the year increased by approximately 50.12%, 39.69%, and 75.54%,
3 
respectively. It can 

be seen that a higher proportion of boys have entered adolescence within two years. 

From the perspective of family characteristics, compared with the seventh 

grade, the average maximum years of schooling of parents and the proportion of only 

children have declined, with 0.3 years and 1% respectively. The decline in parents 

‘years of education may be caused by measurement errors, that is, the parents’ educa-

tion level was answered by the children in the first round of surveys, while the parents 

or their children’s guardians answered in the second round of surveys. The decline in 

the proportion of only children may be related to the “The only child of one parent can 

have a second child” policy that was implemented nationwide in November 2013 and 

can be regarded as a random change. 

The proportion of students with higher family socioeconomic status in the class 

increased by 1.5%, this is majorly related to the type of community in which the student 

lives to identify the family socioeconomic status of the participated student. It is possi-

ble for the student residence community to change within two years, but this change is 

random, and it is difficult to have a substantial impact on student development and ma-

turity in the short term. In terms of school characteristics, the nature of the school has 

not changed in two years; the school ranking has declined slightly. Affected by factors 

such as measurement error, the above changes are all within acceptable ranges. Descrip-

tive statistical results generally support the hypothesis of this study. 



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 434 

Table 1. Summary Statistics of Main Characteristics. 

Description of Variables Type Mean SD Min Max N 

Core Variables 

Class average score from stu-
dents not entering the puberty in 
seventh grade

[1]
 

Continuous -0.171 0.581 -1.707 1.466 2,589 

Class average score from stu-
dents not entering the puberty in 
eighth grade 

Continuous -0.237 0.610 -2.021 1.267 2,589 

Puberty maturity from all students 
in seventh grade

[2]
 

Continuous 17.447 7.347 3 45 2,589 

Puberty maturity from all students 
in eighth grade 

Continuous 26.191 8.234 6 55 2,589 

Puberty maturity from female 
students in seventh grade 

Continuous 13.092 5.512 2 27 2,589 

Puberty maturity from female 
students in eighth grade 

Continuous 18.288 5.873 3 33 2,589 

Puberty maturity from male stu-
dents in seventh grade 

Continuous 4.502 3.631 0 24 2,589 

Puberty maturity from male stu-
dents in eighth grade 

Continuous 7.903 4.677 0 28 2,589 

Family Characteristics 

The ratio of classroom high SES 
in seventh grade 

Continuous 0.385 0.292 0 1 2,589 

The ratio of classroom high SES 
in eighth grade 

Continuous 0.400 0.288 0 1 2,589 

Class average education highest 
years of parents in seventh 
grade

[3]
 

Continuous 16.47 1.104 12.90 19 2,589 

Class average education highest 
years of parents in eighth 

Continuous 16.17 1.196 12.37 18.71 2,589 

The ratio of classroom single-
child in seventh grade 

Continuous 0.410 0.256 0 0.969 2,589 

The ratio of classroom single-
child in eighth grade 

Continuous 0.400 0.265 0 0.969 2,589 

School Characteristics  

The property of school in seventh 
grade

[4]
 

Discrete  1.095 0.408 1 4 2,589 

The property of school in eighth 
grade 

Discrete 1.095 0.408 1 4 2,589 

The rank of school in seventh 
grade 

Discrete 4.123 0.680 2 5 2,560 

The rank of school in eighth 
grade 

Discrete 4.174 0.755 1 5 2,589
[5]

 

Note:  

[1]. The cognitive tests score range of two wave survey is -2.029~2.710,-3.137~ 2.063 respectively, 
and CEPS using z-scores. 

[2]. Using the number of students entering the puberty (namely appearing the first spermatorrhea and 
menarche) as proxies of puberty maturity. 

[3]. Illiteracy, primary schools, junior secondary schools, secondary vocational schools, vocational high 
schools, regular senior secondary schools, higher vocational colleges, undergraduate schools and 
graduate schools and above denoted 0 year, 6 years, 9 years, 12 years,12 years, 12 years,12 
years, 16 years, 19 years, respectively  

[4]. The property of school includes public school, private school subsidized by the government, ordi-
nary private school and private school for children of migrant workers, which is denoted by 1, 2, 3 
and 4, respectively. 

[5]. There is a school that didn’t complete the rank of school in eighth grade, so the sample size of the 
rank of school in seventh is 2589. 



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 435 

Table 2. Puberty Maturity on Score for All Students. 

 Puberty R
2
 N 

Scores 0.0386** (0.0193) 0.2932 7,114 

Note: 1. The table controls for class average education highest years of parents, the ratio of only-child 
from the same classroom and the ratio of classroom single-child and includes school fixed effects. The 
number of sample size is the number of students. 

2. Clustered standard errors are reported in parentheses and standard errors are clustered by class.  

3. **: p<0.05. 

 

 

 

 

Table 3. Peer Effects from Puberty Maturity. 

  
Puberty Maturity from 
All Students 

Class Average Score from Students 
Not Entering the Puberty 

Puberty Maturity from 
All Students 

0.0057*** (0.0011) 0.0009 (0.0020) 

N 184 56 

R
2
 0.0044 0.0001 

Note: 1. Robust standard errors is reported in parentheses 

2. Each column represents a separate regression and the number of sample size is the number of class. 

3. ***: p<0.01. 

 

 

 

 

Table 4. Peer Effects from Puberty Maturity by Sex. 

 
Puberty Maturity from All Stu-
dents 

Class Average Score from Stu-
dents not Entering the Puberty 

Puberty Maturity 
from Female Stu-
dents 

-0.0106*** 
(0.0014) 

 
-0.0142*** 
(0.0026) 

 

Puberty Maturity 
from Male Stu-
dents 

 0.0376*** (0.0018)  0.0338*** (0.0037) 

N 184 184 56 56 

R
2
 0.0086 0.0595 0.0127 0.0334 

Note: 1. Robust standard errors is reported in parentheses 

2. Each column represents a separate regression and the number of sample size is the number of class. 

3. ***: p<0.01. 

 

 

 

 

 



Du & Guo. Peer Effect of Middle School Students 

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Econometric Analysis Results 

The peer effect of adolescent developmental maturity: From Table 2 in the natural ex-

periment, it is not difficult to find that in controlling the family characteristics and 

adopting the fixed school effect method, from the perspective of the individual student, 

the student’s developmental maturity and academic performance are related, that is, 

Table 2 estimates the results, but this result is undoubtedly endogenous. 

In order to further explore the causal relationship between student development maturi-

ty and student performance, we give the estimated results of formulas (3) and (4), which 

are the first and second columns of Table 3. We can find that the development maturity 

of the students in the class is positively related to the students’ performance, but the R2 

in both models is smaller. At the same time, through further analysis of the data, we 

found that in the samples used in column 1 and column 2 of Table 3, the number of 

boys accounted for 51.65% and 83.35%, respectively, and the number of boys had cer-

tain advantages. In addition, from Table 1, we can find that the ratio of girls entering 

adolescence increased by 39.69% within two years, and the proportion of boys entering 

adolescence increased by 75.54%. In summary, we believe that the results given in Ta-

ble 3 more reflect the impact of male students’ developmental maturity on student per-

formance, and do not fully characterize the impact of developmental maturity of all stu-

dents, especially female students, on student performance. Existing physiology and psy-

chological studies show that there is a gender difference in the impact of adolescent 

developmental maturity on males and females, that is, early maturity of boys and late 

maturity of girls are more favorable for individual development. Therefore, in this study, 

    
    in equation (1) was replaced by female development maturity    

  
 and male devel-

opment maturity     
  , respectively. Equations (2) and (4) were treated the same, and 

new equations (3) and Equation (4). The estimation results are shown in Table 4. 

After considering the gender differences in student development maturity, we 

found that the impact of development maturity on student performance became robust 

and the corresponding R2 became relatively reasonable. From the first column of Table 

4, the maturity of the girls in the class is negatively correlated with the class average 

and is very significant. When we focus on the peer effect to students who have not yet 

reached puberty in the class, that is, as shown in column 3 of Table 4, students are still 

negatively affected by the maturity of the development of girls from the class, which is 

very significant. The research conclusions are basically the same. The study by Dubas 

et al (1991) found that the later the girls mature, the higher their academic performance 

ranks. From the second column of Table 4, the development maturity of the boys in the 

class has a very significant positive correlation with the average grade of the class. 

When we only focus on the impact of boys ‘developmental maturity on students who 

have not yet reached puberty in the class, the conclusion is still valid, as shown in col-

umn 4 of Table 4, that is, boys’ developmental maturity has a positive predictive effect 

on student performance. The results of Dubas et al (1991) and Daniel et al (1982) are 

consistent. Both studies show that the sooner a boy matures, the higher his academic 

performance. The above results also confirm our results in Table 3, that is, the results in 



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 437 

Table 3 mainly reflect the impact of male students’ developmental maturity on student 

performance. 

Robustness Test 

The maturity of puberty is a natural life phenomenon, but if there are factors related to 

both puberty development maturity
4 

and academic performance, such as: Family eco-

nomic and social status, learning pressure, then equation (3) the estimation results of 

equation (4) may be inconsistent. Therefore, this study analyzes the above factors one 

by one by sample. We divide the students’ socioeconomic status and the learning pres-

sure of the three major subjects into high and low according to the median, and perform 

regression based on formula (4). The results are shown in Tables 5 and 6. 

From the second line of Table 5, the negative impact of the student’s perfor-

mance on the maturity of the girls in the class still exists in the subgroups with high 

socioeconomic status, low socioeconomic status, high math pressure, and low math 

pressure. This is basically consistent with the conclusions in columns 1 and 3 of Table 

4, which shows that the conclusions of this article are relatively robust. From the fourth 

row of Table 5, the development maturity of the boys in the class is positively correlat-

ed with the academic performance in different groups. This is basically consistent with 

the conclusions in columns 2 and 4 of Table 4, which shows that the influence of fami-

ly socioeconomic status and mathematical pressure on adolescent development and ma-

turity is not serious, and it can basically guarantee that adolescent development and ma-

turity exists independently as exogenous factors. 

From the second row of Table 6, it is not difficult to find that the development 

maturity of class girls has always had a negative impact on student performance, which 

is consistent with the conclusions in columns 1 and 3 of Table 4. The development ma-

turity of female students has a negative effect on student performance prediction. Look-

ing at the fourth row of Table 6, the impact of the developmental maturity of the boys 

in the class on the student’s performance is positive, indicating that the developmental 

maturity of adolescence is not seriously affected by the learning pressure of Chinese 

and English, and the regression results and benchmark regression results (Table 4 col-

umns 2 and 4) are closer. It can be seen that the basic conclusion of this study is rela-

tively stable, that is, the learning pressure does not significantly affect the maturity of 

adolescence, so the latter can exist as an independent natural factor. 

Peer Effect of Developmental Maturity under Different Conditional 

Quantiles: Heterogeneity Model 

Figure 1 shows the impact of girls’ maturity on the performance of non-pubertal stu-

dents in different quantiles. The horizontal axis represents the conditional quantiles of 

class girls’ developmental maturity, and the vertical axis represents the effects of girls’ 

developmental maturity on performance under different conditional quantiles. In overall, 

the peer effect of girls’ developmental maturity is heterogeneous. Student performance 

decreases with the increase of conditional quantiles, and has been shown to have a sig- 



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 438 

 

Table 5. Peer Effects from Puberty Maturity by Sex: Robustness. 

 High SES Low SES 
High Pressure 
From Math 

High Pressure 
From Chinese 

Puberty Maturity from 
Female Students 

-0.0069 
(0.0047) 

-0.0385*** 
(0.0084) 

-0.0112* (0.0060) -0.0203*** (0.0064) 

Puberty Maturity from 
Male Students 

0.0467*** 
(0.0067) 

0.0075 
(0.0087) 

0.0565*** (0.0101) 0.0210*** (0.0061) 

Note: 1. Robust standard errors is reported in parentheses 

2. All results are estimated by equation (4) and each cell represents a separate regression. 

3.*: p<0.1, ***: p<0.01. 

 

 

 

 

Table 6. Peer Effects from Puberty Maturity by Sex: Robustness. 

 High Pressure 
from Chinese

†
 

Low Pressure 
from Chinese 

High Pressure 
from English 

High Pressure 
from English 

Puberty Maturity 
from Female Stu-
dents 

-0.0185 (0.0115) 
-0.0148*** 
(0.0044) 

-0.0300*** 
(0.0047) 

-0.0069 (0.0057) 

Puberty Maturity 
from Male Stu-
dents  

0.0080 (0.0100) 
0.0491*** 
(0.0058) 

0.0450*** 
(0.0063) 

0.0187* (0.0096) 

Note: 1. Robust standard errors is reported in parentheses 

2. All results are estimated by equation (4) and each cell represents a separate regression. 

3.*: p<0.1, ***: p<0.01. 

†: In this subgroup, puberty maturity on score is not significant which result from that the number of size 
is small. 

 

 

 

 

nificant negative impact on most of the quantiles. Before the 70th quantile, the impact 

of class maturity on student achievement was similar to the regression results of OLS; 

after the 70th quantile, the negative impact of class maturity on student achievement 

was affected by the quantile. The increase of the point increases rapidly, and it is obvi-

ously larger than the regression result of OLS. The influence reaches the maximum val-

ue at the 90th quantile. 

Figure 2 shows the influence of boys’ developmental maturity on the average 

performance of non-pubertal students in different quantiles. The horizontal axis repre-

sents the conditional quantiles of class boys ‘developmental maturity, and the vertical 

axis represents the impact of boys’ developmental maturity on performance in different 

conditional quantiles. Overall, the peer effect of boys’ developmental maturity is heter-

ogeneous. Student performance improves with the increase of conditional quantiles, and 

the effect on almost all quantiles is always significantly positive. For the 10th to 30th 

quantiles, student performance decreases as the conditional quantile increases, and for 



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 439 

Figure1. Peer Effects in Different Quantiles in Male. 

 

 

 

 

Figure 2. Peer Effects in Different Quantiles in Female. 

 

 



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 440 

the 30th to 80th quantiles, student performance increases as the conditional quantile 

increases. After the 80th quantile, the student’s performance decreases again with the 

increase of the conditional quantile, and the effect reaches the maximum at the 90th 

quantile. 

Conclusion and Discussion 

Peer effect, as a classic problem in economics, pedagogy, psychology, and sociology, is 

of great significance to school placement, school enrollment, and parents’ choice of 

school. However, there are not many domestic studies on the peer effect in mainland 

China; especially the related studies that have effectively solved the endogenous nature 

are still scarce. We used the national survey data of CEPS to design natural experiments 

using changes in the development and maturity of middle school students, and empiri-

cally test the peer effect of middle school students in mainland China. This is one of the 

earlier studies in mainland China to analyze the peer effects of middle school students. 

This study found that peer maturity has an impact on the academic performance of mid-

dle school students, and that this effect has a gender difference. The developmental ma-

turity of boys has a very significant positive correlation with the average class perfor-

mance, while the developmental maturity of girls has a very significant negative corre-

lation with the average class performance. 

This study has certain policy implications for adjusting the school age of 

school-age children. We found that the peer effect of middle school students ‘develop-

mental maturity has gender differences, which confirms and expands the common sense 

that boys’ mental maturity is later than that of girls. Therefore, from the perspective of 

adolescent development and maturity, the age at which boys and girls enter school 

should be different. The enrollment age of boys should be slightly behind that of girls of 

the same age, in order to give full play to the positive impact of higher development 

maturity and lower maturity of girls on classmates. 

This article basically solves the endogenous problem of peer effect estimation, 

and has played a positive role in enriching related research. However, the following 

limitations exist: (1) This study analyzes the peer effect of middle school students from 

the perspective of adolescent development and maturity, but this is only one type of 

peer effect, and the overall analysis of all types of peer effects has not been achieved. 

The peer effect has various types and strong endogenous characteristics. It is very diffi-

cult to measure all kinds of peer effects completely. Therefore, in order to accurately 

measure peer effects, existing research can often only identify some types of peer ef-

fects. Of course, these studies are undoubtedly helpful for the subsequent overall analy-

sis of all types of peer effects, which is the direction of future efforts. (2) In theory, the 

most ideal peer effect should be based on the analysis of friends, for example: analysis 

based on social networks, but this type of research often requires higher quality data, 

data acquisition is relatively difficult, and everyone’s friends change often. It should be 

said that this type of peer effect is very effective, but it is also not easy to achieve, 

which is undoubtedly a point for future research.  

 



Du & Guo. Peer Effect of Middle School Students 

Vol.4, No. 1, 2020 441 

Notes 

1. Refers to samples of boys who have entered their age at menarche and girls who have entered 

their age for the first time, and boys who have not responded to the age of their first sperm and 

girls who have not responded to the age of their menarche, as well as samples of menarche and 

the time when their first sperm is younger than 9 years old. 

2. When considering only the results of adolescent students (e.g., columns 3 and 4 of Table 4), the 

valid sample is 2,589 students from 56 classes in 30 schools. 

3. Female: (18.288-13.092) /13.092 = 0.3969; Male: (7.903-4.502) / 4. 502 = 0.7554; all students: 

(26.191-17.447) /17.447 = 0.5012. 

4. Studies have shown that girls 'menarche sooner or later, and boys' first sperm emission sooner or 

later are affected by factors such as genetics, nutritional status, economic income level, and pres-

sure, and the impact of these factors on the maturity of men and girls can be attributed to differ-

ences in family economic and social status The resulting nutritional differences. 

 

 

 

 

 

 

 

 

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Received: 13 November 2019 

Revised: 04 December 2019 

Accepted: 17 December 2019 

 

The Chinese version of this article has been published in Education and Economy, 2019; 03:40-48. 

The English version has been authorized for being publication in BECE by the author(s) and the Chi-

nese journal. 

杜育红, 郭艳斌. 初中生的同伴效应: 基于发育成熟度的自然实验. 教育与经济, 2019; 03:40-48. 

 


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