middle school or junior high? how grade-level configurations affect academic achievement

Middle school or junior high? Howgrade-level configurations affect academicachievement

Elizabeth Dhuey Department of Management, University ofToronto, Scarborough

Abstract. Does the grade-level configuration of a school affect academic achievement?This research examines the effect of attending a middle/junior high school on academicoutcomes in British Columbia, Canada, relative to attending a school from kindergartenthrough grade 8. Using an OLS strategy, I find that attending a middle/junior high schoolreduces grades 4 to 7 achievement gains in math and reading by 0.125–0.187 and 0.055–0.108, respectively. Similar-sized estimates are found for math using a 2SLS strategy.Finally, large negative effects on grade 10 and grade 12 English exams are also found. JELclassification: I2

College ou stage intermediaire entre primaire et secondaire? Comment ces configurationsaffectent les resultats scolaires. Est-ce que la configuration des programmes en niveauxprimaire, college, secondaire affecte les resultats scolaires? Ce texte examine les effets del’introduction d’un segment intermediaire entre primaire et secondaire sur les resultatsscolaires en Colombie Britannique (Canada) par rapport a un cursus continu du jardind’enfance a la 8ieme annee. A l’aide de la methode des moindres carres ordinaires, onmontre le passage par ce stade intermediaire entre la 4ieme et la 7ieme annee reduit laperformance scolaire en mathematiques et en lecture de 0.125 a 0.187, et de 0.055 a0.108 respectivement. Ces resultats sont confirmes pour les mathematiques en utilisantla methode des moindres carres a deux etapes. Enfin, on decouvre aussi de forts effetsnegatifs sur les notes en anglais en 10ieme et 12ieme annees.

1. Introduction

Does the grade-level configuration of a school affect student achievement? Whatconstitutes a ‘standard’ configuration has changed many times over the past

The author is also affiliated with the Centre for Industrial Relations and Human Resources,University of Toronto. I would like to thank Kelly Bedard, Harry Krashinsky, Justin Smith, andvarious seminar participants for helpful comments. I would also like to gratefully acknowledgethe financial support of the Social Sciences and Humanities Research Council of Canada.Email: [email protected]

Canadian Journal of Economics / Revue canadienne d’Economique, Vol. 46, No. 2May / mai 2013. Printed in Canada / Imprime au Canada

0008-4085 / 13 / 469–496 / C© Canadian Economics Association

470 E. Dhuey

century, and the current push is to merge middle and junior high schools withtheir elementary counterparts to create kindergarten through grade 8 schools(Schwartz et al. 2011). This paper examines the effect of different grade-levelconfigurations on student achievement in British Columbia, Canada, by test-ing whether students who attend a middle or junior high school have differ-ent academic achievement gains than do students who attend one school fromkindergarten until the beginning of high school.

Understanding the impact of grade-level configuration on academic achieve-ment is important, as rearranging grade-level configurations within schools maybe a comparatively inexpensive policy lever compared with other school re-forms, and it is something over which individual districts often have control.Grade-level configuration may have an effect on student achievement, as it canimpact schools’ practices and policies such as curriculum development and de-livery. It can also have an effect on school and cohort size, and it determines thenumber and timing of structural transitions a student takes during his or hereducational career. Finally, it can affect peer composition and age distributionwithin schools. All of these factors can greatly influence student achievement,yet despite the extensive research that has been conducted on other factorsthat may affect achievement growth – such as teacher quality, class size, andschool resources – very little attention has been paid to the effect of grade-levelconfigurations.

During the early 1900s in the United States, education reformers experimentedwith splitting the elementary school grades into two school types, one for theearly elementary grades and one for the later grades, termed junior high school.Educators during that time believed that the kindergarten through 8th gradeschooling structure was unsupported by psychological research and ignored thedevelopmental needs of the students (Fleming and Toutant 1995). The creation ofjunior high schools in Canada generally lagged behind their establishment in theUnited States by more than a decade. However, by 1920, two junior high schoolshad opened in the country – one in Winnipeg, Manitoba, and one in Edmonton,Alberta (Johnson 1968). British Columbia’s first junior high school, which servedgrades 7 through 9, opened in Penticton, in 1926 (Fleming and Toutant 1995).By 1950, many junior high schools existed in British Columbia, and over 5,000junior high schools existed in the United States (Lounsbury 1960). Despite thepopularity of this trend, the British Columbia Ministry of Education later decidedto return grade 7 to the elementary system, and during the 1950s reorganizedall provincial schools into three groups: kindergarten through grade 7 schools,grades 8 through 10 schools, and grades 11 through 12 schools. However, evenafter this reorganization the debate continued in British Columbia regardingthe ‘best’ grade-level configuration. In the 1960s, education reformers beganto advocate for middle schools that is, schools that started in grade 6. By the1980s, many middle schools existed in British Columbia. Currently, local schooldistricts in British Columbia are allowed to determine the nature of the grade-level configurations in their own district. However, the British Columbia Ministry

Middle school or junior high? 471

of Education does not officially recognize institutions as middle or junior highschools.1

I use panel data from the province of British Columbia, which has a variety ofgrade-level configurations by district and within districts, to measure the effectsof alternative grade-level configurations on a variety of measures of academicachievement. Approximately 16% of students in British Columbia attend a middleschool that begins in grade 6, and another 16% of students attend a juniorhigh school that begins in grade 7. Therefore, about 32% of students attend astand-alone middle or junior high school, and the other 68% attend a schoolwhose grades extend through grade 7 and higher. I find that grade 7 math andreading scores are significantly negatively affected by middle or junior high schoolattendance. Specifically, using an ordinary least squares estimation strategy, I findthat math scores of students who attended a middle or junior high school werebetween 0.125–0.187 standard deviations lower than students who attended akindergarten through grade 7 or higher school, and reading scores were 0.055–0.108 standard deviations lower. In addition, the effect was similar betweenstudents who entered a middle school in grade 6 and students who entered ajunior high school in grade 7. I also find that students who attended a middleor junior high school scored 0.039–0.085 standard deviations lower in grades 10and 12 English exams.

The choice to attend middle or junior high school in upper elementary gradelevels may be endogenous and may be related to unobservable time-varyingfactors. Therefore, following Rockoff and Lockwood (2010), I construct an in-strumental variable using the terminal grade of the school the student attendedin grade 4 for middle or junior high school entry. The subsequent results using atwo-stage least squares regression strategy find that students who attended mid-dle or junior high school scored 0.116–0.215 standard deviations lower in grade7 math exams and 0.088–0.118 standard deviations lower in grade 10 Englishexams than the students who did not.

I find that students on the bottom half of the test score distribution weredisproportionately negatively affected by attending a middle or junior high schoolbut I find no relationship between the effect of grade-level configuration andgender, being aboriginal, or being a student with English as a second language.I also find little relationship between the district being in a rural area and theestimates finding that students who attended middle or junior high school scorelower in math.

2. Related literature

Relatively few studies have examined the impact of grade-level configuration onstudent achievement, despite its potential importance. Earlier education work

1 Middle school refers to a school that starts in grade 6, and junior high school refers to a schoolthat starts in grade 7.

472 E. Dhuey

used cross-sectional data to examine this issue and generally found that therewas a relationship between attending middle or junior high school and loweracademic performance (see, e.g., Alspaugh 1998a,b; Byrnes and Ruby 2007;Franklin and Glascock 1998; Wihry, Coladarci, and Meadow 1992). Owing tothe cross-sectional nature of the data, these studies were unable to concludewhether these differences were due to differences in grade-level configurations ordue to differences in student characteristics across these different configurations.

The research most relevant to this study includes Bedard and Do (2005),Schwartz et al. (2011), and Rockoff and Lockwood (2010). All three examinethe effect of grade-level configuration using longitudinal data. Bedard and Do(2005) estimated the effect on on-time high school graduation of moving froma junior high school system, where students stay in elementary school longer,to a middle-school system. They found that moving to a middle-school systemdecreases on-time high school graduation by 1–3%. Rockoff and Lockwood(2010) used a two-stage least squares approach and Schwartz et al. (2011) usedan ordinary least squares approach using the same longitudinal data as wasemployed for New York City. Both found that moving students from elementaryto middle school in 6th or 7th grade causes significant drops in both math andEnglish test scores.

Using an instrumental variables estimation strategy similar to that of Rockoffand Lockwood (2010), this paper explores the issue of middle and junior highschools in a Canadian context. In addition, this paper uses longitudinal datafrom an entire province versus a single city. This is an important exercise, as NewYork City has a unique educational environment, and results from that city maynot be generalizable to other settings and locations. For instance, unlike NewYork City, British Columbia has a wide variety of urban and rural schools overa very large geographic area. In addition, the per pupil funding in New York isapproximately twice as large as the per pupil funding in British Columba. Thesealong with many other institutional differences make it important to examinethe effect of grade-level configurations in British Columbia. In addition, I amable to explore longer-run outcomes and examine whether attending middle orjunior high school causes students to perform differently in high school.

3. Methodology

The main analysis uses a value-added specification of achievement growth inmath and reading from grade 4 to grade 7. This strategy uses the variation ofgrade-level configurations across the province of British Columbia to estimatethe effect on student achievement gains of attending a middle or junior highschool. The initial estimation strategy is as follows:

y7ist = β0 + β1y4

ist + β2Mi + x′itβ3 + s

′stβ4 + c

′stβ5 + εist, (1)


where y7ist is the grade 7 math or reading score for student i, in school s, in year

t; y4ist is the student’s corresponding grade 4 score; Mi is an indicator equal to

one if the student changed from an elementary school to a middle or junior highschool between grade 4 and grade 7; x′

it is a vector of student-level demographiccharacteristics, s′

st is a vector of school-level characteristics, and c′st is a vector

of community-level characteristics; and εist is an idiosyncratic error term.2 Inaddition, some specifications will include city or district fixed effects becausemiddle/junior high school geographic locations may not be orthogonal to un-observed factors. Therefore, the city or district fixed effects force the identifyingvariation to come from within a particular city or district. Other specificationsthat allow for differences in the effect based on whether the student attended amiddle or junior high school will also be explored.

The coefficient of interest is β2, which measures the differential effect on astudent’s test score growth of attending a middle or junior high school comparedwith staying in an elementary school from kindergarten through grade 7 orhigher.3 This coefficient measures whether the trajectories of student achievementfrom grade 4 to grade 7 for students entering middle and junior high schools aredifferent than they are for students who never attended a middle or junior highschool.

An ordinary least squares identification strategy may not produce causal es-timates because the choice to attend a middle or junior high school in upperelementary grades may be related to time-varying factors that are unobservable.For instance, a student who is currently in a kindergarten through grade 7 schoolmay move to a middle school in grade 6, owing to unobservable factors relatedto achievement such as a residential move or a family disruption. However, gen-erally, school choice is based on residential location.4 But in cases where there is

2 Because this model includes a lagged dependent variable, β2 may be biased downwards and maybe interpreted as a lower bound (see Angrist and Pischke 2009; Andrabi et al. 2011). In theory,this bias could be corrected by applying the dynamic panel methods of Arellano and Bond(1991), Arellano and Bover (1995), or Blundell and Bond (1998), but in this data it is notpossible to apply these methods because there are only two periods of time.

3 Student test scores are often considered to be measured with error that may attenuate thecoefficient on the lagged dependent variable and may bias the coefficient on middle/junior highschool in an undetermined direction. However, Andrabi et al. (2011) note that ‘correcting formeasurement error alone may be worse than doing nothing.’ These authors are referring to thefact that because I am unable to correct for the bias from including the lagged dependentvariable (because my data includes only two periods), it is wise for me to not correct formeasurement error. However, all estimates using the math test scores as an instrument forreading test scores or using reading test scores as an instrument for math test scores are notsubstantively different than the estimates presented in this paper and are available upon requestfrom the author.

4 Prior to 2002, students attending public schools were required to attend the school determinedby their catchment area. If they wanted to attend a school outside their designated area,students needed permission from both the catchment school principal and the out-of-catchmentprincipal. Since 2002, legislation has existed that allows parents to choose any public school,regardless of catchment, with the exception that if a student wants to transfer to a school thathas excess demand, the student needs to obtain permission from the principal.

474 E. Dhuey

an endogenous move, the ordinary least squares estimate would not be able tountangle the effect of moving to middle school from the effect of these factors.

Therefore, following Rockoff and Lockwood (2010), I created an instrumentfor middle or junior high school entry using the grade-level configuration of theschool attended in grade 4. If the student attends a school that ends in grade 5 orgrade 6 when they are in grade 4, I create an indicator variable that indicates thestudent should enter a middle or junior high school in grade 6 or 7.5 A threat tothe validity of this instrument would be if the configuration of the school attendedin grade 4 is related to something unobserved that affects test score growth fromgrade 4 to grade 7 that is not controlled for by the inclusion of the grade 4 test scorealong with the large quantity of student, school, and community characteristics.The estimates produced using this estimation strategy can be interpreted as localaverage treatment effects.6 The estimates apply to students who are induced tomove into a middle or junior high school because they attended a school endingin grade 5 or grade 6. This may be different from the average treatment effect.

In addition to the main analysis, I also examine a few longer-run academicoutcomes using the following estimation strategy:

Oist = δ0 + δ1y4ist + δ2Mi + x

′itδ3 + s

′stδ4 + c

′stδ5 + νist. (2)

In these cases, Oist is one of the following outcomes: grade 10 mandatoryprovincial English exam, grade 12 mandatory provincial English exam, highschool graduation, or high school grade point average conditional on gradua-tion. The rest of the variables are the same as in equation (1).7 In these specifica-tions, δ2, which measures the differential effect on these outcomes of attendinga middle or junior high school compared with staying in an elementary schoolfrom kindergarten through grade 7 or higher.

A possible concern with this analysis is the potential for non-random attritionfrom public schools in British Columbia. This could cause a bias in an unknowndirection. Only 10% of students in British Columbia attend private schools, butit is possible that a high-achieving child who was initially sent to a school thatended in grade 5 or grade 6 may be sent to a private middle school. It is alsoequally possible that a child who was a low-achieving student during the early

5 Some schools changed their grade-level configuration during this sample period. Therefore, theinstrument reflects these changes when they occur. In addition, in section 5.1, the analysis isbroken down into whether the student attended a middle school versus a junior high school.Therefore, one instrument was created for students in grade 4 whose school ended in grade 5,and another instrument was created for students in grade 4 whose school ended in grade 6.

6 Monotonicity is required to allow for this interpretation. In this case, the behaviour that wouldviolate monotonicity is if a student (a) attends a middle/junior high school when they are notexpected to, given their grade 4 configuration; and (b) does not attend a middle/junior highschool when they are expected to, based on their grade 4 configuration. Unfortunately, thisassumption is untestable, but in this circumstance it seems reasonable.

7 95.3% of students will have transitioned to a high school by grade 10. Including an indicatorvariable for the approximately 5% of students who have not transitioned does not affect theresults.


elementary years may be sent to a private middle school. Therefore, in this short-run analysis, a balanced panel of students who were in the public school system inBritish Columbia in both grade 4 and grade 7 is used. Hence, the interpretation ofthe results pertains only to those students. However, in section 5.3, I will furtherexplore the possible effects of attrition bias in this analysis.

4. Data and analysis sample

4.1. Data sourcesThe main data sets used in this study were four linked files obtained from theMinistry of Education in British Columbia. The first contains observations on allstudents writing the Foundation Skills Assessment, an annual low-stakes stan-dardized test in the areas of mathematics, reading, and writing for students ingrades 4 and 7. Data from 1999 through 2006 were used. For these students,the percentage score on each test, the school in which the test was written,and whether the student was excused from the test are known.8 Student scoresare linked over time via an encrypted student identifier. The second file con-tains data on these students’ grades 10 and 12 English exams, on whether ornot they graduated from high school, and on what their grade point averagewas at the time of high school graduation conditional on graduating from highschool. This file is linked via encrypted student identifiers to the first file. Studenttest scores and outcomes are linked via the student identifier to the third file,which contains the administrative records of all public school students in BritishColumbia from 1999 to 2006 in grades 4 to 7. These data include demographicinformation such as gender, aboriginal status, date of birth, and home language,along with information on whether they participate in special education or En-glish as a second language (ESL) programs. The fourth file contains informationon all public schools in British Columbia. For each school, the following areknown: which grades are offered, the number of teachers, and whether schoolis standard or other type, and the year of opening and/or closing data fromthe Canada Census is appended to this main set of files. To proxy for student-level socioeconomic status characteristics (SES), various census variables at theDissemination/Enumeration Area (DA) level are attached using the students’residential postal codes. Information on household income, education levels, un-employment rates, ethnic and immigrant composition, and the age distributionof each DA is attached to the data.

Therefore, the demographic, school, and community control variables in-cluded in the analysis are dummy variables for whether the student is male,aboriginal, ESL, in special education, or has moved schools. Also included is theschool’s percentage of male students, aboriginal students, ESL students, special

8 Students with poor English abilities and some students with severe disabilities are excused fromwriting provincial exams.

476 E. Dhuey

education students, students excused from the math test, and students excusedfrom the reading test. In addition, the teacher:pupil ratio and whether the schoolis in a rural location are included. Finally, the census DA-level community con-trol variables include the average household income, average dwelling value, thepercentage of individuals with no high school degree, the percentage of individ-uals with a high school degree, the percentage of individuals with a universitydegree, the unemployment rate, the percentage of immigrants, the percentage ofvisible minorities, and the percentage of the population over 65 years old.

4.2. Regression sampleBecause a value-added model in test scores is estimated, the sample is restrictedto students who wrote both the grade 4 and the mathematics and reading exams.Since test scores were observed between 1999 and 2006 and, since three years passbetween each test, most such students were observed between 2002 and 2006.There were 229,337 students observed writing the grade 7 test between 2002and 2006. Of these students, 24,026 (10.5%) who were not observed in grade 4were dropped from the sample, and a further 14,692 students (6.5%) who didnot have a valid test score in both years were also dropped. Additionally, 3,260students (1.4%) who had abnormal data or grade progression were dropped,9

657 students (<1%) who were missing school information in grades 5 or 6 weredropped, as were 1,532 students (<1%) who attended schools with irregulargrade-level configurations.10 The final analysis sample consists of 185,170 studentobservations.

For the longer-run sample, the grade 7 students who were tested between2002 and 2006 were followed until 2010 or until high school graduation. Eachlonger-run outcome variable has a unique sample size discussed below and usesa different sample from the FSA value added regressions. The first longer-runoutcome is the grade 10 mandatory provincial English exam. This exam is worth20% of a student’s final mark in their grade 10 English class and is mandatoryfor all grade 10 students with the exception of students with special needs. Ofthe 185,170 student observations in the main analysis sample, 12,043 (6.5%)students are not included in the Ministry of Education data attending grade10. This discrepancy could be due to students’ moving out of province, due tostudents’ moving to a private school, or due to administrative errors in recordkeeping. An additional 10,392 (5.6%) students do not have a grade 10 Englishexam. These are students who are not required to take the exam because ofexemptions related to factors such as having an individual education plan for

9 For instance, students who were retained more than once, skipped a grade level, or moved downa grade level.

10 Irregular grade-level configurations generally occur in special types of schools such as onlinedistance education schools or schools with other special characteristics.


special needs.11 Therefore, the final analysis sample for this outcome variable is162,735 observations.

The second longer-run outcome, the grade 12 mandatory provincial Englishexam score, is worth 40% of a student’s final mark in grade 12 English class.Of the 113,714 student observations in the main analysis sample who were ingrade 7 between 2002 and 2004, 16,543 (15.5%) students are not included in theMinistry of Education data. This discrepancy is due to issues similar to thoseattending the grade 10 exam, along with counting students who dropped outof high school. An additional 15,690 (13.8%) students do not have a grade 12English exam score. Therefore, the final analysis sample for this outcome variableis 81,481 observations.

The final two longer-run outcomes, high school graduation and high schoolgrade point average, use the grade 7 cohorts from 2002 and 2003. This samplerestriction allows students five years to graduate from high school. Of the 75,942student observations in the main analysis sample, I use the sample of 71,479students that attended grade 9 between 2003 and 2008. In this sample, I maymiscode students that have left the province or have moved to a private schoolduring high school as dropping out of high school. Finally, I have informationon high school grade point average only for students who have graduated fromhigh school. Therefore, conditional on graduating high school, I have 58,292observations. This sample is reduced to 58,232 because 60 students had missinginformation for this variable.

4.3. Descriptive statisticsTable 1 displays descriptive statistics for the data by grade-level configuration ofthe student’s grade 4 school. Column 1 includes only students who were attendinga school ending in grade 5, column 2 includes only students who were attendinga school ending in grade 6, and column 3 includes students who were attending aschool ending in grade 7 or higher.12 A bold number in columns 1 or 2 indicatesthat that mean of the variable is statistically significantly different from the meanlevel of that variable in column 3.

Panel A includes the descriptive statistics for the student-level variables. Ascan be seen by comparing columns, the difference in mean characteristics acrossthe groups can be relatively small in some variables yet are still statistically sig-nificantly different. In addition, there are also some large differences betweenthe samples. In terms of notable differences in student characteristics, there arefewer aboriginal students in schools that end in grade 5 and more ESL stu-dents in schools that end in grade 7 or higher. Panel B displays the community

11 The grade 4 test scores of the students missing from the sample are significantly lower thanthose of the students in the sample. However, they are not statistically significantly differentbased on whether or not they attended middle school.

12 Only 2.5% of students attended a school ending in a grade higher than grade 7. All results of thepaper are similar if this sample of students is excluded.

478 E. Dhuey

TABLE 1Descriptive statistics

Ending grade of school, grade 4

Grade 5 Grade 6 Grade 7 or later(1) (2) (3)

Panel A: Student characteristicsMale 0.509 0.498 0.504

(0.500) (0.500) (0.500)Aboriginal 0.079 0.139 0.103

(0.270) (0.346) (0.304)ESL 0.168 0.060 0.245

(0.374) (0.237) (0.430)In special education 0.065 0.061 0.058

(0.247) (0.240) (0.234)Number of observations 24,257 25,241 135,672

Panel B: Community characteristicsAverage household income 56553 49547 57242

(18072) (15984) (22725)Average dwelling value 232170 185686 248776

(97016) (99618) (133107)% no high school degree 0.228 0.271 0.258

(0.095) (0.096) (0.108)% high school degree 0.268 0.266 0.265

(0.061) (0.063) (0.057)% university degree 0.196 0.144 0.197

(0.102) (0.076) (0.116)% unemployed 0.063 0.078 0.072

(0.047) (0.060) (0.057)% immigrant 0.239 0.131 0.263

(0.134) (0.059) (0.174)% visible minority 0.169 0.044 0.231

(0.181) (0.053) (0.249)% of population over 65 yrs old 0.132 0.138 0.120


Panel C: Grade 4 test scoresMath 0.183 0.031 0.053

(0.905) (0.896) (0.931)Reading 0.146 0.071 0.063


Panel D: Grade 7 test scoresMath −0.017 −0.132 0.047

(0.907) (0.880) (0.951)Reading 0.073 −0.003 0.071


Panel E: Longer-run outcomesEnglish grade 10 exam 0.110 0.007 0.070

(0.934) (0.969) (0.952)Number of observations 21,639 21,667 119,429English grade 12 exam 0.030 −0.088 0.049


(Continued )


TABLE 1(Continued )


Grade 5 Grade 6 Grade 7 or later(1) (2) (3)

High school graduation 0.838 0.796 0.816(0.369) (0.403) (0.388)

Number of observations 7,965 9,555 53,959High school GPA 2.850 2.841 2.870


NOTES: Standard deviations in parentheses. Test scores represent the z-score by year, grade, and skillamong the population of schools prior to sample exclusions. A bold number indicates the significanceat the 5% level from a t-test that compares the mean value in column 3 with the mean value incolumn 1 or column 2, respectively.

characteristics gathered from the census for each type of grade-level configura-tion. Panels C and D include the mean levels of grade 4 and grade 7 test scores.The means of test scores are slightly positive in all columns, which indicatesthat the students who were excluded from the samples scored marginally worsethan the students who were included in the sample.13 There are also statisti-cally significant differences in grade 4 math and reading test scores. The studentswho attended a school that ended in grade 5 scored higher math and readingscores than the other students in different grade-level configurations. However,a different pattern emerges for the grade 7 test scores. Students in schools thatended in grade 7 or later did better in both math and reading. The students inschools that ended in grade 6 – the same students who were doing better thanthe rest in grade 4 – scored lower compared with the students in column 3. Thisprovides some indication that the analysis will find negative effects associatedwith attending middle or junior high school. Finally, in Panel E, the summarystatistics, along with the corresponding sample sizes, are listed for the longer-runoutcomes.

Overall, table 1 illustrates that the grade configuration of the school a studentattends in grade 4 is not exogenous. However, using the grade 4 test score as acontrol in the model eliminates differences in achievement levels across studentsin grade 4. But the type of school attended in grade 4 could be correlated withunobserved student characteristics that affect learning trajectories after grade 4.Unfortunately, in these data there is no information on other tests in differentgrades to estimate if the trajectory between students in different grade config-urations before middle or junior high school attendance is different. However,

13 These scores are standardized to have a mean of zero and standard deviation of one in thepopulation.

480 E. Dhuey

in the New York City data, Rockoff and Lockwood (2010) find no difference intrajectories before middle school attendance. This provides some evidence thatthe learning trajectories of students in varying grade configurations in BritishColumbia may be similar.14

These data allow students to be followed along their individual academicpaths. The earliest that students are observed in the data is in grade 4. Thegrade span of the school the student is attending in grade 4 is used to split thestudents into three samples and each of these samples of students is split intotwo groups, the first group includes students that are ‘on path’ and the secondgroup includes students that are ‘off path.’ An example of a student who is ‘onpath’ is a student in the grade 5 sample, which means that this student is in aschool in grade 4 that ends after grade 5. In grade 6, this student is observedentering a middle school. The same student would be ‘off path’ if, in grade 6,they moved to a school that was not a middle school. Table 2 includes descriptivestatistics for these different samples of students. Overall, approximately 12%of students are ‘off path.’ However, this percentage varies by the ending gradeof the grade 4 school. For instance, about 12% of students are ‘off path’ inthe grade 5 and grade 7 samples, whereas 21% are ‘off path’ in the grade 6sample. The differences in characteristics between students ‘on path’ and ‘offpath’ are tested for statistical significance. Overall, students who are ‘off path’tend to score worse in math and reading in both grade 4 and grade 7. They aremore likely to be male, aboriginal, and in special education. The communitycharacteristic patterns are less pronounced. The ‘off path’ students in the grade5 sample come from communities with lower average household income andaverage dwelling values, whereas these students in the grade 6 sample come fromcommunities that have higher household incomes and dwelling values. However,what is clear is that the estimates from the instrumental variables estimationstrategy apply to students who are different from the students who are ‘offpath.’15

14 Table 1 in the technical appendix (available from the CJE online archive at cje.economics.ca)includes summary statistics regarding the schools in the sample. There are approximately 200schools in each of the grade 5 and grade 6 samples and approximately 1,000 schools in the grade7 sample.

15 Table 2 in the technical appendix explores the summary statistics of the three estimationsamples used in this research. The grade 4 test scores in the three samples are similar inmagnitude but statistically different from each other. The similarity in magnitude is reassuring,as it implies that districts and cities that have a large number of middle and junior high schoolsare not radically different in terms of their ability to produce grade 4 test scores. Therefore, theanalysis can assume that the students are starting at a relatively similar level in grade 4 in allthree samples. However, a large significant difference can be seen between the grade 7 test scoresin the three samples. This once again gives some indication that students who attend a middle orjunior high school score worse in grade 7 than their counterparts who do not attend a middle orjunior high school. Finally, in Panel D, the longer-run outcomes are examined.


TABLE 2Descriptive statistics of students by whether the student is on or off path


Grade 5 Grade 6 Grade 7 or later

On path Off path On path Off path On path Off path(1) (2) (3) (4) (5) (6)

Panel A: Student characteristics

Male 0.508 0.515 0.494 0.513 0.504 0.504(0.500) (0.500) (0.500) (0.500) (0.500) (0.500)

Aboriginal 0.071 0.137 0.135 0.153 0.101 0.120(0.258) (0.344) (0.342) (0.360) (0.301) (0.325)

ESL 0.170 0.158 0.049 0.098 0.257 0.138(0.375) (0.365) (0.217) (0.297) (0.437) (0.345)

In special education 0.065 0.070 0.059 0.071 0.058 0.061(0.246) (0.255) (0.235) (0.258) (0.234) (0.239)

Panel B: Community characteristicsAverage household income 57245 51468 49431 50089 57867 52038

(18066) (17297) (15853) (16462) (23319) (16070)Average dwelling value 235757 205800 180683 204669 253461 209783

(97336) (90379) (86555) (136743) (136440) (92400)% no high school degree 0.222 0.269 0.271 0.271 0.258 0.256

(0.093) (0.098) (0.095) (0.098) (0.110) (0.096)% high school degree 0.269 0.259 0.266 0.266 0.264 0.266

(0.060) (0.065) (0.061) (0.070) (0.058) (0.054)% university degree 0.201 0.160 0.143 0.146 0.198 0.183

(0.102) (0.096) (0.074) (0.081) (0.118) (0.096)% unemployed 0.062 0.072 0.077 0.082 0.072 0.071

(0.047) (0.049) (0.060) (0.060) (0.058) (0.051)% immigrant 0.243 0.210 0.127 0.143 0.271 0.196

(0.132) (0.143) (0.052) (0.076) (0.178) (0.124)% visible minority 0.173 0.145 0.040 0.060 0.242 0.138

(0.178) (0.198) (0.039) (0.087) (0.254) (0.173)% of population over 65 yrs old 0.130 0.146 0.140 0.127 0.119 0.132

(0.100) (0.112) (0.100) (0.087) (0.088) (0.091)

Panel C: Grade 4 test scoresMath 0.198 0.070 0.044 −0.019 0.057 0.018

(0.898) (0.951) (0.883) (0.941) (0.931) (0.932)Reading 0.165 0.006 0.083 0.024 0.067 0.034

(0.848) (0.946) (0.859) (0.938) (0.901) (0.933)

Panel D: Grade 7 test scoresMath −0.004 −0.106 −0.132 −0.132 0.066 −0.108

(0.894) (0.995) (0.858) (0.957) (0.952) (0.925)Reading 0.094 −0.082 0.009 −0.047 0.080 −0.008

(0.864) (1.003) (0.877) (0.997) (0.908) (0.948)Number of observations 21,353 2,904 19,976 5,265 121,121 14,551

NOTES: Standard deviations in parentheses. Test scores represent the z-score by year, grade, and skillamong the population of schools prior to sample exclusions. A bold number indicates the significanceat the 5% level from a t-test that compares the mean value in column 2 (4, 6) with the mean value incolumn 1 (3, 5).

482 E. Dhuey

5. Results

5.1. Main effectsThe analysis begins by estimating equation (1) using the short-run data describedin section 4. Table 3 contains these results. Panel A includes the results fromthe ordinary least squares specification.16 All specifications include standarderrors that are clustered at the district level. Column 1 lists the estimates from aspecification that includes no control variables and was run using the full sampleof students. The point estimates indicate that students who attended a middle orjunior high school in grade 6 or grade 7 scored 0.158 standard deviations lowerthan students who did not. The student, school, and census control variables areadded in column 2, and the point estimates decrease in magnitude to −0.125standard deviations. Because grade-level configurations are determined at thedistrict level, it is appropriate to take into account differences between districtsthat choose different grade-level configurations. Therefore, district fixed effectsare added in column 3. Including district fixed effects does not substantiallyaffect the estimated coefficient. Column 4 limits the sample to include onlyschool districts that contained 15% of more of their students in a middle orjunior high school in grade 7.17 This estimate is based on only students thatwere in districts that offered middle or junior high schools to at least 15% of thestudent body. The point estimate for this sample, which includes district fixedeffects, is −0.141.18 Finally, a district may offer middle or junior high school,but only in certain cities, and the identification in the previous column may befrom differences across individuals from different cities. Therefore, the sampleis again limited to include only cities in which more than 15% of the studentsattend a middle or junior high school.19 In this specification, city fixed effects areincluded, so that the identification comes from students within cities, rather thanacross cities.20 Using this sample, I find that attending a middle or junior high

16 The complete set of coefficients for these specifications can be found in table 3 of the technicalappendix.

17 These districts are Southeast Kootenay, Rocky Mountain, Kootenay Lake, Kootenay-Columbia, Central Okanagan, Abbotsford, New Westminster, Powell River, OkanaganSimilkameen, Bulkley Valley, Prince George, Nicola-Similkameen, Peace River South,Greater Victoria, Sooke, Gulf Islands, Alberni, Fraser-Cascade, and Cowichan Valley.

18 These specifications include only 19 districts, so having too few clusters may be a problem.Therefore, following Cameron and Miller (2010) and Cohen and Dupas (2010), the tables usecritical values from a tG-1 distribution where G is 19 (for each cluster). The critical values for 1%,5%, and 10% significance are 2.878, 2.101, and 1.734, respectively. However, Hansen (2007) hasshown that the standard errors listed in the tables, which were computed with the STATAcluster command, are reasonably good at correcting for serial correlations in panels with as lowas 10 clusters.

19 These cities are Abbotsford, Armstrong, Castlegar, Cranbrook, Fruitvale, Hope, LakeCowichan, Lumby, New Westminster, Pemberton, Powell River, Prince George, Princeton,Salmon Arm, Smithers, Trail, Victoria, and Whistler. Figure 1 in the technical appendixprovides a visual representation of the districts and cities that contain more than 15% ofstudents who attend a middle or junior high school.

20 The estimates are similar if district fixed effects are included. Also, the magnitudes of theestimates are similar but are less precise if the samples include districts and cities with more than

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school decreases math scores by 0.187 standardized units. Columns 6 through 10display the coefficients for the reading test. Overall, the point estimates are abouthalf the size of the math estimates. Compared with the estimates of Rockoff andLockwood (2010), which dealt with one-year gains, the estimates in Panel A oftable 5, which are for three-year gains, are slightly lower in magnitude but overallconsistent with their findings.

The first stage of the two-stage least squares specification can be found inPanel B. This specification regresses the indicator for whether a student attendeda middle or junior high school on an indicator variable that indicates the studentshould have entered a middle or junior high school in grade 6 or grade 7 alongwith the same control variables in equation (1). The coefficient on the latterindicator variable is listed in Panel B.21 As can be seen, the instrumental variableis strongly correlated with actual entry into middle or junior high school. The F-statistic ranges from 36 to 408. The coefficients in columns 1 and 2 are similar inmagnitude to coefficients found in Rockoff and Lockwood (2010). The first-stageresults found are consistent with the finding that some students are ‘off path’ –that is, they don’t follow the prescribed path set by the grade-level configurationin grade 4. The magnitude of the coefficient decreases when district or city fixedeffects are included, but the instrument remains valid. The coefficient decreasesbecause the average percentage of students being ‘on path’ in some districts isvery low. For instance, in District 85 – Vancouver Island North – there are 10schools in the district: six schools that are kindergarten through grade 7, oneschool that is kindergarten through grade 5, one school that is kindergartenthrough grade 10, and two schools that are grade 8 through grade 12 schools.The individuals attending the kindergarten through grade 5 school in grade 4cannot follow the ‘correct’ path and attend a middle school as there are no middleschools in this district, so all of these students move to a kindergarten throughgrade 7 school or kindergarten through grade 10 school in grade 6. Therefore, thefirst-stage coefficient for this district is incredibly low. In addition, some schoolschange their grade-level configurations during this period of time. The studentsin these schools will be ‘off-path’ in the sense that their grade 4 school grade-levelconfiguration will not predict their school movements over time due to the changein grade-level configurations. Hence, it is important to remember that the resultsfrom the two-stage least squares estimates are local average treatment effects.They apply only to students who follow the ‘correct’ path of schools predictedby their grade 4 grade-level configuration.

Panel C reports the estimates from the two-stage least squares estimates.22

Overall, the coefficients for math are slightly larger than the ordinary least squaresestimates but continue to be statistically significant. The estimates are not statis-tically significant in the reading specifications when district or city fixed effects

25% of the students attending a middle or junior high school. This is probably due to thedecrease in sample size.

21 Full estimates from these specifications can be found in table 4 of the technical appendix.22 The full estimates for these specifications can be found in table 5 of the technical appendix.

486 E. Dhuey

are included. Estimates from Rockoff and Lockwood (2010) found that mathachievement falls by roughly 0.17 standard deviations and English achievementfalls by 0.14–0.16 standard deviations when measured in grade 8. The yearlymagnitude estimated by Rockoff and Lockwood (2010) is approximately threetimes larger than the effects estimated in this paper. In addition, Rockoff andLockwood (2010) found significant results for the English tests, whereas I findlittle to no statistically significant results for the reading test scores once districtor city fixed effects are included. These differences may be due to the differencein types of test between the two jurisdictions.

Next, I explore whether moving to a middle school in grade 6 has a differenteffect from moving to a junior high school in grade 7. Panels D–F have theresults for the specification that includes two dummy variables, one for movingto a middle school in grade 6 and one for moving to a junior high school ingrade 7. The estimates for middle school and junior high school are roughly thesame for both math and reading in Panel D. This implies that there might bea one-time shock to test scores, but that spending two years in a middle schoolbefore the exam in grade 7 is not necessarily worse than spending one year ina junior high school before taking the exam. Panel E includes first-stage resultssimilar to those in Panel B. In Panel F, there exist some non-significant results forthe junior high school coefficients for both math and reading.23 Therefore, thereis some evidence of a larger negative effect for attending middle school versusjunior high school when testing takes place in grade 7. This is a slightly surprisingresult, as the disruption of moving to a junior high school would be fresher thanif the student had moved the year prior. However, Rockoff and Lockwood (2010)found a similar pattern using New York City data.

5.2. Heterogeneous effectsTable 4 explores whether the negative effect of attending middle and junior highschool varies across demographic and district characteristics. Panel A examinesgender by interacting an indicator variable for male with the middle/junior highschool indicator variable. The first column in table 4 corresponds to the thirdcolumn in table 3. It includes the entire sample along with district fixed effects.Column 2 corresponds to the sample of only districts with 15% or greater ofstudents attending a middle or junior high school along with district fixed effects.Column 3 includes cities with 15% or greater of students attending a middleor junior high school along with city fixed effects. These three columns arerepeated for the reading test and for the math and reading test results using two-stage least squares. Overall, there is very little evidence that males are affecteddifferently than females. The same is true for aboriginal students (Panel B) andESL students (Panel C). However, Panel D includes an indicator for whetherthe student scored in the lowest 50% of test takers in grade 4. This indicator is

23 The full estimates for Panels D–F can be found in tables 6–8 of the technical appendix.

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interacted with the middle/junior high school variable. Here we see a very largenegative effect for those on the lower half of the ability distribution. In particular,in reading, the whole effect is driven by these lower-achieving students. Thesefindings correspond to those of Rockoff and Lockwood (2010) but have somedissimilarities with those of Schwartz et al. (2011), as they found no differentialimpacts for females, special education students, or limited English proficiency-eligible students in math. However, they did find large positive effects for limitedEnglish proficiency-eligible students in reading. I find no heterogeneous effectsin reading for ESL students. These differences may be due to differences in theprograms available to the ESL students in these two locations. Panel E includesan indicator variable for whether the district is rural and its interaction withthe middle/junior high school indicator. A district is considered rural if morethan 50% of the students in that district live in a rural postal code. Overall,the interaction effect for both the small districts and the rural districts are notstatistically significantly different than the main middle/junior high school effect.

5.3. Attrition and sample selectionAs mentioned in section 3, this sample does not include students who have movedout of province or moved to private schools. There are also a variety of samplerestrictions that needed to be made that are outlined in detail in section 4. Inthis data, students who are excluded from the sample are more likely to be male,aboriginal, in special education, and English as a second language speakers.Therefore, the loss of these students from the sample may bias the estimates forthe population of students if the test scores of the students who are excludedfrom the sample is correlated with the intended path of grades. While correctingfor this bias is difficult for this type of estimation strategy and data structure, Inevertheless conduct two types of analysis to explore the potential for bias.

First, following Schwartz et al. (2011), I calculate an inverse Mills ratio andinclude this ratio in equation (1). Notwithstanding the fact that my currentdata may not fully explain the reasons for attrition from my sample, I use theavailable data to estimate a probit model that predicts the probability that astudent will attrit. I use this predicted probability to try to address the possibleomitted variable bias caused by non-random attrition. I do not have a variablethat causes students to leave the sample and can be excluded from the mainspecifications, so identification relies on functional form. In table 5, I redo theanalysis from Panel A in table 3 by including the inverse Mills ratio, denotedlambda, in the estimating equation. Overall, the main effects of middle/juniorhigh school attendance are very similar to the estimates in table 3. Interestingly,lambda is statistically significant at the 5% level in columns 1–3 and columns6–8 but not in the restricted sample analysis found in columns 4–5 and columns9–10.

Second, I explore the implications of different plausible assumptions aboutmissing data. In the spirit of Horowiz and Manski (2000) and Lee (2002), I create

TA

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bounds of my estimates.24 First, I estimate the lower- and upper-bound estimates.This is accomplished by assuming the ‘worst case scenario’ for the data. The lower(upper) bound is calculated by imputing the minimum (maximum) value of testscores for students who attended middle school and by imputing the maximum(minimum) value of the test scores for students who did not attend middle school.These bounds are labelled ‘Lower’ and ‘Upper.’ Next, I impute the lower (upper)bound by calculating the mean minus (plus) 0.10 standard deviations. Finally,I impute the lower (upper) bound by calculating the mean minus (plus) 0.25standard deviations. As can be seen from the estimates in Panel B, the effectof middle/junior high school may vary from no effect to a −0.272 standarddeviations in math and −0.188 standard deviations in reading. However, otherthan the lower bound for reading, all the estimates are negative, which gives someindication that despite potential sample selection bias, middle/junior high schoolattendance causes a negative effect in terms of math and reading test score gains.

5.4. Longer-run outcomesThe results for the grades 4–7 math and reading test score gains indicate thatattending a middle or junior high school has negative effects on academic achieve-ment. However, it could be the case that these negative effects are temporary andthat students who attend middle or junior high school ‘catch’ up academically.Therefore, it is important to examine longer-run outcomes.

Table 6 examines four longer-run outcomes: (1) the mandatory grade 10provincial English exam, (2) the mandatory grade 12 provincial English exam,(3) whether or not the student graduated from high school, and (4) the GPA ofthe student conditional on graduating from high school. Columns 1–3 report theordinary least square (Panel A) and instrumental variables (Panel B) estimatesfor the grade 10 English exam. Column 1 includes district fixed effects and finds anegative effect of middle or junior high school attendance. Column 2 restricts thesample to districts with more than 15% of students attending a middle or juniorhigh school and column 3 restricts the sample to cities with more than 15% ofstudents attending a middle or junior high school. The instrumental variablesestimates find that attending a middle or junior high school decreases grade 10English exam scores by 0.088–0.118 standard deviations. Columns 4–6 repeatthis exercise with the grade 12 English exam scores and find a larger negativebut more imprecise effect that ranges from 0.164–0.221 standard deviations forthe instrumental variables analysis. These estimates show evidence that middleor junior high school attendance has long run impacts on academic outcomes.Columns 7–9 explore whether, conditional on being 9 in observed in grade, at-tending a middle or junior high school makes a student more or less likely to

24 Two key assumptions needed for this process are (1) ‘as good as’ random assignment oftreatment and (2) a monotonicity condition. In this analysis, I do not meet these assumptionsbut include the estimates of the bounds to provide readers with some information on thepossible bounds of the estimate due to non-random sample selection.

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graduate from high school within five years. Using the instrumental variables es-timates, there is little evidence that there exists any relationship. Finally, columns10–12 examine whether, conditional on graduating from high school, attending amiddle or junior high school affects that student’s overall high school grade pointaverage. There is no evidence of a relationship in columns 10 and 11, but a nega-tive relationship arises after the sample is restricted to only cities with more than15% of students attending a middle or junior high school. This provides someevidence that the grade configuration may affect a student’s GPA conditional onthe student’s graduating from high school.25

All the estimates in table 6 come from estimation strategies that include thegrade 4 FSA exam score as a control variable. An interesting exercise is to alsoinclude the grade 7 FSA exam as a control variable, as doing so may shed lighton the academic achievement trajectories of these students. Clearly, this may bea problematic strategy, as the grade 7 FSA scores may be endogenous, but theoutcome to this exercise can provide some intuition. Therefore, in table 10 of thetechnical appendix, table 6 is re-estimated with the addition of the grade 7 examscores as a control variable. When grade 7 exam scores are included as controlvariables, the negative relationship found in table 10 for the grades 10 and 12English exams is no longer statistically significant. This supports the possibilitythat the negative relationship between attending middle and junior high school isa localized effect that hurts students in the initial years after moving schools, butthat the student trajectories follow a path similar to that of non-middle/juniorhigh school attenders in high school. Owing to lack of data, this is as far as thisexercise can go, but these findings suggest that further investigation is warrantedregarding achievement trajectories.

5.5. Moving or middle/junior high school?A possible interpretation of these findings is that the effects found concern onlythe act of moving schools and have nothing to do with attending a particulartype of grade-level configuration. The literature generally finds negative effects ofmoving schools on the student’s academic achievement (see Engec 2006; Grumanet al. 2008; Ingersoll Scamman, and Eckerling 1989; Mehana and Reynolds 2004).However, it is difficult to separate whether this negative effect is due to the actof moving or due to the characteristics and circumstances of the students whomove. Therefore, is it difficult to disentangle whether the results found above aredue to simply moving schools versus moving to a middle or junior high school.

Ideally, one could find an exogenous reason for students to move schoolsand then compare the effects of moving schools for those students with theeffects of moving to a middle or junior high school. Unfortunately, finding an

25 Table 9 of the technical appendix repeats the exercise conducted in table 5 to examine the effectof attrition on these longer-run samples. Overall, the upper and lower bounds become muchlarger than in table 5 but the other bounds and results, including the Inverse Mills Ratio, showroughly consistent estimates compared with those of table 6.

494 E. Dhuey

TABLE 7Effect of moving schools on test score gains from grade 4 to grade 7

Math Reading

(1) (2) (3) (4) (5) (6)

Panel A: MoversChanged schools −0.057 −0.038 −0.050 −0.047 −0.044 −0.051

(0.008) (0.010) (0.014) (0.008) (0.012) (0.017)Panel B: Movers due to school closing

Changed schools 0.031 0.026 0.038 0.029 0.015 0.043(0.019) (0.022) (0.031) (0.017) (0.025) (0.035)

Number of observations 185170 47264 29935 185170 47264 29935Control variables

Student/school/census variables yes yes yes yes yes yesDistrict fixed effects yes yes no yes yes noCity fixed effects no no yes no no yes

SampleFull sample yes no no yes no noOnly districts > 15% no yes no no yes noOnly cities > 15% no no yes no no yes

NOTES: Standard errors corrected for clustering at the district level are in parentheses. Critical valuesfor columns 2, 3, 5, and 6 are from a t-distribution with 18 degrees of freedom. Bold coefficientsare statistically significant at the 5% level. Bold italic coefficients are statistically significant at the10% level. See section 4 for a description of the demographic and census variables included in theregressions.

exogenous reason is difficult in these particular data. However, in table 7, Iexplore the test score effects of moving for two different samples of movers. InPanel A, an indicator variable is used that equals one for all students who movedschools during this sample whose move was not related to attending a middle orjunior high school. The point estimates indicate a negative relationship betweenchanging schools and test score gains from grade 4 to grade 7. The magnitudeis between one-third and one-half as large as the negative effects found formiddle/junior high school attendance. However, this sample of students maybe negatively academically selected to start with (Pribesh and Downey 1999). Itmay be that these students are likely to do worse than other students in termsof academic gains because of other unobservable characteristics. However, it isinteresting that the correlation is much smaller than the point estimates foundfor middle/junior high school attendance.

Starting in 2000, many schools were closed in British Columbia, owing todecreasing student enrolments. In this sample, 56 schools closed between 2000and 2005. In Panel B, I use the students that were forced to move schools due toschool closure to estimate the effect of mobility on test score gains. The schoolclosures were not exogenous events, as the schools were selected to be closedbecause of decreasing enrolments, and this may have been correlated with otherunobserved factors. However, this is still informative, as it may remove some ofthe selection into the movers’ sample found in Panel A. Interestingly, moving


schools due to school closures did not have any statistically significant effect onstudents’ test score gains in math or reading.

Neither Panel A nor Panel B shows conclusive evidence of whether the effectsfound in this research are due to moving schools versus moving to a middle orjunior high school. However, they do show suggestive evidence that the move tomiddle or junior high school may be significantly worse for student achievementgains than just changing schools during the elementary years.

6. Conclusion

Overall, I find large, statistically significant negative effects of attending a middleor junior high school. The magnitudes are similar to those of other educationinterventions such as improving a teacher by one standard deviation (Aaronson,Barrow, and Sander 2007) or reducing class size (Harris 2009). The large effect sizeand the potential easy policy reform make changing grade-level configurations animportant and viable education reform. The adoption of a kindergarten throughgrade 8 configuration is becoming more popular with a variety of U.S. schooldistricts that are moving in that direction, such as New York City, Cleveland,Cincinnati, Philadelphia, and Boston (Schwartz et al. 2011). This research showsthat such reorganization may be quite beneficial and that British Columbia schooldistricts may want to rethink their grade-level configuration options.

Despite the consistent and large effects found in this research, it is still un-clear exactly what is causing the negative effect of middle and junior high schoolattendance. Is it the grade distribution of the students in the school? Are mid-dle/junior high schools less efficient? Do the peer effects matter? These are allquestions that cannot be answered with these data but that are important forfuture research.

References

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middle school or junior high? how grade-level configurations affect academic achievement

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