THESIS

Universidad Alberto Hurtado andGeorgetown University

Faculty of Economics and Business

Thesis to opt to the Master of Applied Economics degree given byGeorgetown University and the Magíster en Economía Aplicada a

Políticas Públicas given by Universidad Alberto Hurtado

The Effect of Grade Retention onStudents’ Outcomes: Evidence from

Chile

Juan Carvajal

supervised byDr. Marcela Perticara University of Texas A&M

Santiago, Chile2016

Universidad Alberto Hurtado andGeorgetown University

Faculty of Economics and Business

The Effect of Grade Retentionon Students’ Outcomes:

Evidence from Chile

Juan Carvajal

supervised byDr. Marcela Perticara University of Texas A&M

Director of MasterDr. Lucas Navarro Georgetown University

Santiago, Chile2016

Contents1 Introduction 2

2 Chilean educational system, data and variables 52.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Estimation strategy using an IV framework 123.1 GPA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 Probability of Attending Secondary School . . . . . . . . . . . 143.3 Probability of Dropping Out . . . . . . . . . . . . . . . . . . . 14

4 Results 154.1 Model 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.1.1 Academic Achievement . . . . . . . . . . . . . . . . . . 154.2 Model 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.2.1 Attending Secondary School . . . . . . . . . . . . . . . 184.3 Model 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.3.1 School Abandonment . . . . . . . . . . . . . . . . . . . 18

5 Conclusions 20

6 Appendix 226.1 Cohort 2003 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

6.1.1 Tables for ever repeating between third and fourth grade 226.1.2 Tables for ever repeating between first and fourth grade 256.1.3 Tables for ever repeating between first and eighth grade 27

7 Literature 28

1

AbstractThis article estimates the effect of early grade retention on students’ out-comes in Chile by using administrative data from the ministry of education(MINEDUC) on academic achievement. Using the 2003 cohort of studentsstarting first grade of primary school and an instrumental variables approachto control for grade retention’s endogeneity based on unobserved qualities ofthe student, I find that early grade retention has a negative effect on 6th and8th grade’s academic performance (GPA). I also find a negative effect on theprobability of attending secondary school with a 25 percentage point reductionif the student repeated any time between 1st and 2th grade. Finally, I findthat early grade retention has a positive effect in the probability of droppingout of secondary school with a 33.4 percentage point increase in the probabil-ity. This article concludes with possible policies to counterattack the negativeresults on students outcomes given the actual retention policy in the Chileaneducational system.

1 IntroductionMost Latin American countries have been relying on grade retention as aneffective way to re-prepare low achieving students who could not succeedwith the standard academic requirements needed to be promoted to the nextacademic year along with his peers. Grade retention is understood as aneducational practice of having a child repeat a grade in school. However, inrecent years, most developed countries have switched from a grade retentionsystem to an automatic promotion system requiring that all student shouldbe promoted to the following year. Chile, in this case, falls in the LatinAmerican category of countries with very high index of grade retention.

In recent years, economists have spent a great amount of resources inresearch on the importance of education and the economical results it hasin the labor market. Aware of this importance, economists have focused onacademic achievement and different remedial programs that either encour-ages or deviate students from achieving their required scores to be promotedto the following year along with his peers. Grade retention as a remedialprogram, therefore, has been a very wide subject that economists have triedto decode and explain, given its economical implications.

There has been a wide debate on whether children should, in fact, re-peat grades given the negative social, emotional and cognitive impacts that

2

this includes. Most literature, Jacob and Lefgren (2009), Manacorda (2012),Elodie Allet (2010), Eide and Showalter (2001) and more, allude to the factthat grade retention does have some emotional impact on children that couldaffect them academically. In the mentioned literature, there is a mix of viewsabout the effects of grade retention. The first is that there is a positive effecton children since it provides them with more maturity relative to their peersand it strengthens the basic and necessary knowledge for posterior years,Fertig (2004), Jacob and Lefgren (2004). The second; however, reflects graderetention as to being correlated with later poor academic performance andeventually abandonment of continued studies. The majority of grade reten-tion studies find that the practice of requiring students to repeat a gradedecreases self-esteem, school adjustment, and academic achievement, and in-creases dropout rates, Eide and Showalter (2001).

The main purpose of this work is to try to explain what are the effectsof early grade retention on children’s academic performance, access to sec-ondary school in Chile, and probability of dropping out of secondary school.I want to see if repeating a grade is in fact beneficial for the child given thecharacteristics of Chile or rather damaging for future cognitive development.One of the main problems involving this analysis, however, is that theremight be a problem of self-selection, kids who repeat a grade tend to be verydifferent from children who never do allowing for selection bias. The problemwith this is that we cannot compare one group to the other, which limits thetype of methodology needed to perform this study. Failing to account for theselection of students into repeating a grade can potentially exaggerate theharm of retention. Having this in mind, I focused on finding a possible de-terministic rule to compare students who are close to the cut off line such asManacorda (2012) as he uses the fact that in Uruguay if a student fails morethan 3 classes, then he is obliged to repeat the grade. Another work is that ofJacob and Lefgren (2009) who use the Chicago Accountability Policy wherea student from 3rd and 6th grade is required to perform at predefined levelsof both reading and mathematics in order to be promoted to the next grade1.

Following this idea we found that in Chile, the ministry of education en-forced a rule in Article 10 of the supreme decree of education No 40, whereif the student fails to attend more than 85% of the classes throughout theacademic year in addition to achieving a GPA lower than 4 (out a 1-7 chartbeing 7 the highest score) then the student would be forced to repeat thegrade. While students moving from 1st to 2nd and from 3rd to 4th grade

1Jacob and Lefgren (2009)

3

would only require to fill the assistance requirement given that they havea two year period to achieve the required GPA. One of the problems withthis notion is that “assistance to class” can be easily altered by teachers andallows manipulation in the event that the student might be slightly underthat threshold in order to promote them. Figure (1) shows that is in fact thecase since there is a big jump right in the 85% assistance rate. This can onlymean that teachers in Chile tend to alter their assistance reports in order toallow students who are right in that threshold to achieve the necessary re-quirements to pass. Moreover, being this the only explicit deterministic ruleof enforcement that we could find, the empirical analysis with a regressiondiscontinuity cannot be used as an empirical method to estimate the effectof early retention in this article.

Due to a lack of a deterministic rule combined with poor background in-formation from the database we relied on the instrumental variable approachto try and correct the endogeneity from our grade retention variable since itinvolves unobserved characteristics of the student such as prior cognitive de-velopment, early academic motivation, maturity, parental involvement, etc.In order to do this, I had to find a variable that was correlated with myendogenous variable but which did not explain the output in place. In otherwords, I want a variable capable of explaining grade repetition without anyexplanatory power over GPA in 6th and 8th grade, probability of attend-ing secondary school and the probability of dropping out while in secondaryschool.

Using standard literature about the subject I will follow Fertig (2004),Elodie Allet (2010) and Eide and Showalter (2001) and exploit the “relativematurity” of the student with the number of days from his birthday at thetime of entry in first grade and the quarter of birth as instrumental variables.According to Eide and showalter (2001) one of the biggest worries when us-ing this approach is that the instrument would in fact be correlated with thedependent variable, in this case GPA. Their argument is that children whostarted younger relative to their peers have a higher probability of repeat-ing a grade than those who started older given that they are more matureand faster learners. However, there is reasonably good evidence that agedifferences in scholastic performance at school entry are temporary2. Shep-ard and Smith (1986,1987) find that first grade classes typically have 8 or9 percentile point differences in reading achievement tests between the old-est and youngest students, but that the age effect disappears by the third

2Eide and Showalter (2001)

4

grade. Finally, Reynolds (1992) finds that age at school entry does not haveany significant effect on grade 4 outcomes, independent of grade retention3.Therefore, we can utilize this argument to prove that maturity at the timeof entry does not have a significant effect on students’ outcomes nor do theyhave a significant long-term effect on GPA. Therefore, we can conclude thatthe instruments used here are in fact exogenous and do not affect the aca-demic achievements and outcomes in secondary school.

The results found in this study, while applying the instrumental vari-able approach, show that repeating at an early age lowers sixth grade GPAby 0.72 points on average. Eight grade GPA shows similar results with adecrease of 0.6 points on average. The study also found that early graderepetition decreases the probability of ever attending secondary school by 25percentage points at the one percent level of confidence. Finally, the studyshowed that there was a 33.4 percentage point increase in the probabilityof dropping out of secondary school when repeating at an early age. Thisfollows the results of Eide and Showalter (2001) as they find repetition tohave a negative impact on students scores and academic achievement.

The remainder of this article is going to be sectioned in 4 parts. Section2 will give a brief description of the Chilean background and educationalsystem, the database, and the empirical method used while giving some de-scriptive statistics. Section 3 will describe the estimation strategy with 3models used to explain the outcomes. Section 4 will show the table resultsof the models and explain the direction and magnitude of the coefficients.Finally, Section 5 will end with a conclusion and some critics to the negativeresults found in section 4.

2 Chilean educational system, data and vari-ables

2.1 BackgroundChile’s educational system is made up by 2 cycles, primary school (enseñanzabásica) and secondary school (enseñanza media). Primary goes from 1stgrade to 8th grade with a minimum age of entry in first grade of 6 yearsold, and secondary school from 9th to 12th. According to law 19.876 pri-

3Ibid

5

mary and secondary education in Chile is mandatory for all children untilthe age of 21, which means that every child in the country has the option offree education without exclusion in certain establishments. The educationalestablishments in Chile are distributed into three different types: Public ormunicipal schools which represent 41% of total enrollment, non-fee-chargingprivate schools with 51% of enrollment and fee-charging schools with 7% ofenrollment, Caceres and Giolito (2014). With this in mind, most of the fee-charging schools in Chile are located in the capital which at them time ofanalyzing our data distorts the sample since it is not representative to thecountry itself.

In 2008 the government passed the Subvención escolar preferencial (SEP)or targeted-voucher school law, which establishes that all children consideredvulnerable in the economical sense can apply to any non-fee-charging schools(private-voucher school) they desire, without any admission test and com-pletely free. This law was meant to reduce the inequality gap built by theschool system itself and allow a more heterogeneous distribution of studentsamong schools. One of the feature of this law, is that it provides funds toall schools that absorb these incoming students which at the same time areallowed to repeat a grade at least one time per grade without consequence.However, for this article we wont touch this law since we will be using acohort of 2003.

Another important distinction that the Chilean educational system hasis that it allows children to choose between two different type of tracks forsecondary education. There is a Scientific-Humanistic track which encour-ages and prepares the student for future college education, providing himwith different classes and tools to excel. On the other hand, there is theTechnical-Professional track that prepares the student for immediate techni-cal work after secondary school. This later track, however, has a duration offive years instead of the standard four such as the former one.

The basic motivation of this article comes from the relative change thatrepetition has had over the past few years. This change, following a recentstudy by the ministry of education (2015) and UNESCO4, shows that in 2012the repetition rate for primary school (taking into account only the first sixgrades) was 4.7%, in 2013, however, it changed to 3.7%. This one percentagepoint change represents a question mark in our study since it might hinta difference in opinion about the effectiveness of the promotion policy in

4National revision 2015 for ”educaci’on para todos”

6

place. An efficient system is the one where repetition rates are closer to zero,find the reason why these rates are so high in Chile, represents the type ofquestions that this article will try to address.

2.2 DataI use the detailed administrative data of academic achievement from the min-istry of education, which provides data from 2002 to 2014 on specific birthdates, code of the establishment, code of the county and region, an identifi-cation number specific to each student that allows me to follow them evenin the case of transferring to another establishment throughout the period,gender, and general GPA after the end of the academic year. I exploit thefact that the data base provides a 12 year period to construct a panel datathat allows me to follow a student from the first day he joined the educa-tional system all the way until he finished. Therefore, the data allows meto observe a specific cohort for an entire period of time. Constructing thepanel, I obtained my 2003 cohort5 with students all over Chile; however,to avoid too much heterogeneity between establishments I focused on non-fee-charging private and municipal establishments since they constitute themajority of the student body that have similar characteristics, leaving theprivate fee-charging establishments out of the study. The data also provideswith important information of the final situation of the student at the endof the academic year. This allows for the creation of most of the variablesof interest, such as whether the student dropped out of secondary school orhow his GPA looked like. I am also able to construct the repetition variablesby observing the amount of times the ID number is seen on a determinedgrade and establishment. I therefore use a predetermined cohort (2003) anduse it as a cross-section study having only one observation per individual,but allowing for dummies such as repeated any time between first and secondgrade, third and fourth grade and finally first and eight grade. Making theanalysis in this way more manageable.

5I also applied this same study using a 2002 cohort given the fact that students ob-served in 2002 in first grade could also be repeaters from the previous year, and since theinformation for it did not come with the data, we used the following year to see what thefraction of repeaters looked like and concluded that the difference was significant; thereforecausing distortions

7

2.3 VariablesFor my outcome variables I study the direct effect of repetition of 6th and8th grade GPA. I focus specially on early grade repetition and the effect thisone has on later outcomes in primary and secondary school. With it I intendto see the impact that repeating at an early age has on the psychological andacademical outcomes of the student. In the case of the probability of assistingsecondary school, I generated a dummy equal to 1 if the student’s identifi-cation number appeared at least once in the records of secondary school, Idid this in order to see the probability the repeater has to ever graduatefrom primary school and enroll in the subsequent level. Finally, I createdmy dropout variable focusing only in secondary school due to administrativeerrors in the data, where students would suddenly disappear in early gradescausing error and noise in the estimations. This last variable was created bylooking at the last year the student appeared in the database and creating adummy equal to 1 if the last year observed was less to 2014.

When creating my repetition variables I wanted to explain the effect ofearly repetition on the outcomes the student might have in the future. There-fore, I focused on four different possibilities of repetition. The first is havingrepeated a grade at least once while coursing 1st and 2nd of primary school.the second explains having ever repeated 3rd or 4th grade, the third explainsrepetition between 1st to 4th grade and finally, the fourth repetition variableshow having ever repeated grade in primary school (1st to 8th grade). Thesevariables will try to explain the real effect that early repetition has on long-run effects in student achievement. To have ever repeated primary schoolcan affect directly the output of the student the subsequent year, moreover,I expect to see a bigger effect on dropout and the probability of attendingsecondary school in the upcoming results.

The instruments I utilize in this article come from the literature of Fertig(2004), Elodie Allet (2010) and Eide and Showalter (2001). This literatureuses the physical maturity of the student at the time he first joins the educa-tional system in first grade of primary school relative to his peers. The mainidea is that the younger the child is relative to his classmates the more will theprobability be of repeating first and second grade. Elodie Allet (2010) usesthe number of days from the birthday to the cut off date and determines adifference in days from the youngest to the oldest to account for how youngeris one student relative to anotherr. Elodie Allet (2010) experiments with twovariables of the number of days and estimates their respective coefficients.The first is using the variable as continuous and the second as dummy vari-

8

ables. One conclusion she provides is that the difference in implied effect ofretention between the dummy variable estimates and the ndays estimate isthat ndays gives equal weight to days far beyond the cut-offs which some-times is not supported by the data. Therefore, the correct way and the oneused in this article is to use dummies to correct for the weight distributionwithin days from the cut off date. The literature also uses the quarter ofbirth as a controlling variable of the cut off date when the children must joinschool, which happens to be in March 31st, McEwan and Saphiro (2006),with a flexible period for late entering students of three months or until July1st. The quarter of birth will also control for those students that just missedthe cut off date and will eventually have to wait another year to be submittedinto first grade.

Finally, given that the data used in this work is limited to characteris-tics of the establishment and some characteristics of the student, there is nofamily background or social status that will allow me to control for certaindifferences between the students within an establishment. However, I utilizegender of the student to control for possible heterogeneity between boys andgirls, which is standard in this literature. I will eventually find that there is anegative correlation between being a boy and having a higher GPA, having ahigher probability of attending secondary school, and a lower dropout rates.The following models will describe the real purpose of this article and whatis it that this study is trying achieve by explaining he effect of early graderetention of long-term student’s outcomes.

Some Descriptive statistics are shown below to specify the variables usesin this study.

Table 1 shows a summary statistics of the variables that will be utilizedin the models. As shown, the general point average (GPA) for students atthe end of sixth grade grade is 5.6 out of a scale of 1 through 7 in the Chileanscore system. This is an elevated score for a sample of over 139 thousandobservations, meaning that in general students do very well in their scoresby the end of their academic year. GPA for eighth grade is very similar tosixth, which only shows that students, on average, tend to be persistent intheir scores throughout primary school. As for the probability of attendingsecondary school, we observe that about 93 percent of the student bodyin our sample get to graduate primary school, which in fact is mandatory.Nonetheless, there is still a big part of the sample, about 6.7 percent, thatdo not get to finish primary and either disappear from the sample. Dropoutis about a tenth of the sample in secondary school only. The variables for

9

Table 1: Summary statisticsVariable Mean Std. Dev. Min. Max. N

Establishment (RBD) 8778.523 7000.187 5 25810 139613ID number 10875154.995 6696498.007 150 25024246 139613RBD in 6th grade 9394.735 7418.757 5 40403 135626RBD in 8th grade 9556.023 7609.111 5 40436 132458RBD in Primary 9321.127 7337.136 5 40298 139613GPA in 6th grade 5.608 0.616 1 62 135626GPA in 8th grade 5.579 0.583 1 48 132458Prob.attending S. School 0.933 0.25 0 1 139613Repeated between 1-2 0.028 0.164 0 1 139613Repeated between 3-4 0.054 0.227 0 1 139613Repeated between 1-4 0.077 0.266 0 1 139613Repeated between 1-8 0.18 0.384 0 1 139613Dropout 0.105 0.307 0 1 139613ndays 128.519 125.963 -382 678 139602ndaysme271 0 0.011 0 1 139613ndaysme181_270 0.001 0.039 0 1 139613ndaysme91_180 0.004 0.059 0 1 139613ndaysme61_90 0.043 0.204 0 1 139613ndaysme31_60 0.055 0.229 0 1 139613ndaysme30_30 0.141 0.348 0 1 139613ndaysma31_60 0.077 0.266 0 1 139613ndaysma61_90 0.081 0.273 0 1 139613ndaysma91_180 0.249 0.433 0 1 139613ndaysma181_270 0.244 0.429 0 1 139613ndaysma271_360 0.074 0.262 0 1 139613ndaysma361 0.03 0.17 0 1 139613Student’s gender 0.509 0.5 0 1 139613Quarter of Birth 2.546 1.123 1 4 139613

10

the number of days a student has from his birthday to the last cut off datehe can be admitted that year ranges from a year early to about two years. Inother words, ages go from five to seven years of age in the sample. Anotherimportant statistic to notice is that about 50% of the students in the sampleare within the range of 91 and 270 days of age from the cut off date whichimplies that about half of the students will belong to the second quarter ofthe year and will most likely have to wait another year to be admitted tofirst grade. Table 2 shows in more detail the outcome variables used in thisarticle.

Table 2: Tabulations

Item Number Per centDropped out in S. SchoolAttending 124,888 89Dropout 14,725 11Total 139,613 100Repeated between 1-4Didn’t repeat 128,919 92Repeated grade 10,694 8Total 139,613 100Repeated between 1-2Didn’t repeat 135,732 97Repeated grade 3,881 3Total 139,613 100Repeated between 3-4Didn’t repeat 132,010 95Repeated grade 7,603 5Total 139,613 100Repeated in Primary SchoolDidn’t repeat 114,459 82Repeated grade 25,154 18Total 139,613 100Attended S. SchoolAttending S. School 130,224 93Not attending S. School 9,389 7Total 139,613 100

11

Table 2 shows some detailed descriptions for the major variables used,taking into account both exogenous and endogenous variables. It is impor-tant to notice that our dropout rate in secondary school is 11%, meaningthat about a tenth of the children disappear from the data before finishingin 2014. Dropout rate in primary school shows up to be smaller that thesecondary school dropout rate, which might be counter intuitive since mostof the children tend to quit school at an early age. However, these resultsaccount for administrative errors for which the students in first grade tendto disappear. Moreover, we will be using only the dropout rate for secondaryschool in this study. Another interesting statistic is that of ever repeating agrade between first and second, third and fourth, and first and fourth. Thefraction of students who did not attend secondary school is very low for thesize of the data of only 7%; however, it has a high positive correlation withthose students who repeated grade at an early age.

3 Estimation strategy using an IV frameworkI begin by presenting three simple models of grade retention as a key to ana-lyze some of the most important effects that early repetition has on student’soutcomes 6.

3.1 GPAThe first outcome I present is divided into two separate models to show theimpacts of early retention into immediate and long-term outcomes. The firstexplains the effect of early repetition as function of immediate academic out-comes, in this case, 6th grade GPA. The second, focuses on the impact in8th grade GPA. This important distinction is made in order to see whetherrepeating as an early child has long lasting effects on GPA or if this effectactually dissipates over time.

6th Grade Model:

GPA_6ir = β0 + β1Repite_1_2ir + γXir + δr + uir (1)6This study was made to see the true effect of grade repetition at an early age, which

we account as ever repeating between first and second grade. The results and models arealso presented in the appendix for grade repetition in third to fourth grade, first to fourthgrade, and first to eight grade. We focus on repetition between first and second gradegiven the fact that our instruments are only relevant during the first years of primaryschool education.

12

From equation (1) we have that the subscript i represents the individualstudent and r represents the establishment where he is located at that mo-ment 7. The vector Xir is the vector of the control variables described in theprevious section, in this case, we only focus on the gender of the individual.

This model will try to explain the causal effect that repeating a gradein the early years of primary school has on the academic achievement of thechild at the end of the school year. To do this, I use the instrumental variableapproach using the quarter of birth and the relative age in days from the cutoff date as variables describing the physical maturity of the child. Moreover,I will run a first stage where I will test the relevance of the instruments inthe model. Equation (2) shows the structure of the first stage where Zir

represents the vector of my instrumental variables.

Repite_1_2ir = γ0 + γXir + θZirδr + eir (2)8th Grade Model:

The second model provides information about the achievement of thechild in the subsequent years after repeating grade at an early age for thefirst time. It tries to explain whether the effects of repetition in a student’sperformance (if it helps him or if it hurts him) have a long lasting effect inprimary school. This is important to address, given the implications thatpoor academic scores mean in the development of the student. Jacob andLefgren (2004), use a regression discontinuity approach to study this par-ticular effect, the results they obtained showed a positive effect of takingsummer school and repeating a grade on third grade achievement in math aswell as reading. However, the impact that it had on later years became lesssignificant and they concluded that it started to fade by roughly 25 to 40%all the way to sixth grade8.

GPA_8ir = β0 + β1Repite_1_2ir + γXir + δr + uir (3)By looking at GPA, this article will attempt to explain the effect that re-

peating grade has on achievement and academic progression. If by repeatinga grade a student will move higher in achievement, then that will give provethat the current Chilean system works. However, if the contrary happens,we will see that repeating a grade will cause a student to go even lower in

7The establishment will change according to the outcome variable, and with it thenumber of observations.

8They also explain that this effect is consistent with the fadeout of program effectsfound in other evaluations (Bernett 1995)

13

his academic achievement affecting him psychologically in the long term formultiple reasons.

3.2 Probability of Attending Secondary SchoolFor the second model I want to estimate the probability of attending sec-ondary school when the child has repeated at an early age. The purpose isto see the real impact that repetition has on children. The negative psycho-logical effects this generates, and the possible solutions we could address toavoid this damage.

The model starts with the definition of attending secondary school, bythis we mean having ever completed primary school and entering first gradeof secondary school between the period of 2002 and 2014. Whether the stu-dent left for a long period of time or not, if the observation we have of thestudent appears once in our data base in secondary school, then we considerthat individual as part of the sample in study.

emediair = βo + β1Repite_1_2ir + γXir + δr + uir (4)What equation (5) will try to explain is the true effect of early grade

repetition on the probability that a student ever attends secondary school.In Chile, secondary school is, by law, mandatory9. However, it can be seenthroughout the country that a vast majority of rural schools still experiencelarge quantities of their students who finish primary school without contin-uing to secondary school as the following step for their education.

3.3 Probability of Dropping OutOur last model shows the effect of early grade retention in the probability ofdropping out of secondary school. This model tries to imitate the literatureof Eide and Showalter (2001). They found that retaining a child results inan 8.8% increase in the probability of dropping out of high school10 usingOLS. However, they find this result to be not economically significant giventhat OLS would not capture the causal effect of repetition since this variableis endogenous on unobserved characteristics. When controlling for IV, they

9Mandatory only means that the government provides all the possibilities and resourcestowards municipal schools and non-fee-charging schools for all students to attend it.

10Eide and Showalter (2001)

14

find expected signs implying a positive effect of retention on dropout.

Dropoutir = β0 + β1Repite_1_2ir + γXir + δr + uir (5)As Eide and Showalter (2001) show, I also find, after controlling for the endo-geneity of early grade retention, that there is a positive correlation betweenrepeating a grade in primary school and dropping out of secondary school.I use the instrumental variable approach to find the causal effect of thisrelation; however, there might still be some bias regarding the students char-acteristics making the coefficients to be exaggerated upwards. Given that Iuse administrative data that has no records on family background, I am notable to control for parents education (which previous literature focus on);however, I expect that controlling for establishment captures most of thiseffect. Chilean education is very segregated and usually the establishmentcan capture the social status of the family11.

4 Results4.1 Model 14.1.1 Academic Achievement

Table 3 shows the ordinary least squares, fixed effect and instrumentalvariable estimations of early repetition on students GPA. When interpretingthis table casually, we can see that OLS and FE give similar estimators forthe effect of retention on GPA. In sixth grade GPA we can see that by repeat-ing at an early age the average score will fall by 0.5 points on average withOLS, and about 0.47 points with FE. This decrease on GPA allows us to havean idea of the direction repetition has on academic achievement. However,we cannot rely on these results to make the ultimate conclusions given thatthey contain the selection bias explained before. What is interesting as wellis the effect that gender has on average scores. This implies that being a malereduces also the academic achievement of the child. Eight grade scores show

11This will change later on with a targeting voucher policy (SEP) that was put in place in2008. This policy allows vulnerable students with no resources to apply to any municipal,private-voucher school in the country without paying, as long as they qualify for it. Theremight also be an effect in retention given that vulnerable students are allowed to repeatgrade at least once for a specific grade without affecting their eligibility. Nonetheless, itdoes not apply to our study since the 2003 cohort I use does not experience this policy forthe time studied.

15

Tabl

e3:

Mod

el1:

The

effec

tof

repe

atin

gin

1-2

grad

eon

6th

and

8th

grad

eG

PAG

PA6t

hG

PA6t

hG

PA6t

hG

PA8t

hG

PA8t

hG

PA8t

hO

LSFE

IVO

LSFE

IVR

epea

ted

betw

een

1-2

-0.5

05∗∗

∗-0

.464

∗∗∗

-0.7

24∗∗

∗-0

.387

∗∗∗

-0.3

62∗∗

∗-0

.595

∗∗∗

(0.0

105)

(0.0

109)

(0.0

273)

(0.0

111)

(0.0

113)

(0.0

294)

Gen

der

-0.1

83∗∗

∗-0

.186

∗∗∗

-0.1

85∗∗

∗-0

.156

∗∗∗

-0.1

58∗∗

∗-0

.158

∗∗∗

(0.0

0328

)(0

.003

79)

(0.0

0327

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16

a similar result, nevertheless, the impact is not as negative as the immediateeffect in sixth grade. We see on the results that early repetition reduces GPAin around 0.4 points for both OLS and FE.

Table 3 also shows the results for our instrumental variable approach. Aswe can see, the direction of the coefficient follows that the standard litera-ture and shows that early grade repetition has a negative effect on 6th gradeand 8th grade GPA. We can see that repeating in first or second grade, af-ter controlling for the maturity of the child, lowers sixth grade GPA in 0.72points on average being statistically significant at the 1 percent level. 8thgrade GPA shows a similar result of about 0.6 points. These results attemptto show the causal effect of grade repetition on academic achievement on6th and 8th grade. To see, however, the effect that the results are in factunbiased we will see the first stage results in table 4 to test whether ourinstruments are exogenous and statistically significant.

Table 4 shows the first stage for 6th and 8th grades respectively. Oneof the most interesting results that we found in our first stage is that of thenumber of days the student has with respect to the cut off date in first grade.As we can see, there is a negative correlation between repeating a grade asan early child and the number of days. This only supports the theory behindthe previous literature, implying that the younger the student is the morethe probability of repeating. We can also see that for the quarter of birth.Our second quarter accounts for a negative correlation with grade repetition,while the first and third show a positive correlation. This also makes sensedue to the cut off date where children are allowed to be submitted into theirfirst year. According to the Chilean educational system, children born afterMarch 31st have to wait until the next year to be admitted into first grade,therefore, those born in the second quarter will always be older that thoseborn in the first, giving a negative correlation between being older and re-peating a grade (supporting in this way the theory planted in this article).The coefficients of our instruments follow the signs expected in the studyand they are also statistically significant at the one percent level. We cantherefore argue that the instruments used in this article will in fact controlfor the endogenous features of repetition.

Therefore, this first model shows that academic achievement in the formof average general points throughout the year has a negative relation withgrade repetition. This can only pinpoint the fact that, if GPA is really thebest measure of student academic achievement, then grade repetition is af-fecting negatively their performance instead of repairing the problem. Most

17

schools and universities focus on this measure of achievement as a reliablesource to select their students and allow them to continue studying. How-ever, if repeating hurts the student in the long run, as it is shown in theregression, then it might not be the most effective policy.

4.2 Model 24.2.1 Attending Secondary School

Table (5) shows the effect that early grade retention has on the probabilityof the child to ever attend secondary school and graduate from primaryschool. As we can see, OLS estimation overestimates the result given theselection bias. When using fixed effects to control for the heterogeneity ofthe establishment and control for some of the parental background, we can seethat the coefficient becomes less negative to a 16 percentage point decreasein the probability of attending secondary school. Moreover, we expect thecoefficient of out instrumental variable approach to be smaller than whenusing OLS estimation, for which this is the case. IV estimation shows a25 percentage point decrease in the probability of ever attending secondaryschool being statistically significant at the one percent level. This result iseconomically significant since it represents a big decrease in the probability.Allowing children to repeat grade at an early age therefore, results in a verynegative outcome in the long run. If this is the causal effect that repetitionhas on attending secondary school, it then requires a closer focus by theChilean educational authority.

4.3 Model 34.3.1 School Abandonment

Table 6 shows the final set of regression results which focus on the effectthat early grade retention has on the probability of a student to dropout ofsecondary school. Its important to notice that there is a positive correla-tion between repetition and secondary school dropout. Column 1 shows thecoefficients of ordinary least squares estimation with a 5.7 percentage pointincrease in the probability of dropping out of secondary school. This result isimportant since it provides us with information about the size and direction

18

Table 4: First Stage - Repeating betw een 1-2 (6th grade GPA)Variable Coefficient (Std. Err.)

Student’s gender .0013703 (.0007226)

ndays < -271 -.3854225 (.0333188)

-270 < ndays < -181 -.3525221 (.0094594)

-180 < ndays < -91 -.3626432 (.0064068)

-90 < ndays < -61 -.3751106 (.0032886)

-60 < ndays < -31 -.3754839 (.0031936)

-30 < ndays < 30 -.3752266 (.002792)

31 < ndays < 60 -.3741157 (.0029857)

61 < ndays < 90 -.3769847 (.0029314)

91 < ndays < 180 -.3818646 (.0031299)

181 < ndays < 270 -.3665173 (.0030901)

271 < ndays < 360 -.3302267 (.002979)

ndays > 360 0 (omitted)

First Quarter 0 (empty)

Second Quarter .0022029 (.0017097)

Third Quarter -.0116519 (.0029583)

Fourth Quarter .0050125 (.0033092)

Intercept .3888705 (.0028034)Number of Obs 135626 135626

19

Table 5: Model 2: The effect of repeating in 1-2 grade on the probability ofattending s. school

S. School S. School S. SchoolOLS FE IV

Repeated between 1-2 -0.463∗∗∗ -0.163∗∗∗ -0.249∗∗∗

(0.00803) (0.00823) (0.00748)

Gender -0.0270∗∗∗ -0.00578∗∗∗ -0.00616∗∗∗

(0.00127) (0.000837) (0.000794)

Constant 0.959∗∗∗ 0.975∗∗∗ 0.981∗∗∗

(0.000795) (0.000928) (0.000818)Observations 139613 132458 132458Standard errors in parentheses∗ p < .1, ∗∗ p < .05, ∗∗∗ p < .01

of the bias. Column 2 shows the results controlling for establishment and theoutput becomes smaller by this with a 3.5 percentage point increase. Boththese results are not too relevant considering the magnitude of the coefficientand the size of its standard error. However, when applying the instrumentalvariable approach we can observe that the direction of the result remains,while the magnitude changes describing a 33.4 percentage point increase inthe probability of dropping out when repeating a grade at an early age beingstatistically significant at the one percent level and economically significant.

5 ConclusionsGrade retention has remained a controversial remedial policy all around de-veloping countries. There are those who argue that it provides the neces-sary tools and additional maturity to withstand the following grades. Othersuggest that retention put negative psychological restraint on children fortheir academical and cognitive development. In this article, we analyze theeffect that early grade retention has on children in their academic achieve-ment along primary school, their probability of graduation and progressionto secondary school and their probability of abandonment. We also try todemonstrate that through an instrumental variable approach we can approx-imate the causal effect and counter-strike the endogenous characteristics ofrepetition.

20

Table 6: Model 3: The effect of repeating in 1-2 grade on the probability ofdropping out of s. school

S. School Dropout S. School Dropout S. School DropoutOLS FE IV

Repeated between 1-2 0.0572∗∗∗ 0.0358∗∗∗ 0.334∗∗∗

(0.00598) (0.00647) (0.0122)

Gender 0.0173∗∗∗ 0.0153∗∗∗ 0.0133∗∗∗

(0.00164) (0.00172) (0.00169)

Constant 0.0951∗∗∗ 0.102∗∗∗ 0.0927∗∗∗


For the three models described in this study, we demonstrate that graderepetition has a negative impact on students outcomes. The first model ex-plains that having ever repeated between first and second grade reduces thegeneral point average by 0.72 points. This reduction becomes significantsince it describes a decrease in the most important achievement determinantand therefore, describes future outcomes of the child. The second model isprobably the most significant one since it explains the graduation rate fromprimary school. With a reduction of 25 percentage points in the probabilityof attending secondary school there is a significant negative effect on futureoutcomes for the child. This reduction in the probability represents a bigresult given that labor market options will become narrower in the futureand the probability of criminal acts will increase. Finally, The probabilityof dropout from secondary school provides a glimpse of the lack of deter-mination to complete school. The fact that early repetition has a positiveand significant correlation with dropout with 33 percentage point increasein the probability suggests that schools that allow this remedial policy aresentencing the child to under-perform in their future classes allowing themto chose abandonment in the future. Looking at these results one can arguethat in the Chilean educational system grade repetition might not be the bestremedial policy to counter-attack the growing difficulty levels in primary andsecondary school, at least in the early stages. Moreover, other options of re-medial policies should be suggested to avoid most of these negative outcomes.

Most developed countries have switched towards a more linear approach

21

which is the automatic progression policy, which allows the student to auto-matically pass the grade regardless of their final grade. In the case of Finland,students who score lower than the required threshold obtain special supportby specific professors to allow them to strengthen the courses in which theyare failing. This policy allows students to continue with their initial group ofpeers and corrects for some of the psychological effects concerned with graderepetition. Jacob and Lefgren (2009) explain that another possible remedialsolution might be a pre-course or summer course before making the decisionto repeat the grade. They showed that summer school has a positive effectin math and reading scores in the short run allowing the students to improveand enhance those skills that weren’t learned during the course of the firstprogram. Even though these effects were only noticeable in the first few yearsafter summer school and were not significant in following years, this could bemore than necessary to correct for the immediate necessity of strengtheningtheir weak subjects and still give the children the opportunity to continuewith their initial group.

Finally, there are many other methods already used in many developedcountries who have already seen the negative effects of early grade repetition.Some will continue to utilize, however, grade retention as the main remedialpolicy continuing, in this way, with this controversial subject. In the case ofChile, what is important in not necessarily trying find what the best remedialmethod for children is, but to understand the real causes of this decrease inproductivity and academic achievement for students whose only fault is theirlack of initial maturity.

6 Appendix6.1 Cohort 20036.1.1 Tables for ever repeating between third and fourth grade

22

Figure 1: Yearly Assistance Rate

Table 7: Model 1: The effect of repeating in 3-4 grade on 6th and 8th gradeGPA

GPA 6 GPA 6 GPA 6 GPA 8 GPA 8 GPA 8MCO FE IV MCO FE IV

Repeat 3-4 -0.539∗∗∗ -0.489∗∗∗ -3.827∗∗∗ -0.432∗∗∗ -0.396∗∗∗ -3.571∗∗∗

(0.00607) (0.00675) (0.183) (0.00661) (0.00701) (0.212)

Gender -0.174∗∗∗ -0.178∗∗∗ -0.110∗∗∗ -0.150∗∗∗ -0.153∗∗∗ -0.108∗∗∗

(0.00325) (0.00375) (0.00628) (0.00314) (0.00390) (0.00564)

Constant 5.723∗∗∗ 5.742∗∗∗ 5.871∗∗∗ 5.673∗∗∗ 5.681∗∗∗ 5.806∗∗∗

(0.00224) (0.00379) (0.00900) (0.00222) (0.00407) (0.00970)Observations 135626 135626 135626 132458 132458 132458Standard errors in parentheses∗ p < .1, ∗∗ p < .05, ∗∗∗ p < .01

23


S. School S. School S. SchoolMCO FE IV

Repeated 3-4 -0.289∗∗∗ -0.108∗∗∗ -0.732∗∗∗

(0.00547) (0.00461) (0.0473)

Gender -0.0237∗∗∗ -0.00449∗∗∗ 0.00373∗∗∗

(0.00128) (0.000830) (0.00125)

Constant 0.961∗∗∗ 0.977∗∗∗ 1.008∗∗∗



Dropout Dropout DropoutMCO FE IV

Repeated 3-4 0.0401∗∗∗ 0.0244∗∗∗ 0.797∗∗∗

(0.00414) (0.00424) (0.0617)

Gender 0.0168∗∗∗ 0.0150∗∗∗ -0.00276(0.00164) (0.00173) (0.00240)

Constant 0.0948∗∗∗ 0.102∗∗∗ 0.0634∗∗∗


24

6.1.2 Tables for ever repeating between first and fourth grade

Table 10: Model 1: The effect of repeating in 1-4 grade on 6th and 8th gradeGPA

GPA 6 GPA 6 GPA 6 GPA 8 GPA 8 GPA 8MCO FE IV MCO FE IV

Repeat 1-4 -0.538∗∗∗ -0.497∗∗∗ -0.787∗∗∗ -0.426∗∗∗ -0.398∗∗∗ -0.661∗∗∗

(0.00548) (0.00613) (0.0271) (0.00590) (0.00637) (0.0294)

Gender -0.173∗∗∗ -0.177∗∗∗ -0.172∗∗∗ -0.150∗∗∗ -0.153∗∗∗ -0.149∗∗∗

(0.00323) (0.00373) (0.00328) (0.00313) (0.00390) (0.00314)

Constant 5.731∗∗∗ 5.753∗∗∗ 5.774∗∗∗ 5.679∗∗∗ 5.689∗∗∗ 5.704∗∗∗

(0.00223) (0.00380) (0.00417) (0.00222) (0.00408) (0.00415)Observations 135626 135626 135626 132458 132458 132458Standard errors in parentheses∗ p < .1, ∗∗ p < .05, ∗∗∗ p < .01

25



Repeat 1-4 -0.334∗∗∗ -0.118∗∗∗ -0.242∗∗∗

(0.00471) (0.00405) (0.00754)

Gender -0.0211∗∗∗ -0.00434∗∗∗ -0.00296∗∗∗

(0.00124) (0.000825) (0.000809)

Constant 0.969∗∗∗ 0.980∗∗∗ 0.991∗∗∗




Repeat 1-4 0.0529∗∗∗ 0.0358∗∗∗ 0.309∗∗∗

(0.00362) (0.00387) (0.0123)

Gender 0.0162∗∗∗ 0.0146∗∗∗ 0.00735∗∗∗

(0.00164) (0.00173) (0.00174)

Constant 0.0932∗∗∗ 0.101∗∗∗ 0.0797∗∗∗


26

6.1.3 Tables for ever repeating between first and eighth grade



Repeat all Primary -0.246∗∗∗ -0.103∗∗∗ -0.232∗∗∗

(0.00283) (0.00234) (0.00771)

Gender -0.0112∗∗∗ 0.000260 0.00794∗∗∗

(0.00122) (0.000805) (0.000943)

Constant 0.983∗∗∗ 0.988∗∗∗ 1.009∗∗∗


27



Repeat all Primary 0.103∗∗∗ 0.0961∗∗∗ 0.297∗∗∗

(0.00262) (0.00289) (0.0128)

Gender 0.00960∗∗∗ 0.00801∗∗∗ -0.00752∗∗∗

(0.00163) (0.00171) (0.00197)

Constant 0.0821∗∗∗ 0.0883∗∗∗ 0.0571∗∗∗


7 Literature

References[1] Cáceres-Delpiano, J. and Giolito, E. The impact of age of entry on aca-

demic progression. Journal of Economic Literature, 2014.

[2] Eide, E. and Showalter, M. The effect of grade retention on educationaland labor market outcomes. Economics of Education Review, Vol. 20,issue 6, December 2001.

[3] Elodie, A. Is grade repetition a second chance?. Journal of EconomicLiterature, January 2010.

[4] Fertig, M. and Kluve, J. The effect of age at school entry on educationalattainment in Germany. The institute for the Study of Labor (IZA),March 2005.

[5] Jacob, B. and Lefgren, L. Remedial education and student achievement: Aregression discontinuity analysis. The Review of Economics and Statistics,Vol. 86, issue 1, February 2004.

[6] Jacob, B. and Lefgren, L. The effect of grade retention on High Schoolcompletion. Journal of Pubic Economics, Vol. 1, issue 3, July 2009.

28

[7] Manacorda, M. The cost of grade retention. The Review of Economicsand Statistics, Vol. 94, issue 2, May 2012.

[8] McEwan, P. and Shapiro, J. The benefits of delayed primary school en-rollment: Discontinuity estimates using exact birth dates. The Journal ofHuman Resources, July 2006.

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