!
!
!
!
!
A!DIFFERENCE*IN*DIFFERENCES!ANALYSIS!OF!AN!EXTRA!YEAR!OF!COMPULSORY!
EDUCATION!IN!BRAZILIAN!PRIMARY!SCHOOLS!!
!
!
Marcelo!Martins!
Master!of!Arts!Paper!
International!Comparative!Education!
Graduate!School!of!Education!
Stanford!University!
July!2014!
!
!
!
!
Graduate!School!of!Education!
Stanford!University!
!
!
!
INTERNATIONAL COMPARATIVE EDUCATION
!
!
A!difference*in*differences!analysis!of!an!extra!year!of!
compulsory!education!in!Brazilian!primary!schools!!
!
Marcelo!Martins!
!
!
July!2014!
!
!
!
!
A!Master!of!Arts!Paper!in!partial!fulfillment!!
of!the!requirements!for!the!degree!of!Master!of!Arts!
!
!
!
!
Approvals:!
!
ICE/IEAPA!Master’s!Program!Director:!!____________________________________!
!
!
!
!
!
!
!Christine!Min!Wotipka,!Ph.D.,!date!
!
!
!
!
!
!
!!!!!!!Advisor:! ____________________________________!
!
!
!
!
!
!
!!Martin!Carnoy,!Ph.D.,!date!
Acknowledgements.
I!would!like!to!express!my!deepest!gratitude!for!all!the!support,!guidance,!and!
advice!that!my!advisor,!program!director,!teaching!assistants,!program!cohort!
members,!classmates,!and!family!have!given!me!throughout!the!thesis*writing!
process.!
!
In!particular,!I!wish!to!thank!the!following!people!and!organizations:!
Martin!Carnoy,!my!advisor,!for!his!guidance,!constructive!feedback!
and!insightful!talks!through!this!entire!program.!
Christine!Min!Wotipka,!my!program!director,!who!guided!me!
through!the!research!process!and!helped!me!with!her!precious!
comments!on!my!research!!
Sen!Zhou,!TA,!who!helped!me!with!her!insightful!comments!and!her!
patient!explanations!!
The!2014!ICE/IEAPA!cohort,!who!have!been!with!me!through!this!
entire!program!and!been!a!support!through!good!times!and!bad!
Luz!Jimenez,!Makaela!Anderson,!Annabell!Suh,!for!their!valuable!
editorial!assistance!in!different!versions!of!this!paper!
The!Lemman!Foundation,!whose!generous!contribution!helped!
finance!my!tuition!
My!ex*wife!Camila!Oliboni,!for!making!this!year!a!truly!transition!
from!marriage!to!friendship!and!paving!the!way!to!happier!lives!
for!our!children!!
And!last,!but!not!least:!my!parents,!Marcia!Martins!and!Silvio!
Martins,!for!being!an!unending!source!of!guidance,!support,!and!
inspiration.!
!
Abstract.
!
This!study!is!an!impact!evaluation!of!the!policy!that!added!an!extra!year!in!the!
Brazilian!compulsory!education.!I!use!difference*in*differences!to!estimate!the!effect!
of!the!increase!in!instructional!time!on!students’!academic!achievement!at!the!end!
of!the!primary!school!level.!The!findings!are!(a)!the!program!had!a!positive!effect!on!
students’!achievement!in!both!mathematics!and!Portuguese!language;!(b)!the!effect*
size!on!Portuguese!language!achievement!was!.2558!standard!deviations!and!for!
math!was!.2581!standard!deviations!after!controlling!for!student!individual!and!
family!covariates!as!well!as!state!differences!(c)!students!with!higher!socioeconomic!
status!had!a!greater!benefit!from!the!extra!year!of!education!when!compared!to!
students!from!lower!socioeconomic!backgrounds.!
!
Key!words:!!
Educational!economics!!
Input–output!analysis!!
Resource!allocation!
Instructional!time!
Difference*in*differences!
!
!
!
!
1..Introduction.
Adding!instructional!time!to!compulsory!education!is!being!increasingly!
implemented!as!an!educational!reform!in!Latin!America!(for!example,!more!hours!
per!school!day,!such!as!in!Chile!and!Mexico)!with!rather!mixed!empirical!support!for!
its!effectiveness.!In!Brazil,!the!reform!has!taken!the!form!of!starting!school!a!year!
earlier!(six!rather!than!seven!years!old)!and!staying!in!basic!(compulsory)!education!
an!additional!year!(nine!rather!than!eight!years).!!
Research!that!has!examined!the!effect!of!instructional!time!on!educational!
outputs!can!be!divided!into!two!groups.!The!first!group!of!studies!examined!the!
effects!of!policies!that!increased!or!reduced!the!amount!of!instructional!time!on!
student!achievement.!Studies!in!this!group!usually!compare!student!achievement!
either!before!or!after!the!implementation!of!the!policy,!or!of!those!students!who!
were!affected!by!the!policy!versus!those!who!were!not.!These!policies!implemented!
changes!in!instructional!time!in!the!form!of!hours!within!the!school!day,!days!within!
a!school!year,!and!years!within!an!educational!level!(Andrade*Baena,!G.,!2014;!
Bellei,!2009;!Cooper,!Charlton,!Valentine,!Muhlenbruck,!&!Borman,!2000;!
Krashinsky,!2006).!There!is!another!group!in!which!natural!experiments!set!the!
conditions!for!the!study.!Studies!in!this!group!include!papers!that!compared!
students!of!the!same!age!but!different!numbers!of!years!of!schooling!as!a!result!of!
starting!school!date!cut*offs!and!research!that!compared!students!that!had!a!
!
1!
different!number!of!school!days!per!year!as!a!result!of!severe!winter!conditions!
(Agüero!&!Beleche,!2013;!Luyten,!Peschar,!&!Coe,!2008;!Marcotte!&!Hemelt,!2008).!!
The!present!study!combines!elements!of!these!two!groups!of!studies.!It!
examines!the!effects!of!a!policy!implemented!in!2007!that!added!one!year!to!Brazil’s!
compulsory!education,!and,!at!the!same!time,!benefits!from!a!natural!experiment!
created!by!the!policy,!which!allowed!schools!to!decide!when!to!implement!the!
additional!year.!In!other!words,!this!study!compares!the!academic!achievement!of!
students!that!took!the!same!standardized!test,!but,!as!a!result!of!a!policy!change,!
with!different!numbers!of!years!of!schooling.!To!my!knowledge,!this!is!the!first!
study!to!investigate!the!effects!on!educational!achievement!of!adding!an!entire!year!
of!instructional!time.!!
These!conditions!of!the!reform!allow!me!to!use!the!“difference*in*
differences”!analytic!approach!to!provide!an!unbiased!estimate!of!the!causal!effect!
of!the!extra!year!of!compulsory!education!on!Brazilian!students’!academic!
achievement.!By!using!this!approach,!I!find!that!Brazilian!students!that!had!access!to!
the!extra!year!of!education!performed!one*quarter!standard!deviation!better!than!
students!not!affected!by!the!change!in!the!legislation.!I!also!find!evidence!that!
students!with!a!high!socioeconomic!status!disproportionately!benefit!from!the!extra!
year!of!instructional!time!than!students!with!a!low!socioeconomic!status.!!
!
2!
2..The.addition.of.one.year.in.the.Brazilian.compulsory.education.and.the.national.
educational.assessment.
With!57.8!million!students!enrolled!in!2010,!Brazil!has!one!of!the!world’s!
largest!school!systems.!The!largest!portion!of!the!enrollment!was!at!the!primary!
school!level,!with!16.8!million!students.!The!last!instructional!time!increase!in!
Brazilian!education!law!occurred!in!1971,!when!the!country!augmented!compulsory!
education!from!six!to!eight!years,!starting!from!the!age!of!seven!(MEC,!2004).!In!
2006,!Brazil’s!legislature!enacted!a!law!requiring!schools!to!gradually!implement!a!
nine*years!cycle!of!compulsory!education!with!children!starting!school!at!the!age!of!
six!(Law!Number!11,274).!!
Figure!1!depicts!the!Brazilian!education!system!levels!before!and!after!the!
change.!The!Brazilian!Ministry!of!Education!included!among!the!motivations!for!
increasing!the!amount!of!compulsory!education:!(a)!to!guarantee!a!longer!period!of!
opportunity!to!learn!for!all!children!(b),!to!improve!students!performance!and!(c)!to!
provide!education!at!this!age!for!families!with!lower!socioeconomic!status,!since!
families!from!middle!and!upper!classes!already!enrolled!their!six!year!olds!in!school!
(Ministério*da*Educação*do*Brazil,*Secretaria*de*Educação*Básica,*2007).!!
The!nine*year*compulsory!education!began!to!be!implemented!in!2007,!and!
the!municipalities!and!states!were!the!entities!responsible!for!progressively!
implementing!this!change!in!schools!under!their!control.!In!2010,!all!schools!had!to!
be!ready!to!provide!nine!years!of!public!school!for!every!Brazilian!child.!This!
legislation!added!roughly!3.3!million!students!per!year!to!the!Brazilian!primary!
school!system!(Ministério*da*Educação*do*Brazil,*Secretaria*de*Educação*Básica,*
!
3!
2007).!!.!It!is!also!important!to!mention!that!even!though!the!Ministry!of!Education!
provided!pedagogical!guidelines!for!municipalities!on!how!to!fulfill!this!extra!year!of!
education,!educational!systems!under!each!of!these!municipalities!had!autonomy!to!
decide!the!curriculum!to!be!taught!during!this!additional!instructional!time!and!how!
much!of!this!time!would!be!dedicated!to!each!subject.!
[Figure!1!about!here]!
One!important!aspect!of!this!legislation!is!that!it!gave!freedom!to!schools!and!
school!districts!(municipalities)!to!decide!when!to!implement!the!new!compulsory!
education!period.!As!a!result,!in!2007,!the!first!year!of!the!implementation,!there!
were!schools!that!had!six*year*old!students!enrolled!in!first!grade!classrooms,!and!
schools!that!had!not!implemented!the!new!compulsory!period!yet!and!had!only!
seven*year*old!students!enrolled!in!first!grade!classrooms.!The!group!of!schools!
that!implemented!the!extra!year!of!compulsory!education!in!2007!includes!15.4!
thousand!schools!or!62%!of!the!total.!The!group!of!schools!that!implemented!the!
change!in!the!following!years!includes!9.2!thousand!schools!or!38%!of!the!total!
(Ministério*da*Educação*do*Brazil,*Secretaria*de*Educação*Básica,*2007).!!
In!2005,!almost!concurrently!with!the!law!that!increased!compulsory!
education,!Brazil!implemented!its!first!comprehensive!national!assessment!system.!
Before!2005,!the!national!assessment!of!compulsory!education!(called!Prova'Brasil',
Brazilian!National!Assessment!System!of!Basic!Education)!only!assessed!
randomized!samples!of!students!enrolled!in!the!Brazilian!educational!system.!From!
that!year!on,!the!comprehensive!assessment!was!administered!recurrently!every!
other!year,!targeting!students!in!every!primary!and!middle!public!school,!and!
!
4!
assessing!math!and!Portuguese!language!subjects.!In!2011,!it!was!the!first!time!that!
cohorts!that!started!basic!school!at!the!age!of!six!were!assessed!by!Prova'Brasil!
when!they!finished!fifth!grade,!the!last!grade!of!Brazilian!primary!school.!In!this!
year,!for!the!reasons!described!above,!Prova'Brasil!also!assessed!cohorts!of!students!
that!were!exposed!to!only!four!years!of!primary!education!starting!from!the!age!of!
seven.!
3..The.effects.of.additional.instructional.time.
In!this!critical!literature!review!I!analyze!five!different!groups!of!studies.!
First,!I!present!Human!Capital!theory!and!Lifecycle!of!Human!Skill!Formation!theory!
as!rationales!for!the!creation!of!the!law!that!increased!compulsory!education!in!
Brazil,!adding!a!year!to!the!beginning!of!the!primary!school.!These!theories!also!
allow!me!to!hypothesize!that!the!effects!of!the!extra!year!are!positive!and!the!
benefits!are!greater!for!disadvantaged!students.!Then,!I!explore!three!groups!of!
previous!studies!that!examined!the!effects!of!different!amounts!of!instructional!
time,!but!through!different!perspectives:!(a)!instructional!time!and!achievement!
through!the!lens!of!natural!experiments!of!the!effects!of!extra!time!of!schooling,!(b)!
increasing!instructional!time!by!policy,!and,!finally!(c)!the!effects!of!starting!school!
early.!!
!
3.1$Human$Capital$Theory$
Human!Capital!theory!has!important!implications!for!this!study!in!two!major!
ways.!First,!it!serves!as!a!possible!implicit!motivation!as!to!why!the!Brazilian!
!
5!
government!increased!its!compulsory!education.!Additionally,!since!this!stream!of!
research!generally!finds!positive!effects!of!quantitative!measures!of!education!on!
different!kinds!of!student!outcomes,!Human!Capital!theory!also!serves!as!a!
foundation!for!the!hypothesis!that!there!is!also!a!positive!and!statistically!significant!
relationship!between!the!increase!in!the!Brazilian!compulsory!schooling!and!
student!achievement!at!the!end!of!the!primary!school!level.!
Literature!in!Human!Capital!theory!often!finds!significant!positive!
association!between!quantitative!measures!of!schooling!and!national!economic!
growth!(Barro!&!Lee,!2001;!Doppelhofer,!Miller,!&!Sala*i*Martin,!2000;!Sianesi!&!
Reenen,!2003;!J.!R.!W.!Temple,!2001).!The!explanation!for!this!dynamic!is!education!
can!increase!the!human!capital!stock!of!a!country,!which!increases!the!country’s!
labor!force!productivity,!which!in!turn!leads!to!economic!growth!(Mankiw,!Romer,!&!
Weil,!1992).!The!majority!of!the!literature!investigating!the!effects!of!education!on!
economic!growth!employs!measures!of!quantity!of!schooling.!The!most!common!
proxy!used!in!these!studies!is!the!average!years!of!schooling!(Wößmann,!2003).!
Overall,!these!studies!find!a!one*year!increase!in!average!education!raises!the!
output!per!capita!between!three!and!seven!percent!per!year,!depending!on!the!level!
of!development!of!the!country!and!the!methods!used!in!the!research!(Sianesi!&!
Reenen,!2003).!In!particular,!primary!schooling!has!been!associated!with!higher!
rates!of!return!than!any!other!school!level!(Behrman,!Ross,!&!Sabot,!2008;!
Colclough,!1982;!Psacharopoulos,!2004).!!
Research!have!also!sought!to!answer!the!question!of!how!one!extra!year!of!
schooling!can!influence!variables!like!health!outcomes,!future!earnings,!and!other!
!
6!
variables.!For!example,!Oreopoulos!(2006),!looking!at!data!from!Canada,!the!UK!and!
the!US,!finds!that!one!extra!year!of!compulsory!schooling!is!related!to!15%!more!
lifetime!wealth,!as!well!as!smaller!probabilities!of!poor!health,!unemployment,!and!
unhappiness!for!students!who!remain!longer!in!school.!!
!
3.2$Lifecycle$of$Human$Skill$Formation$theory$
The!Lifecycle!of!Human!Skill!Formation!theory!argues!that!there!is!a!window!
of!opportunity!in!the!early!childhood!period!when!skills!and!knowledge!then!
acquired!can!leverage!future!acquisition!of!the!same!attributes.!Having!a!strong!
foundation!of!skills!and!knowledge!built!at!that!particular!stage!of!development!can!
put!a!child!on!track!for!a!higher!learning!path!for!life.!If!this!foundation!is!not!
constructed!by!a!certain!age,!the!window!is!closed!and!the!child!will!not!have!the!
opportunity!to!benefit!from!this!virtuous!circle!of!learning.!As!a!result,!the!earlier!
the!investment!in!education,!the!higher!the!rates!of!return!(Carneiro!&!Heckman,!
2003;!Cunha!et!al.,!2006;!Heckman!&!Masterov,!2007).!This!stream!of!research!also!
found!evidence!that!disadvantaged!children!have!greater!benefits!from!earlier!
intervention!than!their!advantaged!counterparts!(Heckman,!2006).!!
Brazil!has!opted!to!add!a!year!of!instructional!time!at!the!beginning!of!
primary!schooling,!making!compulsory!school!begin!at!the!age!of!six.!In!contrast,!in!
the!past,!other!educational!systems!such!as!those!found!in!the!UK's!and!some!US!
states'!opted!to!improve!compulsory!education!by!increasing!the!minimum!age!
students!are!allowed!to!leave!school!(Oreopoulos,!2006).!The!Lifecycle!of!Human!
!
7!
Skill!Formation!theory!also!fulfills!two!purposes!for!this!study.!First,!it!serves!as!a!
possible!explanation!for!why!the!Brazilian!government!decided!to!add!this!extra!
instructional!time!at!the!beginning!instead!of!at!the!end!of!the!compulsory!
education.!Second,!this!theory!allows!me!to!hypothesize!that!the!benefits!of!this!
extra!year!of!schooling!will!be!greater!for!disadvantaged!Brazilian!students!than!for!
their!higher!socioeconomic!status!counterparts.!! !
!
3.3.$Instructional$time$and$achievement$through$the$lens$of$natural$experiments$
Random!assignment,!the!gold!standard!of!evaluation!methods,!for!ethical!or!
operational!reasons1!cannot!often!be!used!to!assess!educational!inputs.!In!the!
absence!of!random!assignment,!natural!experiment!research!designs!are!powerful!
alternatives!to!estimate!causal!effects!of!these!inputs.!For!example,!Marcotte!&!
Hemelt!(2008)!investigated!the!difference!in!math!and!reading!test!scores!between!
Maryland!students!that!attend!different!numbers!of!school!days!due!to!unscheduled!
closures!related!to!snowstorms.!The!authors!found!that!in!third!grade!student,!five!
unscheduled!closures!drives!math!and!reading!test!scores!down!three!percent!lower!
than!the!scores!of!students!that!attend!school!uninterrupted.!!
In!a!similar!study,!Agüero!&!Beleche!(2013)!examined!the!differences!in!
academic!achievement!resulting!from!exogenous!variation!from!across!states!and!
overtime!from!the!day!the!school!year!started!to!the!day!when!the!test!was!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1!Denying!control!group!children!access!to!an!educational!service!in!order!to!have!
better!conditions!for!academic!research!can!be!consider!unethical.!Additionally,!for!
some!certain!types!of!educational!interventions,!random!assignment!is!not!feasible!
as!a!result!of!the!environment!conditions!or!nature!of!the!intervention.!!
!
8!
administered!in!Mexico.!The!authors!found!positive!but!diminishing!marginal!effects!
on!academic!achievement!for!students!that!attended!more!days.!Interestingly!for!the!
present!study,!the!authors!also!found!that!students!attending!schools!in!better*off!
areas!had!greater!benefits!from!the!extra!school!days!when!compared!to!students!in!
worse*off!areas.!!
Using!a!regression!discontinuity!approach!and!taking!advantage!of!a!strict!
adherence!criterion!to!a!cutoff!date!to!allow!students!to!start!compulsory!schooling,!
Luyten!et!al.(2008)!estimated!the!effect!of!an!extra!year!of!schooling!on!the!reading!
performance!of!15!year*old!students!from!the!UK!on!PISA.!The!results!of!this!study!
show!that!the!effect!of!an!extra!year!of!schooling!on!reading!achievement!is!.12!
standard!deviations!after!controlling!for!age.!In!this!case,!disadvantaged!students!
benefited!more!from!the!extra!year!of!schooling!(.15)!than!their!advantaged!
counterparts!(.044).!Also!taking!advantage!of!cutoff!dates,!Luyten!&!Veldkamp!
(2011)!found!that!the!cross!national!effect!size!on!student!achievement!of!an!extra!
year!of!education!is!.46!for!math!and!.35!for!science.!This!study!used!TIMMS*95!
data,!which!relate!student!achievement!to!both!mathematics!and!science!in!15!
different!countries.!!
The!problem!with!the!regression!discontinuity!strategy!used!to!measure!the!
effect!of!the!extra!year!of!schooling!is!that!it!does!not!take!into!account!the!peer!and!
relative!age!effects.!It!turns!out!that!the!students!that!had!access!to!an!extra!year!of!
schooling!in!the!UK!also!were!the!younger!students!in!their!cohort,!whereas!the!
students!that!had!access!to!fewer!years!were!also!the!older!students!in!their!
cohorts.!As!a!result,!peer!and!relative!age!effects!might!be!confounding!the!
!
9!
estimations!found!in!this!study.!Given!these!shortcomings,!my!study!is!able!to!better!
estimate!the!effects!of!the!extra!year!of!education!because!it!compares!whole!
cohorts!of!students!that!experienced!average!age!distribution!set*ups.!!
!
3.4.$Increasing$instructional$time$by$policy$
!
Instructional!time!is!an!educational!input!just!like!class!size!or!textbooks.!
When!faced!with!the!dilemma!of!where!to!invest!to!increase!educational!outputs,!
countries!or!school!districts!can!opt!to!increase!instructional!time!among!all!sorts!of!
options!(Krashinsky,!2006).!Research!in!this!arena!examined!policies!that!changed!
the!amount!of!hours,!days!and!years!of!instructional!time!offered!to!students.!For!
example,!Cooper!et!al.'s!(2000)!review!of!the!literature!of!summer!school!programs!
in!the!United!States!found!clear!evidence!that!these!programs!have!positive!effects!
on!student!achievement.!Using!methods!unique!to!meta*analysis,!they!concluded!
that!students!who!complete!summer!programs!is!expected!to!score!about!one!fifth!
of!a!standard!deviation!higher!than!students!who!did!not!attend!summer!schools!on!
outcome!measures.!The!authors!also!concluded!that!summer!school!programs!have!
more!positive!effects!on!the!achievement!of!middle*class!children!(effect!sizes!
ranging!from!.44!and!.56!standard!deviation)!than!on!their!disadvantage!
counterparts!(ranging!from!.20!to!.24!standard!deviation).!!
!
In!1996,!the!Chilean!government!implemented!a!policy!that!increased!the!
school!day!by!two!hours.!Similar!to!the!Brazilian!policy!that!added!an!extra!year!in!
compulsory!education,!the!Chilean!implementation!of!the!full!school!day!did!not!
!
10!
affect!all!schools!at!the!same!time.!As!a!result,!Bellei!(2009)!used!this!exogenous!
variation!from!the!perspective!of!the!students!to!evaluate!the!impact!of!the!Chilean!
longer!day!program.!Using!a!difference*in*differences!approach,!the!author!found!
that!the!program!had!positive!effect!on!student’s!academic!achievement,!ranging!
from!.05!to!.07!standard!deviations!for!language!and!from!0.00!to!0.12!for!
mathematics.!Another!main!finding!of!this!study!is!that!students!situated!in!the!
upper!part!of!the!achievement!distribution!as!well!as!rural!public!school!students!
benefitted!most!from!the!longer!school!day.!The!study!also!included!SES!covariates,!
but!found!no!evidence!of!heterogeneous!program!effects!in!this!measure.!!
!
Curiously,!policies!have!also!gone!in!the!opposite!direction!regarding!
instructional!time.!In!1999,!the!province!of!Ontario,!Canada,!eliminated!the!fifth!year!
of!education!from!its!high!school!level.!This!policy!change!created!two!cohorts!of!
students!who!finished!high!school!together,!but!with!different!intakes!of!high!school!
education.!Using!several!different!econometric!approaches,!Krashinsky!(2006),!
examined!university!level!academic!achievement!of!these!two!cohorts!and!
concluded!that!students!with!one!year!less!of!high!school!performed!worse!than!
their!counterparts!in!all!subjects!examined!by!the!study!(effect!sizes!ranging!from!
.53!to!1.24!standard!deviations).!!
The!Canadian!study!is!closely!related!to!the!present!study!because!it!
investigated!the!same!amount!of!instructional!time!changed!by!a!policy:!one!year.!
However,!some!shortcomings!related!to!the!conditions!of!the!Canadian!study!create!
some!threats!for!its!external!validity!and!comparability.!First,!as!the!study!only!
examined!the!performance!of!students!that!enter!university!after!finishing!high!
!
11!
school,!its!estimates!do!not!extrapolate!for!the!portion!of!students!that!do!not!enroll!
in!university!after!completing!the!high!school!level.!Another!problem!arises!from!
the!fact!that!the!students!that!completed!the!five*year!high!school!in!Canada!are!also!
one!year!older!than!students!that!completed!the!four*year!high!school!students.!
Since!academic!achievement!is!often!related!to!age!(Smith,!2009),!the!estimates!in!
this!Canadian!study!might!be!partially!measuring!an!age!effect!as!well.!An!
alternative!explanation!that!arises!from!the!older!cohort!is!that!older!students!might!
choose!to!enroll!in!classes!that!are!more!suitable!for!their!tastes!and!abilities.!If!this!
is!the!case,!the!better!performance!the!older!students!presented!is!a!result!of!
maturity!and!not!of!the!extra!year!of!high!school.!In!this!case,!the!model!of!this!study!
might!be!overestimating!the!effect!size!of!the!additional!year!of!schooling.!!
Fortunately,!in!the!case!of!the!Brazilian!reform!investigated!by!this!study,!
since!both!groups!of!children!affected!and!not!affected!by!the!reform!have!similar!
age!distributions,!and!because!all!children!in!these!two!groups!take!the!same!
standardized!test,!the!estimates!produced!in!this!study!do!not!have!the!same!biases!
than!the!Canadian!study.!!
!
3.5.$The$effects$of$starting$school$early$
Also!significant!for!the!present!work!is!a!series!of!studies!addressing!the!
question!of!whether!students!benefit!from!starting!school!earlier.!Using!US!data!and!
relying!on!a!regression!discontinuity!approach,!Mayer!&!Knutson!(1997)!looked!at!
differences!in!math!and!reading!achievement!of!children!who!were!in!the!same!
!
12!
grades!but!started!school!roughly!one!year!apart!from!each!other.!The!authors!find!
that!children!who!started!school!earlier!had!higher!achievement.!Starting!school!a!
year!younger!results!in!a!reading!score!increase!of!0.403!of!a!standard!deviation!and!
a!math!score!increase!of!0.261!of!a!standard!deviation.!
Leuven,!et!al.!(2004)!study!the!effects!of!being!exposed!to!primary!school!at!
an!earlier!age!in!the!Netherlands.!Dutch!parents!have!the!option!of!enrolling!their!
children!in!regular!school!between!the!first!day!after!their!fourth!birthday!and!the!
day!before!they!turn!five,!at!which!point!children!must!be!enrolled!in!school.!The!
results!of!this!study!show!that!enrolling!children!one!month!early!increases!test!
scores!on!average!by!0.6!standard!deviation.!!
!
Contrary!to!the!abovementioned!studies,!a!group!of!authors!reached!the!
opposite!conclusion:!children!that!start!school!at!an!older!age!reach!higher!
achievement.!Analyzing!a!1999!Early!Childhood!Longitudinal!Study!completed!in!
the!US,!Datar!(2006)!finds!that!entering!kindergarten!a!year!older!increases!test!
scores!for!the!first!two!years!of!regular!school.!He!also!finds!that!this!benefit!is!
greater!for!at*risk!children.!Analysis!of!Swedish!(Fredriksson!&!Ockert,!2005)!and!
German!(Puhani!&!Weber,!2005)!datasets!shows!that!entering!school!at!an!older!age!
increases!pupil!test!scores!and!longterm!school!attainment.!Fredriksson!&!Ockert!
(2005)!find!that!starting!school!one!year!later!increases!school!performance!by!0.2!
standard!deviation,!whereas!Puhani!&!Weber!(2005)!find!that!entering!school!at!7!
instead!of!6!years!old!increases!test!scores!at!the!end!of!primary!school!by!0.42!
standard!deviation.!!
!
13!
It!is!important!to!notice!that!the!amount!of!schooling!that!both!the!treatment!
and!the!control!groups!in!these!studies!were!exposed!were!held!constant,!and!the!
variable!of!interest!for!these!researcher!was!the!age!that!children!started!school.!
However,!students!in!these!studies!were!tested!when!they!had!different!ages!as!
well.!As!a!result,!the!research!design!used!in!these!studies!is!not!able!to!disentangle!
the!joint!effect!of!entry!age,!test!age!and!relative!age.!Consequently,!they!fail!to!
explain!whether!the!students!that!start!school!older!perform!better!because!they!
enter!school!later!or!because!they!are!in!a!favorable!position!compared!to!their!
younger!peers.!!
4..Research.design.
!
The!2006!reform!gave!schools!and!school!districts!(municipalities)!in!Brazil!
the!prerogative!to!decide!when!to!implement!the!new!compulsory!education!period.!
As!a!result,!in!2007!there!were!two!categories!of!schools:!schools!that!had!six*year*
old!students!enrolled!in!first!grade!classrooms,!and!schools!that!had!not!
implemented!the!new!compulsory!period!yet,!which!only!had!seven*year*old!
students!enrolled!in!the!old*system!first!grade!classrooms.!Consequently,!the!2011’s!
Prova'Brasil!edition!assessed!two!groups!of!students:!those!who!had!access!to!five!
years!of!basic!education!starting!at!the!age!of!six,!namely!the!“treatment”!group,!and!
students!who!had!access!to!only!four!years!of!basic!education!starting!at!the!age!of!
seven,!namely!the!“control”!group.!!
!
14!
Brazil!has!5,565!municipalities!and!each!used!its!own!criteria!to!decide!when!
each!school!would!implement!the!new!five*year!primary!education!policy!since!the!
federal!law!did!not!dictate!any!criteria.!However,!independent!of!the!existence!of!an!
improbable!coincident!criterion!for!the!implementation!of!the!law,!from!the!
students’!perspective,!the!timing!of!program!implementation!was!completely!
arbitrary,!which!rules!out!selection!bias!on!the!individual!level!(Bellei,!2009).!
Therefore,!I!anticipate!that!any!historical!trend!that!differentiates!pre*!and!post*
implementation!cohorts!will!impact!students!in!treatment!and!control!schools!in!a!
similar!way.!As!a!result,!this!set!of!conditions!allows!me!to!obtain!unbiased!
estimates!of!the!causal!effect!of!the!additional!year!of!instruction!on!students’!
academic!achievement.!
In!this!study,!I!report!an!impact!evaluation!of!the!addition!of!one!year!of!
instructional!time!in!the!Brazilian!compulsory!education.!Empirically,!I!used!a!
difference*in*differences!strategy!(Meyer,!1995)!to!investigate!whether!schools!that!
offered!five!years!of!primary!education!had!higher!academic!achievement!than!
comparable!schools!that!offered!only!four!years!of!primary!school.!Additionally,!I!
took!advantage!of!the!long!series!of!data!available!(Prova'Brazil!from!2007!to!2011)!
and!carried!out!additional!difference*in*differences!analyses!exclusively!using!data!
points!before!the!implementation!of!the!Brazilian!reform!to!investigate!the!
existence!of!previous!trends!that!could!be!possibly!in!place!before!this!
implementation.!Cook,!Shadish,!&!Wong!(2008)!compared!randomized!and!non*!
randomized!studies,!most!of!which!were!carried!out!in!educational!settings,!and!
!
15!
found!that!difference*in*differences!studies!with!long!series!of!pre*data!exhibited!
similar!results!to!experimental!studies.!!
!
4.1.$Data$
I!combine!two!datasets!to!evaluate!the!impact!of!the!addition!of!the!extra!
year!of!compulsory!education!on!student!achievement!in!Brazil.!The!first!is!the!
Prova'Brasil'from!2007!to!2011.!Since!2007,!every!two!years,!all!students!enrolled!in!
grades!five!and!nine!in!every!Brazilian!public!school!are!subjected!to!the!Prova'
Brasil!assessment.!This!assessment!includes!questionnaires!directed!at!schools,!
principals,!teachers!and!students,!as!well!as!an!exam!which!tests!student!proficiency!
in!math!and!the!Portuguese!language.!The!results!of!this!exam!are!considered!the!
official!measure!of!quality!of!the!educational!system!by!the!Brazilian!government.!
The!2011!Prova'Brasil!includes!the!student!achievement!variables!of!the!treatment!
and!control!groups!as!well!as!the!covariates!described!later!in!this!section.!This!
study!also!uses!the!student!achievement!variable!from!the!2007’s!and!2009’s!Prova'
Brasil!editions!to!tackle!potential!selection!bias!that!might!emerge!when!studies!use!
only!one!period!of!observation.!!
The!second!dataset!is!the!Brazilian!School!Census!2007,!the!country’s!official!
school!census!which!is!administered!every!year!by!the!Brazilian!Ministry!of!
Education.!This!dataset!contains!data!about!all!students,!teachers,!and!schools!from!
kindergarten!through!high!school,!and!has!more!than!40!million!observations!at!the!
student!level.!The!Brazilian!School!Census!of!2007!dataset!includes!a!variable!that!
!
16!
allowed!me!to!identify!which!schools!had!already!implemented!the!nine*year!
compulsory!education!period!five!years!prior!to!the!abovementioned!Prova!Brasil!
2011!assessment.!!
The!combination!of!these!two!datasets!generates!24,599!observations!of!
schools!that!met!three!criteria.!First,!these!observations!are!from!schools!in!which!
more!than!20%!of!the!students!took!the!Prova'Brasil!test!in!2011;!so!the!dataset!
contains!the!average!test!score!per!school!for!this!year.!Second,!these!observations!
contain!information!on!whether!these!schools!implemented!the!fifth!year!of!primary!
education!in!2007!or!after!2007.!Third,!these!observations!contain!measures!of!
previous!academic!achievement!for!2009!and!2007!for!these!schools.!
!
4.2.$Measures$
Here,!I!define!the!basic!variables!involved!in!the!difference*in*differences!
estimates!including!the!covariates!added!to!the!models.!All!analyses!in!this!study!
use!school!level!variables.!
Outcome!variables:!(a)!mathematics!Prova'Brasil!score,!and!(b)!Portuguese!
language!Prova'Brasil!score.!!
Question!predictor:!the!question!predictor!is!TREATED,!a!dummy!variable!
that!indicates!whether!the!student!attended!a!five*year!primary!school!after!the!
change!in!the!legislation!that!increased!the!Brazilian!compulsory!education!(for!five*
year!primary!school!POST*legislation,!TREATED=1;!otherwise!=!0).!The!variable!
!
17!
TREATED!is!an!interaction!variable!created!by!the!multiplication!of!two!variables!
described!below:!FIVE*YEAR!and!POST.!!
Control!predictors:!the!main!control!predictors!are:!(a)!FIVE*YEAR,!a!dummy!
variable!indicating!whether!the!student!attended!a!five*year!primary!school!(FIVE*
YEAR=1)!or!a!control!school!(FIVE*YEAR=0),!and!(b)!POST,!a!dummy!variable!
indicating!whether!the!student!attended!school!after!the!change!in!the!legislation!
(POST!=!1),!or!before!the!implementation!of!the!legislation!(POST=0).!Finally,!I!also!
included!several!individual!level!student!and!student!family!covariates.!
In!the!student!individual!level!covariates!group!I!included!two!variables:!(a)!
Student!age.!Since!the!dataset!I!use!do!not!hold!a!repetition!rate!variable,!I!use!the!
student!average!age!to!identify!students!that!are!behind!their!cohort!and!to!control!
for!this!effect!on!average!achievement.!(b)!Access!to!Preprimary!schooling.!This!
study!looks!at!the!effects!of!an!extra!year!of!education!on!achievement.!Importantly,!
intellectual!and!academic!achievement!have!been!found!to!be!related!to!early!
childhood!educational!interventions!(Campbell!&!Ramey,!1994,!1995).!Thus,!it!is!
critical!to!control!for!school!average!access!to!this!lower!level!of!education!as!well.!!
In!the!student!family!level!covariates!group!I!included!two!additional!
variables:!(a)!Student’s!maternal!education:!Since!the!number!of!years!of!schooling!
completed!by!mothers!are!found!to!be!positively!related!to!the!cognitive!skills!of!
their!children!(Leibowitz,!1977;!Murnane,!1981),!it!is!crucial!to!control!for!the!
influence!of!the!mothers’!education.!(b)!Socioeconomic!status!(SES):!This!variable!is!
an!index!composed!by!items!at!home!and!parents’!education.!This!index!with!the!
!
18!
weight!that!it!gives!to!each!item!is!considered!the!official!socioeconomic!
classification!in!Brazil!(Colom!&!Flores*Mendoza,!2007).!!!
!
4.3.$Data$analysis$
In!order!to!estimate!the!effect!the!extra!year!of!primary!education!had!on!
students’!achievement!I!used!a!difference*in*differences!strategy.!This!difference*in*
differences!estimator!computes!the!difference!between!the!2011!average!test!score!
of!schools!that!implemented!the!fifth!year!in!2007!and!the!2011!average!test!score!
of!schools!who!implemented!it!later.!At!the!same!time,!this!estimator!deducts!from!
the!first!difference!mentioned!above!the'difference!between!the!average!test!scores!
of!the!same!two!groups!of!schools!in!2009!and!2007,!before!the!implementation!of!
the!law!in!any!school.!This!approach!allows!me!to!isolate!any!contextual!trend!that!
disproportionately!affected!members!of!the!two!cohorts.!I!represent!this!difference*
in*differences!strategy!in!the!following!regression!model:!
!
TestScore!j!=!β0!+!β1'FIVE*YEAR'j!+!β2'POST'j!+β3'FIVE*YEAR'j!∗POST'j!+ε'j'(I)!
where!TestScore'j!is!the!average!mathematics!or!Portuguese!language!Prova'Brasil!
score!of!school!j;!β1'captures!the!net!difference!between!treatment!and!control!
schools!in!2011;!β2!captures!the!net!difference!between!treatment!schools!tested!in!
2011!(post!treatment)!and!2009!(pre!treatment);!β3!FIVE*YEAR*POST!(TREATED)!
is!an!interaction!term!representing!the!difference*in*differences!estimate!of!the!
impact!of!the!extra!year!of!compulsory!education!in!Brazil;!and!ε'j!is!the!school*level!
!
19!
error!term.!In!(I),!if!β3'is!positive!and!statistically!significant,!it!is!possible!to!
conclude!that!the!increase!in!the!Brazilian!compulsory!education!has!increased!the!
academic!achievement!of!students!enrolled!in!schools!that!offered!the!additional!
year!of!instruction.!!
In!order!to!account!for!possible!bias!introduced!by!a!treatment!condition!
where!treatment!and!control!groups!were!not!randomly!assigned,!I!also!estimated!
the!following!regression!equations:!
TestScore!j!=!β0!+!β1'FIVE*YEAR'j!+!β2'POST'j!!
+β3'FIVE*YEAR'j!∗POST'j!+β4'X'j!+ε'j'(II)!
TestScore!j!=!β0!+!β1'FIVE*YEAR'j!+!β2'POST'j!!
+β3'FIVE*YEAR'j!∗POST'j!+β4'X'j!+β5'Y'j!+ε'j'(III)!
TestScore!j!=!β0!+!β1'FIVE*YEAR'j!+!β2'POST'j!!
+β3'FIVE*YEAR'j!∗POST'j!+β4'X'j!+β5'Y'j!+!µ'j!+ε'j'(IV)!
where!X'j!is!a!vector!of!student!individual!level!covariates,!Yj'is!a!vector!of!student!
family!covariates,!and!µ'j!is!a!state!fixed!effect.!If!the!FIVE*YEAR!variable!of!primary!
school*effect!estimate!is!not!impacted!by!the!introduction!of!these!covariates,!I!will!
conclude!that!the!non*random!assignment!did!not!affect!the!original!estimate.!
!
Finally,!in!order!to!investigate!whether!some!students!benefited!more!from!
the!program,!I!also!explored!the!presence!of!heterogeneous!treatment!effects!by!
introducing!interaction!terms!between!treatment!and!student!average!
socioeconomic!characteristics.!!
!
20!
5..Findings.
5.1.$DifferenceGinGdifference$estimates$of$fiveGyear$primary$school$effect$
!
!
Table!1!shows!the!average!Prova'Brasil*test!scores!for!mathematics!and!
language!for!treatment!(five*year!primary!school)!and!control!under!both!PRE!and!
POST!conditions.!As!shown,!on!average,!treatment!schools!score!higher!than!control!
schools!in!both!math!and!language.!However,!as!known,!for!a!difference*in*
difference!estimate,!the!absolute!difference!between!treatment!and!control!groups!
is!less!relevant!than!the!difference!in!change!between!pre!and!post!conditions!
within!the!treatment!and!control!groups!after!controlling!for!covariates.!
Subsequently,!Table!2!presents!the!results!of!regression!models!fitted!using!the!
equations!I!to!IV!described!in!section!5.!The!coefficients!in!model!1!present!the!
effect!of!the!reform,!unadjusted!for!the!impact!of!covariates.!In!this!model!the!effect!
of!the!five*year!school!reform!is!6.23!additional!points!in!math!test!scores!and!5.33!
additional!points!in!language!test!scores!(p>0.001).!Also!in!Table!2,!Model!2!
includes!student!individual!covariates,!Model!3!builds!on!Model!2!with!family!
covariates,!and!Model!4!adds!a!state!fixed!effect!to!the!variables!in!Model!3.!The!R2!
substantially!increases!from!Model!1!to!Model!4,!rising!from!0.02!to!0.56!and!0.05!to!
0.59!for!math!and!language,!respectively.!In!other!words,!the!variables!added!from!
Model!1!to!Model!4!increased!the!portion!of!variance!in!test!scores!that!can!be!
explained!by!the!regression!equation!fitted,!making!Model!4!a!better!predictor!of!the!
outcome!variables.!Model!4!shows!the!magnitude!of!the!reform!effect!on!both!math!
and!language!remains!practically!unaffected!and!statistically!significant!(p>0.001),!
!
21!
after!controlling!for!all!the!aforementioned!covariates.!The!coefficient!of!6.24!for!
math!represents!an!effect*size!of!.2581!standard!deviations!and!the!coefficient!of!
5.34!for!Portuguese!language!represents!an!effect!size!of!.2558!standard!deviations.!
These!results!confirm!the!hypotheses!presented!at!the!beginning!of!this!paper,!
namely!that!the!additional!year!of!primary!school!in!Brazil!positively!affected!the!
academic!achievements!of!the!students!that!were!exposed!to!an!extra!year!of!
schooling.!
[Table!1!and!2!about!here]!
5.2.$Was$there$a$treatmentGeffect$before$the$treatment?$
!
In!order!to!determine!whether!a!treatment*effect!was!present!before!the!
introduction!of!the!treatment!I!conducted!a!test!proposed!by!Winship!&!Morgan!!
(1999).!In!this!test,!the!regression!equations!I!and!IV!were!fitted!using!only!PRE*
treatment!observations!in!both!treatment!and!control!groups.!In!other!words,!the!
regressions!were!run!using!only!the!2009!test!scores,!when!no!school!had!offered!
five!years!of!primary!schooling,!and!comparing!the!exact!same!school!in!treatment!
and!control!group!of!2011,!when!the!treatment!group!had!schools!with!students!
that!had!just!finished!five!years!of!primary!schooling.!As!shown!in!the!first!row!of!
Table!3,!schools!in!the!treatment!group!scored!higher!than!the!control!group!on!
both!math!and!language!outcomes!(p>0.001).!However,!both!coefficients!become!
statistically!insignificant!after!the!inclusion!of!covariates!(equation!IV).!Since!no!
treatment!was!applied!in!the!two!groups,!the!absence!of!a!statistically!significant!
!
22!
difference!between!these!groups!suggests!that!there!is!no!unobserved!factor!
confounding!the!outcome!of!the!difference*in*differences!estimates.!
[Table!3!about!here]!
5.3.$Was$there$a$trend$before$treatment$that$could$explain$the$FiveGyear$primary$
school$effect?$
!
The!difference*in*differences!coefficients!shown!in!Table!2!indicates!that!
treatment!schools!present!higher!average!test!scores!than!control!group!schools!
even!after!discounting!the!past!difference!between!the!two!groups.!In!other!words,!
the!schools!that!implemented!the!five*year!primary!school!were!able!to!improve!
their!student!test!scores!more!than!the!schools!that!did!not!implement!it.!In!section!
6.2.,!coefficients!indicate!that!in!2009,!when!no!treatment!was!applied,!test!scores!in!
treatment!schools!were!no!different!than!those!in!control!schools.!However,!there!is!
still!the!question!of!whether!treatment!schools!were!coming!from!a!steeper!
trajectory!of!improvement!than!control!group.!Treatment!schools!could!have!
achieved!greater!test!scores!in!2011!because!of!a!preexisting!trend!that!started!
before!2009!and!that!had!no!relationship!with!the!treatment!per!se.!In!order!to!
examine!this!possibility,!I!included!in!the!analyses!2007!math!and!language!test!
scores!from!treatment!and!control!schools.!Table!4!shows!the!absolute!average!test!
scores!for!2007,!2009,!and!2011.!Using!these!test!scores!and!applying!equation!IV,!I!
obtained!two!additional!difference*in*differences!estimates.!In!the!second!row!of!
Table!5,!I!show!the!estimates!for!2011!and!2007.!The!coefficients!are!still!significant!
even!considering!this!longer!period!(p>0.001).!As!shown!in!the!third!row!of!Table!4,!
!
23!
the!estimates!for!the!period!of!2009!to!2007!are!not!statistically!significant.!These!
two!additional!analyses!demonstrate!that!there!were!no!previous!trends!that!could!
be!confounded!with!the!five*year!primary!school!effect.!
[Tables!4!and!5!about!here]!
5.4.$Was$the$FiveGyear$primary$school$effect$equally$distributed$among$different$levels$
of$SES?$$
!
Figure!2!presents!the!effect*sizes!in!standard!deviation!units!of!the!extra!year!
of!primary!schooling!per!quintile!of!SES.!Contrary!to!the!hypotheses!proposed!at!the!
beginning!of!this!paper,!students!with!higher!socioeconomic!status!benefitted!more!
from!the!extra!year!of!education!than!students!from!the!less!advantaged!positions,!
after!controlling!for!student’s!individual!and!family!characteristics!as!well!as!state!
differences!(equation!IV).!Treatment!schools!with!students!positioned!in!the!lower!
quintile!of!the!SES!scale!scored!.22!and!.23!standard!deviations!for!mathematics!and!
language,!respectively.!Treatment!schools!with!students!positioned!in!the!upper!
quintile!of!the!SES!scale!benefited!from!effect!sizes!almost!twice!as!large!as!those!
from!their!less!advantaged!counterparts:!.38!standard!deviations!for!both!math!and!
language.!
[Figure!2!about!here]!
6..Discussion.
The!natural!experiment!created!by!the!policy!that!added!an!extra!
instructional!year!in!Brazilian!primary!education!along!with!the!strategies!used!to!
both!measure!the!size!effect!of!this!policy!and!eliminate!possible!biases!allows!me!to!
!
24!
make!causal!inference!while!interpreting!the!findings.!Few!studies!on!input!based!
educational!reforms!benefit!from!such!fortunate!conditions!and!can!claim!causality!
between!the!inputs!and!output!analyzed.!!
Applying!a!difference*in*differences!strategy!and!using!Prova'Brasil’s!2011!
and!2009!data,!I!found!that!the!effect!sizes!of!one!extra!year!of!compulsory!
schooling!in!Brazil!on!student!achievement!are!.26!standard!deviations!for!both!
math!and!Portuguese!language.!I!also!carried!out!two!additional!analyses!that!
reinforce!the!strength!of!these!effect!sizes:!(a)!by!running!a!ordinary!linear!square!
regression!with!the!same!covariates!and!using!the!Prova'Brasil’s!2009!data,!I!found!
that!there!was!no!“treatment!effect”!before!the!implementation!of!the!treatment,!
and!(b)!by!running!a!difference*in*differences!analysis!and!using!Prova'Brasil’s!2007!
and!2009!data,!I!found!that!there!was!no!previous!trend!in!the!test!score!trajectory!
of!both!treatment!and!control!groups!that!could!explain!the!effect!size!found!in!this!
paper!for!the!extra!year!of!compulsory!education!in!Brazil.!Moreover,!I!found!that!
students!positioned!on!both!extremes!of!the!socioeconomic!distribution!benefited!
from!the!extra!year!of!compulsory!education.!However,!the!effect!sizes!of!this!extra!
year!for!high!SES!students!are!almost!twice!as!large!as!the!effect!sizes!for!low!SES!
students.!!
It!is!important!to!mention,!that!even!with!the!fortunate!condition!of!natural!
experiment!and!the!strong!research!design,!one!should!be!cautious!to!extrapolate!
the!findings!to!different!conditions.!As!children’s!brains!go!through!great!
development!during!the!school!career,!the!effect!size!found!for!an!extra!year!of!
schooling!at!the!age!of!six!might!be!different!from!an!extra!year!at!the!age!of!five!or!
!
25!
any!other!age!within!the!school!year.!As!a!result,!this!effect!size!cannot!be!taken!for!
granted!in!a!context!different!from!the!one!presented!in!this!study.!Brazil!intends!to!
invest!in!two!more!extra!years!of!education,!making!compulsory!education!start!at!
the!age!of!4!by!2016.!The!present!study!helps!Brazilian!authorities!to!conclude!that!
the!policy!change!implemented!in!2007,!which!intended!to!improve!student!
achievement,!accomplished!this!goal.!However,!for!the!reason!mentioned!above,!it!is!
hasty!to!assume!that!the!additional!two!years!of!instruction!that!are!planned!to!be!
implemented!by!2016!will!have!the!same!results.!Consequently,!future!research!
should!examine!whether!the!effect!size!of!these!two!extra!years!are!equally!positive!
for!the!academic!performance!of!Brazilian!students.!
!
Even!though!the!additional!analyses!carried!out!in!this!study!dismissed!the!
hypotheses!of!schools!in!the!treatment!group!either!were!better!before!the!
implementation!of!the!treatment!or!were!coming!from!a!steeper!trajectory!of!
student!score!improvement!than!control!schools,!there!is!still!the!possibility!of!
another!unobserved!factors,!which!could!be!both!correlated!with!the!score!
improvement!and!the!implementation!of!the!extra!year!of!compulsory!education,!be!
partially!responsible!for!the!effect!sizes!found!in!this!study.!!
!
Since!past!research!found!different!magnitudes!of!effect!sizes!for!the!same!
amount!of!additional!instructional!time!(Agüero!&!Beleche,!2013),!the!applicability!
of!the!findings!of!this!study!to!other!countries’!contexts!is!also!limited.!
!
It!is!also!important!to!mention!that!the!findings!of!this!paper!are!connected!
to!the!first!time!schools!system!implemented!the!policy!that!added!an!extra!year!of!
instructional!time!to!the!Brazilian!compulsory!education.!The!implementation!of!
!
26!
this!police!required!schools!and!municipalities!to!deal!with!issues!such!as!the!
provision!of!extra!space,!definition!of!curriculum,!resizing!the!teacher!supply!and!
training,!as!well!as!organization!of!the!additional!time.!It!is!natural!to!assume!that!
because!of!the!complexity!of!these!issues,!it!would!take!some!cycles!of!the!supply!of!
this!new!first!year!of!instruction!until!most!schools!have!mastered!the!provision!of!
this!additional!educational!input.!As!a!result,!the!effect!sizes!found!in!this!study!
might!be!different!from!the!ones!found!in!the!following!years!of!the!implementation!
of!this!policy,!when!the!learning!curve!of!this!implementation!potentially!fades!out.!!
!
Prior!research!found!positive!and!statistically!significant!effects!of!additional!
instructional!time!and!student!achievement!(Bellei,!2009).!The!present!study!not!
only!adds!extra!empirical!evidence!for!the!direction!of!this!relationship,!but!also!
uses!strong!research!design!and!finds!substantially!large!effect!sizes!of!the!extra!
year!of!education!when!compared!to!other!additions!of!instructional!time!found!in!
the!extant!literature.!!
The!results!that!high!SES!students!have!larger!benefits!from!the!extra!year!of!
schooling!than!low!SES!are!similar!to!findings!of!other!studies!on!educational!inputs!
(Agüero!&!Beleche,!2013).!One!possible!explanation!for!this!relationship!is!that!
more!disadvantage!children!start!from!a!less!privileged!position!and,!as!a!result,!
need!more!education!inputs!to!reach!the!same!level!of!achievement.!As!this!
Brazilian!reform!had!a!universal!characteristic!that!offered!the!extra!year!for!every!
student,!the!ones!that!started!from!a!more!favorable!position!consequently!reached!
greater!levels!of!achievement.!!
!
27!
The!document!from!the!Brazilian!Ministry!of!Education!that!provides!
guidelines!for!the!implementation!of!the!extra!year!of!compulsory!education!
attributes!importance!to!the!fact!that!the!policy!would!privilege!low!socioeconomic!
status!families,!since!the!middle!and!upper!classes!already!have!access!to!more!
years!of!education!through!private!sources.!The!findings!in!this!paper!provide!
evidence!that!the!universal!provision!of!an!extra!year!of!education!might!have!
resulted!in!equality!of!resources!of!this!educational!input,!but!this!universal!
provision!failed!to!result!in!equal!outcomes!for!children!coming!from!families!with!
different!socioeconomic!backgrounds.!If!Brazilian!authorities!intend!to!ensure!
equity!in!education,!offering!access!to!the!same!opportunities!in!life!for!children!
starting!from!different!positions,!policy!makers!should!develop!laws!that!are!able!to!
compensate!for!disadvantaged!starts!like!the!ones!suggested!by!the!findings!of!this!
paper.!!
Finally,!in!2015!the!first!cohort!that!had!access!to!the!additional!year!of!
instruction!in!Brazil!will!finish!the!whole!nine*year!cycle!of!compulsory!education,!
and!the!Prova'Brasil'test!will!assess!them.!This!will!be!an!important!opportunity!for!
future!research!to!examine!whether!the!effect!of!the!extra!year!of!schooling!in!Brazil!
lasts!for!longer!periods,!as!it!was!the!case!of!the!English!students!who!also!had!
access!to!an!extra!year!of!education!in!Luyten!et!al.’s!(2008)!study.!Nevertheless,!
other!studies!that!investigated!the!relationship!between!additional!instructional!
time!at!the!early!stages!of!life!and!academic!achievement!found!that!the!positive!
effects!tend!to!fade!as!some!groups!of!students!progress!in!school!(Anderson,!2008;!
!
28!
Helms,!2013).!These!two!contradictory!streams!of!findings!make!even!more!
important!future!investigations!on!the!long*term!effects!of!the!Brazilian!reform.!!
This!study!provides!evidence!that!additional!instructional!time!at!the!
beginning!of!formal!schooling!can!increase!student!achievement!at!the!end!of!
primary!school.!This!evidence!might!help!decrease!policy!makers’!frustration!by!
showing!that!policies!that!tweak!with!educational!inputs!can!be!effective.!The!
findings!also!suggest!that!an!additional!year!of!instructional!time!is!an!educational!
input!that!deserves!to!be!considered!by!public!authorities!when!they!face!the!
dilemma!of!choosing!among!education!inputs!in!which!to!invest.!This!is!especially!
the!case!for!authorities!from!countries!that!currently!do!not!offer!public!compulsory!
education!before!the!age!of!seven.!
.
!
29!
References(
!
Agüero,!J.!M.,!&!Beleche,!T.!(2013).!Test:Mex:!Estimating!the!effects!of!school!year!
length!on!student!performance!in!Mexico.!Journal!of!Development!
Economics,!103,!353–361.!
Anderson,!M.!L.!(2008).!Multiple!Inference!and!Gender!Differences!in!the!Effects!of!
Early!Intervention:!A!Reevaluation!of!the!Abecedarian,!Perry!Preschool,!and!
Early!Training!Projects.!Journal!of!the!American!Statistical!Association,!
103(484),!1481–1495.!!
Barro,!R.!J.!(2000).!Education!and!Economic!Growth.!Harvard!University.!
Barro,!R.!J.,!&!Lee,!J.:W.!(2001).!International!data!on!educational!attainment:!
updates!and!implications.!Oxford!Economic!Papers,!53(3),!541–563.!!
Behrman,!J.!R.,!Ross,!D.,!&!Sabot,!R.!(2008).!Improving!quality!versus!increasing!the!
quantity!of!schooling:!Estimates!of!rates!of!return!from!rural!Pakistan.!
Journal!of!Development!Economics,!85(1–2),!94–104.!!
Bellei,!C.!(2009).!Does!lengthening!the!school!day!increase!students’!academic!
achievement?!Results!from!a!natural!experiment!in!Chile.!Economics!of!
Education!Review,!28(5),!629–640.!!
Campbell,!F.!A.,!&!Ramey,!C.!T.!(1994).!Effects!of!Early!Intervention!on!Intellectual!
and!Academic!Achievement:!A!Follow:up!Study!of!Children!from!Low:Income!
Families.!Child!Development,!65(2),!684–698.!!
Campbell,!F.!A.,!&!Ramey,!C.!T.!(1995).!Cognitive!and!School!Outcomes!for!High:Risk!
African:American!Students!at!Middle!Adolescence:!Positive!Effects!of!Early!
Intervention.!American!Educational!Research!Journal,!32(4),!743–772.!!
Carneiro,!P.,!&!Heckman,!J.!J.!(2003).!Human!Capital!Policy!(IZA!Discussion!Paper!No.!
821).!Institute!for!the!Study!of!Labor!(IZA).!!
Cohen,!D.,!&!Soto,!M.!(2007).!Growth!and!human!capital:!good!data,!good!results.!
Journal!of!Economic!Growth,!12(1),!51–76.!!
Colclough,!C.!(1982).!The!impact!of!primary!schooling!on!economic!development:!a!
review!of!the!evidence.!World!Development,!10(3),!167–185.!!
Colom,!R.,!&!Flores:Mendoza,!C.!E.!(2007).!Intelligence!predicts!scholastic!
achievement!irrespective!of!SES!factors:!Evidence!from!Brazil.!Intelligence,!
35(3),!243–251.!!
Cook,!T.!D.,!Shadish,!W.!R.,!&!Wong,!V.!C.!(2008).!Three!conditions!under!which!
experiments!and!observational!studies!produce!comparable!causal!
estimates:!New!findings!from!within:study!comparisons.!Journal!of!Policy!
Analysis!and!Management,!27(4),!724–750.!!
Cooper,!H.,!Charlton,!K.,!Valentine,!J.!C.,!Muhlenbruck,!L.,!&!Borman,!G.!D.!(2000).!
Making!the!Most!of!Summer!School:!A!Meta:Analytic!and!Narrative!Review.!
Monographs!of!the!Society!for!Research!in!Child!Development,!65(1),!i–127.!
!
Cunha,!F.,!Heckman,!J.!J.,!Lochner,!L.,!&!Masterov,!D.!V.!(2006).!Chapter!12!
Interpreting!the!Evidence!on!Life!Cycle!Skill!Formation.!In!E.!Hanushek!and!F.!
Welch!(Ed.),!Handbook!of!the!Economics!of!Education!(Vol.!Volume!1,!pp.!
697–812).!Elsevier.!!
!
Datar,!A.!(2006).!Does!delaying!kindergarten!entrance!give!children!a!head!start?!
Economics!of!Education!Review,!25(1),!43–62.!!
Doppelhofer,!G.,!Miller,!R.!I.,!&!Sala:i:Martin,!X.!(2000).!Determinants!of!Long:Term!
Growth:!A!Bayesian!Averaging!of!Classical!Estimates!(BACE)!Approach!
(Working!Paper!No.!7750).!National!Bureau!of!Economic!Research.!!
Fredriksson,!P.,!&!Ockert,!B.!(2005).!Is!Early!Learning!Really!More!Productive?!The!
Effect!of!School!Starting!Age!on!School!and!Labor!Market!Performance!(SSRN!
Scholarly!Paper!No.!ID!760728).!Rochester,!NY:!Social!Science!Research!
Network.!!
Hanushek,!E.!A.!(2003).!The!Failure!of!Input:based!Schooling!Policies.!The!Economic!
Journal,!113(485),!F64–F98.!!
Heckman,!J.!J.!(2006).!Skill!Formation!and!the!Economics!of!Investing!in!
Disadvantaged!Children.!Science,!312(5782),!1900–1902.!!
Heckman,!J.!J.,!&!Masterov,!D.!V.!(2007).!The!Productivity!Argument!for!Investing!in!
Young!Children.!Applied!Economic!Perspectives!and!Policy,!29(3),!446–493.!!
Krashinsky,!H.!(2006).!How!Would!One!Extra!Year!of!High!School!Affect!Academic!
Performance!in!University?!Evidence!from!a!Unique!Policy!Change.!
Manuscript,!University!of!Toronto.!!
Leibowitz,!A.!(1977).!Parental!Inputs!and!Children’s!Achievement.!Journal!of!human!
resources,!242:251.!
Leuven,!E.,!Lindahl,!M.,!Oosterbeek,!H.,!&!Webbink,!D.!(2004).!New!evidence!on!the!
effect!of!time!in!school!on!early!achievement.!(No.!WP!47/04).!
!
Luyten,!H.,!Peschar,!J.,!&!Coe,!R.!(2008).!Effects!of!Schooling!on!Reading!
Performance,!Reading!Engagement,!and!Reading!Activities!of!15:Year:Olds!in!
England.!American!Educational!Research!Journal,!45(2),!319–342.!!
Luyten,!H.,!&!Veldkamp,!B.!(2011).!Assessing!Effects!of!Schooling!With!Cross:
Sectional!Data:!Between:Grades!Differences!Addressed!as!a!Selection:Bias!
Problem.!Journal!of!Research!on!Educational!Effectiveness,!4(3),!264–288.!
Mankiw,!N.!G.,!Romer,!D.,!&!Weil,!D.!N.!(1992).!A!Contribution!to!the!Empirics!of!
Economic!Growth.!The!Quarterly!Journal!of!Economics,!107(2),!407–437.!!
Marcotte,!D.!E.,!&!Hemelt,!S.!W.!(2008).!Unscheduled!School!Closings!and!Student!
Performance.!Education!Finance!and!Policy,!3(3),!316–338.!!
Mayer,!S.!E.,!&!Knutson,!D.!(1997).!Does!Age!at!Enrollment!in!first!Grade!Affect!
Children’s!cognitive!Test!Scores!(Working!Paper!No.!9706).!Harris!School!of!
Public!Policy!Studies,!University!of!Chicago.!!
Meyer,!B.!D.!(1995).!Natural!and!Quasi:Experiments!in!Economics.!Journal!of!
Business!&!Economic!Statistics,!13(2),!151–161.!!
Ministério)da)Educação,)Secretaria)de)Educação)Básica.'(2007)'Ensino'fundamental'
de#nove#anos#:#orientações#para#a#inclusão#da#criança#de#seis#anos#de#idade.#
organização*Jeanete*Beauchamp,*Sandra*Denise*Pagel,*Aricélia*Ribeiro*do*
Nascimento,!135!p.!:!il.!
Murnane,!R.!J.!(1981).!New!evidence!on!the!relationship!between!mother’s!
education!and!children’s!cognitive!skills.!Economics!of!Education!Review,!
1(2),!245–252.!!
!
Oreopoulos,!P.!(2006).!Estimating!Average!and!Local!Average!Treatment!Effects!of!
Education!When!Compulsory!Schooling!Laws!Really!Matter.!The!American!
Economic!Review,!96(1),!152–175.!
Psacharopoulos,!G.!(2004).!Returns!to!Investment!in!Education:!A!Further!Update.!
Education!economics,!12(2),!111:134.!
Puhani,!P.!A.,!&!Weber,!A.!M.!(2005).!Does!the!Early!Bird!Catch!the!Worm?!
Instrumental!Variable!Estimates!of!Educational!Effects!of!Age!of!School!Entry!
in!Germany!(IZA!Discussion!Paper!No.!1827).!Institute!for!the!Study!of!Labor!
(IZA).!
Sianesi,!B.,!&!Reenen,!J.!V.!(2003).!The!Returns!to!Education:!Macroeconomics.!
Journal!of!Economic!Surveys,!17(2),!157–200.!!
Smith,!J.!(2009).!Can!Regression!Discontinuity!Help!Answer!an!Age:Old!Question!in!
Education?!The!Effect!of!Age!on!Elementary!and!Secondary!School!
Achievement.!The!B.E.!Journal!of!Economic!Analysis!&!Policy,!9(1).!!
Temple,!J.!(1999).!A!positive!effect!of!human!capital!on!growth.!Economics!Letters,!
65(1),!131–134.!!
Temple,!J.!R.!W.!(2001).!Growth!Effects!of!Education!and!Social!Capital!in!the!OECD!
Countries!(SSRN!Scholarly!Paper!No.!ID!276787).!Rochester,!NY:!Social!
Science!Research!Network.!!
Winship,!C.,!&!Morgan,!S.!L.!(1999).!The!Estimation!of!Causal!Effects!from!
Observational!Data.!Annual!Review!of!Sociology,!25,!659–706.!
Wößmann,!L.!(2003).!Specifying!Human!Capital.!Journal!of!Economic!Surveys,!17(3),!
239–270.!
!
Appendix(
!
!
Table(1(!
PRE!and!POST!Prova!Brasil2test!scores!for!treatment!and!control!groups!
!
Five2year!primary!school!
! Control!
!
PRE,!n:!15,362! POST,!n:!15,362! ! PRE,!n:!9,237!
Outcome!(School!level)!
!
!
! !
Math!
203.07!
210.34!
! 200,32!
Language!
183.20!
191.28!
! 179.54!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
POST,!n:!9,237!
!
201.35!
182.28!
Table(2!
Taxonomy!of!fitted!multiple!regression!models,!demonstrating!the!relationship!between!student’s!test!score!and!five2years!of!
primary!school,!controlling!for!covariates.!
!
!
!
Intercept!
FIVE%YEAR*POST.
POST!
FIVE2YEAR!
Average!Student!Age!
Average!Student!Preschool!
Average!Student!Mothers!Ed!
SES!
Language!
Model!1
!
!
200.32***! 374.13***! 164.75***! 155.42***! 179.54***!
6.23***.
6.24***.
6.24***.
6.24***.
5.33***.
1.0**!
1.03***!
1.03***!
1.03*!
2.74***!
2.7***!
7.04***!
3.62***!
0.65!
3.66***!
!
54.63***! 45.70***! 38.29***! !
!
219.59***! 26.41***!
22.62*!
!
!
!
212.82***! 14.26**!
!
!
!
3.92***!
2.51***!
!
State!RO!
State!AC!
State!AM!
State!RR!
State!PA!
State!AP!
State!TO!
State!MA!
State!PI!
State!CE!
State!RN!
State!PB!
State!PE!
State!AL!
State!SE!
State!BA!
State!MG!
State!ES!
State!RJ!
State!PR!
State!SC!
State!RS!
State!MS!
State!MT!
State!GO!
State!DF!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
23.19**!
0.63!
28.51***!
217.62***!
29.01***!
219.47***!
25.55***!
216.51***!
27.22***!
28.68***!
218.77***!
211.03***!
213.87***!
217.64***!
211.78***!
210.50***!
12.76***!
2.64***!
21.08!
9.11***!
24.74***!
21.80!
21.03!
210.95***!
0.74!
9.16***!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
0.07!
7.90***!
23.25**!
29.92***!
21.07!
211.67***!
20.52!
27.92***!
20.42!
20.7!
212.45***!
25.20***!
28.78***!
211.68***!
26.60***!
24.45**!
12.15***!
5.11***!
1.33!
6.11***!
23.03**!
20.08!
1.91*!
25.56***!
5.48***!
10.49***!
Source:!Author!elaboration!
*p>0.05;!**p>0.01;!p>0.001!
!
!
!
!
!
!
!
!
R2!
n!
!
Mathematics!
Model!1!
Model!2!
0.02!
24,597!
0.31!
24,597!
!
Model!3!
0.47!
24,597!
!
Model!4!
0.56!
24,597!
0.05!
24,597!
Model!2!
!
Model!3!
!
Model!4!
327.17***!
5.34***.
2.74***!
7.30***!
45.63***!
216.60***!
!
!
141.31***!
5.34***.
2.74***!
4.39***!
34.59***!
24.58***!
5.79***!
3.25***!
134.08***!
5.34***.
2.74***!
1.42!
29.61***!
22.54*!
17.77***!
2.61***!
0.33!
24,597!
0.51!
24,597!
0.59!
24,597!
!
Table(3!
Average!fitted!difference!in!Prova!Brazil2test2scores!in!the!PRE2treatment!situation!between!treatment!and!control!schools,!
without!selected!covariates!(model!I)!and!with!selected!covariates!(model!IV).!
!
.
.
Without.covariates!
With.covariates!
.
Number.of.schools!
Source:!Author!elaboration!
*p>0.05;!**p>0.01;!p>0.001!
Outcome.
Mathematics!
2.43**!
.92!
!
24,597!
!
.
Language!
2.91***!
1.29!
!
24,597!
!
!
Table(4!
Average!language!and!mathematics!achievement!for!students!in!treatment'and!control'schools!in!2007,!2009!and!2011.!
!
!
!
!
2007!
2009!
2011!
!
!
!
Average!Prova!Brasil2test!score!
Language!
!
!
Treated!
Control!
!
172.26!
170.84!
!
183.20!
179.54!
!
191.28!
182.28!
!
Mathematics!!
Treated!
189.65!
203.07!
210.34!
!
Control!
188.21!!
200.32!
201.35!
!
!
Table&5!
Alternative!difference.in.differences!estimates.!
!
!
Language! !
DID!2011.2009!
5.34***!
!
DID!2011.2007!
7.57***!
!
DID!2009.2007!
2.23!
!
Source:!Author!elaboration!
*p>0.05;!**p>0.01;!p>0.001!
!
!
!
Before**
2007*reform
Grades
Early*Childhood*
education
Grade*1
Grade*2
Grade*3
Primary*and* Grade*4
middle*schools Grade*5
Grade*6
Grade*7
Grade*8
High*School
!
!
Age
0*years
1*years
2*years
3*years
4*years
5*years
6*years
7*years
8*years
9*years
10*years
11*years
12*years
13*years
14*years
15*years
16*years
17*years
Mathematics!!
6.24***!
7.55***!
1.31!
!
After**
2007*reform
Grades
Early*
Childhood
education
Grade*1
Grade*2
Grade*3
Primary*and* Grade*4
middle*
Grade*5
schools
Grade*6
Grade*7
Grade*8
Grade*9
High*School
Compulsory*education
!
!
Figure'1'
Primary!and!secondary!level!of!Brazilian!educational!system!before!and!after!the!
2006’s!Educational!reform,!which!added!an!additional!year!at!the!beginning!of!
primary!school!level!!
!
!
Estimated effect-size (S.D.)
0.40'
0.35'
0.30'
0.25'
Language!
0.20'
0.15'
Math!!
1st'
2nd'
3rd'
4th'
5th'
Quintile distribution of the outcome variable
!
Figure'2'
Estimated!program!effect!at!different!levels!of!the!students’!SES!distribution.!
Difference.in.differences!estimates!of!the!five.year!of!primary!school!effect!for!each!
of!the!5!quintiles!of!student’s!SES!distributions!in!both!mathematics!and!language.!
Out.come!variable:!Prova!Brazil!test.scores!2009.2011(effect.size!calculated!in!
standard!deviation!units).!Source:!author!elaboration.!
!
&
!