Can teaching be taught? Improving teachers' pedagogical skills at scale in rural Peru

Cas o, Juan F ancisco; Glewwe, Paul; He edia-Mayo, Alexand a; Maje owicz,
S ephanie; Mon e o, Rica do
A icle
Can eaching be augh ? Imp o ing eache s' pedagogical
skills a scale in u al Pe u
Quan i a i e Economics
P o ided in Coope a ion wi h:
The Econome ic Socie y
Sugges ed Ci a ion: Cas o, Juan F ancisco; Glewwe, Paul; He edia-Mayo, Alexand a; Maje owicz,
S ephanie; Mon e o, Rica do (2025) : Can eaching be augh ? Imp o ing eache s' pedagogical
skills a scale in u al Pe u, Quan i a i e Economics, ISSN 1759-7331, The Econome ic Socie y, New
Ha en, CT, Vol. 16, Iss. 1, pp. 185-233,
h ps://doi.o g/10.3982/QE2079
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Quan i a i e Economics 16 (2025), 185–233 1759-7331/20250185
Can eaching be augh ? Imp o ing eache s’ pedagogical
skills a scale in u al Pe u
Juan F. C as o
Depa men o Economics, Uni e sidad del Paci ico
Paul Glewwe
Depa men o Applied Economics, Uni e si y o Minneso a
Alexand a He edia-Mayo
Depa men o Economics, Uni e sidad del Paci ico
S ephanie Maje owicz
School o Go e nmen , Uni e sidad de los Andes
Rica do Mon e o
Depa men o Applied Economics, Uni e si y o Minneso a
We e alua e he impac o a la ge-scale eache coaching p og am in Pe u, a con-
ex wi h high eache u no e , on eache s’ pedagogical skills and s uden lea n-
ing. P e ious s udies ind ha small-scale coaching p og ams can imp o e each-
ing o eading and science in de eloping coun ies. Howe e , scaling up can e-
duce p og ams’ e ec i eness, and eache u no e can e ode compliance and
cause spillo e s on o non-p og am schools. We de elop a amewo k ha de ines
di e en ea men e ec s when eache u no e is p esen , and explains which
e ec s can be es ima ed. We e alua e his eache coaching p og am, exploi ing
andom assignmen o ha p og am’s expansion o 3797 u al schools in 2016.
A e wo yea s, eache s assigned o he p og am inc eased hei agg ega e ped-
agogical skills by 0.20 s anda d de ia ions. The p og am also inc eased s uden
Juan F. Cas o: [email p o ec ed]
Paul Glewwe: [email p o ec ed]
Alexand a He edia-Mayo: [email p o ec ed]
S ephanie Maje owicz: [email p o ec ed]
Rica do Mon e o: [email p o ec ed]
We would like o hank semina pa icipan s a he Depa men o Applied Economics o he Uni e si y
o Minneso a, he Depa men o Economics o Uni e sidad del Rosa io, he LACEA 2019 Annual Mee -
ing, he Depa men o Ag icul u al and Consume Economics a he Uni e si y o Illinois, and he De-
pa men o Ag icul u al Economics and Ru al De elopmen a Seoul Na ional Uni e si y o hei alu-
able commen s. We also hank se e al anonymous e e ees, whose commen s we e e y help ul o im-
p o ing ou pape . We a e also g a e ul o Hugo Fe nández o excellen esea ch assis ance, and o Di-
ana Ho a h o p epa ing he eplica ion ma e ials. Any emaining e o s a e ou s alone. The andomized
e alua ion was planned by Pe u’s Minis y o Educa ion. The s uden assessmen s and eache obse a-
ion ins umen used in his s udy we e designed by he Minis y o Educa ion o gene al in e nal use. We
used anonymized da a p o ided by he Minis y o Educa ion. The eplica ion package o his pape is a :
h ps://doi.o g/10.5281/zenodo.13738582.
©2025 The Au ho s. Licensed unde he C ea i e Commons A ibu ion-NonComme cial License 4.0.
A ailable a h p://qeconomics.o g.h ps://doi.o g/10.3982/QE2079
186 Cas o, Glewwe, He edia-Mayo, Maje owicz, and Mon e oQuan i a i e Economics 16 (2025)
lea ning; a e 1 yea , G ade 2 s uden s’ ma hema ics and eading sco es inc eased
by 0.106 and 0.075 s anda d de ia ions (o he dis ibu ions o hose es sco es),
espec i ely. A e h ee yea s, he cumula i e e ec inc eases sligh ly, o 0.114 and
0.100, espec i ely. One eason why hese impac s a e low is ha some uncoached
eache s mo ed in o ea ed schools in yea s 2 and 3. Following ou amewo k,
we es ima e ha he impac s on s uden s o ha ing a “ ully” coached eache o
all h ee yea s a e 0.18 and 0.16 s anda d de ia ions o ma hema ics and eading
comp ehension, espec i ely.
Keywo ds. Educa ion, eache coaching, pedagogical skill, s uden lea ning,
eache u no e .
JEL classi ica ion. I21, O15.
1. In oduc ion
Teache quali y is an essen ial de e minan o s uden lea ning (Das, De con, Habya i-
mana, and K ishnan (2007), Clo el e , Ladd, and Vigdo (2010), Che y, F iedman, and
Rocko (2014)). Ye many eache s lack mas e y in he subjec s hey each o lack he
pedagogical skills o each hem e ec i ely. This is especially ue o eache s in de el-
oping coun ies (Wo ld Bank (2018)). Can hese eache s’ skills be imp o ed?
E e y yea , de eloping coun ies spend o e $1 billion on eache aining (Loyalka,
Popo a, Li, Liu, and Shi (2019)). Popo a, E ans, and A ancibia (2016) ind ha abou
wo- hi ds o he Wo ld Bank educa ional p ojec s be ween 2000 and 2012 included in-
se ice eache aining. Such aining is a ac i e because i can be cen ally designed
and coo dina ed by he Minis y o Educa ion and is usually suppo ed by eache s’
unions (E ans and Popo a (2016)).
In his s udy, we e alua e he impac o a la ge-scale eache coaching p og am, op-
e a ing in a con ex o high eache u no e , on eache s’ pedagogical skills as well as on
s uden lea ning ou comes. E idence on he impac s o in-se ice aining in de elop-
ing coun ies is mixed, and p og ams a y widely in o m and con en . A su ey by E ans
and Popo a (2016) ound ha p og ams wi h ace- o- ace aining, ollow-up isi s, en-
gagemen o eache s o ob ain hei ideas, and adap a ion o local con ex , end o ha e
la ge e ec s on s uden lea ning. Coaching p og ams o en ha e hese ea u es as hey
in ol e school isi s, class oom obse a ions, and pe sonalized eedback o eache s by
ained pee s o coaches. Thus, coaching p og ams a e a p omising al e na i e o adi-
ional in-se ice aining ha o e s in ensi e sessions o la ge numbe s o eache s a a
cen alized enue.
When p og ams a e o e ed a he school le el bu a e in ended o ope a e h ough
eache s, and eache s can mo e be ween schools, es ima es o he a e age ea men
e ec (ATE) o he p og am based on a andomized con ol ial may be biased. In pa -
icula , mo emen o eache s ac oss schools may lead o spillo e s ha will in oduce
biases when compa ing ea ed and con ol schools, e en when all schools comply wi h
hei andom assignmen and he e a e no biases due o he selec ion o a i ion o s u-
den s.
Educa ion in e en ions ha ope a e h ough eache s o en ha e all eache s in a
school sha e ea men s a us (i.e., all eache s a e ei he ea ed o un ea ed). Mos
Quan i a i e Economics 16 (2025) Can eaching be augh ? 187
s udies o he e ec i eness o hese ypes o in e en ions ocus on s uden ou comes
and compa e ea men schools wi h con ol schools, and some o hem e alua e esul s
a e enough ime has passed o eache s o swi ch schools (Lucas, McEwan, Ngwa e,
and Oke ch (2014), Jukes e al. (2017), Cillie s, Fleisch, P insloo, and Taylo (Cillie s e al.
(2020))). These s udies usually add ess po en ial biases due o s uden a i ion, ye hey
a ely men ion he possibili y o eache u no e o he po en ial bias i may induce.
This isk o bias may occu no only o educa ion in e en ions bu also o any es i-
ma ion o ea men e ec s in clus e andomized con ol ials (RCTs) wi h mo emen
o se ice p o ide s o p og am bene icia ies ac oss clus e s. Indeed, high u no e is e-
po ed o many non-educa ion con ex s. Fo example, Ko ne , B ewe , Fa ehi, and Jun
(2014) epo ha 17.5% o new nu ses in he U.S. lea e hei jobs wi hin 1 yea o s a -
ing, and Bane jee, Cha opadhyay, Du lo, Kenis on, and Singh (2021) ind, in hei con-
ol sample, ha one- hi d o police o ice s in India changed s a ions o e an 18-mon h
pe iod. Despi e i s equency, u no e is usually igno ed in p og am e alua ions. Fo ex-
ample, Geo giadis and Pi elis (2016) compa e ea ed and con ol en e p ises (clus e s)
in a job aining p og am bu do no discuss he possibili y o wo ke s mo ing ac oss
i ms.
We make a me hodological con ibu ion by de eloping a amewo k ha cla i ies
he assump ions and da a needed o ob ain unbiased es ima es o a e age ea men
e ec s (ATE), in en o ea e ec s (ITT), and a e age causal esponse (ACR, an ex en-
sion o local a e age ea men e ec s (LATE)) in a clus e ed RCT wi h mo emen o se -
ice p o ide s ac oss clus e s. In ou con ex , his amewo k explains how ea men
e ec s di e , depending on whe he one ocuses on a pa icula se o eache s, ollow-
ing hem i hey mo e o o he schools (in which case he ou come a iables a e hose
eache s’ skills), o on he eache s and s uden s in pa icula schools (in which case he
ou come a iables a e he skills o hese schools’ eache s and he lea ning p og ess o
hese schools’ s uden s). Bo h se s o ea men e ec s a e highly ele an om a policy
pe spec i e. The i s se is ele an o policies ha ocuses on imp o ing he skills o a
pa icula g oup o eache s, such as eache s whose pedagogical skills a e hough o be
de icien . The second se is ele an o policies aimed a imp o ing he eaching skills
and lea ning p og ess, espec i ely, o he eache s and s uden s in a pa icula g oup o
schools, such as schools whe e s uden s’ academic pe o mance is pa icula ly low. We
show how he la e se o e ec s depends no only on he di ec e ec o he p og am
on pa icipa ing eache s’ skills bu also on he indi ec e ec o he p og am on eache
composi ion: which eache s s ay in hese schools, which eache s lea e hese schools,
and which eache s mo e in o hese schools. P e ious esea ch based on clus e RCTs
whe e se ice p o ide s mo e ac oss clus e s has igno ed hese composi ion e ec s.
We show ha , in gene al, i is no possible o es ima e a e age ea men e ec s
(ATEs) o eache skill and s uden lea ning, al hough unde ce ain condi ions lowe
bounds o ATEs can be es ima ed. We also show ha compa isons o eache s in ea ed
and con ol schools a e u no e has occu ed will, in gene al, lead o biased es ima es
o in en o ea (ITT) e ec s o eache s in he p og am schools when he p og am
s a ed. Howe e , i is possible o es ima e hese ITT e ec s i one has a sample o each-
e s ha ollows hem when hey change schools, o using he da a o eache s in ea ed
188 Cas o, Glewwe, He edia-Mayo, Maje owicz, and Mon e oQuan i a i e Economics 16 (2025)
and con ol schools a e u no e has occu ed i ha u no e is un ela ed o he p o-
g am. This las esul is impo an because ollowing eache s who change schools and,
mo e gene ally, ollowing se ice p o ide s who change clus e s, can be di icul , which
aises he isk o a i ion bias in ITT es ima es.
We es ima e he e ec s on eache s’ pedagogical skills and on s uden lea ning o
a eache coaching p og am implemen ed in u al mul ig ade schools in Pe u. T ained
coaches isi class ooms and gi e speci ic ad ice o eache s on hei pedagogical p ac-
ices, p o iding cus omized s a egies o imp o e hem. Iden i ica ion exploi s andom
assignmen o 6218 schools (3797 ea ed schools, 2421 con ol schools) when he p o-
g am expanded in 2016. Teache skills we e measu ed in la e 2017 (a e nea ly 2 yea s o
ea men ) by obse ing eache -s uden in e ac ions and a b oad ange o ins uc ional
p ac ices in a andomly selec ed subsample o 166 ea ed and 174 con ol schools. S u-
den skills we e es ed in g ades 2 (la e 2016) and 4 (la e 2018) o all public schools wi h
i e o mo e s uden s in hose g ades, which p o ides s uden es sco e da a o 2567 o
he 6218 andomly assigned schools.
As in many de eloping coun ies, Pe u’s u al schools ha e e y high a es o eache
u no e ;1o he eache s in he subsample o 340 schools wi h eache skills da a, abou
43% had mo ed be ween 2016 and he s a o 2017. Impo an ly, class oom obse a ion
da a we e collec ed no only in hese 340 schools, bu also in many (bu no all) o he
schools ha ecei ed he eache s who mo ed om hese schools o o he schools be-
ween 2016 and 2017.
Ou main indings a e as ollows. Fo he eache s who, a e u no e occu ed (i.e.,
in 2017), we e eaching in he schools assigned o he p og am, we ind ha he ITT e ec
o 2 yea s o coaching on hei pedagogical skills is 0.20 s anda d de ia ions (s.d.) o he
dis ibu ion o hose skills. This is also ou p e e ed es ima e o he ITT e ec on he
skills o he eache s in he p og am schools when he p og am began, many o whom
le hose schools in he nex yea . We also show ha his ITT es ima e is, unde plausible
assump ions, a lowe bound o he ATEs o bo h se s o eache s. Tu ning o speci ic
skills, he la ges ITT e ec s a e o lesson planning and, o a lesse ex en , encou aging
s uden s’ c i ical hinking.
We also es ima ed ea men e ec s o he p og am on s uden lea ning a e 1 and 3
yea s (we ha e no da a o he second yea ). A e 1 yea , he p og am inc eased lea ning
among he G ade 2 s uden s who ook he 2016 Na ional S uden E alua ion by 0.106 s.d.
in ma hema ics and 0.075 s.d. in eading comp ehension (o he dis ibu ions o hose
es sco es in he con ol schools). These a e bo h ITT and ATE e ec s, since all each-
e s ollowed hei andom assignmen in he i s yea . A e 3 yea s o exposu e, he
ITT e ec inc eases only sligh ly, o 0.114 s.d. o ma hema ics and 0.100 s.d. o eading
comp ehension; hese es ima es, which a e lowe bounds o ATE (which canno be es-
ima ed in yea 3), e lec he ac ha many eache s in p og am schools in yea 3 did
no ha e 3 ull yea s o coaching, and some eache s who had mo ed o con ol schools
1High eache u no e is common in de eloping coun ies: Zei lin (2021) epo s u no e o abou 20%
pe yea in Rwanda, and Scha ne , Glewwe, and Sha ma (2024) epo 18–21% u no e pe yea o each-
e s in Nepal.

Quan i a i e Economics 16 (2025) Can eaching be augh ? 189
by yea 3 had been coached in p e ious yea s. The a e age causal esponse (ACR) es i-
ma es a e 3 yea s, which adjus he ITT es ima es o es ima e he impac o 3 yea s o
exposu e o eache s who we e coached in all 3 yea s, a e 0.180 s.d. o ma hema ics and
0.162 s.d. o eading comp ehension.
Ou es ima es o he e ec o coaching on pedagogical skills a e smalle han hose
ound in de eloped coun ies (0.49 s.d. on ins uc ional p ac ices, see K a , Blaza , and
Hogan (2018)). This may e lec he scale o he p og am, and Pe u’s high a e o eache
u no e . Ye we add ess wo un esol ed ques ions on coaching’s impac on eache s’
pedagogical skills in de eloping coun ies. We show ha : (i) A p og am implemen ed a
scale, e en wi h high eache u no e , can s ill exhibi posi i e impac s; and (ii) Gene al
pedagogical skills can be inc eased.
Fu he mo e, while ou es ima ed e ec s on s uden lea ning may seem small, hey
a e simila , and in one sense la ge , han hose ypically ound in de eloping coun ies.
E ans and Yuan (2022) su eyed 224 educa ion s udies and ound ha he median e ec
on lea ning ou comes is 0.10 s.d., and hese e ec sizes dec ease wi h he size o he
s udy. Fo la ge s udies, hose wi h o e 5000 s uden s, he median e ec is only 0.05 s.d.
To ou knowledge, no p io s udy has e alua ed he e ec s on pedagogy and s u-
den lea ning o a la ge-scale eache coaching p og am in a de eloping coun y. Mos
in-se ice aining p og ams e alua ed in hose coun ies a e small-scale pilo s o e i-
cacy ials un by esea che s o NGOs (E ans and Popo a (2016)). Fo example, Cillie s
e al. (2020) es ima ed he impac o coaching and cen alized eache aining on s u-
den eading skills implemen ed in 180 public schools in Sou h A ica, and Albo noz,
Anaua i, Fu man, Luzu iaga, Podes a, and Taylo (Albo noz e al. (2020)) es ima ed he
impac o eache coaching o imp o e s uden lea ning o science implemen ed in 70
public schools in A gen ina. In con as , we e alua e a p og am implemen ed in 3797
u al schools in Pe u.
The issue o scale is ele an o coaching p og ams’ e ec i eness because o wo
ea u es o his ype o in-se ice aining. Fi s , he p og am’s success depends on he
supply o quali ied coaches. I hese skills a e sca ce, expanding he p og am likely will
educe i s quali y, and hus i s e ec i eness. Second, class oom obse a ion and pe son-
alized eedback equi es coaches o a el o se e al schools. This can be cos ly and can
complica e p og am deli e y i scaling-up implies se ing schools in e y emo e a eas.
This is e y likely o u al schools in de eloping coun ies, whose eache s o en equi e
addi ional aining.
Teache u no e no only complica es iden i ica ion o p og am e ec s, as dis-
cussed abo e, bu may also make coaching less e ec i e by educing compliance. Teach-
e s who lea e a school be o e he p og am ends may no ecei e he ull “dose” o coach-
ing, and p og am schools ha ecei e new eache s may ha e s a who a e only pa ially
coached.
We know o only one o he s udy ha conside ed eache u no e when e alua -
ing a eache aining p og am. Ma sumu a, Ga nie , Co en i, Junke , and Bickel (2010)
es ima ed he e ec o a li e acy coaching p og am in 32 elemen a y schools in Texas.
S essing how such u no e can hwa schools’ e o s o imp o e ins uc ion h ough
eache aining, he au ho s es ima ed he p og am’s e ec on he eading skills o he
190 Cas o, Glewwe, He edia-Mayo, Maje owicz, and Mon e oQuan i a i e Economics 16 (2025)
s uden s o eache s ec ui ed o eplace hose who le hei school in he i s yea o
he p og am. They ound a posi i e associa ion be ween eache s’ p og am pa icipa ion
and hei s uden s’ eading skills. Howe e , he non andom composi ion o hei sample
( ec ui ed eache s in p og am and nonp og am schools may no be compa able) cas s
doub on he causal in e p e a ion o hei esul s.
Finally, he li e a u e hus a does no p o ide a clea indica ion as o whe he
coaching can imp o e gene al pedagogical skills. Mos e alua ions o coaching p o-
g ams ocus on pedagogy o a speci ic opic o cou se. Fo example, Albo noz e al.
(2020) ocus on imp o ing eaching o science, and Cillie s e al. (2020) ocus on ead-
ing. K a , Blaza , and Hogan (2018) highligh a lack o causal e idence on he e ec o
coaching o subjec s o he han eading o li e acy. Some pape s measu e he e ec o
aining on eache ime alloca ion (B uns, Cos a, and Cunha (2018)) o on using spe-
ci ic ypes o eaching (Ko ze, Fleisch, and Taylo (2019)), bu no on hei eaching skills.
The pedagogical skills o public-school eache s in de eloping coun ies a e gene ally
low, and a key policy ques ion is whe he coaching can imp o e a b oad se o eaching
skills.
The es o he pape is o ganized as ollows. Sec ion 2desc ibes he p og am and
explains he e alua ion design. Sec ion 3p esen s ou analy ical amewo k, de ines se -
e al ea men e ec s, and explains which can be es ima ed. Sec ions 4and 5p esen es-
ima es o he p og am’s impac on eache s’ pedagogical skills and on s uden lea ning,
espec i ely. Sec ion 6p o ides concluding ema ks, policy implica ions, and ad ice o
u u e esea ch. The Supplemen al Appendix (Cas o, Glewwe, He edia-Mayo, Maje ow-
icz, and Mon e o (Cas o e al. (2024a))) con ains addi ional ables and de i a ions.
2. The coaching p og am and i s e alua ion design
2.1 Teache hi ing and mo emen in Pe u
The e a e wo ypes o eache s in he Pe u ian school sys em: Tenu ed (ci il se an )
eache s (nomb ados), who ha e a pe manen posi ion in a pa icula school, and con-
ac eache s (con a ados) on empo a y 1-yea con ac s who a e illing in o enu ed
eache s who a e empo a ily absen o o un illed acancies in pa icula schools. In
he schools we conside —mul ig ade and monolingual—mos (70–75%) o eache s a e
enu ed.
Teache s become enu ed h ough a selec ion p ocess wi h wo s ages. The i s s age
consis s o a na ionally adminis e ed exam ha co e s eading comp ehension, logical
easoning, and knowledge o pedagogical p ac ices. Teache s wi h he minimum passing
g ade on he exam p oceed o a second s age ha is ca ied ou by egional educa ion
o ices and includes an in e iew and in-class oom obse a ion o eaching p ac ices.
Teache s who do no each a minimum passing g ade in an exam in he i s s age
o he selec ion p ocess, o who ecei e a passing g ade bu a e unsuccess ul a he sec-
ond s age, can ill empo a y eaching posi ions as con ac eache s (and can con inue
ying o ob ain enu e). Con ac eache s ha e annual con ac s: a he end o each
school yea , hey mus apply o ei he a enewed con ac a hei cu en school o o
a con ac posi ion a ano he school. When applying o new schools, con ac eache s
Quan i a i e Economics 16 (2025) Can eaching be augh ? 191
can apply o as many schools as hey wan wi hin one egion. They a e hen anked ac-
co ding o hei sco es on he la es exam, and eache s wi h he bes sco es ge hei op
p io i y o schools. Teache s can maximize hei p obabili y o ge ing placed by anking
as many schools as hey a e willing o go o, and by selec ing less popula schools (e.g.,
schools loca ed in emo e u al a eas).
Tenu ed eache s end o mo e less equen ly gi en hei pe manen posi ion in
hei schools, bu hey can eques a ans e o ano he enu ed posi ion. In o de o do
his, hey mus mee h ee equi emen s: ha e been in a enu ed posi ion o a leas 3
yea s, ha e been in he cu en enu ed posi ion o a leas 2 yea s, and canno mo e
o ano he school wi hin he same school dis ic (Pe u has abou 250 school dis ic s
(UGELs)).
2.2 The coaching p og am
In 2010, he Pe u ian go e nmen ini ia ed coaching p og ams o imp o e public p i-
ma y school eache s’ pedagogical p ac ices. As pe Minis y o Educa ion guidelines,
he school dis ic au ho i y (UGEL) hi es coaches o eache s in he schools a ge ed
by he p og am, who a e selec ed om op-pe o ming eache s. Coaches mus ha e a
pedagogical college o uni e si y deg ee, 5 o mo e yea s o p ima y school eaching ex-
pe ience, and a leas 1 yea o expe ience aining o p o iding suppo o eache s. Ad-
minis a i e da a show ha coaches ank much highe han o he eache s in he Min-
is y’s eache e alua ions. Coaches we e paid he equi alen o US$ 1200 pe mon h,
abou double he a e age eache ’s wage.
The Minis y o Educa ion se s he s anda ds o hi ing coaches, and o he gene al
p og am design, bu he UGELs selec and hi e he coaches. Each coach wo ks wi h eigh
eache s, and UGELs decide how o ma ch coaches o eache s. Coaches a e hi ed annu-
ally. Abou 20% con inue o ano he yea , bu only 5% s ay in he same school he nex
yea .
The coaching p og am is a subs an ial in es men by Pe u’s go e nmen , cos ing
o e US$ 130 million pe yea .2By 2016, eache s in o e 14,000 public schools wi h mo e
han 900,000 s uden s we e being coached unde se e al coaching p og ams. O e 90%
o hese schools a e p ima y schools. The e a e h ee e sions o he p og am o p ima y
schools: (i) bilingual coaching ( o schools whe e mos s uden s speak a Pe u ian indige-
nous language); (ii) monolingual mul ig ade coaching ( o schools whe e mos s uden s
speak Spanish and he e a e ewe eache s han g ades augh ); and (iii) monolingual
ull- eache coaching ( o schools la ge enough o ha e one eache pe g ade and whe e
mos s uden s speak Spanish).
This pape e alua es he second ype o coaching p og am,3which ope a es p ima -
ily in u al a eas.4O e 90% o Pe u’s u al public p ima y schools a e mul ig ade, which
2I was no implemen ed in 2021 and 2022 due o Co id-19, a e which i was es a ed, bu on a smalle
scale.
3Al hough he h ee ypes o coaching p og ams ha e some di e ences (such as he eache - o-coach
a io o he bilingual ce i ica ion o coaches), wha happens du ing he coaching sessions is e y simila in
all h ee ypes.
4Abou 95% o he 6218 schools in ou s udy a e loca ed in u al a eas.
192 Cas o, Glewwe, He edia-Mayo, Maje owicz, and Mon e oQuan i a i e Economics 16 (2025)
ypically ha e wo eache s and abou 30 s uden s. Ru al mul ig ade schools a e he ma-
jo i y o schools wi h coaching p og ams. The monolingual mul ig ade p og am is pa -
icula ly expensi e because he a ge schools end o be e y a apa , so he p og am
equi es a la ge numbe o coaches and signi ican a el expenses. This e sion o he
p og am alone, called Acompañamien o Pedagógico Mul ig ado (APM) in Spanish, cos
he go e nmen abou US$ 40 million in 2016 and se ed 174,000 s uden s. This implies
an annual cos o US$ 228 pe s uden , which is o e 20% o he o al expendi u e pe
s uden in Pe u’s p ima y schools (in 2015, a e age spending pe p ima y school s u-
den was 2800 soles, o abou US$ 940).
A coach’s wo k consis s o se e al asks. Fi s , he coach mee s he school p inci-
pal and ga he s in o ma ion abou he educa ional con ex . Then he coach a ends all
eache s’ class sessions (one eache pe day) o obse e hei class oom pe o mance
and make an ini ial diagnos ic assessmen . The coach uses his assessmen o iden-
i y he compe encies ha he eache s mus imp o e and de elops an imp o emen
plan wi h each eache . Du ing he school yea , he coach obse es eigh mo e o each
eache ’s class sessions a egula in e als. The p og am is usually implemen ed o 3
consecu i e yea s. A e each class oom obse a ion, he coach and he eache mee o
discuss he p og ess made in e ms o he imp o emen plan. The coach sends mon hly
and qua e ly epo s o he UGEL, and o he school p incipal, on each eache ’s
p og ess, and on a eas o imp o emen . A he end o he yea , he coach p o ides a
inal eedback session o each eache , collec ing his o he imp essions o he p ocess,
and hen w i es a inal epo o each eache on he achie emen s, ac ions, and a eas
equi ing u he e o , e e encing he ini ial imp o emen plan.
In addi ion o he class oom obse a ions, each coach o ganizes eigh wo kshops
pe yea o his o he eache s o discuss pedagogical p ac ices and encou age he ex-
change o ideas. In he wo kshops, all he eache s o a gi en coach ga he wi h he
coach o discuss a pa icula pedagogical opic o in e es . The coach encou ages and
guides he exchange o ideas and success ul p ac ices among eache s and p o ides he-
o e ical suppo on he chosen subjec . A he end o each wo kshop, he g oup chooses
a new opic o he nex ga he ing.
Ins ead o con en knowledge o he ma e ial, he p og am ocuses on s eng hening
pedagogical skills and on de eloping he abili y o eache s o pe iodically e lec on
hei own s eng hs and weaknesses and adjus hei beha io acco dingly:
“The pedagogical coaching p omo es he de elopmen and s eng hening o skills ela ed
o unde s anding he s uden in he con ex , cu icula planning, guiding lea ning, ensu -
ing a sa e school en i onmen , and e alua ing s uden lea ning. In addi ion, i p omo es
he de elopmen o c i ical hinking skills like sel - e lec ion and analysis, h ough exe -
cises ha seek e lec ion and c i ical analysis o he eache ’s own pe o mance.” (APM
Manual)
APM uses a cascade sys em. Each coach is ained, suppo ed, and moni o ed by a
pedagogical specialis . Each specialis is equi ed o moni o each coach a leas wice
pe yea du ing he coach’s class oom isi s. The specialis also p o ides wo wo kshops
pe yea di ec ly o eache s. Coaches and specialis s ollow he “F amewo k o Good
Quan i a i e Economics 16 (2025) Can eaching be augh ? 199
In yea 2, he e may be in e ac ions (deno ed by γk
1,2) o he coaching in yea s 1 and 2:
y2
j=y1
j+λj+δkT2
j+γk
1,2T1
jT2
j
=θ2
j+δkT1
j+T2
j+γk
1,2T1
jT2
j, o k=R, L, D, M. (3)
The second line subs i u es ou y1
jusing (2), and θ2
jdeno es θ1
j+λj=y0
j+2λj. I , o
example, he second yea ’s impac o coaching is less han ha o he i s yea , hen he
in e ac ion e m γk
1,2 is <0. Also, γk
1,2 can include dep ecia ion o eache skills p oduced
by he p og am.
Fo yea 3, u he in e ac ion e ec s a e needed. The equa ion o y3
jis
y3
j=y2
j+λj+δkT3
j+γk
1,2T1
jT2
j+T1
jT3
j+T2
jT3
j+γk
1,2,3T1
jT2
jT3
j
=θ3
j+δkT1
j+T2
j+T3
j+γk
1,2T1
jT2
j+T1
jT3
j+T2
jT3
j+γk
1,2,3T1
jT2
jT3
j,
o k =R, L, D, M, (4)
whe e he second line uses (3) o subs i u e ou y2
j,andθ3
j=θ2
j+λj=y0
j+3λj.No e ha
he in e ac ion e ec o any combina ion o 2 yea s o coaching is assumed o be he
same, ega dless o which 2 yea s hey a e; allowing o di e en in e ac ion e ec s o
each possible pai o yea s would do li le beyond complica ing he no a ion. The iple
in e ac ion γk
1,2,3 can include dep ecia ion o he skills o eache s who a e coached o
all 3 yea s.
Fo he APM p og am, h ee s anda d ea men e ec s can be de ined o eache
skills. The i s is he a e age ea men e ec (ATE), APM’s impac on he a e age
eache (when all eache s a e ea ed, i.e., ecei e coaching). The coun e ac ual is ha
no eache s a e ea ed, o equi alen ly ha he p og am does no exis . ATE o yea is
de ined as
ATE ch ( )≡Ey
1−y
0=Ey
1−Ey |No p og am exis s,(5)
whe e he “ ch ” subsc ip indica es ha he ea men e ec e e s o eache s’ skills.
Fo y, he supe sc ip is s ill yea s since he p og am s a ed, bu subsc ip s indica e po-
en ial ou comes (1 = ea ed, 0 =no ea ed). Implici in his de ini ion is ha he wo
po en ial ou comes in yea (y
1and y
0) main ain he same po en ial ou come s a us
( ea ed o no ea ed) since yea 1, so a eache who is ea ed in yea 1 is ea ed o
all yea s be ween 1 and , and a eache who is no ea ed in yea 1 is no ea ed o
check his assump ion wi h ou da a, ye he e a e h ee easons why i is unlikely ha a coached eache
will ha e sizeable impac s on he skills o o he eache s in he same school. Fi s , abou 20% o he schools
in he es sco e da a, and 49% in he eache skill da a, ha e only one eache ; o hese schools pee e ec s
a e no possible. Second, almos all schools ha ha e mo e han one eache ha e only wo o h ee each-
e s, and hey all each di e en g ades. Fo example, one eache eaches g ades 1–3 and ano he eaches
g ades 4–6. Thi d, coaching is gene ally eache -speci ic, add essing he pedagogical weaknesses o a spe-
ci ic eache and he needs o ha eache ’s s uden s; o he eache s a e likely o ha e di e en pedagogical
weaknesses and s uden s wi h di e en needs; his u he educes oppo uni ies o pee e ec s. I pee
e ec s do occu , such a SUTVA iola ion would lead o unde es ima ion o ITT e ec s, so ou ITT es ima es
would be lowe bounds o he ue ITT pa ame e s.

200 Cas o, Glewwe, He edia-Mayo, Maje owicz, and Mon e oQuan i a i e Economics 16 (2025)
all yea s be ween 1 and . The popula ion o eache s o which his ea men e ec is
de ined is all eache s who we e eaching in mul ig ade monolingual schools in Pe u in
yea 1.
A mo e speci ic example o equa ion (5)is o yea 2( =2), which is he only yea o
which eache skill da a a e a ailable. This can be exp essed as
ATE ch (2)≡Ey2
1−y2
0=2δ+γ1,2,
whe e δ=δRpR+δLpL+δDpD+δMpM,γ1,2 =γR
1,2pR+γL
1,2pL+γD
1,2pD+γM
1,2pM,andp
k
is he p opo ion o ype k eache s. Appendix B in Cas o e al. (2024a) gi es exp essions
o ATE ch (1)and ATE ch (3).
Nex , conside he in en ion o ea (ITT) e ec . This is he p og am’s impac on
skills in yea o eache s andomly assigned o APM schools in yea 1, ega dless o
he school hey we e in (APM o non-APM) in la e yea s. The coun e ac ual is andom
assignmen o a non-APM school in yea 1, ega dless o whe e hey augh in la e yea s.
I is de ined as
ITT ch ( )≡Ey |R ch ,yea 1 =1−Ey |R ch ,yea 1 =0,(6)
R ch ,yea 1 e e s o he eache ’s school in yea 1, which can di e om his o he school
in yea . An example o equa ion (6) is o yea 2, he yea wi h eache skill da a:14
ITT ch (2)≡Ey2|R ch ,yea 1 =1−Ey2|R ch ,yea 1 =0
=δ+pRδR+γR
1,2+pLγL
1,2 +pMτγM
1,2,
whe e τis he p opo ion o eache posi ions in APM schools among he popula ion
o all monolingual mul ig ade schools. The in ui ion is ha δis he e ec o he i s
yea , when all eache s ollow hei andom assignmen , and he o he e ms a e he
e ec s on he eache s ea ed in he second yea ( emaine s, like s, and he mo e s who
andomly end up in APM schools in yea 2). The coun e ac ual o emaine s is being
in a non-APM schools o bo h yea s, while he coun e ac ual o like s, and o mo e s
who andomly (wi h p obabili y τ) end up in an APM school in yea 2, is being in a non-
APM school in yea 1 and an APM school in yea 2.
A inal impo an poin is ha , unlike ATE ch (2),ITT
ch (2)depends on τ.Ina
“small-scale” RCT, τwould be almos ze o and so could be igno ed, bu in an “a -scale”
RCT τwill be la ge and will a ec ITT ch (2). The in ui ion is ha a p opo ion τo
mo e s in APM schools in yea 1 will also be in APM schools in yea 2, which “ u ns on”
he in e ac ion e ec om 2 yea s o coaching; i he p opo ion o APM schools had
been e y small, e y ew mo e s who mo ed in o APM schools in yea 2 would ha e
been ea ed in yea 1.
In addi ion, he e is a mo e sub le impac o τon ITT ch (2): i de e mines he le el
o compe i ion among “po en ial like s” o mo e in o APM schools, and simila ly he ex-
en o compe i ion among “po en ial dislike s” o mo e in o non-APM schools. This will
14No e a sligh abuse o no a ion: “R” is used in wo di e en ways. I i is “no mal” size (no a supe sc ip )
i indica es a school’s andom assignmen , bu i i is a supe sc ip , i deno es emaine eache s.
Quan i a i e Economics 16 (2025) Can eaching be augh ? 201
ul ima ely de e mine he p opo ions o eache s who a e ac ual like s and dislike s, and
hus he p opo ions o eache s who a e emaine s and mo e s. Howe e , i he e a e no
like s o dislike s, hen he alue o τwould no a ec he p opo ions o emaine s and
mo e s.
Ano he ea men e ec ha is o en es ima ed o andomized con ol ials is a
local a e age ea men e ec (LATE).15 I is de ined only o a bina y ea men a iable,
bu he APM ea men a iable can ha e mo e han wo alues since eache s can swi ch
schools: he ea men can be 0, 1, 2, o 3 yea s. Ang is and Imbens (1995)ex ended
LATE o nonbina y ea men s, which hey call an a e age causal esponse (ACR). The
gene al de ini ion is
ACR ch ( )≡

s=1
Ey
s−y
s−1|T
1≥s>T
0P obT
1≥s>T
0

=1
P obT
1≥ >T
0
,(7)
whe e T
0is he (po en ial) numbe o yea s o coaching up h ough yea o eache s
assigned o non-APM schools in yea 1, and T
1is he (po en ial) yea s o coaching up
h ough yea o a eache assigned o an APM school in yea 1.16 The subsc ip s on
y indica e he alue o y gi en a (po en ial) numbe o yea s o ea men (which a ies
om 0 o 3), no he alue o y gi en a bina y “ ea ed o no ea ed” a iable, in con as
o he de ini ion o ATE ch ( ).
Conside equa ion (7) o yea 2, he only yea wi h eache skill da a:
ACR ch (2)≡Ey2
1−y2
0|T2
1≥1>T2
0P obT2
1≥1>T2
0
P obT2
1≥1>T2
0+P obT2
1=2>T2
0
+Ey2
2−y2
1|T2
1=2>T2
0P obT2
1=2>T2
0
P obT2
1≥1>T2
0+P obT2
1=2>T2
0
=δ+pRδR+γR
1,2+pLγL
1,2 +pMτγM
1,2/1+pR=ITT ch (2)/1+pR.
The in ui ion behind his equa ion is he ollowing. The e m E[y2
1−y2
0|T2
1≥1>T2
0]is
he impac on eache skills o ecei ing 1 yea o ea men , ela i e o ha ing ze o yea s
o ea men , as indica ed by he subsc ip s on he y e ms, o eache s who would ha e
had a leas 1 yea o ea men by yea 2 i assigned o an APM school in yea 1 (T2
1≥1),
bu would no ha e been ea ed by yea 2 i assigned o a non-APM school in yea 1
(T2
0<1). O he ou eache ypes, his includes all emaine s and dislike s, and mo e s
who andomly swi ched o a non-APM school in yea 2 ( o whom T2
0=0andT
2
1=1).
15Fo he APM con ex , he e is no ATT (a e age ea men e ec on he ea ed) because ATT equi es
ha some eache s assigned o he ea men (R ch ,yea 1 =1) a e ne e ea ed. Such eache s do no exis
in he APM con ex because all he eache s who we e andomly assigned o he APM schools we e ea ed
in yea 1.
16Fo he gene al case, possible alues o bo h T
0and T
1a e in ege s om 0 o . Ye , o he APM p o-
g am, all eache s ollowed hei andom assignmen in yea 1, so possible alues o T
0a e 0 o −1, and
o T
1a e 1 o .
202 Cas o, Glewwe, He edia-Mayo, Maje owicz, and Mon e oQuan i a i e Economics 16 (2025)
The e m E[y2
2−y2
1|T2
1=2>T2
0]is he impac on eache skills o ecei ing a second yea
o he ea men , ela i e o ha ing 1 yea o ea men , as indica ed by he subsc ip s on
he y e ms, o eache s who would ha e had 2 yea s o ea men in yea 2 i assigned o
an APM school in yea 1 bu only 0 o 1 yea o ea men in yea 2 i assigned o a non-
APM school in yea 1. This includes all emaine s, all like s, and mo e s who andomly
swi ched o APM schools in yea 2 ( o whom T2
0=1andT
2
1=2). Tu ning o he sums o
he p obabili ies in he denomina o s, P ob[T2
1≥1>T2
0]is he p obabili y ha a eache
is a emaine , a dislike , o a mo e who andomly swi ches o a non-APM school in
yea 2, and P ob[T2
1=2>T2
0]is he p obabili y ha a eache is a emaine , a like , o
a mo e who andomly swi ches o an APM school in yea 2. Thei sum is g ea e han
1; emaine s a e “coun ed wice” since hey a e included in bo h p obabili ies. Like s,
dislike s, and mo e s a e “coun ed” only once.
In e ec , ACR ch (2)is an a e age o : (a) he (a e age) impac on eache skills o go-
ing om no ea men o 1 yea o ea men o emaine s, dislike s, and hose mo e s
who andomly mo e o a non-APM school in yea 2; and (b) he (a e age) impac on
hose skills o going om 1 o 2 yea s o ea men o emaine s, like s, and he mo e s
who andomly mo e o APM schools in yea 2. Thus, ACR ch (2)is he a e age o he im-
pac on eache skills o each addi ional yea o ea men due o andom assignmen in
yea 1 o an APM school, wi h emaine s ge ing “double weigh ” since ha assignmen
aises hei yea s o ea men by 2 yea s, bu o all o he s ha assignmen aises yea s
o ea men by only 1 yea . Impo an ly, no e ha , o any , ACR ch ( )is a pe yea (no
a cumula i e) impac , a e aging o e yea s o ea men induced by schools’ andom as-
signmen o APM in yea 1. The cumula i e e ec is ACR ch ( )mul iplied by he yea s
o coaching induced by a school’s andom assignmen o APM ( he denomina o in (7)):
his equals ITT ch ( ). A inal aspec o ACR ch (2) o no e is ha , like ITT ch (2),i isa
unc ion o τ, since i s nume a o is ITT ch (2).
The h ee ea men e ec s discussed so a ocus on pa icula eache s, and so hey
ollow eache s who mo e o o he schools. Bu many eache aining o coaching p o-
g ams ocus on pa icula schools, so i is use ul o de ine ea men e ec s o he each-
e s cu en ly in he schools ha implemen ed APM.
The e a e wo possibili ies o ea men e ec s ha ocus on schools.17 The i s is
an a e age ea men e ec (ATE) on eache skills o hose schools, whe e he coun e -
ac ual is no p og am a all, which we deno e as ATEsch.Thisisde inedas ollows o
yea :
ATEsch( )≡Ey |R=1−Ey |P og am does no exis .(8)
As abo e, conside again he speci ic case o yea 2, he only yea wi h eache skill da a:
ATEsch(2)=2δR+γR
1,2pR+δL(1+τ)+γL
1,2τpL/τ+δM(1+τ)+γM
1,2τpM(μ/τ)
+θ2,LpL(1−τ)/τ−θ2,DpD+θ2,MpM(μ/τ)−1,
17ACRsch( )is no well-de ined since eache s who mo e in o he 6218 schools ha e no ins umen al
a iable.
Quan i a i e Economics 16 (2025) Can eaching be augh ? 203
whe e μis he p opo ion o all mo e s who mo e o an APM school in yea 2 o yea
3, and he θ2,k e ms a e a e ages o θ2
j o yea 2 o ype k eache s.18 The i s line o
ATEsch(2)is he “di ec ” ea men e ec and he second is a “composi ion” e ec , which
accoun s o di e ences in a e age θbe ween like s, who mo e in o APM schools in yea
2, and dislike s, who mo e ou o APM schools in yea 2 (and also accoun s o changes in
he dis ibu ion o mo e s ac oss he wo ypes o schools, who compe e wi h like s o ge
in o APM schools and wi h dislike s o ge in o non-APM schools). No e ha ATEsch(2),
and mo e gene ally ATEsch( )wi h ≥2, also depends on τ.In ui i ely,τde e mines he
p opo ions o like s and mo e s in APM schools (and o dislike s and mo e s in non-
APM schools), ye his is no longe he case i he e a e no like s o dislike s, as explained
below.
The second ea men e ec o eache skills ha ocuses on schools is ITTsch;i
is simila o ATEsch excep ha he coun e ac ual is he skills o eache s in non-APM
schools:
ITTsch( )≡Ey |R=1−Ey |R=0.(9)
Fo yea 2, his is
ITTsch(2)=2δR+γR
1,2pR+δL(1+τ)+γL
1,2τpL/τ+δM(1+τ)+γM
1,2τpM(μ/τ)
−δDpD(τ/(1−τ))+δMτpM(1−μ)/(1−τ)
+θ2,LpL/τ+θ2,MpM(μ/τ)
−θ2,DpD/(1−τ)+θ2,MpM(1−μ)/(1−τ).
The i s wo lines a e he (ne ) ea men e ec ; he las wo a e he composi ion e ec .
As wi h ATEsch( ),ITT
sch( )depends on he p opo ion o schools ha a e ea ed (τ)
when ≥2.
3.3 T ea men e ec s o s uden lea ning
Nex , conside ea men e ec s on s uden skills. Assume ha he skill (measu ed by a
es sco e) o s uden i a he end o yea , deno ed by s
i, is de e mined by his o he
skill a he end o he p e ious yea (s −1
i) and he skills o his o he eache in yea (y
j),
whe e j is he eache ha s uden i had in yea , and πis he impac o eache skill on
s uden skills:
s
i=σs −1
i+πy
j. (10)
18To see whe e he μ/τ e m comes om, no e ha he numbe o eaching posi ions in a school a ely
changes. I he numbe o hose posi ions is ixed in all schools, his de ini ion o μ(whe e μis de e mined
by he applica ion p ocess ha also de e mines he p opo ions o eache s who a e like s, dislike s, mo e s,
and emaine s; see Sec ion 2.1), implies ha , among all eache s in APM and non-APM schools, he p opo -
ion who a e mo e s in APM schools in yea 2 o 3 is μpM. Focusing on APM schools, his p opo ion mus
be di ided by τ, yielding (μ/τ)pM. Simila de i a ions show he p opo ion o mo e s in non-APM schools
in yea 2 o 3 is [(1−μ)/(1−τ)]pM.
204 Cas o, Glewwe, He edia-Mayo, Maje owicz, and Mon e oQuan i a i e Economics 16 (2025)
Each school is andomly assigned o be ei he an APM (R =1) o non-APM (R =0)
school, an assignmen ha is ixed o e ime. Analysis o s uden skills is simpli ied by
he ac ha ew s uden s change schools (see Sec ion 4.2), and each school ollows i s
andom assignmen .
We de ine h ee ea men e ec s o s uden skills. The i s wo, ATEs ud and ITTs ud,
a e analogous o he wo ea men e ec s de ined o hei schools (ATEsch and ITTsch).
All h ee ea men e ec s o yea s 2 and 3 a e complex due o se e al possible “his o-
ies” o s uden s’ eache s in hose yea s. Fo example, in yea 2 a s uden ’s eache in
an APM school could be a like who was in an APM school in yea s 1 and 2, o a like who
was in a non-APM school in yea 1 bu in an APM school in yea 2. Ano he example is a
s uden in an APM school in yea 3; i he o she was augh by a ea ed eache in yea 1
( his is ce ain as he s uden was in an APM school in yea 1), and by a eache in yea 2
who had APM in yea 2 bu no yea 1, and by a eache in yea 3 who had APM in yea s
2 and 3 bu no yea 1, he o she was exposed o 4 yea s o eache coaching, and he
cumula i e lea ning gain om his exposu e is a e aged o e he 4 yea s. The gene al
de ini ion o ATEs ud o yea is
ATEs ud( )≡Es |R=1−Es |P og am does no exis . (11)
Applying his de ini ion o yea 1 yields ATEs ud(1)=πδ. Applying i o yea 3 ( ecall ha
es sco e da a exis only o 2016 and 2018) yields (see Appendix B in Cas o e al. (2024a)
o he de i a ions):
ATEs ud(3)=σATEs ud(2)+πATEsch(3)=σσATEs ud(1)+πATEsch(2)+πATEsch(3)
=σ2πδ +σπ2δR+γR
1,2pR+δL(1+τ)+γL
1,2τpL/τ
+δM(1+τ)+γM
1,2τpM(μ/τ)
+π3δR+3γR
1,2 +γR
1,2,3pR+δL(2+τ)+γL
1,2(2τ+1)+γL
1,2,3pL/τ
+δM(1+2τ)+γM
1,2τ(2+τ)+τ2γM
1,2,3pM(μ/τ)
+σπθ2,LpL(1−τ)/τ−θ2,DpD+θ2,MpM(μ/τ)−1
+πθ3,LpL(1−τ)/τ−θ3,DpD+θ3,MpM((μ/τ)−1).
Fo ATEs ud(3), he i s ou lines a e he ea men e ec , and he las wo lines a e he
composi ion e ec . Again, o =2o =3, ATEs ud( )depends on τ.
Tu n nex o ITT. The gene al de ini ion o yea is
ITTs ud( )≡Es |R=1−Es |R=0. (12)
Fo yea 1, ITTs ud(1)=ATEs ud(1)=πδ, as all eache s ollow hei schools’ andom
assignmen in yea 1. Fo yea 3, applying he gene al de ini ion yields (Appendix B in
Cas o e al. (2024a) gi es de ails):
ITTs ud(3)=σITTs ud(2)+πITTsch(3)=σσITTs ud(1)+πITTsch(2)+πITTsch(3)
=σ2πδ +σπ2δR+γR
1,2pR+δL(1+τ)+γL
1,2τpL/τ

Quan i a i e Economics 16 (2025) Can eaching be augh ? 205
+δM(1+τ)+γM
1,2τpM(μ/τ)
−δDpD(τ/(1−τ))+δMτpM(1−μ)/(1−τ)
+π3δR+3γR
1,2 +γR
1,2,3pR+δL(2+τ)+γL
1,2(2τ+1)+τγL
1,2,3pL/τ
+δM(1+2τ)+γM
1,2τ(2+τ)+τ2γM
1,2,3pM(μ/τ)
−πδDpD(τ/(1−τ))+δM2τ+τ2γM
1,2pM(1−μ)/(1−τ)
+σπθ2,LpL/τ+θ2,MpM(μ/τ)
−θ2,DpD/(1−τ)+θ2,MpM(1−μ)/(1−τ)
+πθ3,LpL/τ+θ3,MpM(μ/τ)
−θ3,DpD/(1−τ)+θ3,MpM(1−μ)/(1−τ).
The i s six lines a e he (ne ) ea men e ec , and he las ou a e he composi ion
e ec . No e again ha , o =2o 3, ha ITT
s ud( )depends on τ.
The hi d ea men e ec o s uden s is he (a e age) impac o an addi ional yea
o eache coaching on s uden lea ning, a e aged o e all addi ional yea s o ha coach-
ing ha a s uden expe iences. In e ec , his is a ans e o he ACR ch ea men e ec s
on eache skill on o s uden lea ning, which is complica ed by he many di e en “his-
o ies” a s uden can ha e o ea ed eache s in yea s 2 and 3. We call hese ea men
e ec s ACRs ud, hough hey di e om ACR ch (and so di e om he Ang is and Im-
bens ACR e ec s) since s uden s a e no di ec ly ea ed bu ins ead a e indi ec ly ea ed
by exposu e o ea ed eache s.
The gene al de ini ion o ACRs ud in yea (1, 2, o 3) is
ACRs ud( )≡Es |R=1−Es |R=0
Eh ch ( )|R=1−Eh ch ( )|R=0, (13)
whe e h ch ( )is he cumula i e “his o y” om yea 1 o yea o a s uden ’s exposu e o
eache s wi h APM coaching. Fo example, a s uden in a ea ed school in yea 2 had a
coached eache in yea 1, bu in yea 2 he eache could ha e 1 o 2 yea s o coaching
(e.g., 1 o a eache in a non-APM school in yea 1), so he s uden ’s h ch (2)could be 2
o 3. The expec ed alue o h ch ( )a e ages o e he ypes o eache s in he school om
yea 1 o yea .
Fo yea 1, ACRs ud(1)=ATTs ud( )=ITTs ud( )since all eache s ollow hei an-
dom assignmen in yea 1, so ACRs ud(1)=πδ. Fo yea 3, applying he de ini ion in (13)
yields
ACRs ud(3)=Es3|R=1−Es3|R=0
Eh ch (3)|R=1−Eh ch (3)|R=0
=ITTs ud(3)
1+5pR+(3+2τ)pL/τ +(2+3τ)pM(μ/τ)−2τpD/(1−τ)+3τpM(1−μ)/(1−τ).
206 Cas o, Glewwe, He edia-Mayo, Maje owicz, and Mon e oQuan i a i e Economics 16 (2025)
To unde s and his de i a ion, no e ha he nume a o is ITTs ud(3). The i s exp es-
sion in b acke s in he denomina o , 1 +5pR+(3+2τ)pL/τ +(2+3τ)pM(μ/τ),is
E[h ch (3)|R=1], he a e age cumula i e exposu e o yea s o eache coaching o a s u-
den in an APM school in yea 3. The “1 +” e m is exposu e o a coached eache in yea
1. In yea s 2 and 3, he p obabili y o ge ing a emaine eache is pR, and he p obabil-
i ies o ge ing a like o mo e eache a e pL/τ and pM(μ/τ), espec i ely. I a s uden
ge s a emaine eache in yea 2, he o she is exposed o 2 mo e yea s o accumula ed
coaching since ha eache has had 2 yea s o coaching by yea 2, and i he s uden ge s
a emaine eache in yea h ee he o she will ge 3 mo e yea s o accumula ed coaching,
o a o al o i e addi ional yea s (beyond yea 1). I he s uden ge s a like eache in
yea 2, he a e age like eache will ha e had (1+τ) yea s o coaching (one in yea 2 and
one mo e o a p opo ion τo hose eache s in yea 1), and i he s uden ge s a like
eache in yea 3, ha will expose him o he o an addi ional 2 +τyea s o accumula ed
coaching, so o e all exposu e o like eache s will p o ide 3 +2τyea s o accumula ed
coaching. Finally, exposu e o a mo e eache in yea 2 leads o 1 +τaddi ional yea s
o accumula ed coaching, and exposu e o a mo e in yea 3 adds ano he 1 +2τ(since
mo e s mo e andomly e e y yea ). Simila calcula ions o s uden s who andomly end
up in non-APM schools in yea 1 (and he nex 2 yea s) lead o accumula ed coaching
om dislike s and mo e s o 2τpD/(1−τ)+3τpM((1−μ)/(1−τ)).
As wi h ACR ch (2),ACR
s ud(3)is a pe yea e ec (a e aged o e he ele an yea s
o exposu e o coached eache s). To ob ain a cumula i e e ec o exposu e o ully
coached eache s in all 3 yea s, which is a weigh ed a e age o e he ou eache ypes
(whe e he weigh s a e p obabili ies o eache ypes being in ea ed schools), mul iply
ACRs ud(3)by 6.
3.4 T ea men e ec s i no like s o dislike s
The ea men e ec s o yea s 2 and 3 in Sec ions 3.2 and 3.3 a e much simple i he e
a e no like s o dislike s, lea ing only emaine s and mo e s. The equa ions simpli y o19
ATE ch (2)=2δ+γ1,2,whe eδ=δRpR+δMpMand γ1,2 =γR
1,2pR+γM
1,2pM,
ITT ch (2)=δ+pRδR+γR
1,2+pMτγM
1,2,
ACR ch (2)=δ+pRδR+γR
1,2+pMτγM
1,2/2pR+pM=ITT ch (2)/1+pR,
ATEsch(2)=2δR+γR
1,2pR+δM(1+τ)+γM
1,2τpM,
ITTsch(2)=δ+δR+γR
1,2pR+pMτγM
1,2.
No e ha ITTsch(2)=ITT ch (2),bu ATE
sch(2)= ATE ch (2).
ATEs ud(3)=σ2πδ +σπ2δR+γR
1,2pR+δM(1+τ)+γM
1,2τpM
+π3δR+3γR
1,2 +γR
1,2,3pR+δM(1+2τ)+γM
1,2τ(2+τ)+τ2γM
1,2,3pM,
19They ollow om he esul s in Sec ions 3.2 and 3.3:p
L=pD=0 and μ=τi he e a e no like s o
dislike s.
Quan i a i e Economics 16 (2025) Can eaching be augh ? 207
ITTs ud(3)=σ2πδ +σπ2δR+γR
1,2pR+δM+γM
1,2τpM
+π3δR+3γR
1,2 +γR
1,2,3pR+δM+γM
1,2τ2+τ2γM
1,2,3pM,
ACRs ud(3)=πσ2δ+(3+2σ)δR+(3+σ)γR
1,2 +γR
1,2,3pR+δM(σ+1)+γM
1,2τ(σ+2)+γM
1,2,3τ2pM
1+5pR+2pM
=ITTs ud(3)
1+5pR+2pM.
No e ha he e a e no composi ion e ec s o ATEsch(2),ITT
sch(2),ATE
s ud(3),and
ITTs ud(3). Also, he absence o like s and dislike s (pL=pD=0) implies ha he e a e
only emaine s and mo e s, and ha μ=τ(mo e s a e equally dis ibu ed o e APM
and non-APM schools since hey do no compe e wi h like s o dislike s o mo e in o an
APM o non-APM school).
3.5 Wha do OLS and IV eg essions es ima e?
Mos , bu no all, o hese ea men e ec s can be es ima ed by OLS o IV eg ession. We
ha e wo samples o eache s, one (impe ec ly) ollows he eache s who we e in APM
and non-APM schools in yea 1 (Sample 1), and he o he ocuses on he eache s in he
APM and non-APM schools in any gi en yea (Sample 2). OLS eg ession o Sample 1
eache s’ skills in yea on a cons an e m and a dummy a iable o assignmen o an
APM school in yea 1 yields an unbiased es ima e o he ITT ch ( ) ea men e ec .20 Fo
example, conside yea 2:
ˆ
βy
1OLS, =2=Ey2|R ch ,yea 1 =1−Ey2|R ch ,yea 1 =0
=δ+pRδR+γR
1,2+pLγL
1,2 +τpMγM
1,2 =ITT ch (2).
The “1” subsc ip indica es Sample 1 eache s. Appendix B in Cas o e al. (2024a)
p esen s his de i a ion, as well as hose o yea s 1 and 3. I also p esen s he de i a ions
o he o he OLS and IV es ima o s in his subsec ion, o all 3 yea s, and shows ha
OLS es ima ion applied o Sample 2 eache s es ima es ITT ch ( )( ecall ha ITT ch ( )=
ITTsch( )i he e a e no like s o dislike s).
Nex , conside IV es ima ion using Sample 1 eache s. Le TTo , deno e he numbe
o yea s ha a eache has pa icipa ed in he p og am up h ough yea . IV eg ession
uses andom assignmen as an ins umen o TTo , o es ima e he (a e age) impac o
a yea o exposu e o he p og am on eache skills. This yields unbiased es ima es o
ACR ch ( ). Fo yea 2:
ˆ
βy
1IV, =2=Ey2|R ch ,yea 1 =1−Ey2|R ch ,yea 1 =0
ETTo , 2 |R ch ,yea 1 =1−ETTo , 2 |R ch ,yea 1 =0
=δ+pRδR+γR
1,2+pLγL
1,2 +pMτγM
1,2/1+pR=ACR ch (2).
20Almos all o he eg essions in his pape ha e o he explana o y a iables, bu since andom assign-
men is by de ini ion unco ela ed wi h hese o he a iables, he i s line in he ˆ
βy
1OLS, =2equa ion s ill
holds by he F isch–Waugh heo em. Reg essions wi hou hese explana o y a iables (e.g., Table 6)yields
e y simila esul s.
208 Cas o, Glewwe, He edia-Mayo, Maje owicz, and Mon e oQuan i a i e Economics 16 (2025)
One can also apply OLS o Sample 2 eache s, he eache s who, in any gi en yea ,
each in he schools ha we e andomly assigned in yea 1 o be APM o non-APM
schools. An OLS eg ession o Sample 2 eache s’ skills in yea on a cons an and a
dummy o eaching in an APM school in yea yields an unbiased es ima e o ITTsch( ).
So, o yea 2:
ˆ
βy
2OLS, =2=Ey2|R=1−Ey2|R=0
=2δR+γR
1,2pR+δL(1+τ)+γL
1,2τpL/τ
−[δDpDτ/(1−τ)+pMδMμ−τ2/τ−τ2+μγM
1,2
+θ2,LpL/τ+θ2,MpM(μ/τ)
−θ2,DpD/(1−τ)+θ2,MpM(1−μ)/(1−τ)=ITTsch(2).
In gene al, IV es ima ion canno be used o Sample 2 eache s in yea 2 since some o
hose eache s mo ed in o bo h APM schools and non-APM schools ha we e no pa
o he ini ial andom assignmen , such as eache s wo king in monolingual mul ig ade
schools in yea 1 ha had ECE sco es abo e he h eshold ha de e mined eligibili y o
he andomized expansion (see Sec ion 2.3). These Sample 2 eache s ha e no ins u-
men , so IV es ima ion canno be done o Sample 2 eache s.
Nex , conside OLS eg ession o s uden es sco es, mo e speci ically eg essing
hose sco es on a cons an and a dummy indica ing being in an APM school. OLS e-
g ession o s uden s’ es sco es in yea on a cons an and a dummy o being en olled
in an APM school in yea yields an unbiased es ima e o ITTs ud( ). Fo yea s 1 and 3,
his implies ha
ˆ
βs
OLS, =1=Es1|R=1−Es1|R=0=πδ =ATEs ud(1)=ITTs ud(1)=ACRs ud(1),
ˆ
βs
OLS, =3=Es3|R=1−Es3|R=0
=σ2πδ +σπ2δR+γR
1,2pR+δL(1+τ)+γL
1,2τpL/τ
+δM(1+τ)+γM
1,2τpM(μ/τ)−δDpDτ/(1−τ)+δMτpM(1−μ)/(1−τ)
+π3δR+3γR
1,2 +γR
1,2,3pR+δL(2+τ)+γL
1,2(2τ+1)
+τγL
1,2,3pL/τ+δM(1+2τ)+γM
1,2τ(2+τ)+τ2γM
1,2,3pM(μ/τ)
−πδDpDτ/(1−τ)+δM2τ+τ2γM
1,2pM(1−μ)/(1−τ)
+σπθ2,LpL/τ+θ2,MpM(μ/τ)
−θ2,DpD/(1−τ)+θ2,MpM(1−μ)/(1−τ)
+πθ3,LpL/τ+θ3,MpM(μ/τ)
−θ3,DpD/(1−τ)+θ3,MpM(1−μ)/(1−τ)
=ITTs ud(3).
Quan i a i e Economics 16 (2025) Can eaching be augh ? 215
Figu e 2. Balance in eache cha ac e is ics o he o iginal and obse ed in yea 2 eache s
who wo ked in an e alua ion sample school in 2016 (Sample 1). No e: All eg essions include
UGEL ixed e ec s. S anda d e o s clus e ed a he school le el. Es ima es indica e di e ences
in he s anda dized cha ac e is ics o con ol and ea men g oups. Thick and hin lines indica e
90% and 95% con idence in e als, espec i ely. We do no p esen he di e ences in eache
expe ience and pedagogical deg ee o he o iginal sample because we do no ha e in o ma ion
on hose a iables o he eache s ha we e no obse ed a he end o yea 2.
Figu e 3. Balance in school cha ac e is ics in he o iginal and obse ed e alua ion sample
schools. No e: All eg essions include UGEL ixed e ec s. Es ima es indica e di e ences in he
s anda dized cha ac e is ics o con ol and ea men g oups. Thick and hin lines indica e 90%
and 95% con idence in e als, espec i ely.

216 Cas o, Glewwe, He edia-Mayo, Maje owicz, and Mon e oQuan i a i e Economics 16 (2025)
We do no compa e Sample 2 eache s’ baseline cha ac e is ics in 2017 (yea 2) be-
ween APM and non-APM schools o check o balance a baseline because andom
assignmen o schools in 2016 (yea 1) does no ensu e such balance ac oss hese wo
g oups o schools in yea 2. In pa icula , i ce ain ypes o eache s sel -selec in o APM
o non-APM schools in yea 2, Sample 2 eache s’ baseline cha ac e is ics may be co e-
la ed wi h he ea men s a us o he schools whe e hey wo ked in yea 2.
Thi d, we used da a om exams gi en o eache s in 2014 and 2015 ha we e used
as pa o he p ocess by which con ac eache s could become pe manen ci il se -
ice eache s and ci il se ice eache s apply o p omo ion. We ound ha each-
e s who sco ed highe on hose exams we e less likely o mo e om o he schools in
Pe u o ei he an APM school o a non-APM school in ou 6218 andomized expansion
schools, and also ha eache s who sco ed highe we e less likely o mo e ou o he
6218 andomized expansion schools o o he schools in Pe u (see Table A10 in Cas o
e al. (2024a)). Mos impo an ly, he e is no ela ionship be ween hese es sco es and
whe he he eache s mo ed o an APM o a non-APM school, which shows ha he e is
no sys ema ic mo emen o be e (o wo se) eache s in o APM o non-APM schools.
Fo he s uden -le el da a, he e is li le a i ion. Using adminis a i e da a on en-
ollmen , we ound almos all he s uden s who s a ed in ou sample in 2016 (yea 1).
S uden u no e , unlike eache u no e , is ela i ely a e in u al p ima y schools, es-
pecially among hose a ge ed by APM since almos 95% a e in u al a eas whe e he e
a e e y ew schools o choose om. Excluding s uden s in hei inal yea o p ima y
school, and a e aging o e he yea s 2013 o 2016, only 6.9% o he s uden s in ou 6218
p ima y schools in a gi en yea we e no in he same school in he nex yea .
4.3 Teache u no e and he p opo ions o he ou ypes o eache
We use adminis a i e da a on he loca ion o eache s as well as he amewo k es ab-
lished in Sec ion 3 o examine eache u no e and he p opo ions o he ou ypes o
eache s in he sample.22 Table 4shows he 2016–2017 u no e beha io o Sample 1
eache s (i.e., he 12,18923 eache s in he 6218 andomized schools in 2016).
By compa ing he p opo ions o eache s in APM and non-APM schools in yea 1
who mo ed o an APM school in yea 2 ( he di e ence be ween equa ions (A4) and (A1)
in Table A5 o Cas o e al. (2024a)), we es ima e ha σpL=−0.024, whe e σis he p o-
po ion o like s in an APM school in a gi en yea (e.g., yea 1) who emain in he same
school in he nex yea (e.g., yea 2), a he han mo ing o a di e en APM school.24
22Table A5 in Cas o e al. (2024a) shows whe e eache s assigned o APM and non-APM schools in he
andomiza ion yea end up in each ype o school 1 yea la e acco ding o hei ype and ini ial so ing.
23Table 4excludes 951 eache s (7.8% o he 12,189 eache s) in he 2016 andomiza ion sample who
we e no ound in he adminis a i e da a in 2017; hey mos likely le he public educa ion sys em.
24To see how his was calcula ed, his de ini ion o σimplies ha he p opo ion o like s who mo e o
ano he APM school is 1-σ.Recall ha μis he p opo ion o mo e s in any school who ( andomly) mo e o
an APM school in he ollowing yea . Thus, o all eache s in an APM school in yea 1, pL(1−σ)+pMμis he
p opo ion who mo e o o he APM schools in yea 2, and ou da a show ha his p opo ion is 0.121 (see
Table A5 in Cas o e al. (2024a)). Simila ly, he p opo ion o eache s in non-APM schools in yea 1 who
mo e o an APM school in yea 2 is pL+pMμ, and his p opo ion equals 0.097 in ou da a. The di e ence
Quan i a i e Economics 16 (2025) Can eaching be augh ? 217
Table 4. Dis ibu ion o yea 1 eache s by hei des ina ion school in yea 2.
T ea men A m in 2016 2016–2017 Tu no e Teache s Pe cen
APM school S ayed in he same school 4222 63.2
Mo ed o an APM school 806 12.1
Mo ed o a non-APM school 1649 24.7
To al 6677 100.0
Non-APM school S ayed in he same school 2847 62.4
Mo ed o an APM school 440 9.7
Mo ed o a non-APM school 1274 27.9
To al 4561 100.0
Simila ly, by compa ing he p opo ions o eache s in APM and non-APM schools who
mo ed o a non-APM school om yea 1 o yea 2 ( he di e ence be ween equa ions A5
and A2 in Table A5 o Cas o e al. (2024a)), we es ima e ha νpDequals −0.032, whe e
νis he p opo ion o dislike s in a non-APM school in a gi en yea (e.g., yea 1) who e-
main in he same school in he nex yea (e.g., yea 2), a he han mo ing o a di e en
non-APM school.
Bo h σpLand νpDa e e y close o 0. Fo σpL o equal 0, ei he σo pL(o bo h) mus
equal 0. I σ=0, hen all like s change om one APM school o ano he APM school in
he ollowing yea . Simila ly, ν=0 implies ha all dislike s al eady in a non-APM school
in a gi en yea mo e o ano he non-APM school he nex yea . Such u no e seems
e y unlikely since mos eache s (63%) emained in he same school e en be o e he
andomized expansion o he APM p og am (see Table 5). By de ini ion, like s and dis-
like s ha e s ong incen i es o mo e be ween schools i , in yea 1, hey ind hemsel es
in a school ha is he opposi e o hei p e e ence (like s s a ing in a non-APM school
o dislike s s a ing in an APM school), bu when hey a e placed in he school o hei
p e e ed ype, we would expec u no e o be simila o wha was obse ed in he sam-
ple be o e he p og am s a ed, 36.6%, no 100%. The e o e, bo h σ=0andν=0 seem
e y unlikely. The o he op ion, which we conside he mos ealis ic, is ha pLand pD
a e equal o 0: he e a e no like s o dislike s.
The conclusion ha he e a e no like s o dislike s is a s ong claim, so we o e
wo addi ional pieces o suppo ing e idence. Fi s , we analyze how eache u no e
changed o e ime. I he e a e like s and dislike s, we would expec an inc eased mo e-
men o eache s in he i s yea a e he andomized expansion o APM as like s and
dislike s mo e o he schools o hei p e e ed ype. Since schools s ick o hei andom
assignmen in la e yea s, we would expec ha mos o his ex a u no e would occu
in yea 2 (2017), al hough some could occu in la e yea s i some “po en ial” like s and
dislike s a e unable o mo e o hei p e e ed schools in yea 2. The e o e, i he e a e
like s o dislike s, he e should be a la ge spike in he numbe o eache s mo ing ac oss
ea men a ms be ween 2016 and 2017, ollowed by a g adual e u n o egula le els
be ween hese wo p opo ions equals σpL,whichis−0.024 in ou da a. No e ha his di e ence includes
he es ima es o he men ioned pa ame e s as well as andom di e ences in p opo ions ha a ise due o
sampling. Thus, small nega i e es ima es a e possible i a pa ame e equals 0.
218 Cas o, Glewwe, He edia-Mayo, Maje owicz, and Mon e oQuan i a i e Economics 16 (2025)
Table 5. Teache u no e be ween APM and non-APM schools.
APM schools 2015 o 2016 2016 o 2017 2017 o 2018 2018 o 2019
S ayed in same school 63% 65% 62% 65%
Mo ed o an APM school 8% 10% 10% 9%
Mo ed o a Non-APM school 14% 14% 15% 12%
Mo ed ou o a ge schools 15% 12% 14% 13%
Non-APM schools 2015 o 2016 2016 o 2017 2017 o 2018 2018 o 2019
S ayed in same school 63% 66% 62% 65%
Mo ed o an APM school 11% 12% 12% 11%
Mo ed o a Non-APM school 11% 10% 11% 10%
Mo ed ou o a ge schools 15% 12% 15% 14%
All schools 2015 o 2016 2016 o 2017 2017 o 2018 2018 o 2019
S ayed in same school 63% 65% 62% 65%
Mo ed o an APM school 10% 11% 11% 10%
Mo ed o a Non-APM school 12% 12% 13% 11%
Mo ed ou o a ge schools 15% 12% 14% 14%
No e: This able shows he yea - o-yea u no e s a us o eache s who s a ed each 2-yea pe iod in a school wi hin one
o he 6218 andomized expansion schools.
o mo emen ( om mo e s andomly mo ing be ween APM and non-APM schools, and
like s and dislike s mo ing o ano he school o hei p e e ed ype). Table 5shows he
e olu ion o eache mo emen ac oss ea men a ms om 2015 o 2019. The e is no
spike in he mo emen om APM o non-APM schools om 2016 o 2017; i emains a
14%, he same a e as om 2015 o 2016, and sligh ly less han om 2017 o 2018. A simi-
la pa e n holds o mo emen om non-APM o APM schools, which om 2016 o 2017
inc eased sligh ly o 12% ( om 11% om 2015 o 2016) and emained a 12% om 2017
o 2018. These ends a e consis en wi h he claim o no like s o dislike s.
A second piece o addi ional e idence o he claim o no like s o dislike s is com-
pa isons o he cha ac e is ics o eache s who wo ked in he andomized pedagogical
skill sample in 2017 (Sample 2). I he e we e like s o dislike s, one would expec he
cha ac e is ics o eache s o di e be ween APM and non-APM schools a e u no e ,
as like s would be only in APM schools and dislike s would be only in non-APM schools.
Figu e 4shows es ima es o ea men e ec s o APM on a wide se o eache cha ac-
e is ics in he andomized expansion sample in 2017. We ind no e ec o any o he
cha ac e is ics, sugges ing ha he e was no sys ema ic selec ion o eache s in o ei he
APM o non-APM schools, u he suppo ing he claim o no like s o dislike s.
5. The ea men e ec s o APM
5.1 Teache skills
O e all eache skills This subsec ion p esen s es ima es o E[y2|R ch ,yea 1 =1]−
E[y2|R ch ,yea 1 =0], ha is, es ima es o ITT ch (2)in equa ion (6), and E[y2|R=1]−
Quan i a i e Economics 16 (2025) Can eaching be augh ? 219
Figu e 4. T ea men e ec s on he composi ion o eache cha ac e is ics among he eache s
in andomized pedagogical skill sample schools in 2017 (Sample 2). No e: All eg essions include
UGEL ixed e ec s. Es ima es indica e di e ences in he s anda dized cha ac e is ics o con ol
and ea men g oups. Thick and hin lines indica e 90% and 95% con idence in e als, espec-
i ely.
E[y2|R=0], es ima es o ITTsch(2)in equa ion (9), using OLS eg essions o he 455
Sample 1 eache s and he 640 Sample 2 eache s (see Table 3), espec i ely. We also
p esen he es ima es ob ained by eg essing y2on he p edic ed yea s o ea men , in-
s umen ed by andom assignmen in yea 1, using Sample 1 eache s. As explained in
Sec ion 3.5, his IV app oach p o ides a consis en es ima e o he ACR ch (2) ea men
e ec . Fo all es ima es, he dependen a iable, y2, is an index o pedagogical skills ha
a e ages he s anda dized sco es o he eigh indica o s ob ained om class oom obse -
a ions (see Sec ion 2.3). We p esen es ima es wi h and wi hou eache cha ac e is ics
as co a ia es when using Sample 1.25 Table 6p esen s hese esul s.
Be o e discussing he esul s, ecall he claim (Sec ion 4.3) ha ou popula ion o
eache s has no like s o dislike s. Recall also (Sec ion 3.4) ha , i he e a e no like s
o dislike s, bo h ˆ
βy
1OLS, =2and ˆ
βy
2OLS, =2es ima e ITT ch (2), which equals ITTsch(2).
Thus, all OLS es ima es in Table 6consis en ly es ima e he same pa ame e .
The i s and second columns o Table 6p esen es ima es o ITT ch (2).Thees i-
ma e in column (1), which does no con ol o eache cha ac e is ics, indica es ha
o e ing APM o 2 yea s inc eases eache s’ pedagogical skills by 0.28 s anda d de ia-
ions (s.d.). The es ima e in column (2), when eache cha ac e is ics a e added as co-
a ia es, is e y simila : 0.30 s.d. The es ima e o ITTsch(2)in column (3), 0.20 s.d., is
25The use o eache cha ac e is ics as co a ia es is app op ia e only o Sample 1 because cha ac e is-
ics o Sample 2 eache s can be a ec ed by he ea men . In Table A6 o Cas o e al. (2024a), we es o
in e ac ions be ween he ea men s a us and he cha ac e is ics o Sample 1 eache s. We ind no e idence
o he e ogenei y by eache expe ience, ype o con ac , posi ion in he eache ca ee , o sex. These esul s
suppo he linea i y assump ion o he eache skills p oduc ion unc ion in equa ion (1).
220 Cas o, Glewwe, He edia-Mayo, Maje owicz, and Mon e oQuan i a i e Economics 16 (2025)
Table 6. Agg ega e skill: o dina y leas squa es (OLS) es ima es and IV es ima es.
O dina y Leas Squa es Es ima es IV Es ima es
Sample 1 Sample 2 Sample 1
(1) (2) (3) (4) (5)
T ea men 0.275 0.300 0.197 0.152 0.166
(0.103) (0.097) (0.098) (0.052) (0.048)
[0.008] [0.002] [0.046] [0.003] [0.001]
Expe ience – 0.000 – – −0.000
(0.009) (0.008)
Con ac eache – 0.139 – – 0.133
(0.155) (0.138)
Teache ca ee le el – 0.109 – – 0.107
(0.044) (0.039)
Sex (men =1) – −0.300 – – −0.301
(0.095) (0.085)
Age – −0.028 – – −0.027
(0.009) (0.008)
R20.29 0.37 0.23 0.29 0.37
Sample size 455 455 640 455 455
No e: All eg essions include UGEL ixed e ec s. S anda d e o s clus e ed a he school le el a e p esen ed in pa en heses,
and p- alues shown in b acke s.
somewha lowe , e en hough ITTsch(2)should equal ITT ch (2). Recall ha Sample 1
eache s had high a es o a i ion due o di icul ies inding eache s who mo ed; his
implies ha emaine s a e e y likely o e ep esen ed in Sample 1. In con as , he p o-
po ions o emaine s and mo e s in Sample 2 should co espond o hei p opo ions
in he popula ion o eache s in he 6218 andomized expansion schools. Thus, he col-
umn (3) es ima e is ou p e e ed es ima e o ITT ch (2), which also equals ITTsch(2); he
e ec a e 2 yea s on eache s’ agg ega e pedagogical skill o assigning hem o an APM
school in yea 1 is a 0.20 s.d. inc ease in hose skills
Ou es ima e ha ITT ch (2)=ITTsch(2)=0.20 sheds some ligh on o he pa a-
me e s o in e es . Recall ha , in gene al, ATE ch (2)≥ITT ch (2), and i he e a e no lik-
e s and dislike s hen ATEsch(2)≥ITTsch(2). Thus, he e ec o 2 yea s o APM coaching
on he agg ega e pedagogical p ac ice o he a e age eache , ATE ch (2), and he e ec
o APM on he agg ega e pedagogical p ac ice o he eache s in APM schools in yea 2,
ATEsch(2), a e a leas as la ge as, and likely la ge han, 0.2 s.d.
Columns (4) and (5) in Table 6p esen ou IV es ima es o ACR ch (2)using Sample
1 eache s. They show ha , a e aging o e all yea s o coaching ecei ed, an addi ional
yea o coaching inc eases by 0.15 o 0.17 s.d. he a e age pedagogical skill o all each-
e s, bu his a e age gi es emaine s a “double weigh ” because andom assignmen o
an APM school induces hem o ob ain 2 yea s o coaching. Consis en wi h he ac ha
ACR ch (2)equals ITT ch (2)/(1+pR), his IV es ima e, which is a pe yea es ima e, is
somewha la ge han (hal o ) he Sample 1 es ima e o ITT ch (2),anes ima eo cu-
mula i e impac o e 2 yea s, in column (2).

Quan i a i e Economics 16 (2025) Can eaching be augh ? 221
Speci ic pedagogical skills The discussion hus a has ocused on he agg ega e index
o pedagogical skills, bu one can also es ima e ITT ch (2) o each o he eigh mo e
speci ic pedagogical skills shown in Table 1.Table7shows hese esul s. To minimize
spu ious s a is ical signi icance due o mul iple hypo hesis es ing, Table 7also p esen s
adjus ed p- alues, using he Romano and Wol (2016)s epdownme hod oaccoun o
mul iple hypo hesis es ing; hese a e in b acke s below he s anda d e o s.
The es ima es in Table 7indica e ha he bigges impac o assigning eache s o he
APM p og am, in e ms o bo h he size and he s a is ical signi icance o he es ima ed
pa ame e s, is on eache s’ lesson planning; he poin es ima es a e 0.34 s.d. o Sample
1 and 0.39 s.d. o Sample 2. The e is also e idence ha APM aises eache s’ pedagogical
skills in de eloping hei s uden s’ c i ical hinking, al hough he s a is ical signi icance
is a bes only ma ginal a e con olling o mul iple hypo hesis es ing.
5.2 S uden lea ning
This subsec ion explo es he impac o he APM coaching p og am on s uden lea n-
ing, as measu ed by he Na ional S uden E alua ion (ECE) aken 1 and 3 yea s a e he
p og am began (i.e., 2016 and 2018). We compa e s uden es sco es in he APM and
non-APM schools in he much la ge s uden es sco e sample. This sample is no e-
s ic ed o he 340 schools wi h pedagogical p ac ices da a, bu i is es ic ed o hose
schools ha pa icipa ed in he 2016 ECE and he 2018 ECE. As explained ea lie , only
schools wi h i e o mo e s uden s in he ele an g ade ake he ECE, so we ha e es
sco es o only 2567 o he 6218 andomized expansion schools.
Table 8p esen s es ima es o he APM coaching p og am’s ea men e ec s on a -
e age ECE sco es o he sample o 2567 schools in 2016 and 2018, a e 1 and 3 yea s
o coaching. The ECE is aken a he end o he school yea (which is also he end o
he calenda yea ), so he 2016 ECE yields es ima es o he APM p og am’s impac a e
1 yea o s uden s in g ade 2. All eache s complied wi h hei andom assignmen in
2016, so his is an es ima e o ATEs ud(1), he a e age ea men e ec o 1 yea o APM
on s uden lea ning. In 2018, he ECE was conduc ed again, bu his ime i was done in
g ade 4, which in gene al con ains he same s uden s who we e es ed in 2016 in g ade
2, excep ha i excludes s uden s who epea ed g ade 2 o 3 (abou 7–8% o s uden s e-
pea each yea ). The 2018 ECE allows us o es o he impac o he p og am a e 3 ull
yea s o implemen a ion. S uden s almos always comply wi h ea men assignmen s,
ye many eache s swi ched schools be ween 2016 and 2018, so we canno es ima e he
a e age ea men e ec , ATEs ud(3) o 3 yea s. Ra he , we es ima e ITTs ud(3),whichis
alowe boundo ATE
s ud(3)i he e a e no like s o dislike s.
5.2.1 Resul s a e 1yea Table 8p esen s es ima es o he p og am’s ea men e ec s
on s anda dized es sco es o ma hema ics and eading comp ehension.26 Columns
26Recall ha ECE sco es exis only o schools wi h i e o mo e s uden s in a gi en g ade; his g ea ly
educes he numbe o schools in he s uden es sco e sample. Table A1 in Cas o e al. (2024a)shows ha
almos all cha ac e is ics o he schools wi h es sco es a e e y simila o hose o he 6218 andomized
expansion schools. The baseline balance in Table 2is o his smalle subsample o schools, which is he
ele an sample o analysis.
222 Cas o, Glewwe, He edia-Mayo, Maje owicz, and Mon e oQuan i a i e Economics 16 (2025)
Table 7. Disagg ega ed skills: O dina y leas squa es es ima es.
(1) (2) (3) (4) (5) (6) (7) (8)
Lesson
Planning
Time
Managemen
C i ical
Thinking
S uden
Pa icipa ion
Class
Feedback
W i en
Feedback
Class oom
Rela ionships
Beha io
Managemen
Panel A. Sample 1
T ea men 0.338 0.083 0.248 0.162 0.199 0.136 0.069 0.114
(0.106) (0.108) (0.092) (0.103) (0.107) (0.096) (0.112) (0.098)
[0.018] [0.692] [0.064] [0.474] [0.339] [0.499] [0.692] [0.561]
N 448 450 450 450 450 448 450 450
R-squa ed 0.307 0.221 0.281 0.364 0.371 0.332 0.263 0.277
Panel B. Sample 2
T ea men 0.387 −0.073 0.186 0.062 0.094 0.173 0.022 0.019
(0.091) (0.099) (0.090) (0.089) (0.103) (0.097) (0.091) (0.088)
[0.002] [0.917] [0.274] [0.917] [0.898] [0.428] [0.966] [0.966]
N 633 633 633 632 633 631 633 632
R-squa ed 0.245 0.171 0.200 0.260 0.277 0.236 0.209 0.238
No e: E ec s a e measu ed in s anda d de ia ions. Reg essions o panel A include he ollowing con ol a iables: expe ience, con ac eache , eache ca ee le el, sex, and age. All
eg essions include UGEL ixed e ec s. S anda d e o s clus e ed a he school le el a e epo ed in pa en heses and adjus ed p- alues o mul iple hypo heses es ing a e epo ed in
b acke s. We calcula e he adjus ed p- alues using he s epdown me hod o Romano and Wol (2016).
Quan i a i e Economics 16 (2025) Can eaching be augh ? 223
Table 8. Resul s on s uden lea ning a e 1 and 3 yea s o coaching.
Ma hema ics Reading
1 Yea 3 Yea s Combined 1 Yea 3 Yea s Combined
OLS OLS IV IV OLS OLS IV IV
(1) (2) (3) (4) (5) (6) (7) (8)
T ea men 0.106 0.114 0.075 0.100
(0.034) (0.033) (0.032) (0.031)
[0.002] [0.001] [0.019] [0.001]
Cumula i e yea s ea ed 0. 030 0.107 0.027 0.076
(0.009) (0.034) (0.008) (0.032)
[0.001] [0.002] [0.001] [0.017]
Cumula i e yea ea ed ×
yea 3 dummy a iable
−0.075 −0.049
(0.032) (0.029)
[0.018] [0.095]
Sum o abo e wo ows 0.032 0.027
(0.009) (0.008)
[0.000] [0.001]
Coe icien on andom
assignmen in i s -s age
eg ession
3.739 3.739
(0.048) (0.048)
F-s a is ic ( o cumula i e
yea s ea ed)
6123 5315 6127 5316
F-s a is ic ( o cumula i e)
yea s ea ed ×yea 3)
3854 3856
Con ol Mean 0.003 0.004 0.004 0.004 0.004 0.003 0.003 0.004
Obse a ions 22,198 18,261 18,261 40,459 22,199 18,275 18,275 40,474
Schools 2547 2053 2053 2547 2547 2053 2053 2547
R20.142 0.182 0.184 0.143 0.162 0.168 0.169 0.153
No e: This able shows ea men e ec s o he coaching p og am on s anda dized s uden es sco es. Columns 1 and 5
show he ITT e ec s a e 1 yea o ea men in 2016, while columns 2 and 6 show he ITT e ec s a e 3 yea s o ea men
in 2018. Columns 3 and 7 p esen 2SLS es ima es o ACR using he andom ea men assignmen as an ins umen o he
o al coaching yea s o which s uden s we e exposed h ough hei eache s o e he cou se o 3 yea s. Finally, columns 4 and 8
combined he IV eg essions o yea s 1 and 3 (because o almos pe ec compliance in yea 1, IV and OLS es ima es a e almos
iden ical); see he ex o how o in e p e he coe icien s o hese eg essions. All speci ica ions include school dis ic (UGEL)
ixed e ec s and con ol o school size (numbe o eache s and s uden s), which is no balanced a baseline (See Table A3 o
addi ional speci ica ions). All esul s use s anda dized exam sco es and can be in e p e ed as s anda d de ia ions. Reg essions
a e un a he s uden le el, wi h obus s anda d e o s, clus e ed by school, p esen ed in pa en heses, and p- alues shown in
b acke s.
(1) and (5) show es ima es o ATEs ud(1)a e 1 yea o implemen a ion, columns (2),
(3), (6), and (7) show ITT and ACR es ima es a e 3 yea s o he p og am, and columns
(4) and (8) p esen combined ACR esul s o yea s 1 and 3. While he p og am was de-
signed by he Minis y o Educa ion, i was implemen ed by each local school dis ic
(UGEL),27 so ou p e e ed speci ica ion, shown in his able, includes school dis ic
ixed e ec s, which also con ol o any di e ences in ac ual p og am implemen a ion
27Pe u’s 225 school dis ic s (UGELs) a e managed by school boa ds, which implemen educa ion poli-
cies in hei dis ic s. Each UGEL is o e seen by i s Regional Educa ion Boa d (Di ección de Educación
Regional).
224 Cas o, Glewwe, He edia-Mayo, Maje owicz, and Mon e oQuan i a i e Economics 16 (2025)
wi hin each egion. All Table 8 eg essions also con ol o school size (numbe o each-
e s and s uden s), which was sligh ly unbalanced a baseline. We clus e s anda d e o s
a he school le el in all eg essions, ollowing Abadie, A hey, Imbens, and Woold idge
(2023), since he ea men is assigned a he school le el.
The APM coaching p og am has signi ican ly posi i e impac s on s uden lea ning.
A e 1 yea , a e age es sco es inc ease by 0.106 and 0.075 s anda d de ia ions (s.d.)
in ma h and eading comp ehension, espec i ely. These a e a e age ea men e ec s,
ATEs ud(1), and hey sugges ha coaching ha p o ides egula , indi idualized suppo
o eache s can be an e ec i e policy o inc ease s uden lea ning. Fo pe spec i e, no e
ha he e ec a e 1 yea is simila in magni ude o he median e ec on lea ning ou -
comes o 234 educa ion s udies in low and middle income coun ies e iewed by E ans
and Yuan (2022). And when compa ed o he median o la ge s udies ( hose wi h o e
5000 s uden s), he e ec o he APM p og am a e only 1 yea is almos double ha
median e ec (0.05 s.d.).
Table A3 in Cas o e al. (2024a) shows how es ima es change when using egional,
a he han school dis ic , ixed e ec s, and when excluding con ols. Bo h o hose
changes educe he size o he coe icien sligh ly, bu he esul s a e gene ally obus
o hese changes.28 Table A3 includes ano he speci ica ion, column (4), ha adds o he
analysis he panel da a a ailable om 2010 o 2018 and adds school-le el ixed e ec s
and s a e-speci ic ime ends, wi hou any con ols; i s esul s a e e y close o hose o
main OLS speci ica ion in Table 8.
5.2.2 2 esul s a e 3yea s Columns (2) and (6) o Table 8show he e ec s o he APM
p og am in 2018, a e 3 yea s. Recall ha in 2018 he s anda dized es is o g ade 4, so
ha , excep o epea e s, we ollow he same s uden s obse ed in 2016 in g ade 2 a e
2 mo e yea s o exposu e o APM. The es ima ed p og am e ec s, which a e now ITT
e ec s (ITTs ud(3)) and so a e lowe bounds o ATE (ATEs ud(3)), emain posi i e a e
3 yea s o he p og am and a e sligh ly highe ( han he es ima es a e 1 yea shown in
columns (1) and (5)): 0.114 s.d. o ma h, 0.100 s.d. o eading comp ehension.
These ITT esul s show he a e age e ec on s uden s lea ning a e 3 yea s o
schools ha we e andomly assigned o he APM p og am in 2016. Ye he exposu e o
s uden s o ea ed eache s and, he e o e, he e ec i e ea men dose, di e s widely
among APM schools as a esul o eache u no e . To es ima e he impac on s uden s
o being exposed o 1 mo e yea o eache coaching, we use andom assignmen in 2016
o ins umen s uden s’ exposu e o coached eache s in each school. We ha e da a on
eache s’ school assignmen s, so we cons uc ed a a iable ha cap u es he in ensi y
o coaching o he eache s p esen in each yea (since he p og am s a ed) in a gi en
school. This inco po a es he coaching his o y o all eache s ha he s uden s had o e
hecou seo 3yea s.
29
28The excep ion is eading comp ehension sco es a e 1 yea o APM; hey a e signi ican only i con ols
a e included. Ye he ea men e ec s a e h ee yea s a e obus e en when excluding con ols o bo h
subjec s.
29S ic ly speaking, we cons uc and a e age “his o y” o e all eache s in a gi en school in a gi en yea ,
since we canno ma ch s uden s o indi idual eache s. No e, howe e , ha 20% o he schools in ou s u-
den es sco e sample had only one eache , so o hese schools we a e ma ching s uden s o hei speci ic
eache .
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