Beh man, Je e R.; Pa ke , Susan; Todd, Pe a; Zhang, Weilong
A icle
P ospe ing h ough p ospe a: A dynamic model o CCT
impac s on educa ional a ainmen and achie emen in
Mexico
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: Beh man, Je e R.; Pa ke , Susan; Todd, Pe a; Zhang, Weilong (2025) : P ospe ing
h ough p ospe a: A dynamic model o CCT impac s on educa ional a ainmen and achie emen in
Mexico, Quan i a i e Economics, ISSN 1759-7331, The Econome ic Socie y, New Ha en, CT, Vol. 16,
Iss. 1, pp. 133-183,
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Quan i a i e Economics 16 (2025), 133–183 1759-7331/20250133
P ospe ing h ough P ospe a: A dynamic model o CCT impac s
on educa ional a ainmen and achie emen in Mexico
Je e R. Beh man
Depa men o Economics, Uni e si y o Pennsyl ania
Susan W. Pa ke
School o Public Policy, Uni e si y o Ma yland
Pe a Todd
Depa men o Economics, Uni e si y o Pennsyl ania, NBER, HCEO, and IZA
Weilong Zhang
Facul y o Economics, Uni e si y o Camb idge
This pape de elops and es ima es a dynamic model, which in eg a es alue-
added and school-choice models, o e alua e g ade-by-g ade and cumula i e im-
pac s o he Mexican P ospe a condi ional cash ans e (CCT) p og am on edu-
ca ional achie emen . The empi ical applica ion ad ances he p e ious li e a u e
by es ima ing policy impac s on lea ning, accoun ing o dynamic selec i e school
a endance, and inco po a ing bo h obse ed and unobse ed he e ogenei y. A
dynamic amewo k is c i ical o es ima ing cumula i e lea ning e ec s because
lagged achie emen s a e impo an de e minan s o cu en achie emen s. The
model is es ima ed using ich na ionwide Mexican adminis a i e da a on school-
ing p og ession and ma hema ics and Spanish es sco es in g ades 4–9 along wi h
s uden and amily su ey da a. The es ima es show signi ican CCT impac s on
lea ning and educa ional a ainmen , pa icula ly o s uden s om poo e house-
holds. Resul s show ha eleseconda y schools (dis ance lea ning) play a c ucial
ole in acili a ing school a endance and in os e ing skill accumula ion.
Keywo ds. Condi ional cash ans e s, dynamic modeling, educa ional a ain-
men , lea ning achie emen , Mexico.
Je e R. Beh man: [email p o ec ed]
Susan W. Pa ke : [email p o ec ed]
Pe a Todd: [email p o ec ed]
Weilong Zhang: [email p o ec ed]
We a e g a e ul o inancial suppo om NSF awa d 1948943 and om he Uni e si y o Pennsyl ania
School o A s and Sciences in e nal g an s “Making a Di e ence in Di e se Communi ies” and he “Dean’s
Global Inqui ies Fund.” We also hank Gab ielle Vasey, Rod igo Deiana, Eliza e a B o e , Pina Gok as, Mi a
Po e -Schwa z, and E ika T e ino-Al a ado o esea ch assis ance. We hank Hec o Robles Vasquez o
p epa ing da abases and o assis ance in wo king wi h hese da a. We hank Miguel Szekely o con e -
sa ions abou he Mexican educa ional sys em. This pape was p esen ed a he Uni e si y o Camb idge,
he Uni e si y o A izona, he Uni e si y o Ma yland, McGill Uni e si y, he Uni e si y o Pennsyl ania, he
S an o d Ins i u e o Theo e ical Economics, and he Uni e si y o Glasgow. We hank E ic F ench, Magne
Mogs ad, and Ch is ophe Tabe o help ul sugges ions.
©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/QE2291
134 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
JEL classi ica ion. C53, I25, I38, J24.
1. In oduc ion
Condi ional cash ans e (CCT) p og ams aim o alle ia e cu en po e y h ough
ans e s o poo amilies and o educe u u e po e y by making hese ans e s con-
di ional on in es men s in he human capi al o child en and you h. In 1998–2000, a
la ge-scale andomized e alua ion o he Mexican PROGRESA CCT p og am demon-
s a ed subs an ial impac s on schooling en ollmen and a ainmen , child wo k, and
amily income (Pa ke and Todd (2017)). These indings con ibu ed o a la ge scaling-
up in Mexico and an imp essi e adop ion o simila p og ams in mo e han 60 coun ies
on i e con inen s (Fiszbein and Schady (2009)).
This pape analyzes he unde s udied, subs an i e ques ion o whe he CCTs im-
p o e lea ning by de eloping and es ima ing a dynamic model o academic achie e-
men and school p og ession. Se e al s udies, using a ious me hods including he o ig-
inal expe imen , ma ching and s uc u al dynamic models, ha e examined he impac s
o PROGRESA/Opo unidades/P ospe a on school en ollmen and, in some cases, on
longe - e m schooling a ainmen (e.g., Schul z (2004), Beh man, Sengup a, and Todd
(2005), Beh man, Pa ke , and Todd (2005,2009), Todd and Wolpin (2006), A anasio,
Meghi , and San iago (2012), Pa ke and Vogl (2023)). This li e a u e demons a ed pos-
i i e p og am impac s on school en ollmen and a ainmen . Howe e , a longs anding
conce n has been whe he and o wha ex en his inc eased school en ollmen ans-
la es in o highe academic achie emen , a likely de e minan o he ex en o which
CCTs can imp o e ea nings po en ial and o he longe - e m ou comes. Mos p io s ud-
ies did no analyze academic achie emen impac s, because he o iginal e alua ion da a
did no include achie emen es sco es.1
Wi h newly a ailable da a, we a e now able o examine he e ec s o he P ospe a
p og am ( he p og am name du ing he ime o ou da a collec ion) no only on school
en ollmen and a ainmen bu also on academic achie emen in ma hema ics and
Spanish. Na ionwide s anda dized longi udinal adminis a i e es -sco e da a (called
he ENLACE da a) as well as comple e en ollmen os e s we e me ged wi h adminis-
a i e in o ma ion on which s uden s come om P ospe a households and on school
loca ions. They we e also me ged wi h su ey in o ma ion ob ained om s uden s and
hei pa en s. These da a allow he s udy o how s uden s’ P ospe a bene icia y s a us a -
ec s hei school en ollmen , school choice, g ade p og ession, and academic achie e-
men s o e ime.
Al hough ou longi udinal adminis a i e and su ey da a a e ich and ha e he ad-
an ages o na ional co e age and la ge sample sizes, he da a we e no collec ed explic-
i ly o he pu pose o e alua ing he P ospe a p og am. The e a e a leas i e signi ican
1In 2003, Woodcock–Johnson es s in ma hema ics and Spanish we e applied o a single c oss-sec ion.
Using hese da a, Beh man, Pa ke , and Todd (2009) ound no impac s o PROGRESA pa icipa ion on
achie emen , based on compa ing es sco es o he o iginal ea men and con ol g oups. Howe e , be-
cause he o iginal con ol g oup was en olled in he p og am 1.5 yea s a e he o iginal ea men g oup,
he schooling di e ences be ween hem we e ela i ely small, a abou 0.2 yea s o addi ional schooling.
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 135
s a is ical challenges in using obse a ional da a o his kind o assess p og am impac s:
(i) selec i e p og am pa icipa ion, la gely due o eligibili y c i e ia ha es ic access
o high-po e y households, (ii) non andom school d opou , which mainly occu s a e
g ade 6, (iii) g ade e en ion in any g ade, (i ) he a ailabili y o mul iple school ypes
and school choice, and ( ) he p esence o a small ac ion o s uden s suspec ed o ha e
chea ed on he es s. This pape de elops a me hodological app oach o e alua ing he
e ec s o P ospe a and illumina ing he mechanisms h ough which p og am e ec s op-
e a e while accoun ing o hese di e en ea u es o he da a and he con ex .
Some ea lie s udies conside he selec ion p oblem a ising om non andom
d opou in he con ex o analyzing educa ional ou come de e minan s (see, e.g.,
Came on and Heckman (1998,2001), Glewwe (2002)). As is common in adminis a-
i e schooling da a, including ou da a, he es sco es a e only obse ed o en olled
child en who ook he es s a school. The selec ion p oblem is dynamic as i occu s a
each g ade and he s uden s a isk o d opping-ou in a pa icula g ade depend on he
sample ha s ayed in school om p e ious g ades. The P ospe a CCT p og am induced
s uden s om high-po e y backg ounds who we e a high isk o d opping-ou o s ay
in school longe . I he CCT p og am induces weake s uden s o emain in school, hen
a e age es sco es could all as a esul o mo e ma ginal s uden s being included in he
es ing. This kind o selec ion p oblem a ises whene e es s a e adminis e ed in school,
ega dless o whe he he da a analyzed a e expe imen al o nonexpe imen al.2
Ou goal in his pape is o examine how he P ospe a p og am a ec s schooling and
academic achie emen , accoun ing o he s a is ical p oblems no ed in (i)–( ) in he
penul ima e pa ag aph. To his end, we de elop and es ima e a dynamic model o s u-
den s’ school p og ession ha inco po a es decision making in each g ade (4–9) wi h
ega d o en ollmen , school choice, and d opping-ou as well as g ade- and subjec -
a ying models o academic achie emen . Speci ically, ou modeling amewo k com-
bines alue-added academic achie emen models wi h school-choice models and links
equa ions ac oss ages/g ades, allowing o bo h obse ed and unobse ed he e ogene-
i y. Valued-added models ypically speci y a ela ionship among academic achie emen ,
key lea ning inpu s in he cu en pe iod, and lagged achie emen , which is a su i-
cien s a is ic o pas lea ning inpu s unde some assump ions abou coe icien s o
pas lea ning inpu s ollowing geome ic pa e ns (Summe s and Wol e (1977), Boa d-
man and Mu nane (1979), Hanushek (1979), Todd and Wolpin (2003), Cunha, Heck-
man, Lochne , and Mas e o (2006), Cunha, Heckman, and Schennach (2010)).3School-
choice models gene ally ocus on he decision o wha ype o school o a end (Neal
(1997), McEwan (2001), Al onji, Elde , and Tabe (2005), Sapelli and Vial (2002), Gallego
2This selec ion p oblem also a ec s c oss-coun y compa isons o s anda dized es s, such as PISA es
sco es. The PISA es s a e gi en in schools a age 15 and, in some coun ies, signi ican ac ions o child en
ha e d opped-ou by ha age.
3The e is some deba e abou whe he alue-added models wi h eache ixed e ec s should be used
o measu e eache e ec i eness (see, e.g., Kane and S aige (2008), Kane, McCa ey, Mille , and S aige
(2013), Che y, F iedman, and Rocko (2014a,b)). Ou ocus is a he on using hese models o cap u e he
cumula i e lea ning p ocess.
136 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
and He nando (2009)).4Value-added models and school-choice models a e usually es-
ima ed in isola ion, al hough he e a e a ew pape s ha combine hem (e.g., Has ings,
Neilson, and Zimme man (2012), Allende e al. (2019), Schellenbe g and Wal e s (2020)).
Ou model also inco po a es d opou decisions and g ade e en ion.
The model begins when s uden s inish 4 h g ade and con inues h ough he 9 h
g ade.5S uden s in ou sample di e in e ms o hei amily backg ounds and hei
4 h-g ade knowledge in ma hema ics and Spanish as measu ed by s anda dized es
sco es. The as majo i y o child en a end gene al p ima y schools close o home, bu
some amilies li ing in a eas wi h high indigenous popula ions can choose be weengen-
e al and bilingual indigenous schools. A he end o each g ade, s uden s can p og ess
o he nex g ade, epea he same g ade o (a e g ade 6), d op ou . Condi ional on
p og essing o lowe -seconda y school (a he end o g ade 6), s uden s/pa en s make
a one- ime choice o a lowe -seconda y school ype, om up o h ee public school
op ions—gene al, eleseconda y, o echnical schools—all o which a e academically
o ien ed.6
In each pe iod, we model skill accumula ion in ma hema ics and Spanish using
alue-added p oduc ion unc ions, wi h coe icien s ha a y by g ade, school ypes,
and g ade- e en ion s a us. The dynamic-panel speci ica ion cap u es he no ion ha
skill accumula ion a one s age a ec s skill a ainmen a o he s ages, which has been
shown o be essen ial o cha ac e izing human-capi al-skill o ma ion p ocesses (e.g.,
Cunha e al. (2006), Cunha, Heckman, and Schennach (2010)). When s uden s/pa en s
choose om among di e en school ypes, hey essen ially choose a lea ning echnol-
ogy. The same inpu s (including P ospe a pa icipa ion) may gene a e subs an ially di -
e en ou come ajec o ies depending on he school ypes ha a e a ailable and a e
selec ed.
As p e iously no ed, he model we es ima e con ols o selec ion a ising om
school-en ollmen , d opou , g ade- e en ion, and school- ype choices, all o which po-
en ially a ec s uden s’ g ade p og ession and academic achie emen s. I also accoun s
o selec i e p og am pa icipa ion a ising om he ac ha only high-po e y house-
holds a e eligible o pa icipa e in P ospe a. In pa icula , we limi ou analysis sub-
4Some s udies use school-choice models o es ima e school- ouche e ec s (Rouse (1998), Figlio and
Elena Rouse (2006), Hsieh and U quiola (2006), B a o, Mukhopadhyay, and Todd (2010), Ang is , Be inge ,
Bloom, King, and K eme (2002), Ang is , Be inge , and K eme (2006)), o s udy pa en s’ p e e ences o
school quali y, and o analyze he wel a e e ec s o school policies (Epple, Jha, and Sieg (2018), Has ings,
Kane, and S aige (2009), Allende e al. (2019)).
5The P ospe a cash ans e s o a ending school ac ually s a in g ade 3. We s a ou model a g ade 4,
because he da a we e collec ed o e a 6-yea ime ame and we wan o ollow s uden s h ough g ade 9,
which is he las g ade o lowe -seconda y school. The e a e no na ionwide s anda dized es s in he 10 h
and 11 h g ades. By s a ing he model a g ade 4, we do no cap u e po en ial p og am impac s in p io
g ades and po en ially unde s a e p og am bene i s.
6Technical schools di e om gene al schools by including oca ional/ echnical educa ional cu icula
componen s. Teleseconda y schools a e dis ance-lea ning schools ha la gely se e u al communi ies and
ha en oll almos 20% o lowe -seconda y school s uden s. P ospe a-bene icia y amily child en a end
eleseconda y schools in g ea e p opo ions han a e age. We exclude p i a e schools om he choice se
as almos no P og esa bene icia ies a end p i a e school. Sec ion wo p o ides mo e de ail on how he
school ypes di e .
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 137
sample o households ha a e es ima ed o ha e posi i e p obabili y o being a p o-
g am bene icia y and, in addi ion, con ol o obse ed he e ogenei y be ween P ospe a
and non-P ospe a s uden s using a ich se o amily demog aphics. Ou da a se con-
ains in o ma ion on mos o he a iables used o de e mine P ospe a eligibili y, bu
we also allow o he possibili y o selec ion on some unobse ed ac o s.7The unob-
se ed he e ogenei y is modeled as disc e e la en mul inomial ypes, as in Heckman
and Singe (1984), Came on and Heckman (1998). These ypes en e mul iple model
equa ions and, in doing so, allow o ac oss-equa ion co ela ed e o s uc u es. We
allow he unobse ed- ype dis ibu ion o a y by P ospe a bene icia y s a us and an
index measu e o local po e y.
The da a we analyze also con ain in o ma ion on small pe cen ages o s uden s in
each g ade ha a e suspec ed o ha e copied answe s on he mul iple-choice s anda d-
ized es s. In he con ex o a alue-added es -sco e model, copying induces one-sided
measu emen e o s in he dependen a iables, he lagged dependen a iables, o
bo h, which we explici ly ake in o accoun in ou maximum likelihood es ima ion p o-
cedu e. The ou comes a di e en ages/g ades a e school en ollmen , school choices,
ma hema ics, and Spanish es sco es, d opping-ou , and g ade e en ion. We do no
know o p e ious esea ch ha es ima es alue-added models accoun ing o possible
chea ing, al hough chea ing on s anda dized es s is a ubiqui ous p oblem.
We use ou es ima ed model amewo k o e alua e how P ospe a-bene icia y s a us
a ec s schooling p og ession and academic achie emen s in di e en g ades. In pa ic-
ula , we simula e school-choice decisions, school-en ollmen decisions, and academic
achie emen s wi h and wi hou he P ospe a p og am, o child en om di e en am-
ily backg ounds. The e a e mul iple channels h ough which P ospe a pa icipa ion can
a ec hese ou comes. Fi s , pas pa icipa ion may inc ease lagged achie emen , which
can acili a e p esen lea ning. Fo example, g ea e comp ehension o 6 h-g ade ma h-
ema ics can acili a e lea ning and comp ehension o he 7 h-g ade cu iculum.8Sec-
ond, con empo aneous p og am pa icipa ion can di ec ly a ec lea ning i he p og am
encou ages egula school a endance, s uden engagemen , and s udy e o s. The e
a e wo easons why we migh expec he P ospe a p og am o in luence s uden s in
his way. P ospe a p og am ules s ipula ed ha child en mus a end school a leas
85% o days and can only ail a g ade once o ecei e he cash ans e s. Addi ionally,
P ospe a ans e s may educe he p essu e on child en/you h o wo k in labo ma ke s
while in school and he eby allow o g ea e ocus on schoolwo k (Skou ias and Pa ke
(2001)).
Ou analysis yields a numbe o indings ega ding P ospe a-p og am e ec s and he
e ec i eness o di e en school ypes. Fi s , we ind ha P ospe a pa icipa ion educes
lowe -seconda y school d opou a es by 0.06–0.09 pe cen age poin s. This e ec is mos
7As discussed in Todd and Wolpin (2003), Ri kin, Hanushek, and Kain (2005) o alue-added models
and in nume ous o he s udies o schooling (e.g., Beh man, H ubec, Taubman, and Wales (1980), Beh man
and Rosenzweig (1999), Al onji, Elde , and Tabe (2005), Ro hs ein (2009)), i is impo an o con ol o un-
obse ed inhe en s uden abili ies, pe sonali y ai s, o mo i a ion, ha ma e o child en’s achie emen
g ow h.
8Cunha e al. (2006) e m his ea u e o cogni i e achie emen p oduc ion unc ions “sel -p oduc i i y.”
138 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
p onounced du ing he ansi ion om 6 h o 7 h g ade and appea s simila o bo h
gi ls and boys.9In p ima y-school g ades (g ades 5 and 6), ou indings do no show any
signi ican impac o he p og am on es sco es. Howe e , in lowe -seconda y g ades
(g ades 7 o 9), we obse e posi i e and s a is ically signi ican imp o emen s in es
sco es. The e ec s a e mo e subs an ial in ma hema ics, wi h a cumula i e e ec o 0.21
s anda d de ia ions by he 9 h g ade, compa ed o 0.04 in Spanish. Gi ls end o ha e
highe gains in ma hema ics, whe eas boys show g ea e gains in Spanish. The e o e, he
P ospe a p og am na ows exis ing gende es sco e gaps ha a o boys in ma hema -
ics and gi ls in Spanish. Addi ionally, and as expec ed, he e ec s o p og am pa icipa-
ion accumula e o e ime and in ensi y wi h p olonged exposu e. In iguingly, child en
om mo e disad an aged backg ounds exhibi signi ican ly la ge imp o emen s in es
sco es.
Ou esul s con ibu e o he unde s udied ye subs an i e ques ion o whe he
CCTs imp o e lea ning. Fiszbein and Schady (2009), Bai d, Fe ei a, Özle , and Wool-
cock (2014) sys ema ically e iewed a ange o CCT p og ams wo ldwide and concluded
ha he e ec s o CCTs on achie emen es s we e disappoin ingly “small, a bes .” One
ca ea is ha hese conclusions a e mos ly d awn om ela i ely sho e alua ion pe-
iods and based on ela i ely small sample sizes.10 When e alua ing CCT p og ams
o e longe ho izons, some s udies epo s a is ically signi ican e ec s on academic
achie emen . Fo example, Ba ham, Macou s, and Maluccio (2013)used he andom-
ized phase-in o he Red de P o eccion Social CCT p og am in Nica agua o s udy e -
ec s on schooling a ainmen and lea ning o boys 10 yea s la e . They ound a hal -
g ade inc ease in schooling and subs an ial gains (app oxima ely 0.25 s anda d de ia-
ions) in ma hema ics and language achie emen sco es. Compa ing wo coho s (2007
and 2013), Hadna and Ka ika (2017) ound s a is ically signi ican e ec s o a CCT p o-
g am called P og am Kelua ga Ha apanin in Indonesia on h ee subjec s (Bahasa In-
donesia, ma hema ics, and English) as well as na ional ma hema ics examina ions o
junio /high-school s uden s. Ou esul s can econcile some o he mixed indings in
he li e a u e by highligh ing he accumula i e ea u e o he CCT p og am e ec s.
Ou s udy sheds ligh on he e icacy o a ious ypes o Mexican schools in enhanc-
ing es sco es. This includes eleseconda y schools, which p edominan ly u ilize ideo-
based eaching me hods and a e o en he only accessible op ion o s uden s in u al
a eas. Ou indings indica e ha eleseconda y schools a e, in many ins ances, as e -
ec i e o e en mo e so han egula public schools o hei a endees. When we use
he es ima ed model o analyze he e ec o emo ing he eleseconda y op ion om
he choice se , we ind ha he d opou a e would be subs an ially highe and a e -
age schooling a ainmen lowe wi hou hese schools. Model simula ions also show
ha eleseconda y schools a e also impo an de e minan s o P ospe a p og am im-
pac s. Ou inding ha hese schools play an impo an ole in os e ing educa ion in
9Some s udies ha e sugges ed a g ea e impac o PROGRESA on seconda y-school en ollmen o gi ls
(Schul z (2004), Pa ke and Vogl (2023)), bu o he esea ch inds simila e ec s o bo h gende s in lowe -
seconda y educa ion (Beh man, Sengup a, and Todd (2005), Todd and Wolpin (2006)).
10Due o da a limi a ions, he e a e many ewe s udies o achie emen han he e a e o en ollmen . Fo
ins ance, Snils ei e al. (2017) e iewed 38 s udies o he e ec s o ans e s on en ollmen ; only 11 o he
p og ams analyzed e ec s on achie emen .
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 139
Mexico is consis en wi h he di e ence-in-di e ence analysis o Fab egas and Na a o-
Sola (2023) ha ound ha he expansion o eleseconda y schools led o subs an ial
inc eases in schooling a ainmen s o local s uden s.11
Las ly, we also explo e how in e ences based on ou model depend on speci ica-
ion assump ions. As a benchma k, we es ima e a simple alue-added model g ade-by-
g ade, wi hou con olling o selec ion om mul iple sou ces (d opou , school choice,
g ade e en ion). Compa ing he esul s o hose de i ed om ou iche model, he cu-
mula i e p og am impac s a e no iceably smalle . Thus, ailing o con ol o dynamic
selec ion would lead o unde es ima ion o P ospe a’s impac . We iden i y h ee po en-
ial easons o downwa d biases. Fi s , he p og am causes s uden s a he ma gin o
d opping-ou o s ay in school longe and ailu e o con ol o his changing compo-
si ion o s uden s would lead o a downwa d bias in he impac es ima es. Second, he
simple model does no allow he e ogeneous impac s ac oss di e en ypes o schools
and, he e o e, does no cap u e ha eleseconda y schools a e pa icula ly e ec i e o
P ospe a bene icia ies. Las ly, he simple model igno es he nega i e selec ion o unob-
se ed ypes, which also leads o an unde es ima ion o p og am impac s. We ind ha a
iche modeling amewo k is equi ed o cap u e he e ogeneous p og am impac s and
o con ol o mul iple sou ces o selec ion bias.
The pape de elops as ollows. Sec ion 2b ie ly desc ibes he Mexican school sys-
em and he da a se s used in his s udy. Sec ion 3desc ibes he model and Sec ion 4 he
es ima ion app oach. Sec ion 5p esen s he empi ical esul s. Sec ion 6p esen s he es-
ima ed cumula i e P ospe a p og am e ec s. I also pe o ms model simula ions whe e
he eleseconda y schooling op ion is emo ed, examines he obus ness o p og am im-
pac es ima es o al e na i e modeling assump ions and explo es longe - e m p og am
impac s (up o g ade 12). Sec ion 7concludes. The Supplemen al Appendix (Beh man,
Pa ke , Todd, and Zhang (2024)) p o ides addi ional de ails on da a sou ces and com-
ple e model es ima es. The Supplemen al Appendix will be e e ed o h oughou he
pape as SA.
2. Backg ound
2.1 Mexican educa ional sys em and child-labo laws
The Mexican educa ional sys em consis s o h ee le els: p ima y, seconda y, and e -
ia y educa ion. Fo mal basic educa ion includes p eschool, p ima y school (g ades 1–
6), and lowe -seconda y school (g ades 7–9), all o which a e compulso y. Howe e , com-
pulso y schooling laws a e no well en o ced. Many child en d opou be o e comple ing
g ade 9, pa icula ly child en om lowe -SES amilies, indigenous backg ounds, and u-
al a eas.
Ou analysis ocuses on public schools. Al hough P ospe a bene icia ies may choose
which school o a end, in p ac ice, almos all a end public schools (in ou da a only
11A ecen pape by Bo ghesan and Vasey (2024) also s udies he e ec i eness o Mexican eleseconda y
schools using a ma ginal ea men e ec s (MTE) es ima ion app oach applied o a Roy model and using
he same da a we analyze bu ocusing on 7 h g ade s.
140 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
0.28% o bene icia ies in 6 h g ade a e en olled in p i a e schools). Public p ima y and
lowe seconda y schools, as pa o “educacion basica,” a e ee o cha ge. The Sec-
e a ia o Public Educa ion (SEP) s anda dizes cu iculum con en , which includes
Spanish, ma hema ics, na u al sciences, his o y, geog aphy, a , and physical educa-
ion.12 Seconda y school is di ided in o lowe -seconda y school (g ades 7–9) and uppe -
seconda y school (g ades 10–12). Lowe -seconda y school is ee and s uden s may ol-
low ei he a gene al academic ack o a echnical ack, which has mo e o a oca ional
ocus. Bo h acks a e designed o p epa e s uden s o u he educa ion. The e a e
ewe lowe -seconda y schools han p ima y schools and a ending lowe -seconda y
schools o en equi es a eling some dis ance om home, pa icula ly o child en
li ing in mo e emo e a eas. Public schools do no gene ally p o ide anspo a ion.
Uppe -seconda y educa ion (g ades 10–12) did no become compulso y un il 2012.
Some uppe -seconda y schools a e a ilia ed wi h la ge public uni e si ies, while o h-
e s a e SEP o s a e-con olled. A he e ia y le el, he Mexican educa ional sys em has
many di e en p og ams and deg ee op ions.
The Mexican Cons i u ion p ohibi s child labo o mino s unde 14 yea s o age.
Howe e , he child-labo laws a e no well en o ced. 8% o child en age 12 epo wo k-
ing o pay in he 2010 Mexican census da a.13
2.2 ENLACE es -sco e da a and addi ional su ey da a
F om 2006 o 2013, he SEP applied he E aluación Nacional de Log o Académico en Cen-
os Escola es, called he ENLACE (SEP (2018a)). The es e alua ed s uden pe o mance
in ma hema ics, Spanish, and a o a ing subjec o all 3 d- o-9 h g ade s a he end o
each academic yea . The es is di ec ly based on he cu iculum (see SEP (2010)) and
in ended o be an assessmen ha is in o ma i e abou lea ning ou comes o SEP and
o pa en s. In p ima y school and in lowe -seconda y school, he g ades s udied in his
pape , he es has no bea ing on s uden s’ GPA o g ade p og ession, so i can be consid-
e ed o be low s akes. Beginning in 2008, ENLACE was also gi en o s uden s in hei inal
yea o uppe -seconda y school (g ade 12).14 The exams we e designed o ha e a mean
o 500 and a s anda d de ia ion o 100 in hei i s yea o implemen a ion, and subse-
quen es yea s we e calib a ed o allow measu emen o changes in lea ning o e ime
(see SEP (2010)). The es -comple ion a e is close o 90%. As desc ibed by De Hoyos,
Es ada, and Va gas (2018), 15.1 million s uden s in 136,000 schools ook he examina-
ion in 2013, he las yea he es was applied. In addi ion o es sco es, he ENLACE
da a (me ged wi h school os e da a) also con ain in o ma ion on he age, gende , P os-
pe a bene icia y s a us, whe he he child a ended he day o he es , school ID, and
school ype o each s uden . We examine a coho o s uden s who we e in g ade 4 in
12The Na ional Ins i u e o Assessmen o Educa ion (INEE) moni o ed s anda ds du ing ou pe iod o
s udy.
13Based on he au ho s’ abula ions.
14The ENLACE exams ha e been used as a means o e alua ing educa ional in e en ions by se e al
pape s (A i abile and De Hoyos (2018), De Hoyos Na a o, A anasio, and Meghi (2019), De Hoyos, Ga cia-
Mo eno, and Pa inos (2017)). Sco es on hese exams ha e been shown o ha e p edic i e powe on impo -
an li e ou comes including uni e si y en ollmen and wages (De Hoyos, Es ada, and Va gas (2018)).
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 147
Figu e 2. Ma hema ics and Spanish es sco es dis ibu ions by g ade and lowe -seconda y
school ypes.
p e alen among he P ospe a s uden s. Mo eo e , chea ing is gene ally associa ed wi h
less es sco e in la ion among non-P ospe a han P ospe a s uden s.
148 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
Table 5. A e age es sco es and p opo ion chea ing, by P ospe a s a us.
G ades
Non-P ospe a P ospe a
No chea ing Chea ing No chea ing Chea ing
G ade 4 F ac ion 93.8% 6.2% 90.1% 9.9%
Ma h 529 554 480 519
Spanish 521 538 468 496
G ade 5 F ac ion 96.6% 3.4% 94.6% 5.4%
Ma h 533 585 494 557
Spanish 534 568 488 533
G ade 6 F ac ion 96.9% 3.1% 95.1% 4.9%
Ma h 560 616 525 594
Spanish 557 590 515 561
G ade 7 F ac ion 98.2% 1.8% 96.5% 3.5%
Ma h 500 578 492 602
Spanish 490 542 465 534
G ade 8 F ac ion 96.2% 3.8% 92.7% 7.3%
Ma h 524 627 526 683
Spanish 497 567 476 579
G ade 9 F ac ion 97.2% 2.8% 95.1% 4.9%
Ma h 548 636 562 654
Spanish 501 541 481 532
No e: This able shows a e age ma hema ics and Spanish es sco es, along wi h he p opo ion o s uden s lagged o
chea ing, disagg ega ed by P ospe a s a us and g ade. “Chea ing” e e s o s uden s lagged by a copying beha io indica o .
2.5 Local school supply and quali y
As p e iously no ed, Mexican amilies can choose among di e en ypes o schools, bu
hei op ions depend on he local supplies. We nex examine he supplies o di e en
ypes o schools and also hei quali y cha ac e is ics. Table 6p o ides in o ma ion on
he supplies o local schools o di e en ypes a he indi idual le el. In Mexico, mul i-
ple school sessions a e o en held in he same building, such as a mo ning and a e noon
session. The di e en sessions may ha e di e en p incipals and eache s; so, in he da a
se hey a e conside ed o be di e en schools.17 P ima y schools end o be small, wi h
an a e age en ollmen o less han 200 and, consequen ly, he e a e a la ge numbe o
p ima y schools. Thei small size pa ly e lec s ha he school sys ems do no usually
p o ide anspo a ion and s uden s ypically walk o school. Also, 77% o child en do
no ha e access o indigenous schools, which a e ypically loca ed in a eas wi h signi i-
can indigenous popula ions. A he lowe -seconda y le el, he e a e ewe schools and
hey a e la ge .
Table 7compa es he di e en school ypes in e ms o some a e age school qual-
i y cha ac e is ics, including pupil– eache a ios and eache educa ional le els. The
17In SA Figu e B1, we show one illus a i e example o local p ima y school sessions in Aguascalien es, a
ci y in cen al Mexico. I has 316 school sessions dis ibu ed in 250 unique coo dina es wi hin 10 kilome e s.
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 149
Table 6. Numbe o local schools o di e en ypes.
Mean S d p10 p50 p75 No a ailable
P ima y school (wi hin 5 km)
Gene al 63 78 9 25 100 3.4%
Indigenous 5 6 1 3 6 77.2%
Seconda y school (wi hin 10 km)
Gene al 46 67 4 17 60 14.9%
Teleseconda y 13 11 4 10 19 8.5%
Technical 10 11 2 6 15 16.1%
No e: Columns 3–5 epo selec ed pe cen iles. The las column gi es he pe cen ages o indi iduals o whom a gi en
school ype a e no locally a ailable.
i s wo columns show cha ac e is ics o gene al and indigenous p ima y schools. In-
digenous p ima y schools ha e on a e age 94 s uden s in compa ison o 174 s uden s
in gene al p ima y schools. The pe cen ages o s uden s who a e disabled anges om
1–2%. Despi e ha ing o e all ewe s uden s, he s uden – eache a io in indigenous
schools is highe —33 in compa ison o 24. Ano he di e ence is ha eache s in in-
digenous schools a e mo e likely o ha e only uppe -seconda y school deg ees (17% in
compa ison o 3%). A he same ime, he ac ion o eache s wi h an unde g adua e o
highe deg ee is 7 pe cen age poin s highe . Thus, eache schooling a ainmen exhibi s
highe a iance in indigenous schools.
The las h ee columns o Table 7compa e he a e age school cha ac e is ics o gen-
e al, echnical, and eleseconda y schools. Technical schools end o be la ge , wi h an
a e age en ollmen o 395 in compa ison o 296 o gene al schools and 75 o elesec-
onda y. Again, he p opo ion o disabled s uden s ac oss all ypes o schools is 1–2%.
The s uden – eache a io is 14 in gene al schools, 19 in echnical schools, and 24 in
eleseconda y schools.18 Thus, we see a gene al pa e n o he smalle schools in u al
a eas ha ing highe s uden – eache a ios, which could ei he e lec ha ideo lea n-
ing is less eache -in ensi e o ha eache o esou ce sho ages a e mo e common
in u al a eas. Compa ing eache educa ional p o iles ac oss he di e en kinds o sec-
onda y schools, we see ha a e age cha ac e is ics a e ai ly simila . The main di e ence
is ha gene al school eache s a e mo e likely o ha e unde g adua e deg ees a he
han eaching-college deg ees, compa ed o eache s in echnical and eleseconda y
schools.
3. Model
Ou modeling amewo k combines a school-choice model o a endance decisions a
di e en ypes o schools wi h models o academic achie emen in ma hema ics and
Spanish ha a e linked ac oss ages/g ades. In pa icula , we speci y es -sco e gains
om yea - o-yea using a alue-added amewo k ha ela es cu en achie emen o
18These abula ions a e based on egula eache s and exclude a and music eache s who o en each
a mul iple schools.
150 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
Table 7. Mean p ima y and lowe -seconda y school cha ac e is ics by school ypes (wi h s an-
da d de ia ions in pa en heses).
Cha ac e is ic
P ima y Lowe Seconda y
Gene al Indigenous Gene al Teleseconda y Technical
Numbe o s uden s 174 94 296 75 395
(175) (95) (244) (64) (247)
P opo ion disabled 0.02 0.01 0.01 0.01 0.02
(0.06) (0.07) (0.04) (0.03) (0.05)
S uden – eache a io 24 33 14 24 19
(18) (12) (7) (9) (8)
Teache s wi h HS deg ee 0.03 0.17 0.03 0.03 0.02
(0.09) (0.30) (0.07) (0.16) (0.06)
Teache s wi h eache college 0.47 0.26 0.34 0.41 0.42
(0.35) (0.34) (0.34) (0.42) (0.32)
Teache s wi h unde g adua e deg ee 0.47 0.56 0.54 0.44 0.47
(0.34) (0.39) (0.34) (0.42) (0.32)
Teache s wi h pos -g ad deg ee 0.03 0.01 0.07 0.11 0.08
(0.10) (0.07) (0.12) (0.23) (0.11)
No e: Tabula ions based on a school census da a se called he 911 da a.
lagged achie emen , amily and school inpu s in o he lea ning p ocess, and s uden
unobse ed he e ogenei y (e.g., a ising om abili y o p e e ences). Ou amewo k also
allows echnology o p oducing es -sco e gains o a y by ype o school. In addi-
ion, i inco po a es d op-ou decisions and allows o g ade e en ion, as desc ibed be-
low.
Ou modeling amewo k can be conside ed quasis uc u al. The educa ional p o-
duc ion unc ion has a s uc u al in e p e a ion as a echnology ela ing inpu s o ou -
pu s. Howe e , he school-choice model is educed o m, likely e lec ing he decisions
o s uden s, pa en s, and school adminis a o s. As discussed below, he ou side op ion
in he school-choice model is o d op ou .
3.1 Gene al en i onmen and sequen ial ou comes
Indi iduals a e indexed by i,i=1, ,nand each model pe iod co esponds o
one school yea . In he ini ial pe iod (a , co esponding o he age a g ade 4), s u-
den s/pa en s can choose o a end one o wo ypes o p ima y schools: gene al (j=1)
o indigenous (bilingual) (j=4), depending on he ypes locally a ailable (wi hin 5 km).
A he end o g ade 6, s uden s simul aneously make school-en ollmen decisions (wi h
j=0 indica ing nonen ollmen ) and school- ype choices om up o h ee op ions: gen-
e al (j=1), eleseconda y (j=2), o echnical (j=3), depending on he ypes locally
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 151
Figu e 3. Po en ial sequen ial ou comes om g ades 4 o 9.
a ailable (wi hin 10 km). We can summa ize he choice se Jg
ia a di e en g ades as
jia ∈Jg
ia =⎧
⎪
⎪
⎨
⎪
⎪
⎩
{1, 4}∩M1
i,Ga=4&a=a ,
{0, 1, 2, 3}∩M2
i,Ga−1=6&IPass
i,a−1=1,
{0, ji,a−1},Ga−1≥7,
(1)
whe e a is he age when he s uden en e s in o he sample a g ade 4. M1
ideno es he
a ailable local p ima y school ypes and M2
ideno es he a ailable local lowe -seconda y
school ypes.19
Le Dija =1 i he indi idual iis en olled in school ype j(j∈{1, 2, 3, 4})a agea,else
Dija =0. Le Di0a=1 i he indi idual does no en oll in school a age a,elseDi0a=0. Le
IPass
ia =1 i he indi idual passes he g ade in which she is en olled a age a,elseIPass
ia =0.
We assume he passing ou come IPass
ia is ealized a he end o he school yea , p io o he
o he decisions being made. The po en ial sequen ial ou comes om g ade 4 o g ade 9
a e illus a ed in Figu e 3.
As seen in Figu e 3, un il g ade 6 he possible ou comes a e whe he a s uden is e-
ained in he cu en g ade (IPass
ia =0) o p og esses o he nex g ade (IPass
ia =1), condi-
ioning on hei p ima y school ypes when en e ing in o he model a g ade 4, hei am-
ily backg ound, and hei P ospe a-bene icia y s a us. Upon passing g ade 6 (IPass
ia =1),
s uden s simul aneously make en ollmen decisions Di0aand school choices Dij a ,de-
pending on locally a ailable school ypes.20 Once en olled in a seconda y school, s u-
den s decide in each pe iod whe he o d op ou o o s ay in school. In each g ade,
he e is a p obabili y o passing o ha ing o epea he g ade. Le Gia deno e he g ade
19In pa icula , M1
i∈{{1},{4},{1, 4}} and M2
i∈{{1, 2, 3},{1, 2},{1, 3},{2, 3},{1},{2},{3}}.
20Because school en ollmen is e y high du ing p ima y school, we assume s uden s do no d op-ou
du ing p ima y g ades. The e o e, hey do no make choices abou con inuing in school un il he end o
g ade 6.
152 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
ha he indi idual is eligible o a end a age a, which inc eases by one i he s uden
passes he cu en g ade:
Gi,a+1=Gia +IPass
ia .
3.2 Accoun ing o selec i e p og am pa icipa ion
Ou aim is o use ou es ima ed model o assess he impac s o P ospe a pa icipa ion on
schooling p og ession and academic achie emen , whe e we ea P ospe a bene icia y
s a us as a amily cha ac e is ic. Pi=1 deno es ha a child/you h comes om a P os-
pe a-bene icia y amily, else Pi=0. Al hough he su ey da a we use we e no collec ed
o he pu pose o asce aining P ospe a eligibili y, he da a a e ich and con ain in o -
ma ion on mos o he eligibili y de e minan s.21 P og am eligibili y is no means- es ed
by income, because income can be di icul o measu e in a coun y wi h a signi ican in-
o mal sec o and whe e many low-income indi iduals a e engaged in ag icul u al wo k.
The p og am-eligibili y c i e ia a he depend mainly on households’ asse s (such as ca
owne ship), on cha ac e is ics o he household’s esidence (such as whe he i has di
loo s, piped wa e , and how many ooms he e a e pe pe son li ing in he house) and
on household demog aphics, such as numbe o child en and numbe s o dependen s
pe wo ke .22 The as majo i y o eligible households op o pa icipa e, e lec ing ha
he cash ans e s a e subs an ial.23
Ou empi ical s a egy in e alua ing he impac o P ospe a on s uden es sco es
and educa ional p og ession is o i s limi he compa ison g oup subsample o chil-
d en whose amilies mee a leas a subse o he eligibili y c i e ia. We do so by i s es i-
ma ing a p obi model o he p obabili y ha each amily is eligible o and pa icipa es
in he P ospe a p og am gi en he a ailable in o ma ion. Tha is, we use in o ma ion on
housing cha ac e is ics and demog aphics ha we e ga he ed h ough he s uden and
pa en su eys o es ima e a household’s p obabili y o being eligible and pa icipa ing
in he p og am (a p opensi y sco e). The es ima ed coe icien s om his p obi eg es-
sion a e shown in SA Table A.3. The pe cen age co ec ly classi ied as being bene icia ies
o no unde he es ima ed model is high (90%).
Figu e 4plo s he p opensi y-sco e dis ibu ions o child en om P ospe a-bene-
icia y households (in ed) and nonbene icia y households (in g een). As seen in he
igu e, a la ge ac ion o nonbene icia ies all in he i s his og am bin, meaning ha
hey ha e ex emely low p obabili ies o pa icipa ing in P ospe a, gene ally because
hei cha ac e is ics make hem ineligible. To inc ease compa abili y be ween he P os-
pe a and he compa ison-g oup subsamples, we impose a common suppo es ic ion
and exclude in ou impac analysis P ospe a bene icia ies and he nonbene icia ies wi h
21The p ecise eligibili y c i e ia a e no made public, bu some o he au ho s o his pape we e in ol ed
in he design o he c i e ia.
22Families who apply o he p og am ypically ill ou a ques ionnai e o de e mine hei eligibili y and
hei answe s on he ques ionnai e may be checked h ough home isi s.
23As discussed in Pa ke and Todd (2017), hey ep esen on a e age abou a 20% inc ease in household
income.
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 153
Figu e 4. The p opensi y sco e dis ibu ion by P ospe a s a us (P). No e: The ed his og am ep-
esen s he p opensi y sco e dis ibu ion o P ospe a child en/you h and he g een his og am
o non-P ospe a child en/you h.
p opensi y sco es below he 1% quan ile ( he lowes bin o he his og am).This h eshold
excludes 383 child en om P ospe a amilies and 50,798 nonbene icia y child en.24
In addi ion, ou school-choice/d opou and alue-added models also include ob-
se ed co a ia es o u he con ol o di e ences be ween P ospe a and non-P ospe a
households (such as pa en s’ schooling a ainmen ). We also allow o he possibili y ha
child en/you h om P ospe a bene icia y amilies may di e in unobse ed ways by in-
cluding la en unobse ed he e ogenei y, speci ied as ou disc e e mul inomial ypes
ha en e in o all he model equa ions.25 Le μil =1 deno e ha indi idual iis o ype l,
=0else,whe el∈{1, ,L}and L=4.
Ideally, one could allow o he unobse ed ypes o be a bi a ily co ela ed wi h
he obse ed a iables. Howe e , iden i ying such a model poses challenges, as i can be
di icul o dis inguish he di ec e ec s o hese obse ed a iables om hei indi ec
e ec s ope a ing h ough he unobse ed ype dis ibu ion. Fo his eason, we es ic
he ype p obabili y dis ibu ion o depend only on a child’s P ospe a s a us (P∈{0, 1})
and a bina y ma ginali y indica o (M∈{0, 1}), which is a measu e o he po e y le el
in he locali y whe e he household li es. We deno e he condi ional ype p obabili y
as ρl(P,M)≡P (μil =1|P,M); i ep esen s he ac ion o ype lamong s uden s wi h
P ospe a s a us Pand ma ginali y index M.No e ha lρl(P,M)=1, P∈{0, 1},M∈
{0, 1}.
24This ype o imming is common in he applica ion o ma ching es ima o s as a way o imposing “com-
mon suppo .” Heckman, Ichimu a, and Todd (1997) showed, in he con ex o e alua ing a job- aining
p og am, ha ha ing a highly compa able compa ison g oup is impo an o p oducing eliable nonexpe -
imen al impac es ima es ha eplica e expe imen al es ima es.
25See, o example, Heckman and Singe (1984), Cunha and Heckman (2008). Al e na i ely, we could
impose a con inuous dis ibu ion o he unobse ed he e ogenei y, o example, a mix u e o no mal dis-
ibu ions. M oz (1999) shows he disc e e- ype assump ion pe o ms as well as he no mal assump ion
when he ue dis ibu ion is no mal. When he ue dis ibu ion is no no mal, howe e , he inds ha he
disc e e- ype me hod pe o ms be e .
154 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
3.3 The model
As desc ibed in Sec ion 2.4, ou modeling and es ima ion app oach is designed o ad-
d ess se e al s a is ical challenges ha a ise in e alua ing he P ospe a p og am aca-
demic achie emen impac s. Fi s , we add ess he p oblem o selec i e p og am pa ic-
ipa ion by es ic ing ou analysis sample o child en es ima ed o ha e a posi i e p ob-
abili y o pa icipa ing in he p og am.26 Second, ou school-a endance and school-
choice amewo k, which models he sequen ial choices shown in Figu e 3,explici lyad-
d esses dynamic selec ion in school choices and d opou decisions. These decisions a e
pe mi ed o depend bo h on obse ed amily backg ound cha ac e is ics as well as on
unobse ed ac o s ha a e assumed o ollow a mul inomial dis ibu ion (i.e., disc e e
ypes). We also inco po a e exogenous a iables, such as impu ed local hou ly wages,
dis ances o he nea es school o each ype, and he numbe o local schools o each
ype, as exclusion es ic ions ha a ec school- ype choices and d opou decisions bu
do no en e he es sco e ou come equa ions di ec ly. Thi d, ou model explici ly ac-
coun s o g ade e en ion o cap u e ha child en may be obse ed mul iple imes in
he same g ade. Fou h, as desc ibed la e in Sec ion 4.1, we add ess po en ial es -sco e
dis o ions caused by a small ac ion o s uden s suspec ed o chea ing (copying).
We nex desc ibe ou mul iequa ion model o academic achie emen o e mul i-
ple g ade le els, which includes he ollowing componen s: alue-added models in each
g ade, he school-choice/d opou models in p ima y school and a he s a o sec-
onda y school, and he g ade- epe i ion p ocess.
Value-added model: Achie emen s in ma hema ics and Spanish e ol e o e ime wi h
school a endance. Le m=1 deno e ma hema ics, m=2 Spanish, and gdeno es he
g ade le el. The alue-added model is g ade-speci ic and school- ype (j) speci ic. The
coe icien s also a y depending on whe he he s uden passed he p e ious g ade
IPass
i,a−1=1 o is epea ing he g ade IPass
i,a−1=0.27 Le ZA
ia deno e he ec o o obse ed
cha ac e is ics o he you h and o he amily ha en e he achie emen p oduc ion
unc ion:
Am
ia =δmgI
0jl +Ai,a−1δgI
1j+δmgI
2jPi+ZA
iaδmgI
3j+ωmgI
ija .(2)
In his equa ion, δmgI
0jl is he ype-speci ic in e cep ha allows o unobse ed he e o-
genei y (ldeno es he ype). Ai,a−1={A1
i,a−1,A2
i,a−1}is a 2 ×1 ec o including bo h he
ma hema ics sco e and he Spanish sco e om he p e ious pe iod a−1. The lagged
es -sco e e ms a e assumed o be su icien s a is ics o he impac s o pas inpu s
in he lea ning p ocess. This speci ica ion allows o c oss-e ec s be ween Spanish and
ma hema ics. Fo example, be e Spanish skills may enhance s uden ’s unde s anding
in hei ma hema ics classes, implying a posi i e e ec o pas Spanish sco es on cu -
en ma hema ics sco es. The impac o he P ospe a p og am is cap u ed by δmgI
2j.We
26The alue o imposing common suppo on he p opensi y sco e dis ibu ion in he con ex o social
p og am e alua ion is emphasized in Heckman, Ichimu a, and Todd (1997).
27I a s uden epea s a g ade, hen he lagged es sco e pe ains o he same g ade as in he cu en ime
pe iod and would he e o e ha e a di e en associa ed coe icien om he case whe e he lag pe ains o
he p e ious g ade.
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 155
assume ha he e o e ms ωmgI
ija , condi ional on he unobse ed ypes, a e i.i.d. and
no mally dis ibu ed. Mos o he li e a u e conside s lea ning echnology o be exoge-
nous. By combining a school-choice model wi h alue-added models ha a y by school
ype, we allow s uden s/pa en s o selec om di e en a ailable lea ning echnologies.
School-choice model: We nex speci y how indi iduals make hei schooling choice Dij a
om he a ailable op ions, Jg
ia (depending on his/he g ade and geog aphic loca ion, as
de ined in equa ion (1)). Assuming a andom-u ili y model wi h Type I ex eme- alue
e o s ( as e he e ogenei y) yields a mul inomial logis ic model o he p obabili y o
choosing op ion jia:
P Dija =1|˜
(a),μl
=⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
expμg
0jl +Aia−1φg
1j+Piφg
2j+ jZD
ia,wia,Sdis ance
ija ,Snumbe
ija
j∈Jg
a
expμg
0jl+Aia−1φg
1j+Piφg
2j+ jZD
ia,wia,Sdis ance
ija,Snumbe
ija i jia ∈Jg
a,
0i jia /∈Jg
a,
(3)
whe e μg
0jl is a ype-speci ic in e cep (ldeno es he ype). The pa ame e φg
1jcap u es
he e ec o es sco es on schooling choices, and φg
2jcap u es he impac o P ospe a
on schooling choices. ZD
ia ∈˜
(a)includes demog aphic and amily-backg ound cha -
ac e is ics. The e a e h ee addi ional a iables ha en e he school-choice equa ions
bu no o he pa s o he model: (i) he impu ed hou ly wage wia; (ii) he dis ance o
he closes school o each ype Sdis ance
ija ; and (iii) he local supply o schools o each ype
Snumbe
ija .
As p e iously no ed, he ou side op ion in ou school-choice model is o d op ou o
school, which could be a mo e a ac i e op ion in a eas ha pay highe wages o child
labo . Due o he absence o wage in o ma ion in ou es -sco e da abases, we ely on
da a om he 2010 Mexican census o impu e wages o indi iduals based on cha ac-
e is ics such as hei age, gende , schooling le el, and geog aphical egion o esidence.
Addi ionally, ou impu a ion p ocedu e inco po a es a selec ion co ec ion mechanism
o accoun o selec i e labo - o ce pa icipa ion.28 The impu ed wage, deno ed as wia,
ep esen s he oppo uni y cos s associa ed wi h being en olled in school. Two o he
impo an a iables in he school-choice model a e he dis ance o he nea es school
(Sdis ance
ija ) and he log numbe o local schools o a ious ypes (Snumbe
ija ). These a iables
a e included o cap u e he e ec o local school a ailabili y on indi iduals’ schooling
decisions.
We assume ha he h ee exogenous a iables {wia,Sdis ance
ija ,Snumbe
ija }a ec school-
choice decisions bu do no di ec ly en e he es -sco e equa ions (i.e., exclusion e-
s ic ions). These a iables a e help ul o iden i y sepa a ely he pa ame e s in he alue-
28Fo a mo e de ailed explana ion, please e e o he SA Table A.2.
156 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
added models om pa ame e s in he school-choice/d opou model.29 Howe e , he ex-
clusion es ic ion could be in alid, o example, i highe wages p o ide incen i es o
s uden s o wo k pa - ime while en olled in school, which di ec ly a ec ed hei es -
sco e pe o mance. Ano he po en ial h ea o alidi y is ha he a el dis ance may
di ec ly a ec he commu ing ime equi ed o a end schools. Bo h channels may neg-
a i ely impac academic pe o mance h ough a igue o educed abili y o concen a e
on s udying. To examine he empi ical ele ance o such conce ns, we also es ima ed
a speci ica ion in which he a iables {wia,Sdis ance
ija ,Snumbe
ija }a e added o he alue-
added equa ion (3). We examined (i) whe he he coe icien s associa ed wi h P ospe a-
bene icia y s a us change and (ii) whe he he es ima ed coe icien s associa ed wi h
he a iables {wia,Sdis ance
ija ,Snumbe
ija }a e signi ican ly di e en om 0. We did no ind
e idence o di ec impac s o {wia,Sdis ance
ija ,Snumbe
ija }on es sco es, condi ional on he
o he model co a ia es.
As we will elucida e in Sec ion 3.5, one way o in e p e ing ou school-choice
p obabili y equa ion is an app oxima ion o a policy unc ion de i ed om a ull
dynamic e sion o ou s uc u al model ( o ela ed discussion see, e.g., Heckman,
Humph ies, and Ve amendi (2016)). To accoun o po en ial nonlinea e ec s o he
s a e a iables on decision making, we adop a lexible unc ional o m, deno ed as
(ZD
ia,wia,Sdis ance
ija ,Snumbe
ija ).30
G ade e en ion: Las ly, we speci y a p obabilis ic model o whe he a s uden passes
a g ade, which depends on he unobse ed ype μl, he cu en school ype a ended jia,
academic knowledge as p oxied by he achie emen sco es Aia, he g ade le el Gia,P os-
pe a bene icia y s a us Pias well as some demog aphic and amily-backg ound cha ac-
e is ics, ZI
ia ∈˜
(a):
P IPass
ia =1|˜
(a),μl=γg
0l+Aiaγg
1+γg
2Pi+jiaγg
3+ZI
iaγg
4.(4)
The coe icien s o he passing p obabili y p obi model a e g ade-speci ic and γg
0lis a
unobse ed ype-speci ic in e cep .
3.4 T ea men -e ec he e ogenei y
P ospe a may ha e he e ogeneous impac s o s uden s om di e en backg ounds. In-
spi ed by he ma ginal- ea men -e ec (MTE) li e a u e, we di ide he analysis sample
in o qua iles based on he P ospe a-eligible p opensi y sco es and allow he P ospe a
impac o a y by qua ile.31 Families in he highes qua ile, ha is, wi h cha ac e is ics
29In a pa ame ic se ing, exclusion es ic ions a e no s ic ly equi ed. None heless, independen a i-
a ion in he de e minan s o d opou and school-choice decisions p o ides addi ional sou ces o iden i i-
ca ion ha do no ely on unc ional o m es ic ions.
30In SA Sec ion D, we desc ibe how we use Bayesian In o ma ion C i e ion (BIC) o de e mine ou inal
econome ic speci ica ion.
31We cap u e po en ial he e ogenei y mo e pa simoniously han a s anda d app oach in he li e a u e,
which is o es ima e he ea men e ec nonpa ame ically as a unc ion o he p opensi y-ma ching sco e
(e.g., Heckman and Vy lacil (2001,2005,2007)). Howe e , mos li e a u e implemen s MTE in a s a ic se up
whe eas ou model is dynamic.
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 163
once a he s a o p ima y school and he lowe -seconda y school ype is chosen once
a he s a o lowe -seconda y school. Second, we assume ha indi iduals who d op
ou o school do no a e wa ds een oll.43 Thi d, because he ac ion o s uden s who
epea g ades is ai ly small (see Table 2), we es ima e a sepa a e alue-added model o
e ained s uden s bu es ic he model coe icien s o no a y ac oss g ades, sepa a ely
wi hin p ima y school and lowe -seconda y school g ades.44
4.4 E alua ing he e ec s o P ospe a-p og am pa icipa ion
P ospe a p o ides cash ans e s o child en o bene icia y households who a e en olled
in school in g ades 3–12. Fo child en in g ades 3–9, he ans e s ypically go o he
mo he s. Whe he a ans e is ecei ed o each child depends, howe e , on whe he
ha child egula ly a ends school (a leas 85% o school days). We conside he am-
ily’s P ospe a s a us as a ime-in a ian cha ac e is ic, so i is con ained in he ini ial
s a e space (0). Once amilies a e en olled in he p og am, hey a ely lose hei eligi-
bili y. E en i one child is no a ending school, he amily may s ill ecei e ans e s o
o he child en and is s ill conside ed o be pa icipa ing. We use he es ima ed schooling
model o simula e school-going and es -sco e ou comes o P ospe a amilies’ child en
had hey no pa icipa ed in P ospe a. In his way, we a e able o assess he g ade-speci ic
p og am impac s as well as he cumula i e impac s o pa icipa ing in P ospe a o mul-
iple yea s.
5. Model es ima es
We es ima e he model pa ame e s by maximum likelihood. The key pa ame e s, speci -
ically hose linked o P ospe a e ec s, a e shown in SA Sec ion C, whe eas he comple e
se o pa ame e s can be ound in SA Sec ion D. In his sec ion, we ocus on wo aspec s:
examining sco e dis o ion s emming om po en ial copying beha io , and e alua ing
he model’s goodness-o - i based on ou adjus ed es sco es ha accoun o es -sco e
in la ion esul ing om chea ing beha io .
5.1 Tes -sco e measu emen equa ion
A unique ea u e o ou da a se is ha i con ains in o ma ion on which s uden s we e
lagged by he SEP as po en ial copie s. Ou es -sco e measu emen equa ion allows
he ue es sco e o di e om he measu ed es sco e in he e en o copying and also
allows o he e ogenei y in he gains om copying ac oss g ades and ypes o schools
( o e lec po en ial di e ences in moni o ing). In he con ex o a alue-added model,
43In ou aw da a se , a me e 0.2% (378 indi iduals) swi ched schools o a di e en ype du ing hei
p ima y-school yea s, while 3.2% (6220 indi iduals) changed school ypes in lowe -seconda y school. Ad-
di ionally, we no e ha 1.99% (3770 indi iduals) een olled in school a e ini ially lea ing.
44Tha is, we es ic δm4I
kj =δm5I
kj ,δm6I
kj =δm7I
kj =δm8I
kj ,k={1, 2, 3}in he alue-added equa ion (2) and
γ4
k=γ5
k=γ6
k,γ7
k=γ8
k,k={1, 2, 3, 4}in equa ion (4) in he pe iods when IPass
ia =0.Bu hein e cep e ms
δmgI
0jl and γg
0la e g ade-speci ic.
164 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
Table 8. Es ima ed es -sco e dis o ion om copying, by g ade and school ype.
Pe cen ages
Ma h Spanish
Raw T ue Di Raw T ue Di
G ade 5
Gene al 4.2% 570 525 45 549 521 28
Indigenous 7.0% 540 474 66 515 468 46
O e all 4.4% 568 521 47 546 517 29
G ade 6
Gene al 4.0% 606 554 52 578 545 33
Indigenous 6.3% 566 510 56 536 499 37
O e all 4.1% 603 551 52 575 542 33
G ade 7
Gene al 1.7% 558 499 59 523 489 34
Teleseconda y 4.1% 619 525 94 540 486 54
Technical 2.5% 573 498 75 536 489 47
O e all 2.6% 588 510 78 534 488 46
G ade 8
Gene al 3.3% 614 529 85 555 508 47
Teleseconda y 9.9% 698 580 118 585 517 68
Technical 4.1% 613 528 85 554 511 43
O e all 5.3% 656 554 102 570 513 57
G ade 9
Gene al 2.6% 631 549 82 531 505 26
Teleseconda y 5.7% 667 607 60 529 509 20
Technical 3.8% 621 553 68 536 510 26
O e all 3.8% 642 574 68 532 508 24
No e: The pe cen ages in he second column gi e he pe cen ages o s uden s suspec ed o copying in ei he ma hema ics
o Spanish es s.
copying can lead o a one-sided measu emen e o in ei he he dependen a iable
( he es sco e) o in an independen a iable (lagged es sco es) o in bo h a iables, bu
only o s uden s who copied. Table 8shows he pe cen ages o s uden s suspec ed o
copying, which anges om a low o 1.7% in 7 h g ade in gene al schools o a high o 9.9%
in 8 h g ade in eleseconda y schools. A he p ima y-school le el, indigenous schools
exhibi highe copying a es. We es ima e ha copying dis o s a e age es sco es by
20–118 poin s o copie s. Ou ea lie -desc ibed es ima ion app oach accoun s o his
po en ial dis o ion.
5.2 Model goodness-o - i
Ou model in ol es a subs an ial numbe o pa ame e s, in pa due o ou delibe a e
choice no o impose cons ain s in he alue-added model coe icien s ac oss a ious
g ade le els. These pa ame e s a e mos ly p ecisely es ima ed due o ou la ge sam-
ple sizes. Tables 9and 10 p o ide e idence on he model’s goodness-o - i . In Table 9,
we compa e a e age es sco es ac oss g ades and by P ospe a bene icia y s a us in he
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 165
Table 9. Goodness-o - i o a e age es sco es by P ospe a s a us (P).
P ospe a
Ma hema ics sco e Spanish sco e
P=0P=1P=0P=1
Da a Sim Da a Sim Da a Sim Da a Sim
G ade 5 521 522 495 496 520 519 490 490
G ade 6 550 551 526 527 545 543 515 517
G ade 7 489 489 492 491 477 477 465 465
G ade 8 516 515 529 526 487 487 480 480
G ade 9 540 539 564 563 490 489 481 481
No e: We simula e he es sco es 100 imes o each indi idual. In his able, we adjus o any copying in bo h he simula-
ion and he da a.
da a and based on model simula ions. The da a a e ages closely align wi h he model-
simula ed a e ages, wi h ew excep ions. The es ima ed model ep oduces he obse ed
pa e n whe e P ospe a bene icia ies ha e lowe a e age es sco es in p ima y g ades
o bo h subjec s. I also cap u es he end o es -sco e dispa i ies be ween bene icia-
ies and nonbene icia ies diminishing in lowe -seconda y g ades, and e en e e sing in
ma hema ics.
Table 10 shows how well ou model i s he school- ype dis ibu ion. The model’s
p edic ed p opo ions closely ma ch he da a, wi h di e ences o no mo e han 0.02. Ou
model e ec i ely cap u es wo impo an da a ea u es: he highe p obabili y o P os-
pe a-bene icia y child en a ending eleseconda y lowe -seconda y schools and hei
highe a es o d opping ou . Addi ionally, i ep oduces he obse ed d opou pa e ns
ac oss di e en g ades.
6. Assessing cumula i e P ospe a-p og am e ec s
6.1 The cumula i e P ospe a-p og am e ec s
A e age ea men e ec on ea ed As p e iously desc ibed, educa ional p oduc ion
unc ions ypically assume ha knowledge acquisi ion in ma hema ics and Spanish is
Table 10. Goodness-o - i o school- ype dis ibu ion.
Lowe -seconda y
choice
Gene al Teleseconda y Technical D opou
Da a Sim Da a Sim Da a Sim Da a Sim
Nonbene icia y (P =0)
G ade 7 0.49 0.47 0.13 0.13 0.31 0.30 0.08 0.09
G ade 8 0.46 0.44 0.12 0.12 0.29 0.28 0.13 0.15
G ade 9 0.41 0.40 0.11 0.11 0.26 0.26 0.23 0.23
P ospe a bene icia y (P =1)
G ade 7 0.26 0.24 0.43 0.44 0.21 0.22 0.10 0.10
G ade 8 0.24 0.23 0.41 0.41 0.20 0.20 0.16 0.16
G ade 9 0.21 0.20 0.36 0.36 0.17 0.18 0.26 0.26
No e: We simula e he es sco es 100 imes o each indi idual.
166 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
a cumula i e p ocess. The alue-added model speci ica ion allows lagged knowledge o
ha e an e ec on con empo aneous knowledge accumula ion, so ha he his o y o in-
pu s in o he lea ning p ocess ma e s. I P ospe a pa icipa ion inc eases knowledge a
a pa icula g ade, hen his bene i can ha e a pe sis en e ec on lea ning in u u e
g ades. Tha is, p og am pa icipa ion can ha e bo h di ec e ec s on cu en es sco es
as well as indi ec e ec s ope a ing h ough lagged es sco es.
In Table 11, we use ou es ima ed model o simula e he e ec s o being a P ospe a
bene icia y o e mul iple g ades, s a ing wi h g ade 4. Ou es ima ion p ocedu e allows
o P ospe a e ec s ha ope a e h ough all o he di e en channels o ou school p o-
g ession and achie emen model and ha may di e o gi ls and boys. Columns labeled
P=1 show he ou comes o P ospe a-bene icia y child en/you h wi h hei pa icipa-
ion in he p og am. Columns labeled ˜
P=0 show he simula ed (coun e ac ual) ou -
comes we e hey no o pa icipa e in he p og am.45
I is only possible o assess es -sco e impac s o child en/you h who would a end
school bo h wi h and wi hou P ospe a. The e o e, ou epo ed p og am impac s on
es sco es in column “Di ” ep esen lowe bounds, as hey do no include po en ial
academic achie emen gains o child en/you h who in he absence o P ospe a would
no be a ending he g ade.46 Ou esul s show posi i e bene i s o being a P ospe a ben-
e icia y in lowe -seconda y g ades bu essen ially no e ec o ma h and Spanish in p i-
ma y g ades. In lowe -seconda y school, he cumula i e P ospe a impac in ma hema -
ics inc eases wi h he g ade le el and eaches a high o 0.21 s anda d de ia ions by g ade
Table 11. Cumula i e p og am impac s.
Ma hema ics sco e Spanish sco e
P=1˜
P=0Di S.E.P=1˜
P=0Di S.E.
G ade 5 495 496 −0.2 0.7 490 491 −0.9 0.7
G ade 6 527 522 4.3 0.8 517 521 −4.1 0.7
G ade 7 492 478 13.7 2.0 465 459 6.3 1.6
G ade 8 527 513 14.2 1.8 481 476 4.8 1.5
G ade 9 562 541 20.8 2.2 482 478 4.0 1.8
D opou a e Re en ion a e
P=1˜
P=0Di S.E.P=1˜
P=0Di S.E.
G ade 5 – – – – 0.04 0.04 −0.004 0.002
G ade 6 – – – – 0.02 0.03 −0.003 0.001
G ade 7 0.11 0.17 −0.07 0.01 0.003 0.002 0.000 0.000
G ade 8 0.16 0.23 −0.08 0.01 0.003 0.004 −0.001 0.001
G ade 9 0.25 0.33 −0.08 0.01 0.003 0.004 −0.001 0.001
No e: We epo es sco e impac s o child en/you h who would a end school bo h wi h andwi hou P ospe a. The cumu-
la i e impac s a e ob ained h ough boo s ap simula ion wi h 100 eplica ions. In pa icula , we i s d aw he model pa ame-
e s om hei es ima ed dis ibu ions and simula e he cumula i e es sco es and impac s o each boo s ap i e a ion. Then
we ob ain s anda d e o s om he empi ical dis ibu ions. The columns “Di ” cap u e he es -sco e gain o hese subg oups.
The columns “S.E.” epo he s anda d e o s o he es -sco e gains om he p og am.
45Ou simula ion keeps he dis ibu ion o unobse ed ypes o P ospe a bene icia ies ixed.
46As we show in Figu e 6and Figu e 7, absen child en a e disp opo ionally om mos disad an aged
amily backg ounds and, he e o e, end o ha e la ge p og am gains on a e age.
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 167
9. In Spanish, he cumula i e gains a e subs an ially smalle — abou 0.04 s anda d de-
ia ions.47
We migh expec he es ima ed p og am e ec s o be la ge in lowe -seconda y
school han p ima y school because he ans e amoun s ha amilies ecei e o
school a endance a e much la ge .48 Also, olde child en ypically ha e mo e demands
on hei ime ha compe e wi h schoolwo k han do younge child en, such as aking
ca e o younge siblings, housewo k, wo king o amily businesses, o wo king o pay
a e school. The P ospe a cash ans e s may educe hese ou side ime uses, allowing
hem o ocus mo e on schoolwo k.
The lowe panel o Table 11 epo s he P ospe a impac on he d opou a e (cu-
mula i e) and on he p obabili y o epea ing a g ade. The esul s show ha P ospe a
educes he d opou a e by 0.08 be o e he s a o g ade 9, wi h he mos p onounced
e ec du ing he p ima y o lowe -seconda y school ansi ion. We also ind ha P os-
pe a p ima ily educes he e en ion p obabili y du ing p ima y school bu has no sig-
ni ican e ec on e en ion du ing lowe -seconda y school.
Compa ison o p og am e ec s o emale and male s uden s The P ospe a p og am
p o ides g ea e subsidies o gi ls han boys o a ending school in pos -p ima y g ades.
Table 12 examines whe he p og am e ec s di e by gende . The es -sco e impac s a e
signi ican ly posi i e o bo h gi ls and boys in all g ades excep o g ade 5. The la ges
impac s a e obse ed in lowe -seconda y school g ades and impac s a e la ge in ma h-
ema ics han in Spanish.
In e es ingly, he es ima es indica e ha pa icipa ion in P ospe a leads o a sligh
educ ion in gende academic achie emen gaps. Male s uden s ha e a 7-poin ad an-
age in a e age ma hema ics sco es o e emales a g ade 6. Pa icipa ion in he P ospe a
p og am h ough g ade 9 boos s emale s uden s’ ma hema ics sco es by 21.8 poin s in
compa ison o 19.6 o males and educes he gende gap by 3.0 poin s (=(564-560)-
(542-541)). In e ms o Spanish es sco es, emale s uden s ha e on a e age a 29-poin
ad an age o e males a g ade 6. P ospe a pa icipa ion is also associa ed wi h a educ-
ion in he gende gap in Spanish sco es by g ade 9, albei by a sligh ly smalle ma gin o
2.0 poin s (=(495-467)-(492-462)).
The p og am also na ows he gende gap in d opou a es. Fo he cu en P ospe a
bene icia ies, he cumula i e d opou a e by g ade 9 is 23.3 pe cen age poin s o e-
males and 27.0 pe cen age poin s o males. When we simula e he model aking away
he P ospe a p og am, we ind ha he gende di e ence inc eases om 3.7 (=27.0-23.3)
pe cen age poin s o 6.3 (=36.4-30.1) pe cen age poin s. Tu ning o he bo om panel o
he able, we do no ind signi ican gende di e ences in he P ospe a e ec on g ade
e en ion. In summa y, ou esul s show ha bo h emales and males bene i om P os-
pe a pa icipa ion and ha he p og am gene ally educes gende dispa i ies in ma he-
ma ics and Spanish es sco es and in d opou a es.
47The a e age e ec on he Spanish sco e displays subs an ial he e ogenei y among P ospe a bene icia-
ies, as will be shown below.
48In he all semes e o 2008, he ans e s anged om 130 o 265 pesos o p ima y school and 405 o
495 (385 o 430) o emales (males) in lowe -seconda y school (US1=11 pesos in 2008).
168 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
Table 12. Gende di e ences in cumula i e P ospe a e ec s (by g ade 9).
Female Male
P=1˜
P=0Di S.E.P=1˜
P=0Di S.E.
Ma hema ics sco e
G ade 5 500 499 0.7 0.9 491 492 −1.1 1.1
G ade 6 530 525 4.7 1.1 523 519 3.9 1.2
G ade 7 495 481 14.2 2.4 488 475 13.3 2.2
G ade 8 525 511 14.9 2.0 530 516 13.5 2.0
G ade 9 564 542 21.8 2.5 560 541 19.6 2.5
Spanish sco e
G ade 5 503 505 −1.3 0.9 476 476 −0.5 1.0
G ade 6 531 536 −4.5 0.9 502 506 −3.6 1.0
G ade 7 484 480 4.6 1.9 446 437 8.1 1.7
G ade 8 498 494 4.2 1.8 462 456 5.5 1.7
G ade 9 495 492 3.2 1.9 467 462 5.0 2.1
D opou a e
G ade 7 0.10 0.16 −0.06 0.01 0.11 0.18 −0.07 0.012
G ade 8 0.15 0.22 −0.07 0.01 0.16 0.25 −0.09 0.011
G ade 9 0.23 0.30 −0.07 0.009 0.27 0.36 −0.09 0.009
Re en ion a e
G ade 4 0.03 0.03 −0.003 0.002 0.05 0.06 −0.004 0.003
G ade 5 0.01 0.02 −0.002 0.002 0.03 0.04 −0.003 0.002
G ade 6 0.001 0.001 0.000 0.000 0.004 0.004 0.000 0.000
G ade 7 0.001 0.002 −0.001 0.001 0.005 0.006 −0.001 0.002
G ade 8 0.002 0.002 −0.001 0.001 0.005 0.007 −0.002 0.001
No e: Es ima es ob ained h ough model simula ion. See he no e o Table 11.
P ospe a e ec s by p opensi y-sco es qua iles We nex explo e he he e ogeneous P os-
pe a impac s o s uden s om di e en backg ounds in Figu es 6and 7. Figu e 6shows
he e ec s o P ospe a pa icipa ion on es sco es b oken down by p opensi y-sco es
qua iles. As desc ibed in Sec ion 3.4, he p opensi y sco e is a summa y s a is ic o s u-
den s’ amily backg ound, wi h qua ile 1 deno ing he mos ad an aged amilies and
qua ile 4 deno ing he mos disad an aged amilies. Ou es ima es show la ge im-
pac s in la e g ades and smalle impac s in ea lie g ades, ega dless o p opensi y-sco e
qua iles. These pa e ns a e consis en wi h he P ospe a e ec s being cumula i e wi h
g ea e exposu e associa ed wi h g ea e impac . Among he ou qua iles, we obse e
he la ges es ima ed cumula i e impac s o s uden s in he highes qua ile, who a e
he ones om he mos disad an aged backg ounds. P ospe a inc eases hei es sco es
in ma hema ics by 0.29 s anda d de ia ions and hei es sco es in Spanish by 0.09 s an-
da d de ia ions and bo h e ec s a e s a is ically signi ican . The op p opensi y sco e
qua ile con ains he majo i y (52.7%) o he P ospe a bene icia ies.
Figu e 7displays he cumula i e e ec s o P ospe a on h ee key ou comes: (i) Panel
(a) p esen s g ade a ainmen ; (ii) Panel (b) p esen s he cumula i e d opou a e; and
(iii) Panel (c) p esen s he o al numbe o e en ions du ing p ima y school. The i s
wo ou comes a e e alua ed a he end o a 6-yea pe iod, co esponding o he end
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 169
Figu e 6. P ospe a academic achie emen e ec s by p opensi y-sco e qua iles. No e: 95% con-
idence in e als, depic ed as ba s, a e de i ed using a pa ame ic boo s ap me hod wi h 100
eplica ions.
o g ade 9 ( o s uden s who do no expe ience g ade e en ion o d op ou ). The hi d
ou come, he cumula i e numbe o e en ions, is assessed upon comple ion o p ima y
school. The es ima ed impac s a e shown condi ional on he p opensi y sco e qua ile.
No ably, he mos subs an ial impac s (wi h he excep ion o cumula i e e en ions) a e
Figu e 7. P ospe a e ec s on schooling g ade a ainmen , d opou , and numbe o e en ions
by p opensi y-sco e qua iles. No e: 95% con idence in e als, depic ed as ba s, a e de i ed using
a pa ame ic boo s ap me hod wi h 100 eplica ions.
170 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
obse ed in he ou h qua ile, comp ised o he mos disad an aged s uden s. Because
s uden s op ing o d op ou a e gene ally lowe pe o ming, dis ega ding he selec ion
bias associa ed wi h dynamic d opou s ends o exagge a e he downwa d bias when
es ima ing he p og am e ec s, pa icula ly o s uden s in he ou h qua ile compa ed
o hose in o he qua iles.
Compa ing ATT wi h ATU Nex , we compa e he a e age ea men e ec on indi idu-
als who ecei ed ea men , commonly e e ed o as “ATT,” wi h he a e age ea men
e ec on hose who did no ecei e ea men , commonly e e ed o as “ATU.” In ou
analysis, he “un ea ed” g oup consis s o child en/you h who a e no bene icia ies o
he P ospe a p og am (P=0)bu who had a posi i e p obabili y o being a bene icia y,
as de e mined by hei household cha ac e is ics. (Recall ha we imposed common sup-
po as desc ibed p e iously.)
The esul s in Table 13 indica e ha he impac o he P ospe a p og am is signi -
ican ly g ea e o he ea ed g oup compa ed o he un ea ed g oup. Fo ins ance,
he P ospe a p og am leads o subs an ial imp o emen s in ma hema ics and Spanish
sco es o he ea ed s uden s, wi h inc eases o 20.8 and 4.0. Fo he un ea ed g oup,
he p og am only esul s in a ma hema ics sco e imp o emen o 12.3 and has li le e -
ec on Spanish sco es. A he ex ensi e ma gin, P ospe a educes he d opou a e by
0.08 o he ea ed g oup bu by only 0.05 o he un ea ed g oup. Las ly, P ospe a also
has a g ea e impac on educing e en ion p obabili ies o he ea ed g oup compa ed
o he un ea ed g oup.
These di e ences a e in line wi h ou ea lie indings, shown in Figu e 6.Those ig-
u es showed ha he mos subs an ial impac s a e obse ed among he mos disad an-
aged g oups. Now conside ing ha hese highly disad an aged s uden s a e disp o-
po iona ely mo e likely o be p og am bene icia ies, hey p edominan ly all in o he
ea ed g oup a he han he un ea ed g oup. Thus, i is expec ed ha he ATT would
be highe han he ATU.
6.2 The impo ance o he eleseconda y-school op ion
As p e iously desc ibed, child en/you h om P ospe a-bene icia y households o en
li e in u al a eas whe e eleseconda y schools a e a ailable and hey mo e o en a end
his school ype. We nex e alua e he impo ance o eleseconda y school as a de e -
minan o P ospe a impac s on school en ollmen . In pa icula , we use ou es ima ed
model o simula e wha educa ional ou comes would look like we e he eleseconda y-
school op ion no a ailable. The simula ion akes in o accoun ha s uden s migh hen
ha e o a el u he dis ances o ge o schools o d opou i eleseconda y schools had
been hei only op ion. Table 14 shows he dis ibu ion o local lowe -seconda y school-
choice se s in he da a (baseline) and a e emo ing he eleseconda y op ion. Fo 6.9%
o s uden s, eleseconda y schools a e he only op ion.
The uppe panel o Table 15 shows he simula ed d opou p opo ion (a g ade 9) o
cu en P ospe a eleseconda y en ollees when he eleseconda y schools a e emo ed
om hei choice se s. The d opou p opo ion inc eases d ama ically om 0.18 o 0.52.
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 171
Table 13. Compa ing ATT, ATU, and o e all ea men e ec .
ATT ATU O e all
Mean S.E. Mean S.E. Mean S.E.
Ma hema ics sco e
G ade 5 −0.2 0.7 0.8 1.1 0.4 0.8
G ade 6 4.3 0.8 5.2 1.1 4.9 0.9
G ade 7 13.7 2.0 9.1 1.8 10.7 1.7
G ade 8 14.2 1.8 7.6 1.9 9.9 1.7
G ade 9 20.8 2.2 12.3 2.4 15.2 2.1
Spanish sco e
G ade 5 −0.9 0.7 0.1 1.0 −0.3 0.8
G ade 6 −4.1 0.7 −2.5 1.0 −3.1 0.8
G ade 7 6.3 1.6 3.5 1.6 4.5 1.5
G ade 8 4.8 1.5 1.6 1.7 2.7 1.5
G ade 9 4.0 1.8 −0.2 1.8 1.2 1.7
D opou a e
G ade 7 0.07 0.01 0.03 0.007 0.05 0.01
G ade 8 0.08 0.01 0.04 0.007 0.06 0.01
G ade 9 0.08 0.01 0.05 0.007 0.06 0.01
Re en ion a e
G ade 4 −0.004 0.002 −0.002 0.002 −0.001 0.001
G ade 5 −0.0025 0.0015 −0.0016 0.0011 −0.0009 0.0006
G ade 6 0.0001 0.0002 −0.0001 0.0002 0.0001 0.0001
G ade 7 −0.0009 0.0011 −0.0006 0.0008 −0.0003 0.0003
G ade 8 −0.0010 0.0008 −0.0005 0.0007 −0.0003 0.0002
No e: “ATT” deno es he a e age ea men e ec on indi iduals who ecei ed he ea men , while “ATU” deno es he
a e age ea men e ec on hose who did no ecei e i . The “un ea ed” g oup consis s o child en and you h who a e no
P ospe a bene icia ies (P=0)bu had a posi i e p obabili y o eligibili y, based on household cha ac e is ics. Es ima es a e
de i ed om model simula ions.
A e age educa ional a ainmen o e he 6 yea s o ou obse a ion pe iod (up o g ade
9) alls om 8.76 g ades o 7.57 g ades. Despi e using di e en da a sou ces and e alua-
ion app oaches, ou esul s align wi h e idence on eleseconda y schools’ impo ance
epo ed in Na a o-Sola (2019).49
The lowe panel o Table 15 shows simula ed academic achie emen o cu en
P ospe a eleseconda y en ollees who con inue hei educa ion e en a e eleseconda y
schools a e no longe a ailable. A g ade 9, we obse e a dec ease in a e age ma hema -
ics es sco es, om 602 o 535, and a dec ease in a e age Spanish es sco es om 492 o
473. This inding is consis en wi h he es sco e dis ibu ional di e ences seen in Fig-
u e 2, which sugges ed ha eleseconda y schools a e ela i ely e ec i e in enhancing
s uden s’ es sco es, pa icula ly in ma hema ics,
49Using a di e ence-in-di e ence app oach and Employmen and Occupa ion Na ional Su ey (EONS)
da a se , she showed ha he cons uc ion o an addi ional eleseconda y pe 50 child en would encou age
10 indi iduals o en oll in lowe -seconda y educa ion, causing an a e age inc ease o one addi ional g ade
o educa ion among indi iduals ha could ha e a ended i .
172 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
Table 14. The school-choice dis ibu ion wi h and wi hou he eleseconda y op ion.
Baseline No eleseconda y
Gene al, echnical and eleseconda y 0.696 N/A
Gene al and eleseconda y 0.072 N/A
Gene al and echnical 0.061 0.757
Teleseconda y and echnical 0.078 N/A
Only gene al 0.012 0.090
Only eleseconda y 0.069 N/A
Only echnical 0.008 0.080
No local schools 0.004 0.073
6.3 Quan i ying he impo ance o dynamic selec ion
The mul iequa ion modeling amewo k ha we implemen ed con olled o mul iple
sou ces o dynamic selec ion—due o d opou , school choice, and g ade e en ion—as
well as o chea ing and missing da a. I inco po a ed unobse ed ypes o con ol o
po en ial selec i i y on unobse ed ac o s. A guably, in Mexico, selec ion is an impo -
an conside a ion, gi en ha school en ollmen d ops signi ican ly in lowe -seconda y
school g ades and ha pa en s can selec om a ailable schools.50 In he US con ex ,
alue-added models a e o en implemen ed wi hou accoun ing o selec ion.
To explo e he impo ance o con olling o mul iple sou ces o selec ion, we com-
pa e ou baseline esul s wi h esul s ob ained om a simple alue-added model ha
we es ima e g ade-by-g ade wi hou dis inguishing school ypes:
Am
ia =δmg
0+Ai,a−1δg
1+δmg
2Pi+ZA
iaδmg
3+ωmg
ia .
Compa ed wi h equa ion (3), he con empo aneous P ospe a e ec δmg
2is homogeneous
ac oss school ypes and we do no model school choice. Also, his model does no in-
clude pe manen unobse ed he e ogenei y ( ypes). The cumula i e p og am e ec can
Table 15. Simula ed d opou , educa ional a ainmen , and achie emen o P ospe a elesec-
onda y en ollees when he eleseconda y op ion is emo ed.
Wi h eleseconda y Wi hou eleseconda y
D opou a e 0.18 0.52
G ades a ained 8.76 7.57
Tes sco es a g ade 9
Ma h sco e 602 535
Spanish sco e 492 473
No e: The simula ion is based on he P ospe a bene icia ies who a e cu en ly en olled in eleseconda y school a g ade 7.
The ou comes a e measu ed by g ade 9.
50Came on and Heckman (2001) conside he p oblem o selec ion in modeling g ade p og ession in US
high schools, bu hey do no analyze es -sco e da a.
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 179
Beh man, Je e R., Susan W. Pa ke , and Pe a E. Todd (2009), “Schooling impac s o con-
di ional cash ans e s on young child en: E idence om Mexico.” Economic De elop-
men and Cul u al Change, 57 (3), 439–477. [0134]
Beh man, Je e R., Susan W. Pa ke , Pe a E. Todd, and Weilong Zhang (2024), “Supple-
men o “p ospe ing h ough P ospe a: A dynamic model o cc impac s on educa ional
a ainmen and achie emen in Mexico”.” Quan i a i e Economics Supplemen al Ma e-
ial. [0139]
Beh man, Je e R. and Ma k R. Rosenzweig (1999), ““Abili y” biases in schooling e u ns
and wins: A es and new es ima es.” Economics o Educa ion Re iew, 18 (2), 159–167.
[0137]
Beh man, Je e R., Piyali Sengup a, and Pe a Todd (2005), “P og essing h ough PRO-
GRESA: An impac assessmen o a school subsidy expe imen in u al Mexico.” Eco-
nomic De elopmen and Cul u al Change, 54 (1), 237–275. [0134,0138]
Be nal, Raquel and Michael P. Keane (2010), “Quasi-s uc u al es ima ion o a model o
childca e choices and child cogni i e abili y p oduc ion.” Jou nal o Econome ics, 156
(1), 164–189. [0162]
Boa dman, An hony E. and Richa d J. Mu nane (1979), “Using panel da a o imp o e
es ima es o he de e minan s o educa ional achie emen .” Sociology o Educa ion,52
(2), 113–121. [0135]
Bo ghesan, Emilio and Gab ielle Vasey (2024), “The ma ginal e u ns o dis ance edu-
ca ion: E idence om Mexico’s elesecunda ias.” Ame ican Economic Jou nal: Applied
Economics.[0139]
B a o, Da id, Sanka Mukhopadhyay, and Pe a E. Todd (2010), “E ec s o school e o m
on educa ion and labo ma ke pe o mance: E idence om Chile’s uni e sal ouche
sys em.” Quan i a i e Economics, 1 (1), 47–95. [0136]
Came on, S ephen V. and James J. Heckman (1998), “Li e cycle schooling and dynamic
selec ion bias: Models and e idence o i e coho s o Ame ican males.” Jou nal o Po-
li ical Economy, 106 (2), 262–333. [0135,0137]
Came on, S ephen V. and James J. Heckman (2001), “The dynamics o educa ional a -
ainmen o black, Hispanic, and whi e males.” Jou nal o Poli ical Economy, 109 (3),
455–499. [0135,0172]
Che y, Raj, John N. F iedman, and Jonah E. Rocko (2014a), “Measu ing he impac s o
eache s I: E alua ing bias in eache alue-added es ima es.” Ame ican Economic Re-
iew, 104 (9), 2593–2632. [0135]
Che y, Raj, John N. F iedman, and Jonah E. Rocko (2014b), “Measu ing he impac s
o eache s ii: Teache alue-added and s uden ou comes in adul hood.” Ame ican Eco-
nomic Re iew, 104 (9), 2633–2679. [0135]
Cunha, Fla io, James J. Heckman, Lance Lochne , and Dimi iy V. Mas e o (2006), “In-
e p e ing he e idence on li e cycle skill o ma ion.” Handbook o he Economics o Ed-
uca ion, 1, 697–812. [0135,0136,0137]
180 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
Cunha, Fla io and James J. Heckman (2008), “Fo mula ing, iden i ying and es ima ing
he echnology o cogni i e and noncogni i e skill o ma ion.” Jou nal o Human Re-
sou ces, 43 (4), 738–782. [0153]
Cunha, Fla io, James J. Heckman, and Susanne M. Schennach (2010), “Es ima ing he
echnology o cogni i e and noncogni i e skill o ma ion.” Econome ica, 78 (3), 883–
931. [0135,0136]
De Hoyos Na a o, Ra ael E., O azio A anasio, and Cos as Meghi (2019), “Can schola -
ships inc ease high school g adua ion a es? E idence om a andomized con ol ial
in Mexico.” Policy Resea ch Wo king Pape 8826, Wo ld Bank, h ps://hdl.handle.ne /
10986/31581.[0140]
De Hoyos, Ra ael, Rica do Es ada, and Ma ía José Va gas (2018), “P edic ing indi id-
ual wellbeing h ough es sco es: E idence om a na ional assessmen in Mexico.” The
Wo ld Bank. [0140]
De Hoyos, Ra ael, Rica do Es ada, and Ma ía José Va gas (2021), “Wha do es sco es
eally cap u e? E idence om a la ge-scale s uden assessmen in Mexico.” Wo ld De el-
opmen , 146, 105524. [0175]
De Hoyos, Ra ael, Vicen e A. Ga cia-Mo eno, and Ha y An hony Pa inos (2017), “The
impac o an accoun abili y in e en ion wi h diagnos ic eedback: E idence om Mex-
ico.” Economics o Educa ion Re iew, 58, 123–140. [0140]
Epple, Dennis, Akshaya Jha, and Holge Sieg (2018), “The supe in enden ’s dilemma:
Managing school dis ic capaci y as pa en s o e wi h hei ee .” Quan i a i e Eco-
nomics, 9 (1), 483–520. [0136]
Fab egas, Raissa and Laia Na a o-Sola (2023), “B oadcas ing educa ion a scale: The
long- e m e ec s o Mexico’s elesecunda ias.” Wo king pape , URL, h ps://cega.
be keley.edu/wp-con en /uploads/2020/03/Fab egas_PacDe 2020.pd .[0139]
Figlio, Da id N. and Cecilia Elena Rouse (2006), “Do accoun abili y and ouche h ea s
imp o e low-pe o ming schools?” Jou nal o Public Economics, 90 (1-2), 239–255. [0136]
Fiszbein, A iel and No be R. Schady (2009), Condi ional Cash T ans e s: Reducing
P esen and Fu u e Po e y. Wo ld Bank Publica ions. [0134,0138]
Fox, Je emy T., Kyoo il Kim, S ephen P. Ryan, and Pa ick Baja i (2012), “The andom
coe icien s logi model is iden i ied.” Jou nal o Econome ics, 166 (2), 204–212. [0159]
Gallego, F ancisco and And és He nando (2009), “On he de e minan s and implica ions
o school choice: S uc u al es ima es and simula ions o Chile.” Documen o de T a-
bajo, 343. [0135,0136]
Glewwe, Paul (2002), “Schools and skills in de eloping coun ies: Educa ion policies and
socioeconomic ou comes.” Jou nal o Economic Li e a u e, 40 (2), 436–482. [0135]
Hadna, Agus He uan o and Dyah Ka ika (2017), “E alua ion o po e y alle ia ion pol-
icy: Can condi ional cash ans e s imp o e he academic pe o mance o poo s uden s
in Indonesia?” Cogen Social Sciences, 3 (1), 1295548. [0138]
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 181
Hanushek, E ic (1979), “Concep ual and empi ical issues in he es ima ion o educa-
ional p oduc ion unc ions.” Jou nal o Human Resou ces, 14, 351–388. [0135]
Has ings, Jus ine, Thomas J. Kane, and Douglas O. S aige (2009), “He e ogeneous p e -
e ences and he e icacy o public school choice.” Vol. 2145, 1–46. NBER wo king pape .
[0136]
Has ings, Jus ine S., Ch is ophe A. Neilson, and Se h D. Zimme man (2012), “The e -
ec o school choice on in insic mo i a ion and academic ou comes.” Wo king Pa-
pe 18324, Na ional Bu eau o Economic Resea ch, URL h p://www.nbe .o g/pape s/
w18324.[0136]
Heckman, James J., John E ic Humph ies, and G ego y Ve amendi (2016), “Dynamic
ea men e ec s.” Jou nal o Econome ics, 191 (2), 276–292. [0156,0158,0159]
Heckman, James J., John E ic Humph ies, and G ego y Ve amendi (2018), “Re u ns o
educa ion: The causal e ec s o educa ion on ea nings, heal h, and smoking.” Jou nal o
Poli ical Economy, 126 (S1), S197–S246. [0157,0159]
Heckman, James J., Hidehiko Ichimu a, and Pe a E. Todd (1997), “Ma ching as an
econome ic e alua ion es ima o : E idence om e alua ing a job aining p og amme.”
Re iew o Economic S udies, 64 (4), 605–654. [0153,0154]
Heckman, James J. and Sal ado Na a o (2007), “Dynamic disc e e choice and dynamic
ea men e ec s.” Jou nal o Econome ics, 136 (2), 341–396. [0157,0159,0160]
Heckman, James J. and Bu on Singe (1984), “A me hod o minimizing he impac o
dis ibu ional assump ions in econome ic models o du a ion da a.” Econome ica, 52,
271–320. [0137,0153]
Heckman, James J. and Edwa d Vy lacil (2001), “Policy- ele an ea men e ec s.” Ame -
ican Economic Re iew, 91 (2), 107–111. [0156]
Heckman, James J. and Edwa d Vy lacil (2005), “S uc u al equa ions, ea men e ec s,
and econome ic policy e alua ion 1.” Econome ica, 73 (3), 669–738. [0156]
Heckman, James J. and Edwa d J. Vy lacil (2007), “Econome ic e alua ion o social p o-
g ams, pa I: Causal models, s uc u al models and econome ic policy e alua ion.”
Handbook o Econome ics, 6, 4779–4874. [0156]
Hono é, Bo E. and Eka e ini Ky iazidou (2000), “Panel da a disc e e choice models wi h
lagged dependen a iables.” Econome ica, 68 (4), 839–874. [0159]
Hsieh, Chang-Tai and Miguel U quiola (2006), “The e ec s o gene alized school choice
on achie emen and s a i ica ion: E idence om Chile’s ouche p og am.” Jou nal o
Public Economics, 90 (8-9), 1477–1503. [0136]
Kane, Thomas J., Daniel F. McCa ey, T ey Mille , and Douglas O. S aige (2013), “Ha e
we iden i ied e ec i e eache s? Valida ing measu es o e ec i e eaching using andom
assignmen .” Resea ch Pape . MET P ojec . Bill & Melinda Ga es Founda ion, Ci esee .
[0135]
182 Beh man, Pa ke , Todd, and Zhang Quan i a i e Economics 16 (2025)
Kane, Thomas J. and Douglas O. S aige (2008), “Es ima ing eache impac s on s uden
achie emen : An expe imen al e alua ion.” Wo king Pape 14607, Na ional Bu eau o
Economic Resea ch, URL h p://www.nbe .o g/pape s/w14607.[0135]
Keane, Michael P., Pe a E. Todd, and Kenne h I. Wolpin (2011), “The s uc u al es ima-
ion o beha io al models: Disc e e choice dynamic p og amming me hods and appli-
ca ions.” In Handbook o Labo Economics, Vol. 4, 331–461, Else ie . [0157]
Lei e, Phillippe G., Amba Na ayan, and Emmanuel Skou ias (2011), “How do ex an e
simula ions compa e wi h ex pos e alua ions? E idence om he impac o condi ional
cash ans e p og ams.” Policy Resea ch wo king pape WPS 5705, Wo ld Bank, h ps:
//hdl.handle.ne /10986/3469.[0157]
Manski, Cha les F. (1988), “Iden i ica ion o bina y esponse models.” Jou nal o he
Ame ican s a is ical Associa ion, 83 (403), 729–738. [0159]
McEwan, Pa ick J. (2001), “The e ec i eness o public, ca holic, and non- eligious p i-
a e schools in Chile’s ouche sys em.” Educa ion Economics, 9 (2), 103–128. [0135]
M oz, Thomas A. (1999), “Disc e e ac o app oxima ions in simul aneous equa ion
models: Es ima ing he impac o a dummy endogenous a iable on a con inuous ou -
come.” Jou nal o Econome ics, 92 (2), 233–274. [0153]
Na a o-Sola, Laia (2019), “Seconda y school expansion h ough ele ised lessons: The
labo ma ke e u ns o he Mexican elesecunda ia.” HCEO wo king pape , Uni e -
si y o Chicago, h ps://humcap.uchicago.edu/RePEc/hka/wpape /Na a oSola_2021_
seconda y-schools- ele ised-lessons.pd .[0171]
Neal, De ek (1997), “The e ec s o ca holic seconda y schooling on educa ional achie e-
men .” Jou nal o Labo Economics, 15 (1, Pa 1), 98–123. [0135]
Pa ke , Susan W. and Pe a E. Todd (2017), “Condi ional cash ans e s: The case o p o-
g esa/opo unidades.” Jou nal o Economic Li e a u e, 55 (3), 866–915. [0134,0143,0152,
0157]
Pa ke , Susan W. and Tom Vogl (2023), “Do condi ional cash ans e s imp o e economic
ou comes in he nex gene a ion? E idence om Mexico.” The Economic Jou nal, 133
(655), 2775–2806. h ps://doi.o g/10.1093/ej/uead049. [0134,0138]
Ri kin, S e en G., E ic A. Hanushek, and John F. Kain (2005), “Teache s, schools, and
academic achie emen .” Econome ica, 73 (2), 417–458. [0137]
Ro hs ein, Jesse (2009), “S uden so ing and bias in alue-added es ima ion: Selec ion
on obse ables and unobse ables.” Educa ion Finance and Policy, 4 (4), 537–571. [0137]
Rouse, Cecilia Elena (1998), “P i a e school ouche s and s uden achie emen : An e al-
ua ion o he Milwaukee pa en al choice p og am.” Qua e ly Jou nal o Economics, 113
(2), 553–602. [0136]
Sapelli, Claudio and Be na di a Vial (2002), “The pe o mance o p i a e and public
schools in he Chilean ouche sys em.” Cuade nos de Economía, 39 (118), 423–454.
[0135]
Quan i a i e Economics 16 (2025) P ospe ing h ough P ospe a 183
Schellenbe g, Jona han and Ch is ophe R. Wal e s (2020), “Do pa en s alue school e -
ec i eness?” Ame ican Economic Re iew, 110 (5), 1502–1539. [0136]
Schul z, T. Paul (2004), “School subsidies o he poo : E alua ing he Mexican P og esa
po e y p og am.” Jou nal o De elopmen Economics, 74 (1), 199–250. [0134,0138]
SEP (2010), “Enlace: Manual ecnico 2010.” Wo king pape , URL h p:// ed.se alladolid.
mx/pd /20150721121435997529manual_ ecnico_enlace10.pd .[0140,0146]
SEP (2018a), “Cues iona ios de con ex o (enlace).” h ps://xabe .o g.mx/
eposi o io-de-da os/, las accessed on 2018-11-15. [0140]
SEP (2018b), “Resul ados de ap endizaje (enlace).” h ps://xabe .o g.mx/
eposi o io-de-da os/, las accessed on 2018-11-15. [0141]
Skou ias, Emmanuel and Susan W. Pa ke (2001), “Condi ional cash ans e s and hei
impac on child wo k and schooling: E idence om he p og esa p og am in Mexico.”
Economia, 2 (1), 45–96. [0137]
Snils ei , Bi e, Emma Gallaghe , Daniel Phillips, Ma ina Voj ko a, John Eye s, Da ni
Skaldiou, Jenni e S e enson, Ami Bha sa , and Philip Da ies (2017), “P o ocol: In e -
en ions o imp o ing lea ning ou comes and access o educa ion in low-and middle-
income coun ies: A sys ema ic e iew.” Campbell Sys ema ic Re iews, 13 (1), 1–82.
[0138]
Summe s, Ani a A. and Ba ba a L. Wol e (1977), “Do schools make a di e ence?” Ame i-
can Economic Re iew, 67 (4), 639–652. [0135]
Todd, Pe a E. and Kenne h I. Wolpin (2003), “On he speci ica ion and es ima ion o he
p oduc ion unc ion o cogni i e achie emen .” Economic Jou nal, 113 (485), F3–F33.
[0135,0137]
Todd, Pe a E. and Kenne h I. Wolpin (2006), “Assessing he impac o a school subsidy
p og am in Mexico: Using a social expe imen o alida e a dynamic beha io al model o
child schooling and e ili y.” Ame ican Economic Re iew, 96 (5), 1384–1417. [0134,0138,
0157]
Co-edi o Limo Golan handled his manusc ip .
Manusc ip ecei ed 22 No embe , 2022; inal e sion accep ed 19 Sep embe , 2024; a ailable
online 9 Oc obe , 2024.
The eplica ion package o his pape is a ailable a h ps://doi.o g/10.5281/zenodo.13771826.
The Jou nal checked he da a and codes included in he package o hei abili y o ep oduce
he esul s in he pape and app o ed online appendices.
