Expansion of piped water and sewer networks: The effects of regulation

dos San os, Ca olina Tojal Ramos; Guide i, B una Mo ais
Wo king Pape
Expansion o piped wa e and sewe ne wo ks: The e ec s
o egula ion
IDB Wo king Pape Se ies, No. IDB-WP-1734
P o ided in Coope a ion wi h:
In e -Ame ican De elopmen Bank (IDB), Washing on, DC
Sugges ed Ci a ion: dos San os, Ca olina Tojal Ramos; Guide i, B una Mo ais (2025) : Expansion o
piped wa e and sewe ne wo ks: The e ec s o egula ion, IDB Wo king Pape Se ies, No. IDB-
WP-1734, In e -Ame ican De elopmen Bank (IDB), Washing on, DC,
h ps://doi.o g/10.18235/0013622
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/324841
S anda d-Nu zungsbedingungen:
Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen
Zwecken und zum P i a geb auch gespeiche und kopie we den.
Sie dü en die Dokumen e nich ü ö en liche ode komme zielle
Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich
machen, e eiben ode ande wei ig nu zen.
So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen
(insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en,
gel en abweichend on diesen Nu zungsbedingungen die in de do
genann en Lizenz gewäh en Nu zungs ech e.
Te ms o use:
Documen s in EconS o may be sa ed and copied o you pe sonal
and schola ly pu poses.
You a e no o copy documen s o public o comme cial pu poses, o
exhibi he documen s publicly, o make hem publicly a ailable on he
in e ne , o o dis ibu e o o he wise use he documen s in public.
I he documen s ha e been made a ailable unde an Open Con en
Licence (especially C ea i e Commons Licences), you may exe cise
u he usage igh s as speci ied in he indica ed licence.
h ps://c ea i ecommons.o g/licenses/by/3.0/igo/
Expansion o Piped Wa e and Sewe
Ne wo ks:
The E ec s o Regula ion
Ca olina Tojal R. dos San os
B una Mo ais Guide i
WORKING PAPER No IDB-WP-1734
In e -
A
me ican De elopmen Bank
Depa men o Resea ch and Chie Economis
July 2025
* In e -
A
me ican De elopmen Bank
** Uni e si y o Michigan
Expansion o Piped Wa e and Sewe
Ne wo ks:
The E ec s o Regula ion
Ca olina Tojal R. dos San os*
B una Mo ais Guide i**
In e -
A
me ican De elopmen Bank
Depa men o Resea ch and Chie Economis
July 2025
Ca aloging-in-Publica ion da a p o ided by he
In e -Ame ican De elopmen Bank
Felipe He e a Lib a y
Tojal, Ca olina.
Expansion o piped wa e and sewe ne wo ks: he e ec s o egula ion /
Ca olina Tojal R. dos San os, B una Mo ais Guide i.
p. cm. — (IDB Wo king Pape Se ies ; 1734)
Includes bibliog aphical e e ences.
1. Wa e -supply-Law and legisla ion -B azil. 2. Wa e u ili ies-Law and
legisla ion-B azil. 3. Sewe -pipe-B azil. 4. D inking wa e -B azil. I. Mo ais
Guide i, B una. II. In e -Ame ican De elopmen Bank. Depa men o
Resea ch and Chie Economis . III. Ti le. IV. Se ies.
IDB-WP-1734
h p://www.iadb.o g
Copy igh © 2025 In e -Ame ican De elopmen Bank ("IDB"). This wo k is subjec o a C ea i e
Commons license CC BY 3.0 IGO (h ps://c ea i ecommons.o g/licenses/by/3.0/igo/legalcode). The
e ms and condi ions indica ed in he URL link mus be me and he espec i e ecogni ion mus be
g an ed o he IDB.
Fu he o sec ion 8 o he abo e license, any media ion ela ing o dispu es a ising unde such license
shall be conduc ed in acco dance wi h he WIPO Media ion Rules. Any dispu e ela ed o he use o
he wo ks o he IDB ha canno be se led amicably shall be submi ed o a bi a ion pu suan o he
Uni ed Na ions Commission on In e na ional T ade Law (UNCITRAL) ules. The use o he IDB's name
o any pu pose o he han o a ibu ion, and he use o IDB's logo shall be subjec o a sepa a e
w i en license ag eemen be ween he IDB and he use and is no au ho ized as pa o his license.
No e ha he URL link includes e ms and condi ions ha a e an in eg al pa o his license.
The opinions exp essed in his wo k a e hose o he au ho s and do no necessa ily e lec he iews o
he In e -Ame ican De elopmen Bank, i s Boa d o Di ec o s, o he coun ies hey ep esen .
Abs ac *
This pape in es iga es s a egies o expand piped wa e and sewe h ough p i a e
p o ide s. Using billing da a om a majo p o ide in B azil and a s uc u al model o
consume sani a ion demand and se ice expansion, we assess he iabili y o con-
nec ion a ge s and he wel a e e ec s o connec ion subsidies and p ice incen i es. We
ind ha uni e sal connec ion a ge s a e la gely un easible due o low sewe ake-up.
Combining connec ion subsidies wi h highe sewe p ices boos s expansion and adop-
ion bu equi es go e nmen unding. Cha ging consume s upon sewe a ailabili y is
sel -sus aining and p omo es adop ion and expansion, bu i shi s cos s o households.
JEL classi ica ions: L95, Q25, L51
Keywo ds: Piped wa e , Sani a ion, Regula ion, S uc u al model
∗We a e g a e ul o Ying Fan, Ca he ine Hausman, Zach B own, and F ancine La on aine o hei
guidance h oughou his p ojec . We also hank pa icipan s a semina s and con e ences hos ed by he
Uni e si y o Michigan, Be keley Ene gy Camp, MSU & UM Ene gy and En i onmen al Economics Day, he
Semina on Wa e Economics (SWELL), he Annual Con e ence on Taxa ion (NTA), he Uni e si y o Sou h
Ca olina, he In e -Ame ican De elopmen Bank, Miami Uni e si y (Ohio), PUC Chile, ITAM, Uni e si y
o Chicago Ha is, Michigan S a e Uni e si y, Inspe , Obe lin College, LACEA-LAMES, he Encon o da
Sociedade B asilei a de Econome ia (SBE), and he WASH Con e ence o hei eedback and sugges ions.
We a e also hank ul o Rene Alejand o Nie o o excellen esea ch assis ance. The iews exp essed in his
pape a e hose o he au ho s and do no necessa ily e lec he iews o he In e -Ame ican De elopmen
Bank.

1 In oduc ion
Access o clean wa e and sani a ion emains a c i ical global challenge, wi h 2.2 billion
people lacking sa ely managed d inking wa e and 3.4 billion wi hou adequa e sani a ion as
o 2022 (UNICEF and WHO, 2023). Expanding piped wa e and sewe sys ems is pa icula ly
di icul in de eloping coun ies, whe e go e nmen s o en ace inancial cons ain s ha
limi in as uc u e in es men . A widely adop ed s a egy o add ess his issue is a ac ing
p i a e in es men in in as uc u e de elopmen and se ice p o ision, as seen in B azil,
A gen ina, Chile, he Philippines, Indonesia, and Sou h A ica (Ma in, 2009). Howe e , his
app oach p esen s a ade-o be ween inancial iabili y and social inclusion, as unde -se ed
popula ions ha e a low willingness o pay o se ices and i is cos ly o each hem (Fay
e al., 2021). While ex ensi e esea ch highligh s he bene i s o imp o ed access o wa e
se ices (Gampe -Rabind an e al., 2010; De o o e al., 2012; Alsan and Goldin, 2019; K esch
e al., 2023), he e is limi ed e idence on policy and egula ion o p omo e in as uc u e
expansion while ensu ing ha households connec o a ailable se ices.
This pape add esses his gap by examining he case o B azil, whe e a la ge sha e
o he popula ion is s ill no connec ed o piped wa e and sewe se ices, pa icula ly in
he No he n egion.1To ackle his issue, he go e nmen in oduced he New Sani a ion
Regula o y F amewo k in 20202, which encou ages municipali ies o con ac wi h p i a e
p o ide s and se s connec ion a ge s o 99% o households wi h piped wa e and 90% wi h
piped sewe collec ion wi hin each concession by 2033. These connec ion a ge s ollow
he Uni ed Na ions Sus ainable De elopmen Goals (UN, 2022), bu i is unclea i hey
a e iable o p i a e p o ide s. Mo eo e , he egula ion o e looks a c ucial ac o : while
p o ide s ins all he pipes up o he sidewalk, i is ul ima ely up o consume s o comple e
he connec ion o hei homes. Thus, he easibili y o hese connec ion a ge s hinges on
bo h i ms ha ing incen i es o expand he pipes and consume s aking up he se ice when
i is a ailable.
1In he No he n egion, only 54% o he popula ion had access o piped wa e , and jus 14% we e
connec ed o piped sewe se ices in 2017, acco ding o he Na ional Sani a ion Su ey (Pesquisa Nacional
de Saneamen o B´asico - PNSB) om IBGE. Appendix Figu e A1 p o ides connec ion a es o o he egions
o he coun y.
2No o Ma co Regula ´o io do Saneamen o - Fede al Law 14.026, B azil, July 15, 2020.
2
In his pape , we in es iga e he easibili y o achie ing uni e sal access o se ices
h ough p i a e p o ide s unde cu en egula ed p ices. Speci ically, we assess whe he
connec ion a ge s would be me i he i m expanded in as uc u e ac oss all concession
a eas. Ou indings sugges ha a subs an ial sha e o households would choose o emain
unconnec ed o piped sewe se ices e en i he in as uc u e we e a ailable. We hen
explo e policies o encou age ake-up and expansion, e alua ing he e ec i eness o sewe
connec ion subsidies, p ice adjus men s, and cha ging consume s based on sewe a ailabili y
ega dless o connec ion s a us. Finally, we analyze he implica ions o hese policies o
wel a e dis ibu ion be ween consume s and he p o ide .
We answe hese ques ions using no el billing da a om a p i a e p o ide in B azil.
Ou da ase includes mon hly billing eco ds a he add ess le el om consume s in a ious
municipali ies ac oss he coun y unde he i m’s concessions, co e ing h ee yea s be o e
he new egula ion. These da a, combined wi h demog aphic in o ma ion om he Census,
p o ide de ailed consump ion in o ma ion and show which pos al codes3 he i m expanded
o and which se ices hey ins alled (wa e o wa e and sewe ) wi hin i s concessions.
We i s use he da a o documen key pa e ns in he i m’s expansion decisions, con-
sume connec ions, and wa e consump ion choices. We show ha pos al codes ha ecei e
expansion o bo h se ices ha e, on a e age, highe incomes han pos al codes ha ecei e
only wa e . Mo eo e , he i m is mo e likely o expand in pos al codes close o he ins alled
ne wo k. We also documen ha pa o households do no connec when he se ices a e
a ailable. Wi hin pos al codes whe e bo h wa e and sewe se ices a e a ailable, on a -
e age, app oxima ely 71% o households ake up bo h se ices, while oughly 20% op o
wa e -only connec ions. Fu he mo e, highe -income a eas exhibi , on a e age, highe a es
o se ice adop ion.
In ou se ing, connec ed consume s ace non-linea p icing s uc u es4 o hei wa e
and sewe and espond o he a e age p ice. Two pieces o e idence sugges ha consume s
espond o he a e age p ice o hei bill a he han he ma ginal p ice. Fi s , we ind no
e idence o consump ion bunching a p ice schedule kinks whe e ma ginal p ices inc ease.
3In B azil, pos al codes a e e e ed o as CEPs (C´odigos de Ende e¸camen o Pos al), which unc ion
simila ly o zip codes in he Uni ed S a es.
4Inc easing block a es wi h a ixed ee.
3
Second, we obse e consump ion changes in esponse o p ice adjus men s ha a ec he
a e age p ice wi hou al e ing he ma ginal a e. Accu a ely iden i ying which p ice con-
sume s espond o is c ucial o modeling demand and assessing he impac o p ice changes
on p o ide e enues.
We use a s uc u al model o p edic bo h demand in a eas wi hou se ices, based on
p ices and demog aphics, and o eco e expansion cos s, which allows us o simula e he
e ec s o a ious policies. The demand side consis s o wo componen s: i) a disc e e-choice
model whe e households selec which se ice o connec o among he a ailable op ions in
hei pos al code, and ii) a con inuous-choice model whe e connec ed households decide
on hei wa e consump ion. On he supply side, he i m aces a disc e e-choice p oblem
when deciding which se ices o ins all in each pos al code based on p o i abili y. We use
c oss-sec ional a ia ion in demog aphics and exogenous p ice changes o iden i y consume
p e e ences and hei esponsi eness o a e age p ices. Using he es ima ed demand, we
p edic he po en ial e enue om expansion and es ima e cos pa ame e s om obse ed
expansions.
Using he es ima ed model, we i s assess he easibili y o mee ing he connec ion a ge s
by simula ing he i m expanding wa e and sewe se ices ac oss all pos al codes in i s
concessions. We ind ha household connec ions would no mee he a ge s due o limi ed
consume ake-up, wi h only abou 51% o households connec ing o piped sewe once i
is uni e sally a ailable. We hen allow he i m o op imally selec expansion a eas and
examine h ee policies aimed a inc easing he sha e o connec ed households: i) o e ing a
connec ion subsidy o co e he cos o ins alling he inal segmen be ween homes and he
main sewe line, ii) combining his subsidy wi h an inc ease in mon hly sewe bills, and iii)
imposing a cha ge o sewe a ailabili y, i espec i e o whe he households connec .5
The connec ion subsidy inc eases sewe ake-up in a eas wi h exis ing in as uc u e bu
does no incen i ize i m expansion. In some egions, he p ice cha ged o consume s is in-
su icien o co e p o ision cos s, making addi ional connec ions inancially de imen al o
he i m and de e ing u he expansion. To add ess his, we pai he subsidy wi h a 50%
5Unde his policy, in e e y pos al code wi h sewe pipes, consume s who ecei e a wa e bill will also
be cha ged o sewe se ice, ega dless o whe he hey a e connec ed.
4
inc ease in he a e age sewe p ice paid by households on hei mon hly bills. This combi-
na ion encou ages i m expansion, esul ing in app oxima ely 82% o households connec ing
o he sewe ne wo k, p ima ily d i en by adop ions in pos al codes ecei ing he se ice.
While his scena io bene i s bo h consume s and p o ide s, i equi es go e nmen unding
o subsidies, which could be poli ically and iscally challenging.
An al e na i e ha does no equi e di ec go e nmen in e en ion is he Sewe A ail-
abili y Cha ge, a policy al eady pe mi ed unde exis ing egula ions bu a ely implemen ed
by p o ide s. Unde his policy, consume s in pos al codes wi h piped sewe in as uc u e
mus pay o he se ice e en i hey do no connec . I e ec i ely wo ks as an ex e nali y ax
ha in e nalizes pa o he social cos o emaining unconnec ed. This app oach encou ages
i m expansion and consume adop ion, inc easing sewe connec ions o app oxima ely 55%
o he households. Howe e , unlike he subsidy-based app oach, his policy shi s he inan-
cial bu den en i ely on o consume s, aising a o dabili y conce ns despi e i s e ec i eness in
boos ing o e all connec ion a es.
The con ibu ions o his pape a e h ee old. Fi s , we endogenize i m expansion de-
cisions and link hem o consume choices in he wa e and sani a ion ma ke , p o iding a
amewo k o e alua e incen i es o inc ease se ice co e age. This app oach adds o ex-
is ing wo k ha ocuses on he bene i s o imp o ed sani a ion access (Cou y e al., 2024;
K esch e al., 2023; De o o e al., 2012; Alsan and Goldin, 2019; Gampe -Rabind an e al.,
2010; Ba e o e al., 2007) by add essing how expansions can be achie ed. Conside ing
bo h demand and supply allows us o iden i y ade-o s c ea ed by di e en policies. This
pe spec i e is essen ial o a oiding unin ended consequences, such as hose obse ed wi h
ene gy subsidies in India and Colombia, whe e unde p icing esul ed in unde in es men in
in as uc u e (Mahade an, 2024; Bu gess e al., 2020; McRae, 2015).
Second, we con ibu e o he g owing li e a u e on he adop ion o sani a ion echnolo-
gies, which has la gely ocused on oile s and sep ic anks (Deu schmann e al., 2024, 2023;
Gau am, 2023). We ex end his wo k by adap ing empi ical s a egies om he ene gy de-
mand li e a u e (Resende e al., 2025; Ba eca and Clay, 2016; Da is and Kilian, 2011; Dubin
and McFadden, 1984) and le e aging de ailed billing da a o model household ake-up and
consump ion o piped wa e and sewe se ices. Ou indings e eal ha low sewe ake-up
5
o bo h wa e and sewe in subsequen yea s indica e ha sewe se ices we e expanded.
Fo he cos es ima ion and he simula ions, we ocus on concessions in he No h and
No heas , whe e he e is s ill signi ican oom o expansion wi hin he i m’s bounda ies.
In con as , concessions in he Sou h and Sou heas al eady ha e nea -uni e sal wa e and
sewe co e age in ou da a.
4 Desc ip i e E idence
This sec ion p o ides desc ip i e e idence o he se ice expansion, connec ions, and
consump ion om ou da a. Fi s , he i m expands close o he exis ing ne wo k and o
weal hie pos al codes, consis en wi h a p o i -maximizing s a egy. Second, once he pipes
a e ins alled, a signi ican sha e o consume s do no connec ; demog aphics, such as income,
a e good p edic o s o ake-up. Thi d, o connec ed households, we also ind e idence ha
he wa e demand esponds o a e age p ices a he han ma ginal p ices, which is key o
compu ing consume s’ demand p ice elas ici y. These pa e ns guide he model p esen ed in
Sec ion 5.
4.1 Fi m Expansion
The i m builds pipes o only wa e , o wa e and sewe , in pos al codes unde i s con-
cessions. Table 2 shows ha pos al codes wi h bo h wa e and sewe pipes end o ha e
highe a e age incomes compa ed o pos al codes wi h only wa e pipes o no se ice a all.
This pa e n holds o pos al codes ha o iginally had pipes ins alled (“old”) and o pos al
codes whe e he i m expanded he pipes (“new”).
12

Table 2 – Pos al Code Cha ac e is ics by Pipe Ne wo k A ailabili y
Pipe ne wo k Numbe o
Pos al codes A g. income
Dis ance om
Only wa e ne wo k (km)
Dis ance om
Wa e and sewe ne wo k (km)
Old wa e and sewe 2188 4163
Old only wa e 2542 2543 8.41
Old only wa e /new sewe 67 3148 3.30
New wa e and sewe 36 4360 0.08 0.15
New only wa e 219 3252 0.12 20.63
No hing 539 2827 3.75 22.00
No es: This able summa izes demog aphic and in as uc u e cha ac e is ics (columns) by ype o se ice a ailabili y
( ows). I includes only pos al codes wi hin he i m’s concession a eas in he No h and No heas egions o he coun y.
Pos al codes wi h a leas one bill o he se ice in 2017 a e classi ied as “old.” Pos al codes ha i s appea ed in he
wa e billing eco ds in 2018 o 2019 a e ca ego ized as “new.” The emaining pos al codes, wi h no billing eco ds du ing
he pe iod, a e conside ed o ha e no se ice.
The i m expands close o he ins alled ne wo k. The las wo columns o Table 2 show
ha he pos al codes whe e he i m expanded a e on a e age close o he ne wo k o he
speci ic se ice ins alled. This pa e n is unsu p ising gi en he in e connec ed na u e o
wa e and sewe pipelines wi hin a b oade ne wo k. I is economically ad an ageous o
ins all pipes nea exis ing in as uc u e; he cos s ela ed o in as uc u e end o inc ease
as he dis ance om he ins alled ne wo k g ows. Addi ional e idence ha he i m expands
se ice nea i s exis ing ne wo k is shown in Appendix Figu e A3.
4.2 Incomple e Se ice Take-up
We show ha many households do no ake up he se ices in pos al codes wi h he pipes
a ailable. As depic ed in Figu e 2, on a e age app oxima ely 24% o households choose no
o connec o he wa e se ice when i is he only se ice a ailable in hei pos al code. In
a eas whe e bo h wa e and sewe se ices a e a ailable, app oxima ely 71% o households
connec o bo h se ices, while 20% p e e o connec o wa e only. Connec ing o he sewe
sys em in ol es connec ing he house o he main pipeline, a subs an ial inc ease in he bill,
and use s may no di ec ly pe cei e bene i s. These ac o s may help explain he incomple e
ake-up o wa e and sewe se ices.
Demog aphic ac o s in luence he connec ion o he main wa e and sewe pipelines.
The eg ession analysis p esen ed in Appendix Table A1 examines he ela ionship be ween
demog aphic a iables and he sha e o connec ed households in each pos al code whe e
se ices a e a ailable. Income is posi i ely co ela ed wi h comple e ake-up and nega i ely
13
Figu e 2. A e age Se ice Take-up
0 .2 .4 .6 .8 1
Sha e o households connec ed
Zips wi h only wa e pipes Zips wi h wa e and sewe pipes
Take-up only wa e Take-up wa e and sewe
No es: This igu e illus a es he a e age se ice ake-up ac oss pos al codes. The blue
ba s ep esen he a e age sha e o households connec ed o only wa e , while he o ange
ba s indica e he a e age sha e o households connec ed o bo h wa e and sewe . The le
ba co esponds o pos al codes wi h only wa e pipelines, whe eas he igh ba ep esen s
pos al codes wi h bo h wa e and sewe in as uc u e.
co ela ed wi h incomple e ake-up.17 Addi ionally, la ge households a e mo e likely o
adop he se ices ully, while hose wi h al e na i e sewe collec ion me hods a e, on a e age,
less likely o connec .
4.3 Consump ion Responds o A e age P ice
We in es iga e whe he consume s acing non-linea p ice schedules espond o ma ginal
o a e age p ices, as his dis inc ion is c ucial o accu a ely es ima ing hei p ice elas ici y.
We ind sugges i e e idence ha consume s eac o a e age p ice, consis en wi h o he wo k
in he wa e and ene gy ma ke s (I o and Zhang, 2020; Sea s, 2023; I o, 2014; Wichman,
2014; I o, 2013; Bo ens ein, 2009). Howe e , his esul goes agains o he ela ed pape s on
wa e ma ke s ha model consume s eac ing o ma ginal p ices as Szabo (2015), Olms ead
(2009), and Hewi and Hanemann (1995). The di e ence migh be associa ed wi h how he
p ices a e p esen ed o consume s and o he pa icula i ies o he con ex whe e he u ili y
bills a e cha ged.
17Comple e ake-up is de ined as connec ing o all he se ices a ailable a he pos al code, while con-
nec ing o only wa e when bo h wa e and sewe a e a ailable is conside ed incomple e.
14
1. No Bunching a he Kinks
All he concessions included in ou sample ha e non-linea p ice schedules cha ac e ized
by inc easing block a es. These p ice schedules esul in budge se s ha exhibi con ex
kinks a he poin s whe e he ma ginal p ice ises. I consume s we e esponsi e o changes
in ma ginal p ices, we would expec o obse e a bunching o consump ion a hese kinks,
as shown by Hausman (1985) and Mo i (1990). In ou con ex , he ma ginal p ice o he
ini ial consump ion b acke is se a ze o ac oss all concessions. Consequen ly, i consume s
we e esponsi e o ma ginal p ices, he e would be an incen i e o hem o maximize hei
consump ion wi hou su passing he h eshold o he nex b acke , whe e he ma ginal p ices
become s ic ly posi i e.
To in es iga e whe he such bunching beha io exis s, we plo his og ams depic ing he
esiden ial wa e consump ion pa e ns o he concessions in ou sample. In Figu e ??, we
p esen he his og ams o wo municipali ies: Municipali y X (Figu e 3a) and Municipali y
Y (Figu e 3b), wi h he p ice discon inui ies ep esen ed by he e ical lines. He e, we show
he g aphs sepa a ed by concession because hey ace di e en p ice schedules, al hough all
ha e he same ea u e o inc easing block a es wi h ze o ma ginal p ice in he i s block. The
his og ams e eal a smoo h dis ibu ion o consump ion a ound he kink poin s, indica ing
an absence o bunching.
The absence o bunching can be in e p e ed in wo ways: ei he consume s exhibi ze o
elas ici y o p ices o hey espond o an al e na i e measu e o p ice. To dis inguish be ween
hese possibili ies, we ocus on households ha consis en ly consume wi hin he i s con-
sump ion b acke , whe e he ma ginal p ice is ze o, bu he a e age p ice is s ic ly posi i e
due o he ixed ee. Analyzing his speci ic g oup o households allows us o dis inguish i
demand esponds o a e age p ice, gi en ha ou se ing lacks p ice a ia ion ha would
mo e a e age p ices and ma ginal p ices in di e en di ec ions, as explo ed by I o (2014).
In ou se ing, when p ice changes occu , all he ma ginal p ices abo e he i s b acke
and he ixed ee change a he same a e, while he ma ginal p ice o he i s b acke
emains cons an a ze o. Consequen ly, o consume s who consis en ly consume below he
i s h eshold, an inc ease in he ixed ee leads o a a ia ion in he a e age p ice bu no
15
Figu e 3. No bunching in esiden ial wa e consump ion
(a) Municipali y X
0
50000
100000
150000
Numbe o bills
0 10 20 30 40 50 60 70 80 90 100
Measu ed wa e consump ion (m3)
(b) Municipali y Y
0
5000
10000
15000
20000
Numbe o bills
0 10 20 30 40 50 60 70 80 90 100
Measu ed wa e consump ion (m3)
No es: This igu e shows he his og am o measu ed wa e consump ion o wa e bills om consume s
in municipali y X (Figu e (a)) and municipali y Y (Figu e (b)). The e ical lines on he g aphs ep esen
he end o he b acke s, whe e he ma ginal p ices inc ease. The ma ginal p ice is ze o in he i s b acke ,
i.e., o olumes o he le o he dashed e ical line, and inc eases in he emaining b acke s. The g aphs
include bills o consume s connec ed since he beginning o ou sample and in single-uni esidences wi h
indi idual billing.
in he ma ginal a e.
To isola e he e ec o changes in he ixed ee om wea he shocks and o he changes
ha may be happening a he concession le el, we le e age he case o one concession ha
spans ac oss wo di e en s a es whe e consume s ace di e en p ices depending on which
s a e hey a e loca ed in. Gi en he p oximi y, hey a e exposed o simila wea he e en s
bu a e cha ged di e en p ices. Mo eo e , we include o he concessions in he same s a e o
isola e he e ec o p ice changes om o he economic changes happening a he s a e le el.
Appendix Figu e A4 illus a es his scena io.
Using his subse o wa e bills, we employed a speci ica ion simila o he one used by
I o (2014) o es whe he consume s eac o he ixed ee:
∆ln(qiusj ) = α∆ln( eeusj )+∆ln(Ic ) + δs +γu +uiusj (1)
whe e qiusj ep esen s he me e ed wa e consump ion o household (add ess) iin concession
u, s a e s, and connec ed o se ice jdu ing billing mon h . eeusj deno es he minimum
16
paymen equi ed om any add ess connec ed o se ice jin ha concession s a e. Ic
ep esen s he income a he census ac whe e household i is loca ed. δs deno es s a e-
billing mon h ixed e ec s, while γu ep esen s concession-billing mon h ixed e ec s. We
u ilized he di e ence ∆ln(qiusj ) = ln(qiusj )−ln(qiusj0) be ween he consump ion cha ged a
ime and he same billing mon h in he p e ious yea 0, which elimina es household-mon h
o he yea ixed e ec s ha accoun o household cha ac e is ics and seasonal componen s
o wa e demand. ∆ln( eeusj ) = ln( eeusj )−ln( eeusj0) and ∆ln(Ic ) = ln(Ic )−ln(Ic0)
ep esen he equi alen di e ence o he ixed ee and he income, espec i ely.
I households esponded o he ma ginal p ice, hey would no educe hei consump ion
in esponse o inc eases in he ixed ee, as educing consump ion would no a ec he o al
amoun cha ged in hei wa e bills. In pa icula , since ou sample only includes p ice
inc eases and no p ice dec eases o e he gi en ime ame, we would expec he coe icien
α o be ze o. Howe e , he esul s p esen ed in Table 3 indica e ha consume s educe hei
consump ion in esponse o inc eases in he ixed ee. The p e e ed speci ica ion desc ibed
by equa ion 1 is epo ed in column (3), bu we also epo he esul s o speci ica ions
including only ime- ixed e ec s in column (1) and concession- ime ixed e ec s in column
(2).
This inding sugges s ha consume s do no di e en ia e be ween ixed and a iable cos s,
which is consis en wi h e idence ound in hea ing demand in China (I o and Zhang, 2020).
Al hough consume s do no di ec ly espond o ma ginal p ices, his beha io demons a es
ha hey eac o p ices. Conside ing consume s’ misconcep ions ega ding he non-linea
p ice schedule, we ea hem as esponding o a e age p ices in he demand model.
5 Model
To explo e he easibili y o se ice manda es and al e na i e policies, we use a s uc u al
model ha inco po a es he key pa e ns ound in he da a. The model encompasses he
supply and demand o piped wa e and sewe collec ion wi hin he geog aphic limi s unde
he esponsibili y o a p i a e i m. Ha ing won he concession, he i m is he sole p o ide
17

Table 3 – Consump ion Response o Changes in he Fixed ee
∆ln(quan i y) (1) (2) (3)
∆ln( ee)−0.193** −0.211* −0.250*
(0.083) (0.114) (0.145)
∆ln(income) 0.024* 0.027* 0.027*
(0.014) (0.014) (0.014)
Time FE yes no no
Concession- ime FE no yes yes
S a e- ime FE no no yes
Obse a ions 384,704 384,704 384,704
No es: This able p esen s eg ession es ima es o he coe i-
cien s in equa ion 1. The dependen a iable is he change in he
loga i hm o wa e consump ion in a gi en mon h ela i e o he
same mon h in he p e ious yea . The key independen a iables
a e he co esponding change in he minimum wa e bill paymen
and he census ac ’s income. The columns di e in ixed e ec s
speci ica ions: Column (1) includes mon h-by-yea ixed e ec s,
Column (2) adds concession-by-mon h-by-yea ixed e ec s, and
Column (3) u he includes s a e-by-mon h-by-yea ixed e ec s.
The sample is es ic ed o add esses wi h con inuous wa e billing
h oughou he pe iod, no se ice ype changes (wa e only s.
wa e and sewe ), and consump ion consis en ly wi hin he i s
b acke . Only single-uni households billed indi idually a e in-
cluded. S anda d e o s a e clus e ed a he add ess le el. ***
p<0.01, ** p<0.05, * p<0.1.
o hese se ices in he egion and ope a es as a monopolis . The supply side o he model
uses a disc e e choice app oach o ep esen he i m’s decision-making p ocess ega ding
en y and se ice o e ings a speci ic pos al codes o eco e he ixed cos o expansion and
a iable cos s associa ed wi h se ice p o ision. On he demand side, he model consis s o
disc e e-con inuous consume choice o se ice ake-up and he amoun o wa e consumed
a e connec ing o he ne wo k o es ima e hei p e e ences ega ding he se ices.
The ma ke ou comes depend on he in e play be ween he monopolis ’s expansion de-
cisions and he households’ demand decisions. In pa icula , he a ailabili y o se ices, he
sha e o connec ed households, and he quan i y o wa e consumed depend on he unde -
lying p e e ences o households and he ixed cos s aced by he monopolis . O e all, his
model p o ides a amewo k o examining he economic incen i es and ou comes o di e en
policies ela ed o he p o ision o wa e and sewe se ices in p i a e monopoly se ings wi h
egula ed p ices.
18
5.1 Demand
Households (add esses) in each pos al code ha e p e e ences o piped wa e and sewe
se ices, which a ec hei decision o connec o he ne wo k and hei wa e demand. We
ep esen he decision using a disc e e and con inuous model, whe e each household decides
whe he o connec o only wa e o wa e and sewe when he se ice ne wo k is a ailable in
hei pos al code and, condi ional on being connec ed, households choose hei wa e usage.
1. Take-up
Households in a gi en pos al code choose o connec o only wa e , j=w, bo h wa e
and sewe se ices, j=s, o emain unconnec ed, j=o. Mo e speci ically, i he pos al code
has wa e and sewe pipes a ailable, households can choose o connec o bo h se ices o
only wa e , while i he pos al code has only wa e pipes, he households can only choose o
connec o wa e o emain unconnec ed.
The indi ec u ili y o household (add ess) i, loca ed a pos al code z(in concession uni
uand census ac c), o se ice j∈(w, s, o) in yea yis:
Uijzy =Vjzy +εijzy (2)
Vjzy =




α0jus +α1jcjcy +α2ja gpjuy +α3jIcy +α0
4jDcy +ξjzy i j=w, s
0 i j=o
(3)
whe e cjcy ep esen s he ins alla ion cos s o connec ing a household o he s ee pipe
ne wo k o se ice j.a gpjuy deno es he a e age p ice aced by a ep esen a i e consume in
concession u o se ice j.Icy indica es a e age income, while Dcy is a ec o o demog aphic
cha ac e is ics in luencing he decision o connec o he ne wo k. These cha ac e is ics in-
clude household size, u ban loca ion, he sha e o households on pa ed s ee s, he p opo ion
o en al uni s in he census ac , he sha e o households wi h access o al e na i e wa e
sou ces (such as uck deli e y, cis e ns, o pi s), and he sha e wi h access o al e na i e
sewage disposal me hods (such as sep ic anks, chemical oile s, o compos ing pi s). Finally,
19
ξjzy cap u es an unobse ed demand shock a he se ice-yea -pos al code le el.
The pa ame e α0jus is a p oduc -concession-s a e ixed e ec ha inco po a es p e e -
ences o speci ic se ices common o all consume s in a concession-s a e. The pa ame e
α1jcap u es consume s’ sensi i i y o he ins alla ion cos s o each se ice. The pa ame e
α2jcap u es he willingness o ade o he p ice pe uni o wa e , wi h o wi hou sewe ,
agains o he se ice ea u es. Pa ame e s α3jand α4jinco po a e in e ac ions be ween de-
mog aphic and census ac cha ac e is ics, espec i ely, and se ice al e na i es, while εijzy
is an idiosync a ic p e e ence shock.
We assume ha he idiosync a ic u ili y shocks ha e a nes ed s uc u e wi h one nes
(g) ha includes he inside op ions, Jg={w, s}, which in ou se ing a e he se ices o
only wa e o wa e and sewe , espec i ely. The only op ion ou side o he g oup is no
connec ing o any se ice. Speci ically, εijzy =ζigzy +(1−σ)µijzy, whe e µijzy is i.i.d. ex eme
alue and ζigzy is he same o all p oduc s in g oup g and has a dis ibu ion ha depends on
he nes ing pa ame e σ∈[0,1) such ha εizjy is dis ibu ed ex eme alue ollowing Ca dell
(1997). As σapp oaches 1, he u ili y wi hin-g oup co ela ion goes o one, and only g oups
ma e , meaning households ca e p ima ily abou whe he hey a e connec ed o any se ice
a he han he speci ic ype o se ice. As σapp oaches 0, he wi hin-g oup co ela ion
goes o ze o, educing he model o a s anda d logi whe e choices a e independen . This
s uc u e allows o mo e lexible subs i u ion pa e ns. In pa icula , we expec ha i one
se ice op ion is una ailable, households a e mo e likely o choose he emaining se ice
a he han op ou o connec ion al oge he .
Unde hese assump ions, he p obabili y o selec ing se ice j, condi ional on choosing
o connec o any se ice (g), is gi en by
Sjzy|g=exp(Vjzy/(1 −σ))
Pj∈Jgexp(Vjzy/(1 −σ)) (4)
The p obabili y o choosing o connec o any se ice is
Sgzy =(Pj∈Jgexp(Vjzy/(1 −σ)))(1−σ)
1+(Pj∈Jgexp(Vjzy/(1 −σ)))(1−σ)(5)
Finally, he choice p obabili y o p oduc j, which ep esen s he ake-up, when se ice
20
jis a ailable a pos al code zis gi en by he ollowing mul iplica ion.
Sjzy =Sjzy|gSgzy (6)
2. Wa e Consump ion
The demand o wa e is ep esen ed by:
ln(qijz ) = β0+β1ln(a gpiju ) + β2ln(Icy) + β0
3Dcy +δj+δmτ +ηijz (7)
such ha qijz is he amoun o wa e consumed by a household (add ess) ia pos al code
z(loca ed in concession uni uand census ac c), connec ed o se ice ja a billing mon h
.a gpiju deno es he a e age p ice aced by household i.Icy is he a e age income a he
census ac le el, and Dcy is a ec o ha includes he numbe o people pe household and
an indica o o whe he he census ac is in an u ban a ea. δjis a se ice ixed e ec and
δmτ is a municipali y-mon h-o - he-yea ixed e ec . ηijz ep esen s an idiosync a ic demand
shock o wa e .
We model households as esponding o he a e age p ice, a gpiju , which is compu ed
based on he inc easing block schedule o each concession. Households ha consume only
wi hin he i s b acke pay a ixed ee. Households wi h consump ion in highe b acke s (b)
pay he ixed ee plus he cos o he quan i ies ha exceed each b acke ’s limi , mul iplied by
he co esponding ma ginal p ices, mpbju . The a e age p ice aced by household is exp essed
below as a unc ion o he ixed ee, eeju , he b acke limi s, ¯qbu, and he ma ginal p ices,
mpbju .
a gpiju = eeju +PB
b=2 max(min(qijz −¯qub−1,¯qub −¯qub−1),0)mpbju
qijz
(8)
5.2 Supply
The e is a single monopolis i m ha o e s di e en se ices in he pos al codes wi hin
i s concessions. Fo each pos al code, he i m decides which se ice o o e in o de o
21
ins umen al a iable is he a e age p ice he household would pay unde he p ice schedule
o hei own concession and ime i hey consumed he a e age consump ion o households
in he same g oup bu loca ed in o he concessions. This ins umen is con enien because
i cap u es exogenous a ia ion in he p ice schedule, bu i is no a ec ed by he quan i y
consumed by he household.
Addi ionally, we assess he obus ness o ou a e age p ice ins umen by compa ing i o
an al e na i e app oach ha uses obse ed ma ginal p ices o each b acke as ins umen s,
ollowing Olms ead (2009). The ad an age o using ma ginal p ice-based ins umen s in ou
se ing is ha consume s gene ally do no swi ch b acke s, as shown in Appendix Figu e A7.
By holding consump ion le els ixed, we can le e age a ia ion in p ice schedules o e ime
and ac oss concession s a es o iden i y p ice elas ici y.
We ollow Ba eca and Clay (2016), Da is and Kilian (2011), and Dubin and McFad-
den (1984) o add ess he po en ial selec ion p oblem, allowing he disc e e and con inuous
componen s o demand o be co ela ed. Speci ically, he expec ed alue o he con inuous
wa e demand shock, ηijz , is assumed o be a linea unc ion o he demand shock o he
se ice choice, εjzy, o compu e he selec ion con ols based on he es ima ed ake-up o he
se ice, ˆ
Sjzy. Fo households in pos al codes wi h only wa e a ailable, we include a single
selec ion e m accoun ing o he choice be ween connec ing o wa e and he ou side op ion
o emaining unconnec ed. In pos al codes whe e bo h wa e and sewe se ices a e o e ed,
we include wo selec ion e ms: one cap u ing he choice ela i e o he ou side op ion and
ano he e lec ing he inside op ion no chosen (e.g., choosing wa e only s. bo h wa e and
sewe ).24
The esul s a e p esen ed in Table 5. Column (1) epo s es ima es wi hou an ins umen
o selec ion con ols. Column (2) ins umen s o he a e age p ice using ma ginal p ices
o each b acke . Column (3) eplaces his wi h he simula ed a e age p ice ins umen .
Finally, Column (4) builds on Column (3) by accoun ing o po en ial selec ion, making i ou
p e e ed speci ica ion. Appendix Table A2 epo s he i s -s age esul s, while Appendix
24In ou se ing, o a household connec ed o any inside op ion j, he selec ion e m o he ou side op ion
is gi en by ˆ
Sozy
ln(ˆ
Sozy )
(1−ˆ
Sozy )+ln(ˆ
Sjzy ). I he e is ano he inside op ion ka ailable, which happens when he e is
bo h wa e and sewe , he e is ano he selec ion e m gi en by ˆ
Skzy
ln(ˆ
Skzy )
(1−ˆ
Skzy )+ln(ˆ
Sjzy ).
28

Table A3 p esen s he educed- o m esul s.
In summa y, he esul s indica e ha households educe hei wa e consump ion in
esponse o highe a e age p ices, hough he elas ici y is small. Highe -income households
consume mo e wa e , wi h a s able coe icien ac oss IV speci ica ions. Households wi h piped
sewe connec ions use mo e wa e han hose wi h only wa e connec ions. As expec ed,
wa e consump ion inc eases wi h household size. Addi ionally, households in u ban a eas
end o consume less wa e on a e age han hose in u al a eas. No e ha he p ice elas ici y
emains simila ega dless o he ins umen used o he inclusion o he selec ion con ol.
Howe e , i di e s signi ican ly om he OLS es ima es, sugges ing ha ou ins umen
e ec i ely co ec s he downwa d bias.
Ou analysis ocuses on selec ion bias a ising om consume s’ decisions o connec o
he pipe ne wo k. We assume he i m decides whe e o expand pipes based on obse able
demand ac o s and cos s, wi h demand shocks occu ing only a e hese decisions a e
made. This implici ly assumes ha he i m does no ha e access o demand shocks ha a e
unobse ed by us as econome icians. Howe e , i he i m did an icipa e posi i e demand
shocks, i migh p io i ize expansion in hose a eas, in oducing an addi ional selec ion issue
ha could lead us o o e es ima e uncondi ional wa e demand. We belie e his conce n is
minimal in ou con ex . While he i m may ecei e addi ional inpu om echnicians on he
g ound, we ely on he same adminis a i e da a hey use. Gi en he scale o ope a ions, i is
unlikely his in o ma ion is sys ema ically inco po a ed. The e o e, any bias om unobse ed
demand shocks known o he i m bu no o us is likely minimal.
To p edic he consump ion o connec ed add esses, we use he educed- o m es ima es
p esen ed in Appendix Table A3. Using he educed o m simpli ies he p oblem by allowing
us o ely on he simula ed a e age p ice o de e mine a single p ice ha households espond
o, enabling s aigh o wa d consump ion p edic ions. In con as , using he 2SLS esul s o
p edic ion would equi e join ly sol ing o consump ion and he a e age p ice. Gi en he
nonlinea shape o he a e age p ice unc ion in ou se ing, his app oach would gene a e
wo equilib ium consump ion quan i ies –— one in he i s b acke and ano he in he highe
b acke s —– o cing us o ely on an ad hoc ule o selec be ween hem.
29
Table 5 – Con inuous Demand Model Es ima es
(1) (2) (3) (4)
OLS Mg. p ices IV Simula ed IV Simula ed IV
wi h selec ion
ln(A g. p ice) −1.030*** −0.249*** −0.214*** −0.213***
(0.002) (0.006) (0.009) (0.009)
ln(Income) 0.157*** 0.123*** 0.122*** 0.123***
(0.003) (0.003) (0.003) (0.003)
Piped sewe 0.548*** 0.090*** 0.070*** 0.070***
(0.003) (0.004) (0.006) (0.006)
U ban −0.112*** −0.158*** −0.160*** −0.154***
(0.020) (0.023) (0.023) (0.023)
Household size 0.053*** 0.054*** 0.054*** 0.053***
(0.004) (0.005) (0.005) (0.005)
Selec ion inside op . −0.013***
(0.005)
Selec ion ou side op . 0.014***
(0.005)
Municipali y-mon h FE yes yes yes yes
F-s a is ic 13,545 32,034 32,241
Obse a ions 8,643,951 8,643,951 8,643,951 8,643,951
No es: This able p esen s he pa ame e es ima es om he wa e consump ion model.
The dependen a iable is he loga i hm o wa e consump ion, and he key independen
a iable is he loga i hm o he a e age p ice. Column (1) epo s OLS es ima es. Col-
umn (2) uses he ma ginal p ice o wa e as an ins umen . Column (3) ins umen s
o p ice using a simula ed a e age p ice, cons uc ed by g ouping households in o 16
ca ego ies based on income qua ile, se ice ype (wa e only o wa e and sewe ), and
u ban o u al loca ion. Fo each g oup, he a e age consump ion o households in di e -
en concessions is compu ed, hen used o calcula e he p ice each household would ace
unde i s own concession’s p icing schedule i i consumed he g oup’s a e age usage in
o he concessions. Column (4) builds on Column (3) by accoun ing o po en ial selec ion
bias among households ha op ed o connec . The sample includes only add esses wi h
wa e bills o all pe iods in he da ase ha did no swi ch se ice ype. The epo ed
F-s a is ics co espond o he Kleibe gen-Paap k Wald F-s a is ic. S anda d e o s a e
clus e ed a he household le el. *** p<0.01, ** p<0.05, * p<0.1.
Using he es ima ed model, we compu e ˆqjz , which ep esen s he p edic ed consump ion
o a ep esen a i e consume in a gi en billing mon h, loca ed in pos al code z, and connec ed
o se ice j. This calcula ion assumes a e age income and household size wi hin he pos al
code. We hen agg ega e his mon hly consump ion o ob ain he yea ly consump ion, Qjzy,
and calcula e he co esponding e enue gene a ed by he i m, deno ed as Rjzy, based on
he p ice schedule.
30
6.3 Cos
To es ima e he cos s associa ed wi h p o iding a se ice in di e en pos al codes, we
conside he wa e consump ion and e enue a i m would gene a e o he nex i e yea s i
i ins alled only wa e o bo h wa e and sewe pipes in ha pos al code. We assume ha
he i m has pe ec o esigh o u u e in e es a es, popula ion g ow h, and income in he
a eas hey ha e concession o e he p o ision o piped wa e and sewe . The i m chooses
whe e o ins all pipes conside ing hei ex-an e p o i , gi en by hei expec ed ake-up and
wa e demand, he ma ginal cos o p o iding he se ices and he sunk cos o building he
pipes.
We conside ha he ixed ees and ma ginal p ices a e upda ed annually based on in-
la ion p ojec ions om 2017. The popula ion o each pos al code g ows a he same a e
as he municipal popula ion p ojec ions. The income pe capi a also g ows a he same a e
as he municipal income p ojec ions epo ed by he B azilian Ins i u e o Geog aphy and
S a is ics (IBGE).
Using he demand es ima es and andom d aws om he empi ical dis ibu ion o ξand
η, we compu e he expec ed p edic ed ake-ups ( ˆ
Sjzy), he a e age mon hly household wa e
consump ion (ˆqjz ) and he associa ed e enue (R(ˆqjz )).
We es ima e he ma ginal cos associa ed wi h each se ice, mcj, and he ixed cos
pa ame e , ωj, ia maximum likelihood using he p edic ed choice p obabili y o connec ing
pos al code zwi h se ice j(equa ion 13) and he obse ed expansion choices in 2018 and
2019. The key idea is o iden i y he cos pa ame e alues ha maximize he likelihood o
obse ing he i m’s ac ual choices, gi en he model’s assump ions.
The es ima ion esul s a e a ailable in Table 6. They indica e ha he cos o supplying
one cubic me e o wa e is oughly 6.13 B azilian eais (R$). When including he collec ion
o piped sewe wi h he same amoun o wa e , he cos inc eases o abou 12.71 B azilian
eais. These cos s a e based on he me e ed wa e consump ion a each add ess and co e
expenses associa ed wi h wa e ea men , deli e y, and sewe collec ion, and accoun o
po en ial wa e losses du ing dis ibu ion.
The sunk cos o cons uc ing one kilome e o wa e pipes is app oxima ely R$10869.47,
31
R$12569.58 o a kilome e o combined piped wa e and sewe and R$2141.60 o ex end
sewe pipes o pos al codes ha had only wa e . These cos s encompass no only he pipes
bu also all he ma e ials and labo equi ed o exca a ion and es o ing he pa h a e pipe
ins alla ion. Appendix Tables A4 and A5 p esen al e na i e cos es ima es, assuming he
i m eco e s sunk in es men cos s o e 10 o 30 yea s.
Table 6 – Cos Es ima es
Cos s
Mg. cos wa e (m3) 6.130***
(0.157)
Mg. cos wa e and sewe (m3) 12.706***
(0.472)
Cos pe dis ance wa e (km) 10869.465***
(3982.539)
Cos pe dis ance wa e and sewe (km) 12569.585**
(5350.286)
Cos pe dis ance sewe (km) 2141.603***
(376.737)
Numbe o zip codes 3,279
No es: This able p esen s cos es ima e pa ame e s unde he
assump ion ha i ms conside p ojec ed p o i s o e he nex 5
yea s when making decisions. The es ima ion includes pos al codes
wi hin he i m’s concessions in he No h and No heas egions
o he coun y. F om he o al 3403 pos al codes wi hou se ice o
wi h only wa e in 2017, we missed 124 whe e we could no p edic
he demand based on ou es ima ed model. These pos al codes a e
d opped ei he because when ma ched wi h he census, hey a e
missing ele an demog aphics o because he e was only one pos al
code in he municipali y, so we could no es ima e municipali y-
mo h ixed e ec s. All es ima ed cos s a e epo ed in B azilian
eais (R$). In 2017, he exchange a e was app oxima ely 3.3R$
pe 1U$. *** p<0.01, ** p<0.05, * p<0.1.
Compa ing ou es ima es wi h exis ing li e a u e is challenging. Enginee ing s udies,
such as on Spe ling and Salaza (2013), ypically conside only accoun ing cos s and ocus
on a limi ed numbe o p ojec s. Addi ionally, s udies based on su ey da a om di e en
coun ies, such as B iche i e al. (2021), o en do no dis inguish be ween he cos s incu ed
by i ms when ins alling he ne wo k and he cos s consume s bea o connec hei homes
o s ee pipes.
32
7 Coun e ac ual Simula ions
Fo he simula ions, we assume connec ion a ge s o 99% o households wi h piped wa e
and 90% wi h sewe and use he es ima ed model o analyze incen i es o achie ing hem.
Reaching hese a ge s depends on bo h he company’s expansion decisions and consume s’
choices o adop se ices. To disen angle hese ac o s, we i s simula e a scena io whe e he
i m expands se ices in all pos al codes, such ha he gap be ween connec ion a es and he
a ge s depends solely on consume decisions. Nex , we allow he i m o endogenously selec
expansion a eas and in oduce di e en policies, ocusing on sewe connec ion subsidies and
sewe a ailabili y cha ges. These policies encou age consume adop ion and may incen i ize
he i m o ex end se ices o unco e ed pos al codes.25
To p edic he ou comes, we use demand es ima es and he empi ical dis ibu ion o ξ
and η o compu e he p edic ed ake-up a es, wa e consump ion, and he esul ing i m
e enue unde he di e en scena ios. By combining p edic ions wi h he cos es ima es,
we calcula e he a iable p o i he i m would gene a e and he sunk cos s in ol ed in he
expansion.
We also measu e he changes in consume su plus and in an dea hs ha a ise om hese
policy changes. Consume su plus is compu ed using he disc e e-choice componen o he
model, whe e consume s decide which se ice o connec o when i is a ailable. While
consume su plus is a commonly used wel a e measu e, he in e p e a ion equi es cau ion in
con ex s wi h high inequali y. The willingness o pay o he se ices may no ully cap u e
he bene i s consume s would expe ience upon connec ing. Ne e heless, we p esen his
measu e o unde s and i s impac on consume s who can a o d he se ice and may no
choose o connec unde he di e en simula ions.
We compu e he numbe o a e ed in an dea hs in each simula ion o cap u e consume
heal h bene i s. We c ea e a back-o - he-en elope measu e using he es ima ed impac o
piped wa e and sewe in B azil om Gampe -Rabind an e al. (2010) and he numbe o
li e bi hs om DATASUS. This measu e inco po a es bo h p i a e bene i s om wa e
25In he coun e ac ual scena ios, we assume ha he i m canno emo e se ices om a eas whe e pipes
had al eady been ins alled by 2019.
33

connec ions and ex e nali ies om sewe connec ions. I is impo an o no e ha i does
no encompass all dimensions o ex e nal bene i s, as discussed by K esch and Schneide
(2020), bu p o ides an ex a dimension o compa e he policies.26
7.1 Full Expansion o Piped Wa e and Sewe
In he i s exe cise, we simula e a scena io whe e he company expands wa e and sewe
se ices o all pos al codes wi hin i s concessions in he no he n egion. In his se ing,
connec ion a es depend solely on consume ake-up, as all households could po en ially
connec o he se ices.
Ou esul s show ha connec ion a ge s would no be me a cu en p icing le els e en
i he i m expanded o all pos al codes, due o low ake-up, especially o sewe . Despi e
uni e sal a ailabili y in his scena io, 85.95% o he households would connec o wa e
and only 51.09% would connec o he sewe ne wo k. Figu e 4a illus a es he 99% piped
wa e co e age a ge ( ed line), he p e-policy connec ion a e (g ay ba ), and he simula ed
expansion ou come (blue ba ). Simila ly, he igh panel o Figu e 4b depic s he 90% sewe
co e age a ge ( ed line), wi h he baseline and ull-expansion connec ion a es shown in
g ay and o ange, espec i ely.
Table 7 p o ides mo e de ails o he simula ion esul s. Panel A displays in o ma ion on
he sha e o pos al codes wi hin each concession whe e each se ice is a ailable, while Panel
B p esen s wel a e measu es o each al e na i e policy ela i e o he baseline si ua ion. We
p esen a iable p o i and consume su plus o e a i e-yea pe iod in line wi h ou cos
es ima ion amewo k. Column (1) p esen s he baseline scena io, while column (2) shows
he ou comes unde ull expansion. By design, he la e ensu es all pos al codes ha e access
o wa e and sewe se ices, as e lec ed in he i s wo ows. Howe e , no all households
adop hese se ices, as indica ed in he hi d and ou h ows and he colo ed ba s in Figu e
4.
26The numbe o a e ed in an dea hs ep esen s a lowe bound o he ex e nali ies gene a ed by inc easing
connec ions o piped wa e and sewe . Fo ins ance, he se ices migh also educe he incidence o wa e -
bo ne diseases, such as dia hea, which do no always esul in child dea h (Ba e o e al., 2007). Social
ex e nali ies could in luence he decisions o neighbo s o adop al e na i e me hods o wa e sani a ion
and was ewa e disposal (Deu schmann e al., 2024). Addi ionally, ex e nali ies could mani es as inc eased
housing p ices in neighbo hoods wi h he se ice (Cou y e al., 2024).
34
Figu e 4. Sha e o Household Connec ions
(a) Piped wa e
0 10 20 30 40 50 60 70 80 90 100
% o households connec ed o piped wa e
Baseline Full expansion
(b) Piped sewe
0 10 20 30 40 50 60 70 80 90 100
% o households connec ed o piped sewe
Baseline Full expansion
No es: This igu e compa es he baseline pe cen age o households connec ed o piped wa e (Figu e (a))
and piped sewe (Figu e (b)) o a scena io in which he i m expands se ice e e ywhe e. The ed lines
indica e he connec ion a ge s se by he 2020 Sani a ion Regula o y F amewo k. The connec ion sha e is
calcula ed as he numbe o households connec ed o he se ice di ided by he o al numbe o households
wi hin he No h and No heas concession a eas. Unde he “Full Expansion” scena io, all pos al codes
ha e piped wa e and sewe , and he p edic ed ake-up de e mines he sha e o connec ions o each se ice.
Addi ionally, we show in column (2) o Table 7 ha ex ending se ices o all pos al
codes is no iable o he company, as he subs an ial sunk cos s ou weigh he inc eased
a iable p o i om new connec ions. Howe e , he expansion inc eases consume su plus,
as mo e consume s ha e he se ices a ailable and decide o connec . The ull expansion
also gene a es a educ ion o 10.37% in in an mo ali y among child en below 1-yea -old,
amoun ing o oughly 22 ewe dea hs when con as ed wi h he baseline scena io wi hou
expansion.
7.2 Endogenous Expansion o Piped Wa e and Sewe
In his se o simula ions, we allow he i m o de e mine which pos al codes o expand
wa e and sewe se ices o while p o iding incen i es o consume s o connec o sewe ia
subsidies and he sewe a ailabili y cha ge. We ocus on sewe adop ion and expansion as i
p esen s he la ges gap o he connec ion a ge s, while o wa e mos people connec o i
35
Table 7 – Simula ions
(1) (2) (3) (4) (5)
Baseline Full expansion End. expansion End. expansion End. expansion
Connec ion subsidy
Connec ion subsidy
P ice inc ease A ailabili y cha ge
Panel A: Se ice co e age and household connec ions
% o zips wi h wa e and sewe 41.36 100.00 41.36 78.20 71.75
% o zips wi h only wa e 48.77 0.00 48.77 12.00 18.41
% o households connec ed o wa e 79.71 85.95 83.38 84.13 78.86
% o households connec ed o sewe 33.43 51.09 55.17 81.58 54.77
Panel B: Wel a e impac ela i e o he baseline
∆ Va iable p o i (mi R$)−95.77 −127.15 188.62 282.81
Sunk cos (mi R$) 249.69 0.00 4.34 3.83
∆ Consume su plus (mi R$) 3.37 53.03 65.46 −4.40
Connec ion subsidy (mi R$) 0.00 127.16 281.94 0.00
∆% In an dea hs −10.37 −2.60 −2.66 −0.02
Expansion: i m choice yes no yes yes yes
Expansion: all zips wi h sewe no yes no no no
Subsidy sewe connec ion no no yes yes no
Sewe p ice inc ease no no no 50% no
Sewe a ailabili y cha ge no no no no yes
No es: This able p esen s coun e ac ual esul s, wi h each column co esponding o a di e en coun e ac ual simula ion. Column (1) shows he baseline. Column
(2) conside s ull expansion. Column (3) allows he i m o expand endogenously while p o iding consume s wi h a subsidy o connec . Column (4) adds a p ice
inc ease o he policy implemen ed in Column (3). Column (5) combines endogenous i m expansion wi h cha ging o sewe se ice based on a ailabili y a he han
connec ion. Panel A epo s se ice co e age ou comes, while Panel B p esen s wel a e ou comes. Di e ences in a iable p o i , consume su plus, and in an mo ali y
a e measu ed ela i e o he baseline. Va iable p o i and consume su plus a e calcula ed o e i e yea s, while he change in in an dea hs is based on he es ima ed
inc ease in household connec ions, ollowing Gampe -Rabind an e al. (2010). The baseline scena io includes 216 in an dea hs. All cos es ima es a e in B azilian
eais (R$). In 2017, he exchange a e was app oxima ely 3.3 R$pe 1 U$.
when i is a ailable.
1. Connec ion Subsidies
The second simula ion examines he impac o a one- ime sewe connec ion subsidy, which
co e s he cos o connec ing homes o s ee pipes. This subsidy applies only o households
connec ing o bo h wa e and sewe , excluding hose op ing solely o wa e . Once connec ed,
consume s mus con inue paying hei bills o emain in he sys em and canno ecei e he
subsidy again i hey disconnec .
The subsidy e ec i ely inc eases household sewe connec ions bu has no impac on i m
expansion. As shown in Table 7, column (3), he sha e o connec ed households ises o
app oxima ely 55.17%, ye se ice co e age emains a 41.36%. This indica es ha he new
connec ions occu in a eas whe e sewe in as uc u e was al eady a ailable. Fu he mo e,
he subsidy educes i m p o i s in loca ions whe e sewe pipes we e p e iously ins alled,
sugges ing ha he e enue om wa e and sewe bills is insu icien o co e he cos s o
se ice p o ision o newly connec ed households.
The subsidy signi ican ly inc eases consume su plus, alued a 53.03 million B azilian
eais, by enabling mo e households o access se ices. Howe e , he policy is cos ly, amoun -
36
ing o 127.16 million B azilian eais. We do no ake a s and on how he go e nmen would
inance his subsidy o whe he i would compensa e i ms o incu ed losses.
Appendix Figu e A8 shows ha subsidies co e ing mo e han 50% o he cos do no
u he imp o e connec ion a es, which is mainly d i en by consume ake-up. Appendix
Figu e A9 sugges s ha o e ing subsidies only o low-income households does no signi i-
can ly boos connec ions because he i m does no subs an ially expand.
2. Connec ion Subsidies wi h P ice Inc eases
In ou hi d simula ion, we show ha combining connec ion subsidies wi h an inc ease in
sewe p ices can e ec i ely boos connec ion a es. In some concessions, he new sewe p ice
is high enough o co e he cos s o sewage collec ion, which encou ages i ms o expand
hei ne wo k. As shown in Table 7, column (4), pai ing he subsidy wi h a 50% inc ease
in he sewe p ice aises sewe connec ions o 81.58% o households. Appendix Figu e A10
shows ha u he p ice inc eases beyond 50% yield only a ma ginal inc ease in connec ions,
as he i m does no expand signi ican ly beyond his h eshold.
On he consume side, he inc ease in consume su plus om he subsidy mo e han
o se s he highe sewe p ice. Howe e , he expansion makes he subsidy mo e expensi e o
he go e nmen , as mo e consume s use i o connec o newly a ailable sewe in as uc u e.
Despi e he signi ican ise in sewe connec ions, he educ ion in in an mo ali y emains
small.
3. Sewe A ailabili y Cha ge
In ou ou h simula ion, we in oduce he “Sewe A ailabili y Cha ge,” which equi es
consume s o pay o sewe in hei mon hly bills once pipes a e a ailable in hei pos al code,
e en i hey a e only connec ed o wa e . Al hough es ablished unde he 2007 Sani a ion
Regula o y F amewo k, his policy has been a ely implemen ed, wi h only a ew municipal-
i ies adop ing i . In ou da ase , jus one municipali y employs his p icing s a egy.27 This
cha ge wo ks as a ax, incen i izing consume s o in e nalize he ex e nali y c ea ed when
27The a ailabili y cha ge was in oduced in his municipali y midway h ough he s udy pe iod, so i is
excluded om demand and cos es ima ions.
37
Wichman, C. J. (2014). Pe cei ed p ice in esiden ial wa e demand: E idence om a na u al
expe imen . Jou nal o Economic Beha io & O ganiza ion 107, 308–323.
Wollmann, T. G. (2018). T ucks wi hou bailou s: Equilib ium p oduc cha ac e is ics o
comme cial ehicles. Ame ican Economic Re iew 108 (6), 1364–1406.
44

A1 Appendix Figu es
Figu e A1. Sha e o he Popula ion Connec ed by Region in B azil
(a) Piped wa e
54%
76%
90%
85%
82%
(b) Piped sewe
14%
34%
81%
46%
38%
No es: This igu e illus a es he sha e o people connec ed o piped wa e (Figu e (a)) and sewe collec ion
(Figu e (b)) ac oss he coun y’s egions in 2017. Da a sou ce: Na ional Sani a ion Su ey (Pesquisa Nacional
de Saneamen o B´asico - PNSB) om IBGE.
45
Figu e A2. Sha e o Households wi h Sani a ion Se ices by Income pe cen ile
(a) Wa e
0 .2 .4 .6 .8 1
Sha e o households wi h piped wa e
0 20 40 60 80 100
Income pe cen ile
O he p o ide s Company
(b) Sewe
0 .2 .4 .6 .8 1
Sha e o households wi h piped sewe
0 20 40 60 80 100
Income pe cen ile
O he p o ide s Company
No es: This igu e illus a es connec ions o piped wa e (Figu e (a)) and sewe se ices (Figu e (b)).
Each obse a ion ep esen s he a e age sha e o households connec ed ac oss census ac s wi hin income
pe cen iles. In he le g aph, a eas wi hin ou i m’s concession a e highligh ed in blue, while o he s a e
shown in g ay. The igh -hand g aph ma ks ou i m’s concession a eas in o ange, wi h all o he a eas in
g ay. The da a come om he 2010 Census.
Figu e A3. Dis ances o he Ins alled Ne wo k
(a) Only wa e
0 .2 .4 .6 .8 1
Sha e o zip codes wi hou se ice in 2017
[0,200] (200,400] (400,600] (600,800] (800,1000] abo e 1000
Dis ance o he only wa e ne wo k (m)
Expansion only wa e Expansion wa e and sewe
No Expansion
(b) Wa e and sewe
0 .2 .4 .6 .8 1
Sha e o zip codes wi h no sewe in 2017
[0,200] (200,400] (400,600] (600,800] (800,1000] abo e 1000
Dis ance o he wa e and sewe ne wo k (m)
Expansion sewe Expansion only wa e
No expansion
No es: This igu e depic s he dis ance om new expansions o he exis ing ne wo k. Figu e (a) shows
he dis ance o he ins alled wa e ne wo k, while Figu e (b) includes bo h wa e and sewe ne wo ks. These
g aphs co e all pos al codes wi hin he i m’s concession a eas in he No h and No heas e n egions o he
coun y ha lacked se ice in 2017.
46
Figu e A4. Di e ences in he P ice Schedule ac oss Concessions and S a es
No es: This igu e illus a es he a ia ion in he p ice schedule ac oss concessions and s a es. Concession
u1is en i ely wi hin S a e A, whe e consume s ace p ice pu1. Concession u2spans S a e A and S a e
B, leading o di e en p ices (p0
u2and p00
u2) o consume s in he same concession bu in di e en s a es.
This se up gene a es bo h wi hin-concession and wi hin-s a e p ice a ia ion, which helps iden i y consume
esponses o ixed ee changes.
Figu e A5. Dis ance o New Pos al Codes pe Mon h
(a) Only wa e
0 .1 .2 .3 .4 .5 .6
A g. dis ance o he wa e ne wo k (km)
Jan 18 May 18 Sep 18 Jan 19 May 19 Sep 19
Mon h o expansion
(b) Wa e and sewe
0 .1 .2 .3 .4 .5 .6
A g. dis ance o he sewe ne wo k (km)
Jan 18 May 18 Sep 18 Jan 19 May 19 Sep 19
Mon h o expansion
No es: This igu e depic s he dis ance o ne wo k expansions om he exis ing in as uc u e in 2018 and
2019. Figu e (a) includes pos al codes whe e only wa e pipes we e expanded, while Figu e (b) on he igh
highligh s pos al codes ha ecei ed expansions o bo h wa e and sewe pipes in he No h and No heas
egions.
47
Figu e A6. P edic ed s. Obse ed Se ice Take-up
(a) Wa e ake-up in pos al codes wi h only wa e
pipes
0.00
0.20
0.40
0.60
0.80
F ac ion o zip codes
-1 -.5 0 .5 1
P edic ed - obse ed ake-up only wa e
(b) Wa e ake-up in pos al codes wi h wa e and
sewe pipes
0.00
0.20
0.40
0.60
F ac ion o zip codes
-1 -.5 0 .5 1
P edic ed - obse ed ake-up only wa e
(c) Wa e and sewe ake-up in pos al codes wi h
wa e and sewe pipes
0.00
0.10
0.20
0.30
0.40
0.50
F ac ion o zip codes
-1 -.5 0 .5 1
P edic ed - obse ed ake-up wa e and sewe
No es: These igu es show he di e ence be ween he obse ed and es ima ed ake-up a es. Figu e (a)
shows his di e ence o only wa e ake-up in pos al codes whe e only wa e pipes we e a ailable. Figu e
(b) p esen s his di e ence o only wa e ake-up in pos al codes wi h bo h wa e and sewe pipes. Figu e
(c) p esen s his di e ence o wa e and sewe ake-up in pos al codes whe e bo h wa e and sewe pipes
a e a ailable.
48
Figu e A7. B acke Change
0 .2 .4 .6 .8
Sha e o households
Jan
#days .
measu ed
Feb
.
Ma
29
Ap
30
May
30
Jun
30
Jul
29
Ago
31
Sep
30
Ou
30
No
31
Dec
28
2018
0 .2 .4 .6 .8
Sha e o households
Jan
32
Feb
29
Ma
31
Ap
29
May
31
Jun
29
Jul
31
Ago
29
Sep
30
Ou
30
No
32
Dec
30
2019
Block inc ease Same block Block dec ease
No es: This igu e illus a es he sha e o households ha swi ch b acke s om one mon h o he nex .
The da a only includes households al eady connec ed in 2017 and had wa e bills o all mon hs o 2017 and
2018. The g aphs also include he numbe o days in he billing cycle om Ma ch 2018 o Decembe 2019,
which whe e no a ailable o p e ious mon hs.
49

Figu e A8. Va ying le els o subsidy
(a) Sha e o households connec ed o sewe
0 10 20 30 40 50 60 70 80 90 100
% o Households wi h sewe
0 10 20 30 40 50 60 70 80 90 100
Sewe connec ion subsidy (% o he cos )
(b) Sha e o pos al codes wi h sewe
0 10 20 30 40 50 60 70 80 90 100
% o Zip codes wi h sewe
0 10 20 30 40 50 60 70 80 90 100
Sewe connec ion subsidy (% o he cos )
(c) Fi m P o i s
-150 -100 -50 0
Fi m p o i s (mi R$)
0 10 20 30 40 50 60 70 80 90 100
Sewe connec ion subsidy (% o he cos )
No es: These igu es p esen ou comes om coun e ac ual simula ions unde a ying subsidy le els,
anging om 0% o 100% o he connec ion cos s o he sewe ne wo k. Figu e (a) illus a es he impac
on he pe cen age o households wi h sewe access. Figu e (b) shows he e ec s on he sha e o pos al codes
wi h sewe pipes. Figu e (c) depic s changes in he i m’s p o i .
50
Figu e A9. Subsidies o Di e en Income Le els
(a) Sha e o households connec ed o sewe
0 10 20 30 40 50 60 70 80 90 100
% o Households wi h sewe
12345678910
Sewe connec ion subsidy (up o x- h income decile)
(b) Sha e o pos al codes wi h sewe
0 10 20 30 40 50 60 70 80 90 100
% o Zip codes wi h sewe
12345678910
Sewe connec ion subsidy (up o x- h income decile)
(c) Fi m P o i s
-150 -100 -50 0
Fi m p o i s (mi R$)
12345678910
Sewe connec ion subsidy (up o x- h income decile)
No es: These igu es p esen ou comes om coun e ac ual simula ions whe e subsidies a e a ge ed o
di e en income deciles. Figu e (a) illus a es he impac on he pe cen age o households wi h sewe access,
Figu e (b) shows he e ec s on he sha e o pos al codes wi h sewe pipes, and Figu e (c) depic s changes in
he i m’s p o i . The subsidy is alloca ed o households up o he x- h income decile, meaning ha o he
10 h decile, all households ecei e he subsidy.
51
Figu e A10. Subsidies wi h P ice Inc eases
(a) Sha e o households connec ed o sewe
0 10 20 30 40 50 60 70 80 90 100
% o Households wi h sewe
0 10 20 30 40 50 60 70 80 90 100
Sewe p ice inc ease(%)
(b) Sha e o pos al codes wi h sewe
0 10 20 30 40 50 60 70 80 90 100
% o Zip codes wi h sewe
0 10 20 30 40 50 60 70 80 90 100
Sewe p ice inc ease(%)
(c) Fi m P o i s
-200 0 200 400 600
Fi m p o i s (mi R$)
0 10 20 30 40 50 60 70 80 90 100
Sewe p ice inc ease(%)
No es: These igu es p esen ou comes om coun e ac ual simula ions wi h a 100% subsidy on connec ion
cos s, combined wi h a ying inc eases in sewe p ices. Figu e (a) illus a es he impac on he pe cen age
o households wi h sewe access. Figu e (b) shows he e ec s on he sha e o pos al codes wi h sewe pipes.
Figu e (c) depic s changes in he i m’s p o i .
52
A2 Appendix Tables
Table A1 – Take-up Reg ession
(1) (2) (3)
Take-up only wa e
(Zips wi h only wa e )
Take-up wa e and sewe
(Zips wi h wa e and sewe )
Take-up only wa e
(Zips wi h wa e and sewe )
ln(Connec ion cos ) −0.073*** −0.080*** −0.073***
(0.014) (0.020) (0.005)
ln(Income) 0.121*** 0.126*** −0.039***
(0.010) (0.005) (0.003)
U ban −0.215*** 0.113*** −0.051***
(0.049) (0.034) (0.019)
Household size 0.199*** 0.174*** −0.043***
(0.018) (0.008) (0.004)
Sha e en ed 0.347*** 0.443*** −0.052***
(0.042) (0.022) (0.013)
Sha e o he wa e −0.024 0.319*** −0.181***
(0.033) (0.029) (0.017)
Sha e o he sewe 0.147*** −0.092*** 0.070***
(0.014) (0.009) (0.005)
Municipali y-yea FE yes yes yes
Obse a ions 7,068 24,335 24,335
R-squa ed 0.614 0.2 0.371
No es: This able epo s he ela ionship be ween demog aphic a iables and he sha e o con-
nec ed households in each pos al code whe e se ices a e a ailable. In column (1), he dependen
a iable is he p obabili y o a household being connec ed o only wa e in pos al codes ha ha e
only wa e pipes. In column (2), he dependen a iable is he p obabili y o a household being
connec ed o bo h wa e and sewe in pos al codes ha ha e wa e and sewe pipes. In column (3),
he dependen a iable is he p obabili y o a household being connec ed o only wa e in pos al
codes ha ha e bo h wa e and sewe pipes. *** p<0.01, ** p<0.05, * p<0.1.
53
A3.2 Es ima ion
1. Empi ical Bayes es ima o ake-up
One challenge in he se ice ake-up es ima ion is ha in some pos al codes, all he
add esses connec o he a ailable pipes, gene a ing ma ke sha es ha a e equal o 1 o
he inside op ion and 0 o he ou side op ion. In hese cases, we would no be able o
use he s anda d demand es ima ion me hods Be y (1994); Be y e al. (1995) because he
in e sion s ep equi es s ic ly posi i e ma ke sha es o each good in he ma ke , in ou
case, o each se ice in he pos al code. One common al e na i e is o agg ega e ma ke s,
bu in his se ing, agg ega ing pos al codes would no cap u e he ele an ake-up aced
by he i m when making expansion decisions. Ano he simple al e na i e, such as d opping
he ze os/ones, would unde es ima e he se ice ake-up.
We ollow Li (2019) and use a pa ame ic empi ical Bayes o sh inkage es ima o o
gene a e s ic ly posi i e pos e io ake-up p obabili ies using in o ma ion om simila pos al
codes. The numbe o add esses connec ed o se ice jin pos al code z, gi en by Kjz, is
modeled as a d aw om a binomial dis ibu ion wi h Nz ials, ep esen ing he o al numbe
o add esses in he pos al code. He e we omi he yea subsc ip s o acili a e he no a ion.
The ake-up p obabili ies S0
jz o each se ice in each pos al code a e d awn om a Be a
p io dis ibu ion wi h pa ame e s λ1jz and λ2jz. Such ha Kjz ∼Binomial(Nz, S0
jz) and
S0
jz ∼Be a(λ1jz, λ2jz). The pos e io dis ibu ion o he ake-up is also a Be a dis ibu ion
Sjz ∼Be a(λ1jz +Kjz, λ2jz +Nz−Kjz)
wi h pos e io mean
ˆ
SP
jz =λ1zj +Kjz
Nz+λ1jz +λ2jz
Fo each pos al code zand se ice j he Be a p io is o med using he 100 closes in
income pe capi a ha also ha e pipes o j,l∈ζz, whe e lis a pos al code om he se
o simila pos al codes ζz. The pa ame e s o he be a p io dis ibu ion λ1jz and λ2jz a e
60

es ima ed om maximizing he log-likelihood o e he ake-up o simila ma ke s
(Kjz, l ∈ζz|λ1jz, λ2jz) = Y
l∈ζzKlj
NlΓ(λ1jz +λ2jz)Γ(λ1jz +Klj)Γ(Nl−Klj +λ2jz)
Γ(λ1jz)Γ(λ2jz)Γ(λ1jz +Nlλ2jz)
Wi h he es ima ed pa ame e s, we cons uc he pos e io mean o he ake-up p oba-
bili ies o each pos al code and se ice ˆ
SP
jz =ˆ
λ1jz +Kjz
Nz+ˆ
λ1jz +ˆ
λ2jz , which a e s ic ly be ween 0 and
1. The igu es below show he empi ical Bayes pos e io mean ake-ups and he obse ed
ake-ups o only wa e and wa e and sewe .
Figu e OD.1. Take-up Only wa e : Empi ical Bayes Pos e io s. Obse ed
(a) All ake-ups
0
.2
.4
.6
.8
1
Empi ical bayes pos e io mean ake-up
0 .2 .4 .6 .8 1
Obse ed ake-up only wa e
(b) Zooming in on obse ed ake-ups below 0.1
0
.01
.02
.03
.04
.05
Empi ical bayes pos e io mean ake-up
0 .002 .004 .006 .008 .01
Obse ed ake-up only wa e
No es: These g aphs show he empi ical Bayes Pos e io Mean o each obse ed ake-up o only wa e
se ices.
61
Figu e OD.2. Take-up Wa e and Sewe : Empi ical Bayes Pos e io s. Obse ed
(a) All ake-ups
0
.2
.4
.6
.8
1
Empi ical bayes pos e io mean ake-up
0 .2 .4 .6 .8 1
Obse ed ake-up wa e and sewe
(b) Zooming in on obse ed ake-ups abo e 0.9
.92
.94
.96
.98
1
Empi ical bayes pos e io mean ake-up
.99 .992 .994 .996 .998 1
Obse ed ake-up wa e and sewe
No es: These g aphs show he empi ical Bayes Pos e io Mean o each obse ed ake-up o wa e and
sewe se ices.
62