Almag o, Milena; And és-Ce ezo, Da id
A icle
The cons uc ion o na ional iden i ies
Theo e ical Economics
P o ided in Coope a ion wi h:
The Econome ic Socie y
Sugges ed Ci a ion: Almag o, Milena; And és-Ce ezo, Da id (2020) : The cons uc ion o na ional
iden i ies, Theo e ical Economics, ISSN 1555-7561, The Econome ic Socie y, New Ha en, CT, Vol. 15,
Iss. 2, pp. 763-810,
h ps://doi.o g/10.3982/TE3040
This Ve sion is a ailable a :
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Theo e ical Economics 15 (2020), 763–810 1555-7561/20200763
The cons uc ion o na ional iden i ies
Milena Almag o
Depa men o Economics, New Yo k Uni e si y
Da id And és-Ce ezo
Depa men o Economics, Eu opean Uni e si y Ins i u e
This pape explo es he dynamics o na ion-building policies and he condi-
ions unde which a s a e can p omo e a sha ed na ional iden i y on i s e i o y.
A o wa d-looking cen al go e nmen ha in e nalizes iden i y dynamics shapes
hem by choosing he le el o s a e cen aliza ion. Homogeniza ion a emp s a e
cons ained by poli ical un es , elec o al compe i ion and he in e gene a ional
ansmission o iden i ies wi hin he amily. We ind na ion-building e o s a e
gene ally cha ac e ized by as in e en ions. We show ha a ze o-sum con lic
o e esou ces pushes long- un dynamics owa d homogeneous s eady s a es and
ex eme le els o (de)cen aliza ion. We also ind he abili y o os e a common
iden i y is highly dependen on ini ial condi ions, and ha coun y-speci ic his-
o ical ac o s can ha e a las ing impac on he long- un dis ibu ion o iden i ies.
Keywo ds. Cul u al e olu ion, na ion-building, na ional iden i y, cul u al leade ,
op imal con ol, poli ical economy, decen aliza ion.
JEL classi ica ion. B52, D71, D72, D74, H41, H77, P48, Z10, Z13.
1. In oduc ion
Du ing he pas wo cen u ies, na ion-s a es ha e a isen in which he as majo i y o he
popula ion sha es a sense o collec i e belonging, ep esen ed by dis inc i e adi ions,
cul u e, language, and some imes eligion. By con as , we ha e also obse ed cases o
ailed na ion-building, in which go e nmen s we e unable o c ea e a uni ied na ional
cul u e. Simul aneously obse ing such opposi e ou comes na u ally aises wo ques-
ions: Which condi ions lead o he p omo ion o a na ional iden i y? How do go e n-
men s achie e his goal?1
Milena Almag o: [email p o ec ed]
Da id And és-Ce ezo: [email p o ec ed]
We a e g a e ul o he wo anonymous e e ees o e y help ul commen s and sugges ions. We also wan o
hank Jess Benhabib, Albe o Bisin, Juan Dolado, Tomás Domínguez-Iino, Guillaume R. F éche e, And ea
Galeo i, Philipp Ki che , Da id Le ine, Alessand o Lizze i, Da id Ma ínez, Ana Mo eno, Paula Onuchic,
Jacopo Pe ego, Ma heus Sil a, Ennio S acche i, and Thie y Ve die , as well as semina pa icipan s a
CEMFI, ASREC a Lund Uni e si y, ASSET a A hens Uni e si y, he Spanish Economic Associa ion, New
Yo k Uni e si y, and Eu opean Uni e si y Ins i u e. We a e indeb ed o he MacC acken ellowship a New
Yo k Uni e si y and he Sal ado de Mada iaga EUI p og am o inancial suppo as we w o e his pape .
1The analysis in his pape is only posi i e and, he e o e, we do no make any no ma i e s a emen
abou he legi imacy o na ion-building a emp s o he desi abili y o ha ing a uni ied na ional cul u e.
©2020 The Au ho s. Licensed unde he C ea i e Commons A ibu ion-NonComme cial License 4.0.
A ailable a h ps://econ heo y.o g.h ps://doi.o g/10.3982/TE3040
764 Almag o and And és-Ce ezo Theo e ical Economics 15 (2020)
P o iding answe s o hese ques ions is in e es ing o se e al easons. Fi s , many
au ho s ha e iden i ied a sha ed iden i y as a undamen al p e equisi e o economic
g ow h. The eason is ha socie ies pola ized along iden i y clea ages a e p one o
ci il con lic and co up ion, all o which a e ac o s gene ally associa ed wi h poo eco-
nomic pe o mance (e.g., Besley and Reynal-Que ol (2014)).2Second, he absence o
a common na ional iden i y is a sou ce o poli ical ins abili y, as is he case o coun-
ies cha ac e ized by a cen e -pe iphe y ension such as Ca alan and Basque egions in
Spain, Sco land in he UK, Québec in Canada, Flande s in Belgium, Bia a in Nige ia, o
Ogaden in E hiopia. These egions a e epea edly in ol ed in poli ical p ocesses claim-
ing la ge poli ical au onomy, he ecogni ion o hei cul u al dis inc i eness, o e en
he o ma ion o independen na ion-s a es. Mo eo e , iden i y di e ences wi hin a po-
li ical union may p e en he p o ision o public goods, hinde edis ibu ion, and lead
o subop imal economic policies (e.g., Guiso e al. (2016)), because hey educe social
capi al and inc ease he cos s o collec i e ac ion. Thi d, p ocesses o na ion-building
a e equen ly ela ed o poli ical mo emen s o s a e cen aliza ion and decen aliza-
ion. In some cases, such as F ance a he end o he 19 h cen u y (Webe (1976)), he
ela i ely as c ea ion o a uni a y s a e was accompanied by he de elopmen o a com-
mon iden i y among ci izens wi h di e en cul u al backg ounds and a ague sense o
na ional belonging. In o he cases, such as he So ie Union o Yugosla ia, he lack o
s a e cen aliza ion wi hin he poli ical union coincided wi h he consolida ion o op-
posing e i o ial iden i ies (e.g., Bakke and Wibbels (2006); Sekulic e al. (1994)). In his
ega d, some au ho s sugges Eu opean leade s ha e elied on he expec a ion ha a
g adual poli ical in eg a ion would p omo e he con e gence o alues and iden i ies
among he Eu opean popula ion (Spolao e (2013)). Howe e , hese expec a ions ha e
no been ul illed ye (Guiso e al. (2016)), so whe he we should expec he de elopmen
o a Eu opean iden i y in he u u e emains an open ques ion.
In he pape , we de elop a heo e ical model o s a e na ion-building in a pe iph-
e al egion whe e wo iden i y g oups coexis : na ionalis s and egionalis s. The cul u al
alues o na ionalis s a e aligned wi h hose o he es o he coun y, while egionalis s
ha e a cul u ally dis inc i e egional iden i y. Ou amewo k inco po a es wo key ideas
ela ed o na ion-building episodes. Fi s , he abili y o he cen al go e nmen o p o-
mo e he na ional iden i y depends on i s capaci y o cen alize he compe ences o he
pe iphe al egion. By ha ing he powe o ax and spend he e enues, he go e nmen
can implemen policies aimed a p omo ing ce ain cul u al alues.3In ou model, he
main mechanism h ough which hese policies ope a e is by changing he socializa ion
incen i es o he amilies, because pa en s wan o educa e hei child en o make hem
These conside a ions depend on he pa icula con ex and on poli ical philosophy issues beyond he scope
o his pape . Ou aim is solely o unde s and, albei wi h many limi a ions, why some coun ies a e di ided
along e hno- e i o ial iden i y clea ages while o he s a e no .
2This p oblem is especially se e e in Sub-Saha an A ica whe e, acco ding o he A oba ome e , a ound
50% o he popula ion iden i ies mo e wi h hei e hno-linguis ic iden i y han wi h he na ional iden i y.
3Na ion-building policies include, o ins ance, he p omo ion o an o icial language, he in oduc ion
o a “collec i e memo y” in school cu icula, mili a y consc ip ion, o he p o ision o iden i y public goods
such as pa io ic celeb a ions commemo a ing impo an na ional e en s.
Theo e ical Economics 15 (2020) The cons uc ion o na ional iden i ies 765
i be e in he egion whe e hey li e. Second, cen aliza ion and na ion-building poli-
cies usually come wi h episodes o poli ical un es in he o m o p o es s o e en ci il
wa . The eason is ha communi ies wi h a oo ed iden i y eel agg ie ed i hei cul u al
and symbolic demands a e no sa is ied, o i an ex e nal go e nmen imposes a cen al-
ized s a e ha dis ega ds hei cul u al dis inc i eness. Hence, by mobilizing in public
demons a ions, p o es s, and io s, ci izens can in luence go e nmen policies h ough
channels o he han legal ins i u ions.
Speci ically, indi iduals in he pe iphe al egion enjoy u ili y om consuming a pub-
lic good associa ed wi h hei iden i y (o an associa ed cul u al ai , e.g., he egional
language). The o al amoun o public goods is in ixed supply, gi ing ise o a ze o-sum
con lic , which allows us o cap u e cul u al decen aliza ion as he sha e o egionalis
public goods. Iden i ies a e ansmi ed o e gene a ions h ough a p ocess o cul u al
e olu ion wi h wo channels o socializa ion: wi hin he amily ( e ical ansmission)
and by socie y a la ge (ho izon al ansmission). As in s anda d models o cul u al e o-
lu ion (e.g., Bisin and Ve die (2001)), pa en s choose socializa ion e o s by weigh ing
he bene i s o ansmi ing hei own iden i ies agains he po en ial cos s o hei chil-
d en. This e olu iona y p ocess gi es ise o a di e en ial equa ion o he ac ion o he
popula ion a ached o he na ional iden i y, which is a unc ion o he le el o decen al-
iza ion. A o wa d-looking go e nmen in he cen al egion in e nalizes hese dynamics
and shapes hem by modi ying pa en s’ socializa ion incen i es. This go e nmen has
a pa icula objec i e in mind, which o his o ical easons is assumed o include he
p omo ion o he na ional iden i y.4Howe e , he go e nmen is cons ained by wel a e
losses c ea ed by poli ical un es , wi h p o es pa icipa ion le els inc easing as na ion-
building a emp s become s onge . Thus, he p oblem o he go e nmen becomes a
nonlinea op imal con ol p oblem o e an in ini e ime ho izon, in which a ade-o
exis s be ween i s pe cei ed bene i s o ha ing a mo e na ionally-iden i ied popula ion
and he cos s c ea ed by poli ical un es .
In his se ing, we begin by analyzing a p oblem ha is linea in he con ol a i-
able, which allows us o ully cha ac e ize he dynamics o na ion-building episodes and
o de i e h ee key esul s. Fi s , we ind ha op imal na ion-building policies in ol e
quick and ex eme in e en ions, so ha homogeniza ion is achie ed in he as es pos-
sible way.5Conc e ely, op imal con ol ajec o ies ollow a Mos Rapid App oach Pa h
(MRAP) (Spence and S a e (1975)). Second, he op imal long- un s eady s a es a e
cha ac e ized by cul u al homogenei y wi hin he pe iphe al egion. Because iden i-
ies a e mu ually exclusi e, gains om one g oup always come a he expense o he
o he . The e o e, a o wa d-looking cen al go e nmen o ced o sol e his dispu e will
push homogeniza ion o he maximum possible le el, so ha p e e ences in he pop-
ula ion a e aligned and he ze o-sum con lic e en ually disappea s. Hence, in cases
4The desi e o p omo e a na ional iden i y could be mo i a ed by pu e ideological easons, o by ins u-
men al easons such as p ocesses o indus ializa ion ha equi e a popula ion wi h a common language
o he need o an a my willing o de end he na ion.
5Th oughou he ex , we equen ly e e o some policies o ou comes as op imal. This ac ually means
hey a e op imal in a me e ma hema ical sense and om he poin o iew o a go e nmen ha pu sues i s
own goals, which may be di e en om a social wel a e c i e ion.
766 Almag o and And és-Ce ezo Theo e ical Economics 15 (2020)
whe e p omo ing he ull assimila ion o he na ional iden i y is ex emely cos ly, he
go e nmen will g an ull decen aliza ion o he pe iphe al egion and allow egional
iden i ies o h i e. Finally, he abili y o go e nmen s o na ion-build is highly depen-
den on he ini ial dis ibu ion o iden i ies. In pa icula , we p o e he exis ence o a
popula ion h eshold abo e which he go e nmen p omo es he na ional iden i y and
ice e sa. Small di e ences in economic, social, and poli ical ac o s change he lo-
ca ion o his h eshold and may lead o ex emely di e gen ajec o ies, highligh ing
he con ingen na u e o na ion-building p ocesses. In addi ion, he model p esen s se-
e e “ egime changes”: an exogenous shock o he socioeconomic en i onmen can ig-
ge a sudden shi in he policies o he go e nmen . The e o e, ou model can explain
his o ical episodes in which s a es acing simila his o ical con ex s ollowed dispa a e
na ion-building policies.
Then we ex end he benchma k model in se e al di ec ions. Fi s , we check how
obus ou esul s a e o nonlinea speci ica ions o he objec i e unc ion. The non-
con ex dynamics p esen in his p oblem p e en us om using s anda d op imal con-
ol echniques and hinde a ull analy ic cha ac e iza ion o he op imal pa h. Howe e ,
we a e able o iden i y gene al su icien condi ions unde which he long- un dis i-
bu ion o iden i ies emains homogeneous. In e es ingly, hese condi ions a e sa is ied
o ce ain cases in which pa en al socializa ion decisions a e cha ac e ized by cul u al
subs i u ion, in con as o mos esul s in he cul u al-e olu ion li e a u e (Bisin and
Ve ide (2011)). Second, we in oduce democ a ic elec o al compe i ion o he cen-
al go e nmen . In pa icula , we cha ac e ize he Ma ko equilib ium o a di e en ial
game be ween wo o wa d-looking poli ical pa ies. Those wo pa ies ha e aligned
na ion-building mo i es bu compe e o win he bene i s o being in o ice. Whene e
he egionalis g oup is su icien ly pi o al, poli ical pa ies ace a ade-o be ween a -
ge ing his g oup o inc ease he p obabili y o winning, and coope a ing by p oposing
policy pla o ms ha p omo e he na ional iden i y. Compa ed o he case o a secu e
go e nmen , we ind ha , e e y hing else equal, he p ese a ion o egional iden i ies is
mo e likely in democ acies, because egional mino i ies ha e an addi ional ins umen
beyond p o es s o oice hei demands.
The pape is o ganized as ollows. Sec ion 2 e iews he ela ed li e a u e. Sec ion 3
desc ibes he model. Sec ion 4 includes he main heo e ical esul s. Sec ion 5 p o-
ides gene al su iciency condi ions o ou homogeniza ion esul s. Sec ion 6 in o-
duces elec o al compe i ion. In Sec ion 7, we discuss he esul s and we illus a e he
p edic ions o he model wi h ele an case s udies. Sec ion 8 concludes. All p oo s a e
elega ed o he Appendix.6
2. Rela ed li e a u e
The main con ibu ion o he pape is o o malize he condi ions unde which na ion-
building akes place and o cha ac e ize he dynamics o na ional iden i ies. As a gued
by Smi h (1992), “na ional iden i ica ion has become he cul u al and poli ical no m,
6A supplemen a y online appendix is a ailable in a supplemen a y ile on he jou nal websi e, h p://
econ heo y.o g/supp3040/supplemen .pd

Theo e ical Economics 15 (2020) The cons uc ion o na ional iden i ies 767
anscending o he loyal ies in scope and powe .” Ye heo e ical wo k on his opic is
sca ce.7In he economics li e a u e, Dessí (2008) s udies he ole o olde gene a ions
in c ea ing a sha ed iden i y by p omo ing a collec i e memo y ha p aises he alues
and he his o y o he na ion. Ou wo k is complemen a y o he s. Whe eas Dessí (2008)
models he ansmission o iden i ies as a p ocess o s a egic communica ion o in o -
ma ion be ween gene a ions, in ou model, iden i ies co espond o di e en p e e -
ences. Mo eo e , we model i s ansmission as a cul u al e olu iona y p ocess esul ing
om he in e ac ion be ween e ical, oblique, and ho izon al socializa ion.
Ano he se o heo e ical con ibu ions ha explici ly deals wi h he o ma ion o
na ional iden i ies emphasizes he ole o in e s a e and mode n mass wa a e in igge -
ing na ion-building beha io by s a es. Alesina e al. (2017) explo e how changes in wa -
a e echnology incen i ized mass a mies by consc ip ion, which in u n pushed s a es
o c ea e a sense o na ional belonging ha inc eased he willingness o igh o he
coun y.8
Sambanis e al. (2015), building upon Shayo (2009)andSambanis and Shayo
(2013), a gue ha ule s who wan o na ion-build may ind i op imal o p omo e wa
agains an ex e nal powe , as expec a ions o ic o y inc ease he in e na ional s a us
o he coun y. We complemen hese wo ks in wo key espec s. Fi s , we depa om
s a ic models by in oducing cul u al dynamics ha e lec mo e closely he beha io
o na ion-building policies o e ime. Dynamics allow us o make gene al p edic ions
abou he p ocess by which na ional iden i ies a e o med. Second, hese pape s ocus
on he ole o ex e nal wa s and assume no in e nal opposi ion o na ion-building poli-
cies. By con as , ou model allows o addi ional possible causes o na ion-building
and ocuses on he domes ic sou ces o poli ical con lic and cul u al esis ance o hese
policies.
On he empi ical side, some pape s s udy he impac o di e en na ion-building
ools, such as language policy (Aspachs-B acons e al. (2008), Caminal e al. (2018)),
school cu icula (Can oni e al. (2017), Fouka (2020)), compulso y schooling (Bandie a
e al. (2019)), mass media and p opaganda (Voig lände and Vo h (2015), Blouin and
Mukand (2019)), public na ionalis holidays (Mades am and Yanagizawa-D o (2012)),
and na ional oo ball eams (Depe is-Chau in e al. (2018)). We con ibu e o his li -
e a u e by de eloping a heo e ical model ha explo es he long- un consequences o
hese policies and he poli ical economy aspec s ha cons ain hei implemen a ion.
Ou pape also ela es o a ecen s and o he cul u al- ansmission li e a u e ha
s udies how di e en socializa ion agen s shape p e e ence o ma ion, and how di e -
en modes o socializa ion compe e wi h each o he . Wi hin his li e a u e, ou s udy is
closely ela ed o some pape s analyzing how di e en “cul u al leade s,” such as media
o eligious leade s, shape cul u al e olu ion (Hauk and Immo dino (2014), P umme
and Siedla ek (2017), Ca alho and Koyama (2016)). We con ibu e o his li e a u e by
7Fo an ea ly discussion on na ionalism om an economic poin o iew, see B e on (1964).
8In a closely ela ed pape , Alesina and Reich (2015) analyze in a s a ic se ing he di e en incen i es o
p omo e a common iden i y ha democ acies and dic a o ships ace. Aghion e al. (2019) p o ides empi -
ical suppo o he heo y in Alesina e al. (2017), showing ha ex e nal mili a y h ea s encou age public
in es men s in educa ion ha spu na ional iden i ica ions.
768 Almag o and And és-Ce ezo Theo e ical Economics 15 (2020)
s udying he iden i y socializa ion ole o a key cul u al leade ha has ecei ed li le
a en ion in he li e a u e: he na ion-s a e.
We also connec o wo s ands o he li e a u e ha analyze he in e play be ween
elec o al compe i ion and iden i y o ma ion. On he one hand, wi hin he cul u al
ansmission li e a u e, Bisin and Ve die (2000)andTabellini (2008)s udyhowmajo i y
o ing maps he dis ibu ion o cul u al ai s in o public policies, and how his mapping
eeds back in o socializa ion decisions. On he o he hand, Shayo (2009)andGennaioli
and Tabellini (2018) analyze how indi iduals choose he s eng h o hei na ional iden-
i ica ion in he sho - un in esponse o he ela i e salience o his dimension in he
poli ical ealm as compa ed o he class-based dimension o con lic . We con ibu e o
bo h s ands o li e a u e by in oducing pe ec ly o wa d-looking poli ical pa ies ha
pu pose ully shape indi idual iden i ica ions and ully in e nalize he impac o hei
ac ions on he u u e poli ical powe o di e en g oups. As a esul o no being pu ely
oppo unis ic, hey implemen equilib ium policies ha e lec he long- un goals o
pa ies in addi ion o o e s’ policy p e e ences.
F om a me hodological poin o iew, ou key con ibu ion is o in oduce a pe ec ly
o wa d-looking socializa ion agen ha sol es a ze o-sum con lic be ween cul u al
g oups while in e nalizing cul u al dynamics. Ve die and Zenou (2018)explo easim-
ila idea in he con ex o he cul u al assimila ion o eligious communi ies, al hough
hei pape includes no con lic be ween iden i ies, and he leade chooses when o in-
e ene. The p esence o a ze o-sum con lic makes ou esul s undamen ally di e en
om hei s: Whe eas hei op imal solu ion con e ges o a long- un ou come in which
bo h cul u al g oups coexis , ou op imal s eady s a es a e homogeneous. Ne e heless,
gi en he simila amewo k analyzed in bo h pape s, some echnical and concep ual
simila i ies exis . Fo example, we bo h ind ha op imal ajec o ies wi h a linea pe -
pe iod u ili y a e cha ac e ized by an MRAP.
3. Model
Conside a con inuous ime model o a pe iphe al egion o a coun y popula ed a ime
by a s a iona y mass 1o agen s. Agen s can be o wo ypes: a ac ion q o ype
Nindi iduals, na ionalis s, and a ac ion 1−q o ype Rindi iduals, egionalis s.In
each pe iod, all indi iduals ecei e iden ical income pe capi a no malized o 1.The
go e nmen collec s a ac ion ∈[01]o his income h ough axes. The go e nmen
uses o al ax e enue o p o ide iden i y (local) public goods gR
= δ and gN
= (1−
δ ),whe eδ ∈[01]is he ac ion used o p o ide public good gR
.
All indi iduals consume all o hei a e - ax income c =(1− ) de i ing u ili y (1−
),whe e is con inuous, inc easing, and conca e wi h (0)=0, and hei associa ed
iden i y public good, de i ing u ili y gi
. Hence, o al u ili y is gi en by ui
(c gi
gj
)=
(c )+gi
. Because c =1− ,gN
=(1−δ ) ,andgR
=δ , indi ec u ili ies a e gi en by
UN
(  δ )= (1−

c
)+(1−δ )
 
gN
;UR
(  δ )= (1−

c
)+δ

gR

Theo e ical Economics 15 (2020) The cons uc ion o na ional iden i ies 769
In his way, we cap u e na ional/ egional iden i ies as di e en p e e ences o e mu-
ually exclusi e “iden i y” o cul u al goods, ha is, goods ha can only be enjoyed by
indi iduals wi h a pa icula eligion, language, o o he cul u al ai a ached o he
iden i y. Examples a e na ional holidays commemo a ing a his o ical da e, museums,
monumen s o pas leade s o he na ion, a na ional oo ball eam, and so on.9In addi-
ion, he ac ha he o al amoun o club public goods has cons an o al supply in
e e y pe iod allows us o in e p e δ , he ac ion o he egionalis good, as he le el o
decen aliza ion o his egion.10
Cul u al ansmission
We endogenize p e e ences by including cul u al dynamics ollowing he cul u al-
ansmission li e a u e (Bisin and Ve die (2001)). Assume asexual ep oduc ion whe e
each pa en has one child. Child en a e i s exposed o pa en al ( e ical) socializa ion,
which, i unsuccess ul, is ollowed by a andom ma ch o an indi idual om he popu-
la ion, adop ing he ai (ho izon al socializa ion). Hence, ansi ion p obabili ies a e
gi en by
PNN
eN
=eN
+1−eN
q P
NR
eN
=1−eN
(1−q )
PRR
eR
=eR
+1−eR
(1−q ) PRN
eR
=1−eR
q 
whe e Pij is he p obabili y ha a child o a pa en wi h ai iis socialized o ai j,and
eN
∈[01]and eR
∈[01]a e pa en s’ educa ion/socializa ion e o s. No ice ha he
mo e p esen an iden i y ai is, he mo e likely agen s in he young gene a ion a e o
adop i .
Pa en s ake in o accoun how ewa ding is o ha e each iden i y in socie y, and
based on ha hey choose how much e o o pu in ansmi ing hei own iden i ies.
Mo e conc e ely, le Vij be he u ili y ha a ype ipa en de i es om ha ing a child
wi h ai j,andle C(ei
)be he socializa ion cos , assumed o be inc easing and con ex.
Then pa en i’s socializa ion p oblem a ime is
max
ei
∈[01]
Pii
ei
Vii
+1−Pii
e
Vij
−Cei

Unde he assump ion ha pa en s’ choices display impe ec empa hy, socializa ion
u ili ies a e gi en by Vii =c +gi
and Vij =c .11 The ollowing lemma cha ac e izes op i-
mal socializa ion decisions and he co esponding law o mo ion o iden i y dynamics:
9We can also in e p e hem in a b oade sense, as cap u ing he idea ha some indi iduals wi hin he
pe iphe al egion ha e di e en p io i ies and p e e ences wi h espec o go e nmen spending.
10In his iew, decen aliza ion co esponds o he deg ee o cul u al ecogni ion and accommoda ion o
a di e en ia ed na ion wi hin he bounda ies o he s a e. This mus be di e en ia ed om iscal o poli ical
decen aliza ion, ha equi es he exis ence o a local go e nmen wi h iscal and legisla i e powe s. In any
case, all hese de ini ions o decen aliza ion a e highly co ela ed, as he p o ision o egionalis public
goods is usually unde aken by egional go e nmen s wi h some poli ical au onomy.
11As is s anda d in he li e a u e, his assump ion implies pa en s e alua e hei child en’s u ili y using
hei own u ili y unc ion.
770 Almag o and And és-Ce ezo Theo e ical Economics 15 (2020)
Lemma 1. Unde impe ec empa hy and quad a ic cos s,
C(e )=1
2e2

he op imal socializa ion e o s a e gi en by
eN
=(1−q )gN
=(1−q )(1−δ ) 
eR
=q gR
=q δ 
and he law o mo ion o cul u al ansmission becomes
˙
q=q (1−q )eN
−eR
= q (1−q )(1−δ −q )
The p oo o his lemma is mechanical and can be ound in Sec ion S.1 o he Sup-
plemen a y Appendix. On he one hand, he pa en s’ op imal choice o socializa ion
e o akes in o accoun how much wel a e hei child en de i e om holding hei own
iden i y, which depends on he p o ision o i s associa ed public good. On he o he
hand, because ho izon al ansmission is a subs i u e o e ical ansmission, pa en s’
e o will dec ease in he size o he g oup holding hei iden i y in he popula ion a
la ge.
Obse e ha unde cul u al subs i u ion and cons an go e nmen in e en ion o e
ime δ =δ∈(01), h ee s eady s a es exis wi h a unique s able and in e io s eady s a e
gi en by qSS =1−δ. Hence, ou model p ese es he s anda d p edic ion o he cul u al-
e olu ion li e a u e o a he e ogeneous s eady s a e in which bo h iden i ies coexis . The
main di e ence in ou analysis is, p ecisely, ha he go e nmen ailo s dynamics a i s
own will by choosing a pa h o δo e ime.12
Go e nmen dynamic p oblem
We assume he cen al go e nmen has “de ju e” powe o decide o e δ and in e nalizes
he cul u al- ansmission dynamics. The objec i e o he go e nmen is o choose a pa h
{δ } ≥0 ha maximizes:
max
δ ∈[01]∀ ≥0∞
0
e−ρ W(δ
q ;ω)d
s. . ˙
q = q (1−q )(1−δ −q )
q(0)=q0q ∈[01]
12We ha e wo easons o hink ha in he absence o go e nmen in e en ion, long- un he e ogenei y
will exis . Fi s , axes may no be collec ed o no iden i y public good may be p o ided, so ha eN
=eR
=0
and q emains cons an . Second, bo h iden i y public goods gNand gRmay be p o ided in a decen alized
way by each o he g oups. This easoning could explain why bo h na ion-building a emp s and homo-
geneous na ions ha e appea ed ecen ly in his o y, when na ion-s a es ha e ob ained coe ci e powe and
su icien capaci y o ax he people in all egions. The idea ha iscal capaci y is a key de e minan o he
abili y o na ion-build can be ound in Johnson (2015).
Theo e ical Economics 15 (2020) The cons uc ion o na ional iden i ies 777
Figu e 1. Op imal policy δ∗(q) wi h quad a ic p o es s.
This esul is obus ac oss di e en speci ica ions because i s main d i ing o ce is he
ze o-sum na u e o he con lic , in he sense ha he gains o one g oup always come
a he expense o he o he . In ui i ely, a he e ogeneous s eady s a e canno be op imal,
because in he long- un he cen al go e nmen s ill aces a con lic , which can be elim-
ina ed by u he homogenizing he popula ion. The p e ious a gumen goes h ough
whene e he go e nmen aces a s ong enough con lic on how o alloca e ini e e-
sou ces be ween di e en g oups.19
Finally, we can also p o e he op imal policy and long- un dynamics also p ese e
he h eshold p ope y wi h in e als o as and ex eme in e en ions o la gely homo-
geneous popula ions.
Theo em 5. A¯
q0∈(01)exis s such ha
δ∗(q) > 1−qi q≤¯
q0δ
∗(q) < 1−qi q≥¯
q0
Mo eo e , δ∗(q) is con inuous on [0¯
q0)∪(¯
q01], and wo open neighbo hoods o q=0
and q=1exis , say, O(0)and O(1)in [01],such ha
δ∗(q) =1∀q∈O(0) δ∗(q) =0∀q∈O(1)
Figu e 1depic s ou quali a i e cha ac e iza ion o he op imal policy. Un o u-
na ely, a ull analy ic cha ac e iza ion o he op imal policy δ∗(q) becomes in ac able.
Howe e , below we p esen a nume ical example (see Figu es 2and 3). We ollow he ap-
p oach p esen ed in Achdou e al. (2017), which inds he alue unc ion using iscosi y
solu ions. Obse e ha s anda d me hods do no apply in ou model, because ou alue
unc ion is no di e en iable a he h eshold ¯
q0∈(01).
19Su icien condi ions o he la e a e ha ci izens’ alua ions o any le el o p o ision o he pub-
lic good a e la ge enough and pa icipa ion a es in p o es s do no explode o low le els o public-good
p o ision.

778 Almag o and And és-Ce ezo Theo e ical Economics 15 (2020)
Figu e 2. V(q).
Figu e 3. δ∗(q).
To summa ize, he esul s o ex eme homogeniza ion and he exis ence o an in-
di e ence h eshold go h ough beyond he linea speci ica ion. Rega ding he op i-
mal pa h o δ , he nume ical esul s sugges (de)cen aliza ion becomes mo e g ad-
ual when p o es s a e con ex. To see why, conside he case in which he go e nmen
s a s wi h a balanced dis ibu ion o iden i ies and e en ually homogenizes he pop-
ula ion owa d he na ional iden i y. A in e media e alues o q , he a eo change
˙
qis highe and he size o p o es s bigge han o mo e homogeneous dis ibu ions o
iden i ies. The e o e, by se ing an in e io alue o δ a ea ly s ages, he cen al go e n-
men can a oid a la ge pa icipa ion in p o es s o he egionalis g oup and s ill mo e
in he desi ed di ec ion. In e es ingly, e en wi h nonlinea speci ica ions, he op imal
policy apidly app oaches co ne solu ions, sugges ing he MRAP solu ion could be a
good app oxima ion o op imal na ion-building policies. Mo e impo an ly, al hough δ
could ake in e media e alues along he ansi ion pa h o he s eady s a e, i e en ually
eaches a co ne solu ion. In ui i ely, an in e io long- un alue o δ canno be op i-
mal because, due o he iden i y dynamics, he go e nmen will be “in es ing” in wo
opposi e goals a he same ime.
Theo e ical Economics 15 (2020) The cons uc ion o na ional iden i ies 779
6. Na ion-building unde elec o al compe i ion
In his sec ion, we compa e he esul s o ou baseline model o a secu e cen al go -
e nmen wi h he case in which he cen al go e nmen is democ a ically elec ed each
pe iod by ci izens in he cen al and pe iphe al egions. Fo ease o exposi ion, we con-
side he limi ing case in which he pe iphe al egion is ully pi o al in na ional elec ions,
so ha only o e s o g oups Nand Rde e mine he esul o elec ions. None heless, in
he Supplemen a y Appendix S.5.4, we explici ly model o e s in he cen al egion and
we show he esul s a e obus .
We ollow he p obabilis ic o ing model wi h majo i y o ing and agg ega e unce -
ain y p oposed by Pe sson and Tabellini (2000) based on Lindbeck and Weibull (1987).
In his model, wo pa ies Aand Bcompe e o win elec ions in e e y pe iod by making
simul aneous policy announcemen s δAand δB. Poli ical pa ies commi o implemen
hei announced policies i hey happen o be elec ed. When announcemen s a e δA
and δB,pa yA’s p obabili y o being elec ed is gi en by
pAδAδBq=1
2+(1−q)φR−qφN
qφN+(1−q)φRδA−δB=1
2+(q)δA−δB
In he Supplemen a y Appendix S.5.1, we p o ide an explici mic o ounda ion o
pi(δiδ−iq). Fo he momen , no e ha φicap u es he in ensi y o p e e ences owa d
policy δo g oup i.20 By de ini ion, he p obabili y o winning he elec ion o pa y Bis
pB=1−pA.
We assume poli ical pa ies a e o wa d-looking, maximize a discoun ed s eam o
u ili y payo s, and in e nalize he dynamics o iden i ies. They ha e an in insic na ion-
building mo i e, ψNq,wi hψN≥0equal o bo h pa ies, as well as o ice mo i a ions,
ecei ing pe -pe iod u ili y equal o pii hey win he elec ions.21 Hence, when he p o-
po ion o na ionalis is gi en by q, o gi en announcemen s δiand δ−i, he pe -pe iod
u ili y o pa y iis22
Wiqδiδ−i=ψNq+piδiδ−iq
We es ic ou a en ion o Ma ko pe ec equilib ia, whe e s a egies only depend
on he cu en s a e q. The p oblem o playe iis o choose a policy announcemen δi
aking he s a egy o he o he playe , δ−i, as gi en. Equilib ium s a egies a e cha ac-
e ized by
δ∗i=a g max
δ∈[01][01]E0∞
0
e−ρ Wiq δ(q ) δ∗−i(q )d (3)
20φiis a measu e o how much indi iduals wi hin a g oup a e conce ned wi h he cul u al pol-
icy/ e i o ial clea age o policy, ela i e o o he policy dimensions o o in insic p e e ences owa d po-
li ical pa ies.
21The esul s hold when he s eng h o na ion-building mo i es is di e en o bo h pa ies, as long as
bo h ha e s ic ly posi i e na ion-building mo i es.
22Compa ed o he benchma k case, we ha e assumed ψU=ψS=0. This choice o speci ica ion is made
o ac abili y pu poses. Howe e , i poli ical pa ies ha e “wel a e” and “law and o de mo i es,” as in he
case o he secu e go e nmen , simila esul s go h ough. In he benchma k model, he bene i s o holding
o ice o he secu e go e nmen en e as a cons an (which we omi ed) and, he e o e, hey do no al e
he esul s o ha sec ion.
780 Almag o and And és-Ce ezo Theo e ical Economics 15 (2020)
δ∗−i=a g max
δ∈[01][01]E0∞
0
e−ρ W−iq δ∗i(q ) δ(q )d (4)
whe e E0is he expec a ion condi ional on q0. Pa en al socializa ion decisions each pe-
iod a e made a e elec ions ha e aken place and depend on he implemen ed policy.
Hence, om he poin o iew o poli ical pa ies, he alue o ˙
qis a andom a iable
whose ealiza ion depends on he policy implemen ed by he winning pa y (as he e-
sul o elec ions is also a andom a iable). Hence, p oblems (3)and(4)a esubjec o
he ollowing dynamics:
˙
q =gq δiδ−i=q (1−q )1−δi(q )−q wi h p ob. piδi(q ) δ−i(q ) q 
q (1−q )1−δ−i(q )−q wi h p ob. 1−pi
δi(q )δ−i(q ) q 
No e ha o low alues o q , elec o al and na ion-building mo i es a e no aligned.
The e o e, aking wha he o he pa y does as gi en, pa y i aces a ade-o be ween
inc easing he p obabili y o winning elec ions by announcing a policy ha a o s he
egionalis g oup R, o announcing a less popula policy oday ha inc eases qin he
u u e. In his las case, pa y i aces he cos o educing he expec ed bene i s om
o ice as well as he p obabili y ha his na ion-building policy is implemen ed.
Gi en ha wo pa ies sol e iden ical p oblems, we es ic ou a en ion o symme -
ic equilib ia.23 The solu ion o he elec o al-compe i ion game wi h na ion-building
mo i es is cha ac e ized by he ollowing heo em.
Theo em 6. A unique equilib ium in symme ic s a egies o he dynamic elec o al-
compe i ion game wi h na ion-building mo i es exis s. The equilib ium s a egies a e
desc ibed as a h eshold policy gi en by ˜
qDsuch ha
δA∗(q) =δB∗(q) =1i q≤˜
qD
0i q>˜
qD
wi h 0<˜
qD<˜
qS,whe e˜
qSde ines he h eshold o he symme ic equilib ium o he
s a ic elec o al compe i ion game, and is gi en by
˜
qS=φR
φN+φR
As in p e ious cases, depending on he ini ial alue o q, he sys em con e ges o one
o he wo homogeneous s eady s a es. The in insic cul u al-subs i u ion p ope ies
o pa en al socializa ion a e coun e ac ed by he ac ha i is be e o be pa o he
mos powe ul g oup. E en i , ce e is pa ibus, pa en s exe mo e socializa ion e o
when hei g oup becomes smalle , he o ing sys em a o s indi iduals who belong o
he majo i y, c ea ing incen i es o pa en s o socialize hei kids o he p edominan
iden i y.
23An in e es ing ex ension ha me i s a pape on i s own would be o analyze he dynamic elec o al game
be ween o wa d-looking pa ies wi h opposi e na ion-building mo i es. In he Supplemen a y Appendix
S.5.3, we discuss his possibili y as well as he case o sho sigh ed bu ideologically mo i a ed pa ies.
Theo e ical Economics 15 (2020) The cons uc ion o na ional iden i ies 781
Figu e 4. Equilib ium policy o elec o al-compe i ion game wi h mixed mo i es.
P oposi ion 6. In he case in which pa ies only ca e abou o ice (ψN=0):
˜
qD=˜
qS
On he con a y, i pa ies only ca e abou na ion-building, (O=0):
˜
qD=0
No e ha when pa ies a e pu ely o ice mo i a ed, in e e y pe iod hey play he
equilib ium s a egy o he s a ic game.24 S a ing below he h eshold ˜
qS,pu eelec-
o al easons push pa ies o implemen ull decen aliza ion δ=1, because his g oup
is poli ically mo e powe ul due o he combina ion o i s demog aphic weigh and he
in ensi y o p e e ences o he g oup owa d policy δ . Howe e , when bo h pa ies also
ha e a na ion-building mo i e, a egion be ween ˜
qDand ˜
qSexis s in which pa ies a e
no cons ained o a ge announcemen s o he powe ul egionalis g oup and ha e
some ma gin o implemen policies ha a o na ionalis o e s (see Figu e 4). The ea-
son is ha he na ionalis g oup is big enough o gua an ee a su icien ly la ge ex an e
p obabili y o winning he elec ions. In equilib ium, bo h pa ies announce δ=0and,
due o he iden i y dynamics, he demog aphic weigh q inc eases endogenously o e
ime un il ˜
qsis eached and na ion-building and elec o al goals become aligned.
Finally, hese esul s also sugges ha , e e y hing else equal, democ acies end
o be mo e p one o accommoda e and p ese e egional iden i ies han coun ies in
which poli ical powe is no dispu ed. Fo example, conside he baseline model wi h
ψU=ψS=0, so pe -pe iod u ili y o he cen al go e nmen is gi en by W(q
)=ψnq +1,
whe e he las e m is he bene i o holding o ice ob ained wi h ce ain y as no elec-
ions ake place. Clea ly, he op imal solu ion o he secu e cen al go e nmen is o se
δ(q) =0 o all q, so na ion-building will ake place o any ini ial q0∈(01]. By con as ,
24See he Supplemen a y Appendix S.5.2 o mo e de ails abou ou de ini ion o a s a ic poli ical equi-
lib ium.
782 Almag o and And és-Ce ezo Theo e ical Economics 15 (2020)
when he cen al go e nmen is elec ed democ a ically, a egion always exis s in which
equilib ium s a egies a e gi en by ull decen aliza ion, δ=1. Succinc ly, he p ese a-
ion o egional iden i ies is mo e likely unde elec o al compe i ion, because egional
mino i ies ha e mo e oice in he poli ical p ocess. Mo eo e , he egion whe e equilib-
ium s a egies a e δi=1is inc easing in φR, so democ a ic sys ems wi h powe ul and
ideologically mo i a ed egional mino i ies a e mo e likely o p ese e hei iden i ies.
Finally, he ollowing p oposi ion cha ac e izes how incen i es o na ion-build
change wi h he pa ame e s o he model.
P oposi ion 7. The h eshold ˜
qDis dec easing in ψN:
∂
∂ψN˜
qD≤0
wi h limi ing cases
lim
ψN→0
˜
qD=˜
qSlim
ψN→∞
˜
qD=0
On he con a y, ˜
qDis inc easing in ρ:
∂
∂ρ ˜
qD≥0
The p oo can be ound in Sec ion S.5.5 o he Supplemen a y Appendix. I is easy
o see ha when he incen i es o na ion-build a e la ge , na ion-building will occu o
mo e ini ial s a es. Simila ly, when pa ies a e less pa ien , hey a e mo e conce ned
abou sho - un elec o al goals and, he e o e, na ion-building will occu o ewe ini-
ial s a es. Mo eo e , as in he baseline model, small di e ences in he pa ame e s o in
he ini ial size o g oups may ha e a la ge impac on he dynamics o iden i ies.
7. In e p e a ion o he esul s:Case s udies
In his sec ion, we discuss he main p edic ions o he model and we illus a e hem wi h
empi ical e idence om his o ical case s udies. The nonlinea and none godic na u e
o na ion-building p ocesses ha ou model s esses poses a challenge o s anda d em-
pi ical wo k and emphasizes he impo ance o s udying na ion-building episodes on a
case-by-case basis. In addi ion, as P oposi ions 2,3,4,and7sugges , a my iad o di e -
en ac o s may il he balance o s a es abou whe he o implemen na ion-building
policies. Mo eo e , how hese se s o ac o s bundle oge he may di e ac oss ime
and space. Hence, iden i ying he speci ic ac o s ha played a ole in di e en his o -
ical expe iences may be mo e in o ma i e han looking o uni e sal causes o na ion-
building.25
Despi e he absence o a speci ic se o causes igge ing na ion-building episodes,
ou esul s highligh some impo an cha ac e is ics ha hey sha e. Fi s , ou model
25In ac , he as li e a u e in poli ical science on his opic also sugges s ha gene al heo ies on he
causes o na ion-building and na ional iden i ies a e unhelp ul o pa icula cases. See McC one (1998) o
u he elabo a ion o his a gumen , and Wimme and Feins ein (2010) o suppo i e empi ical e idence.

Theo e ical Economics 15 (2020) The cons uc ion o na ional iden i ies 783
has mul iple s eady s a es, accoun ing o he di e si y we obse e ac oss na ions wi h
espec o he sp ead o na ional sen imen s in pe iphe al egions. Second, he s eady
s a e ha is inally eached is e y sensi i e o ini ial condi ions, because small ini ial
di e ences could lead o opposi e choices wi h a high deg ee o pa h dependency. This
p edic ion i s a ich se o his o ical cases in which egions ha we e ini ially simila in
e ms o economic, poli ical, and social ac o s ha e expe ienced comple ely di e gen
ajec o ies.26 Thi d, he model displays d as ic egime changes: Sudden and ex eme
shi s in (de)cen aliza ion policies can be caused by exogenous shocks o he ela i e
cos s and bene i s o na ion-building, leading o opposi e long- un ou comes.27 Fou h,
na ion-building episodes a e ela i ely as and ex eme (MRAP beha io ). Fi h, once
su icien ly sp ead ac oss he popula ion, e i o ial iden i ies a e ema kably s able and
di icul o e e se, because iden i ies a e ep oduced o e ime inside he amily ( e -
ical socializa ion) and ein o ced by he communi y (ho izon al socializa ion). Six h,
egional iden i ies a e mo e likely o h i e in democ acies han in dic a o ships, be-
cause egionalis s may be pi o al in eaching elec o al majo i ies. Se en h, he model
p edic s a wo-way causali y be ween s a e cen aliza ion (δ) and he sp ead o he na-
ional iden i y (1−q), because hey end o ein o ce each o he and o bundle oge he .
Finally, al hough pe iphe al egions exis s in which bo h iden i ies ha e simila le els o
a achmen in he popula ion, he model sugges s ha in he long un, one o he wo
iden i ies will end o become p edominan .
Mo eo e , ou heo y highligh s he undamen al ole played o he s a e in pu pose-
ully shaping na ional iden i ica ions, which is in con as o o he explana ions ha
emphasize a mo e bo om-up na u e o his p ocess and see na ional iden i ica ions as
a byp oduc o s a e mode niza ion.28 Al hough hese explana ions a e able o explain
he ise o na ionalism as an his o ical phenomenon and iden i y some necessa y con-
di ions o na ion-building, hey canno explain why egional iden i ies su i ed wi hin
coun ies ha wen h ough he p ocess o mode niza ion.29 Mo eo e , hey canno ac-
coun o he di e gence o ou comes o ini ially simila egions. In his sense, he wo
case s udies discussed below p o ide suppo o he key ole o op-down s a e social-
iza ion, because he c ucial di e ence in bo h cases was he capaci y and willingness o
go e nmen s o p omo e na ional iden i ies.
26In addi ion, his dependence on p e ious choices explains why sho -sigh ed go e nmen s ha do no
in e nalize iden i y dynamics some imes pu sue cul u al decen aliza ion policies ha become di icul o
e e se.
27Ne e heless, changes in he pa ame e s on he model o in he loca ion o q0a e no necessa ily ex-
ogenous, because s a es may ha e addi ional ins umen s ha a ec hem. Fo ins ance, Sambanis e al.
(2015) no e ha some s a es, such as P ussia in he 19 h cen u y, engaged in in e na ional wa s wi h he
pu pose o uni ying he coun y by changing he alue o q0. O he s ha e elied on in e nal mig a ion o
s a he p ocess o na ion-building in pe iphe al egions (McGa y (1998)).
28The gene al idea unde lying hese heo ies is ha he p ocesses o u baniza ion and indus ializa ion
b oke adi ional pa ochial ne wo ks and spu ed labo mobili y. As a consequence, ci izens om di e en
backg ounds in e ac ed wi h each o he , which, in u n, p omo ed he eme gence o a na ional iden i ica-
ion. Mo eo e , his p ocess o c ea ing “imagined communi ies” was ca alyzed by he ad en o echnolo-
gies pe mi ing mass li e acy in e nacula languages (Ande son (1991)).
29Fo ins ance, (Robinson (2014)) a gues he s eng h o e hnic iden i ica ions in ensi ied pa allel wi h
he p ocess o mode niza ion o A ican coun ies a e decoloniza ion.
784 Almag o and And és-Ce ezo Theo e ical Economics 15 (2020)
Case s udy I: Spanish e sus F ench Ca alonia Ca alonia cons i u es a pa adigma ic
case in which small di e ences in he ini ial condi ions could ampli y o e ime h ough
he e olu iona y p ocess. A he beginning o he 17 h cen u y, Ca alonia was an homo-
geneous egion ha was la e spli be ween F ance and Spain by he ea y o he Py e-
nees in 1659. Since he spli , Ca alan na ional iden i y has pe sis ed in bo h coun ies.
Howe e , his iden i y is p ominen in oday’s Spanish poli ical and social li e, whe eas
i is almos negligible in F ance.30
Acco ding o McRobe s (2001), bo h pa s o Ca alonia emained ela i ely simila
un il he 18 h cen u y. In pa icula , Ca alan egions on bo h sides o he bo de sha ed a
common pas , p esen ed analogous deg ees o linguis ic and cul u al homogenei y, and
e en kep some common legal ins i u ions ha we e ela i ely independen om he
cen al s a es. Despi e hese simila i ies, an ob ious c ucial di e ence was he uling
s a e and, in pa icula , he di e en se o incen i es and cons ain s each s a e aced
du ing he i s decades o he 19 h cen u y. On he one hand, he Spanish s a e lacked
he means o implemen and en o ce na ion-building policies due o i s inabili y o col-
lec axes (De Rique (2001)). Mo eo e , i s poli ical powe in ela ion o Ca alan eli es
was ela i ely low, and he la e we e able o mobilize he popula ion a ound he idea
o a Ca alan iden i y (McRobe s (2001)). On he o he hand, as Webe (1976)no es,
du ing his ime, he F ench s a e was cha ac e ized by a ela i ely s ong s a e capaci y.
The e o e, i had he esou ces o implemen mass schooling wi h a school cu iculum
designed o “make” F ench ci izens.31 By con as , as Engui a (2012) a gues, uni e sal
schooling in Spain was no e ec i e un il he la e 20 h cen u y, because he go e n-
men did no ha e he inancial means o p o ide schooling in u al a eas. Mo eo e ,
he incen i es o bo h s a es we e ela i ely di e en . In pa icula , indus ializing op-
po uni ies in F ance we e g ea e a he beginning o he 19 h cen u y, inc easing he
bene i s o he F ench cen al go e nmen o ha ing an homogeneous popula ion ha
could communica e in he same language (Gellne (1983)). In addi ion, he F ench s a e
was in ol ed in se e al ex e nal wa s ha needed an a my o soldie s willing o igh o
hei na ion (Aghion e al. (2019)). In ou model, hese ini ial di e ences co espond
o sligh ly di e en le els o iscal capaci y ( ), damage c ea ed by egionalis poli ical
un es (1−β), and he na ion-building mo i e pa ame e (ψN), bu no by subs an i e
ini ial di e ences in q0.
The Ca alan case also highligh s he high deg ee o pa h-dependency implied by he
model. As Balcells (2013) shows, he ailu e o he Spanish s a e o sp ead he Spanish
iden i y du ing he pe iod o he “scholas ic e olu ion” enabled he appea ance o a e-
gional e i al mo emen ( he “Renaixença”) ha p omo ed Ca alan cul u al alues. As a
30Fo ins ance, acco ding o E hnologue, Ca alan is he main language o communica ion o a ound
50% o he popula ion in Spanish Ca alonia, whe eas his igu e is 1% in F ance.
31The case o F ench Ca alonia also shows ha success ul na ion-building episodes end o be as and
cha ac e ized by homogeniza ion policies ha dis ega d egional pa icula i ies. As Webe (1976)no es,
wi hin a single gene a ion, locally iden i ied peasan s became loyal “F enchmen.” This iden i ica ion was
achie ed by wha can be conside ed ex eme (MRAP) in e en ions, such as he implemen a ion o manda-
o y schooling and mili a y se ices, he supp ession o he use o he Ca alan language in public adminis-
a ion, and he aboli ion o local ins i u ions.
Theo e ical Economics 15 (2020) The cons uc ion o na ional iden i ies 785
esul , mo e people we e socialized o he Ca alan iden i y. The e o e, when indus ial-
iza ion and s a e capaci y le els in Spain esembled hose in F ance a ew decades ea -
lie , ins illing he na ional iden i y was no longe desi able o he Spanish go e nmen .
In ac , he size o he egionalis g oup con inued o g ow and i s poli ical impo ance
pushed he Spanish s a e o p og essi ely g an mo e decen aliza ion du ing he ea ly
20 h cen u y.
Finally, he Ca alan case exempli ies he di icul ies in e e ing o me ly ins illed
e i o ial iden i ies, as well as he impo ance o exogenous shocks in p o oking d as-
ic changes in na ion-building policies. A e he ci il wa (1936–1939), F anco’s egime
s a ed a p ocess o massi e cen aliza ion, and implemen ed ep essi e and b u al
measu es aimed a elimina ing he Ca alan iden i y, in sha p con as o he ede al ap-
p oach and policies o cul u al ecogni ion o he Second Spanish Republic (1931–1939).
In e ms o he model, he ci il wa and he pos e io es ablishmen o a ascis egime
could be in e p e ed as a la ge shock ha igge ed a se e e egime change in policies.
In pa icula , i can be seen as a shock o he abili y o Ca alan egionalis s o o ganize
and p o es , because du ing he ci il wa many o he Ca alan leade s and ci izens we e
killed, imp isoned, o o ced in o exile (a dec ease in (1−β)). Also, he ideological shi
o he new ascis egime, based on ex eme Spanish na ionalism, can be in e p e ed as
ashock oψN. Howe e , Ca alan iden i y was al eady widesp ead in socie y due o he
weakness o he Spanish s a e du ing he 19 h cen u y (small q0), and he measu es im-
plemen ed by F anco’s egime did no signi ican ly al e hese p e ious iden i ica ions.
In ac , wi h he ad en o democ acy 40 yea s la e , he majo i y o Ca alans we e s ill
a ached o he egional iden i y.32 This new “shock” al e ed again he balance be ween
he cos s and bene i s o p omo ing he na ional iden i y (because he success o he
new democ acy depended in pa on he accep ance by he Ca alan popula ion), which
igge ed a adical swi ch in policies in a o o mo e ede alism and he ecogni ion o
he cul u al dis inc i eness o he Ca alan egion.33
Case s udy II: Tanzania e sus Kenya The case o Tanzania and Kenya is e en mo e
pa adigma ic o he con ingen na u e o na ion-building a emp s and o he di icul ies
p esen in iden i ying a se o undamen al causes behind hem. In a ascina ing wo k,
Miguel (2004) shows how he pos -independence go e nmen s o Kenya and Tanzania,
wo coun ies ha we e simila in many espec s, pu sued adically di e en na ion-
building policies: Whe eas he Tanzania go e nmen p omo ed Swahili as a na ional
language, p aised a na ional iden i y in schools, and disman led ibal au ho i ies, he
Kenyan go e nmen allowed e hnic di ision. O e ime, his di e ence in app oaches
c ea ed a na ional iden i y in Tanzania ha is no p esen in Kenya.
The ins i u ional and his o ical simila i ies be ween hese wo coun ies we e e-
ma kable, bo h in he colonial and ea ly pos -colonial pe iod. Bo h coun ies ha e a
32Gi en he in e gene a ional na u e o his p ocess, possibly no enough ime passed o na ion-
building policies o ha e a signi ican e ec , especially gi en he low a e o change a ea ly s ages.
33This case also highligh s one o he p edic ions o he elec o al model in Sec ion 6 ega ding he possi-
ble di e en beha io o democ acies and dic a o ships. In pa icula , democ acy ga e Ca alan egionalis s
he abili y o in luence he e i o ial and iden i y policies o he cen al go e nmen . In ac , Ca alan pa ies
ha e been pi o al in he na ional pa liamen se e al imes du ing he democ a ic pe iod.
786 Almag o and And és-Ce ezo Theo e ical Economics 15 (2020)
simila geog aphy and popula ion densi y, we e o me B i ish colonies, became inde-
penden in he 1960’s, and s a ed a e wa ds om simila economic condi ions. In he
poli ical ealm, hey bo h o med a one-pa y sys em and inhe i ed simila adminis-
a i e s uc u es om he colonial pe iod (Webe (2010)). Despi e hese simila i ies,
(Ba kan (1994)) claimed ha he undamen al di e ence be ween he wo coun ies lay
in he ac ha Tanzania had a la ge numbe o small e hnic g oups, whe eas Kenya was
popula ed by ewe bu la ge e hnic g oups wi h su icien powe o oppose he go e n-
men ’s policies. Mo eo e , he concen a ion o capi al was ela i ely highe in Kenya
(Ili e (1979)), which enabled some e hnic g oups o a m hemsel es and igh iolen ly
he agains he s a e, p e en ing na ion-building. In ou model, his explana ion co e-
sponds o a di e en ini ial alue o q0and di e en alue o β. Ne e heless, as Miguel
(2004) no es, i seems ha he c ucial bu small ini ial di e ence ha led o di e gen
na ion-building expe iences we e jus “ he pe sonali ies and philosophies o he espec-
i e independence leade s, Jomo Kenya a and Julius Nye e e.”
Mo eo e , he Tanzanian case nicely illus a es how na ion-building policies a e gen-
e ally implemen ed in a as and adical way, as implied by he MRAP solu ion o ou
model. As Miguel no es, “The Tanzanian egime quickly pushed o o al Swahiliza ion
o go e nmen adminis a ion a e independence and es ablished he Na ional Swahili
Council o p omo e i s use in all sphe es o public li e.”
8. Conclusion and ways o wa d
In his pape , we de elop a heo e ical amewo k o illus a e he main mechanisms in
na ion-building p ocesses, highligh ing he impo ance o con ingen his o ical ci cum-
s ances in shaping he abili y o s a es o na ion-build. To conclude, we summa ize he
key esul s o he pape and ou line a ew po en ial ex ensions.
Ou key heo e ical con ibu ion is o analyze he p oblem o a o wa d-looking
leade who in e nalizes cul u al dynamics and sol es a ze o-sum con lic be ween iden-
i y g oups. This exe cise yields h ee main esul s. Fi s , he model displays mul iple
s eady s a es and dependence on ini ial condi ions, a ypical cha ac e is ic o models
wi h a logis ic di e en ial equa ion. Second, al hough he op imal ajec o y o he con-
ol may a y wi h he choice o he objec i e unc ion, all op imal pa hs e en ually ake
ex eme alues o se e al speci ica ions. Tha is, he go e nmen e en ually p o ides
only one ype o public good, because p o iding bo h implies “in es ing” in opposi e
goals a he same ime. Thi d, he op imal long un s eady s a es a e cul u ally homo-
geneous, e en unde cul u al subs i u ion be ween e ical and ho izon al ansmission
channels, in con as o p e ious esul s in he li e a u e (e.g., Bisin and Ve die (2001);
Ve die and Zenou (2018)). We ha e shown ha wo su icien condi ions mus be sa -
is ied o his long- un beha io . Fi s , he cul u al leade mus be able o shape any
nondegene a e iden i y dis ibu ion in any di ec ion. Second, a s ong enough con lic
mus exis o e sca ce esou ces be ween he wo g oups. In e es ingly, he quali a i e
esul s a e simila when we in oduce dynamic elec o al compe i ion, and sol e o he
Ma ko Nash equilib ium o he di e en ial game.
Theo e ical Economics 15 (2020) The cons uc ion o na ional iden i ies 793
s. . ˙
q =g(δ q )and q0=q
Deno e by δS(q) he s a iona y policy unc ion
˙
q=gqδS(q)=0
and de ine unc ion
H(q) =WqδS(q)
I o some in e io ˜
q, we ha e ha δ∗(˜
q) =δS(˜
q) ∈o, such ha {g(˜
qδ)|δ∈[01]} is an
open neighbo hood o 0, hen ˜
qis a local maximum o H(q).
P oo . We p o e i by con adic ion. Assume ha op imal policy is gi en by δ∗(q) and
ha o some ˜
q
δ∗(˜
q) =δS(˜
q)
such ha {g(˜
qδ)|δ∈[01]} is an open neighbo hood o 0so we can mo e in any di-
ec ion a ˜
q,bu ˜
qis no a local maximum o H(q). Wi hou loss o gene ali y, as-
sume H(˜
q) > 0. Pick any unc ion (q) such ha ˙
˜
q=g(˜
qδS(˜
q) +( ˜
q)) > 0wi h policy
δS(q) +(q) easible o an open neighbo hood o ˜
q. De ine ¯
qτsuch ha
¯
qτ=qτ
whe e q ollows he pa h de ined by policy δS(q) +(q).36 Fo e e y τ>0,cons uc
policy
δ
τ(q) =δS(q) i q=¯
qτ
δS(q) +(q) i q= ¯
qτ
The in ui ion o policy δ
τis o mo e away om δSa an (q) a e un il hi ing ¯
qτ,and
s ay a ¯
qτ o e e a e wa ds. Fo example, i τ=0, hen δ(q) =δS(q) o all q.
We wan o compa e δ∗wi h δ
τs a ing a ˜
q.37 Gi en hei de ini ions, he dis-
coun ed u ili y o each policy is gi en by
J˜
qδ∗=∞
0
e−ρ H(˜
q)d 
J˜
qδ
τ=τ
0
e−ρ Wq δ
τ(q )d +e−ρτH(qτ)
De ine F(τ) as he su plus di e ence be ween policy δ
τand δ∗:
F(τ)≡J˜
qδ
τ−J˜
qδ∗
=τ
0
e−ρ Wq δ
τ(q )−H(˜
q)d +e−ρτH(qτ)−H(˜
q)(6)
36We omi he dependence on he ini ial alue q0 o he ease o exposi ion.
37δ
τ(q) migh no be easible o all τand all ini ial alues q0,bu sinceδ∗(˜
q) =δS(˜
q) ∈o,δ
τ(q) will be
well-de ined o su icien ly small τin a neighbo hood o ˜
q.

794 Almag o and And és-Ce ezo Theo e ical Economics 15 (2020)
Because δ∗is he op imal policy, i mus be he case ha F(τ)≤0. Howe e , obse e ha
F(τ)=F(0)τ +oτ2
because F(0)=0. Taking de i a i es om (6) wi h espec o τ38
F(τ) =e−ρτH(qτ)−H(˜
q)−ρe−ρτWqτδ(qτ)−H(˜
q)+e−ρτH(qτ)˙
qτ
and e alua ing a τ=0
F(0)=H(˜
q)˙
˜
q>0
which con adic s he ac ha δ∗is he op imal policy.39
A.2.2 P oo o Theo em 5 We p oceed in s eps. Fi s , conside he co esponding HJB
equa ion o p oblem (2):
ρV (q) =max
δ∈[01]ψNq+αq (1− )+ (1−δ)+(1−α)(1−q)( (1− )+ δ
− 2βqδ2+(1−β)(1−q)(1−δ)2
+ q(1−q)(1−δ−q)V (q)
Taking de i a i es wi h espec o δ,weob ain
(1−α)(1−q) −αq− 22βqδ −(1−β)(1−q)(1−δ)−V(q) q(1−q) (7)
Hence, o an in e io solu ion o δ∗(q),wecanw i e
δ∗(q) =1
βq +(1−β)(1−q)(1−β)(1−q) +(1−α)(1−q) −αq −q(1−q)V (q)
2 
Because he e is no in e io s eady s a e, i mus hold ha δ(q) = 1−q o all q∈(01).
This implies he ollowing esul .
P oposi ion 10. Fo any in e io s a e q∈(01), i ollows ha
V(q) = s(q) ≡2 (1−2β) +1−α
q−α
1−q
P oo . We know ha δ(q) = 1−q o all q∈[01].Se δ=1−qin equa ion (7)and
sol e o V(q).
38Recall ha δ
τimplici ly depends on τand he e m τ
0
∂
∂τ δ(q)eρ (W (q δ(q )) −H(˜
q))d should be
included in he de i a i e, oo. Howe e see he Supplemen a y Appendix S.4.1 o see ha
τ
0
∂
∂τ δ(q)eρ Wq δ(q )−H(˜
q)d =0
39E en when H(˜
q) =0 he esul s ill holds. I his is he case, we can use he second-o de Taylo ap-
p oxima ion o he unc ion F(τ). Fo mo e de ails, see he Supplemen a y Appendix S.4.1.
Theo e ical Economics 15 (2020) The cons uc ion o na ional iden i ies 795
F om he p e ious p oposi ion, i ollows ha V(q)is no di e en iable a some ¯
q∈
(01), ha is,V(q)has a kink a some ¯
q∈(01). This esul is shown in he ollowing
p oposi ion.
P oposi ion 11. V(q) is no con inuous on (01). Mo eo e , in a neighbo hood o q=1
i mus be he case ha V(q) > s(q) and, he e o e, δ∗(q) < 1−qand so ˙
q>0. Simila ly,
in a neighbo hood o q=0,V(q) < 1−q,andδ∗(q) > 1−qand so ˙
q<0.
P oo . We know ha
V(q) = s(q)
o all q∈(01). The only way ha V(q) can be con inuous is o ha e ei he V(q) always
abo e, o always below ha unc ion:
V(q) > s(q) o V(q) < s(q)
o all q∈(01). Wi hou loss o gene ali y, le us assume ha V(q) is con inuous in
(01)wi h
V(q) < s(q) =2 (1−2β) +1−α
q−α
1−q
This means ha V(q) < s(q) in a neighbo hood o q=1. By con inui y o V(q) in (01)
i ollows
lim
q→1−V(q) =−∞
which con adic s he con inui y o V(q) a q=1. The e o e, i mus he case ha
V(q) > s(q) in a neighbo hood o q=1. Following a simila a gumen , V(q) < s(q)
in a neighbo hood o q=0.Hence,V(q) is discon inuous a some q∈(01).
P oposi ion 12. The e is a h eshold ¯
q0such ha
V(q) > s(q) ⇐⇒ q>¯
q0
P oo . We know om P oposi ion 11 aqin (01)exis s a which V(q) jumps unc ion
s(q). We also know V(q) < s(q) nea q=0as well as V(q) > s(q) nea q=1. Assume
o a con adic ion he e is mo e han one jump. Then he e is a poin ¯
q1such ha o
some >0,˙
q<0 o all q∈(¯
q1¯
q1+) and ˙
q>0 o all q∈(¯
q1− ¯
q1)asshownin he
example o Figu e 7. This would imply ha ¯
q1is an in e io s a iona y poin , which is a
con adic ion.40
P oposi ion 13. δ∗(q) =0in a open neighbo hood o q=1.δ∗(q) =1in an open neigh-
bo hood o q=0.
40Obse e limi cycles a e uled ou o dynamic au onomous sys ems o single a iable wi h discoun
ac o ρ>0, since he Jacobian o he canonical sys em, J, sa is ies (J) =ρ>0. Fo a mo e de ailed
discussion, see G ass e al. (2008), P oposi ion 3.83.
796 Almag o and And és-Ce ezo Theo e ical Economics 15 (2020)
Figu e 7. Example o many h esholds.
P oo . Assume o a con adic ion ha δ∗(q) > 0nea q=1. We know om P oposi-
ion 11 ha δ∗(q) < 1−q<1in some open neighbo hood o q=1,sayO(1). The e o e,
o q∈O(1),δ∗(q) is in e io , δ∗(q) ∈(01), and de ined by he solu ion o he i s -o de
condi ion
1>δ
∗(q) =1
βq +(1−β)(1−q)(1−β)(1−q) +(1−α)(1−q) −αq −q(1−q)V (q)
2 
>0
which implies
1−α
q−α
1−q+2 (1−β)
q>V(q) > 1−α
q−α
1−q−2 β
1−q
By con inui y o V(q) in O(1)∩(01)i mus be he case ha
lim
q→1−V(q) =−∞
which con adic s again ha V(q)is con inuous a q=1.
P oposi ion 14. The op imal policy δ∗(q) is con inuous on [0¯
q0)∪(¯
q01].
P oo . I is easy o see ha he op imal con ol sa is ies
δ∗(0)=1δ∗(1)=0
which combined wi h con inui y o V(q) on [0¯
q0)∪(¯
q01]and P oposi ion 13 deli e s
he esul .
Co olla y 7. The long- un s eady s a e o q a e cha ac e ized as ollows:
lim
→∞ q =0i q0≤¯
q0
1i q0≥¯
q0
wi h he p ope y ha ¯
q0is a Skiba poin o he dynamic sys em, ha is, he go e nmen
is indi e en be ween con e ging o 0,lim →∞ q =0o con e ging o 1,lim →∞ q =1a
¯
q0.
P oo . I ollows di ec ly om he he h eshold cha ac e is ic o δ∗(q)
δ∗(q) =>1−qi q0≤¯
q0
<1−qi q0≥¯
q0
Theo e ical Economics 15 (2020) The cons uc ion o na ional iden i ies 797
Pu ing all he p e ious esul s oge he , we a e able o p o e Theo em 5:
Theo em 5. The e exis s ¯
q0∈(01)such ha
δ∗(q) > 1−qi q≤¯
q0δ
∗(q) < 1−qi q≥¯
q0
Mo eo e , δ∗(q) con inuous on [0¯
q0)∪(¯
q01]and he e wo open neighbo hoods o q=0
and q=1, say O(0)and O(1)in [01],such ha
δ∗(q) =1∀q∈O(0) δ∗(q) =0∀q∈O(1)
A.3 Appendix o Sec ion 6
Fo de ails abou he mic o ounda ion o he objec i e unc ion in he elec o al compe i-
ion game, see he Supplemen a y Appendix S.5. Obse e ha because W(qδ
iδ−i)=
ψNq+pi(δiδ−i)≤ψN+1<∞, we know ha he alue unc ions
Vi(q0)=E0∞
0
e−ρ Wiq δ∗i(q ) δ∗−i(q )d 
V−i(q0)=E0∞
0
e−ρ W−iq δ∗i(q ) δ∗−i(q )d 
a e well-de ined and con inuous. The co esponding HJB equa ions a e
ρV i(q) =max
δ∈[01]Wiqδiδ∗−i+Eqgqδδ∗−iVi
q(q)
ρV −i(q) =max
δ∈[01]Wiqδi∗δ+Eqgqδi∗δV−i
q(q)
whe e Eqis he expec a ion condi ional on cu en s a e q. Gi en ha wo pa ies sol e
iden ical p oblems, we can es ic ou a en ion o symme ic equilib ia. Unde sym-
me ic equilib ia, i ollows ha Vi=V−i=V. Fu he mo e, i also holds
Eqgqδiδ−iVq(q)
= q(1−q)1−q−piδiδ−iδi+1−piδiδ−iδ−iVq(q) (8)
Fi s , we p o e some esul s ha a e used in he p oo o Theo em 6.
Claim 1. Le q0( ) and qh( ) wo pa hs de ined by dynamics
˙
q= q(1−q)1−q−δ(q)
wi h ini ial condi ions q0and q0+h, espec i ely. Then
qh( ) > q0( ) ⇐⇒ h>0∀ ≥0
798 Almag o and And és-Ce ezo Theo e ical Economics 15 (2020)
P oo . Obse e bo h unc ions q0( ) and qh( ) a e di e en iable and, he e o e, con-
inuous. We p o e he claim by con adic ion. Suppose i does no hold. Because q0( )
and qh( ) a e con inuous wi h q0(0)=q0<q
h(0)=q0+h, i he claim does no hold, a ˜
exis s such ha
q0( ) < qh( ) ∀ <˜
and q0(˜
) =qh(˜
) =˜
q
The p e ious inequali y implies
˙
q0(˜
)=lim
→0
q0(˜
)−q0(˜
−)
>lim
→0
qh(˜
)−qh(˜
−)
=˙
qh(˜
)
which is a con adic ion because a ˜
bo h dynamics a e de ined as
˙
q0(˜
) =˙
qh(˜
) =˜
q(1−˜
q)1−˜
q−δ(˜
q)
Using he p e ious claim, we ha e he ollowing esul .
Claim 2. A he poin s whe e V(q)is di e en iable, o any symme ic equilib ium o he
na ion-building elec o al compe i ion p oblem i mus hold
Vq(q) ≥0
P oo . Unde any symme ic equilib ium, i ollows
piqδ∗δ∗=1
2
Hence
V(q)=∞
0
e−ρ ψNq +1
2d 
The e o e,
V(q+h) −V(q)=∞
0
e−ρ qh
−q0
d > 0
which implies Vq(q) ≥0 o any symme ic equilib ium δ∗(q) because qh
>q
0
o any
h>0.
Second, we show ha equilib ium s a egies canno be in e io , δ∗(q) /∈(01).
P oposi ion 15. Fo all q∈[01], he e is a unique symme ic equilib ium announce-
men ha is no in e io
δ∗(q) ∈{01}
P oo . We s a by cha ac e izing he bes - esponse unc ion δ∗i o gi en opponen ’s
s a egy δ−iby sol ing he ollowing p oblem:
ρV (q) =max
δ∈[01]ψNq+piδδ−iq+Eqgqδδ−iVq(q)

Theo e ical Economics 15 (2020) The cons uc ion o na ional iden i ies 799
=max
δ∈[01]ψNq+1
2+(q)δ−δ−i
+ q(1−q)1−q−1
2δ+δ−i+(q)δ−δ−i2Vq(q) (9)
whe eweha eusedpi(δ δ−iq)=1
2+(q)(δ −δ−i)wi h
(q) =(1−q)φR−qφN
qφN+(1−q)φR
and equa ion (8). We check o equilib ium s a egies by in oking he one-sho de ia ion
p inciple. Obse e ha in equa ion (9), omo ow’s payo is included in he con inua-
ion alue h ough he e m Eq[g(qδδ−i)Vq(q)]. Tha is, we check i he s a egy o
playe iis a bes - esponse o δ−iassuming ha in he u u e playe s keep playing he
equilib ium wi h associa ed payo V(q).
The i s -o de condi ions o equa ion (9), which a e gi en by
(q) − q(1−q)Vq(q)1
2+2(q)δi−δ−i
wi h second-o de condi ions gi en by
− q(1−q)Vq(q)2(q)
We conside di e en cases, depending on he sign o (q). Obse e ha he sign
o (q) de e mines he equilib ium announcemen o a game wi hou o wa d-looking
pa ies ha only ca e abou winning he elec ions.
Case 1: (q) < 0
When q∈−≡{q|(q) < 0}and aking he o he playe s a egy as gi en δ−i, he
p obabili y o winning he elec ion o pa y iis maximized a δi=0∀δ−i. Since he
con inua ion alue Eq[g(qδδ−i)Vq(q)]is also maximized a δi=0gi en ha Vq(q) ≥0
o all δ−i,weha e ha δi(q) =0is a dominan s a egy o i=AB. The e o e, o
q∈−, he e is a unique equilib ium wi h δA(q) =δB(q) =0.
Gi en he p e ious equilib ium announcemen s, we can sol e o he alue unc ion
in he subspace −. Subs i u ing equilib ium s a egies inside he HJB equa ion, we
ob ain
ρV (q) =ψNq+1
2+ q(1−q)2Vq(q)
When we subs i u e H(q) =ρV (q) −(ψNq+1
2), he esul ing di e en ial equa ion o
H(q) is gi en by
H(q) −ρ
q(1−q)2H(q) =−ψN
ρ
We ob ain he in eg a ing ac o o he p e ious ODE, m(q), by sol ing mq(q) =
−ρ
q(1−q)2m(q). The solu ion is gi en by
m(q) =Ce−ρ
(ln(q)−ln(1−q)+1
1−q)
800 Almag o and And és-Ce ezo Theo e ical Economics 15 (2020)
Hence, he solu ion o he o iginal equa ion is
m(1)H(1)−m(q)H(q) =−1
q
ψN
ρm(q) dq
Bu since m(1)=0, he solu ion o H(q) is
H(q) =1
m(q) 1
q
ψN
ρm0(q) dq
and so
V(q)=ψNq
ρ+1
2ρ+1
m(q) 1
q
ψN
ρm(q) dq (10)
o all q∈−.
Case 2: (q) =0
Obse e ha when (q) =0i mus be q=ˆ
qS. In his case, he p obabili y o winning
is always 1
2and so i is independen o he announcemen s. Then, i Vq(ˆ
qS)>0, hen
δ∗(ˆ
qS)=0is also a dominan s a egy and i Vq(ˆ
qS)=0, hen he whole in e al [01]is
a dominan s a egy.
I is easy o p o e ha we can only ha e Vq(ˆ
qS)>0. Assume no , ha is, Vq(ˆ
qS)=0.
Subs i u ing Vq(ˆ
qS)=0in equa ion (9), i ollows
ρV ( ˆ
qS)=ψNˆ
qS+1
2
By con inui y o V(q),i mus hold
lim
q→ˆ
q+
S
ρV (q) =ρV ( ˆ
qS)
Using he solu ion o he alue unc ion gi en in (10), we ha e
lim
q→ˆ
q+
S
ρV (q) =ψNˆ
qS+1
2+1
m( ˆ
qS)1
ˆ
qS
ψN
ρm(q) dq
and so
1
m( ˆ
qS)1
ˆ
qS
ψN
ρm(q) dq =0
This is a con adic ion because m(q) > 0 o all q∈(01)wi h m( ˆ
qS)<∞whe e ˆ
qS=
φN
φN+φR∈(01).
The e o e, we conclude equilib ium announcemen s sa is y
δ∗(q) =0∀(q) ≤0
Theo e ical Economics 15 (2020) The cons uc ion o na ional iden i ies 801
Case 3: (q) > 0
When q∈+≡{q|(q) > 0}, he e is a ade-o be ween inc easing he p obabili y
o winning elec ions and announcing a policy such ha qinc eases in he nex pe iod.
The bes - esponse unc ion o opponen ’s announcemen δ−iis cha ac e ized by he
i s -o de condi ions
(q) − q(1−q)Vq(q)1
2+2(q)δi−δ−i
because he second-o de condi ions
− q(1−q)Vq(q)2(q) ≤0
gi en ha (q) > 0and Vq(q) ≥0. We p oceed in cases:
•Case Vq(q) =0:I Vq(q) =0, we a e sol ing he s a ic p oblem o which we know
δ(q) =1is a dominan s a egy. The e o e, i Vq(q) =0, he only equilib ium is
δ∗(q) =1.
•Case Vq(q) > 0: We p o e ha he e is no in e io equilib ium by con adic ion. As-
sume ha o some q∈+, he e is such equilib ium wi h an in e io announce-
men , say δ∗(q) ∈(01). Because Vq(q) > 0, he solu ion o he i s -o de condi-
ions is a maximum. This solu ion, gi en opponen ’s s a egy δ−i,is
δi=δ−i+1
2(q)(q)
q(1−q)Vq(q) −1
2=δ−i+(q)
whe e (q) ≡1
2(q)[(q)
q(1−q)Vq(q) −1
2]. Se ing δ−iequal o he bes esponse o he
playe −i, we ha e ha a an in e io equilib ium announcemen i mus hold:
δi=δi+2(q) ⇒(q) =0⇒Vq(q) =2(q)
q(1−q)
I δ∗is an equilib ium announcemen , i mus also hold
ψNq+1
2+ q(1−q)1−q−δ∗Vq(q)
≥ψNq+1
2+(q)δ−δ∗+ q(1−q)
×1−q−1
2δ+δ∗+(q)δ−δ∗2Vq(q)
o all δ∈[01], which implies
q(1−q)Vq(q)1
2+(q)δ−δ∗δ−δ∗≥(q)δ−δ∗
In pa icula , o δ= δ∗,weha e ha
q(1−q)Vq(q)1
2+(q)δ−δ∗=(q) + q(1−q)Vq(q)(q)δ−δ∗≥(q)
802 Almag o and And és-Ce ezo Theo e ical Economics 15 (2020)
whe e we ha e subs i u ed 1
2 q(1−q)Vq(q) =(q). Simpli ying he p e ious ex-
p ession, i mus hold
q(1−q)Vq(q)(q)δ−δ∗≥0
o all δ∈[01]δ= δ∗. Gi en ha Vq(q) > 0and (q) > 0, which implies q<1, o
q>0 he p e ious s a emen can only be ue o all δ∈[01]i and only i δ∗=0,
which is no in e io , a con adic ion. Fo q=0, i is s aigh o wa d o see δ∗=1
is he only equilib ium.
Hence because also δ∗(q) /∈(01) o any q∈+, we inally conclude δ∗(q) ∈{01} o all
q∈[01].
We a e le o p o e ha o all q∈[01] he e is a unique symme ic equilib ium
announcemen . F om he p e ious discussion, we al eady know he only equilib ium
announcemen o qsuch ha (q) ≤0is δ∗(q) =0. Le us look a qsuch ha (q) > 0.
I Vq(q) =0, i is s aigh o wa d o see ha δ=1is a dominan s a egy and, he e o e,
δ∗(q) =1is he unique equilib ium announcemen . Now suppose ha Vq(q) > 0,so
i s -o de condi ions cha ac e ize a maximum and he bes - esponse unc ion is gi en
by
BR(δ) =⎧
⎪
⎪
⎨
⎪
⎪
⎩
1i δ+(q) > 1
δ+(q) i δ+(q) ∈(01)
0i δ+(q) < 0
whe e (q) =1
2(q)[(q)
q(1−q)Vq(q) −1
2].
Obse e we can cha ac e ize equilib ium announcemen s by he ixed-poin o he
opponen ’s bes esponse o a playe ’s bes esponse. In a symme ic equilib ium, he
bes - esponse unc ions o bo h playe s a e iden ical, so equilib ium announcemen s
a e cha ac e ized as he ixed poin o he bes - esponse composi ion
δ=BRBR(δ)=⎧
⎪
⎪
⎨
⎪
⎪
⎩
1i δ+2(q) > 1
δ+2(q) i δ+2(q) ∈(01)
0i δ+2(q) < 0
I immedia ely ollows:
•I (q) > 0, he only ixed poin o he bes - esponse composi ion is δ=1.In his
case, he unique equilib ium is δ∗(q) =1.
•I (q) < 0, he only ixed poin o he bes - esponse unc ion is δ=0.In hiscase,
he unique equilib ium is δ∗(q) =0.
•I (q) =0, we use he p e ious discussion o show ha he e a e no in e io solu-
ions and ha he unique equilib ium announcemen is δ∗(q) =0.
Wi h he ollowing p oposi ion, we show ha he equilib ium policy is also cha ac-
e ized by a bang-bang as in he baseline model, wi h he p ope y ha he h eshold o
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