Unilingual Versus Bilingual Education System: A Political Economy Analysis

Transcription

1 DISCUSSION PAPER SERIES IZA DP No Uiligual Versus Biligual Educatio Syste: A Political Ecooy Aalysis Javier Ortega Thoas P. Tagerås Deceber 2004 Forschugsistitut zur Zukuft der Arbeit Istitute for the Study of Labor

2 Uiligual Versus Biligual Educatio Syste: A Political Ecooy Aalysis Javier Ortega GREMAQ, IDEI, Uiversity of Toulouse, CEPR ad IZA Bo Thoas P. Tagerås IUI, Stockhol Discussio Paper No Deceber 2004 IZA P.O. Box Bo Geray Phoe: Fax: Eail: iza@iza.org Ay opiios expressed here are those of the author(s) ad ot those of the istitute. Research disseiated by IZA ay iclude views o policy, but the istitute itself takes o istitutioal policy positios. The Istitute for the Study of Labor (IZA) i Bo is a local ad virtual iteratioal research ceter ad a place of couicatio betwee sciece, politics ad busiess. IZA is a idepedet oprofit copay supported by Deutsche Post World Net. The ceter is associated with the Uiversity of Bo ad offers a stiulatig research eviroet through its research etworks, research support, ad visitors ad doctoral progras. IZA egages i (i) origial ad iteratioally copetitive research i all fields of labor ecooics, (ii) developet of policy cocepts, ad (iii) disseiatio of research results ad cocepts to the iterested public. IZA Discussio Papers ofte represet preliiary work ad are circulated to ecourage discussio. Citatio of such a paper should accout for its provisioal character. A revised versio ay be available directly fro the author.

3 IZA Discussio Paper No Deceber 2004 ABSTRACT Uiligual Versus Biligual Educatio Syste: A Political Ecooy Aalysis We cosider a ecooy with two laguage groups, where oly agets who share a laguage ca produce together. Schoolig ehaces the productivity of studets ad ay odify their laguage edowet. Uder a uiligual syste, the laguage of the politically doiat group is the oly laguage of istructio, ad the ebers of the politically doiated group who atted school shift laguage. Istead, uder a biligual syste, the ebers of the doiated group who atted school becoe biligual. The doiat group chooses the educatio syste, ad the idividuals decide whether to atted school. While agets do ot get utility fro speakig their ow laguage, we show that a laguage coflict of the expected type edogeously arises i the choice betwee a uiligual ad a biligual syste. Deocracy (ajority rule) always leads to the ipleetatio of the socially optial educatio syste, while the uiligual syste is too ofte ipleeted uder iority rule. I the presece of productivity spillovers, there ay be uaiity for uiligualis, eve if this syste is assued to be techologically iferior. The odel is cosistet with evidece fro Filad i 1919 ad Frace i 1863, showig that the choice of biligualis i educatio ay ot be related to the size of laguage groups. JEL Classificatio: I2, J15 Keywords: educatio, laguage policies, skills, iorities Correspodig author: Javier Ortega GREMAQ Uiversité de Toulouse Maufacture des Tabacs, bât. F 21, allées de Briee Toulouse Frace Eail: javier.ortega@uiv-tlse1.fr We beefited fro discussios with Alai Alcouffe, Raquel Ferádez, Jea Fraysse, Barbara Petrogolo, Ae Ruiz-Gaze, Fraçois Salaié, Jea Tirole, Etiee Waser, ad fro coets by seiar participats i Valecia, Toulouse, T2M (Paris), Uiversidad Pública de Navarra, IUI, EALE (Paris), LSE, SED (Paris), Helsiki, Tiberge Istitute, UQAM, EEA (Madrid), ESSLE-CEPR, ad Popeu Fabra. Päivi Erkkilä, Marjatta Latvus, Doh-Shi Jeo, Mika Helader, Eric Mali, ad Keeth Sella helped us gather iforatio. We are also grateful to Christia Löblad for her editorial assistace. The secod author gratefully ackowledges fudig fro the Ja Wallader ad To Hedelius Research Foudatio.

4 1 Itroductio I 2000, half of the coutries i the world had at least oe laguage iority correspodig to ore tha 10% of their populatio. 1 This laguage diversity has recetly brought laguage policies to the forefrot of political debate i such coutries as Malaysia, Spai, Latvia, the ex-soviet Musli States, Belgiu or the U.S. As stressed by socioliguists, oe crucial copoet behid laguage shift i populatios over geeratios is the choice of the laguage(s) of istructio i school. For exaple, Fisha (1977) argues that for laguage spread, schools have log bee the ajor foral (orgaized) echaiss ivolved... (p.116). 2 I other ters, laguages which are ot give the status of ediu of istructio i school ted to be replaced by the laguages that are. The cases of Frace ad Filad provide two illustratios of the iportace of laguage policies for laguage developet. I the late 18th cetury, aroud 60% of those livig i Frace did actually ot speak Frech (Grégoire, 1794), but rather other laguages. 3 Nowadays, everybody speaks Frech, ad the other laguages are spoke by oly 5% of the populatio. 4 Istruetal i this developet was the ipleetatio of a uiligual educatio syste fro the 1880s which established Frech as the sole laguage of istructio i school. At the other ed of the spectru, the biligual Fiish-Swedish educatio syste ipleeted upo Filad s idepedece fro Russia i 1917, has bee oe of the factors explaiig the relative good shape of Swedish i coteporary Filad. The ative Swedish-speakig populatio has reaied alost costat i absolute ubers (314,000 ative Swedish-speakers i 1920 ad 293,000 i 2000) ad declied to soe extet i relative ters (fro 11 percet of thetotalpopulatioi1920to5.9perceti 2000). 5 Give the iportace of laguage of istructio choice, we set-up a odel for uderstadig why soe ultiligual coutries choose uiligual educatio while others aitai laguage diversity, ad for idetifyig the coditios uder which coßict aog laguage groups ay arise. I additio, we provide a orative characterisatio of the ability of differet political systes to ipleet the socially optial educatio syste. We begi by illustratig a historical puzzle that will be elaborated ad epirically supported i the Þrst sectio. Oe would ituitively guess that the likelihood of observig a uiligual syste is directly related to the size of the laguage ajority. As a Þrst step, a copariso of the Fiish ad the Frech cases does ot go i that directio. Ideed, while a uiligual syste was chose i 40% Frech-speakig Frace, a biligual syste was alost uaiously chose i 1 Data are fro the Ecyclopaedia Britaica (2003). Worldwide, 48.5% of the coutries are ultiligual accordig to a 10% iority deþitio. Proportios vary accross cotiets: 19.4% of the coutries for the Aericas, 43.2% for Europe, 44.9% for Asia, 50% for Oceaia, ad 77.6% for Africa. 2 See also for exaple Hagège (1996) for the case of Frace. 3 The largest regioal laguage was Occita, ad the cae Breto ad Alsacia. Other saller laguage groups were speakig Basque, Catala, Fleish, Fraco-proveçal, Corsica, ad Fracoia. 4 Ecyclopaedia Britaica (2003) 5 Data for 1920 are fro McRae (1997) ad for 2000 fro the Ecyclopaedia Britaica (2003). 2

5 90% Fiish-speakig Filad. Oe ay argue that this cotrast is due to atioal speciþties. However, usig regioal data for 1860s Frace, we show that the proportio of Frech-speakig schools is urelated to the proportio of local Frech-speakers. Our odel explais why ajority size ay ot be the ost relevat variable for uderstadig the choice of educatio syste. Our ecooy cosists of idividuals belogig to oe of two laguage groups, the politically doiat ad doiated, iitially uable to couicate. The doiat group decides Þrst o the characteristics of the educatioal syste ad the idividuals choose whether to atted school or ot. Schoolig ehaces the productivity of the studets ad ca be either uiligual or biligual. Uder a uiligual schoolig syste, the laguage of the politically doiat group is the uique laguage of istructio. As a result, the studets belogig to the doiated group shift laguage whe leavig school. 6 I cotrast, uder a biligual syste, the studets fro the doiated group becoe biligual. Value coes fro bilateral productio after schoolig aog agets who speak the sae laguage. Fially, i order to keep the odel siple, the idividual cost of takig educatio is assued to be the sae uder both laguage systes. 7 This iplies that we give a advatage to the biligual over the uiligual syste, as a studet fro the doiated group gets a richer laguage edowet uder biligualis tha uder uiligualis without bearig a additioal cost. The odel has thus two cetral assuptios. First, idividuals take a ecooic decisio o whether to atted school or ot. This assuptio is i lie with the growig literature showig that ecooic icetives have a ipact o school attedace i developig coutries (see for exaple Bourguigo, Ferreira, ad Leite, 2003). Secod, schoolig is a budle, as it siultaeously ehaces the productivity (or earigs) of the studet ad ca odify its laguage edowet. This is because we are iterested here i the choice of the laguage of istructio, ad ot i laguage traiig i geeral. 8 The positive effect of educatio o earigs is a well established fact i the literature (see Card, 1999) while the choice of the laguage of istructio i schoolig is a iportat factor behid laguage shift accordig to socioliguists (e.g. Fisha, 1977 or Hagège, 1996). Idividual educatio decisios are characterised by couicatio exteralities whose ature varies across educatioal systes. Uder the uiligual syste, a eber of the doiated group who chooses to take educatio loses her iitial laguage, ad therefore reduces the set of productio parters of the other ebers of the doiated group, uless they choose theselves to atted school ad lear the doiat laguage. For this reaso, a positive couicatio exterality liks the educatio decisios across doiated group ebers, ad high educatioal 6 Laguage shift due to schoolig eeds i geeral ore tha oe geeratio to be accoplished, but here we assue it takes places istataeously i order to keep the odel static. 7 Idividuals attach o utility to speakig their othertogue. Addig such a utility ter would coplicate the aalysis, but ot qualitatively affect ay of the results. We retur to this issue at various poits i the paper. 8 Fro a theoretical viewpoit, we are thus assuig away the possibility that agets go to schools that exclusively provide laguage traiig. 3

6 levels reiforce the idividual icetives for takig educatio (a badwago effect). Uder the biligual syste, i cotrast, this effect vaishes, as doiated group ebers who atted school do ot lose their iitial laguage. We show that the doiat group prefers the educatio syste that axiises the equilibriu educatio level of the other group, as higher educatio of the other group traslates ito a larger uber of productio parters, sice ore idividuals lear the laguage of the doiat group. I tur, the doiated group ever prefers the uiligual syste, as the badwago effect arisig uder uiligual educatio locks the i equilibria with udereducatio (overeducatio) whe schoolig is cheap (expesive). All political tesio arisig i equilibriu is of the expected type, i.e., situatios i which the doiat group goes for uiligualis while the doiated group prefers a syste i which their ative laguage is also a laguage of istructio. This is a iterestig result sice it does ot rely o ay direct utility ejoyed by the agets fro speakig their ow ative laguage. The doiated group wats its laguage to be used i schools ot because their ebers like it but rather because abadoig it would force the to overisvest i educatio, due to the badwago effect. The doiat group goes for uiligualis i order to free-ride o the educatioal ivestet of the other group. There ay be uaiity for the biligual syste as well. This happes for exaple whe educatio is very cheap. I this case everybody prefers all to take educatio. We deterie the socially optial educatio syste. Whe a beevolet plaer ca choose the educatio level of each idividual, biligualis is always the optial syste, as for give educatio levels ore people couicate ad hece produce uder the biligual tha uder the uiligual syste. If the cetral plaer ca choose the educatio syste but school attedace reais i the hads of the idividuals, biligualis is ot ecessarily optial ayore, as the badwago effect ay iduce larger educatio levels uder the uiligual syste. Next, we address the issue of failure i political decisio-akig, i.e., we aalyse the circustaces, if ay, uder which the political decisio process leads to the adoptio of the wrog type of educatio syste. We show that a deocratic rule (the ajority decides the educatio syste) always leads to the adoptio of the socially optial decetralised syste i our odel. I cotrast, uder iority rule, the uiligual syste is ipleeted too ofte. Fially, we exted the odel to cosider productivity spillovers aog productio parters, i.e. situatios i which the productivity of each aget positively depeds o the skill level of the other productio parter. Uder spillovers, uaiity for a uiligual educatio syste becoes a equilibriu outcoe whe educatio is ot expesive: i that case, the ebers of the doiated group are willig to give up their ow laguage i order to beeþt froa high educatio equilibriu. This is a iterestig result, as we have attributed a advatage to biligualis over uiligualis. Why does the existece of spillovers ake the doiated willig to support a uiligual syste? The reaso is that spillovers stregthe the badwago effect i 4

7 the uiligual syste, ad do ot alter icetives i the biligual syste. More precisely, i the uiligual syste, the et gai fro schoolig for a doiated group eber becoes icreasig i the uber of educated peers through a additioal chael: by attedig school i a situatio i which ay peers do so, a doiated group eber ot oly gais ay productio parters, but also ehaces her productivity i the atches with these parters. Our odel is related to the growig literature o laguage adoptio, ad i particular to Lazear (1999), Church ad Kig (1993), ad Joh ad Yi (2001). 9 Like i these three papers, agets i our odel choose whether they ake a costly ivestet i learig a laguage that ca be used i trade or productio with other agets. However, i costrast with these papers, we cosider here a ivestet decisio that ties skill acquisitio ad laguage acquisitio, as laguages which are used as edia of istructio are leart while learig other subjects at schools (e.g. while learig atheatics, history...). While i Lazear (1999) agets behave copetitively, i our odel, just as i Church ad Kig (1993) ad Joh ad Yi (2001), the ivestet decisio is strategic ad the equilibriu outcoe depeds o a etwork exterality, i.e. a situatio i which the decisio of a aget to lear a laguage icreases the uber of parters (ad thus the utility) of the idividuals speakig that laguage. 10 Our paper differs fro the two latter cotributios because the type of etwork exteralities uder cosideratio is edogeeised here, as it depeds o the choice betwee a uiligual ad a biligual educatio syste. Aother differece is that our explaatio of laguage shift is based o the choice of schoolig istitutios, while Joh ad Yi (2001) provides a explaatio based o geography (ore precisely, o the existece of igratios at equilibriu) ad o a laguage trasissio rule across geeratios. 11 Fially, the derivatio of laguage coßict or cosesus as a equilibriu outcoe are also ovel. 2 Motivatio ad historical evidece This sectio studies available evidece o the lik betwee the size of laguage iorities ad the choice of a uiligual educatio syste. Oe would ituitively guess that a larger iority reduces the likelihood to observe a uiligual syste. Istead, here we provide evidece that this 9 There are other papers studyig laguage. Breto ad Mieszkowski (1977) studies i a trade odel secod laguage acquisitio as a hua capital ivestet. Lag (1986) proposes a laguage theory of discriiatio. Pool (1991) ad Laiti (1994) aalyse the choice of a official laguage i ultiligual coutries. Mélitz (2002) shows that havig a coo laguage prootes iteratioal trade. Sait-Paul (2001) studies echaiss through which liguistic stratiþcatio ca arise as a equilibriu outcoe. I additio, there is a large literature o laguage proþciecy ad earigs (see e.g. Chiswick ad Miller, 1995) ad a ew literature o the possible liguistic orgaisatio of the Europea Uio (see Gisburgh ad Weber, 2004 ad va Parijs, 2004). 10 The ecooics of etworks has bee extesively studied i the idustrial orgaisatio literature, see Farrell ad Kleperer (2004) for a recet survey. Research alog this lie has geerally focused o the proble of adaptio ad coordiatio fro the perspective of proþt axiisig Þrs. We take a here a political ecooy perspective o etwork adaptio. 11 More precisely, Joh ad Yi (2001) assues that biligual parets have uiligual childre i a certai laguage if the laguage distributio i the locatio is skewed towards that laguage. 5

8 Table 1: Votig o laguage i Filad ( ) Political Party Seats Electoral basis Choices Social Deocrats 80 FI-SWE BI Agrarias 42 FI UNI-BI Natioal Coalitio (coservatives) 28 FI BI Natioal Progressive Party (liberals) 26 FI ostly BI Swedish People Party 22 SWE BI Sources: Jackso (1938) ad McRae (1997) ay ot be the case. We Þrst copare the set-up of the curret Fiish ad Frech educatio systes (see Ortega ad Tagerås, 2003, for ore details). Next, we provide evidece across Frech départeets (sall adiistrative regios). 2.1 Filad versus Frace The curret istitutioal laguage fraework i Filad was set up with the Costitutio of 1919 ad a series of laguage laws, the ost iportat beig approved i I 1920, the Swedish-speakers costituted oly 11% of the Fiish populatio (McRae, 1997) ad the rest of the populatio was Fiish-speakig. 12 Nevertheless, a biligual educatio syste was approved with very large ajorities. 13 Table 1 presets the copositio of the Fiish Parliaet i 1919 ad shows that the support cae fro both laguage groups. The Costitutio recogises Fiish ad Swedish as atioal laguages o a equal basis. Cocerig the educatioal syste, each uicipality has to orgaise schoolig i the iority laguage (Swedish or Fiish) whe a iiu uber of parets requires it. The foudatios of the Frech laguage policy were decided durig the Frech Revolutio ( ). I 1794, the prelate Grégoire preseted before the Covetio (Parliaet) his report o the laguage situatio i Frace (Grégoire, 1794). Grégoire argued that there were oly 15 departeets (out of 83) i which Frech was the oly laguage spoke. Additioally, it ca be stated without exageratio that six illio Frech, especially i the coutryside, do ot kow the atioal laguage; that a equal uber is ore or less uable to aitai a sustaied coversatio; ad that Þally the uber of those who speak it does ot exceed three illio (Grégoire, 1794). Give that the total Frech populatio at that tie was aroud 26 illio, this would ea that roughly oly 2/5 of the populatio was ative Frech-speaker (Calvet, 2002). Aog the other laguage groups, the biggest was Occita (souther-half of the coutry), ad ext 12 Except for a tiy Sai group. 13 The laguage clauses of the Costitutio were approved with a very wide cosesus (173 yes to 23 o, 165 yes to 22 o, 183 yes to 10 o ad 183 yes to 7 o, see Eduskuta-Riksdag, 1920, pp ). 6

9 cae Breto ad Alsacia. Additioally, sall iorities were speakig Fraco-proveçal, Basque, Catala, Corsica or Fleish. Each departeet (with the exceptio of the Basses-Pyréées) had at ost two laguage groups. As stressed by Hagège (1996), laguage policy quickly becae a iportat issue i the political choices of the Revolutio. After a iitial period i which the traslatio of the decrees ito other laguages was decided, 14 the ewly bor Republic cotrolled by the otagards (radical revolutioaries) chose Frech-uiligualis i a period of exteral war ad provicial isurrectio. I Jue 1794, Grégoire preseted a report which argues that: Everythig we said leads us to the coclusio that, i order to extirpate the prejudices, develop all the truths, the talets, the vertues, erge all the citizes i the atioal ass, siplify the political echaiss, we eed idetity of laguage (Grégoire, 1794, p. 341). A series of Frech-uiligual laguage decrees were approved, but did ot survive the fall of the otagards i July As argued by Weber (1976), The [laguage] policy foudered. (...) What survived fro the shipwreck was the priciple (p. 72). Coparig Filad ad Frace opes a puzzle: biligualis arose alost uaiously i a coutry where the ajority represeted 90% of the populatio while uiligualis was the outcoe i a coutry where the biggest laguage group represeted 40% of the populatio. Oe ay argue that this puzzle ca be explaied by referig to the particular characteristics of these two coutries. For exaple, Frech-speakers ad Swedish-speakers were over-represeted i the élites i Frace ad Filad respectively, so the political power of the laguage iority i Filad ay have bee larger tha that of the o-frech speakers i Frace. Alteratively, oe could argue that the ai differece was the existece of ore tha two laguage groups i Frace, ad just two i Filad. However, we show ow that the sae type of puzzle reais whe we look at what happeed iside Frace. 2.2 Lookig iside Frace I 1863, the Miister of Public Istructio uder Napoleo III, Victor Duruy, orgaised a iquiry ito the laguages spoke by the populatio of the by the 89 departets, together with the laguage(s) of istructio i public schools. The data (see Weber, 1976) show that there was iportat cross-regioal variatio i educatioal systes at that tie, before the itroductio of the Ferry Laws i , which istituted free priary educatio ad legally established Frech as the oly laguage of istructio i schools (Chervel, 1992). The data cotai iforatio o the liguistic copositio of the populatio i each departet ( Frech-speakers versus o-frech speakers 15 ), together with the uber of public schools usig Frech oly, usig idio or patois 16 oly or usig both. 14 see Alcouffe ad Bruert (1985). 15 Note that the data are quite aggregated, sice we get iforatio o the uber of ihabitats i Frechspeakig coues ad No-Frech-speakig coues. 16 The ter patois refers to all the laguages ad dialects i Frace, except Frech. 7

10 Figure 1 plots the proportio of public schools usig Frech oly versus the proportio of Frech-speakers i the populatio for the 34 departets that were ot fully Frech-speakig i I additio, each of the 55 fully Frech-speakig departets had a fully Frech-uiligual syste. The scatter plot does ot show ay patter of correlatio betwee the two variables. We ext regress the proportio of Frech-uiligual schools o a uber of departet-level variables for the 89 departets. The results are reported i Table 2. Colu 1 shows that there is a positive relatioship betwee the proportio of Frech-speakers i the populatio ad the proportio of Frech-uiligual schools. I additio, the proportio of Frech-uiligual schools is positively related to the uber of teachers i public schools per 10,000 ihabitats. This result relates to the aalysis by Grew ad Harriga (1991), which shows that goveret ivestet i teachers for public schools started well before the Ferry Laws (1880s). Followig the priciples set up durig the Revolutio, these ew teachers were traied to teach i Frech. The Þrst regressio also cosiders the average direct cost of educatio for parets i each departet. Iterestigly, a higher cost of educatio is positively related to the proportio of Frech-uiligual schools. This ay idicate that parets were willig to ivest ore i educatio if schools were i Frech (ost likely followig a social obility arguet, as Frech was ecessary i skilled occupatios). 1aveyro gers ariège aude corrèze h-garoe basses-pyréées drôe charete eurthe vosges 0.9 ardèche ord Proportio of Frech-uiligual schools fiistère orbiha c-du-ord oselle bas-rhi haut-rhi corsica Proportio of Frech-speakers i the populatio Fig. 1: Educatio systes i Frech departets, This Þrst regressio however does ot take ito accout that i the 55 fully Frech-speakig departets the possibility of havig o-frech speakig schools was ot eve cosidered. For this reaso, we itroduce a duy variable for uiligual Frech-speakig departets i the 8

11 Table 2: The proportio of Frech-uiligual public schools at the departet level i Frace (1863) Depedet variable: Proportio of Frech-uiligual public schools Frech-speakers i the populatio.108 ** (.046) (.080) Teachers i public schools (/10,000 ihab.).004 ** (.002) Aout paid for educatio by a faily.025 ***.004 ** (.002).024 *** (.008) (.008) Log icoe per head.044 (.054).003 (.053) Uiligual Frech-speakig departet (duy).102 * (.054).094 (.072).003 (.002).012 ** (.007).256 *** (.057) Roace laguage other tha Frech (duy).303 *** (.044).006 (.066).003 (.002).013 * (.007).035 (.044).251 *** (.051).251 *** (.041) Notes: The Þgures reported are the coefficiets obtaied fro OLS estiatio. Stadard errors i paretheses. *, ** ad *** deote sigiþcace at 10%, at 5%, ad 1% levels, respectively. Data o laguage are fro the Archives Natioales ad ca be foud i Weber (1976). Data o average icoe levels are fro Vapereau (1867). The reaiig data are fro Miistère de l Istructio Publique (1878). All data refer to regressios of Colus 2 to 4. Colu 2 shows that the relatioship betwee the proportio of Frech-speakers i the populatio ad the proportio of Frech-uiligual schools becoes o sigiþcat whe the duy for uiligual Frech-speakig departets is itroduced. The regressio i Colus 3 ad 4 further icludes a idicator for whether the secod laguage spoke i ultiligual departets is a Roace laguage. These two regressios show that the proportio of Frech-uiligual schools was higher i departets where Frech was coexistig with aother Roace laguage. This ca be easily uderstood by ispectio of Figure 1 if we otice that departets like Ariège, Aude, Corrèze, Haute-Garoe, Ardèche, etc i which Occita (a Roace laguage) was spoke i additio to Frech had a tedecy to adopt a fully Frech uiligual syste. Agai, i both regressios, the coefficiet o the proportio of Frech-speakers reais statistically o-sigiþcat. It appears thus fro this aalysis that o clear-cut relatio ca be established i the case of Frace at the departet level betwee the size of the laguage groups ad the laguage(s) of istructio chose. The odel that follows explais why iority size ay ot be the ost relevat variable for uderstadig the choice of educatio syste. 3 The odel Cosider a coutry ihabited by a cotiuu of idividuals, oralised to uity. There are two laguage groups i the coutry, ad, of sizes M (0, 1) ad N =1 M, respectively. 9

12 Iitially, the s speak ish ad the s speak ish. s ad s are uable to couicate uless they lear to speak a coo laguage. Value is created through bilateral productio betwee idividuals. 17 Each idividual has the opportuity of producig oce with every other idividual. 18 Bilateral productio occurs if ad oly if the two parters are able to couicate, i.e. if they speak a coo laguage. If they caot couicate, the value of productio is equal to zero. Idividuals choose whether to atted school or ot. A idividual who takes educatio becoes skilled ad produces 1+σ (σ > 0) whe eetig ay other aget with who she is able to couicate. A idividual who does ot take educatio produces istead 1 with ay parter speakig the sae laguage. 19 Schoolig also ivolves laguage traiig, the type depedig o the educatioal syste. This paper copares a uiligual to a biligual educatio syste. Uder the uiligual syste, ish 20 is the uique laguage of istructio. For this reaso, the -group is also referred to througout the paper as the doiat group ad the -group as the doiated group. The s who atted school keep their iitial laguage, while the slearish ad lose their iitial laguage. Ideed, as show by liguists (see e.g. Fisha, 1977, for Eglish, ad Hagège, 1996, for the case of Frace) oe crucial factor behid laguage shift i populatios over geeratios is the choice of the laguage(s) of istructio i school. I other ters, laguages ot give the status of ediu of istructio i priary school ted to be replaced by the laguage used i school. Here for siplicity we assue that this laguage shift takes place i the life spa of oe geeratio. 21 Uder the biligual syste, all the ebers of the doiated group who take educatio go to schools which have both ish ad ish as laguages of istructio. For this reaso, they ed up speakig both laguages after leavig school. The doiat group ebers go to schools i which ish is the uique laguage of istructio, as i the uiligual syste. The biligual syste is thus here a syste which protects the laguage of the doiated group, typically the iority laguage i deocracy As e.g. i Diaod (1982) or Lazear (1999). 18 Equivaletly, agets cosider their expected payoffs whe takig decisios. We are assuig away the possibility that agets belogig to a certai laguage group are cocetrated i a particular locatio. For a aalysis icludig this geographical diesio, see Joh ad Yi (2001). 19 I this odel, the value of productio for a idividual is idepedet of the skill level of the productio parter. I sectio 7, we cosider the case with productivity spillovers. 20 The assiget of the doiat role to the group is arbitrary ad without loss of geerality. So far we have ot speciþed the relative sizes of the two groups. Nor have we described the political process by which the educatioal syste is chose. We do ot explai here the reasos for which oe group becoes the politically doiat group. This is as i Lag (1986), where oe group is exogeously assiged the role of the ecooically doiat group because its capital-labour ratio is assued to be larger tha that of the other group. 21 For a dyaic set-up i which the laguage spoke by the childre (exogeously) depeds o the laguage spoke by the parets ad the laguage spoke i the geographical locatio, see Joh ad Yi (2001). 22 I the case of Filad, for exaple, there is oly oe laguage of istructio (Fiish or Swedish), ad the the other laguage is also taught. Oe ay thik that a syetric biligual syste is a better represetatio of 10

13 The persoal cost c of takig educatio is assued costat across the populatio ad idepedet of the educatioal syste. This eas that we give a advatage to the biligual syste over the uiligual syste, as a goig to school i the biligual syste gets (ceteris paribus) access to ore productio parters tha i the uiligual syste after payig exactly the sae cost. 23 Deotig by µ (µ ) the fractio of s (s) that take educatio, we ow deþe the payoffs associated to takig ad ot takig educatio i each of the systes. 3.1 Payoffs i uiligual educatio The expected utility of takig educatio uder a uiligual syste, give expected educatio shares is: 24 U ui (µ )= c +(1+σ)(M + Nµ ). (1) A idividual who atteds school pays cost c, becoes skilled, ad speaks ish whe leavig school. She gets 1+σ fro productio with each of the M ebers of the doiat group ad each of the Nµ ebers of the doiated who have shifted laguage because they have atteded school. This eas that each skilled idividual beeþts fro ore s takig educatio, due to a expasio of her set of productio parters. This positive couicatio exterality (etwork exterality) turs out to be key i educatioal choice. A uskilled has the sae productio parters as the skilled, as she speaks ish. This aget saves o the cost of educatio, but gets oly a value of 1 whe producig: U ui (µ )=M + Nµ. (2) Uskilled s iprove their situatio whe ore s take educatio due to the sae positive couicatio exterality playig for the skilled. However, here the size of the exterality is saller sice each additioal productio parter fro the group icreases the pay-off of a uskilled aget by 1. Fially, the expected utility of ot attedig school for a eber of the doiated group is U ui (µ )=N(1 µ ) (3) the Fiish syste. However, the kowledge of Swedish aog the Fiish-speakig ajority is relatively low. I a previous versio of this paper (Ortega ad Tagerås, 2003) we cosidered the case of a syetric biligual syste, i.e. a syste i which both laguage groups were taught i both laguages. We discuss throughout the paper the results uder a syetric biligual syste wheever they are differet to the results we get here. 23 We could have assued istead differet costs for each syste. We have ot chose that optio for two reasos. The ai reaso is that the results are rich eough with idetical costs across systes. I additio, i a coutry which iitially has two laguage groups, it is ot clear that settig-up a uiligual syste is cheaper tha ipleetig a biligual syste. For exaple, iportat ivestets ay be eeded i order to isure that there is a sufficiet uber of teachers speakig the uique laguage of istructio. 24 There is o eed to ake a distictio betwee s ads who take educatio sice they speak the sae laguage ad have idetical skill levels subsequet to becoig educated. 11

14 uder the uiligual syste. Ideed, a who does ot go to school speaks ish, ad thus ca oly produce with the N(1 µ ) ebers of the doiated group who have ot atteded school. Clearly, every uskilled loses fro ay of her peers takig educatio through a cotractio of her set of productio parters. Hece, educatio iposes a egative couicatio exterality o those of the s who reai uskilled. 3.2 Payoffs i biligual educatio Cocerig the biligual syste, ote Þrst that the expected utilities of the doiat group ebers are the sae as uder the uiligual syste. This is because the s ever lear ish ad thus ay positive productio with ebers of the doiated group takes place i ish, as i the uiligual syste. 25 For this reaso, U bi (µ )=U ui (µ ) (4) U bi (µ )=U ui (µ ). (5) I cotrast, biligual educatio alters the payoffs of the s. Ideed, as the biligual syste guaratees that the s keepish eve if they go to school, either the value of attedig school or the value of ot attedig school for a deped o the educatio choices of her peers. More precisely, a skilled pays c for educatio, produces with everybody, ad gets 1+σ i each case, i.e., U bi = c +1+σ, (6) while a who chooses to reai uskilled ca still produce with all the s, as the s whohave becoe skilled keep ish due to biligual schoolig: 3.3 Equilibriu U bi = N. (7) The tiig of the gae is as follows. First, aticipatig the future levels of educatio, the educatioal syste is chose so as to axiise the expected utility of the doiat group. Secod, all the idividuals idepedetly ad siultaeously choose whether to take educatio. We cosider without loss of geerality syetric Nash Equilibria i which all ebers of each group radoise betwee educatio ad stayig uskilled with the sae probability. 25 I the biligual syste, the doiated group ebers who atted school are biligual, but this does ot affect the payoff of ay of the s, sice the s ever speak ish. 12

15 4 Equilibriu educatio levels 4.1 The uiligual educatio syste We Þrst derive the equilibriu educatio levels uder the uiligual syste. By subtractig (3) fro (1), we obtai the et beeþt of the represetative of takig educatio: 4U ui (µ )= c +(M + Nµ )σ + M + Nµ N(1 µ ). (8) Whe attedig school, this idividual pays cost c, becoes skilled, ad shifts laguage fro ish to ish. I equatio (8), the productivity gai fro educatio is give by (M + Nµ )σ i.e. the argial value of educatio σ ties productio parters after schoolig, aely the s ad the other skilled s. I additio, educatio alters the set of idividuals with who producig is possible. This couicatio effect is captured by the reaiig ters i (8). First, speakig ish after school eables productio with the M ative ish speakers ad with the Nµ ew ish speakers. At the sae tie, the skilled forgets ish ad thus ca o loger produce with the N(1 µ ) uskilled s. Equatio (8) geerates a isight crucial to the uderstadig of the prefereces over educatio systes. For the s, attedig a uiligual school iplies both becoig skilled ad shiftig laguage. Clearly, both features of uiligual schoolig are ore attractive the saller the uber of ish speakers ad i particular the larger the uber of other s goig to the uiligual school. This positive couicatio exteratility is thus at the origi of a badwago or sowball effect i the decisio of takig educatio of the s. Ideed, upo ispectio of (8), it is easy to check that the et beeþt fro schoolig for a is icreasig i the uber of s takig educatio (µ ). This badwago effect gives rise to ultiple equilibria if sufficietly strog. I additio to the possibility of two extree equilibria i which either all or oe of the s takeeducatio,a ixed equilibriu ay exist. 26 Letusturowtothechoiceofarepresetative. Her et beeþt of attedig school is obtaied by subtractig (2) fro (1): 4U (µ )= c +(M + Nµ )σ. (9) Here, oly the productivity gai shows up, sice schoolig does ot alter the laguage edowet of the ad thus her set of productio parters is uchaged by educatio. At the sae tie, ote that the represetative s icetive for takig educatio positively depeds o the educatioal level of the s, as the skilled sspeakish. Figure 2 characterises the set of equilibriu educatio levels (cosult appedix 9.1 for full aalytical details). Let us Þrst cosider the area above the M(c σ) lie i.e. the orth-west part of the Þgure This ustable equilibriu is soeties referred to as a tippig equilibriu, a ter coied by Schellig (1978). 27 M(c σ) is upward slopig for the followig reaso: as the cost of educatio icreases, gettig educated becoes less attractive, ad thus reaiig a ish speaker ay be a good optio eve if the size of the group shriks. 13

16 I this area, the size M of the doiat group is so large ad cosequetly the productivity gai ad couicatio effect so strog relative to the cost of educatio, that each idividual prefers to go to school idepedetly of the choice of the other ebers of the group. I this case, the badwago effect does ot play.a role i educatioal choices. Cocerig the s, they get educated if schoolig is sufficietly cheap (for c<σ, i which case (1, 1) is the uique equilibriu) ad abstai fro takig educatio otherwise (i which case (1, 0) is the uique equilibriu). M 1 ( 1,0) M ( c σ ) (0,1) ( y,1) (1,1) ( 1,1) (0,0) ( y,1) (1,1) (0,0) ( y,0) (1,1) { 0,0), ( y,0), (1,0 )} ( ( 0,0) σ σ / c σ Fig. 2: Equilibriu educatio levels uder the uiligual syste Movig to the south east crossig the M(c σ) lie, the badwago effect starts playig a role. Ideed, as the group gets larger ad educatio becoes ore expesive, reaiig a ish-speaker ad avoidig to pay the cost of educatio becoes a good choice, but oly of course if other ebers of the doiated group choose the sae strategy ad do ot atted school. For this reaso, we get that (i stable coþguratios) either all the s take educatio or oe of the does so. Cocerig the s, they choose to atted school whe educatio is cheap ad the s are i large ubers (i which case the stable equilibria are (0, 1) ad (1, 1)) while they becoe ore ad ore reluctat to take educatio as its cost becoes higher (i this other extree, the stable equilibria are (0, 0) ad (1, 0)). Wheever educatio becoes sufficietly expesive (c >1+σ), the productivity gai ad couicatio effect are isufficiet to cover the cost of educatio eve i case the rest of the populatio would decide to take educatio. The badwago effect vaishes ad obody takes educatio idepedetly of the choices of the other agets. While the aalysis gives rise to a series of differet equilibriu coþguratios, the existece of a positive couicatio exterality across groups is the basis for the followig geeral result: Propositio 1 Uder the uiligual educatio syste, equilibriu educatio levels are positively 14

17 correlated across laguage groups i the followig sese: i the cases with ultiple equilibria high (low) educatio levels aog the s are coupled with high (low) educatio levels aog the s. Proof. Let z ui =(z ui,z ui eed to establish that z ui do. y ui z ui >y ui >z ui cotradicts y ui 0 4U ui. Hece, z ui >z ui. ) ad y ui =(y ui,y ui ) be two distict equilibria of the gae. We ad z ui <y ui caot siultaeously hold. Suppose they (y ui ) 0. 4U ui / µ > 0 4U ui (z ui ) > 4U ui (y ui ) for ad y ui >z ui 4U ui (z ui ) > 0 ad thus z ui =1,which >y ui >y ui 4.2 The biligual educatio syste We ow tur to equilibriu aalysis uder the biligual syste. Subtract (7) fro (6) to get the et beeþt of takig educatio for a : 4U bi = c + M + σ. (10) A who takes educatio pays cost c, reaches M additioal parters as she lears ish, ad gets a additioal aout σ through productio, as she is ow skilled ad she produces with everybody. As we ca see, the s decisio to take educatio is o-strategic uder the biligual syste. The trade-off facig the s uder the biligual syste is idetical to the oe facig the uder the uiligual syste as we assue that the s are ever taught i ish: 4U (µ )= c +(M + Nµ )σ. (11) M 1 ( 1,0) ( 1,1) ( 0,0) 0 1 c σ Fig. 3: Equilibriu educatio levels uder the biligual syste The equilibriu levels of educatio are represeted graphically i Figure 3. Whe educatio is cheap (c <σ), the productivity effect aloe is sufficiet to reder educatio proþtable for the 15

18 ebers of the doiated group. Aticipatig the high educatioal levels of the other group, the s Þd the couicatio exterality sufficietly strog to reder educatio proþtable also for the. Hece (1, 1) is the uique equilibriu i that case. Whe educatio is expesive, (c >σ), the productivity gai is too weak relative to the cost of takig educatio to geerate sufficiet icetives for the ebers of the doiat group to take educatio. The ebers of the doiated group take educatio if ad oly if the couicatio effect is sufficietly strog, i.e. if ad oly if the doiat group is sufficietly large relative to the cost of educatio (M >c σ) Welfare This sectio cosiders the welfare properties of the two respective educatio systes. expected welfare uder educatio syste s {ui, bi} by DeÞe W s (µ) =N[µ U s (µ )+(1 µ )U s (µ )] + M[µ U s (µ )+(1 µ )U s (µ )]. As a Þrst step, we ca copare the welfare levels uder each syste for give educatio levels: Lea 2 Expected welfare is higher uder the biligual syste for give educatio levels. Proof. Let µ =(µ,µ ) be a exogeously Þxed educatio level. We just eed to show that utility is higher for each of the groups. Subtractig (1) fro (6), the et beeþt of a skilled of havig a biligual educatio syste is U bi U ui (µ )=N(1 + σ)(1 µ ) 0. Subtractig (3) fro (7), the correspodig value for a uskilled is U bi (µ ) U ui (µ )=N(1 + σ)µ 0. Fially, for the s, U(µ bi ) U ui (µ )=U bi (µ ) U ui (µ )=0. The ituitio for this lea is siple: the biligual syste eables all the s toaitai couicatio ad thus productio relatios with each other, irrespective of their level of educatio. This is ipossible uder the uiligual syste sice the educated s uder this syste lose the ability to speak ish. Of course, educatio levels are ot exogeously give, hece we caot o the backgroud of the above coparisos coclude that the biligual is superior to the uiligual syste fro a welfare poit of view. We eed to adjust for educatio levels. 28 I a syetric biligual syste, the s get educated i soe cases eve for c σ > 0, as they ca lear ish i school ad there is thus also for the a couicatio effect associated to takig educatio. More precisely, we get i that case that (0, 1) is the uique equilibriu whe c σ >M ad M<1 (c σ) siultaeously hold. Multiple equilibria {(1, 0), (y bi,y), bi (0, 1)} arise wheever M (c σ, 1 (c σ)). I the rest of the paraeter space, the equilibria are as i Fig. 3. We attribute the existece of ultiple equilibria i the syetric biligual syste to a duplicatio effect: the ore people of the other group who lear oe s laguage, the weaker is the ow icetive for learig the other laguage. 16

19 5.1 Cetralisatio Suppose there exists a beevolet social plaer who is able to eforce the level of educatio that axiises welfare uder each syste. The, the followig propositio ca be stated: Propositio 3 Uder cetralisatio, the biligual syste yields higher expected welfare tha the uiligual syste. The socially optial educatio levels uder the biligual syste are (1, 1) c<σ, (1, 0) (c, M) (σ, 2+σ) ((c σ)/2, 1) ad (0, 0) (c, M) (σ, ) (0, i{(c σ)/2; 1}). Proof. Write x s =(x s,x s ) welfare axiisig educatio levels uder s {bi, ui}. Fro Lea 2, W bi (x ui ) W ui (x ui ). Byoptialityofx bi uder the biligual syste, we have W bi (x bi ) W bi (x ui ). Addig the two iequalities produces W bi (x bi ) W ui (x ui ).Socially optial educatio levels: by differetiatig (6)-(5) with respect to µ ad µ ad pluggig i (6)-(5), it is easily veriþed that (subscripts deote partial derivatives): W bi W bi µ (µ) =M(σ c N(1 µ )σ) µ (µ) =N(σ c + M(2 + σµ )). W bi µ (µ) > 0 for all c < σ iplies x = 1 for all c < σ. W bi µ (1,µ ) = M(σ c) iplies x = 1 for all c < σ, as well. W bi µ (µ) < 0 for all c > σ iplies x = 0 for all c > σ. W bi µ (µ, 0) = N(σ c +2M), hece x =1for all (c, M) (σ, 2+σ) ((c σ)/2, 1) ad x =0 for all (c, M) (σ, ) (0, i{(c σ)/2; 1}. The cetral plaer would always choose a biligual syste if able to fully cotrol educatioal levels of the populatio. It is ot hard to uderstad why. For give educatio levels, ore people couicate, hece produce, uder a biligual tha a uiligual syste. As welfare is icreasig ceteris paribus i productio, it iediately follows that the biligual is better tha the uiligual syste. Usurprisigly, optial educatio levels are decreasig i the cost of takig educatio. Wheever educatio costs are relatively high ad it is ot optial that all the idividuals get educated, the cetral plaer chooses to educate the s, as the educatio of the s everhas a ipact o couicatio. Everythig else held equal, optial educatio levels are higher the larger M, as the positive ipact o couicatio associated to the s learigish is i that case larger. 5.2 Decetralised educatioal choice I reality, of course, o cetral plaer ca perfectly cotrol the aout of effort studets put ito their studies, eve i a syste with adatory educatio. 29 To capture this degree of freedo, cosider therefore a situatio i which the cetral plaer chooses the educatio syste takig ito accout the free choices of idividuals cocerig school attedace. Let γ bi ad γ ui be two 29 There is for exaple a growig epirical literature o the effectiveess of Þacial icetives for school attedace i developig ecooies (see e.g. Bourguigo, Ferreira, ad Leite (2003) ad the refereces therei). 17

20 equilibriu levels of educatio uder each respective educatio syste. While it is still the case that W bi (γ ui ) W ui (γ ui ),itisuclearwhetherw bi (γ bi ) W ui (γ ui ). I other ters, the cetral plaer ay prefer the uiligual syste if it leads to a sufficietly higher decetralised educatio level. As previously show, ultiple equilibria soeties arise uder the uiligual syste. I odels with ultiple equilibria, predictios geerally deped o the equilibria that are uder cosideratio. We thus focus o results that hold for coparisos of all equilibria. Soe of our results deped o the exclusio of a iterior ustable equilibriu, but ost do ot. I the subsequet aalysis, we discuss the atter of equilibriu selectio wheever relevat. M M ( c σ ) INDIFFERENCE BILINGUAL (I) UNILINGUAL 0.5 INDIFFERENCE (IIa) BILINGUAL (IIb) σ 0 1 c σ Fig. 4: Optial decetralised educatio syste Figure 4 characterises the optial decetralised educatio syste (appedix 9.3 cotais the foral derivatios). 30 Reeber that the badwago effect is at play oly i the uiligual syste, sice uder biligual educatio all the s keepish. The badwago effect works either to the favour or to the disfavour of society, ad does so i a o-liear fashio. I the polar case whe the doiat group is very large relative to the cost of takig educatio (regio I) the badwago effect is bad for society as it ay lock the ebers of the doiated group i a loweducatio equilibriu. I the other polar case, whe the size of the doiat group is very sall relative to the cost of educatio (regio IIb), the badwago effect is still egative as it ay lock agets i a costly high educatio equilibriu. I the iterediate case (Regio IIa), the biligual syste fails to produce sufficiet icetives for takig educatio, while the badwago effect ca push educatio levels uder the uiligual syste to a level which would be ipossible to reach uder a biligual syste. Thus, despite the fact that the uiligual syste is techologically 30 The Þgure is draw assuig σ > 1. This is irrelevat to the results we have obtaied. 18

21 iferior to the biligual syste, the uiligual syste is evertheless optial i this case sice it provides stroger icetives for takig educatio tha the biligual syste. 31 I the reaiig cases, the badwago effect does ot play ay role at equilibriu i the uiligual syste, as either educatio is very cheap relative to the size of the doiat group, or very expesive. As a result, the two systes lead to idetical educatio ad welfare levels. 6 The choice of educatio syste This sectio aalyses how the s ad the s rak the uiligual educatio syste with respect to the biligual syste, takig ito accout the equilibriu educatio levels arisig uder each syste. I particular, we study whether laguage coßict ca edogeously arise i our set-up, ad whether this coßict is of the expected type, i.e. a situatio i which the s favour biligualis while the s defed uiligualis. I additio, we deterie which political rules (if ay) eable society to reach the decetralised optiu. The prefereces of the doiat group over educatio systes ca be characterised as follows: Lea 4 The doiat group prefers the educatio syste that axiises the doiated group s equilibriu educatio level. Proof. The two systes are idetical fro the poit of view of the s, save the equilibriu educatio levels, hece we eed oly show that the s preferoretolesseducatio. Writeu (γ) idirect utility give a equilibriu γ: u (γ) = M + Nγ + γ 4U (γ ) = M + Nγ + γ ( c +(M + Nγ )σ), ad cosider two equilibria γ s ad γ t,withγ s γ t. Subtract u (γ t ) fro u (γ s ) ad siplify to obtai u (γ s ) u (γ t ) = (γ s γ t )4U (γ s )+γ t (4U (γ s ) 4U (γ t )) + N(γ s γ t ) = (γ s γ t )4U (γ s )+(γ s γ t )N(1 + γ t σ) The Þrst ter is o-egative. This is trivially true for γ s = γ t. γ s > γ t 0 iplies 4U (γ s ) 0 ad γ s < γ t 1 iplies 4U (γ s ) 0, hece (γ s γ t )4U (γ s ) 0 eve for γ s 6= γ t. The secod ter is o-egative [positive] for γ s [>]γ t, hece γ s [>]γ t iplies u (γ s ) [>]u (γ t ). Geerically γ bi s = ui. =1or γ bi =0. I the Þrst case s = bi ad i the secod 31 I Regio IIa, preferece for the uiligual syste depeds o the exclusio of the ustable iterior equilibriu uder the uiligual syste. Ituitively, wheever the size of the doiated group is large ad educatio costly it is better that obody takes educatio tha oly a fractio, sice the productio surplus the created is isufficiet to cover the cost of educatio. 19