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1 econsor Make Your Publicaions Visible. A Service of Wirschaf Cenre zbwleibniz-informaionszenrum Economics Cohen-Zada, Dann; Elder, Todd E. Working Paper Religious Pluralism and he Transmission of Religious Values hrough Educaion IZA Discussion Papers, No Provided in Cooperaion wih: Insiue of Labor Economics (IZA) Suggesed Ciaion: Cohen-Zada, Dann; Elder, Todd E. (217) : Religious Pluralism and he Transmission of Religious Values hrough Educaion, IZA Discussion Papers, No This Version is available a: hp://hdl.handle.ne/1419/ Sandard-Nuzungsbedingungen: Die Dokumene auf EconSor dürfen zu eigenen wissenschaflichen Zwecken und zum Privagebrauch gespeicher und kopier werden. Sie dürfen die Dokumene nich für öffenliche oder kommerzielle Zwecke vervielfäligen, öffenlich aussellen, öffenlich zugänglich machen, verreiben oder anderweiig nuzen. Sofern die Verfasser die Dokumene uner Open-Conen-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gesell haben sollen, gelen abweichend von diesen Nuzungsbedingungen die in der dor genannen Lizenz gewähren Nuzungsreche. Terms of use: Documens in EconSor ma be saved and copied for our personal and scholarl purposes. You are no o cop documens for public or commercial purposes, o exhibi he documens publicl, o make hem publicl available on he inerne, or o disribue or oherwise use he documens in public. If he documens have been made available under an Open Conen Licence (especiall Creaive Commons Licences), ou ma exercise furher usage righs as specified in he indicaed licence.

2 Discussion Paper Series IZA DP No Religious Pluralism and he Transmission of Religious Values hrough Educaion Dann Cohen-Zada Todd Elder februar 217

3 Discussion Paper Series IZA DP No Religious Pluralism and he Transmission of Religious Values hrough Educaion Dann Cohen-Zada Ben Gurion Universi and IZA Todd Elder Michigan Sae Universi februar 217 An opinions expressed in his paper are hose of he auhor(s) and no hose of IZA. Research published in his series ma include views on polic, bu IZA akes no insiuional polic posiions. The IZA research nework is commied o he IZA Guiding Principles of Research Inegri. The IZA Insiue of Labor Economics is an independen economic research insiue ha conducs research in labor economics and offers evidence-based polic advice on labor marke issues. Suppored b he Deusche Pos Foundaion, IZA runs he world s larges nework of economiss, whose research aims o provide answers o he global labor marke challenges of our ime. Our ke obecive is o build bridges beween academic research, policmakers and socie. IZA Discussion Papers ofen represen preliminar work and are circulaed o encourage discussion. Ciaion of such a paper should accoun for is provisional characer. A revised version ma be available direcl from he auhor. Schaumburg-Lippe-Sraße Bonn, German IZA Insiue of Labor Economics Phone: publicaions@iza.org

4 IZA DP No februar 217 Absrac Religious Pluralism and he Transmission of Religious Values hrough Educaion * We analze he role of formal religious educaion in he inergeneraional ransmission of religious values. We firs develop a model of school choice in which he demand for religious schooling is driven parl b he desire of parens o limi heir children s exposure o he influences of compeing religions. The model predics ha when a religious group s share of he local populaion grows, he fracion of ha group s members whose children aend religious schools declines. In addiion, i shows ha if he moivaion o preserve religious ideni is sufficienl srong, he fracion of all children ha aend a given denominaion s school is an inverse u-shaped funcion of he denominaion s marke share. Finall, he model implies ha he overall demand for religious schooling is an increasing funcion of boh he local religiosi rae and he level of religious pluralism, as measured b a Herfindahl Index. Using boh U.S. coun-level daa and individual daa from ECLS-K and NELS:88, we find evidence srongl consisen wih all of he model s predicions. Our findings also illusrae ha failing o conrol for he local religiosi rae, as is common in previous sudies, ma lead a researcher o erroneousl conclude ha religious pluralism has a negaive effec on paricipaion. JEL Classificaion: Kewords: I21, Z12 culural ransmission, school choice, religious pluralism, religious ideni Corresponding auhor: Dann Cohen-Zada Deparmen of Economics Ben-Gurion Universi Beer-Sheva 8415 Israel danoran@bgu.ac.il * This research was suppored b a gran from The Israel Foundaions Trusees. We are graeful o Moshe Jusman for his valuable commens, suggesions, and advice. We also hank Leif Danziger, Daniel Hungerman, Larr Iannaccone, David Voas and paricipans a he 211 ASREC Annual meeing for heir valuable commens. Finall, we are graeful o Hedva Kazin for excellen research assisance.

5 1. Inroducion Religion plas a cenral role in shaping human behavior. As a growing lieraure in he economics of religion shows, religious beliefs and paricipaion influence a number of economic and demographic oucomes, including emplomen, marriage, and ferili (Lehrer (28)). These findings underscore he imporance of undersanding how religion is ransmied across generaions and how individuals choose opimal levels of religious acivi. According o raional choice heories of religious behavior, parens derive uili from passing heir religious beliefs on o heir children. The more inensive a paren s religious acivi, he more she exposes her children o religious pracice, hereb invesing in he children s religious capial. Because mos religious capial is group-specific, aduls picall adop he religious values of he denominaion o which he were exposed in heir childhood (Iannaccone (199)). However, religious socializaion does no ake place onl inside he famil. Building on a long sociological and anhropological lieraure, including Bod and Richerson (1985) and Cavalli-Sforza and Feldman (1981), Bisin and Verdier (2) modeled culural ransmission as he oucome of socializaion effors inside he famil (known as verical socializaion ) and oher socializaion processes ha operae hrough learning from peers and role models ( horizonal socializaion ). As Bisin and Verdier (2) argue, he long-run dnamics of he disribuion of religious beliefs depend cruciall on wheher verical and horizonal socializaion effors are subsiues or complemens. If he are complemens, so ha parens have more incenive o socialize heir children as heir religion s marke share in he local populaion grows, he sead sae is characerized b assimilaion and a religiousl homogenous populaion. If he are insead subsiues, religious pluralism exiss indefiniel, wih minoriies never compleel assimilaing. 2

6 In order o assess wheher horizonal and verical socializaion are complemens or subsiues, several sudies have esimaed he associaion beween a religious denominaion s marke share and religious acivi wihin ha denominaion. For example, Bisin and Verdier (2) and Bisin e al. (24) presen evidence ha, compared o culural maoriies, minori groups exercise greaer effors o preven heir children from marring ou of he group. Abramizk e al. (21) find ha American Jews are more likel o celebrae Hanukkah if he live in areas wih relaivel low Jewish marke shares, suggesing ha he celebraion of religious holidas is parl moivaed b he desire o counerac he influence of ouside religions. Similarl, Iannaccone (1991) shows ha, across seveneen wesern counries, Proesans religious commimen is negaivel relaed o Proesan marke shares. No all sudies suppor he noion ha verical and horizonal ransmission effors are subsiues, however; for example, Phillips (1998) finds greaer raes of Church acivi among Mormons in areas wih large Mormon marke shares. 1 In spie of he recen focus on horizonal and verical socializaion effors, he inerpla beween religious schooling and oher pes of socializaion has largel been ignored. This omission is surprising in ligh of numerous sudies documening he imporance of religious schooling as a means of preserving culure; for example, McDonald (21) wries ha he growh and developmen of American Caholic schools in he nineeenh and firs half of he wenieh cenuries was rooed in a clear sense of purpose and 1 More recenl, Bar-El e al. (213) sud he ransmission of religious norms on he religious ases of children, finding ha horizonal and verical socializaion are complemens in producing religiosi of he nex generaion. A novel sud b Paacchini and Zenou (214) uses an approach based on he ransmission of he srengh of religious beliefs raher he ransmission of religious denominaions. Focusing on he inerpla beween famil and peer effecs, he find ha paren and peer effors are complemens. 3

7 ideni. Defense of he faih, enculuraion, and escape from religious and ehnic preudice were significan facors in he creaion of hese schools (p. 211). 2 In his paper, we develop a model of school choice ha focuses on he role of schooling as a ool for religious socializaion. We posi ha parens enroll heir children in religious schools parl because of he desire o preserve religious ideni b shielding heir children from he influences of compeing religions. 3 An imporan implicaion of his desire is ha a child s likelihood of aending a religious school declines as his denominaion s share of he local populaion grows, i.e., as he srengh of compeing influences in public schools diminishes. Moreover, under a weak regulari condiion on he disribuion of income, if he moivaion o preserve religious ideni is sufficienl srong, he fracion of all children ha aend a given denominaion s school is an inverse u-shaped funcion of he marke share of he denominaion, reaching is maximum a an inerior value of ha marke share. To reveal plausible ranges of he imporance of preserving religious ideni for each religious denominaion ha we sud primiives ha are no pinned down b our empirical work we pursue a calibraion-esimaion exercise based on minimizing he disance beween acual and prediced enrollmen raes among all U.S. counies. The resuls of his exercise show ha, on average, preserving religious ideni is much less imporan for Mainline Proesans han for Caholics and Evangelical Proesans. As a resul, while he model predics ha he fracion of all children ha aend a given denominaion s school is an 2 The imporance of educaion as a socializaion ool for preserving religious ideni is also eviden from he numerous sudies ha claim ha he emergence of Caholic schooling in he Unied Saes a he end of he nineeenh cenur occurred as a response o a public educaion ssem ha promoed Proesan values (La Belle and Ward, 1994; Sander, 1977; Walch, 2; Youniss and Conve, 2). Similarl, Tack (1974) documens he sruggle beween he Proesan maori and Caholic and Jewish immigran groups on he place of religion in public schools. Moreover, hese percepions of he imporance of educaion have a leas some grounding in reali, as sudies such as Pennings e al. (211) have found ha children who aend religious schools are significanl more likel o keep heir religious affiliaion ino adolescence and oung adulhood. 3 As such, we exend previous sudies of school choice ha absrac from he religious moive in privae educaion b modeling he demand for privae schooling as moivaed b differences in desired school quali (see Rangazas, 1995, and Epple and Romano, 1996, among ohers). 4

8 inverse u-shaped funcion of he marke share of he denominaion, for Mainlines he relaionship is much weaker and nearl linear. Our model also has implicaions for a separae bu relaed lieraure on he relaionship beween religious pluralism and religious paricipaion. Tradiionall, sociologiss (cf. Berger, 1969) have argued ha an increase in religious pluralism decreases paricipaion since i undermines he plausibili of belief, causing religion o lose is power as an absolue ruh. On he oher hand, raional choice heories of religious compeiion sugges ha pluralism increases overall religious paricipaion b fosering compeiion, which makes each religious group work harder o arac adherens (Finke and Sark, 1988, 1989, 22). Under some weak regulari condiions, our model predics ha he fracion of children who aend an denominaion of religious schooling is a posiive funcion of religious pluralism and of he share of he populaion ha are adherens of an denominaion. To es he predicions of our model we creae wo novel daases ha combine daa on religious school enrollmens wih daa on denominaional marke shares. We use boh aggregae coun-level daa and individual surve daa from he Naional Educaional Longiudinal Sud of 1988 (NELS:88) and he Earl Childhood Longiudinal Sud- Kindergaren Cohor (ECLS-K). We have hree main subsanive findings, all of which are consisen wih our model s predicions. Firs, he fracion of Caholics who aend Caholic schools is inversel relaed o he share of Caholics in he populaion. We find a similar paern among Evangelical Proesans and among Mainline Proesans. Second, we find ha he fracion of all children ha aend Caholic and Evangelical schools is an inverse u-shaped funcion of Caholic and Evangelical marke shares, respecivel. In conras, he fracion of all children enrolled in Mainline schools is weakl monoonicall increasing in he Mainline marke share. 5

9 Finall, we find ha religious pluralism increases religious school aendance, as prediced b he raional choice heor of religious compeiion. To he bes of our knowledge, his represens he firs esimae of he effecs of pluralism on he demand for religious schooling, as well as he firs use of a model of school choice o inform he appropriae specificaion for assessing he relaionship beween pluralism and religious acivi more generall. The esimaes also demonsrae ha failing o conrol for he local religiosi rae, as is common in previous sudies, ma lead a researcher o erroneousl conclude ha religious pluralism has a negaive effec on paricipaion. 2. A Model of Religious and Secular School Choice 2.1 Marke Shares and Religious Ideni Consider an econom wih a fixed populaion of households of measure one, wih each household comprising one paren and one child. Households differ in heir income level,, and in heir religious denominaion,. The paren of each household belongs o one n of n+1 groups indexed b {,, n}, such ha r 1, where r is he fracion of he populaion ha belongs o group. Groups 1,, n are organized religious groups we will refer o hem as denominaions and group includes non-religious persons. For simplici, we assume ha each paren belongs o onl one denominaion. 4 We allow he disribuion of income o differ across denominaions and denoe he probabili densi funcion of household income of group b f(), is cumulaive densi funcion b F(), is mean b and is median b m. 4 Cohen-Zada (26) uses a varian of his model in which here are onl wo groups, religious and nonreligious. Because his model does no include muliple denominaions, i does no have an implicaions regarding how differen denominaions respond differenl o changes in heir marke share. In addiion, i does no shed an ligh on he relaionship beween religious pluralism and overall religious acivi or have an dnamic implicaions for he long-run disribuion of religions, unlike he model presened here. Finall, i does no analze under wha condiions he relaionship beween q and r is inverse u-shaped and under wha condiions (on he primiives) i is concave. 6

10 Households derive uili from a numeraire consumpion good, c; from educaional services, x; and from he probabili ha heir children will remain in heir denominaion when becoming aduls, z. The uili funcion of a household from group is given b (1) U( c, x, z) c / (1 ) x / z /, where δ < 1, < 1, and. The value of, which reflecs he imporance ha an individual from group assigns o preserving he religious ideni of is child, is fixed across households wihin he same group bu poeniall varies across groups. Public educaion is available free of charge o all households a an exogenous uniform quali x full funded b an exogenous proporional income ax,, imposed on all households. Privae schooling, boh secular and religious, is available as an alernaive o public schooling and can be purchased from a compeiivel-priced privae secor a an desired quali. 5 We assume ha here are n+2 pes of schools indexed b s: pes s =,, n are privae schools corresponding o he differen groups in he populaion (so ha s = represens privae non-secarian schools and s = 1,, n represen denominaions of religious privae schools), and pe s = g represens public schools. We model religious ransmission as a mechanism ha involves socializaion a home, a school and in he socie a large via imiaion and learning from peers and role models. Following Bisin and Verdier (2), we assume ha children are firs exposed o heir famil socializaion effors. Parens choose wheher o vericall socialize heir children onl a home or o also enroll hem in a religious privae school of heir denominaion. If he direc 5 This assumpion neglecs he fixed coss of educaion, which migh limi quali choice in smaller communiies. We also absrac from he possibili of privael supplemening public educaion. 7

11 verical socializaion effors of he famil are unsuccessful, a child is suscepible o he exernal influences of he populaion a large. 6 When boh he household and he school belong o he same denominaion, direc verical socializaion b parens succeeds wih probabili. However, if parens socializaion effors do no succeed, which occurs wih probabili 1, he child picks he denominaion of a role model chosen randoml in he general populaion, impling ha he child picks denominaion wih a probabili equal o he marke share of denominaion in he populaion, r. Thus, he probabili ha a child from denominaion who aends a school of denominaion belongs o denominaion as an adul is, r (1 ) r. (2) If a child from denominaion does no aend a school of her own denominaion, here is no coordinaion beween he socializaion effors of he parens and he school, so direc socializaion succeeds wih a lower probabili,, where s. In his case, he child picks he denominaion of a role model in he general populaion wih a s s higher probabili, 1 s. The size of s depends posiivel on he meaphorical disance beween he denominaion of he household and ha of he school. Thus, he probabili ha a child from denominaion who aends a school of pe denominaion as an adul is,, r (1 ) r. (3) s s s s Comparing equaions (2) and (3) ields s remains in 6 As Bisin (2) noes, an exensive lieraure has documened ha religious rais are usuall adoped in earl childhood, wih famil and peers plaing significan roles in deermining which rais are adoped and o wha exen (Cornwall, 1988; Erickson, 1992; Haes and Pielkow, 1993). In addiion, a vas lieraure on religious choice shows ha religion-specific capial formaion plas a ke role in deermining adherence o a paricular religious group (Iannaccone, 1984, 1991, 1998; Chiswick, 199). 8

12 , r,, r (1 r ) s. (4) s s s Because all pes of privae schooling are available a an desired quali b assumpion, he fac ha, r,, r implies ha each household weakl s s prefers enrolling is child in a religious school of is denominaion o a religious school of an oher denominaion. Thus, he relevan choice for a household of denominaion is beween a free public school and a privae religious school of is denominaion. Compared o he former opion, he laer increases he probabili ha he child remains in he paren s denominaion b 1 r ), impling ha parens have a weaker moivaion o send heir g ( children o privae religious schools as heir religion s marke share r increases. In he limiing case in which r 1, parens have no religious moivaion o enroll heir children in a religious school, regardless of he srengh of heir preferences. Expression (4) implies ha he moivaion o send a child o a religious school also depends on he magniude of g, which reflecs he difference beween he values promoed b denominaion and hose promoed in he public schools. For example, numerous sudies claim ha he emergence of Caholic schooling in he U.S. a he end of he nineeenh cenur occurred as a response o an ani-caholic bias in a public educaion ssem ha srongl promoed Proesan values (La Belle and Ward 1994, Sander 1977, Walch 2). If he public school ssem sill ends o promoe Proesan values more han Caholic values, hen he moivaion of Caholics o send heir children o religious schooling will be sronger, for a given r, han he analogous moivaion for Proesans. For a child from a secular famil, direc verical socializaion b parens succeeds wih he highes probabili when he send heir children o a secular (public or privae) school. Even in his case, however, he probabili of successful verical socializaion ma be lower han he analogous case for a religious famil, as religious schools picall exercise 9

13 grea effors o preserve religious ideni while secular schools do no. Thus, we model he probabili of successful verical socializaion for secular families as (compared o for religious families), where secular when she aends a secular school is. As a resul, he probabili ha a child remains ( 1 r. However, if he child ) aends a religious school of denominaion s, he probabili ha she will remain secular is ( 1 r where s g. Given he assumpion ha all pes onl s s ) s, of privae schooling are available a an desired quali, he relevan choice for a secular household is onl beween public schooling and secular privae schooling, which does no involve a religious moive. 2.2 School Choice We nex consider how households choose beween public, privae secular, and privae religious schools o maximize heir uili. We focus on he opimizaion problem of religious households and hen show how secular households represen a special case of his problem. A household i ha chooses public educaion expecs o obain free schooling of quali x, so i spends all of is afer-ax income on consumpion: c ( 1 ). Equaion (1) hen implies ha a household whose child aends a public school has indirec uili (5) V ( x, r,,, ) (1 ) / (1 ) x / /, wih g g g defined above as g g g g g,, r (1 ) r. A household in group ha sends is child o a privae school of is denominaion solves Max c, x s.. U( c, x) c and has indirec uili c x (1 ) / (1 ) x / / i i 1

14 (6) V (, r, ) d(, ) (1 ) / /, where d 1 1 (, ) (1 ) ( /(1 )) 1 1. Comparing (5) and (6) implies ha for a given level of public school quali, here is a hreshold income level, (7) 1 x (,,,, ) x r g d 1 1, g d 1 such ha children of group aend heir denominaional school if and onl if heir household income exceeds. The firs erm in brackes in expression (7) capures he school-quali moive for enrolling in privae schools (noe ha, for example, he hreshold income level is increasing in public school quali x ). The second erm capures religious moives for privae schooling, as refleced b he have no religious moives because g = and erms. As argued above, secular households, i.e., public schools are secular. Thus, he analogous hreshold income level for secular households involves onl he firs erm: 1 1 x (8) ( x). d 1 Among religious households, he share from group whose children aend heir denominaional schools is F ( ( x, r,,, )). 1 g As we show in Proposiion 1, is a decreasing funcion of group s share of he populaion: Proposiion 1. If g and are boh posiive, he share of households from group whose children aend religious schools,, decreases wih he share of group in he local populaion, r. (Proof in Appendix A, Secion A.1) 11

15 The inuiion of Proposiion 1 is simple: as a religious group s share in he populaion grows, ouside influences from compeing religions become less hreaening. In urn, his weakens parens religious moivaion for sending heir children o heir denominaional schools, so a fewer households from group will op o enroll heir children in such schools. Noe ha Proposiion 1 is onl relevan o he exen ha households assign imporance o preserving religious ideni ( ) and ha public schools pose a hrea o ha ideni ( g ). We nex show ha he share of group households who enroll heir children in heir denominaional schools also depends direcl on and g : Proposiion 2. The share of households from group whose children aend religious schools,, is sricl increasing in boh g and. (Proof in Appendix A, Secion A.2) Proposiion 2 implies ha here are wo possible explanaions for wh, sa, denominaion has a higher religious schooling rae han denominaion k, even if hose denominaions have idenical marke shares. Firs, households from group assign relaivel more imporance o preserving religious ideni han do households from group k, i.e., k. Alernaivel, even if households from groups and k assign he same imporance o preserving religious ideni, public schools pose a bigger hrea o group han o group k in erms of reducing he probabili ha a child mainains her ideni, i.e.,. We now consider he fracion of all children in he populaion ha aend privae religious schools of denominaion s =, defined as (1) q r r ). ( The marke share of group, r, influences his fracion in wo compeing was. Firs, for a given share of parens from group whose children aend religious schooling,, here is a g kg 12

16 linear relaionship beween q and r. However, as long as and g are boh posiive, declines in group s marke share, inducing a non-linear relaionship beween q and r. Specificall, under a weak regulari condiion on he disribuion of income, if is greaer han a hreshold value 1 F ( ) d 1 1 F' ( ), he relaionship beween he g fracion of all children ha aend denominaion schools and r is inverse u-shaped. Proposiion 3. Under he condiion ha f ' 2 1 f d 1 r g, if, hen he relaionship beween q and r is inversel u-shaped. (Proof in Appendix A, Secion A.3) We make several remarks abou Proposiion 3 here. Firs, in Lemma 1, presened in he proof o his proposiion, we show ha he condiion on he income disribuion holds for ever uniform income disribuion, as well as for all log-normal disribuions and Pareo disribuions if he raio of median o mean income is sufficienl high. In Appendix B we use a calibraion-esimaion exercise o gauge how srong his condiion is in pracice if income is log-normal. We find ha i holds for ever denominaion in more han 99% of he counies in he U.S. Moreover, even if his condiion does no hold, i is sill he case ha q reaches is maximum a an inerior value of r when (bu he relaionship beween q and r is no necessaril single-peaked). Second, if he condiion on he income disribuion holds bu, q does no aain is maximum a an inerior value of r, bu is insead concave and increasing hroughou he range of r (we show his resul in he proof of Lemma 1). Third, when = 13

17 , q increases linearl in r. This follows riviall from he proof of Proposiion 3: when =, he proecion of religious ideni plas no role in he decision o send a child o a religious school because he household is eiher indifferen oward preserving religious ideni ( ) or does no view public schooling as a hrea ( g ). As a resul, he fracion of group children who aend religious schools is invarian o r, so he fracion of all children who aend group schools is linear in r. Finall, we noe ha he calibraion-esimaion exercise in Appendix B shows ha varies subsaniall across religions. Specificall, preserving religious ideni is much less imporan for Mainline Proesans han for Caholics and Evangelical Proesans. As a resul, he model predics onl a weak (and nearl linear) relaionship beween he fracion of all children ha aend Mainline schools and he Mainline marke share. We reurn o his issue below in he conex of our empirical findings. We nex consider he implicaions of he model for he relaionship beween religious pluralism and he overall enrollmen rae ino religious schools. For simplici, we model q as quadraic in r for each : 7 (11) q 2 ( r) a r a1 r r. As argued above, if (and if he assumpion in Proposiion 3 holds) hen a 1 is negaive, wih he subscrip reflecing ha denominaions var in heir response o increased compeiion from oher denominaions. If, insead,, hen a 1 also equals. 7 Our calibraed model predics ha q ( r ) is almos perfecl quadraic in r for all groups (he r 2 of a regression of simulaed q ( r ) as a quadraic funcion of r is above.92 for all hree denominaions). 14

18 Aggregaing (11) across denominaions, he oal religious enrollmen rae Q is given b n n 2 (12) Q q a r a r Therefore, in he general case in which a and a 1 var across denominaion, he religious enrollmen rae is a quadraic funcion of he marke share of each denominaion. On he oher hand, if and onl if all religious groups have he same values of and g and also he same income disribuion, hen simplifies o he following: n n 2 1r 1 1 (13) Q a r a. a and a 1 do no depend on, and expression (12) In oher words, esimaing he religious enrollmen rae as a funcion of he overall religiosi n r 1 rae, n r 1, and a Herfindahl index, 2, is usified onl if, g, and he income disribuion do no var across denominaions. Iannaccone (1991) has used a specificaion similar o (12) o invesigae he effecs of religious pluralism on religious aendance, bu several subsequen sudies have used more resricive specificaions similar o ha given b (13) (and (14) below). 8 Finall, noe ha even if a and a 1 are consan across denominaions, i is necessar o conrol for he religiosi rae when assessing he effec of pluralism on religious acivi because he size of he secular group varies across localiies. In he absence of a secular group, one would no need o conrol for he religiosi rae because n r 1 would 8 Addiionall, in he empirical sud we underake below, we srongl reec he resriced specificaions in favor of he general one given b (12). 15

19 equal 1 in all localiies, impling ha he religious enrollmen is a funcion of onl he Herfindahl index: n 2 r. 1 (14) Q a a1 However, in he general case in which he size of he secular group varies across localiies, esimaion of (14) will generae biased esimaes of a because of he mechanical relaionship 1 beween he Herfindahl Index and he religiosi rae. Finall, in an Online Appendix we consider an alernaive o he model described above. 9 In his alernaive framework, he probabili ha a publicl-educaed child remains in group is a funcion of he share of children in public schools raher han he share of children in he populaion who belong o group. Alhough his framework is arguabl more realisic han he model presened above, disaggregaed daa on he religious disribuion of children wihin public schools is no available. As a resul, empirical specificaions based on he alernaive model mus sill relae religious school aendance o he populaion shares r. In order o do so, one mus model he dependence of wihin-public school shares on populaion shares, adding subsanial complexi o he model. The Online Appendix shows ha here is lile benefi o inroducing hese complicaions, in par because he model predics ha populaion shares are nearl idenical o wihin-public school shares across a wide range of values of populaion shares (addiionall, populaion religious shares are nearl idenical o wihin-public school shares in he U.S. as a whole). As a resul, he wo models generae remarkabl similar relaionships beween and r. 9 See hps:// 16

20 2.3 The Dnamics of he Disribuion of Religions To his poin, we have described school choice decisions in onl one generaion and reaed he marke share of each religion as exogenous. However, our model also has implicaions for he evoluion of denominaional marke shares across generaions. Specificall, he long-run disribuion of religious beliefs depend cruciall on he value of, which measures how srongl secular beliefs are passed from one generaion o he nex relaive o religious beliefs. We firs consider he case in which Proposiion 4: If, he secular group grows ever generaion so ha evenuall all religious groups disappear. (Proof in Appendix A, Secion A.4) The underling inuiion is ha if, aending a secular school preserves a secular famil s (non)religious ideni as effecivel as aending a religious school preserves a religious famil s ideni. Secularism ulimael dominaes because secular families have wo secular schooling opions public schools and secular privae schools while religious families relevan choice se includes one secular opion (public school) and one religious one. : In conras, religious beliefs survive in he long run when is posiive: Proposiion 5: If, he disribuion of religions in he populaion converges o a sead sae in which he populaion is muli-religious, wih he marke share of each denominaion implicil defined b g ( 1 ( r )) (Proof in Appendix A, Secion A.5) The expression for he sead-sae marke shares, g ( 1 ( r )), has an inuiive inerpreaion. The larger is, i.e., he less likel ha secular parens socializaion effors are successful, he larger is each religious group s sead-sae marke share r (because 17

21 ( r ) is decreasing in r ). Moreover, he groups wih relaivel large values of g, which are hose whose norms are he leas consisen wih he public school environmen, will have he larges shares of heir children enrolled in religious schools ( r ) Alhough his discussion shows ha our model of school choice has implicaions for he long-run disribuion of religious beliefs, hese predicions are no readil esable because he involve he unobserved primiives g and.. Noneheless, empirical ess of he saic implicaions described in secion 2.2 are poeniall informaive abou he dnamic predicions. We urn nex o empiricall esing hese saic implicaions. 3. Daa Our empirical specificaions are based on boh coun-level daa and individual surve daa from NELS:88 and ECLS-K. We describe each of hese daa sources in urn. 3.1 Coun-level daa We combine daa from several sources. Coun-level daa on elemenar and secondar enrollmen b school pe were creaed using school-level measures from he Privae School Surve of For each school, his surve repors enrollmen b grade, which permis disinguishing beween elemenar (K-8) and secondar enrollmen (9-12). The surve also includes wheher each privae school is religious and, if so, o which denominaion i belongs. I idenifies wen-eigh pes of religious schools, which we aggregaed ino four broader caegories: Caholic, Mainline Proesans, Evangelical Proesans and Oher Religions. 1 1 The caegories and he denominaions included in each are as follows: Caholic, Mainline Proesan (Calvinis, Disciples of Chris, Episcopal, Friends, Evangelical Luheran Church in America, Mehodis, Presberian), Evangelical Proesan (African Mehodis Episcopal, Amish, Assembl of God, Bapis, Brehren, Chrisian (no specific denominaion), Church of Chris, Church of God, Church of God in Chris, Luheran Church Missouri Snod, Wisconsin Evangelical Luheran Snod, Oher Luheran, Mennonie, Penecosal, Sevenh-Da Adveniss), and Oher Religion (Greek Orhodox, Islamic, Jewish, Laer-Da Sain, and all ohers no lised above). 18

22 We supplemened hese enrollmen daa wih daa on elemenar and secondar enrollmen in public schooling aken from he Public Elemenar / Secondar School Universe Surve available a hp://nces.ed.gov/ccd/pubschuniv.asp. These enrollmen daa allow us o calculae he enrollmen rae of each secor of privae schooling. In order o conrol for he suppl of each pe of schooling, we used he Privae School Surve of (en ears prior o he period of he analsis) and consruced he densi of each pe of schooling b dividing he number of schools of each pe in he coun b he area of he coun in 199. Coun daa on he share of each denominaion in he populaion were aken from Jones e al. (22), which provides coun daa for he ear 2 on he marke shares of each of 149 denominaions. We aggregaed hese shares o he four broader caegories menioned above Caholics, Evangelical Proesans, Mainline Proesans and Oher Religions and combined hese daa wih demographic variables aken from he Coun and Ci Daa Book 2, available a Coun daa on he share of he populaion ha lives in a rural area were aken from he STF3 files of he 2 U.S. Census. Table 1 presens summar saisics for he coun-level demographic variables used in he analses below. We weigh each observaion b he coun s populaion o produce weighed summar saisics. The average Caholic, Evangelical, Mainline, and Oher Religions marke shares were 22.4 percen, percen, 9.64 percen, and 4.35 percen, respecivel. Similarl, he Caholic school enrollmen rae was 4.81 percen, he Evangelical enrollmen rae was 2.66 percen, he Mainline enrollmen rae was.47 percen, and he nonsecarian privae enrollmen rae was 1.56 percen. 3.2 NELS:88 and ECLS-K NELS:88 is a naionall represenaive sample of eighh graders ha was iniiall conduced in 1988 b he US Naional Cener for Educaion Saisics (NCES). This surve 19

23 included 24,599 sudens from 132 schools, wih subsamples of hese respondens resurveed in 199, 1992, 1994, and 2 follow-ups. The surve provides informaion on household and individual backgrounds and on aendance a a Caholic school or a non- Caholic religious school (NCES aggregaes all non-caholic religious schools ino an oher religious school caegor). For all sudens included in he base-ear sample, NELS:88 includes deailed Census zip code-level informaion on heir eighh grade school, which allows for idenificaion of he zip code in which he school is locaed; we rea his as he zip code of he suden s home. We hen merge wih he coun-level daa described above, including coun measures of he shares of he populaion who are Caholic, Mainline Proesan, and Evangelical. Table 2A presens summar saisics from he NELS:88 daa. We also analze he base ear of he ECLS-K surve, which includes 18,644 kindergareners from over 1 schools in he fall of he school ear. As in NELS:88, he base ear surve includes informaion on he school s zip code, which permis merging of hese daa wih informaion on he wihin-coun religious disribuion of he populaion and he oher coun-level variables described above. Table 2B presens summar saisics from he ECLS-K daa. 4. Empirical Resuls 4.1 Specificaions Based on Coun-level daa The Share of a Denominaion s Children Enrolled in Religious Schools We firs es Proposiion 1, which saes ha he share of households from group whose children aend religious schools,, is decreasing in he share of group in he local populaion, r. As he coun-level daa do no allow us o idenif which individuals belong o each religious group, we use he raio of denominaion enrollmen o denominaion 2

24 membership as a prox for. 11 A possible approach o esing Proposiion 1 would involve regressing his prox for on r and hen esing wheher he slope parameer is negaive. Using his approach, one would esimae he following equaion separael for each denominaion : ' (2) enroll / members a a r X, cs cs 1 cs cs s cs where enrollcs refers o he number of sudens in coun c in sae s ha are enrolled in school pe, memberscs refers o he number of members of denominaion in ha coun, rcs is defined as above as he fracion of he populaion ha belongs o denominaion, Xcs refers o observed demographic conrols in coun c of sae s, and γs denoes sae fixed effecs, which we include in order o conrol for sae-specific facors ha ma influence he demand for schooling. A poenial problem wih esimaion of (2) sems from he fac ha denominaional membership appears boh in he denominaor of he dependen variable and in he numeraor of rcs, he ke regressor. Because membership is likel measured wih error, OLS esimaes of a1 will picall be biased. To address his problem, we adop an approach in he spiri of Hofrenning and Chiswick (1999), who propose proxing for a responden s religious background wih informaion on heir ancesries when religious background is no available. In our conex, religious background (a he coun level) is no a missing variable bu raher is possibl measured wih error. We propose using coun-level ancesral mix as an insrumenal variable for coun-level religious mix in esimaing (2), which will deliver consisen esimaes under he assumpion ha he measuremen errors in ancesral mix and 11 For example, he raio of Caholic school enrollmen o Caholic membership is equal o he share of Caholic households ha sends heir children o Caholic schools under he assumpion ha no non-caholic households send heir children o Caholic schools. This assumpion holds approximael, bu no sricl, in pracice. Aloni e al. (25) esimae ha fewer han.3 percen of non-caholic households in NELS:88 send heir children o Caholic schools. 21

25 religious mix are addiive and muuall orhogonal. This assumpion is quie likel o hold given ha he wo measures come from differen daa sources. Following Hofrenning and Chiswick (1999), we measure coun-level ancesral mix using he 2 decennial Census SF3 Files, which include he populaion shares of 66 ancesral caegories b coun. Table 3 liss coun-level ancesral shares for he 2 mos common ancesries; for example, across all counies, roughl.51 percen of residens are of Danish ancesr, and roughl percen are of German ancesr. Afer creaing hese ancesral marke shares, we creae prediced religious marke shares based on linear coun-level regressions (for each denominaion) of religious marke shares on all 66 ancesries, weighed b coun populaion size. The logic of his exercise is ha he share of denominaion in he populaion, r, equals k=1 a k S k, where a k is he share of ancesr k in he populaion and S k is he share of ancesr k ha belong o denominaion. Thus, he coefficiens of he firs sage can be inerpreed as reflecing he esimaed S k, wih r = a k S k 66 k=1. We presen hese firs-sage esimaes in Table A2 in he Appendix. As he able shows, he insrumens are powerful predicors of religious marke shares: he correlaions beween he prediced and acual values are above.7 for all denominaions, and he firssage F saisics are for Caholics, for Evangelicals, and 95.4 for Mainline Proesans (each impling p-values well below.1). We hen use he prediced marke share rˆ cs as he ke regressor in (2), separael for each denominaion. Table 4 presens OLS and 2SLS esimaes of a1 from specificaion (2), wih he upper panel of he able showing resuls for Caholic school enrollmen. The firs wo columns show resuls for elemenar schooling (grades K-8), he nex wo columns show resuls for secondar schooling (grades 9-12), and he las wo columns show resuls for combined K-12 enrollmen. Each esimae is based on a specificaion which includes all of 66 22

26 he demographic conrols described above, including a measure of he densi of Caholic schools in 199, which is inended o capure suppl-side capaci effecs. 12 As he op panel of he able shows, he esimaes of a1 are negaive in all specificaions. The 2SLS esimaes are slighl more negaive han he corresponding OLS esimaes, bu he differences beween he wo are small and saisicall insignifican in all cases. The esimaes are much larger for elemenar schooling han for secondar schooling, suggesing ha preserving religious ideni plas an especiall srong role in elemenar school choice. This is consisen wih previous findings (discussed above) ha religious rais are usuall adoped in earl childhood (Cornwall, 1988; Erickson, 1992). The middle panel of he able shows he resuls for enrollmen ino Evangelical schools. The esimaes of a1 are larger in absolue value han hose for Caholic enrollmen in all six cases, and all are saisicall significan a he 1 percen level. The esimaes are again much larger for elemenar schooling han for secondar schooling. The boom panel repors he resuls for enrollmen ino Mainline Proesan schools. All he esimaes are negaive, and he are significan a he 5% level in five of he six cases. In sum, he findings suppor Proposiion 1 for all hree denominaions. In Table A3 in he Appendix, we presen esimaes based on anoher approach o esing Proposiion 1, derived from a logarihmic version of (2): ln enroll / members / pop ln( X ) ' (21). cs cs b b ln members 1 cs cs cs s cs This log-log approach allows for an alernaive soluion o he problem of measuremen error in memberscs because he esimaing equaion can be rewrien as ln( enroll ) b ln( pop ) ln( X ) ' (22). cs ) b b 1 ln( members 1 cs 1 cs cs s cs 12 Specificall, Caholic school enrollmen levels ma be consrained b he number of Caholic schools operaing wihin a coun, and including his measure is a sraighforward wa of conrolling for hese possible effecs. We also esimaed alernaive specificaions in which we include all of he demographic variables excep for he densi of Caholic schools. We found ha conrolling for densi has esseniall no effec on he esimaes in all cases. 23

27 Proposiion 1 implies ha b1 is negaive, so ha he coefficien on ln(memberscs) is less han 1 (impling ha a 1-percen increase in denominaional membership causes a less han 1-percen increase in denominaional enrollmen). In esimaing (22), we follow Burbridge e al. (1988) and MacKinnon and Magee (199) in using he inverse hperbolic sine, raher han he logarihm, of variables ha can ake on values of zero. B using he inverse hperbolic sine, we can inerpre he coefficiens exacl as we would in a logarihmic model, bu we reain counies wih no children enrolled in denominaion schools. 13 We esimae (22) using 2SLS (using he number of people in he coun ha belong o each ancesr o predic memberscs) because alhough he log-log specificaion eliminaes he possibili of division bias, measuremen error in memberscs could sill lead o aenuaion bias in esimaes of (b1 + 1). The esimaes srongl suppor Proposiion 1 for all hree denominaions, as he esimaes of (b1 + 1) are significanl less han 1 in 17 of he 18 cases The Share of All Children Aending a Denominaion s Religious Schools We nex urn o ess of Proposiion 3, which implies ha under a weak regulari condiion on he income disribuion, if he proecion of religious ideni plas a sufficienl large role in school enrollmen decisions, he relaionship beween he fracion of all children ha aend denominaion schools and he marke share of denominaion is inversel u- shaped. To es his predicion, we esimae he following model, again separael for each denominaion : 2 ' (23) q b b r b r X. cs 1 cs 2 cs cs cs 13 The inverse hperbolic sine of, sinh -1 (), equals ln( 2 1), so ha is derivaive is arbiraril close o 1/ as. Using a logarihmic model would require dropping counies wih zero enrollmens, which is unsaisfacor if zero enrollmens are due o behavioral responses of parens, i.e., if hose counies are no randoml assigned. In pracice, our esimaes are subsanivel insensiive o using logarihms versus inverse hperbolic sines, bu he are slighl less precise in he logarihmic case. 24

28 Table 5 presens weighed OLS esimaes of b1 and b2 for all hree denominaions, wih he op panel showing resuls for Caholic school enrollmen. Columns (1) and (2) show esimaes for elemenar schools, boh wih and wihou demographic conrols. The remaining columns of he able show esimaes for secondar schools and overall enrollmen. In each of he six specificaions, he Caholic marke share has a srong concave effec on he overall enrollmen rae ino Caholic schools. The esimaes of b1 are posiive and significan (a he five percen level) in all six cases, while he esimaes of b2 are negaive and significan. Moreover, in all six cases, he fracion of all children ha aend denominaion schools reaches is maximum value a an inerior value of r. For example, in column (1), he esimae of.298 for b1 and for b2 implies ha he maximum Caholic school enrollmen rae is reached a r = In oher words, increases in he Caholic marke share beond percen reduce he number of children enrolling in Caholic schools because he decreased demand for Caholic schools among Caholics dominaes he increased demand due o he increase in he number of Caholics. The middle panel of he able presens analogous resuls for Evangelical Proesans. The resuls are quie similar o hose for Caholics, in ha Evangelical marke shares have a significan inverse u-shape effec on he Evangelical enrollmen rae in all six columns. In all cases, as Evangelical shares increase, evenuall he share of all sudens enrolled in Evangelical schools declines, wih he peak enrollmen rae occurring a an inerior value (roughl 28.8 percen o 35.2 percen across columns). Finall, he boom panel presens esimaes for Mainline Proesans. In conras o he resuls for Caholics and Evangelicals, we do no find evidence ha enrollmen ino Mainline schools is a quadraic funcion of he Mainline marke share. This finding parl reflecs ha Mainline enrollmen raes are uniforml low; udging from he small adused r 2 25

29 values, Mainline enrollmen raes are relaivel unresponsive o all of he demographic conrols, no us he denominaional shares. Overall, our esimaes agree wih he predicions of our calibraed model. Specificall, Proposiion 3 implied ha he relaionship beween marke shares and overall enrollmen raes is non-monoonic onl if he proecion of religious ideni is a sufficienl srong facor in schooling decisions (ha is, if ). We calibrae-esimae our model of he demand for religious educaion in order o minimize, across all U.S. counies, he difference beween acual enrollmen raes and he model s prediced enrollmen raes. The cenral goal of his exercise is o shed ligh on he value of for each denominaion ( and g are no separael recoverable, as he alwas appear muliplicaivel in he relevan momens). We find ha for Mainline Proesans, he magniude of is less han one-fifh of ha of Caholics and abou a quarer of ha of Evangelicals. Inuiivel, his resul sems from he overall low enrollmen raes of Mainlines ino religious schools; he have nearl he same aggregae marke share as Evangelicals, e onl one-fifh he religious school enrollmen rae. Because our calibraed values of show ha he preservaion of religious ideni plas onl a weak role in Mainlines schooling decisions, he implied relaionship beween Mainline marke shares and he fracion of all children ha aend Mainline schools is much less dramaicall u-shaped han he analogous relaionships for Evangelicals and Caholics. Appendix Figure A1 uses he calibraed values of he model o simulae hese relaionships graphicall. The paerns shown in he figure are consisen wih he esimaes in Table 5, in ha he relaionship beween overall Mainline enrollmen raes and Mainline marke shares is g 26

30 much weaker (and much less dramaicall u-shaped o he exen ha i seems almos monoonicall increasing) han he analogous relaionships for Caholics and Evangelicals The Effecs of Pluralism on he Demand for Religious Schooling We urn nex o ess of he final predicion of our model, which relaes he overall demand for religious schooling o quadraic funcions of he marke shares of each denominaion. The empirical counerpar o equaion (12) is n 2 ' (24) Q c [ c r c r ] X, cs 1 cs 2 cs cs cs 1 where Q cs represens he overall enrollmen rae ino religious schools. As noed above, several previous researchers have esimaed resriced versions of his model, such as a version ha imposes equali of he c1 and c2 coefficiens across denominaions: n 2 ' (25) Q c c r c r X. cs n 1 cs 2 cs cs cs 1 1 Ye anoher version, common in he lieraure on he effecs of religious pluralism on religious acivi, addiionall imposes ha he c1 coefficiens all equal zero: 2 ' (26) Q c c r X. cs n 2 cs cs cs 1 As argued above, equaion (24) is heoreicall grounded, while (25) and (26) impose addiional resricions ha ma or ma no hold in pracice. The firs column of Table 6 presens esimaes of he c1 and c2 coefficiens from specificaion (24). The esimaes impl ha he overall enrollmen rae ino religious elemenar schools is a concave funcion of he Caholic and Evangelical marke shares bu no a concave funcion of he marke share of Mainline Proesans. The boom wo rows of 14 Linear regressions ha exclude he quadraic erms generall show small posiive linear effecs of Mainline marke shares on enrollmen raes; for example, he esimaed effec of percen Mainline in he linear analog of column (1) of Table 6 is.17, wih a sandard error of.7. 27