PRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIGIOUS AFFILIATION AND PARTICIPATION

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1 PRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIIOUS AFFILIATION AND PARTICIPATION Danny Cohen-Zada Department of Economcs, Ben-uron Unversty, Beer-Sheva 84105, Israel Wllam Sander Department of Economcs, DePaul Unversty, Chcago, IL May 2007 Abstract. In ths paper, we quantfy the relgous factor n prvate educaton n the Unted States by estmatng a Random Utlty Model of school-choce n whch households choose among publc, prvate-nonsectaran, Catholc and Protestant schools. In our model households dffer not only n ther ncome levels but also n ther relgon and relgosty levels. The model s then estmated usng multnomal logt and multnomal probt regressons of attendance at dfferent types of prvate schools usng ndvdual data from the eneral Socal Survey. We fnd that both relgon and relgosty have mportant effects on the demand for the dfferent types of prvate schools. Further, t s shown that f relgosty s not taken nto account (the usual case), the effect of relgon on demand s based. Our results mply that prevous studes on the treatment effect of Catholc schools that have not taken nto account the selecton of hghrelgosty youth nto Catholc schools overestmate the postve nfluence of Catholc schools. Keywords: School choce; demand for schoolng; relgous educaton EL classfcaton: 15, I20, Z12. Acknowledgements: We are grateful to Chrstopher epsen, Moshe ustman, and Evelyn Lehrer for ther helpful comments and suggestons.

2 I. Introducton Most prvate elementary and secondary school students n the Unted States attend parochal schools. Non-relgous prvate schools only account for about 17% of prvate school enrollment (Unted States Department of Commerce, 2006). Relgous values n the demand for prvate schoolng are clearly mportant although they have not receved much consderaton n studes on prvate schools. Parents send ther chldren to relgous schools n part to help preserve a relgous dentty and nstll relgous values (Cohen- Zada, 2006). Further, partcpants n voucher programs n Mlwaukee and Cleveland have overwhelmngly chosen relgous schools. If we want to better understand why parents choose prvate schools and what effect voucher programs mght have t s mportant to pay more attenton to the relgous factor n prvate educaton. Yet, most of the emprcal and theoretcal studes on prvate schoolng have not drectly taken nto account the effects of relgon and relgosty. Some exceptons nclude a study by Campbell, West, and Peterson (2005) whch consders the effects of relgon and relgosty on partcpaton n a voucher program and Sander (2005) whch consders the effect of Catholc relgosty on the demand for Catholc schoolng. Also, Fglo and Stone (2001) adjust for relgous partcpaton n a study on prvate school creamskmmng. Most estmates of the demand for prvate schools tend to at best adjust for Catholc relgon (or a proxy for Catholc relgon). Non-Catholc relgous effects and the effects of relgosty have usually not been consdered. Further, the broader effects of relgon at the aggregate level that Cohen-Zada and ustman (2003 and 2005) and Ferreyra (2005) show are usually not consdered n ether emprcal or theoretcal studes (Rangazas 1995, Epple and Romano, 1996; lomm and Ravkumar 1998). Also, the 2

3 dfferent determnants of demand for dfferent types of relgous schoolng have not been consdered. The focus s usually on Catholc schools or prvate schools although there s substantal heterogenety wthn the prvate school sector. In ths paper, we frst present a theoretcal model of school-choce n whch households can choose between publc, Catholc, Protestant and non-sectaran prvate schoolng. In our model, households dffer not only n ther ncome levels but also n ther relgon and relgosty levels. The model s used to derve the probablty that a household attends varous types of schoolng. We then estmate ths probablty usng multnomal logt and multnomal probt regressons. Fnally, we llustrate the mportance of quantfyng the relgous factor n prvate educaton for publc polcy. It s shown that households wth a hgher probablty of attendng prvate schools would be more affected by a voucher program than households wth a lower probablty. For the emprcal secton, we use the eneral Socal Survey (SS), a dataset that has not been used very often n studes on prvate schoolng. Both household and communty-level effects of relgon and relgosty on the demand for prvate schoolng are consdered. 1 Probt and multnomal logt estmates of the demand for prvate schools, Catholc schools, Protestant schools, and non-sectaran prvate schools are undertaken. It s shown that both relgon and relgosty have mportant effects on the demand for prvate, Catholc, Protestant, and non-sectaran schools. However, when relgosty s not taken nto account, the effect of relgon on demand s based. For Catholc schools, the share of Catholcs n the local populaton s also demonstrated to be an mportant determnant of demand. It s also shown that as the percentage of Afrcan- 1 The present paper, whch emphaszes relgous dfferentaton, gnores the detrmental mpact of cultural dfferences on productvty (Lazear, 1999) and ts mplcatons for educaton polcy (radsten and ustman, 2000, 2002, 2005). 3

4 Amercans ncrease n an area, there s flght to prvate and Protestant schools. Ths s less an ssue wth Catholc schools. Further, we fnd that blacks are more lkely to opt for Catholc schools all other thngs beng equal whle they are less lkely to opt for Protestant schools even though blacks are dsproportonately Protestant. Fnally, our fndngs ndcate that non-sectaran prvate schools tend to be more eltst n the populaton that they serve relatve to Catholc schools and Protestant schools. Our fndng that relgosty has a substantal and sgnfcant postve effect on the demand for prvate schoolng also bears on research that estmates the treatment effect of Catholc schools. In numerous studes researchers try to control for selecton by frst estmatng the probablty of attendng a Catholc (prvate) school. The predcted probabltes from the frst stage are then used to estmate the treatment effect of Catholc (prvate) school attendance on student outcomes. Most of these studes fal to control for relgosty n estmatng the probablty of attendng a Catholc or prvate school (Evans and Schwab 1995, Sander 1996; Neal, 1997; Dee 2005, among others). Other research ndcates that chldren who grow up n homes wth more relgous nvolvement tend to have better educatonal outcomes (Parcel and eschwender 1995, Elder and Conger 2000, Regnerus 2000, Muller and Ellson 2001, Bankston and Zhou 2002, Regnerus and Elder 2003, lanvlle et. al 2006, among others) mplyng that studes on Catholc school effects have tended to over-estmate the treatment effect of Catholc schools. The paper s organzed as follows. Frst, a bref overvew of related research s gven. Second, a theoretcal model of prvate school choce s presented. Thrd, the emprcal models and data sources are revewed. Fourth, the emprcal results are presented. Ffth, the mportance of quantfyng the relgous factor n prvate educaton to 4

5 the analyss of voucher programs s llustrated. The paper closes wth a dscusson of the fndngs. II. Related Lterature: A Thumbnal Sketch Numerous studes have nvestgated the demand for prvate schoolng, most of whch have not consdered relgous effects beyond the effect of beng Catholc. Studes that show a postve Catholc relgon effect on prvate school attendance nclude Long and Toma (1988), West and Palsson (1988), and Downes and reensten (1996). Several studes use ethnc background as a proxy for Catholc relgon to estmate prvate school choce. These studes nclude Lankford and Wycoff (1992), Hamlton and Macauley (1991), Chswck and Koutroumanes (1996), and Hofrennng and Chswck (1999). Some of the key non-relgous factors that are found to be sgnfcant n these studes nclude postve ncome (and the varablty of ncome), parents educaton, and central cty effects, as well as negatve tuton and publc school qualty effects. Another branch of lterature has focused on the effects of attendng prvate schools on educatonal attanment and academc achevement rather than on the demand for prvate schoolng. To some extent, ths lterature has suggested that parents choose prvate schools for ther chldren f they are superor to publc schools. Most of these studes focus on Catholc schools because they account for the largest share of the prvate school sector. Early studes by Coleman, Hoffer, and Klgore (1982) and Coleman and Hoffer (1987) suggested that Catholc schools have postve effects on test scores and hgh school graduaton rates. Snce these studes, there have been numerous attempts to estmate prvate school effects takng nto account selecton (e.g., Evans and Schwab, 5

6 1995; rogger and Neal, 2000; epsen, 2003; Neal, 1997; Sander, 1996; Sander and Krautmann, 1995). The most recent contrbuton to ths lterature concludes that Catholc hgh schools have a large effect on hgh school graduaton rates, especally for mnortes, but no effect on test scores (Altonj, Elder, and Taber, 2005). These studes try to control for the possblty of postve selecton nto Catholc schools by frst estmatng the probablty of attendng a Catholc school and then usng the predcted probablty of Catholc school attendance to estmate the treatment effect of Catholc schools on student achevement. However, they fal to control for relgosty n the frst stage selecton equaton. In ths case, f students n Catholc schools are relatvely more relgous than students n publc schools and relgosty has a postve effect on student outcomes, then the treatment effect that researchers fnd are lkely to be based upward. Thus, t s mportant to consder how both relgon and relgosty affects school choce. Indeed, many studes show that both relgon and relgosty have mportant effects on economc outcomes (Chswck 1986 and 1988, Freeman 1986, Lehrer 1999, 2004a and 2004b, ruber 2005, among others). These studes show that there s a systematc pattern of dfferences by relgous afflaton n educatonal attanment, and that hgher levels of relgosty tend to be assocated wth more favorable educatonal outcomes. A related lterature has developed causal mechansms for the connecton between relgous nvolvement among youth and benefcal outcomes n many areas ncludng educaton, mental health, and substance use (Wate and Lehrer, 2003). Yet another lne of research has consdered the effects of whte flght to prvate schools. Ths lterature shows that whte parents are more lkely to send ther chldren to prvate schools as the concentraton of Afrcan-Amercan chldren n publc schools 6

7 ncreases (Chswck and Koutroumanes 1996; Farle and Resch, 2002). Betts and Farle (2001) show that mmgrants also ncrease flght to prvate schools. Coleman, Hoffer, and Klgore (1982) also examned the related ssue of segregaton and educatonal opportunty n schoolng. They found that Catholc schools lessened nequalty n educatonal opportunty whle publc schools and other prvate schools ncreased t. Although the effects of relgon and relgosty have not generally been the focus of emprcal studes on the demand for prvate schoolng, there are a few studes where they are consdered. Usng survey data, reeley and Ross (1966) show that parents relgosty had a large effect on Catholc school enrollment. Sander (2005) also shows ths to be the case. Cohen-Zada and ustman (2005) follow another lne of research on the relgous factor n prvate educaton by calbratng the dstrbuton of households' relgosty n a model of school choce where parents choose among publc, prvate non-sectaran, and relgous schools. They then smulate how household ncome and the sze of vouchers affect the demand for prvate schools. In another study, Cohen-Zada and ustman (2003) show that the share of Catholcs n the local populaton has a concave effect on the demand for prvate schools. The reasons that Catholc populaton densty mght affect the demand for Catholc schools nclude the effects of densty on costs through scale economes and tuton subsdes and the effects of the concentraton of Catholcs n publc schools on the demand for Catholc schoolng. For example, an ncrease n the percentage of Catholc students n publc schools mght reduce the demand for Catholc schools f Catholc parents prefer that ther chldren attend school wth other Catholcs (Cohen-Zada, 2006). 7

8 III. Formal Analyss 2 Basc defnton of the model An emprcal model of how households choose among school alternatves should be grounded upon a theoretcal model that descrbes the factors that affect school-choce. In ths secton we post a ratonal model of school choce n whch each household evaluates ts utlty from each type of schoolng and chooses the alternatve that maxmzes ts utlty. Consder an economy wth a fxed populaton of households of measure one, ndexed by, each household comprsng one parent and one chld. The economy conssts of two relgous groups: Catholcs and Protestants of measures r and 1 - r, respectvely. 3 Each household s characterzed by the group to whch t belongs, by ts level of relgosty z, and by ts after-tax ncome y. Each chld attends a publc school, Catholc school, Protestant school, or non-sectaran prvate school. Household utlty depends on consumpton of a numerare good c, on the academc qualty of ther chldren's educaton x, on the relgous orentaton of the school gven the household relgon and relgosty levels, and on unobservables captured by a stochastc term, ε. We set the utlty functon to be equal to U ( c x, z ) ( c ) + (1 α ) ln( x ) ( c ) + (1 α ) ln( x ) a ln + RS + β S z + ε S f relgous school, =, (1) a ln + ε S f non relgous school 2 The formal analyss bulds on prevous efforts by Cohen-Zada and ustman (2005). 3 To smplfy the model we gnore households who belong to other relgons and households that do not belong to any relgon. In our dataset, only 4.5% of the households reported they do not belong to any relgon. 8

9 where R S denotes the utlty or dsutlty that a household of denomnaton = (CA, PRT) wth z = 0 derves from the relgous envronment n relgous schoolng of type S = R CA (, ). For example, reflects the utlty that a Catholc household wth z = 0 derves from the relgous envronment n Catholc schoolng. We assume that R S = > RS, whch means that each household wth z = 0 derves greater utlty (or less dsutlty) from the relgous envronment n relgous schoolng of ts denomnaton than from relgous schoolng of another denomnaton. The matrx { β S } reflects the effect of relgosty on the utlty that households derve from each type of relgous schoolng. Two assumptons are made on the elements of the matrx β. Frst, we assume that β S = > 0, whch mples that relgosty ncreases the utlty that households derve from the relgous schoolng of ther denomnaton. Second, we assume that β S= > β S. That s, the effect of relgosty on household utlty s greater when the school belongs to the denomnaton of the household than when t belongs to another denomnaton. These restrctons leave space for β S to be ether postve or negatve. A postve value of β mples that among households who S belong to denomnaton, relgosty ncreases the utlty they derve from relgous β S schoolng of type S. On the other hand, a negatve value of mples that as households of denomnaton are more relgous, they derve less utlty from a relgous school of type S. Publc educaton s avalable free of charge to all households at an exogenous unform qualty x. Prvate schools, relgous and non-relgous, are avalable as alternatves to publc schoolng, and can be purchased from a compettvely-prced 9

10 prvate sector at any desred qualty. Thus, households can choose to forgo free publc educaton and nstead buy relgous educaton or non-sectaran prvate educaton. We assume that each relgous group operates a relgous school and that the cost per unt of qualty n each relgous school depends negatvely on the share of the relgous group n the local populaton. Ths assumpton s supported by Hoxby (1994) who provdes evdence that Catholc secondary schools receve more revenues from nontuton sources and consequently charge lower tutons n localtes where the share of Catholcs s hgher. In addton, she mentons several other reasons why the prce of a denomnatonal school depends negatvely on the relatve share of the denomnaton n the local populaton. Frst, denomnatonal schools reduce ther costs by sharng facltes and personnel servces wth the church. The supply of these facltes and personnel servces become more avalable as the share of the denomnaton n the local populaton grows. Second, as the share of a relgous group n the populaton grows, the densty of the group's relgous schools ncreases thus reducng transportaton costs to the school. The prce (cost per unt of qualty) of Catholc schoolng s then p γ 1 = r, (2A) and n Protestant schoolng t s p = (1 r) γ 2. (2B) Accordng to these functons, as the share of each denomnaton n the local populaton grows the prce of ts denomnatonal schools decreases. In addton, these functons reflect the dea that scale effects are more pronounced when the share of the 10

11 relgous group n the populaton s relatvely small. That s, school's costs decreases more rapdly when the share of the relgous group n the local populaton ncreases from 0% to 5% than when t grows from 40% to 45%. On the other hand, the prce of non-sectaran prvate schoolng, p NS, s exogenous and does not depend on the relgous composton of the communty. Thus, we set p NS = p. (2C) School Choce Consder how households choose between publc, Catholc, Protestant, and nonsectaran prvate schoolng to maxmze utlty. A household of group that chooses publc educaton receves free schoolng of qualty x. Therefore, t spends all ts dsposable ncome on consumpton, c = y. Denotng by the non-stochastc V S component of the utlty functon of a household of denomnaton from a school of type S, equaton (1) then mples that the utlty of a household that sends ts chld to a publc school equals W ( y ) + (1 α ) ( x ) ε = V + ε = a ln ln +. (3) A household that chooses a Catholc school solves: Max s. t. U ( c x, s ) = a ln( c ) + (1 α ) ln( x ) c + x p, + R + β z + ε = y, and has ndrect utlty 11

12 W [(1 α) / p ] + ln( y + R + β z ε = V + ε = a ln( α) + (1 α) ln ) +. (4) Smlarly, a household that sends ts chld to a Protestant school solves: Max s. t. ( x, s ) = a ln( c ) + (1 α)ln( x ) U c, + R + β z + ε c + x p = y. Its utlty s then W [(1 α) / p ] + ln( y + R + β z ε = V + ε = a ln( α) + (1 α) ln ) +. (5) Fnally, a household that sends ts chld to a non-sectaran prvate school solves: Max s. t. ( x, s ) = a ln( c ) + (1 α)ln( x ) U c, + ε c + x p NS = y NS, and derves utlty W NS NS NS [(1 α) / p ] + ln( y ε = V + ε = a ln( α) + (1 α) ln ) +. (6) NS NS We assume that the error terms n the utlty functons are dentcally and ndependently dstrbuted across ndvduals accordng to the double exponental wth zero mean and varance equal to 2 6 / π (McFadden, 1974). In ths case, the probablty that a household of relgon wll send ts chld to a Catholc school s exp( V ) ( V ) + exp( V ) + exp( V ) + exp( V ) π = ; (7A) exp NS 12

13 to a Protestant school t s, exp( V ) ( V ) + exp( V ) + exp( V ) + exp( V ) π = ; (7B) exp NS to a non-sectaran school t s, exp( V NS ) ( V ) + exp( V ) + exp( V ) + exp( V ) π NS = ; (7C) exp NS and to a publc school t s, exp( V ) ( V ) + exp( V ) + exp( V ) + exp( V ) π =. (7D) exp NS Dvdng (7A), (7B) and (7C) by (7D) we obtan that α 1 α 1 α ( V ) α (1 α ) y exp( R = ( V ) [ p x ] α π exp ) exp( β z ) =, (8A) 1 π exp α 1 α 1 α ( V ) α (1 α ) y exp( R = ( V ) [ p x] α π exp ) exp( β Z ) =, (8B) 1 π exp and α 1 α ( V NS ) α (1 α ) = ( V ) [ p x ] α 1 α π NS exp y =. (8C) 1 π exp NS Substtutng (2A) nto (8A) and takng ts logarthm we obtan that 13

14 π log = f ( α) + (1 α) ln( y ) + R + β z + γ1 (1 α) ln( r) (1 α) ln x. (9A) π Equaton (9A) then presents explctly the factors that affect the odds-rato to attend a Catholc rather than a publc school among Catholcs and among Protestants. It shows that: a) ncome has a postve concave effect on the probablty of attendng Catholc rather than publc schools; b) the share of Catholcs n the populaton has a postve concave effect on the probablty of attendng Catholc rather than publc educaton because t reduces the prce of Catholc schools; c) among Catholcs, relgosty has a postve effect on the probablty of attendng Catholc rather than publc schools; d) among Protestants, the effect of relgosty on the probablty of attendng PRT PRT Catholc rather than publc schools depends on the sgn of β. If β s postve, relgosty ncreases the probablty that a Protestant household wll send PRT ts chld to Catholc rather than publc schools. On the other hand, f β s negatve, relgosty decreases the probablty among Protestants of attendng Catholc rather than publc schools. Smlarly, substtutng (2B) nto (8B) and takng ts logarthm yelds π log = f ( α) + (1 α) ln( y ) + R + β z + γ 2 (1 α) ln(1 r) (1 α) ln x. (9B) π Equaton (9B) ntroduces the determnants of the odds-rato to attend Protestant rather than publc schoolng among Catholcs and among Protestants. It shows that: a) among Protestants, relgosty ncreases the probablty of attendng Protestant rather than publc schools; 14

15 b) among Catholcs, the probablty of attendng Protestant rather than publc schools CA CA depends on the sgn of β : If > 0, Catholcs who are more relgous are β more lkely to choose Protestant rather than publc schoolng, whle f CA β Catholcs who are more relgous are less lkely to choose Protestant rather than publc schoolng. < 0 We next analyze the effect of household relgon on the probablty of attendng Catholc rather than publc schools. For ths purpose, we frst specfy equaton (9A) separately for Catholcs and for Protestants and obtan CA π CA CA log = f ( α) + (1 α) ln( y ) + R + β z + γ1 (1 α) ln( r) (1 α) ln x π PRT π PRT PRT log = f ( α) + (1 α) ln( y ) + R + β z + γ1 (1 α) ln( r) (1 α) ln x π (10A) (10B) Subtractng (10B) from (10A) we obtan the effect of beng Catholc on the probablty of attendng Catholc rather than publc schools CA PRT π π CA PRT CA PRT log log = R R + ( β β ) Z. (11) π π Equaton (11) shows that the effect of beng Catholc on the probablty of attendng CA PRT Catholc rather than publc schools depends on the level of relgosty. As β > β, the effect of beng Catholc on the probablty of attendng Catholc rather than publc schools s larger for hgher values of z. Thus, falng to control for relgosty would yeld an average Catholc effect that s lower than the effect of relgous Catholcs and hgher than the effect of non-relgous Catholcs. Thus, correct estmaton of the 15

16 probablty of attendng Catholc rather than publc schoolng among the whole populaton should nclude nteracton terms between each relgon and relgosty. Such estmatons may take the form: π log π a0 + a1 Catholc + a2 z = + a5 ln( r) a6 ln x + ε Catholc+ a 3 z Protestants + a 4 ln( y ) +. (12) We next show that the specfcaton of equaton (12) s consstent wth our theoretcal model and try to relate each of ts coeffcents to the parameters of the model. In equaton (12), a 1 captures the effect of beng Catholc at z = 0, whch mples that CA= 1, Z= 0 CA= 0, Z= 0 π π CA PRT a1 = log log = R R > π π 0. (13) Smlarly, a 2 captures the ncrease n the Catholc effect when z ncreases by one. Ths s represented n our model by the postve parameter CA β n equaton (10A). That s, CA= 1, Z = Z CA= 1, Z = Z 0 π π CA a2 = log log = β > π π 0. (14) Then, we nterpret a 3 n the terms of our model usng equaton (10B): PRT = 1, Z = Z π π a 3 = log PRT log β π = π (15) PRT = 1 Z = 0 + 1, 0 Z 16

17 Fnally, the coeffcent of the logarthm of ncome s a = 1 α ; the coeffcent of the 4 Catholc share n the populaton s a = γ (1 ) ; and the coeffcent of the qualty of publc schoolng s a = (1 ). 6 α 5 1 α Substtutng equatons (13), (14) and (15) nto (12) we obtan the correct specfcaton for estmatng the probablty of attendng Catholc rather than publc schools among the whole populaton whch s consstent wth our theoretcal model: π log π CA PRT ( R R ) CA a0 + Catholc + β z Catholc+ β = + (1 α) ln( y ) + γ1 (1 α) ln( r) (1 α) ln x + ε PRT z Protestant +, (16) CA PRT CA PRT where R R >0, >0 and can be ether postve or negatve. β β Followng the same steps as outlned above, we obtan that the mpled specfcaton for the probablty to attend Protestant rather than publc schools n the whole populaton n the terms of our model s π log π CA PRT ( R R ) CA PRT a0 + Catholc + β z Catholc+ β z Protestant + =, (17) + (1 α) ln( y ) + γ 2 (1 α) ln(1 r) (1 α) ln x + ε CA PRT PRT CA where R R < 0, >0 and can be ether postve or negatve. β β Fnally, substtutng (2C) nto (8C) and takng ts logarthm yelds π NS log = π f ( α) + (1 α) ln( y ) (1 α) ln x (1 α) ln p. (18) That s, as both publc and non-sectaran prvate schoolng do not nclude any relgous nstructon n ther currculum, relgon and relgosty are not expected to have any effect 17

18 on the odds rato to choose between non-sectaran prvate schoolng and publc schoolng. The only factors that affect the choce between non-sectaran prvate schoolng and publc schoolng are household ncome, whch ncreases the probablty of attendng nonsectaran prvate schoolng rather than publc schoolng, and the qualty of the publc schools whch decreases ths probablty. Equatons (16), (17) and (18) present the factors that affect school-choce between all types of schoolng. Proposton 1 The followng factors affect school-choce between Catholc, Protestant, non-sectaran and publc schoolng: 1) Choce between all types of prvate schoolng and publc schoolng a) Income has a postve effect on the probablty of attendng all types of prvate schoolng rather than publc schoolng. b) The qualty of the local publc schools has a negatve effect on the probablty of attendng all types of prvate schoolng rather than publc schoolng. 2) Choce between Catholc and publc schoolng (Equaton (16)) c) Catholc relgon ncreases the probablty of attendng Catholc rather than publc schoolng. d) The nteracton term between Catholc relgon and relgosty has a postve effect on the probablty of attendng Catholc rather than publc schoolng. e) The share of Catholcs n the local populaton has a postve concave effect on the probablty of attendng Catholc rather than publc schoolng. 18

19 3) Choce between Protestant and publc schoolng (Equaton (17)) f) Catholc relgon decreases the probablty of attendng Protestant rather than publc schoolng. g) The nteracton term between Protestant and relgosty has a postve effect on the probablty of attendng Protestant rather than publc schoolng. h) The share of Protestants n the populaton has a postve concave effect on the probablty of attendng Protestant rather than publc schoolng. In the next secton we estmate equatons (16), (17) and (18) smultaneously usng both multnomal logt and multnomal probt regressons. IV. Emprcal Models and Data We estmate the probablty of attendng a prvate school (all types), a Catholc school, a Protestant school or a non-sectaran prvate school. All of the estmates are relatve to attendng publc schools. In the data set, nformaton s avalable on whether respondents send (sent) ther chldren to Catholc schools, Protestant/Chrstan schools, other non-chrstan relgous schools, and prvate non-sectaran schools. Partcular attenton s gven to attendance at Catholc schools and Protestant schools because they account for the largest shares of the prvate school populaton. We do not estmate attendance at non-chrstan relgous schools because the sample s too small. Frst, we undertake a probt estmate of the probablty of attendng a prvate school. The rght-hand varables nclude relgon (relatve to non-fundamentalst protestant), an nteracton term between attendance at relgous servces and relgon (Catholcs, fundamentalst Protestants, and non-fundamentalst Protestants), household ncome (measured categorcally relatve to ncome of $110,000 and over), educaton of the respondent (relatve to hgh school graduate), age of the respondent, Afrcan-Amercan, 19

20 Hspanc, regon (relatve to west), populaton densty, percent Catholcs n the populaton, percent Afrcan-Amercan n the populaton, percent Hspanc n the populaton, and whether the respondent lves n one of the 100 largest central ctes n the Unted States. In addton, followng the theoretcal model, we also nclude n the estmaton the share of Catholcs n the populaton squared to allow the share of Catholcs n the populaton to have a concave effect on the probablty of attendng Catholc rather than publc schoolng. 4 The ncome varables are defned as follows: Income 1 ndcates household wth ncome less than $8,000; Income 2 ndcates ncome of $8,000 to $17,499; Income 3 ndcates ncome of $17,500 to $24,999; Income 4 ndcates ncome of $25,000 to $39,999; Income 5 ndcates ncome of $40,000 to $59,999; Income 6 ndcates ncome of $60,000 to $89,999; and Income 7 ndcates ncome of $90,000 to $109,000. The densty varables are for the samplng areas (called prmary samplng unts). They are ether metropoltan statstcal areas or nonmetropoltan countes. Second, we undertake two multnomal logt estmates of attendng a Catholc school, Protestant school, non-sectaran prvate school, or a publc school (the omtted category). In the second case, we exclude the relgosty varables. We do ths to show the effects of omtted varable bas f relgosty s excluded. Usng multnomal logt for 4 Whle the theoretcal multnomal logt specfcaton (equaton 16) defnes the odds-rato of attendng Catholc rather than publc schoolng as a functon of the logarthm of %Catholc, we preferred to allow for concavty n our estmaton by ncludng a squared term of %Catholc rather than by takng ts logarthm. The reason for ths s that a squared term for %Catholc allows the share of Catholcs n the populaton, above a crtcal pont, to have a negatve effect on the probablty of attendng Catholc rather than publc schoolng. Although n our model the share of Catholcs n the populaton affects school-choce only through scale effects and thus predcts a postve effect of %Catholc on the probablty of attendng Catholc rather than publc schoolng, %Catholc may also reduce the demand for Catholc schoolng f Catholc parents prefer that ther chldren attend school wth other Catholcs (Cohen-Zada, 2005). In ths case, one could expect that when the share of Catholcs n the populaton s hgh enough and scale effects become less mportant, %Catholc would have a negatve effect on the probablty to attend Catholc rather than publc schoolng. Indeed, we found that by addng a squared term for %Catholc we better predct choce between Catholc and publc schools than f we only take a logarthm term of %Catholc. 20

21 the estmaton has both advantages and dsadvantages. One advantage s that t allows us to make a drect lnk between the theoretcal model and the estmated one. Yet, t s wdely recognzed that a potentally mportant drawback of the multnomal logt model s the ndependence from rrelevant alternatves property. Accordng to ths property, one assumes that the rato of the probabltes of choosng between two alternatves s ndependent of the exstence and attrbutes of any other alternatve. For example, households' choce between publc and Catholc schools does not depend on the exstence of non-sectaran prvate schoolng. We deal wth ths concern by frst testng the valdty of the IIA assumpton usng the Hausman and McFadden (1984) test and also by comparng the results to those obtaned from a multnomal probt estmaton. Last, we present predcted probabltes of attendng Catholc schools, Protestant schools, non-sectaran prvate schools, and publc schools for typcal Catholc households, fundamentalst Protestant households, and black fundamentalst Protestant households. The predcted probabltes are based upon the multnomal logt and multnomal probt regressons wth adjustments for relgosty. One of the shortcomngs n our study s that t s possble that partcpaton n relgous servces s not completely exogenous. For example, parents who send ther chldren to relgous schools mght attend church more often than they would otherwse. It s probably more plausble that some parents mght jon a certan church (synagogue, mosque, etc.) so that they can send ther chldren to a school that s assocated wth t, especally f the school s subsdzed by the relgous nsttuton. Ths does not necessarly ncrease relgous partcpaton by parents. In our sample, 59% of parents attend relgous servces almost every week or more f they are sendng (or have sent) 21

22 ther chldren to relgous schools. For parents less than 40 years old, 51% attend relgous servces regularly f ther chldren attended (or have attended) relgous schools. For older parents who are sendng or have sent (more lkely as parent s age ncreases) ther chldren to relgous schools, rates of church attendance tend to ncrease (61% for parents 50+ and 66% for parents 60+). If attendance by parents was a result of relgous schoolng, older parents wth older chldren who attended relgous schools mght be less lkely to attend relgous servces regularly. Although ths s not rgorous evdence that endogenety s not a problem, t does suggest that t s more plausble that hgher rates of relgous partcpaton by parents are a determnant of the demand for relgous schoolng and less a result of t. More attenton mght be gven to ths ssue n future research. Household data from the Natonal Opnon Research Center s eneral Socal Survey are combned wth aggregate data on the sample area. The SS s a crosssectonal natonal survey that has been carred out snce The sample s lmted to respondents who are at least eghteen years old and lve n a non-nsttutonal settng. For 1998 and 2000, questons were asked of respondents wth chldren older than fve years regardng the type of school they were sendng (or sent) ther chldren. The possble responses were publc school, home school, Catholc school, Chrstan/Protestant school, other (non-chrstan) relgous school, and non-sectaran prvate school. We excluded respondents who home schooled ther chldren, a very small percentage. The SS s a useful data set for ths study because data are also avalable on the respondent s relgon and relgosty as measured by attendance at relgous servces. However, one of the shortcomngs n the data set s that nformaton on tuton s not avalable. Summary statstcs for the data set are provded below (Table 1). In Table 2, 22

23 data are arrayed on attendance at relgous servces for all respondents, Catholc respondents, and Protestant respondents. Respondents were gven nne possble responses from never to more than once per week. For Catholcs and Protestants, about one n three attends at least weekly. About one n three respondents regardless of ther relgous afflaton (ncludng none) attend once or twce per year or less. Table 3 presents attendance at relgous servces for each type of schoolng. It shows that those who choose Catholc and Protestant schoolng attend relgous servces more often than those who choose publc schoolng or non-sectaran schoolng. The ndvdual data from the SS database were combned wth aggregate demographc varables on the sample area. These varables were constructed from several resources. Frst, county-level data on the populaton, Hspanc populaton, Afrcan- Amercan populaton, and on the densty of populaton, were taken from the County and Cty Data Book (2000). Second, data on the number of Catholc members n each county were taken from the Relgous Congregaton and Membershp n the Unted States (2000). Fnally, all of these varables were aggregated to the U level accordng to the county composton of each U. V. Emprcal Results A probt estmate of prvate school attendance s presented n Table 4. Ths estmate shows the probablty of attendng any type of prvate school relatve to a publc school. The results show that the relgon of the respondent s not sgnfcant. However, Catholc relgosty (Catholc x Attend) and fundamentalst Protestant relgosty (Fundamentalst x Attend) have sgnfcant postve effects on attendance. Whle prevous 23

24 studes focused on the effect of relgon on school choce, our results show that respondent s relgosty as measured by partcpaton s a more mportant determnant of school choce. The three lowest ncome varables have sgnfcant negatve effects on attendance. That s, households wth very low ncome levels cannot afford payng tuton to prvate schools and are thus much less lkely to send ther chldren to them. Hgher levels of educaton have a postve effect on the probablty to send a chld to prvate schools. One explanaton for ths result s that gven the ncome of the household, more educated parents attrbute greater mportance to better schoolng relatve to less educated parents. Fnally, the share of Afrcan-Amercans n the local populaton, central cty, and age are also assocated wth hgher levels of attendance. A multnomal logt estmate of Catholc school attendance, Protestant school attendance, and non-sectaran prvate school attendance s presented n Table 5. Publc school attendance s the omtted category. For Catholc school attendance, the results ndcate that Catholc relgon and Catholc relgosty (Attend x Catholc) have sgnfcant postve effects on attendance. The share of Catholcs n the populaton has a sgnfcant concave effect on the probablty of attendng a Catholc school, whch peaks when the share of Catholcs n the populaton s about 27%. Ths result s consstent wth Cohen-Zada (2006) that shows that the share of Catholcs n the populaton may reduce the demand for Catholc schools f Catholc parents prefer that ther chldren attend schools wth other Catholcs. Famly ncome s mostly not sgnfcant apart from a sgnfcant negatve effect for the lowest ncome category. Snce tuton n Catholc schools s subsdzed households wth relatvely low-ncome levels can sometmes afford sendng ther chldren to Catholc schools (except for households wth very low ncome 24

25 levels). Parent s educaton ndcates a sgnfcant postve effect of some college and a sgnfcant negatve effect of hgh school dropout. The college graduate coeffcent s not sgnfcant. Black, age, and central cty are shown to have sgnfcant postve effects. The only relgon varable that s sgnfcant for Protestant schools s a postve effect for fundamentalst relgosty (Attend x Fundamentalst). The other sgnfcant results nclude postve effects of college graduate and the share of Afrcan-Amercans n the populaton and negatve effects of Income 2, age, and Afrcan-Amercan. Nonsectaran prvate schools, other relgon, no relgon, and nonfundamentalst Protestant relgosty (Attend x Nonfundamentalst) are found to sgnfcantly ncrease attendance. All of the ncome coeffcents below Income 7 have sgnfcant negatve effects on attendance whle college graduates are sgnfcantly more lkely to send ther chldren to non-sectaran schools. In ths equaton the ncome effect and the effect of college graduates are much stronger than n the Catholc school attendance equaton and the Protestant school attendance equaton. Ths ndcates that non-sectaran prvate schools tend to be more eltst n the populaton that they serve than Catholc schools and Protestant schools. Fnally, the other sgnfcant coeffcents nclude postve Afrcan- Amercan and central cty effects. As mentoned earler, multnomal logt has the property of ndependence from rrelevant alternatves. Under ths property, the rato of probabltes for any two alternatves s the same whether or not there are other alternatves. Hausman and McFadden (1984) suggest testng f ths property holds n a partcular dataset by estmatng the model on a subset of the alternatves. If IIA holds then the estmated coeffcents obtaned on the subset of alternatves wll not be sgnfcantly dfferent from 25

26 those obtaned on the full set of alternatves. Hausman and McFadden (1984) also provde a statstc for ths test. Applyng ther test we fnd that IIA s not volated n our estmaton. In order to further llustrate that n our estmaton the rato of probabltes for two school-alternatves does not depend on the exstence of a thrd school-alternatve we report the results of a multnomal logt regresson elmnatng the non-sectaran prvate school alternatve. The results are presented n Table 6. It shows that the rato of probabltes between Catholc schoolng and publc schoolng and between Protestant schoolng and publc schoolng s not affected by the exstence of non-sectaran prvate schoolng. To further show that our results are not drven by the IIA assumpton we also run a multnomal probt regresson. The results are very smlar to those obtaned by the multnomal logt estmaton. Table 7 reports the margnal effects, multpled by 100, of each of the rght-hand sde varables on the probabltes of attendng each type of schoolng for the multnomal logt and probt regressons. It shows that the two estmaton procedures yeld very smlar results and that the relgous varables are even slghtly more sgnfcant under the multnomal probt regresson. Multnomal logt estmates of attendng Catholc, Protestant, or non-sectaran prvate schools relatve to pubc schools wthout the relgosty adjustments are presented n Table 8. The key changes n the results from Table 5 nclude Catholc relgon ncreasng n sze and sgnfcance as a determnant of Catholc school attendance, Catholc relgon becomng negatve and sgnfcant as a determnant of Protestant school attendance, and fundamentalst becomng postve and sgnfcant as a determnant of Protestant school attendance. These results are consstent wth what we showed n the 26

27 theoretcal model (.e., that the effect of the relgon varables becomes stronger when one fals to control for relgosty). Table 9 shows how relgosty affects the probablty of attendng Catholc schools, Protestant schools, non-sectaran prvate schools, and publc schools. The predcted probabltes are generated from the multnomal logt and probt regressons presented above (Table 7). The probabltes are for a typcal Catholc household. 5 The results show that church attendance has a large effect on the probablty of attendng a Catholc school. Catholcs who attend church at least weekly are about as lkely to send ther chldren to Catholc schools as they are to send them to publc schools. Catholc attendance at relgous servces s not strongly related wth Protestant school attendance or non-sectaran school attendance. For the typcal Protestant fundamentalst household, Protestant school attendance s also shown to ncrease wth church attendance (Table 10). However, the magntude of the relatonshp s not as strong as was the case for Catholcs and Catholc schools: Protestant fundamentalsts who attend church at least weekly are more than twce as lkely to attend publc schools as Protestant schools. The probablty that fundamentalst Protestants attend Catholc schools or non-sectaran prvate schools s not strongly related to attendance at relgous servces. Fnally, n Table 11 data are presented on the probablty of Catholc school attendance, Protestant school attendance, non-sectaran prvate school attendance, and publc school attendance for a typcal black fundamentalst Protestant famly. The results 5 We set the quanttatve varables of the typcal household equal to ther values at the mean: Age = 52, Percent Black n the populaton = 13.15%, Percent Catholc n the populaton = 20.94%, Percent Hspanc n the populaton = 10.29, and Densty of populaton = We set the dummy varables accordng to the categores that are most frequent: Income category 4 ($25,000 - $40,000), Non-Hspanc, Whte, Regon = North. 27

28 show that both Catholc school attendance and Protestant school attendance ncreases wth relgosty. It s nterestng to note that the relatonshp between Protestant church attendance and prvate school attendance s about the same for Catholc schools and Protestant schools about one n ten wth weekly church attendance send ther chldren to Catholc schools or Protestant schools. Non-sectaran prvate school attendance s very low regardless of church attendance. VI. Vouchers In ths secton we llustrate the mportance of quantfyng the relgous factor n prvate educaton for assessng school-choce programs. Consder, for example, a unversal voucher program of value avalable for use n both relgous and nonsectaran prvate schools. v 0 In ths case a household that chooses publc educaton stll have the utlty level gven by equaton (3). A household that choose a Catholc school now solves: Max s. t. U x p ( c, x, s ) a ln( c ) + (1 α ) ln( x ) c + x p v 0 = = + R + β z + ε y + v 0, and has ndrect utlty 6 W [ α) / p ] + ln( y + v + R + β z ε = V + ε = a ln( α) + (1 α) ln (1 0 ) + (4') 6 As x p v 0 y = α /( 1 α) v0 ths ndrect utlty s correct only for households wth ncome level hgher than a threshold ncome. Below ths threshold ncome households do not supplement the voucher and thus the determnstc part of the ndrect utlty functon s a ln( y ) + (1 α) ln( v0 / p ). We concentrate here on households wth ncome above ths threshold ncome. 28

29 Smlarly, a household that sends ts chld to a Protestant school derves utlty W [(1 α) / p ] + ln( y + v + R + β z ε = V + ε = a ln( α) + (1 α) ln 0 ) + (5') and a household that chooses non-sectaran prvate schoolng derves utlty W NS NS NS [(1 α) / p ] + ln( y + v ε = V + ε = a ln( α) + (1 α) ln 0 ) + (6') NS NS Followng the same steps as n the basc model we obtan for example an equaton that determnes the factors that affect the relatve probablty of attendng Catholc rather than publc schoolng π π exp ( V ) ( V ) α = (1 α ) exp( R α 1 α = exp ) exp( β 1 α α [ p x ] y z ) ( y + v), (8A') Dfferentatng π / π wth respect to the amount of the voucher we obtan: ( π / π ) v α = α (1 α ) 1 α exp( R 1 α α [ p x ] y π ( y + v) ) exp( β z ) = π (19) Ths result mples that the mpact of a voucher program on the relatve probabltes of attendng Catholc rather than publc schoolng s larger among households wth orgnally hgher probablty of attendng Catholc schools. In order to check whether a voucher program s expected to have a dfferent effect on households wth dfferent relgosty levels we dfferentate equaton (19) wth respect to z and obtan 29

30 ( π / π ) v z α = α (1 α ) 1 α exp( R ) exp( β z ) β β 1 α α [ p x ] y π ( y + v) = π > 0 That s, a voucher program s expected to have a larger effect on households who are more relgous. Furthermore, the effect of relgosty on the probablty of attendng Catholc rather than publc schoolng estmated from the basc model wthout vouchers, β, also reflects how much stronger the effect becomes of a gven voucher on the probablty of attendng Catholc rather than publc schoolng as relgosty level ncreases. Of course, smlar patterns exst also wth respect to Protestant schoolng and non-sectaran prvate schoolng. VII. Dscusson One of the key results n ths study s that both relgon and relgosty have mportant effects on the demand for prvate schools. If relgosty s not taken nto account, the measurement of the effect of relgon s serously based. Further, the effects of relgon and relgosty vary dependng upon the type of prvate school n queston. It was shown that Catholc relgosty ncreases the demand for Catholc schools and has no effect on the demand for other types of prvate schoolng. Fundamentalst Protestant relgosty ncreases the demand for Protestant schools and has no effect on the demand for other types of prvate schoolng. Non-fundamentalst Protestant relgosty ncreases the demand for non-sectaran prvate schools and has no effect on the demand for other types of prvate schoolng. It was also shown that households wth no relgon were more lkely to choose non-sectaran prvate schools for ther chldren. These results suggest that relgosty s a key factor that affects who attends prvate schools and who mght 30

31 respond to voucher ntatves. The latter pont s supported by related research (Campbell, West, and Peterson, 2005). Other aspects of relgon also bear upon who goes to prvate schools. It was shown that the share of Catholcs n the populaton has a concave effect on the lkelhood of attendng Catholc schools. Further, t was shown that Afrcan-Amercans, a dsproportonately Protestant group, were more lkely to attend Catholc schools and less lkely to attend Protestant schools. One of the probable reasons for the Catholc result s that Catholc schools have been more open to mnorty students relatve to other prvate schools (see Coleman, Hoffer, and Klgore, 1982). The most recent data puts the mnorty share n Catholc educaton at 27.1% n the Unted States (McDonald, 2005). In bg ctes lke Chcago, the mnorty share s hgher 37% n the Chcago Archdocese. Of the blacks n Chcago Catholc schools, three out of four are not Catholc (Offce of Catholc Schools, 2006). Ths would also help to explan our result that a larger black populaton results n more flght to Protestant schools and non-sectaran prvate schools than t does to Catholc schools. Another result of nterest s that a more favorable famly background n terms of ncome and parents educaton s postvely assocated wth the probablty that chldren attend non-sectaran prvate schools. These factors were less assocated wth the demand for Catholc and Protestant schools. One reason for ths n the case of Catholc schools s that they are subsdzed. However, recent data ndcate that declnes n subsdes and ncreases n costs are resultng n a declne n the ablty of Catholc schools to support students from modest economc backgrounds (Sander, 2005). 31

32 In summary, ths paper contrbutes to a better understandng of the demand for prvate schoolng, whch s necessary n order to analyze how polcy programs mght affect school choce. It dstngushes between dfferent types of prvate schoolng and shows that households tend to send ther chldren to prvate schools belongng to ther denomnaton. Our man fndng that relgosty has a strong and sgnfcant effect on the demand for prvate schoolng mples that prevous studes on Catholc/prvate schoolng effects have tended to overestmate the postve nfluence of Catholc (prvate) schoolng. The reason for ths s that the effects of Catholc and other relgous schoolng are confounded wth the effects of relgosty. Although ths paper adds to our knowledge about prvate schoolng, more work on ths topc s warranted. As noted above, more attenton could be gven to the possbly endogeneous relatonshp between parents church attendance and prvate schoolng. Other measures of relgosty mght be tred ncludng contrbutons, relgous belefs, and so on. Fnally, more attenton could be gven to dfferences for more types of relgous schools lke Lutheran schools, Chrstan schools, ewsh schools, and so on. 32

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