Religious Pluralism and Religious Transmission through Education. Danny Cohen-Zada Ben Gurion University. Todd Elder Michigan State University

Transcription

1 Religious Pluralism and Religious Transmission through Education Danny Cohen-Zada Ben Gurion University Todd Elder Michigan State University October 24 Abstract We analyze the role of formal religious education in the intergenerational transmission of religious values. We develop a model of school choice in which the demand for religious schooling is driven partly by the desire of parents to limit their children s exposure to the influences of competing religions. The model predicts that when a religious group s share of the local population grows, the fraction of that group s members whose children attend religious schools declines. In addition, it implies that the overall demand for religious schooling is an increasing function of both the local religiosity rate and the level of religious pluralism, as measured by a Herfindahl Index. Using both U.S. county-level data and individual data from ECLS-K and NELS:88, we find evidence strongly consistent with the model s predictions. Our findings also illustrate that failing to control for the local religiosity rate in estimating the effect of religious pluralism on religious participation, as is common in previous studies, may lead a researcher to erroneously conclude that pluralism has a negative effect on participation. Keywords: Cultural transmission, school choice, religious pluralism, religious identity JEL Codes: I2, Z2 addresses: danoran@exchange.bgu.ac.il ; telder@msu.edu This research was supported by a grant from The Israel Foundations Trustees (28-2). We are grateful to Moshe Justman for his valuable comments, suggestions, and advice. We also thank Leif Danziger, Daniel Hungerman, Larry Iannaccone, David Voas and participants at the 2 ASREC Annual meeting for their valuable comments. Finally, we are grateful to Hedva Kazin for excellent research assistance.

2 . Introduction A growing literature in the economics of religion has studied the role of religion in shaping behavior. As summarized by Lehrer (28), a host of research has shown that religious beliefs and participation in religious activities influence a number of economic and demographic outcomes including employment, marriage, and fertility. These findings underscore the importance of understanding how religion is transmitted across generations and how individuals choose their optimal level of religious activity. According to rational choice theories of religious behavior, parents derive utility from having children who share their religious beliefs, so they carry out socialization efforts to pass on their own beliefs to their children. The more intensive a parent s religious activity, the more she exposes her children to religious practice, thereby investing in the children s religious capital. As pointed out by Iannaccone (99), most religious capital is group-specific, so adults generally adopt the religious values of the denomination to which they were exposed in their childhood. This notion is supported by the positive empirical association between the intensity of exposure to religious activity during childhood and the individual s current religiosity (see, e.g., Brañas- Garza and Neuman, 27; Clark and Worthington, 987; Hayes and Pittelkow, 993; Hoge et al., 982; Ozorak,989; Thomson et al., 992) However, religious socialization does not take place only inside the family. Following the sociological and anthropological literature (Boyd and Richeson 985; Cavalli-Sforza and Feldman 98; among others), the seminal work of Bisin and Verdier (2) modeled cultural transmission as the outcome of socialization efforts inside the family (known as vertical socialization ) and other socialization processes that take place in society at large through learning from peers and role models ( horizontal socialization ). Vertical and horizontal socialization are defined as cultural complements (substitutes) if parents have more (less) 2

3 incentive to socialize their children as their religion s market share in the local population grows. As Bisin and Verdier (2) argue, the long-run dynamics of religious traits over time depend crucially on whether vertical and horizontal socialization efforts are substitutes or complements. If they are substitutes, then the population dynamics converge to a steady state in which minorities are never completely assimilated. On the other hand, if they are complements, religious assimilation prevails in the steady state, so that the population becomes religiously homogenous. In order to measure whether horizontal and vertical socialization or complements or substitutes, several studies have estimated the association between a religious denomination s market share and religious activity within that denomination. For example, Bisin and Verdier (2) and Bisin et al. (24) present evidence that, compared to cultural maorities, minority groups exercise greater efforts to prevent their children from marrying out of the religion. Similarly, Abramitzky et al. (2) find that American Jews are more likely to celebrate Hanukkah if they live in areas with relatively low Jewish market shares, suggesting that the celebration of religious holidays is partly motivated by the desire to counteract the influence of outside religions. Iannaccone (99) shows that, across seventeen western countries, Protestants religious commitment is negatively related to Protestant market shares. Not all studies support the notion that vertical and horizontal transmission efforts are substitutes, Among sociologists, Stark (992) shows that among forty-five traditionally Christian countries, the Catholic share varies inversely with the ratio of priests to parishioners, and Stark and McCann (993) find that Catholic commitment is inversely related to the proportion of Catholics in the population. Zalenski and Zech (995) find that both Catholics and Mainline Protestants have higher rates of financial giving in areas where they are a small proportion of the population. 3

4 however; for example, Phillips (998) finds greater rates of Church activity among Mormons in areas with large Mormon market shares. 2 In spite of the recent focus on the relationship between horizontal and vertical socialization efforts, the interplay between religious schooling and other socialization efforts has largely been ignored. No study has systematically examined whether religious schooling and horizontal socialization are complements or substitutes in the religious transmission process. This omission is surprising in light of the key role that religious schooling likely plays in the process of religious transmission across generations, as demonstrated by numerous studies that document the importance of religious schooling as a tool for preserving culture and religion. For example, McDonald (2) writes that the growth and development of American Catholic schools in the nineteenth and first half of the twentieth centuries was rooted in a clear sense of purpose and identity. Defense of the faith, enculturation, and escape from religious and ethnic preudice were significant factors in the creation of these schools (p. 2). 3 2 More recently, Bar-El et al. (23) study the transmission of religious norms and, in particular, on the religious tastes of children. They find that direct religious socialization efforts of one generation have a negative effect on secularization within the next generation; that there is an inverse U-shaped relationship between the diversity of religions in the country of residence and secularization; and that the two types of socialization are complements in producing religiosity of the next generation. A novel study by Pattachini and Zenou (24) uses a somewhat different approach analyzing the transmission of the strength of religion rather the transmission of religious denomination. Focusing on the interplay between family and peer effects, they find that parent effort and peer effects are complements. 3 Numerous studies claim that the emergence of Catholic schooling in the United States at the end of the nineteenth century occurred as a response to an anti-catholic bias in a public education system that strongly promoted Protestant values (La Belle and Ward, 994; Sander, 977; Walch, 2; Youniss and Convey, 2). Similarly, Tyack (974), in describing the organizational revolution that took place in American schooling in the nineteenth century, documents the struggle between the Protestant maority and Catholic and Jewish immigrant groups on the place of religion in public schools; and the efforts that Germans exercised in Cincinnati, St. Louis, and other places, to promote bilingualism in local public schools. Similarly, Paley (995) describes the tradeoff that African- Americans in Chicago faced between sending their children to low quality black public schools or exposing them to the undesired white culture of integrated schools. Finally, O Brien and Fugita (99) document the perceived importance for Japanese families of the development of Japanese schools after World War II in the United States. Similar attitudes are documented for many ethnic groups (e.g., Mayer (985) for Jews, Tyack (974) for Germans, and more recently, Glazer (997) for African-Americans). 4

5 In this paper, we develop a model of school choice that focuses on the role of schooling as a tool for religious socialization. We posit that parents decisions to send their children to religious schools reflect a desire to preserve their religious identity by shielding their children from the outside influences of competing religions. 4 An important implication of this desire is that a child s likelihood of attending a religious school declines as his denomination s share of the local population grows, i.e., as the strength of competing influences in public schools diminishes. Moreover, if the motivation to preserve religious identity is strong enough, the fraction of all children that attend a denomination school initially increases in the market share of the denomination but then decreases at large values of that market share. Our model also has implications for a separate but related literature on the relationship between religious pluralism and religious participation. Traditionally, sociologists (cf. Berger, 969) have argued that an increase in religious pluralism decreases participation since it undermines the plausibility of belief, causing religion to lose its power as an absolute truth. On the other hand, rational choice theories of religious competition suggest that pluralism increases overall religious participation by fostering competition, which makes each religious group work harder to attract adherents (Finke and Stark, 988, 989, 22). Under some weak regularity conditions, the model predicts that the fraction of children who attend any denomination of religious schooling is a positive function of religious pluralism, as measured by a Herfindahl index, and of the share of the population that are adherents of any denomination. This result implies that empirical researchers, at a minimum, must control for the 4 As such, we extend previous studies of school choice that abstract from the religious motive in private education by modeling the demand for private schooling as motivated by differences in desired school quality (see Rangazas, 995, and Epple and Romano, 996, among others). Religious content and achievement are not contradictory goals, and evidence has shown that religious schools improves scholastic achievement (see, e.g., Sander and Krautmann, 995; Evans and Schwab, 995; Sander, 996, 997, 999; and Jepsen, 23) while also reducing risky behaviors such as sexual activity and drug use (Figlio and Ludwig, 2). 5

6 share of the population that are church adherents when estimating the effects of pluralism on measures of religious activity. We test the predictions of our model using aggregate county-level data and individual survey data from the National Educational Longitudinal Study of 988 (NELS:88) and the Early Childhood Longitudinal Study-Kindergarten Cohort (ECLS-K). We have four main substantive findings. First, in agreement with the model s predictions, the fraction of Catholics who attend Catholic schools is inversely related to the share of Catholics in the population. A similar pattern holds among both Mainline and Evangelical Protestants. These relationships are stronger in elementary schooling than in secondary schooling, as one might expect if the preservation of religious identity is an especially important concern for the parents of young children. Second, we find that the fraction of all children that attend Catholic and Evangelical schools is an inverse u-shaped function of Catholic and Evangelical market shares, respectively. However, for Mainline Protestants, we find that the religious motive for Catholic schooling is relatively weaker, resulting in a monotonically increasing relationship in Mainline school enrollments as a function of the Mainline market share. Third, we find that religious pluralism increases religious school attendance, as predicted by the rational choice theory of religious competition. To the best of our knowledge, this represents the first estimate of the effects of pluralism on the demand for religious schooling, as well as the first use of a model of school choice to inform the appropriate specification for assessing the relationship between pluralism and religious activity more generally. Finally, our results imply that a commonly-used specification may lead a researcher to mistakenly conclude that religious pluralism has a negative effect on religious activity. 2. A Model of Religious and Secular School Choice 6

7 2.. Market Shares and Religious Identity Consider an economy with a fixed population of households of measure one, with each household comprising one parent and one child. Households differ in their income level, y, and in their religious denomination,. The parent of each household belongs to one of n+ groups = n indexed by {,, n}, such that r =, where r is the fraction of the population that belongs to group. Groups,, n are organized religious groups we will refer to them as denominations and group includes non-religious persons. For simplicity, we assume that each parent belongs to only one denomination. 5 We also assume that the distribution of income is identical in all groups, and we denote its cumulative density function by F and its mean by y. Households derive utility from a numeraire consumption good, c; from educational services, x; and from the probability that their children will remain in their denomination when becoming adults, z. The utility function of a household from group is given by β () U( c, x, z) = αc / + ( α) x / + γ z / β, where and β both lie in the (,) open interval. As equation () shows, the magnitude of the parameter γ, which reflects the importance that an individual from group assigns to preserving the religious identity of its child, is fixed across households within the same group but potentially varies across groups. Public education is available free of charge to all households at an exogenous uniform quality x fully funded by an exogenous proportional income tax, t, imposed on all households. Private schooling, both secular and religious, is available as an alternative to public schooling 5 Cohen-Zada (26) uses a variant of this model in which there are only two groups, religious and nonreligious. Because this model does not include multiple denominations, it does not have any implications regarding the relationship between religious pluralism and overall religious activity. 7

8 and can be purchased from a competitively-priced private sector at any desired quality. 6 We assume that there are n+2 types of schools, where school type is indexed by s: types s =,, n are private schools corresponding to the different groups in the population (so that s = represents private non-sectarian schools and s =,, n represent denominations of religious private schools), and type s = g represents public schools. We model religious transmission as a mechanism that involves socialization at home, at school and in the society at large via imitation and learning from peers and role models. Following Bisin and Verdier (2), we assume that children are born without defined religious preferences, and are first exposed to their family socialization efforts. Parents choose whether to vertically socialize their children only at home for example, by passing religious knowledge on to them and by exposing them to religious practice or also by sending them to a religious private school of their denomination. If the direct vertical socialization efforts of the family are not successful, a child remains naïve and is therefore exposed to external influences by a role model chosen randomly from the population at large. An extensive literature has documented that religious traits are usually adopted in childhood and that family, peers, and role models play a crucial role in determining their adoption (Clark and Worthington, 987; Cornwall, 988; Erickson, 992; Hayes and Pittelknow, 993). In addition, a vast literature on religious choice shows that religion-specific capital formation plays a key role in determining adherence to a particular religious group (Greeley, 989; Iannaccone, 984, 99, 998; Chiswick, 99; Durkin and Greeley, 99). When both the household and the school belong to the same denomination, direct vertical socialization by parents succeeds with the highest probability,ω. However, if parents 6 This assumption neglects the fixed costs of education, which might limit quality choice in smaller communities. We also abstract from the possibility of privately supplementing public education. 8

9 socialization efforts do not succeed, which occurs with probability ω, the child is exposed to the external influence of the population at large and therefore picks the denomination of a role model chosen randomly in the general population. In this case, the child picks denomination with a probability equal to the market share of denomination in the population, r. Thus, the probability that a child from denomination who attends a school of denomination belongs to denomination as an adult is (2) ( ω, r ) = ω + ( ω) r π. However, if a child from denomination is not sent to a school of her own denomination, since there is no coordination between the socialization efforts of the parents and the school, direct socialization succeeds with a lower probability, ω, where < ϕ < ω s. In this case, the child picks the denomination of a role model in the general population with a higher probability, ω +ϕ s. The size of ϕ s depends positively on the metaphorical distance between the denomination of the household and that of the school. Thus, the probability of a ϕ s child from denomination who attends a school of type adult is (3) s ( ω, ϕ s, r ) = ( ω ϕ s ) + ( ω + ϕ s ) r π. Comparing equations (2) and (3) yields (4) ( ω, r ) π ( ω, ϕ, r ) = ϕ ( r ) s π. s s s s s to remain in denomination as an Given the assumption that all types of private schooling are available at any desired quality, the fact that ( ω, r ) π ( ω, ϕ, r ) π implies that each household prefers sending its child to a s s religious school of its denomination to sending her to a religious school of any other denomination. Thus, the relevant choice for a household of denomination is only between a free 9

10 public school and a private religious school of its denomination; compared to the former option, the latter increases the probability that the child remains in the parent s denomination by ϕ g ( r ). Put another way, a central motivation for a household to opt for religious schooling is to increase the probability of preserving its child s religious identity. The expression ϕ g ( r ) implies that an increase in the population share of group, r, increases the probability that a publicly-educated child from that group remains in the group as an adult. Thus, parents have a weaker motivation to incur the added expense of sending their children to private religious schools as their religion s market share increases. In the limiting case in which the entire population belongs to the same group, parents have no religious motivation to enroll their children in a religious school, regardless of the strength of their preferences. In addition, expression (4) implies that the motivation to send a child to a religious school also depends on the size of ϕ g, which reflects the distance between the values promoted by denomination and those promoted in the public schools. For example, numerous studies claim that the emergence of Catholic schooling in the U.S. at the end of the nineteenth century occurred as a response to an anti-catholic bias in a public education system that strongly promoted Protestant values (La Belle and Ward 994, Sander 977, Walch 2). If the public school system still tends to promote Protestant values more than Catholic values, then the motivation of Catholics to send their children to religious schooling will be stronger, for a given r, than the analogous motivation for Protestants. For a child from a secular family, the probability of remaining secular is highest when she is sent to a secular (public or private) school: ω + ( ω) r. However, if the child is sent to a religious school of denomination s, the probability that she will remain secular is only ( ϕ s ) + ( ω + ϕs ) r ω where ϕ > s g. Again, given the assumption that all s,

11 types of private schooling are available at any desired quality, a secular household always prefers sending its child to a secular private school over sending her to any type of religious school. Thus, the relevant choice for a secular household is only between public schooling and secular private schooling. Because the probability of remaining secular is the same under these two options, the choice of a secular household does not involve any religious motive. 2.2 School choice We next consider how households choose between public, private secular, and private religious schooling to maximize their utility. We turn first to the choices of secular households, which is the simplest case, then consider school choice among religious households School choice among secular households A household i that chooses public education expects to obtain free schooling of quality x so it spends all of its after-tax income on consumption: c = ( t) y. Equation () then implies i i that the utility of a secular household whose child attends public school equals β V g ( ω α α γ ω ω β (5) x, r,, y) = [( t) y] / + ( ) x / + [ + ( ) r ] /. Given the assumption that private non-religious schooling is available at any desired quality, a non-religious household will always prefer a secular private school to a religious one. A nonreligious household that sends its child to a secular private school solves β Max c, x U ( c, x) = αc / + ( α) x / + γ [ ω + ( ω) r ] / β s.t. c + x = ( t) y and has indirect utility β ( ω α γ ω ω β (6) V r,, y) = d (, )[( t) y] / + [ + ( ) r ] /,

12 where α α + ( α) α (7) d( α, ) = = ( α) ( α /( α)). + α + α As noted above, the only motivation for a secular household to opt out from public to secular private education is to obtain a higher quality of education. Because education quality is a normal good, the secular households that opt out of public schooling will be those with higher incomes. A comparison of (5) and (6) shows that for a given public education quality x, there exists a threshold income level (8) y ( x ) = d ( α, ) ( t ) x, where ( α α, ) α d = d, such that all non-religious households with incomes below y send their children to public schools and all those with incomes above y send their children to secular private schools (without loss of generality, we assume that the threshold lies in the interior of the support of the income distribution). The share of non-religious households whose children attend secular private schools is then (9) = F( y( )) θ, x and the share of all children that attend non-sectarian private schooling is () q r θ = r F( )]. [ y School choice among religious households 2

13 A religious household that belongs to group whose child attends public school has indirect utility β () V ( x, r, ω, ϕ, y) = α[ ( t) y] / + ( α) x / + γ π / β, with g g π g defined above as π g ( ω, ϕ g, r ) = ( ω ϕ g ) + ( ω + ϕ g ) r g. As noted above, a household in group will always prefer a religious private school of its denomination to any other private school. A household in group that sends its child to a religious private school of its denomination solves Max c, x U ( c, x) = αc / + ( α) x / + γ π / β s.t. c + x = ( t) y and has indirect utility β (2) V ( y, r, ω) = d( α, )[( t) y] / + γ π / β. β Comparing () and (2), we find that for a given level of public school quality, there exists a threshold income level (3) γ β y ( x, r, γ, ω, ϕ g ) = y( x) + π π β ( )( ) { }, g d α t β such that all households of group with incomes below y send their children to public school, and all those with incomes above y send their children to their denominational school. Thus, the share of households from group who send their children to their denominational schools is (4) θ = F( y ( x, r, γ, ω, ϕ )). g As we show in Proposition, θ is a decreasing function of the size of group in the population. Proposition. The share of households from group whose children attend religious schools, θ, decreases with the share of group in the local population, r. 3

14 Proof. θ is given by (4), so that θ ( r ) = F r (5) = F '( y '( y y ( x, r, γ, ω, ϕ )) ( x, r, γ, ω, ϕ )) y g g ( x, r, γ, ω, ϕ ) r ( d α )( t) γ g ω + ϕ β π g g ω. β π Note that ω + ϕ β π g g ω β is always positive because ϕ g > and π g < π. From π α x expression (8), y =, d α t x so α ( α), ( ) d = which is positive because y t x and y are positive and because < α < and < t <. Because γ and y ( x, r, γ, ω) are θ ( r ) also positive, <. r Proposition shows that as the share of group in the population grows, outside influences from competing religions become less threatening, weakening parents religious motivation for sending their children to their denominational schools. Consequently, a lower percentage of households from group will opt to enroll their children in these schools. Q.E.D. We next show that, in addition to religious market shares, two other mechanisms play a central role in the importance of religious schooling as a means of preserving religious identity. Specifically, the share of group households who send their children to their denominational schools is an increasing function of γ and ϕ g. 4

15 Proposition 2. The share of households from group whose children attend religious schools, θ, increases with ϕ g and with γ. Proof. θ γ = F '( y = F '( y y ( x, r, γ, ω, ϕ )) ( x, r, γ, ω, ϕ )) y g g ( x, r, γ, ω, ϕ ) γ β β g ( )( ) ( β π π ). g d α t As shown above, q d α >. Because r >, < t <, and π > π g, >. γ Similarly, θ ϕ g = F = F '( '( y ( x, r, γ, ω, ϕ g ) y ( x, r, γ, ω, ϕ g )) ϕ y ( x, r, γ, ω, ϕ )) y g ( d α )( t) g γ π β g ( r ) >. Proposition 2 shows that there are two explanations for why, say, denomination has a higher religious schooling rate than denomination k. One explanation is that households from Q.E.D. group assign more importance to preserving religious identity than do households from group k, i.e., γ > γ. An alternative explanation is that, even if households from groups and k assign the k same importance to preserving religious identity, public schools are a bigger threat to group than to group k in terms of reducing the probability that a child maintains her identity, i.e., ϕ g > ϕ kg. We next consider the fraction of all children in the population that attend private religious schools of denomination s =, defined as 5

16 (6) q r θ r ). ( The market share of group influences this fraction in two competing ways. First, for a given share of parents from group who send their children to religious schooling, θ, there is a linear relationship between q and the share of group in the population. We show in Lemma that this linear relationship holds whenever either γ = or =. Lemma. When either γ = orϕ g =, q increases linearly in r. Proof. From (6), ϕ g 7 (7) q r = θ θ + r. r Substituting eitherγ = or ϕ = into (3) above, g γ β y ( x, r, γ, ω, ϕ g ) = y( x) + β ( )( ) { } π π, g d α t yields that y = y (if ϕ g =, then π g = π ). Thus, θ F( y ( x, r, γ, ω, ϕ g )) = F ( y ( x )), which is not a function of r. Moreover, substituting y = y in (5) yields β θ ( r ) r = F '( y ) y γ ω + ϕ ( )( ) β β d α π π t g g ω. This expression equals zero if γ = or if ϕ g = (because the latter implies that π g = π, and all other expressions are finite). Thus, if either γ = or ϕ g =, θ θ is not a function of r and =, so that r 7 Thus, when both γ and is close to linear. ϕ g are very close to zero, we would expect to find that the relationship between q and r 6

17 q r θ = θ + r r is not a function of r, i.e., q is linear in r. Q.E.D. The intuition behind Lemma is that when either γ or ϕ g are zero, the protection of religious identity plays no role in the decision to send a child to a religious school, as either the household is indifferent toward preserving religious identity ( γ = ) or does not view public schooling as a threat to that identity ( ϕ = ). Thus, the fraction of group children who attend g religious schools is invariant to religious market shares, and the fraction of all children who attend group schools is a linearly increasing function of r. When γ and ϕ g are positive, however, this is not the case. We show in Propositon 3 that if γ ϕ κ is sufficiently large, the fraction of all children that attend denomination schools initially increases in r and ultimately g decreases, implying that it reaches its maximum value at an interior value of r. Proposition 3. If κ ( F( y ))( d α )( t) F' ( y ) y > value at an interior value of r, then is decreasing in r., then q is increasing in r up to its maximal Proof. From (2) and (3) we obtain that π ( r = g ) = ω ϕ and π ( = ) = ω g r. Substituting this into (3) yields y γ β β = y + ( ω φ g ) ω β ( )( ) ( ) d α t, which is finite. Therefore, it is straightforward that the derivative of θ with respect to r, given by (5), is also finite. Because 7

18 8 r r r q + = θ θ, then ) ( > = = = r y F r q θ, implying that q initially increases in r. Similarly, from (3) and (4), = = = = r r g π π, so (3) implies that y y = and ( ) y F = θ when = r. Substituting all these values into (5) yields ( )( ) α κ θ t d y y F r r r = = ) '( ) (. Thus, r r r q + = θ θ implies that ( )( ) α κ θ θ t d y y F y F r r q r r = + = = = ) '( ) (, which is negative if and only if [ ]( )( ) α κ > ) ( ' ) ( y y F t d y F. Q.E.D. Finally, we consider the implications of the model for the relationship between religious pluralism and the overall enrollment rate into religious schools. For simplicity, we assume that, for each, ) ( r θ can be written as a decreasing linear function of r : (8). ) ( r a a r = θ This assumption is largely innocuous; in Appendix A we present the results of a calibration exercise which shows that under a range of values of the parameters of the model, ) ( r θ is approximately linear in r for all denominations. Proposition implies that a is positive, with the subscript reflecting that denominations vary in their response to increased competition from other denominations (because γ varies across denominations). 8 Similarly, q is quadratic in r : 8 Taking a first order approximation of equation (5) around r = indicates that if different religious groups have a different value of γ, both the intercept and slope in (9) vary across groups.

19 (9) q 2 ( r ) = r ( a a r ) = a r a r = r θ. Aggregating (9) across denominations, the total religious enrollment rate Q is given by n n 2 (2) Q q = ( a r a r ) = = Therefore, in the general case in which. a and a vary across denomination, the religious enrollment rate is a quadratic function of the market share of each denomination. The religious enrollment rate can be interpreted as a function of the weighted market shares in the population and the weighted Herfindahl index, where and only if all religious groups have the same value of γ, then groups, and expression (2) simplifies to the following: n n 2 r = = (2) Q = a r a. a and a are the weights. 9 On the other hand, if a and a are identical among all In this case, the total religious enrollment rate is a function of the share of the population that n r = belongs to any religious group,, and the level of religious pluralism as measured by the n r = Herfindahl index, 2. This insight implies that one should first estimate the more general equation, given by (2), and test the hypothesis that the parameters a and a are identical for all denominations. Only if this hypothesis is true can one ustify estimating the religious 9 Iannaccone (99) used a specification similar to (2) to investigate the effects of religious pluralism on religious attendance among Protestants. However, subsequent studies have used more restrictive specifications similar to that given by (23) below. Our behavioral model of school choice implies that Iannaccone s specification, rather than the more restrictive version, is more appropriate for studying the association between pluralism and participation. Additionally, in the empirical study we undertake below, we strongly reect the restricted specifications in favor of the general one given by (2). 9

20 enrollment rate as a function of the overall religiosity rate (as measured by Herfindahl index, Even if n r 2. = n r = ) and the a and a are constant across denominations, one should control for the religiosity rate when assessing the effect of pluralism on religious activity. This finding stems solely from the fact that the size of the secular group which has no demand for religious schooling varies across localities. In fact, if there were no secular group in the model, one would not need to control for the religiosity rate; to see this, note that if r = in equation (2), n so that r = in all localities, the religious enrollment is a function of only the Herfindahl index: = (22) Q = a a n 2 r. = In the general case, in which the size of the secular group varies across localities, one should estimate equation (2) rather than equation (22); researchers who estimate models based on (22) will generate biased estimates of a because of the mechanical relationship between the Herfindahl Index and the religiosity rate. Appendix B includes further discussion about the effects of simplifying assumptions on the functional form of the relationship between the religious enrollment rate, religiosity, and the level of religious pluralism, and we return to this issue below in the context of our empirical analyses. In Appendix C we consider an alternative to the model described in this section. In this alternative framework, the probability that a publicly-educated child remains in group is a function of the share of children in public schools (rather than the share of children in the 2

21 population) who belong to group. Although this framework is arguably more realistic than the model presented above, data on the religious distribution of children within public schools is not available at the county level. As a result, empirical specifications based on the alternative model must still relate religious school attendance to the population shares r. In order to do so, one must model the dependence of within-public school shares on population shares, adding substantial complexity to the model. Appendix C shows that there is little benefit to introducing these complications, in part because the model predicts that population shares are nearly identical to within-public school shares across a wide range of values of population shares (additionally, Table A in the Appendix shows that population shares are nearly identical to within-public school shares in the U.S. as a whole). As a result, the two models generate remarkably similar relationships between θ and r. 3. Data We use both county-level data and individual survey data from NELS:88 and ECLS-K in the empirical analyses below. We note at the outset that our central specifications are based on the county-level data, which includes all students in each county (rather than a small subset of students, as in NELS:88 and ECLS-K). While the individual-level survey data includes individual-level controls, this advantage is quite limited because the key explanatory variables vary at the county level. 3. County-level data We combine data from several sources. County-level data on elementary and secondary enrollment by school type were created using school-level measures from the Private School Survey of For each school, this survey reports enrollment by grade, which permits distinguishing between elementary (K-8) and secondary enrollment (9-2). The survey also 2

22 includes whether each private school is religious and, if so, to which denomination it belongs. It identifies twenty-eight types of religious schools, which we aggregated into four broader categories: Catholic, Mainline Protestants, Evangelical Protestants and Other Religions. We supplemented these enrollment data with data on elementary and secondary enrollment in public schooling taken from the Public Elementary / Secondary School Universe Survey available at These enrollment data allow us to calculate the enrollment rate of each sector of private schooling. In order to control for the supply of each type of schooling, we used the Private School Survey of (ten years prior to the period of the analysis) and constructed the density of each type of schooling by dividing the number of schools of each type in the county by the area of the county in 99. County data on the share of each denomination in the population were taken from Jones et al. (22), which provides county data for the year 2 on the market shares of each of 49 denominations. We aggregated these shares to the four broader categories mentioned above Catholics, Evangelical Protestants, Mainline Protestants and Other religions according to an aggregation scheme recommended by Jones et al. (22). Finally, we combined these data with demographic variables taken from the County and City Data Book 2, available at County data on the share of the population that lives in a rural area were taken from the STF3 files of the 2 U.S. Census. Table presents summary statistics for the county-level demographic variables used in the analyses below. We weight each observation by the county s population to produce weighted summary statistics. The average Catholic, Evangelical, Mainline, and Other The categories and the denominations included in each are as follows: Catholic, Mainline Protestant (Calvinist, Disciples of Christ, Episcopal, Friends, Evangelical Lutheran Church in America, Methodist, Presbyterian), Evangelical Protestant (African Methodist Episcopal, Amish, Assembly of God, Baptist, Brethren, Christian (no specific denomination), Church of Christ, Church of God, Church of God in Christ, Lutheran Church Missouri Synod, Wisconsin Evangelical Lutheran Synod, Other Lutheran, Mennonite, Pentecostal, Seventh-Day Adventists), and Other Religion (Greek Orthodox, Islamic, Jewish, Latter-Day Saint, and all others not listed above). 22

23 Religions market shares were 22.4 percent, 4.9 percent, 9.64 percent, and 4.35 percent, respectively. Similarly, the Catholic school enrollment rate was 4.8 percent, the Evangelical enrollment rate was 2.66 percent, the Mainline enrollment rate was.47 percent, and the nonsectarian private enrollment rate was.56 percent. 3.2 NELS:88 and ECLS-K NELS:88 is a nationally representative sample of eighth graders that was initially conducted in 988 by the US National Center for Education Statistics (NCES). This survey included 24,599 students from 32 schools, with subsamples of these respondents resurveyed in 99, 992, 994, and 2 follow-ups. The survey provides information on household and individual backgrounds and on attendance at a Catholic school or a non-catholic religious school (NCES aggregates all non-catholic religious schools into an other religious school category). For all students included in the base-year sample, NELS:88 includes detailed Census zip codelevel information on their eighth grade school, which allows for identification of the zip code in which the school is located; we treat this as the zip code of the student s home. This allows for a merging with the county-level data described above, such as county measures of the shares of the population who are Catholic, Mainline Protestant, and Evangelical. Table 2 presents summary statistics from the NELS:88 data. We also analyze the base year of the ECLS-K survey, which includes 8,644 kindergarteners from over schools in the fall of the school year. As in NELS:88, the base year survey includes information on the school s zip code, which permits merging of these data with information on the within-county religious distribution of the population and the other county-level variables described above. Table 3 presents summary statistics from the ECLS-K data. 23

24 4. Empirical Results 4. Specifications Based on County-level data 4.. The Share of a Denomination that Enrolls into Religious Schools We first test Proposition, which states that share of households from group whose children attend religious schools, θ, is decreasing in the share of group in the local population, r. As the county-level data do not allow us to identify which individuals belong to each religious group, we use the ratio of denomination enrollment to denomination membership as a proxy for θ. One possible approach to testing Proposition would involve regressing this proxy for θ on r and then testing whether the regression slope coefficient is negative. For example, one could regress the ratio of Catholic enrollment to Catholic membership on the Catholic share in the local population, including a set of relevant demographic controls. Using this approach, one would estimate the following equations, separately for each denomination : ' (23) enroll / members = a + a r + β X + γ + ε, cs cs cs cs s cs where enroll cs refers to the number of students in county c in state s that are enrolled in school type, members cs refers to the number of members of denomination in that county, r cs is defined as above as the fraction of the population that belongs to denomination, X cs refers to observed demographic controls in county c of state s, and γ s denotes state fixed effects, included to control for state-specific factors that may influence the demand for a particular type of schooling. A potential problem with direct estimation of (23) stems from the fact that denominational membership appears both in the denominator of the dependent variable and in For example, the ratio of Catholic school enrollment to Catholic membership is equal to the share of Catholic households that sends their children to Catholic schools under the assumption that no non-catholic households send their children to Catholic schools. This assumption holds approximately, but not strictly, in practice. Altoni et al. (25) estimate that fewer than.3 percent of non-catholic households in NELS:88 send their children to Catholic schools. 24

25 the numerator of r cs, the key regressor. Because membership is likely measured with error, OLS estimation of (23) will typically produce biased estimates of a. As a potential solution to this problem, we adopt an approach in the spirit of Hofrenning and Chiswick (999), who propose proxying for a respondent s religious background with information on their ancestries, when religious background is not available. In our context, religious background (at the county level) is not a missing variable but rather is possibly measured with error. We propose using countylevel ancestral mix as an instrumental variable for county-level religious mix in estimating (23), which will deliver consistent estimates under the assumption that the measurement errors in ancestral mix and religious mix are linear and mutually orthogonal. Following Hofrenning and Chiswick (999), we measure county-level ancestral mix using the 98 decennial Census, which includes the question What is this person s ancestry or ethnic origin? The 98 Public-Use Microdata Samples includes 4 ancestral categories, which we aggregate to the county level. Table 4 lists county-level ancestral mixes for the 2 most common ancestries; for example, across all counties, roughly.5 percent of residents are of Danish ancestry, and roughly 5.24 percent are of German ancestry. After creating these ancestral market shares, we create predicted religious market shares based on linear regressions (for each denomination) of religious market shares on the 2 most common ancestries and the other demographic variables, weighted by county population size. Again, the key condition for identification of (23) is that measurement error in the ancestral and religious market shares is orthogonal, which is plausible. We weight each observation by the county s population, based on the 2 U.S. Census, and estimate (9) via weighted two-stage least squares. Table 5A presents OLS and 2SLS estimates of a from specification (23), with the upper panel of the table showing results for Catholic school enrollment. The first two columns show 25

26 results for elementary schooling (grades K-8), the next two columns show results for secondary schooling (grades 9-2), and the last two columns show results for combined K-2 enrollment. Each estimate is based on a specification which includes all of the demographic controls described above, including a measure of the density of Catholic schools in 99, which is intended to capture supply-side capacity effects. Specifically, Catholic school enrollment levels may be constrained by the number of Catholic schools operating within a county, and including this measure is a straightforward way of controlling for these possible effects. 2 As the top panel of the table shows, the estimates of a are negative in all six specifications. The 2SLS estimates are slightly more negative than the corresponding OLS estimates in all three cases. The estimates are much larger for elementary schooling than for secondary schooling, which, as noted above, is as expected because the motive to preserve religious identity is presumably a stronger factor in elementary school choice than in secondary school choice. The middle panel of the table shows the results for enrollment into Evangelical schools. The estimates of a are larger (in absolute value) than those for Catholic enrollment in all six cases, and all six estimates are statistically significant at the 5 percent level. The estimates are again much larger for elementary schooling than for secondary schooling. The bottom panel reports the results for enrollment into Mainline Protestant schools. The three OLS estimates of a are negative but insignificantly different from zero, while the 2SLS estimates are positive, in contrast to our expectations. In sum, the findings are supportive of Proposition for Catholics and Evangelicals, but not for Mainline Protestants. 2 We also estimated alternative specifications in which we include all of the demographic variables except for the density of Catholic schools. We found that controlling for the supply of Catholic schools in 99 has essentially no effect on the estimates in all cases. 26

27 Table 5B shows similar estimates to those in Table 5A, but is based on models that do not include demographic controls. The estimates for Catholics and Evangelicals are broadly similar to those shown in Table 5A, but the estimates for Mainline Protestants are substantially different, in that they are strongly negative in all cases. The sensitivity of the results to the inclusion of controls makes us wary of drawing strong inferences about Mainlines based on the estimates of either Table. Finally, in Table A3 in the Appendix, we present estimates based on another approach to testing Proposition, derived from a logarithmic version of (23): ' (24) ln[ enroll / members ] = b + b ln[ members / pop ] + β ln( X ) + γ + ε. cs cs cs cs cs s cs This log-log approach allows for an alternative solution to the problem of measurement error in members cs because the estimating equation can be rewritten as ' (25) ln( enroll ) = b + ( b + ) ln( members ) b ln( pop ) + β ln( X ) + γ + ε. cs cs cs cs s cs Proposition implies that b is negative, so that the coefficient on ln(members cs ) is less than (so that a -percent increase in denominational membership causes a less than -percent increase in denominational enrollment). The estimates strongly support Proposition for all three denominations; specifically, the estimates of (b + ) are significantly less than in 7 of the 8 cases The Share of All Children Enrolling into Religious Schools of a Denomination We next turn to tests of Proposition 3, which implies that if the protection of religious identity plays a sufficiently large role in the decision to send a child to religious schools, the fraction of all children that attend denomination schools initially increases in r and ultimately 27

28 decreases, implying that it reaches its maximum value at an interior value of r. To test this proposition, we estimate the following models, again separately for each denomination : 2 ' (26) q = b + b r + b r +γ X + ε. cs cs 2 cs cs cs Table 6 presents estimates of b and b 2 for all three denominations based on weights OLS, with the upper panel of the table showing results for Catholic school enrollment. Columns () and (2) show estimates for elementary school enrollment, both with and without demographic controls. The remaining columns of the table show estimates for secondary school enrollment and overall enrollment. In each of the six specifications, the Catholic market share has a strong concave effect on the overall enrollment rate into Catholic schools. The estimates of b are positive and significant (at the five percent level) in all six cases, while the estimates of b 2 are negative and significant in all cases. Moreover, in all six cases, the fraction of all children that attend denomination schools reaches its maximum value at an interior value of r. For example, in column (), the estimate of.298 for b and -.28 for b 2 implies that the maximum is at r = percent (= / ( / ). Thus, as Catholic market shares increase above percent, the fraction of all children who attend Catholic school decreases. Even though the fraction of Catholics directly increases Catholic school attendance (because Catholics have much higher attendance rates into Catholic school than non-catholics), at high levels of Catholic market share, the public school system is sufficiently populated with Catholics that Catholic parents have only very weak incentives to enroll their children into religious schools. The middle panel of the table presents analogous results for Evangelical Protestants. The results are quite similar to those for Catholics Evangelical market shares have a significant concave effect on the Evangelical enrollment rate in all six columns. In all cases, as Evangelical shares increase, eventually the share of all students enrolled in Evangelical schools declines, with 28