Religion, religiosity and private school choice: Implications for estimating the effectiveness of private schools

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1 Journal of Urban Economics 64 (2008) Religion, religiosity and private school choice: Implications for estimating the effectiveness of private schools Danny Cohen-Zada a,, William Sander b a Department of Economics, Ben-Gurion University, Beer-Sheva 84105, Israel b Department of Economics, DePaul University, Chicago, IL 60604, USA Received 2 May 2007; revised 9 August 2007 Available online 12 September 2007 Abstract In this paper, we quantify the religious factor in private education in the United States by estimating a random utility model of school-choice in which households choose among public, private-nonsectarian, Catholic and Protestant schools. The model is estimated using a multinomial logit regression of attendance at different types of private schools using individual data from the General Social Survey. We find that both religion and religiosity have important effects on the demand for private schools. We also provide evidence that previous studies that do not take into account religiosity probably over-estimate the positive influence of private schools on measures of educational attainment. Evidence on the magnitude of this bias is presented Elsevier Inc. All rights reserved. 1. Introduction Most private elementary and secondary school students in the United States attend parochial schools. Non-religious private schools only account for about 17% of private school enrollment (US Department of Commerce, 2006). Religious values in the demand for private schooling are clearly important although they have not received much consideration in studies on private schools. Parents send their children to religious schools in part to help preserve a religious identity and instill religious values (Cohen-Zada, 2006). Further, participants in voucher programs in Milwaukee We are grateful to Thomas Dee, Todd Elder, Naomi Feldman, Christopher Jepsen, Moshe Justman, Evelyn Lehrer, the editor, and two anonymous reviewers for their helpful comments and suggestions. * Corresponding author. address: danoran@bgu.ac.il (D. Cohen-Zada). and Cleveland have overwhelmingly chosen religious schools. If we want to better understand why parents choose private schools and what effect private schools and policies that increase the demand for private schools (like voucher programs) might have on educational outcomes it is important to pay more heed to the religious factor in private education. Few of the empirical and theoretical studies on private schooling have directly taken into account the effects of religion and religiosity. These exceptions include Greeley and Rossi (1966) and Sander (2005) who show that Catholic religiosity affects Catholic school enrollment. Other exceptions include Campbell et al. (2005) who consider the effects of religion and religiosity on participation in a voucher program and Figlio and Stone (2001) who adjust for religious participation in a study on private school cream skimming. Most estimates of the demand for private schools tend to at best adjust for Catholic religion (or a proxy for Catholic re /$ see front matter 2007 Elsevier Inc. All rights reserved. doi: /j.jue

2 86 D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) ligion). 1 Non-Catholic religious effects and the effects of religiosity have usually not been considered. Further, the broader effects of religion at the aggregate level that Cohen-Zada and Justman (2003, 2005), Ferreyra (2007) and Cohen-Zada (2006) show are usually not considered in either empirical or theoretical studies (Rangazas, 1995; Epple and Romano, 1996; Glomm and Ravikumar, 1998). 2 Further, the different determinants of demand for different types of religious schooling have not been considered. The focus is usually on Catholic schools or private schools although there is substantial heterogeneity within the private school sector. Another part of the literature focuses on the effects of attending private schools on educational attainment and academic achievement rather than on the demand for private schooling. To some extent, this literature has suggested that parents choose private schools for their children if they are superior to public schools. Most of these studies focus on Catholic schools because they account for the largest share of the private school sector. Early studies by Coleman et al. (1982) and Coleman and Hoffer (1987) suggested that Catholic schools have positive effects on test scores and high school graduation rates. Since these studies, there have been numerous attempts to estimate private school effects taking into account selection (e.g., Dee, 2005; Evans and Schwab, 1995; Grogger and Neal, 2000; Jepsen, 2003; Neal, 1997; Sander, 1996; Sander and Krautmann, 1995). The most recent contribution to this literature concludes that Catholic high schools have a large effect on high school graduation rates, especially for minorities, but no effect on test scores (Altonji et al., 2005a). These studies try to control for the possibility of positive selection into Catholic schools by either using bivariate probit when the outcome measure is binary or by using IV probit when the outcome measure is continuous. In both estimation methods, one estimates the causal effect of Catholic school attendance on outcomes by exploiting the presence of instrumental variables that causally affect Catholic school attendance but do not have a direct effect on the outcome. These estimation methods are valid as long as there is no unobserved determinant of outcome which is correlated 1 Studies that show a positive Catholic religion effect on private school attendance include Long and Toma (1998), West and Palsson (1988), Downes and Greenstein (1996), among many others. 2 Cohen-Zada and Justman (2005) calibrate the distribution of households religiosity in a model of school choice where parents choose among public, private non-sectarian, and religious schools and use the calibrated model to simulate how household income and the size of vouchers affect the demand for private schools. with the IV (conditional on the other controls). However, most of these studies do not control for religiosity in the first stage selection equation. In this case, if students in Catholic schools are relatively more religious than students in public schools and religiosity is correlated with the IV and has a positive effect on student outcomes then the treatment effect that researchers find are likely to be biased upward. Indeed, many studies show that both religion and religiosity have important effects on economic outcomes (Chiswick, 1986, 1988; Freeman, 1986; Lehrer, 1999, 2004a, 2004b; Gruber, 2005, among others). Several studies concentrate on educational outcomes and show that there is a systematic pattern of differences by religious affiliation in educational attainment, and that higher levels of religiosity tend to be associated with more favorable educational outcomes (Parcel and Geschwender, 1995; Elder and Conger, 2000; Regnerus, 2000; Muller and Ellison, 2001; Bankston and Zhou, 2002; Regnerus and Elder, 2003; Glanville et al., in press, among others). A related literature has developed causal mechanisms for the connection between religious involvement among youth and beneficial outcomes in many areas, including education, mental health, and substance abuse (Waite and Lehrer, 2003). In this paper, we first present a theoretical model of school-choice in which households can choose between public, Catholic, Protestant and non-sectarian private schooling. In our model, households differ not only in their income levels but also in their religion and religiosity levels. The model is used to derive the probabilities that a household attends various types of schools. We then estimate these probabilities using multinomial logit regressions. For the empirical section, we use the General Social Survey (GSS). Both household and community-level effects of religion and religiosity on the demand for private schooling are considered. 3 Probit and multinomial logit estimates of the demand for private schools, Catholic schools, Protestant schools, and non-sectarian private schools are undertaken. It is shown that both religion and religiosity have important effects on the demand for private, Catholic, Protestant, and non-sectarian schools. More specifically, church attendance has a large effect on the probability of attending a Catholic school. Catholics who attend church at least weekly are about as likely to send their children to Catholic schools as they are to send 3 The present paper, which emphasizes religious differentiation, ignores the detrimental impact of cultural differences on productivity (Lazear, 1999) and its implications for education policy (Gradstein and Justman, 2000, 2002, 2005).

3 D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) them to public schools. This result implies that previous research on the treatment effect of Catholic schools that did not control for religiosity were likely to overestimate the treatment effect of Catholic schools. As a case in point, we provide evidence that this might be the case in Neal s (1997) important study. We also show with the GSS that if religiosity is not taken into account, the effect of parochial school attendance on educational attainment is highly inflated. 2. Formal analysis Basic definition of the model An empirical model of how households choose among school alternatives should be grounded upon a theoretical model that describes the factors that affect school-choice. In this section, we posit a rational model of school choice in which each household evaluates its utility from each type of schooling and chooses the alternative that maximizes its utility. Consider an economy with a fixed population of households of measure one, indexed by i, each household comprising one parent and one child. The economy consists of two religious groups: Catholics and Protestants of measures r and 1 r, respectively. 5 Each household is characterized by the group to which it belongs, by its level of religiosity z i, and by its aftertax income y i. Each child attends a public school, Catholic school, Protestant school, or non-sectarian private school. Household utility depends on consumption of a numeraire good c, on the academic quality of their children s education x, on the religious orientation of the school given the household religion and religiosity levels, and on unobservables captured by a stochastic term, ε. We set the utility function to be equal to U(c i,x i,z i ) = a ln(c i ) + (1 α)ln(x i ) + R J S + β J S z i + ε J is if religious school, a ln(c i ) + (1 α)ln(x i ) + ε J is if non-religious school, (1) where RS J denotes the utility or disutility that a household of denomination J = (CA, PRT) with z i = 0 de- 4 The formal analysis builds on previous efforts by Cohen-Zada and Justman (2005). 5 To simplify the model we ignore households who belong to other religions and households that do not belong to any religion. In our dataset, only 4.5% of the households reported they do not belong to any religion. rives from the religious environment in religious schooling of type S = (CS, PS). For example, RCS CA reflects the utility that a Catholic household with z i = 0 derives from the religious environment in Catholic schooling. We assume that RS=J J >RJ S J, which means that each household with z i = 0 derives greater utility (or less disutility) from the religious environment in religious schooling of its denomination than from religious schooling of another denomination. The matrix {βs J } reflects the effect of religiosity on the utility that households derive from each type of religious schooling. Two assumptions are made on the elements of the matrix β. First, we assume that βs=j J > 0, which implies that religiosity increases the utility that households derive from the religious schooling of their denomination. Second, we assume that βs=j J >βj S J. That is, the effect of religiosity on household utility is greater when the school belongs to the denomination of the household than when it belongs to another denomination. These restrictions leave space for βs J J to be either positive or negative. A positive value of βs J J implies that among households who belong to denomination J, religiosity increases the utility they derive from religious schooling of type S J.Onthe other hand, a negative value of βs J J implies that as households of denomination J are more religious, they derive less utility from a religious school of type S J. Public education is available free of charge to all households at an exogenous uniform quality x. Private schools, both religious and non-religious, are available as alternatives to public schooling, and can be purchased from a competitively-priced private sector at any desired quality. Thus, households can choose to forgo free public education and instead buy religious education or non-sectarian private education. We assume that each religious group operates a religious school and that the price (cost per unit of quality) in each religious school is a concave decreasing function of the share of the religious group in the local population. 6 More specifically, the price of Catholic schooling is p CS = r γ 1, and of Protestant schooling it is p PS = (1 r) γ 2. On the other hand, the price of nonsectarian private schooling, p NS, is exogenous and does not depend on the religious composition of the community. That is, p NS = p. 6 This assumption is supported by Hoxby (1994) who provides evidence that Catholic secondary schools receive more revenues from non-tuition sources and consequently charge lower tuitions in localities where the share of Catholics is higher.

4 88 D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) School choice Consider how households choose between public, Catholic, Protestant, and non-sectarian private schooling to maximize utility. A household of group J that chooses public education receives free schooling of quality x. Therefore, it spends all its disposable income on consumption, c i = y i. Denoting by VS J the non-stochastic component of the utility function of a household of denomination J from a school of type S, Eq. (1) then implies that the utility of a household that sends its child to a public school equals W J G = V J G + εj ig = a ln(y i) + (1 α)ln( x) + ε J ig. (2) A household that chooses a Catholic school solves: Max U(c i,x i,s i ) = a ln(c i ) + (1 α)ln(x i ) + RCS J + βj CS z i + εics J s.t. c + x p CS = y i, and has indirect utility WCS J = V CS J + εj ics = a ln(α) + (1 α) ln [ ] (1 α)/p CS + ln(y i ) + RCS J + βj CS z i + εics J. (3) Similarly, a household that sends its child to a Protestant school solves: Max U(c i,x i,s i ) = a ln(c i ) + (1 α)ln(x i ) + RPS J + βj PS z i + εips J s.t. c + x p PS = y i. Its utility is then WPS J = V PS J + εj ips = a ln(α) + (1 α) ln [ ] (1 α)/p PS + ln(yi ) + RPS J + βj PS z i + εips J. (4) Finally, a household that sends its child to a nonsectarian private school solves: Max U(c i,x i,s i ) = a ln(c i ) + (1 α)ln(x i ) + ε J ins s.t. c + x p NS = y i, and derives utility WNS J = V NS J + εj ins = a ln(α) + (1 α) ln [ ] (1 α)/p NS + ln(yi ) + εins J. (5) We assume that the error terms in the utility functions are identically and independently distributed across individuals according to the double exponential with zero mean and variance equal to 6/π 2 (McFadden, 1974). This implies that the logarithm of the odds ratio to attend school option A relative to school option B equals the difference between the non-stochastic components of the utilities from these two school options. Thus, the logarithm of the odds ratio to attend Catholic rather than public schooling equals: ( ) J πcs log = VCS J V G J π G = f(α)+ (1 α) ln(y i ) + R J CS + βj CS z i + γ 1 (1 α) ln(r) (1 α) ln x. (6) This equation shows that among Catholics, religiosity has a positive effect on the probability of attending a Catholic rather than a public school. Among Protestants, the effect of religiosity on the probability of attending a Catholic rather than a public school depends on the sign of βcs PRT.IfβPRT CS is positive, religiosity increases the probability that a Protestant household will send its child to a Catholic rather than a public school. But, if βcs PRT is negative, religiosity decreases the probability among Protestants to attend a Catholic rather than a public school. We next analyze the effect of household religion on the probability of attending a Catholic rather than a public school. For this purpose, we first specify Eq. (6) separately for Catholics and for Protestants and then subtract the expression for Catholics from the expression for Protestants. This yields ( ) CA ( ) PRT πcs πcs log log π G π G = RCS CA RPRT CS + ( βcs CA ) βprt CS zi. (7) Equation (7) shows that the effect of being Catholic on the probability of attending a Catholic rather than a public school depends on the level of religiosity. As, the effect of being Catholic on the probability of attending a Catholic rather than a public school is larger for higher values of z i. Thus, failing to control for religiosity would yield an average Catholic effect that is lower than the effect for religious Catholics and higher than the effect for other Catholics. Thus, the correct estimation of the probability of attending a Catholic rather than a public school among the whole population should include interaction terms between each religion and religiosity. Such estimations take the form: βcs CA >βprt CS log ( πcs π G ) = a 0 + a 1 Catholic i + a 2 z i Catholic + a 3 z i Protestant + a 4 ln(r) + a 5 ln(y i ) a 6 ln x + ε i, (8)

5 D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) where a 1 = RCS CA RPRT CS > 0 captures the effect of being Catholic at z i = 0; a 2 = βcs CA > 0 captures the increase in the Catholic effect when z i increases by one; a 3 = βcs PRT captures the effect of Protestant religiosity on the choice between Catholic and public schools, and a 4 = γ 1 (1 α) > 0 captures the effect of the Catholic share in the population on school-choice through scale economics. Finally, the coefficient of the logarithm of income is a 5 = 1 α>0 and the coefficient of the quality of public schooling is a 6 = (1 α) < 0. Following the same steps as outlined above, we obtain a specification for estimating the probability of attending a Protestant rather than a public school in the whole population in terms of our model which is given by ( ) b πps 0 + b 1 Catholic i + b 2 z i Catholic + b log = 3 z i Protestant (9) π G + b 4 ln(1 r)+ b 5 ln(y i ) b 6 ln x + ε i, where b 1 = RPS CA RPRT PS < 0, b 2 = βps PRT > 0, b 3 = βps CA can be either positive or negative and b 4 = γ 2 (1 α) > 0. The other coefficients are the same as in Eq. (8). Finally, the specification for estimating the probability of attending a non-sectarian private school rather than a public school is ( ) πns log = f(α)+ (1 α) ln(y i ) (1 α) ln x π G (1 α) ln p. (10) As both public and non-sectarian private schooling do not include any religious instruction in their curriculum, religion and religiosity are not expected to have any effect on the odds ratio to choose between non-sectarian private schooling and public schooling. Equations (8), (9) and (10) present the factors that affect households choice between all types of schooling. Proposition 1. The following religious factors affect a household s choice between each type of religious schooling and public schooling (Eqs. (8) and (9)): (a) Belonging to a specific denomination increases the probability of attending a religious school of this denomination rather than a public school. (b) The interaction term between a specific religion and religiosity has a positive effect on the probability of attending a religious school of this specific religion rather than a public school. (c) The share of a specific religion in the local population has a positive concave effect on the probability of attending a religious school of this specific religion rather than a public school. 3. Empirical models and data We estimate the probability of attending a private school (all types), a Catholic school, a Protestant school and a non-sectarian private school. All of the estimates are relative to attending public schools. In the data set, information is available on whether respondents send (sent) their children to Catholic schools, Protestant/Christian schools, other non-christian religious schools, or private non-sectarian schools. Particular attention is given to attendance at Catholic schools and Protestant schools because they account for the largest shares of the private school population. We do not estimate attendance at non-christian religious schools because the sample is too small. First, we undertake a probit estimate of the probability of attending a private school. The right-hand side variables include religion (relative to non-fundamentalist Protestant), an interaction term between attendance at religious services and religion (Catholics, fundamentalist Protestants, and non-fundamentalist Protestants), household income (measured categorically relative to incomes of $110,000 and over), education of the respondent (relative to high school graduate), age of the respondent, African-American, Hispanic, region (relative to the South), population density, percent Catholics in the population, percent African-American in the population, percent Hispanic in the population, and whether the respondent lives in one of the 100 largest central cities in the United States. In addition, following the theoretical model, we allow the Catholic share in the population to have a concave effect by also including its squared term. 7 The income variables are defined as follows: Income 1 indicates households with an income of less than $8000; Income 2 indicates an income of $8000 to $17,499; Income 3 indicates an income of $17,500 to $24,999; Income 4 indicates an income of $25,000 to $39,999; Income 5 indicates an income of $40,000 to $59,999; Income 6 indicates an income of $60,000 to $89,999; and Income 7 indicates an income of $90,000 to $109,000. The density variables are for the sampling areas (called primary sampling units), 7 We preferred to allow for concavity by including the squared term of percent Catholic rather then by taking its logarithm. The reason for this is that % Catholic may have, above a critical point, a negative effect on the probability to attend Catholic rather than public schooling if Catholic parents prefer that their children attend a school with other Catholics (Cohen-Zada, 2006).

6 90 D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) which are either metropolitan statistical areas or nonmetropolitan counties. Second, we undertake two multinomial logit estimates of attending a Catholic school, Protestant school, non-sectarian private school, or a public school (the omitted category). In the second case, we exclude the religiosity variables, to show the effects of an omitted variable bias if religiosity is excluded. Using multinomial logit for the estimation has both advantages and disadvantages. One advantage is that it allows us to make a direct link between the theoretical model and the estimated one. Yet, it is widely recognized that a potentially important drawback of the multinomial logit model is the independence from irrelevant alternatives property. According to this property, one assumes that the ratio of the probabilities of choosing between two alternatives is independent of the existence and attributes of any other alternative. For example, a household s choice between a public and Catholic school does not depend on the existence of non-sectarian private schooling. We deal with this concern by first testing the validity of the IIA assumption using the Hausman and McFadden (1984) test and also by comparing the results to those obtained from a multinomial probit estimation. Last, we present predicted probabilities of attending Catholic schools, Protestant schools, non-sectarian private schools, and public schools for typical Catholic households, fundamentalist Protestant households, and black fundamentalist Protestant households. The predicted probabilities are based upon the multinomial logit regression with adjustments for religiosity. One of the shortcomings in our study is that it is possible that participation in religious services is not completely exogenous. For example, parents who send their children to religious schools might attend church more often than they might otherwise. It is probably more plausible that some parents might join a certain church (synagogue, mosque, etc.) so that they can send their children to a school that is associated with it, especially if the school is subsidized by the religious institution. This does not necessarily increase religious participation by parents. In our sample, 59% of parents attend religious services almost every week or more often if they are sending (or have sent) their children to religious schools. For parents less than 40 years old, 51% attend religious services regularly if their children attended (or have attended) religious schools. For older parents who are sending or have sent (more likely as the parent s age increases) their children to religious schools, rates of church attendance tend to increase (61% for parents 50+ and 66% for parents 60+). If attendance by parents was a result of religious schooling, older parents with older children who attended religious schools might be less likely to attend religious services regularly. Although this is not rigorous evidence that endogeneity is not a problem, it does suggest that it is more plausible that higher rates of religious participation by parents are a determinant of the demand for religious schooling and less a result of it. More attention might be given to this issue in future research. Another shortcoming in this study is that we do not take into account the effect of the location choice of households on the demand for private schooling. As Neal (1997) notes, households choose where to send their children to school and where to live simultaneously implying that the quality of public schooling is endogenous in the school choice equation. This is also grist for future research. Household data from the National Opinion Research Center s General Social Survey are combined with aggregate data on the sample area. The GSS is a cross-sectional national survey that has been carried out since The sample is limited to respondents who are at least eighteen years old and live in a non-institutional setting. For 1998 and 2000, questions were asked of respondents with children older than five years regarding the type of school they were sending (or sent) their children. The possible responses were public school, home school, Catholic school, Christian/Protestant school, other (non-christian) religious school, and non-sectarian private school. We excluded respondents who home schooled their children, a very small percentage. The GSS is a useful data set for this study because data are also available on the respondent s religion and religiosity as measured by attendance at religious services. However, one of the shortcomings of the data set is that information on tuition is not available. Summary statistics for the data set are provided below (Table 1). In Table 2, data are arrayed on attendance at religious services for all respondents, Catholic respondents, and Protestant respondents. Respondents were given nine possible responses from never to more than once per week. For Catholics and Protestants, about one in three attended at least weekly, and about one in three respondents regardless of their religious affiliation (including none) attended once or twice per year or less. Table 3 presents attendance at religious services for each type of schooling. It shows that those who chose Catholic and Protestant schooling attended religious services more often than those who chose public schooling or nonsectarian schooling. The individual data from the GSS database were combined with aggregate demographic variables on the

7 D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) Table 1 Summary statistics Variable Mean Standard deviation Private school 12.9% 33.5 Catholic school 7.1% 25.7 Protestant school 3.1% 17.4 Non-sectarian school 2.7% 16.2 Income 1 7.5% 26.4 Income % 33.8 Income 3 9.7% 29.6 Income % 38.1 Income % 36.8 Income % 33.3 Income 7 3.9% 19.3 Income missing 8.3% 27.6 College graduate 21.0% 40.8 Some college 26.3% 44.0 High school dropout 19.9% 39.9 Age 51.7 years 15.4 African-American 17.0% 37.6 Hispanic 5.3% 22.4 Catholic 23.5% 42.4 Fundamentalist Protestant 32.8% 47.0 Other Protestant 27.6% 44.7 Other religion 2.6% 16.0 No religion 10.1% 30.1 Attend Catholic Attend fundamentalist Attend other Protestant East 19.7% 39.8 West 17.6% 38.1 North 24.8% 43.2 Central city 22.1% 41.5 Density (1000s).59/square mile.67 Catholics 20.8% 14.4 African-Americans 13.1% 11.9 Hispanics 10.3% 11.5 N 2447 sample area. These variables were constructed from several resources. First, county-level data on the population, Hispanic population, African-American population, and on the density of population, were taken from the County and City Data Book (US Census Bureau, 2000). Second, data on the number of Catholic members in each county were taken from the Religious Congregation and Membership in the United States (Jones et al., 2000). Third, data on the number of Catholic schools in each county were constructed from the Private School Survey (US Department of Education, National Center for Education Statistics, ) by aggregating school-level data to the county level. Finally, all of these variables were aggregated to the PSU level according to the county composition of each PSU. 4. Empirical results A probit estimate of private school attendance is presented in Table 4. This estimate shows the probability of attending any type of private school relative to a public school. The results show that the religion of the respondent is not significant. However, Catholic religiosity (Catholic attend) and fundamentalist Protestant religiosity (Fundamentalist attend) have significant positive effects on attendance. While previous studies focused on the effect of religion on school choice, our results show that the respondent s religiosity as measured by participation is a more important determinant of school choice. A multinomial logit estimate of Catholic school attendance, Protestant school attendance, and nonsectarian private school attendance is presented in Table 5. Public school attendance is the omitted category. For Catholic school attendance, the results indicate that Catholic religion and Catholic religiosity (Attend Catholic) have significant positive effects on attendance. The share of Catholics in the population has a significant concave effect on the probability of attending a Catholic school, which peaks when the share of Catholics in the population is about 27%. This re- Table 2 Distribution of attendance at religious services by religion Attendance All (%) Catholic (%) Fundamentalist Protestant (%) Never Less than once/year Once or twice/year Several times/year Once/month Two or three times/month Nearly weekly Weekly More than once/week All Non-fundamentalist Protestant (%)

8 92 D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) Table 3 Distribution of attendance at religious services by school type Attendance Catholic (%) Protestant Public (%) (%) Never Less than once/year Once or twice/year Several times/year Once/month Two or three times/month Nearly weekly Weekly More than once/week All Nonsectarian (%) sult is consistent with Cohen-Zada (2006) who showed that the share of Catholics in the population may reduce the demand for Catholic schools if Catholic parents prefer that their children attend schools with other Catholics. The only religion variable that is significant for Protestant schools is a positive effect for fundamentalist religiosity (Attend fundamentalist). For nonsectarian private schools, other religion, no religion, and non-fundamentalist Protestant religiosity (Attend non-fundamentalist) are found to significantly increase attendance. As mentioned earlier, multinomial logit has the property of independence from irrelevant alternatives. Under this property, the ratio of probabilities for any two alternatives is the same whether or not there are other alternatives. Hausman and McFadden (1984) suggest testing if this property holds in a particular dataset by estimating the model on a subset of the alternatives. If IIA holds then the estimated coefficients obtained on the subset of alternatives will not be significantly different from those obtained on the full set of alternatives. Hausman and McFadden (1984) also provide a statistic for this test. Applying their test, we find that IIA is not violated in our estimation. In order to further illustrate that in our estimation the ratio of probabilities for two school-alternatives does not depend on the existence of a third school-alternative we report the results of a multinomial logit regression eliminating the non-sectarian private school alternative. The results are presented in Table 6, and show that the ratio of probabilities between Catholic schooling and public schooling and between Protestant schooling and public schooling is not affected by the existence of non-sectarian private schooling. 8 8 To further check that our results are not driven by the IIA assumption we also run a multinomial probit regression. The results are very Table 4 Probit estimate of private school attendance Variable Coefficient Standard error Marginal effect Catholic Fundamentalist Other religion No religion Attend Catholic.16 *** Attend fundamentalist.06 *** Attend non-fundamentalist Income 1.55 *** Income 2.45 *** Income 3.28 * Income Income Income Income Income missing.26 * College graduate.32 *** Some college.28 *** High school dropout.29 ** Age.007 *** African-American Hispanic East West North Density % Catholic % Catholic squared % African-American.011 *** % Hispanic Central city.26 *** Constant 2.11 N 2447 * Significant at the 10% level. ** Idem, 5%. *** Idem, 1%. Multinomial logit estimates of attending Catholic, Protestant, or non-sectarian private schools relative to pubic schools without the religiosity adjustments are presented in Table 7. The key changes in the results from Table 5 include Catholic religion increasing in size and significance as a determinant of Catholic school attendance, Catholic religion becoming negative and significant as a determinant of Protestant school attendance, and fundamentalist Protestant becoming positive and significant as a determinant of Protestant school attendance. similar to those obtained by the multinomial logit estimation with the religious variables even slightly more significant. The results are available upon request.

9 D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) Table 5 Multinomial logit estimate of Catholic, Protestant, and non-sectarian school attendance with religiosity Catholic Protestant Non-sectarian Coefficient Std. error Coefficient Std. error Coefficient Std. error Catholic.80 * Fundamentalist Other religion *.73 No religion ***.60 Attend Catholic.32 *** Attend fundamentalist ** Attend non-fundamentalist **.09 Income 1.94 * * 1.09 Income 2.64 * ** *.54 Income *.55 Income **.44 Income **.48 Income **.43 Income Income missing *.59 College graduate ***.38 Some college.68 *** High school dropout.81 ** Age.03 *** * African-American.77 *** *** Hispanic West East North Density % Catholic.06 ** % Catholic squared.001 ** % African-American ** **.01 % Hispanic Central city.71 *** *.31 Constant N 2447 * Significant at the 10% level. ** Idem, 5%. *** Idem, 1%. Note. The estimates are relative to public school attendance. Table 8 shows how religiosity affects the probability of attending Catholic schools, Protestant schools, non-sectarian private schools, and public schools. The predicted probabilities are generated from the multinomial regression presented above (Table 5). The probabilities are for a typical Catholic household, a typical Protestant fundamentalist household, and a typical black Protestant fundamentalist household. 9 The results 9 We set the quantitative variables of the typical household equal to their values at the mean: age = 52, percent black in the population = 13.15%, percent Catholic in the population = 20.94%, percent Hispanic in the population = 10.29% and density of population =.59. We set the dummy variables according to the categories that are most frequent: income category 4 ($25,000 $40,000), show that for a typical Catholic household church attendance has a large effect on the probability of attending a Catholic school. Catholics who attend church at least weekly are about as likely to send their children to Catholic schools as they are to send them to public schools. Catholic attendance at religious services is not strongly related to Protestant school attendance or nonsectarian school attendance. For the typical Protestant fundamentalist household, Protestant school attendance non-hispanic, region = North. We also calculated predicted probabilities based on a multinomial probit regression but do not report the results here because of space limitations. These results, which are similar to those obtained from the multinomial logit model, are available from the authors upon request.

10 94 D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) Table 6 Multinomial logit estimate of Catholic and Protestant schooling relative to public schooling, with and without non-sectarian schooling With non-sectarian alternative Without non-sectarian alternative Catholic Protestant Catholic Protestant Coeff. Std. error Coeff. Std. error Coeff. Std. error Coeff. Std. error Catholic Fundamentalist Other religion No religion Attend Catholic Attend fundamentalist Attend non-fundamentalist Income Income Income Income Income Income Income Income missing College graduate Some college High school dropout Age African-American Hispanic West East North Density % Catholic % Catholic squared % African-American % Hispanic Central city Constant N Note. The estimates are relative to public school attendance. is also shown to increase with church attendance. However, the magnitude of the relationship is not as strong as it was for Catholics and Catholic schools: Protestant fundamentalists who attend church at least weekly are more than twice as likely to attend public schools than Protestant schools. The probability that fundamentalist Protestants attend Catholic schools or non-sectarian private schools is not strongly related to attendance at religious services. Finally, for a typical black fundamentalist Protestant family, the results show that both Catholic school attendance and Protestant school attendance increase with religiosity. It is interesting to note that the relationship between Protestant church attendance and private school attendance is about the same for Catholic schools and Protestant schools about one in ten who attend church weekly send their children to Catholic schools or Protestant schools. Non-sectarian private school attendance is very low regardless of church attendance. 5. Implications for measuring the treatment effect of Catholic schools Our main result that religiosity substantially and significantly increases the demand for private schooling has implications for measuring the treatment effect of private schools. If religiosity is positively correlated with student outcomes and is not taken into account in estimates of educational outcomes, one tends to overestimate the causal effect of private schools on outcomes. In this section, we provide a quantitative sense on the magnitude of this bias. First, we use the GSS to estimate educational attainment (years of schooling) as a function of the number of

11 D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) Table 7 Multinomial logit estimates of Catholic and Protestant school attendance without religiosity Catholic Protestant Non-sectarian Coefficient Std. error Coefficient Std. error Coefficient Std. error Catholic 2.43 *** ** Fundamentalist *** Other religion No religion **.40 Income 1.97 * * 1.08 Income ** *.54 Income *.54 Income **.44 Income **.48 Income **.43 Income Income missing *.59 College graduate ** ***.38 Some college.61 *** * High school dropout 1.08 *** Age.04 *** * African-American.90 *** *** Hispanic West East North Density % Catholic.06 * % Catholic squared.001 ** *.0007 % African-American ** **.013 % Hispanic Central city.59 *** *.31 Constant N 2447 * Significant at the 10% level. ** Idem, 5%. *** Idem, 1%. Note. The estimates are relative to public school attendance. years the respondent attended a parochial grade school and/or high school with and without father s religiosity and mother s religiosity. Questions were asked for three years of the GSS on whether the respondent attended a parochial grade school and/or high school and, if so, for how many years. We use two years of the GSS (1988 and 1989) to estimate years of schooling as a function of the number of years the respondent attended a parochial grade school and/or high school, father s schooling, mother s schooling, gender, family income at age sixteen, region at age sixteen, type of residence (big city, suburb, etc.) at age sixteen, black, Hispanic, religious upbringing, mother s religiosity (measured by attendance at religious services), and father s religiosity. Two years of the GSS were used instead of the three because information on important background variables was not available for the third year. If no adjustment is made for parents religiosity, the effect of the parochial school variable was.073 and significant at the one percent level. This implies that if the respondent attended a parochial school for grade school and high school they had about one additional year of schooling relative to other respondents. If adjustments are made for parents religiosity, the parochial school coefficient declines to.04. Although these estimates are problematic because they do not control for selection, they suggest that if religiosity is omitted the parochial schooling coefficient is substantially biased upward. Next, we concentrate our analysis on Neal s (1997) careful study and illustrate the consequences of failing to control for religiosity in the outcome equation. Obviously, since we use a different data set and a different set of control variables we cannot estimate any possible bias in his study. We only aim at providing some

12 96 D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) Table 8 Predicted probabilities of type of school for Catholics, Protestant fundamentalists and black Protestant fundamentalists by church attendance Attendance Catholics Protestant fundamentalists Black Protestant fundamentalists Public Non-sectarian private Protestant Catholic Public Non-sectarian private Protestant Catholic Public Non-sectarian private Protestant Catholic Never Less than once/year Once or twice/year Several times/year Once/month Two or three times/month Nearly weekly Weekly More than once/week sense on the magnitude of this bias. Neal (1997) is well aware that there may be selection of superior students into Catholic schools with respect to some unobserved traits and addresses this issue by estimating a bivariate probit model of the following form: CH i = X i β + Z i δ + u i > 0, GR i = ach i + X i γ + ε i > 0, and [ ] ([ ] [ ]) ui 0 1 ρ N,, ε i 0 ρ 1 where GR i is a latent value of graduating from high school, CH i is a latent value of attending a Catholic school, X is a set of student characteristics and Z is a set of instruments for Catholic school attendance. He estimates two separate versions of this model, one for urban minorities and one for urban whites. For the estimates for whites he uses as instruments the density of Catholic schools and Catholic religion. For his estimates for blacks and Hispanics he uses as instruments Catholic religion and percent of Catholics in the county population. By using these instruments he implicitly assumes that his instruments are orthogonal to religiosity (conditional on the other controls). We can test this assumption using our data. We first run two OLS regressions of religiosity on his instruments and the other exogenous variables of the model, separately for whites and for blacks and Hispanics. In our estimation we include all his instruments but our set of control variables somewhat differ. The results are provided in Table 9, columns (1) and (2). The regression for whites indicates that both being Catholic (1% level) and the density of Catholic schools (10% level) have significant effects on religiosity. However, among minority pupils none of his instruments are found to be correlated with religiosity. These results indicate that while his main conclusion that urban minorities benefit greatly from access to Catholic schooling is robust to controlling for religiosity in the outcome equation, his estimated effect of Catholic schooling among whites is likely to be biased upward if religiosity is positively correlated with outcome as found in previous studies. In order to evaluate the magnitude of the selection bias in a simple way, we follow Altonji et al. (2005a) and ignore the fact that Y is estimated by a probit. Instead, we treat α as though it were estimated by an OLS regression of the latent variable GR i on X and on predicted Catholic school attendance (obtained from a probit estimation of Catholic school attendance on X and Z). Then, GR i = α PRECH + X γ + ε.

13 D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) Table 9 Conditional correlations between religiosity and Neal s instruments Religiosity Religiosity Whites Blacks & Hispanics Whites Blacks & Hispanics (1) (2) (3) (4) Coeff. t-statistics Coeff. t-statistics Coeff. t-statistics Coeff. t-statistics Constant PRECH % Catholics e Catholics schools per square mile Catholic Income Income Income Income Income Income Income Income missing College graduate Some college High school dropout Age African-American Hispanic Fundamentalist Protestant Other religion No religion East West North Central city e Density (1000s) % African-Americans e e 3.48 % Hispanics 7.7e e e e 3.59 N Suppose that the only missing variable in Neal s specification is religiosity. In this case, the true model is given by GR i = α PRECH + X γ + λ RELIGIOSITY, where λ is positive according to the existing literature. In this case, the relationship between the true treatment effect and the estimated one is given by α =ˆα λ R PRECH, (11) where R PRECH is the coefficient of predicted Catholic school attendance obtained from a regression of religiosity on all included regressors. That is, if religiosity is not correlated with predicted Catholic school attendance (R PRECH = 0) the estimated treatment effect is not biased. We can estimate the coefficient R PRECH using our data. This would require two stages. In the first stage, we estimate a probit regression of Catholic school attendance on Neal s instruments and on X. Fromthis regression we can obtain the predicted Catholic school attendance variable, PRECH. Then, we estimate by OLS the effect of PRECH on religiosity and obtain R PRECH. We apply this procedure separately for whites and for minority pupils. The results of the second stage, for whites and for minority students, are provided in Table 9, columns (3) and (4). 10 The results indicate that among minority pupils the correlation between PRECH and religiosity is positive but insignificant. Thus, we can say that Neal s results seem to be robust to controlling for religiosity. However, among whites the effect of predicted Catholic school attendance on religiosity, R PRECH, is very significant and is equal to The size 10 Because of space limitations we do not report here the results of the first stage. These are available from the author upon request. The standard errors of the second stage takes into account the preestimation of predicted Catholic school attendance.

14 98 D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) of R PRECH together with the marginal effect obtained by Neal allows us to find the minimal value of λ that will offset the entire effect of Catholic school attendance on the outcome. 11 Neal reports that the regular effect of Catholic school attendance on high school graduation is.724. He also reports that the sample high school graduation rate among whites is.76, which implies that the marginal effect of Catholic school attendance is.225. Substituting â =.225 and R PRECH = 3.55 we obtain that even an effect of religiosity on graduation from high school that is.063 is enough to offset the entire effect of Catholic school attendance on graduating from high school. In addition, if we assume that λ equals a proportion k of α and substitute this in (11) and solve for α we obtain that the real effect of Catholic school attendance on the outcome as a function of k is α =.225/( k). For example, if the effect of increased religiosity from never attending church to attending church weekly (from attend = 0toattend= 7) on graduating from high school is equal to the effect of Catholic school attendance on this outcome (k = 1/7), then the real effect of Catholic school attendance is.149, which is lower than Neal s estimated effect by 34% By doing this exercise we implicitly assume that the marginal effect of Catholic school attendance on outcome that was obtained by Neal using a probit estimation would be the same if was estimated by OLS. In some cases, however, marginal effects obtained from probit may differ substantially from those obtained by OLS (Altonji et al., 2005b). 12 Unfortunately, the existing literature does not provide rigorous evidence regarding the size of k. Previous studies estimating the probability of graduating from high school did not include both Catholic school attendance and parents religiosity in their estimation which would allow us to infer their relative effects. The only study from which we can infer a crude approximation regarding the size of k is Evans and Schwab (1995), who include in their estimation a dummy variable indicating whether the student attended church at least twice a month relative to never. They found that this variable increased the probability of graduating from high school by.048. Similarly, they found that attending a Catholic high school increases the probability of graduating from high school by.117. Thus, in their study the effect of student s religiosity on graduating from high school equals 41% of the effect of Catholic school attendance on this outcome. As their measure of religiosity differs from ours, we recoded our religiosity measure to a dummy variable indicating attending church at least twice a month relative to never and estimate the effect of predicted Catholic school attendance on this measure. We obtained that the coefficient of predicted Catholic school attendance on this religiosity measure is.787. Thus, if we assume that student s religiosity (used by Evans and Schwab) and parents religiosity (the same measure but for parents) have the same effect on high school graduation and on Catholic school attendance, we can substitute â =.225, R PRECH =.787 and k =.41 in (11) and solve for α. This yields α =.17, which is about 25% lower than Neal s estimated effect. This 6. Discussion One of the key results in this study is that both religion and religiosity have important effects on the demand for private schools. If religiosity is not taken into account, the measurement of the effect of religion will be seriously biased. Further, the effects of religion and religiosity vary depending upon the type of private school in question. It was shown that Catholic religiosity increases the demand for Catholic schools and has no effect on the demand for other types of private schooling. Fundamentalist Protestant religiosity increases the demand for Protestant schools and has no effect on the demand for other types of private schooling. Nonfundamentalist Protestant religiosity increases the demand for non-sectarian private schools and has no effect on the demand for other types of private schooling. It was also shown that households with no religion were more likely to choose non-sectarian private schools for their children. These results suggest that religiosity is a key factor that affects who attends private schools and who might respond to voucher initiatives. The latter point is supported by related research (Campbell et al., 2005). One of the implications of our findings is that competitive pressures in the education market are less substantial than they would otherwise be because of the limited substitutability of some types of (religious) schools. This means that vouchers restricted only to non-sectarian private schools will have a relatively small effect on enrollment in private schools. On the other hand, universal vouchers not only allow households to achieve better schooling for their children but also allow them to express their demand for religious education currently suppressed by the need to pay twice. Further, universal vouchers are likely to have a larger effect on enrollment in private schools since religious schools generally charge subsidized tuition. This conclusion is also supported by Cohen-Zada and Justman (2005) and Ferreyra (2007). Another implication is that locational choice processes work differently than they would in the traditional Tiebout model. According to Tiebout (1956), mobile consumers seek out a residence in a community that best matches their preferences for local public goods. Thus, competition among jurisdictions allows for a variety of bundles of public goods to be produced, and individuals choose among them by moving between jurisdictions. If religion and religiosity were unimportant factors of result is based upon many assumptions and should be interpreted with caution.

15 D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) school choice, then rich households would choose communities with high quality public schools and higher tax rates and housing values. Poor households would choose communities with low quality public schools and lower tax rates and housing values. In this case, households would stratify themselves into communities based on income. However, we show that religious households are substantially more inclined to send their children to religious schools. In this case, even if a religious household has a high income level, it will be less likely to locate in a school district with good public schools. The reason for this is that there is less of a reason to pay higher taxes and higher housing prices for higher quality public schools. As a result, communities will be religiously more homogeneous but varied in incomes. Other aspects of religion also bear upon who goes to private schools. It was shown that the share of Catholics in the population has a concave effect on the likelihood of attending Catholic schools. Further, it was shown that African-Americans, a disproportionately Protestant group, were more likely to attend Catholic schools and less likely to attend Protestant schools. One of the probable reasons for the Catholic result is that Catholic schools have been more open to minority students relative to other private schools (see Coleman et al., 1982). The most recent data puts the minority share in Catholic education at 27.1% in the United States (McDonald, 2005). In big cities like Chicago, the minority share is higher 37% in the Chicago Archdiocese. Of the blacks in Chicago Catholic schools, three out of four are not Catholic (Office of Catholic Schools, 2006). This would also help to explain our result that a larger black population results in more flight to Protestant schools and non-sectarian private schools than it does to Catholic schools. Finally, it was shown that failure to control for the effects of religiosity can result in seriously flawed estimates of the effect of private schools on educational attainment and, perhaps, other measures of academic achievement. It was shown that religiosity probably explains some of the seemingly positive effect of Catholic schools on high school graduation rates for non-hispanic whites in studies by Neal (1997) and others. It was also shown using the GSS that if religiosity is not taken into account, the effect of parochial schools on educational attainment increases by almost 75%. This does not necessarily imply that the effects of Catholic and other private schools are necessarily low or zero. As Neal (1997) and others show, urban minorities appear to gain from Catholic schools. References Altonji, J.G., Elder, T.E., Taber, C.R., 2005a. Selection on observed and unobserved variables: Assessing the effectiveness of Catholic schools. 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