Journal of Urban Economics 64 (2008) 85–100
www.elsevier.com/locate/jue
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.
© 2007 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.
E-mail address: [email protected] (D. Cohen-Zada).
0094-1190/$ – see front matter © 2007 Elsevier Inc. All rights reserved.
doi:10.1016/j.jue.2007.08.005
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-
86
D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) 85–100
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).
D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) 85–100
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 analysis4
2.1. 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 zi , and by its aftertax income yi . 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
⎧
a · ln(ci ) + (1 − α) ln(xi ) + RSJ
⎪
⎪
⎪
⎪ + β J · z + εJ
⎨
i
S
iS
(1)
U (ci , xi , zi ) =
if religious school,
⎪
⎪
J
⎪
a · ln(ci ) + (1 − α) ln(xi ) + εiS
⎪
⎩
if non-religious school,
where RSJ denotes the utility or disutility that a household of denomination J = (CA, PRT) with zi = 0 de4 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.
87
rives from the religious environment in religious schoolCA reflects
ing of type S = (CS, PS). For example, RCS
the utility that a Catholic household with zi = 0 derives from the religious environment in Catholic schoolJ
ing. We assume that RS=J
> RSJ=J , which means that
each household with zi = 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 {βSJ } reflects the effect of religiosity on
the utility that households derive from each type of religious schooling. Two assumptions are made on the eleJ
ments of the matrix β. First, we assume that βS=J
> 0,
which implies that religiosity increases the utility that
households derive from the religious schooling of their
J
denomination. Second, we assume that βS=J
> βSJ=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 βSJ=J
to be either positive or negative. A positive value of
βSJ=J implies that among households who belong to denomination J , religiosity increases the utility they derive from religious schooling of type S = J . On the
other hand, a negative value of βSJ=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 x̄. 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 pCS = r −γ 1 , and of Protestant schooling it
is pPS = (1−r)−γ 2 . On the other hand, the price of nonsectarian private schooling, pNS , is exogenous and does
not depend on the religious composition of the community. That is, pNS = 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.
88
D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) 85–100
2.2. 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 x̄. Therefore, it spends all its disposable income on consumption, ci = yi . Denoting by VSJ 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
J
J
= a · ln(yi ) + (1 − α) ln(x̄) + εiG
.
WGJ = VGJ + εiG
(2)
A household that chooses a Catholic school solves:
Max U (ci , xi , si )
J
J
J
+ βCS
· zi + εiCS
= a · ln(ci ) + (1 − α) ln(xi ) + RCS
s.t. c + x · pCS = yi ,
and has indirect utility
J
J
J
WCS
= VCS
+ εiCS
= a · ln(α) + (1 − α) · ln (1 − α)/pCS
J
J
J
+ ln(yi ) + RCS
+ βCS
· zi + εiCS
.
(3)
Similarly, a household that sends its child to a Protestant
school solves:
Max U (ci , xi , si )
J
J
J
+ βPS
· zi + εiPS
= a · ln(ci ) + (1 − α) ln(xi ) + RPS
s.t. c + x · pPS = yi .
Its utility is then
J
J
J
WPS
= VPS
+ εiPS
= a · ln(α) + (1 − α) · ln (1 − α)/pPS + ln(yi )
J
J
J
+ RPS
+ βPS
· zi + εiPS
.
(4)
Finally, a household that sends its child to a nonsectarian private school solves:
J
Max U (ci , xi , si ) = a · ln(ci ) + (1 − α) ln(xi ) + εiNS
s.t. c + x · pNS = yi ,
and derives utility
J
J
J
WNS
= VNS
+ εiNS
= a · ln(α) + (1 − α)
J
· ln (1 − α)/pNS + ln(yi ) + εiNS
.
(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:
πCS J
J
= VCS
− VGJ
log
πG
J
J
= f (α) + (1 − α) · ln(yi ) + RCS
+ βCS
· zi
+ γ1 · (1 − α) · ln(r) − (1 − α) · ln x̄.
(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
PRT . If β PRT is positive, religiosity inon the sign of βCS
CS
creases the probability that a Protestant household will
send its child to a Catholic rather than a public school.
PRT is negative, religiosity decreases the probaBut, if βCS
bility 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
πCS PRT
πCS CA
− log
log
πG
πG
CA
CA
PRT
PRT
· zi .
= RCS − RCS + βCS − βCS
(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
CA > β PRT , the effect of being Catholic on the probaβCS
CS
bility of attending a Catholic rather than a public school
is larger for higher values of zi . 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:
⎧
a + a1 · Catholici + a2 · zi
⎪
⎨ 0
πCS
· Catholic + a3 · zi · Protestant
=
(8)
log
⎪
πG
⎩ + a4 · ln(r) + a5 · ln(yi )
− a6 · ln x̄ + εi ,
D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) 85–100
CA − R PRT > 0 captures the effect of bewhere a1 = RCS
CS
CA > 0 captures the ining Catholic at zi = 0; a2 = βCS
crease in the Catholic effect when zi increases by one;
PRT captures the effect of Protestant religiosity
a3 = βCS
on the choice between Catholic and public schools, and
a4 = γ1 · (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 a5 = 1 − α > 0 and the coefficient of the quality of public schooling is a6 = −(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 + b1 · Catholici + b2 · zi
⎪
⎨ 0
πPS
· Catholic + b3 · zi · Protestant
=
log
(9)
⎪
πG
⎩ + b4 · ln(1 − r) + b5 · ln(yi )
− b6 · ln x̄ + εi ,
CA − R PRT < 0, b = β PRT > 0, b = β CA
where b1 = RPS
2
3
PS
PS
PS
can be either positive or negative and b4 = γ2 · (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
= f (α) + (1 − α) · ln(yi ) − (1 − α) · ln x̄
log
πG
− (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
89
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).
90
D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) 85–100
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 par-
ents 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 1972. 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
D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) 85–100
Table 1
Summary statistics
Variable
Mean
Standard deviation
Private school
Catholic school
Protestant school
Non-sectarian school
Income 1
Income 2
Income 3
Income 4
Income 5
Income 6
Income 7
Income missing
College graduate
Some college
High school dropout
Age
African-American
Hispanic
Catholic
Fundamentalist Protestant
Other Protestant
Other religion
No religion
Attend × Catholic
Attend × fundamentalist
Attend × other Protestant
East
West
North
Central city
Density (1000s)
Catholics
African-Americans
Hispanics
N
12.9%
7.1%
3.1%
2.7%
7.5%
13.2%
9.7%
17.6%
16.2%
12.7%
3.9%
8.3%
21.0%
26.3%
19.9%
51.7 years
17.0%
5.3%
23.5%
32.8%
27.6%
2.6%
10.1%
95.7
151.9
107.5
19.7%
17.6%
24.8%
22.1%
.59/square mile
20.8%
13.1%
10.3%
2447
33.5
25.7
17.4
16.2
26.4
33.8
29.6
38.1
36.8
33.3
19.3
27.6
40.8
44.0
39.9
15.4
37.6
22.4
42.4
47.0
44.7
16.0
30.1
215
268
221
39.8
38.1
43.2
41.5
.67
14.4
11.9
11.5
91
tion, 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, 1999–2000) 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
sample area. These variables were constructed from
several resources. First, county-level data on the population, Hispanic population, African-American popula-
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 (%)
Non-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
18.2
7.7
10.7
12.4
7.2
8.9
6.0
19.9
9.1
100
13.2
7.7
13.2
12.9
6.6
8.0
4.9
29.4
4.2
100
10.6
7.2
8.5
11.3
7.7
9.3
7.2
20.9
17.2
100
14.5
7.8
11.2
13.6
8.7
12.0
8.1
17.3
6.7
100
92
D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) 85–100
Table 3
Distribution of attendance at religious services by school type
Table 4
Probit estimate of private school attendance
Attendance
Nonsectarian (%)
Variable
Coefficient
18.2
3.0
4.5
12.1
13.6
9.1
7.6
16.7
15.2
100
Catholic
Fundamentalist
Other religion
No religion
Attend × Catholic
Attend × fundamentalist
Attend × non-fundamentalist
Income 1
Income 2
Income 3
Income 4
Income 5
Income 6
Income 7
Income missing
College graduate
Some college
High school dropout
Age
African-American
Hispanic
East
West
North
Density
% Catholic
% Catholic squared
% African-American
% Hispanic
Central city
Constant
N
.04
.07
.04
.20
.16***
.06***
.03
−.55***
−.45***
−.28*
−.20
−.18
−.18
−.12
−.26*
.32***
.28***
−.29**
.007***
−.09
−.08
.01
−.04
.03
.06
.02
−.00027
.011***
−.006
.26***
−2.11
2447
Catholic Protestant Public
(%)
(%)
(%)
Never
7.5
Less than once/year
2.9
Once or twice/year
5.7
Several times/year
10.9
Once/month
3.4
Two or three times/month 6.9
Nearly weekly
8.0
Weekly
43.1
More than once/week
11.5
All
100
7.9
3.9
5.3
14.5
5.3
7.9
7.9
27.6
19.7
100
19.4
8.4
11.5
12.4
7.4
9.1
5.8
17.8
8.4
100
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 assump-
tion we also run a multinomial probit regression. The results are very
Standard
error
.18
.18
.24
.17
.03
.02
.02
.19
.15
.15
.13
.13
.13
.18
.15
.10
.09
.12
.003
.11
.17
.16
.13
.13
.08
.01
.00019
.004
.005
.09
Marginal
effect
.01
.01
.01
.04
.03
.01
.005
−.07
−.07
−.04
−.03
−.03
−.03
−.02
−.04
.06
.05
−.05
.001
−.02
−.01
.002
−.007
.005
.01
.003
−.00005
.002
−.001
.05
* 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.
D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) 85–100
93
Table 5
Multinomial logit estimate of Catholic, Protestant, and non-sectarian school attendance with religiosity
Catholic
Coefficient
Catholic
Fundamentalist
Other religion
No religion
Attend × Catholic
Attend × fundamentalist
Attend × non-fundamentalist
Income 1
Income 2
Income 3
Income 4
Income 5
Income 6
Income 7
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
.80*
−.69
−.89
−.01
.32***
.13
−.01
−.94*
−.64*
−.33
−.35
.19
−.42
−.08
−.18
.16
.68***
−.81**
.03***
.77***
.03
−.22
.35
.20
.03
.06**
−.001**
.011
−.009
.71***
−6.3
2447
Protestant
Non-sectarian
Std. error
Coefficient
Std. error
Coefficient
Std. error
.46
.67
1.08
.55
.05
.09
.08
.53
.38
.39
.35
.32
.37
.45
.36
.26
.23
.33
.01
.29
.35
.37
.43
.35
.19
.03
.0005
.013
.01
.23
−.79
.38
−.63
−.48
−.17
.13**
.02
−.68
−1.38**
−.52
.06
−.44
.20
−.64
−.73
.56
.50
.06
−.018*
−1.06***
−.77
−.39
−.81
.30
.12
.06
−.001
.026**
−.003
.06
−3.5
.98
.54
1.09
.63
.25
.06
.09
.72
.70
.56
.44
.48
.44
.81
.70
.35
.32
.44
.009
.41
1.06
.48
.72
.40
.34
.04
.001
.011
.02
.34
−.02
.69
1.25*
1.65***
.03
.11
.19**
−2.03*
−.93*
−.96*
−.95**
−1.21**
−1.00**
−.30
−1.14*
1.43***
.39
−.73
.01
−.44
−.90
.49
−.35
−.70
.46
−.06
.0011
.028**
−.01
.55*
−4.8
1.1
.77
.73
.60
.18
.09
.09
1.09
.54
.55
.44
.48
.43
.54
.59
.38
.42
.61
.01
.43
1.07
.47
.63
.55
.30
.04
.0007
.01
.02
.31
* 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.
94
D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) 85–100
Table 6
Multinomial logit estimate of Catholic and Protestant schooling relative to public schooling, with and without non-sectarian schooling
With non-sectarian alternative
Catholic
Catholic
Fundamentalist
Other religion
No religion
Attend × Catholic
Attend × fundamentalist
Attend × non-fundamentalist
Income 1
Income 2
Income 3
Income 4
Income 5
Income 6
Income 7
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
Without non-sectarian alternative
Protestant
Catholic
Protestant
Coeff.
Std. error
Coeff.
Std. error
Coeff.
Std. error
Coeff.
Std. error
.80
−.69
−.89
−.01
.32
.13
−.01
−.94
−.64
−.33
−.35
.19
−.42
−.08
−.18
.16
.68
−.81
.03
.77
.03
−.22
.35
.20
.03
.06
−.001
.011
−.009
.71
−6.3
2447
.46
.67
1.08
.55
.05
.09
.08
.53
.38
.39
.35
.32
.37
.45
.36
.26
.23
.33
.01
.29
.35
.37
.43
.35
.19
.03
.00
.01
.01
.23
−.79
.38
−.63
−.48
−.17
.13
.02
−.68
−1.38
−.52
.06
−.44
.20
−.64
−.73
.56
.50
.06
−.018
−1.06
−.77
−.39
−.81
.30
.12
.06
−.001
.026
−.003
.06
−3.5
.98
.54
1.09
.63
.25
.06
.09
.72
.70
.56
.44
.48
.44
.81
.70
.35
.32
.44
.009
.41
1.06
.48
.72
.40
.34
.04
.001
.011
.02
.34
.80
−.70
−.91
−.01
.32
.13
−.01
−.94
−.63
−.34
−.36
.18
−.40
−.10
−.19
.15
.67
−.82
.03
.77
.03
−.20
.35
.19
.02
.06
−.001
.011
−.009
.71
−6.3
2447
.46
.67
1.1
.55
.05
.09
.08
.53
.38
.39
.35
.32
.38
.45
.36
.26
.23
.33
.01
.29
.35
.37
.43
.35
.19
.03
.0005
.013
.01
.23
−.79
.37
−.65
−.47
−.17
.14
.01
−.69
−1.38
−.53
.09
−.46
.21
−.63
−.73
.56
.50
.07
−.018
−1.07
−.79
−.39
−.84
.28
.12
.06
−.001
.026
−.004
.07
−3.4
.98
.54
1.09
.63
.25
.06
.09
.72
.70
.57
.44
.48
.44
.81
.70
.35
.32
.44
.009
.41
1.06
.48
.72
.40
.34
.04
.001
.011
.02
.34
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
D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) 85–100
95
Table 7
Multinomial logit estimates of Catholic and Protestant school attendance without religiosity
Catholic
Coefficient
Catholic
Fundamentalist
Other religion
No religion
Income 1
Income 2
Income 3
Income 4
Income 5
Income 6
Income 7
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
2.43***
.06
−.80
.11
−.97*
−.59
−.35
−.41
.18
−.38
−.02
−.003
.31
.61***
−1.08***
.04***
.90***
.12
−.18
.40
.28
−.10
.06*
−.001**
.012
−.007
.59***
−6.5
2447
Protestant
Non-sectarian
Std. error
Coefficient
Std. error
Coefficient
Std. error
.26
.32
1.04
.47
.52
.37
.38
.34
.31
.36
.44
.35
.25
.22
.32
.01
.29
.34
.36
.42
.34
.18
.03
.0005
.013
.01
.22
−1.36**
.64
.29
1.05
.57
.72
.70
.56
.44
.47
.44
.81
.70
.34
.32
.44
.009
.41
1.1
.48
.72
.40
.34
.04
.001
.012
.02
.34
−.70
.42
.44
.84**
−2.10*
−.98*
−.96*
−.98**
−1.2**
−.97**
−.27
−1.15*
1.53***
.46
−.78
.013
−.35
−.78
.43
−.27
−.65
.42
−.07
.0013*
.028**
−.012
.55*
−4.0
.53
.34
.58
.40
1.08
.54
.54
.44
.48
.43
.54
.59
.38
.42
.61
.01
.43
1.1
.47
.62
.54
.30
.04
.0007
.013
.02
.31
1.01***
−.69
−.51
−.74
−1.44**
−.53
.04
−.44
.23
−.64
−.74
.65**
.53*
.03
−.016*
−.99***
−.70
−.42
−.83
.30
.09
.06
−.001
.027**
−.002
.06
−3.5
* 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 ad-
justment 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
91.3
90.2
89.0
87.6
86.2
84.6
82.8
80.9
78.8
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:
.4
.4
.4
.5
.5
.6
.6
.7
.8
and
ui
0
1
∼N
,
0
ρ
εi
8.4
11.3
15.0
19.5
25.1
31.6
38.8
46.6
54.6
3.5
2.9
2.3
1.9
1.5
1.2
.9
.6
.5
.3
.3
.3
.3
.3
.2
.2
.2
.2
87.8
85.5
82.4
78.3
73.2
67.1
60.1
52.5
44.8
1.9
2.1
2.3
2.6
2.8
3.1
3.4
3.8
4.1
11.1
12.5
14.0
15.6
17.4
19.3
21.4
23.6
26.0
.5
.6
.6
.7
.8
.8
.9
1.0
1.0
86.5
84.9
83.1
81.1
79.0
76.7
74.3
71.7
68.9
4.3
4.8
5.4
6.0
6.7
7.5
8.3
9.2
10.1
GRi = aCH i + Xi γ + εi > 0,
4.1
4.6
5.2
5.9
6.6
7.4
8.3
9.3
10.3
CH i = Xi β + Zi δ + ui > 0,
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
Black Protestant fundamentalists
Protestant fundamentalists
Catholics
Attendance
Catholic Protestant Non-sectarian
Public
Catholic Protestant Non-sectarian
Public
Catholic Protestant Non-sectarian
Public
school (%) school (%) private school (%) school (%) school (%) school (%) private school (%) school (%) school (%) school (%) private school (%) school (%)
D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) 85–100
Table 8
Predicted probabilities of type of school for Catholics, Protestant fundamentalists and black Protestant fundamentalists by church attendance
96
ρ
1
,
where GRi 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 GRi on X and on
predicted Catholic school attendance (obtained from a
probit estimation of Catholic school attendance on X
and Z). Then,
GRi = α · PRECH + X γ + ε.
D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) 85–100
97
Table 9
Conditional correlations between religiosity and Neal’s instruments
Religiosity
Religiosity
Whites
Blacks & Hispanics
(1)
Constant
PRECH
% Catholics
Catholics schools per square mile
Catholic
Income 1
Income 2
Income 3
Income 4
Income 5
Income 6
Income 7
Income missing
College graduate
Some college
High school dropout
Age
African-American
Hispanic
Fundamentalist Protestant
Other religion
No religion
East
West
North
Central city
Density (1000s)
% African-Americans
% Hispanics
N
(2)
t-statistics
Coeff.
2.75
7.36
3.58
−.01
12.52
.67
−.37
.02
−.30
−.19
−.04
.10
−.03
.27
1.14
.19
−.82
.02
−1.50
1.77
4.08
−1.17
.09
−1.09
−.83
−.17
.43
−.08
.98
6.68
1.22
−4.52
4.57
4.3e–3
−4.30
−.35
−.27
−.68
.16
−.12
.91
.28
.53
−.48
.74
.56
−.45
.02
−.13
.40
−.32
−.84
−.52
−1.38
.30
−.23
1.74
.47
.59
−.84
1.78
1.97
−1.54
2.66
−.34
4.41
−2.97
−12.93
.42
−1.47
.75
.93
−2.99
1.51
.93
.65
1.71
−1.78
−.42
−.70
−.57
−.41
.16
6.3e–3
5.6e–3
2.30
1.34
−3.98
−.76
−1.60
−1.30
−1.50
.27
.49
.48
1786
GRi = 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 = α̂ − λ · RPRECH ,
t-statistics
4.36
519
Suppose that the only missing variable in Neal’s specification is religiosity. In this case, the true model is given
by
(11)
where RPRECH 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 (RPRECH = 0) the estimated treatment effect is
not biased. We can estimate the coefficient RPRECH 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. From this
Blacks & Hispanics
(3)
Coeff.
.70
−1.08
−2.77
.12
−.32
.16
.17
−.95
.01
7.7e–3
Whites
(4)
Coeff.
t-statistics
2.82
3.55
−.01
7.98
4.83
−1.35
−.23
.09
−.26
−.08
−.01
.25
.01
.25
1.14
.10
−.60
.01
.72
−1.01
−2.82
.35
−.27
.31
9.8e–3
−.45
.01
7.1e–3
Coeff.
t-statistics
3.35
.61
4.38
.37
−1.25
−.10
−.73
.34
−.95
−.35
−.05
1.04
.04
.93
6.70
.64
−3.24
2.93
−.24
−.62
.23
−.10
.87
.22
.46
−.48
.63
.53
−.44
.02
.09
−.46
−1.23
.44
−.19
1.62
.36
.50
−.85
1.40
1.74
−1.49
2.43
.28
4.63
−2.80
−13.54
1.25
−1.28
1.52
.05
−3.25
1.43
.87
.78
2.94
1786
−1.61
−.53
−.61
−.65
−.43
.09
6.1e–3
6.7e–3
−3.81
−.84
−1.34
−1.38
−1.54
.16
.48
.59
515
regression we can obtain the predicted Catholic school
attendance variable, PRECH. Then, we estimate by
OLS the effect of PRECH on religiosity and obtain
RPRECH . 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,
RPRECH , is very significant and is equal to 3.55. 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.
98
D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) 85–100
of RPRECH 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 RPRECH = 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/(1 +
3.55k). For example, if the effect of increased religiosity
from never attending church to attending church weekly
(from attend = 0 to attend = 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%.12
11 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,
RPRECH = .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.
D. Cohen-Zada, W. Sander / Journal of Urban Economics 64 (2008) 85–100
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.
99
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