Catholic schools, dropout rates and educational attainment.

Sander, William ; Krautmann, Anthony C.

I. INTRODUCTION

Several studies suggest that Catholic schools have a positive effect on academic achievement (Bryk, Lee, and Holland [1993], Chubb and Moe [1990], Coleman and Hoffer [1987], Coleman, Hoffer, and Kilgore [1982b], Greeley [1982], and Hoffer, Greeley, and Coleman [1985]). One of the criticisms of studies on Catholic and other private schooling is that private schools select their students. Thus, seemingly favorable private school effects could be a result of selection rather than causation (Goldberger and Cain [1982], Hanushek [1986], Murnane [1985], Noell [1982]).

This is an important issue because private school choice is perceived by some as a solution to problems in many school systems in the United States - particularly in big cities like Chicago. If positive private school effects are the result of selection, school choice initiatives may not help.

None of the key studies on Catholic schools (those cited above) have adequately solved the selection problem. Although they adjust for many observable variables that might affect academic achievement, the problem of unobservable effects on achievement remains unsolved.

In this paper, we examine the effect of Catholic school attendance on high-school dropout rates and educational attainment. Particular attention is given to the effect of selection on educational outcomes. We focus on Catholic schools because they dominate the private secondary school sector. In 1991, about 11 percent of primary and secondary school students attended private schools. Within the private school sector, about 54 percent attended Catholic schools, 32 percent attended other parochial schools, and 15 percent attended non-sectarian schools (U.S. Department of Commerce [1991]). At the high-school level, 91 percent of secondary school students in the private sector attended parochial schools; of these, 80 percent were in Catholic schools (U.S. Department of Commerce [1993]). Thus, the private secondary school sector is dominated by Catholic schools. Another reason for our focus on Catholic schools is that a relatively large number of observations are available on students in Catholic schools making it easier to identify the effects of Catholic schooling on academic achievement. Data sets are usually too small to identify the effects of other types of private schooling on academic achievement.

Our results indicate that after adjusting for self-selection, Catholic schooling reduces the odds that sophomores do not graduate with their class by about ten percentage points. Although Catholic schools have favorable effects on the dropout rate, we do not find any favorable effect on educational attainment for seniors six years after their senior year in high school. That is, after adjusting for self-selection seniors in Catholic schools were not more likely to acquire more schooling than seniors in public schools after taking into account other background factors. Further, we find that self-selection explains why Catholic schools' seniors tend to acquire more schooling.

The paper is organized as follows. First, background issues are discussed. Second, a model is presented. Third, the data are reviewed. Fourth, the empirical results are examined. The paper closes with a brief concluding section. The paper also includes an appendix using a different data set to examine the effect of parochial schooling on educational attainment.

II. BACKGROUND

Economic theory suggests that investments in schooling are related to supply and demand factors (Becker and Tomes [1986], Blaug [1970], Chiswick [1988]). The demand for schooling derives, in part, from parents' utility being related to their children's well-being. The demand curve is downward sloping because at lower rates of return there would be less of an incentive to invest in schooling. The demand curve of better endowed children is to the right of the demand curve of other children because of either innate ability or because they come from households that produce more acquired ability. Numerous studies indicate that parents with more ability, higher income, and more schooling tend to produce children who acquire more ability through schooling (Becker and Tomes [1986], Chiswick [1988], Haveman, Wolfe, and Spaulding [1991]).

The supply of funds for schooling is related to the marginal cost of the investment. The supply curve is upward sloping because at higher interest rates more funds would be available for investments in schooling. The supply curve is to the right for those who can self-finance the expenditure, rather than borrow the funds, because of imperfect access to market debt. Thus, family background might also affect education through the family's ability to supply funds for investments in schooling.

Many other background factors, including race, religion, and ethnicity, could affect investments in schooling. Religious background is of particular interest because a Catholic school effect on academic achievement could be confounded with religion effects. Coleman and Hoffer [1987] argue that there is a positive Catholic effect on academic achievement because the Catholic community provides social capital which contributes to educational attainment. A Catholic background might have other effects on education. For example, Lenski [1963] and Hardy [1974] argue that Catholics have a relatively low preference for education. Greeley ([1976; 1981; 1990]) and others have largely discredited this view. Some studies indicate that Catholics have had, at least in the past, a relatively high fertility rate (Mosher, Johnson, and Horn [1986], Westoff and Jones [1979]). If there is a tradeoff between number of children and education, then a Catholic background could have a negative effect on schooling (Becker [1991]). If the "cost" of divorce is higher for Catholics (Freidan [1974], Michael and Tuma [1985]), this could result in higher levels of academic achievement through higher levels of marital stability.

Several studies on Catholic schools indicate that Catholic high schools are superior to public high schools, other things being equal (Bryk, Lee, and Holland [1993], Coleman, Hoffer, and Kilgore [1982b], Coleman and Hoffer [1987], Greeley [1982], Hoffer, Greeley, and Coleman [1985]). Some of the arguments that are made for these positive effects include the emphasis on a core curriculum, Catholic schools being embedded within a larger communal organization, and the decentralized nature of Catholic education. The results for non-Catholic private schools are less conclusive. Coleman, Hoffer, and Kilgore's study indicates that academic achievement is relatively high in non-Catholic private schools; the Coleman and Hoffer study finds that the dropout rate in other private schools is no lower than it is in public schools. As noted above, these studies are controversial because of the problem of self-selection. Critics claim that a positive Catholic/private school effect has not been properly demonstrated (Goldberger and Cain [1982], Hanushek [1986], Murnane [1984]). Further, Noell [1982] reanalyzed the data used by Coleman, Hoffer, and Kilgore [1982b] and could not confirm a positive Catholic school effect on achievement.(1)

We would note that a positive Catholic school effect on academic achievement cannot be attributed to higher expenditures - Catholic schools spend substantially less than public schools. In 1991, the average tuition in Catholic schools was $2,593, while the per pupil expenditures in the public school sector was $5,824 (U.S. Department of Commerce [1993]). Although tuition is not perfectly correlated with per pupil expenditures, all of the evidence shows that Catholic school expenditures are substantially less. Some of the reasons for this include a relatively small bureaucracy, lower teacher salaries, and fewer students with disabilities in the Catholic schools.

Other religious orientations might also affect educational attainment. Perhaps the most important finding on other religions is that a Jewish background has a strong positive effect on student achievement (Chiswick [1983; 1986; 1988]). Sander [1992] finds that Catholics, Episcopalians, Methodists, and Mormons acquire more schooling than Baptists, Lutherans, other Protestants and those with no religion.

Regarding race, studies indicate that Blacks receive lower quality schooling (e.g., Card and Krueger [1992b]). This should reduce educational attainment. Important ethnic relationships include negative Hispanic effects - particularly on achievement tests related to language (Rosenthal, Baker, and Ginsburg [1983]) - and positive effects of an Asian heritage on educational attainment (Hirschman and Wong [1986]).

Location could also affect education attainment. T. W. Schultz [1967; 1981; 1990] has long argued that public schools in the rural sector are of relatively low quality; he now makes this argument for public schools in big cities as well. Location could affect the quality of schooling in several ways. Most importantly, location could affect the quantity and quality of resources that are available for schools, as well as how efficiently resources are used. For example, schools in rural areas are often too small to efficiently exploit economies of scale. There is some disagreement on the effect of resources. On the one hand, Hanushek [1986] and Chubb and Moe [1990] find little empirical support for the hypothesis that resources affect academic achievement. On the other hand, recent studies by Card and Krueger [1992a], Ferguson [1991], and Sander [1993] indicate that resources are very important - particularly if they are used to improve the number and quality of teachers.

III. MODEL

If self-selection is ignored, estimates of the effect of Catholic schools on educational attainment can be biased because relevant variables are omitted (Goldberger and Cain [1982], Barnow, Cain and Goldberger [1986]). We control for self-selection by separately estimating a model of the Catholic school participation decision (see Maddala [1983]). In the case of the educational attainment model, our estimation procedure follows that suggested by Heckman [1979]. For estimating the dropout rate, we estimate a bivariate probit as suggested by Greene [1993].

More formally, let an individual's educational outcome, Y, depend on a vector of individual-specific characteristics X, as well as the type of school attended, I:

(1) [Y.sub.i] = f([X.sub.i], [I.sub.i]) + [u.sub.i]

where [I.sub.i] is a dummy variable indicating whether the individual goes to a Catholic (I = 1) or a public ([I.sub.i] = 0) school. Because the individual (or parents) endogenously decide upon the type of school, ordinary-least-squares estimates of the effect of I, the type of school, will be biased. This problem can be overcome in the following manner. Let us assume that the students who attend both Catholic and public schools are drawn from a common population and that the coefficients in (1) are independent of school choice.(2) The participation decision on type of schooling can be modeled as

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is an unobservable index determining whether an individual goes to a Catholic school, and (u, [Epsilon]) are distributed as bivariate normal [0, 0, [[Sigma].sub.u], [[Sigma].sub.[Epsilon]], [[Sigma].sub.u[Epsilon]]]. That is, if [Mathematical Expression Omitted], the individual attends a Catholic school; if [Mathematical Expression Omitted], he attends a public school. Even though we cannot observe [Mathematical Expression Omitted], we can observe the individual's school choice. This observable choice is represented by the binary index [I.sub.i] such that

[Mathematical Expression Omitted].

For the educational attainment model, we have

(4) [Y.sub.i] = [X.sub.i][Beta] + [I.sub.i][Alpha] + [u.sub.i].

Let f([center dot]) denote the standard normal probability density function and F ([center dot]) denote the standard normal cumulative distribution function. For Catholic school students, we have

(5) E[[Y.sub.i] [where] [I.sub.i] = 1] = [X.sub.i][Beta] + [Alpha] + E[u [where] [I.sub.i] = 1] = [X.sub.i][Beta] + [Alpha] ([[Sigma].sub.u[Epsilon]]/[[Sigma].sub.e]) f([Z.sub.i][Tau])/F([Z.sub.i][Tau]).

For public school students, the counterpart to (4) is given by

(6) E[[Y.sub.i] [where] [I.sub.i] = 0] = [X.sub.i][Beta] + E[u [where] [I.sub.i] = 0] = [X.sub.i][Beta] + ([[Sigma].sub.u[Epsilon]]/[[Sigma].sub.e]) {-f([Z.sub.i][Tau])/[1 - F([Z.sub.i][Tau])]].

Equations (5) and (6) show that the empirical model for educational attainment includes selection-correction terms as relevant variables when regressions are fitted on selected samples, even though it does not arise in the underlying structural model.

Heckman [1979] suggests the following two-stage procedure for estimating the parameters of this type of self-selection model. In the first stage, one estimates [Tau] in (2) with a probit model, which is then used to compute the selection-correction terms in (5) and (6). In the second stage, consistent estimates of [Beta], [Alpha], and [[Sigma].sub.u[Epsilon]] are obtained by least squares regression. A test for selectivity bias is then a test of the hypothesis that [[Sigma].sub.u[Epsilon]] = 0.

For the dropout rate, a probit model is estimated, given by

(7) [Y.sub.i] = [X.sub.i][Beta] + [I.sub.i][Alpha] + [u.sub.i]

where [Y.sub.i] = 1 if the individual quits high school before graduating, and 0 otherwise. Equation (7) is estimated simultaneously with (2). Assuming ([u.sub.i], [[Epsilon].sub.i]) are distributed as a bivariate normal [0, 0, 1, 1, [[Sigma].sub.u[Epsilon]]], we obtain the full-information maximum likelihood estimates of (7) and (2). The simple t-test of the hypothesis [[Sigma].sub.u[Epsilon]] = 0 is equivalent to the Wald test.

For identification, it is desirable to utilize a different set of exogenous variables for the structural and selection equations.(3) Ideally, one would like a set of identifying variables that are highly correlated with the selection process yet uncorrelated with the dependent variable in the structural equation. In preliminary work with the data, we tried several different identifying procedures. Following Noell [1982], we first used Catholic to identify the model; then Catholic was excluded in the second stage. We subsequently rejected this approach because being Catholic could affect educational outcomes (see Sander [1992]). Next we considered using a measure of religiosity (frequency of church attendance) to identify the model because there is evidence that "religious" parents tend to send their children to Catholic schools. Once again, we rejected this approach because religiosity could affect educational outcomes (see Sander [1992]). The procedure that we ultimately selected for identification included using five interaction terms. Four of the interaction terms are between urban and region; four regions with high concentrations of Catholics were selected. The other interaction term is between urban and Catholic. The rationale for our approach is that Catholic school attendance is more likely in such areas because of economies of scale; i.e., Catholic schools need a relatively large number of Catholics to support a Catholic school - particularly a high school. It seems reasonable that these variables are relatively exogenous to school choice because Catholics are unlikely to migrate to these locations simply because of the higher quality Catholic schooling. The other variables in the first stage of our model include most of the same variables that are used to estimate educational outcomes.

In addition to Catholic school, the independent variables in the second stage include region (relative to Pacific), urban and suburban (relative to rural), father's schooling (in years), mother's schooling (in years), family income, religion (relative to Protestants who are not Baptists), male, Black, Hispanic, and Asian. The two educational outcomes estimated are: (1) the odds that sophomores did not graduate with their class (called the dropout-rate model) and (2) the years of schooling attained by seniors, six years after their senior year (called the educational-attainment model).

Two-stage least squares is used to estimate educational attainment and bivariate probit is used to estimate the dropout rate. Two forms of each model are estimated to investigate the effect of selectivity on parameter estimates. In the first estimate, there is no correction for selectivity bias; in the second estimate, there is a correction.

IV. DATA

The data for the dropout-rate estimates are taken from the third follow-up survey of the "High School and Beyond 1980 Sophomore Cohort Survey." The data for the educational attainment estimates are taken from the third follow-up survey of the "High School and Beyond 1980 Senior Cohort Survey." The base year survey in 1980 was used by Coleman, Hoffer, and Kilgore [1982b] in their High School Achievement. Also, Bryk, Lee and Holland [1993] use data from the "High School and Beyond" data set.

The third follow-up was undertaken in 1986 and consists primarily of a subsample of the base year survey. The base year survey was comprised of students from different types of high schools including public schools, Catholic schools, and other private schools. Further, certain types of schools were oversampled. There were about twelve thousand seniors who were sampled and fifteen thousand sophomores. The response rate was 88 percent for seniors and 91 percent for sophomores. In this study, we use data from the regular sample of public schools and Catholic schools which reflects the proportion found in the general population. We would note that because of missing data on some of the key variables, we were only able to use part of the sample. However, in other work with the data that is not reported, we could not find any important bias that resulted from excluding observations with missing values. Summary statistics for the data sets are presented below in Table I. Table II contains data on the dropout rate and educational attainment broken down by type of school.

V. RESULTS

Probit estimates of the odds of attending a Catholic high school (the first stage of our model) are presented in Table III. The results for sophomores indicate that regional and suburban locations, parents' education, family income, being Catholic, and living in a Middle Atlantic urban area all have significant positive effects on the odds of attending a Catholic school. Being Hispanic or male has a significant negative effect on this probability.

For seniors, regional and suburban locations, family income, being Catholic or Black, and having a middle Atlantic urban residency as well as being Catholic and urban, have significant positive effects on the odds of attending a Catholic school. Being male and living in an urban area have significant negative effects on the likelihood of going to a Catholic school.

The results in Table IV indicate that Catholic schooling has a highly significant negative effect on the odds of dropping out. Further, the magnitude of the Catholic school effect is relatively large. If the other coefficients in the "corrected" estimate are evaluated at their mean values, the estimated probability of dropping out in the public school sector is .12; it declines to .02 for the Catholic school sector. Thus, Catholic schooling reduces the odds of dropping out by .10. The "not corrected" and "corrected" estimates of the dropout rate are very similar and are not statistically different.(4) Consistent with the slight differences between the corrected and not-corrected models, the selection-correction term (Lambda) was not significant.

The other significant determinants of the dropout rate are as follows. Middle Atlantic residence, father's schooling, mother's schooling, income, and Black or Asian ethnicity have significant negative effects on the dropout rate. The Urban, Baptist, other religion, and no religion variables have significant positive effects on the odds of dropping out.

TABLE I
Summary Statistics

 Standard
 Mean Deviation

Sophomores

Dropout 11.9% 32.4
Catholic School 16.2% 36.9
Father's Schooling 13.1 years 2.7
Mother's Schooling 12.7 years 2.1
Family Income (1980 $s) $22,802 12,303
Urban 15.6% 36.3
Suburban 50.2% 50.0
Catholic 40.0% 49.0
Baptist 18.1% 38.5
Jewish 1.0% 9.9
Other Religion (non-Protestant) 4.2% 20.1
No Religion 4.6% 21.2
Male 48.8% 50.0
Black 6.5% 24.6
Hispanic 11.1% 31.4
Asian 2.0% 14.1
New England 5.7% 23.2
Middle Atlantic 17.6% 38.1
South Atlantic 13.0% 33.7
East South Central 6.5% 24.7
West South Central 8.3% 27.5
East North Central 23.4% 42.4
West North Central 11.9% 32.3
Mountain 3.8% 19.2

Seniors

Educational Attainment 13.2 years 1.7
Catholic School 7.2% 25.8
Father's Schooling 12.9 years 2.7
Mother's Schooling 12.6 years 2.1
Family Income (1980 $s) $22,914 12,792
Urban 20.6% 40.5
Suburban 47.0% 49.9
Catholic 32.3% 46.8
Baptist 23.9% 42.7
Jewish 1.6% 12.6
Other Religion (non-Protestant) 3.6% 18.7
No Religion 4.8% 21.3
Male 46.1% 49.9
Black 17.2% 37.7
Hispanic 13.5% 34.2
Asian 3.0% 17.2
New England 5.5% 22.8
Middle Atlantic 15.1% 35.8
South Atlantic 16.6% 37.2
East South Central 7.2% 25.8
West South Central 9.1% 28.8
East North Central 22.0% 41.5
West North Central 9.2% 28.9
Mountain 3.7% 18.9
TABLE II
Academic Achievement by Sector

 Standard
 Mean Deviation

Catholic Sector

Dropout Rate 1.5% 12.3
Educational Attainment 13.7 years 1.9

Public Sector

Dropout Rate 13.9% 34.6
Educational Attainment 13.1 years 1.7

The "uncorrected" estimate of educational attainment indicates that Catholic schooling has a significant positive effect (Table V). However, the "corrected" estimate shows that, after adjusting for selection in the Catholic sector, the Catholic school coefficient becomes insignificant. Together with the significantly positive coefficient on Lambda, the selection-correction term, our estimates suggest that this Catholic school effect is primarily a result of selection.

The other determinants of educational attainment are about the same in the two models. The significant positive coefficients include the regional variables for New England, Middle Atlantic, South Atlantic, East South Central, East North Central, and West North Central, father's schooling, mother's schooling, income, Jewish, and Asian. Being Baptist, of no religion, male, Black, and Hispanic have significant negative effects on educational attainment.

VI. CONCLUSIONS

Our findings indicate that Catholic high schools have a large negative effect on the high-school dropout rate. Thus, our results provide support for other studies including Bryk, Lee and Holland [1993], Coleman, Hoffer and Kilgore [1982b] and Greeley [1982] that also find that Catholic high schools have a significant negative effect on the dropout rate. On the other hand, seniors in Catholic high schools are no more likely to acquire more schooling than seniors in public high schools if adjustments are made for selectivity and other background factors. This may simply indicate that parents who send their children to Catholic high schools value education highly and are willing to spend more for their children's education.

The Catholic school effect on the dropout rate is particularly noteworthy since many inner-city high schools have very high rates. For example, the rate in Chicago is about 50 percent (Sander [1993]). Since high dropout rates are associated with low earnings, welfare dependency, illegitimacy, crime, and many other social ills, strategies to reduce it are essential. Our study suggests that the Catholic school experience is very relevant.

In closing, it is important to note that our findings do not necessarily hold for non-Catholic private schools. As Bryk, Lee, and Holland [1993] demonstrate, favorable Catholic school effects on academic achievement are at least partly the result of the specific nature of Catholic education. Thus, an expansion of the non-Catholic private school sector through voucher programs or other means might not result in improvements in education. On the other hand, an expansion of the non-Catholic private school sector could have large, positive effects on the quality of education. At a minimum, more research is needed on other types of private schooling.

TABLE III

Probit Estimates of Probability of Attending Catholic School
(Standard Errors in Parentheses)

 Sophomores Seniors

New England .61(***) .23
 (.12) (.17)
Middle Atlantic .39(***) .46(***)
 (.10) (.13)
South Atlantic .12 -.15
 (.15) (.18)
West South Central .84(***) .47(***)
 (.13) (.16)
East North Central .33(***) .38(***)
 (.10) (.13)
West North Central .50(***) .44(***)
 (.12) (.16)
Urban .16 -1.04(**)
 (.22) (.46)
Suburban .52(***) .58(***)
 (.08) (.10)
Father's Schooling .03(***) .02
 (.01) (.02)
Mother's Schooling .07(***) .01
 (.01) (.02)
Income x [10.sup.-2] .00087(***) .0008(**)
 (.00023) (.0003)
Catholic Religion 1.69(***) 1.49(***)
 (.07) (.10)
Black -.09 .41(***)
 (.16) (.14)
Hispanic -.52(***) -.13
 (.10) (.10)
Asian -.20 -.02
 (.22) (.24)
Male -.13(**) -.28(***)
 (.05) (.07)
New England x Urban -4.56 -3.49
 (25,000) (50.09)
Mid Atlantic x Urban .95(***) 1.06(***)
 (.22) (.27)
East North Central x Urban .32 .31
 (.23) (.28)
West North Central x Urban -4.40 -3.32
 (12110) (41.98)
Urban x Catholic -.21 1.04(**)
 (.19) (.41)
Constant -4.11(***) -3.55(***)
 (.21) (.27)
Chi-Squared 1,473(***) 716(***)
N 4,816 4,397

* Significant at the 10% level.

** Significant at the 5% level.

*** Significant at the 1% level.
TABLE IV

Probit Estimates of the Dropout Rate
(Standard Errors in Parentheses)

 Not Corrected Corrected

Catholic School -.81(***) -.76(**)
 (.13) (.35)
New England -.10 -.10
 (.14) (.15)
Middle Atlantic -.24(**) -.25(**)
 (.11) (.11)
South Atlantic .04 .04
 (.11) (.11)
East South Central -.001 -.003
 (.12) (.13)
West South Central .18 .17
 (.12) (.12)
East North Central -.13 -.13
 (.10) (.10)
West North Central -.10 -.11
 (.11) (.11)
Mountain .05 .05
 (.14) (.14)
Urban .18(**) .18(**)
 (.07) (.07)
Suburban .002 .0002
 (.06) (.06)
Father's Schooling -.08(***) -.08(***)
 (.01) (.01)
Mother's Schooling -.07(***) -.07(***)
 (.02) (.02)
Income x [10.sup.-2] -.00044(*) -.00044(*)
 (.00024) (.0024)
Catholic Religion -.09 -.10
 (.07) (.11)
Baptist .13(*) .13(*)
 (.07) (.07)
Jewish .16 .16
 (.31) (.31)
Other Religion .20(*) .20(*)
 (.12) (.12)
No Religion .63(***) .63(***)
 (.10) (.10)
Male .04 .04
 (.05) (.05)
Black -.21(**) -.21(**)
 (.10) (.10)
Hispanic .13(*) .13(*)
 (.07) (.08)
Asian -.70(***) -.70(***)
 (.25) (.25)
Lambda -- .03
 (.20)
Constant .85(***) .86(***)
 (.22) (.23)
Chi-Squared 408.7(***) 408.7(***)
N 4,816 4,816

* Significant at the 10% level.

** Significant at the 5% level.

*** Significant at the 1% level.
TABLE V

Estimates of Educational Attainment
(Standard Errors in Parentheses)

 Not Corrected Corrected

Catholic School .36(***) -.26
 (.10) (.36)
New England .39(***) .40(***)
(.13) (.13)
Middle Atlantic .35(***) .41(***)
 (.10) (.10)
South Atlantic .18(*) .20(**)
 (.10) (.10)
East South Central .24(**) .27(**)
 (.12) (.12)
West South Central .05 .09
 (.11) (.11)
East North Central .25(***) .29(***)
 (.09) (.09)
West North Central .35(***) .38(***)
 (.11) (.11)
Mountain -.22 -.21
 (.15) (.15)
Urban -.02 -.01
 (.07) (.07)
Suburban -.04 -.02
 (.06) (.06)
Father's Schooling .07(***) .07(***)
 (.01) (.01)
Mother's Schooling .08(***) .08(***)
 (.01) (.01)
Income x [10.sup.-2] .0010(***) .0011(***)
 (.0002) (.0002)
Catholic Religion -.003 .12
 (.06) (.09)
Baptist -.14(**) -.14(**)
 (.07) (.07)
Jewish .78(***) .76(***)
 (.20) (.20)
Other Religion -.15 -.14
 (.14) (.14)
No Religion -.24(**) -.24(**)
 (.12) (.12)
Male -.08(*) -.10(**)
 (.05) (.05)
Black -.27(***) -.26(***)
 (.07) (.07)
Hispanic -.48(***) -.49(***)
 (.07) (.08)
Asian .49(***) .50(***)
 (.15) (.15)
Lambda - .36(*)
 (.20)
Constant 10.95(***) 10.88(***)
 (.18) (.19)
[R.sup.2] .11 .11
N 4,392 4,392

* Significant at the 10% level.

** Significant at the 5% level.

*** Significant at the 1% level.

APPENDIX

In preliminary work on this paper, we estimated the effect of parochial schooling on educational attainment using data from the National Opinion Research Center's "General Social Survey." Below, we review this work and findings.

The first stage of our model consists of a probit estimate of the odds that the individual attended a parochial primary or secondary school. The second stage consists of estimating educational attainment controlling for parochial school attendance, self-selection, and other background variables. In the first stage, three different specifications of the parochial schooling variable are considered. In the first model, the odds that the individual has at least eight years of parochial schooling is estimated. The odds that the respondent has at least nine years of parochial schooling (at least some parochial high schooling) is estimated in the second model. In the third model, the likelihood that the respondent has twelve years of parochial primary and secondary schooling is estimated. Only respondents with at least twelve years of schooling are included in the third model. (In other work with the data we also estimated a model where the respondent had at least one year of parochial schooling. These results were not significantly different from the results for at least eight years of parochial schooling). Our three specifications give us the effect, if any, of at least an elementary education in a parochial school (model 1), some secondary education in a parochial school (model 2), and all primary and secondary education in a parochial school (model 3). We would note that all of our probit models are significant at the 1 percent level.

To identify the first stage of the model, we used all of the variables in the second stage apart from the suspected endogenous variables (the parochial schooling variables) and three additional variables for identification. The three identifying variables are interaction terms between Catholic and Urban, Catholic and East, and Catholic and North Central. These variables were selected for identification because parochial school attendance is more likely in areas where there are relatively large concentrations of Catholics (i.e., urban areas, the East, and the North Central region).

The other background variables in the estimates of educational attainment include mother's schooling (in years), father's schooling (in years), being Black, Hispanic, or male, region of residence at age sixteen (relative to South), religious upbringing (Catholic or Jewish), type of residence at age sixteen (relative to metropolitan areas of over 250,000), age and age squared. Dummy variables that are not reported are included for the survey year.

The General Social Survey consists of a sample of approximately 1,500 English-speaking persons eighteen years of age or older living in non-institutional arrangements in the United States. The survey is cross-sectional rather than longitudinal; that is, a new sample is drawn each year. The survey has been undertaken since 1972 (excluding 1979 and 1981). For 1988, 1989, and 1991, respondents were asked how many years they attended a parochial primary or secondary school. We use the data from these three years of the survey. Unfortunately, we cannot separate out respondents who attended a non-parochial private school (less than 2 percent of the population). Thus, our analysis focuses on the effect of parochial schools relative to public schools and other private schools. Since the other private sector is relatively small (it accounts for about 2 percent of the non-parochial sector), the bias that might be associated by including it should be very small.

The sample employed in the model is restricted to American-born respondents between the ages of twenty-five and fifty-four. Younger respondents are excluded because a high percentage are still in school. Older individuals are excluded because of the problems associated with aggregating cohorts of different vintages. Ideally, one would like to estimate parochial school effects for different age groups; unfortunately, the data set is not large enough.

Summary statistics on the dependent variable are presented below in Table VI. They indicate that respondents who have attended parochial schools have acquired more schooling. For example, respondents with at least nine years of parochial schooling have an average of 14.7 years of schooling while respondents in the non-parochial sector have only 13.7 years.

TABLE VI
Summary Statistics

Years of Parochial Schooling Years of Schooling

0 13.7
8 14.3
9 14.7
12(*) 15.0

* For respondent with at least twelve years of schooling.

The OLS estimates of educational attainment, uncorrected for selection, for respondents of ages twenty-five to fifty-four are presented in Table VII. In this specification, the dummy variables for parochial schooling are treated as exogenous variables. The results indicate eight or more years of parochial schooling (Parochial 8+) has no effect on educational attainment. Nine or more years of parochial schooling (Parochial 9+), however, does have a significant positive effect; this is also the case for twelve years of parochial schooling (Parochial 12).

Table VIII presents the second set of estimates where the parochial schooling dummies are treated as endogenous variables; i.e., when the models have been corrected for selection. The results indicate that if corrections are made for selectivity bias, all of the parochial schooling dummies become statistically insignificant. Further, the selection-correction term (Lambda) is positive in all three estimates, and significant in (2) and (3), indicating that unobservables which tend to select individuals into parochial schools also positively affect the level of educational attainment. These results suggest that much of the supposed parochial-school effect is actually self-selection, consistent with our results obtained by using the "High School & Beyond" data set.

The other results are similar to those found in Table VII apart from Catholic being significant at the 10 percent level in one case and almost significant at the 10 percent level in the other two cases. We note this result because Catholic was used as an identifying variable in a related study (Noell [1982]).

TABLE VII
Estimates of Educational Attainment, Not Corrected for
Self-Selection (Standard Errors in Parentheses)

 (1) (2) (3)

Parochial 8+ .21
 (.22)
Parochial 9+ .52(**)
 (.25)
Parochial 12 .77(***)
 (.25)
Mother's Schooling .19(***) .19(***) .13(***)
 (.03) (.03) (.03)
Father's Schooling .18(***) .18(***) .14(***)
 (.02) (.02) (.02)
Black -.26 -.26 -.22
 (.23) (.23) (.22)
Hispanic .41 .43 .73(*)
 (.38) (.38) (.40)
Male .29(**) .28(**) .33(***)
 (.12) (.12) (.12)
East .02 .03- .35(**)
 (.18) (.18) (.17)
North Central .04 .04 -.24
 (.16) (.16) (.15)
West -.10 -.08 -.30
 (.19) (.19) (.19)
Catholic .15 .10 .03
 (.16) (.15) (.14)
Jewish 1.48(***) 1.49(***) 1.94(***)
 (.42) (.42) (.39)
Rural -.18 -.16 -.10
 (.18) (.18) (.17)
Town -.08 -.06 -.06
 (.16) (.16) (.15)
Small City -.04 -.03 -.05
 (.19) (.19) (.18)
Age .20(***) .20(***) .05
 (.07) (.07) (.07)
Age Squared -.0023(**) -.0022(**) -.0003
 (.001) (.0010) (.009)
Intercept 5.19(***) 5.27(***) 9.76(***)
 (1.44) (1.44) (1.42)
[R.sub.2] .23 .23 .16
N 1,515 1,515 1,367

* Significant at the 10% level.

** Significant at the 5% level.

*** Significant at the 1% level.
TABLE VIII

Estimates of Educational Attainment, Corrected for Self-Selection
(Standard Errors in Parentheses)

 (1) (2) (3)

Parochial 8+ -.47
 $ (.66)
Parochial 9+ -.75
 (.78)
Parochial 12 -.91
 (.86)
Mother's Schooling .19(***) .20(***) .14(***)
 (.03) (.03) (.03)
Father's Schooling .18(***) .18(***) .14(***)
 (.02) (.02) (.02)
Black -.25 -.26 -.23
 (.23) (.23) (.23)
Hispanic .27 .28 .59
 (.40) (.39) (.41)
Male .29(***) .30(**) .36(***)
 (.12) (.12) (.12)
East .03 .03 -.33(*)
 (.18) (.18) (.17)
North Central .10 .09 -.18
 (.17) (.16) (.16)
West -.12 -.13 -.36(*)
 (.19) (.20) (.19)
Catholic .37 .38(*) .33
 (.26) (.23) (.21)
Jewish 1.43(***) 1.43(***) 1.86(***)
 (.42) (.42) (.39)
Rural -.24 -.26 -.24
 (.19) (.19) (.19)
Town -.15 -.17 -.19
 (.18) (.18) (.17)
Small City -.06 -.08 -.13
 (.19) (.20) (.19)
Age .22(***) .22(***) .06
 (.07) (.07) (.07)
Age Squared -.0024(**) -.0025(**) -.0005
 (.0010) (.0010) (.0009)
Lambda .41 .77(*) 1.01(**)
 (.38) (.45) (.49)
Intercept 4.95(***) 4.89(***) 9.42(***)
[R.sup.2] .23 .23 .16
N 1,515 1,515 1,367

* Significant at the 10% level.

** Significant at the 5% level.

*** Significant at the 1% level.

1. One of the shortcomings in the Noell study is that he used Catholic to identify his estimates. This is probably an inappropriate instrument because Catholic is not necessarily independent of measures of academic achievement.

2. If the structural parameters in (1) are different between the two types of schools, then one would need to estimate a separate model for each population (Murnane et al. [1985]).

3. Structural parameters might still be estimable, however, even if the same set of exogenous variables are used in both equations because of the nonlinear nature of the probit model (see Willis and Rosen [1979]).

4. The chi-squared statistic of a likelihood-ratio test is only 0.022.

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WILLIAM SANDER and ANTHONY C. KRAUTMANN, Professor and Associate Professor, respectively, Department of Economics, DePaul University. The authors would like to thank Steven Rivkin, an anonymous reviewer, and their colleagues at DePaul for their comments on a preliminary draft, and DePaul's College of Commerce for research support. Further, they would like to thank Charles Koretke for typing the manuscript. A preliminary version of this paper was presented at the American Economic Association's annual meeting in Boston, 1994.