Table 1 Descriptive Statistics for Test Scores, Behavior, and Absenteeism
Grade 1 Cohort Grade 4 Cohort
Public Catholic
Public Catholic
Reading 1992 mean test score
554.4 558.8
687.3 687.4
66.32 56.96
48.17 44.62
1993 mean test score 620.8
630.7 698.9
698.4 73.52
65.24 51.49
48.42 Mathematics
1992 mean test score 512.8
502.8 690.1
683.0 70.79
60.47 47.46
48.23 1993 mean test score
598.2 595.7
714.4 713.8
64.90 55.53
45.00 41.95
Observations 6,134
870 6,790
758 Behavior
Compliance scale 1.404
1.394 1.458
1.438 0.441
0.425 0.467
0.449 Motivation scale
1.715 1.678
1.762 1.744
0.584 0.569
0.592 0.585
Class participation 2.017
2.006 2.049
2.032 0.551
0.584 0.584
0.606 Absenteeism
Days missed 7.255
6.570 6.236
5.692 6.408
6.070 6.020
5.791 Excessive absenteeism
0.089 0.077
0.079 0.099
0.284 0.267
0.270 0.298
Observations 10,503
1,094 10,615
1,018
Notes: Standard deviations are in parentheses. Descriptive statistics for student demographics are in Appen- dix Table A1.
III. Econometric Approaches
For each cohort, I estimate the effects of Catholic schooling on achievement by using the following value-added equation:
1 Y 5 X ¢b 1 C¢a 1 T ¢l 1 e
In this equation Y is the student’s 1993 standardized test score in mathematics or reading, X is a vector of student characteristics, C is a dummy variable for Catholic
schooling, T is a vector containing 1992 test scores in mathematics and reading, and
e is unobservable student achievement.
7
By including the 1992 test scores, the value- added model measures the effect of Catholic schooling that is independent of prior
achievement, as measured by these scores. Despite the controls for 1992 test scores, selection bias still may remain in the
value-added models. The traditional approach to control for selection bias is the use of Heckman 1979 selection models.
8
Early work by Coleman, Hoffer, and Kilgore 1982 and others rely on Catholic religion as an instrument. However, Ludwig
1997 and others show that Catholic religion is often not a valid instrument because it should be included in the outcome equation. More recent work on Catholic school-
ing utilizes demographic differences in variables that are correlated with Catholic school attendance, such as the percent of the county population that is Catholic Neal
1997 or the availability of public transportation in the MSA Figlio and Ludwig 2000.
I explore the possibility of controlling for selection bias with a Heckman and a 2SLS model with a linear probability model in the rst stage. However, the only
candidates for valid instruments are Census region East, South, Midwest, or West and community type urban, suburban, or rural; I do not have more detailed mea-
sures of location, nor any measure of student religion. The results from the Heckman 1979 model with no instruments are quite similar to the results using instruments.
This nding strongly suggests that the instruments provide little or no explanatory power in the model. The results from the 2SLS model are imprecisely estimated and
differ greatly from those in the Heckman model, providing further concern for the appropriateness of these instruments. The results using interactions between region
and community type as instruments display the same sensitivity. Therefore, I con- clude that the Prospects data do not contain any reliable instruments to use in a
Heckman or a 2SLS model.
Instead, I rely on an alternative method for controlling for the nonrandom selection of students into Catholic schools. The following equation, estimated only for students
in the fourth-grade cohort, uses the distribution of the 1992 test scores of the rst- grade cohort to control for selection bias:
2 Y 5 X ¢b 1 C¢a 1 T ¢l 1 S ¢q 1 e
In this model, Y, X, C, and e are dened as in previous equations, and S contains the median 1992 reading and mathematics test score for the rst-grade cohort in
each school.
9,10
The underlying theory is that S captures the school level selection in test scores. Because the estimate of the Catholic schooling coefcient a in Equa-
tion 2 is independent of S, it is independent of the selection bias that is common to students in the rst- and fourth-grade cohorts. An example of such a school-level
selection is a school-level admission requirement testing verbal ability.
7. The results in the next section are simlar to unreported results that include the following school charac- teristics: Percent white, percent low-income, and typical class size.
8. Recent exceptions are Altonji, Elder, and Taber 2000 and Figlio and Ludwig 2000. Goldhaber 1996 uses an approach similar to Heckman 1979 model that includes the inverse Mill’s ratio.
9. Unreported results including the 10th and 90th percentile in addition to the median are nearly identical to the results when only the median is included.
10. Because the Prospects data contain the test scores for each student in at least four classrooms, if not the entire grade, the estimate of S provides a reliable estimate of grade-level test scores.
Catholic school attendance likely affects many components of education in addi- tion to academic achievement. Figlio and Ludwig 2000 nd mixed evidence that
Catholic high school attendance is associated with lower probabilities of delinquent behavior such as drug use, but essentially nothing is known about the effect of
Catholic primary schooling on outcomes other than test scores. The Prospects data- base contains data on classroom behavior and attendance. Both of these outcomes
are positively correlated with market behavior. Children who are not in class or who are poorly behaved are less likely to graduate from high school. Perhaps more
importantly, social behavior and attendance are important aspects of the education process that should be studied in their own right.
Data on these outcomes are available for 1992 but not for 1993, so it is not possible to estimate value-added models. Instead, the following levels model is estimated:
3 Z 5 X ¢b 1 C¢a 1 v,
where Z is a measure of behavior attendance, X is a vector of student characteristics, C is a dummy variable for Catholic schooling, and e is unobservable student
behavior attendance. For the fourth-grade cohort, I also estimate models that include the rst-grade school median test scores from 1992 as controls for selection bias.
IV. Results for Test Score Models
