205 D.M. Brasington Economics of Education Review 18 1999 201–212
Table 2 Means and sources
Variable Mean
Standard deviation Source
CENTRAL CITY 0.01
0.10 —
SUBURBAN 0.22
0.42 —
PARENT NO DIPLOMA 0.16
0.08 1
PARENT HIGH SCHOOL 0.45
0.11 1
ONLY PERCENT WITH BOTH
0.81 0.09
1 PARENTS
INCOME 29 117
9961 1
POVERTY RATE 0.10
0.08 1
NEWCOMER 0.15
0.05 1
PUPILTEACHER 18.5
2.0 2
TEACHER OVER B.A. 0.32
0.10 2
TEACHER MASTERS PLUS 0.42
0.13 2
TEACHER EXPERIENCE 15.33
2.02 2
Math 0.59
0.14 2
Citizenship 0.75
0.11 2
Reading 0.81
0.08 2
Writing 0.70
0.15 2
Attrition rate 0.03
0.02 2
Notes: 602 observations. Sources: 1 5 School District Data Book MESA Group, 1994; 2 5 Ohio Department of Education, Division of Education Management Information Services.
If there is a dichotomous outcome at the individual level pass or fail but the result is aggregated to the
district level, and each district has a different number of students, then using OLS will result in heteroskedasticity
Kennedy, 1992. I address the heteroskedasticity prob- lem by using a minimum chi-square method of weighting
Maddala, 1983.
6
6. Empirical results
Table 3 shows the full results of the weighted least squares regression.
Endogeneity is a concern. School-specific factors are chosen by the voters through the school board, so a two-
stage least squares framework is also presented using instrumental
variables for
PUPILTEACHER, TEACHER OVER B.A., TEACHER MASTER’S PLUS
and TEACHER EXPERIENCE. This is an extension of Akerhielm 1995, who treats class size as endogenous.
The results are found in Table 4.
The results in Tables 3 and 4 conform closely to Hanushek 1986 and the Coleman Report Coleman et
al., 1966. Parents’ education levels and the presence of two parents in a household significantly affect student
performance. Poverty depresses scores, but recent moves
6
For example, for the math section regression, the weight is [fall enrollmentMath1 2 Math]
12
.
and income have no consistent, independent effect on test scores. None of the school inputs has a consistently
significant impact on student scores.
7
The focus variables are the central city and suburban dummies. Table 5 summarizes the sign and significance
level for each of the proficiency test sections. The signs of the central city and suburban dummies
are almost uniformly negative across the test sections. For math, reading and citizenship, these dummies are
soundly significant. Only for writing are the dummies insignificant, although the signs are almost all negative.
Writing is the only section not graded by multiple choice bubble-sheet scanning. The scores may be biased
because they are sent to a subcontractor in North Carol- ina grouped by district, by building, and they are not
randomized before they are graded. This sequential grad-
7
Aggregation bias is a potential concern Hanushek et al., 1996. It is possible that at the classroom level the school inputs
would be statistically significant Summers and Wolfe, 1977, but the current study attempts to capture unmeasured environ-
mental effects due to the type of school district. District-level or school building-level analysis seems appropriate for the current
study’s purposes. School building-level analysis would be pref- erable to school district-level analysis to capture unmeasured
harmful environmental effects; however, this data is unavail- able. Using building-level data instead of district-level data may
not influence the results because only 32 of the 602 school dis- tricts have multiple high school buildings Ohio Department of
Education, 1993. Further study is warranted.
206 D.M. Brasington Economics of Education Review 18 1999 201–212
Table 3 Proficiency test results: weighted least squares
Variable Math
Citizenship Reading
Writing CENTRAL CITY
2 0.048
2 0.094
2 0.058
2 0.032
2.00 4.00
3.39 0.94
SUBURBAN 2
0.029 2
0.022 2
0.024 2
0.0029 2.57
2.15 3.25
0.19 PARENT NO
2 0.45
2 0.36
2 0.20
2 0.17
DIPLOMA 6.16
5.31 4.61
1.68 PARENT HIGH
2 0.28
2 0.21
2 0.22
2 0.23
SCHOOL ONLY 4.99
4.15 6.35
3.24 PERCENT WITH
0.63 0.34
0.36 0.27
BOTH PARENTS 10.22
5.91 8.95
3.17 INCOME
0.11 3 10
− 5
0.52 3 10
− 6
0.30 3 10
− 6
0.12 3 10
− 5
1.99 1.01
0.88 1.92
POVERTY RATE 2
0.33 2
0.28 2
0.17 2
0.34 3.32
3.09 2.63
2.60 NEWCOMER
2 0.080
2 0.14
2 0.21
2 0.14
0.84 1.57
3.38 1.15
PUPILTEACHER 0.00032
0.0019 0.0016
0.0056 0.15
0.99 1.14
1.96 TEACHER OVER B.A.
0.040 0.066
0.057 0.0037
0.70 1.31
1.61 0.05
TEACHER MASTERS 0.038
0.00078 0.012
0.071 PLUS
0.78 0.02
0.36 1.07
TEACHER 0.0038
0.0015 0.0026
0.00012 EXPERIENCE
1.70 0.75
1.81 0.04
INTERCEPT 0.21
0.58 0.61
0.51 2.23
6.91 10.43
4.16 Adjusted R-squared
0.69 0.56
0.62 0.33
Notes: Number of observations 5 602. Dependent variable 5 percent passing the specified portion of proficiency test in 1992. Parameter estimates are reported with t-ratios in parentheses below. 5 significant at 0.05, 5 significant at 0.10.
ing by cohort may color the scores the subcontractor gives the students, so that inadvertently students may be
compared to other students in the same building or dis- trict, but not to students in other districts. Thus, it is
likely that the writing section does not accurately meas- ure student performance across districts. Table 1 also
shows less differences in the writing section passage among central city, suburban and non-metropolitan dis-
tricts. In contrast, suburban and non-metropolitan dis- tricts outpace central city students to a much larger
extent on the math, reading and citizenship sections of the test.
The results indicate that holding all other included fac- tors constant, central city schools’ students perform
worse than non-metropolitan schools’ students. The same holds true for suburban schools’ students. Note that
this is a different argument than saying large classrooms hurt student performance: the studentteacher ratio has
an insignificant effect on test scores. In addition, this is a different argument than saying that school consolidation
depresses school outcomes.
8
The significantly negative dummy variables suggest that there is something about
being in an urban area, either in a central city or its sub- urbs, that depresses students’ scores independent of the
remaining explanatory
variables. This
is E
: the
unmeasurable, harmful environmental influences. The central city dummy parameter estimates in Table 5 are
consistently more negative than the suburban dummy parameter estimates. The empirical test thus suggests that
E
is highest in central city schools, second-highest in
8
In unreported regressions, I include district enrollment and an approximation of high school building enrollment. The
results are qualitatively identical. A similar analysis is presented in Brasington 1998.
207 D.M. Brasington Economics of Education Review 18 1999 201–212
Table 4 Proficiency test results: 2SLS
Variable Math
Citizenship Reading
Writing CENTRAL CITY
2 0.071
2 0.11
2 0.064
2 0.090
2.34 4.00
3.26 2.01
SUBURBAN 2
0.035 2
0.022 2
0.026 0.013
2.42 1.78
3.03 0.63
PARENT NO 2
0.39 2
0.32 2
0.18 2
0.094 DIPLOMA
4.72 4.37
3.80 0.77
PARENT HIGH 2
0.19 2
0.15 2
0.18 2
0.12 SCHOOL ONLY
3.01 2.65
4.83 1.30
PERCENT WITH 0.67
0.40 0.38
0.40 BOTH PARENTS
8.39 5.68
8.08 3.53
INCOME 0.52 3 10
− 6
0.26 3 10
− 6
0.62 3 10
− 7
0.14 3 10
− 5
0.74 0.41
0.15 1.53
POVERTY RATE 2
0.33 2
0.26 2
0.17 2
0.20 2.85
2.60 2.53
1.26 NEWCOMER
2 0.080
2 0.097
2 0.20
0.050 0.58
0.81 2.34
0.26 PUPILTEACHER
ˆ 2
0.0061 2
0.0015 2
0.00095 0.0070
1.80 0.50
0.45 1.41
TEACHER OVER B.A.ˆ 0.0098
2 0.084
0.061 2
0.96 0.03
0.31 0.32
2.21 TEACHER MASTERS
0.37 0.11
0.15 2
0.23 PLUS
1.54 0.49
0.90 0.69
TEACHER 2
0.0014 0.0011
0.00065 0.0095
EXPERIENCEˆ 0.17
0.15 0.12
0.81 INTERCEPT
0.21 0.58
0.59 0.55
1.40 4.39
6.56 2.56
Adjusted R-squared 0.63
0.52 0.59
0.09 Notes: Number of observations 5 602. Dependent variable 5 passing the specified portion of proficiency test in 1992. Parameter
estimates are reported with t-ratios in parentheses below. 5 significant at 0.05, 5 significant at 0.10. ˆ 5 endogenous variable. Instruments: state revenue per pupil, community unemployment rate, at-risk students, community living in district 311years,
residential property value per pupil, commercial property value per pupil, population density, community dropout rate, community education level, single in community.
Table 5 Locational effects summary
Variable Math
Citizenship Reading
Writing CENTRAL CITY
1
2 0.048
2 0.094
2 0.058
2 0.032
SUBURBAN
1
2 0.029
2 0.022
2 0.024
2 0.0029
CENTRAL CITY
2
2 0.071
2 0.11
2 0.064
2 0.090
SUBURBAN
2
2 0.035
2 0.022
2 0.026
0.013 Notes: Parameter estimates shown. 5 significant at 0.05, 5 significant at 0.10. Dependent variable 5 percent passing each
section in 1992.
1
From weighted least squares regressions.
2
From 2SLS regressions.
208 D.M. Brasington Economics of Education Review 18 1999 201–212
suburban schools and lowest in non-metropolitan dis- tricts.
Even though test scores may be lower ceteris paribus in central city and suburban districts, suburban schools
still outperform central city schools on the proficiency tests. This occurs because suburban school districts have
parent and community characteristics that are more fav- orable to learning than central city school districts. Fur-
thermore, the regression results suggest that if the sub- urban school districts retained the same studentparent
mixture but were transported to a rural district, students’ test scores would be even better than they currently are.
The results support the theoretical model’s prediction that dkdE , 0. Given this result, I now investigate the
effect of E on graduation rates, expecting to find dddE ,
0, that with more E, central city districts in particular will depress graduation rates, all else equal.
7. Graduation rates
