270 T. Aksoy, C.R. Link Economics of Education Review 19 2000 261–277
Table 1 Means and standard deviations of variables: All races
a
Means Standard deviations Variable
Years 123 n =
964 Years 12 n
= 1086
Years 13 n =
706 Math-IRT score
44.82 14.08 35.13 12.48
43.72 14.78 Weekly hours of math homework
3.06 3.55 1.89 2.85
2.83 3.45 Number of hours per week student works
7.93 10.11 6.40 10.28
8.43 9.28 Hours per day watching TV
2.60 1.51 2.70 1.59
2.56 1.54 Student attended private school
0.03 0.17 0.02 0.14
0.05 0.21 School in urban area
0.23 0.42 0.24 0.43
0.26 0.44 School in rural area
0.50 0.50 0.41 0.49
0.38 0.49 Number of legal days in school year
179.39 3.06 178.96 3.01
179.07 3.25 Student’s family income in 1000s
41.18 23.80 33.75 21.91
41.17 24.83 Beginning district teacher salary
21.51 2.94 19.74 2.59
21.76 2.95 Hispanic math teacher
0.01 0.12 0.03 0.17
0.02 0.15 Black math teacher
0.10 0.31 0.11 0.32
0.07 0.25 Female math teacher
0.56 0.50 0.51 0.50
0.56 0.50 Years of teaching experience
14.92 8.06 14.41 8.00
15.24 8.00 Students parents divorced
0.12 0.33 0.12 0.33
0.12 0.32 Minutes per math class
NA 52.79 4.90
NA Number of students in student’s math class
NA NA
25.55 10.49 Hours per week of math class
NA NA
4.36 0.92
a
There are 191 Blacks, 75 Hispanics, and 60 Asian students in the balanced 123; 184 Blacks, 104 Hispanics, and 37 Asian students in the balanced 12; and 115 Blacks, 52 Hispanics, and 64 Asian students in the balanced 13.
samples and, therefore, estimation results for white stu- dents are reported separately.
22
4. Results
This section reports the panel estimations for the determinants of math achievement based on balanced
samples from the National Education Longitudinal Study of 1988 NELS. Regression results are shown in Table
3 for the pooled all races samples and Table 4 for the white samples. The constant term in the regression cap-
tures students who came from families that did not go through a divorce between 1988 and 1992,
23
who
22
The means and standard deviations for whites in these bal- anced samples are similar to those from the larger samples of
the NELS population. None of the means was statistically dif- ferent. The balanced samples tend to have fewer private school
students and slightly fewer students from suburban areas.
23
Because we were not able to identify schools the student attended each year in the version of NELS used in the analysis,
it is possible that an unknown bias could exist in the esti- mations. Some students may have the same teachers and as a
result school specific unobserved effects may exist which could bias the estimated standard errors. That is, two students may
have a particularly talented or inept teacher which would affect both students in a positive or negative way. If such a
situation arises we have cross sectional serial correlation.
attended public schools located in suburban areas, and who had white male teachers.
24
4.1. Teacher and school factors According to Hanushek 1986 and Ehrenberg and
Brewer 1994, the most important exogenous factors affecting student achievement relate to teacher and
school inputs. One of the important conclusions to be drawn from our results is that the variable measuring the
minutes per each class period spent on mathematics is important in terms of the size of its coefficient and its
statistical significance. For the year one and two 12 samples column 2 of Tables 3 and 4 the estimate for
the coefficient ranges from 0.20 to 0.23. Increasing the length of the class by 10 min is associated with a gain
of 2–2.3 points in mathematics achievement, or a change which equals 5.4–6.2 of the relevant sample averages.
Considering that the average class length for the sample is 53 minutes, a 10 minutes increase certainly is possible.
Each additional hour per week spent on mathematics homework increases student achievement scores by 0.67,
24
We take into account those parents who got divorced and remarried, and also parents who got married and divorced, i.e.
multiple divorces and marriages are accounted for. As long as the parents are married the dichotomous variable, DIVORCED,
has the value 0, and changes to 1 as a divorce takes place.
271 T. Aksoy, C.R. Link Economics of Education Review 19 2000 261–277
Table 2 Means and standard deviations of variables: white samples
Means Standard deviations Variable
Years 123 n =
638 Years 12 n
= 761
Years 13 n =
475 Math-IRT score
47.66 13.36 37.19 12.71
45.66 14.00 Weekly hours of math homework
2.99 3.34 1.94 2.89
2.88 3.43 Number of hours per week student works
8.67 10.73 6.66 10.38
8.37 9.20 Hours per day watching TV
2.48 1.42 2.70 1.53
2.40 1.48 Student attended private school
0.05 0.21 0.02 0.14
0.06 0.24 School in urban area
0.20 0.40 0.20 0.40
0.22 0.41 School in rural area
0.53 0.50 0.44 0.50
0.40 0.49 Number of legal days in school year
179.27 3.18 178.80 3.02
178.85 3.45 Student’s family income in 1000s
46.20 22.83 37.43 21.66
45.05 23.93 Beginning district teacher salary
21.35 2.74 19.54 2.50
21.48 2.80 Hispanic math teacher
0.01 0.08 0.01 0.11
0.02 0.13 Black math teacher
0.05 0.21 0.07 0.26
0.02 0.14 Female math teacher
0.58 0.49 0.52 0.50
0.59 0.49 Years of teaching experience
14.12 7.88 14.06 7.57
14.77 8.07 Students parents divorced
0.10 0.29 0.11 0.32
0.11 0.31 Minutes per math class
NA 52.72 5.10
NA Number of students in math class
NA NA
25.02 10.11 Hours per week of student’s math class
NA NA
4.33 0.92
Table 3 Mathematics achievement: balanced panel estimation results for the all races samples
a,b
Coefficients Variable
1 Years 123 2 Years 12 n
= 1086 3 Years 13 n
= 706
n =
964 Weekly hours of math homework
0.67 6.14 0.36 3.14
0.81 4.24 Number of hours per week student works
0.18 4.66 0.10 2.95
0.25 3.50 Hours per day watching TV
20.84 22.96 20.19 20.81
21.59 23.70 Student attended private school
20.68 20.16 9.03 2.47
2.42 0.29 School in urban area
1.27 0.64 26.39 23.19
21.25 20.49 School in rural area
22.33 21.12 21.18 20.45
22.72 20.95 Number of legal days in school year
0.003 0.02 0.13 0.80
0.32 1.23 Student’s family income in 1000s
0.04 1.65 0.15 4.49
0.11 3.75 Beginning district teacher salary
0.61 3.44 0.51 3.23
0.94 3.21 Hispanic math teacher
6.80 2.02 20.35 20.19
21.36 20.33 Black math teacher
24.88 23.31 22.78 22.36
27.28 22.60 Female math teacher
20.23 20.28 20.51 20.74
23.31 22.57 Years of teaching experience
0.04 0.87 0.02 0.57
0.15 1.73 Student’s parents divorced
20.13 20.10 21.44 21.48
1.08 0.49 Minutes per math class
NA 0.20 2.35
NA Hours per week of student’s math class
NA NA
20.34 20.47 Number of students in math class
NA NA
20.08 21.22 Constant
29.20 1.00 212.49 20.42
233.44 20.73 Lagrange Multiplier test statistic prob. value
168.76 0.000000 196.03 0.000000
32.60 0.000000 Hausman test statistic prob. value
26.36 0.023298 31.12 0.008463
27.15 0.039809
a
Figures in parentheses are t-ratios.
b
Coefficient significant at 5 and 10 level.
272 T. Aksoy, C.R. Link Economics of Education Review 19 2000 261–277
Table 4 Mathematics achievement: balanced panel. Estimation results for the white samples
a,b
Coefficients Variable
1 Years 123 n =
638 2 Years 12 n
= 761
3 Years 13 n =
475 Weekly hours of math homework
0.72 5.95 0.48 3.43
0.76 3.56 Number of hours per week student works
0.13 3.52 20.10 20.16
0.28 3.61 Hours per day watching TV
21.15 23.91 20.55 21.90
21.31 22.69 Student attended private school
3.32 1.24 13.12 4.25
212.88 20.88 School in urban area
3.41 2.09 22.18 21.46
25.81 21.12 School in rural area
21.94 21.44 22.52 21.92
24.30 21.08 Number of legal days in school year
20.18 21.195 0.40 2.42
0.03 0.10 Student’s family income in 1000’s
0.004 0.21 0.10 4.58
0.02 0.50 Beginning district teacher salary
0.84 5.02 0.46 2.62
1.06 3.13 Hispanic math teacher
1.45 0.27 0.16 0.05
211.92 22.10 Black math teacher
24.92 22.50 25.26 23.24
25.39 21.16 Female math teacher
21.08 21.26 20.68 20.80
23.10 22.03 Years of teaching experience
0.10 1.98 0.13 2.37
0.12 1.28 Student’s parents divorced
20.75 20.53 21.48 21.16
23.94 21.51 Minutes per math class
NA 0.23 2.66
NA Hours per week of student’s math class
NA NA
20.20 20.26 Number of students in math class
NA NA
20.04 20.48 Constant
60.69 2.30 258.55 21.98
21.83 0.44 Lagrange Multiplier test statistic prob. value
149.22 0.000000 89.06 0.000000
23.24 0.000009 Hausman test statistic prob. value
21.92 0.080257 20.88 0.140856
35.77 0.003113
a
Figures in parentheses are t-ratios.
b
Coefficient significant at 5 and 10 level.
0.36, and 0.81 points for the pooled all race samples including all three years 123, years one and two 12,
and years one and three 13 respectively. Results for the white student samples are similar to the those of the
pooled all race samples. As with the pooled samples, hours spent on mathematics homework is always
important in both the statistical sense as well as its mar- ginal impact on student achievement. Each additional
hour spent on weekly mathematics homework is associa- ted with an increase in mathematics achievement scores
from 0.48 to 0.76 points, or 1.3 and 1.7 respectively compared to their mean achievement score. The slightly
lower effects which show up for the sample for years 1 and 2 see column 2 of Tables 3 and 4 are due to the
inclusion of the variable for ‘minutes per daily math per- iod’ which has a strong positive and statistically signifi-
cant coefficient. Not surprisingly, students who have longer math classes are also assigned more homework
which will lower the impact of the homework variable. But the effect of homework remains strong even with
the inclusion of minutes per class period. The mean num- ber of hours of homework per week in the data ranges
between 2 and 3 hours and the standard deviation is approximately 3.5 hours. Therefore, an increase of 1 or
2 hours per week devoted to mathematics homework is quite possible. These results are consistent with previous
studies of the effects of homework. Each additional hour during the school week spent
watching the television lowers the math achievement score by between 0.55 and 1.31 points for whites and by
between 0.84 and 1.59 points for the pooled race samples. The coefficient is statistically significant for all
but the all races years 1 and 2 sample.
For the all races 13 and white 13 samples the only years the data are available, student achievement
in mathematics is not affected by how many hours of instruction per week a student received since the coef-
ficient is not statistically significant at the 5 level. The conclusion about the effects of the number of hours of
instruction per week is different from the findings of Gilby et al. 1993 who found small positive effects for
extra hours of math instruction. However, theirs was a panel sample of elementary school students while ours
is high school students. There may be larger returns to the extra hours of instruction in the early years of edu-
cation which decline as one advances through the school system. But keep in mind that the result we found for
minutes of math per class period is consistent with Gilby et al. 1993.
The length of the school year in a school district is statistically significant only for the whites in the base
year and first follow-up year 12 sample Table 4, col- umn 2, where the coefficient is statistically significant
and large—an extra day adds 0.40 points to math
273 T. Aksoy, C.R. Link Economics of Education Review 19 2000 261–277
achievement. An additional 5 days would add 2 points to math achievement, a 5.4 increase compared to the
sample mean. Teacher salary is an important determinant of achieve-
ment for all samples. In the pooled all races samples, the effect of each 1000 rise in the beginning salary of tea-
chers is associated with an increase in mathematics achievement of between 0.51 and 0.94 points. Results for
whites range from 0.46 to 1.06 points. Students taught by a black math teacher score from approximately 2.8 to
7.3 points lower than those who have a white male teacher. The results for black teachers are similar to
those found by Goldhaber and Brewer 1997, who also used NELS. Results for the effects of being taught by
an Hispanic teacher were mixed. The all races 123 and white 123 samples suggest a positive Hispanic
effect while the two year panels suggest no effect at all or a negative effect. The effect on achievement of being
taught by females is also mixed. In four of the six mod- els, there was no significant difference in performance
of female and white male teachers. In the two panels which include the 1st and 3rd years, students with a
female teacher scored lower. This is different from Gold- haber and Brewer 1997 who found a positive effect of
being taught by a female. However, they did not use the third year, which is where the negative coefficients
appear. In conclusion, with the exception just noted these results are consistent with Hanushek 1992, who notes
that there is no strong indication of differences in per- formance for male and female teachers.
In the two panel samples including observations from the first and the second years 12, students attending
private schools score significantly higher on the math achievement tests. However, private school attendance is
not a significant determinant of achievement for any of the other samples analyzed. In fact, the significant results
should be interpreted with extreme caution since only 2 of the students in these samples were attending priv-
ate schools. The sensitivity of the coefficients is undoubt- edly due to the low number of private school students
in the balanced samples underlying our research.
For the pooled races 13 and white 13 samples, student achievement in mathematics is not affected by
class size. The coefficient is negative, indicating smaller classes are consistent with higher achievement, but does
not approach statistical significance. This is consistent with the findings of Hanushek 1992 and Ehrenberg and
Brewer 1994. The coefficient of teacher experience, always positive, was statistically significant for two of
three samples for white students. When significant, how- ever, the coefficient is only about 0.10, indicating that it
takes 10 years of experience to cause a 1 point increase in math achievement. This result is consistent with other
findings in the literature. Although students attending schools located in urban and rural areas tended to score
lower on the math tests compared to their counterparts in suburban schools, the effects of the variables were
not generally significant. The one exception occurred for white students who had data in all three years where the
urban students outscored suburban by almost 3.5 points. However, when controls were entered for minutes of the
math class period, the coefficient became insignificant.
4.2. Student and family related factors As expected, the coefficient of the family income vari-
able is always positive and is statistically significant in four of the six models. The coefficient shows up as more
important, both statistically and in magnitude, for the all races samples containing only two years of information
compared to similar samples containing all three years of information. The insignificant income coefficient in
the 123 and 13 samples is surprising. However, earlier in section III, we argued that biased estimates are likely
in a cross-section if unobservables such as industri- ousness or motivation are excluded from the model. To
the extent that more motivated and industrious students come from a higher income background, using panel
techniques may lessen the effect of income.
Students from a home where there is a divorced parent do not appear to be negatively affected in terms of lower
math achievement. This finding is consistent with other studies in the literature, especially since the panel allows
for control of unobservables. Working in the labor mar- ket does not appear to be an impediment to math
achievement when controls are entered for unobservable variables. In fact, the coefficient on the hours worked
per week variable is statistically significant and positive in all but the white 12 sample where it is not signifi-
cant. For whites, the coefficient ranges from 0.13 to 0.28.
5. Conclusions and policy implications
