econometrics term paper

1. Statement of the problem

This paper will address the effect of investment on school facilities to student performance. We are interested especially in seeing whether additional money spend on school buildings lead to improvement of student performance, keeping every other factors constant.

2. Review of the literature

There are a lot of literature which attempted to explain the effects of school resources on student performance, but the relationship between school resources and student performance has been controversial. First of all, Hanushek (1997) provided huge volume of literature review about the effects of school resources on student performance. After review of around 400 previous studies of student achievement, he found that there is not a strong or consistent relationship between student performance and school resources including the real resources of the classroom (teacher education, teacher experience, and teacher-pupil ratios), financial aggregates of resources (expenditure per student and teacher salary), and measures of other resources in school (specific teacher characteristics, administrative inputs, and facilities).

On the other hand, Eide and Showalter (1998) studied the effect of school quality on student performance. In this paper, they found that the number of school enrollment and school year length have positive relation with student performance. They also observed that there may be differential school quality effects at different points in the test score gain conditional distribution.

Wӧßmann (2003) investigated that the effects of family background, resources and institutions on students’ mathematics and science performance using an international database of more than 260,000 students from 39 countries. His result showed that international differences in student performance cannot be attributed to resource differences, but they are considerably related to institutional differences. He found that centralized examinations and control mechanisms, school autonomy in personnel and process decisions, individual teacher influence over

teaching methods, limits to teacher unions’ influence on curriculum scope, scrutiny of students’ achievement and competition from private schools have positive effects on the student performance.

3. The data

The data for this paper consists of 1,967 observations of Ohio Elementary School buildings for 2001-2002 year. For each observation we have 1) the number of teachers, 2) teacher attendance rate, 3) average years of teaching experience, 4) average teacher salary, 5) per pupil spending on instruction, 6) per pupil spending on building operations, 7) per pupil spending on administration, 8) per pupil spending on pupil support, 9) per pupil spending on staff support, 10) median of 4th grade prof scores(student performance), 11) building enrollment, 12) per capita income in the zip code area, 13) percent of population that is non-white, 14) poverty percent of population in poverty, 15) % of population attending public schools.

After pre-screening of data set, 5 observations are excluded from original dataset because they have abnormal values (decimal points on the number of teachers, negative amount for per pupil spending on pupil support and staff support). So our final sample consists of 1,962 observations.

4. The empirical results and conclusions

At first, we include all variables that might have relationship with the student performance. Here the first ordinary least squares regression is:

, se in parentheses, R2=.357, n=1962.

This regression shows that there is relationship between per pupil spending on building operation and median of 4th grade proficiency score, but only at the relatively high p-value (p<0.1). In addition, some variables are not statistically significant even at the p-value of 0.1 (the rate of teacher attendance, per pupil spending on administration and staff support). Thus, we excluded those variables and get the new regression model.

In this model, all variables are statistically significant (p<0.01), except spending on building operation (p<0.06) and building enrollment (p<0.05). In addition, although we excluded some variables, the value of R2 doesn’t change. To check multi collinearity problem, we checked the VIF (Variance Inflation Factors) values of all variables. All VIF values of variables are below 10, so we can assume that there is no multi collinearity problem in the model. However, the White’s test shows that there is heteroskedasticity problem in the model ( P[Chi-square(77) > 558.405]=0.000 ). To solve this problem, we regress the model again with robust standard errors.

In this final model, we can see that there is positive relationship between spending on building operation and student performance at the 5% level. It means that we would predict for the median proficiency score of students to increase by 0.002 for 1 unit increase in per pupil spending on building operation. We also see that number of teachers, spending on pupil support are significant at the 5% level, and average year of teaching, average of teacher salary, per capita income, percent of non-white, percent of poverty, and percent of attending public school are significant at the 1% level. However, with robust standard errors, spending on instruction and building enrollment are no longer significant in this model.

5. Possible extensions and limitations of your study

One of limitation in this study is the interpretation of the results. We cannot find plausible explanation for the unexpected signs of variables. Unlike our expectation, the sign of number of teachers was negative, and the sign of percent of attending public school was positive. In addition, the coefficient for the main independent variable is too small, so it is hard to conclude that there is meaningful relationship between dependent variable and independent variable, although existence of the statistical significance in coefficient and overall model. It could be the result of omitted variables, such as some important factors which were not included in the data set. In the future study, scrutiny with each variables will be needed.

Finally, it would be better if we can include the qualitative variables in the model. As previous studies suggested, qualitative factors might have important impacts on the performance of students. In the future study, we can improve quality of the study including those kinds of variables.

6. References

Hanushek, Eric A., “Assessing the Effects of School Resources on Student Performance: An Update.” Educational Evaluation and Policy Analysis, Vol. 19, No. 2, pp. 141-164, 1997.

Eide, Eric and Showalter, Mark H., “The effect of school quality on student performance: A quantile regression approach.” Economics Letters, Vol 58, pp. 345-350, 1998.

Wӧßmann, Ludger., “Schooling Resources, Educational Institutions and Student Performance: the International

Evidence.” Oxford Bulletin of Economics and Statistics, Vol 65, Issue 2, pp. 117-170, 2003.