2. Page | 2
I Introduction
The United States has been the world’s largest economic power for over half a century. The
United States is also home to some of the most powerful companies and innovations that have
changed the world. A large part of The United States’ economic success is due to American
students’ performance in school relative to the rest of the world. Many of the world’s best
universities are in the United States, and students from all over the world come to the US to study.
However, students in the American public school system have been struggling in
international competitiveness relative to other developed countries. In PISA1
standardized testing,
American students rank 25th in math scores, 17th in science, and 14th in reading scores among 34
OECD nations2
. There are many varying opinions as to why American students are not performing
as well as their foreign counterparts, making educational reform one of the hottest issues today.
Inadequate spending, bad teachers, misallocation of resources, and poor district-level control are
some of the most popular theories, each having a different solution to the problem. There have
been many proposed types of reform, but the most common are private school vouchers, merit-
based pay, and charter schools.
Private school vouchers and charter schools are proposed programs that seek to decrease the
amount of students in overpopulated and underperforming school districts. Vouchers are
scholarships that are paid to students so that they are able to afford and attend certain private
schools.3
Charter schools are public schools where families choose to enroll their kids and are
granted more flexibility on operations in exchange for greater accountability for student
1 Program for International Student Assessment (PISA) is a worldwide evaluation of 15-year-old students
2 Highlights from PISA 2009: Performance of U.S. 15-Year-Old Students in Reading, Mathematics, and Science Literacy
in an International Context
3 National Council of State Legislatures, School Voucher Laws: State-By-State Comparison
3. Page | 3
performance4
. Merit-based pay attempts to promote better student performance by structuring
salaries based on how well a teacher’s students perform on certain criteria.
The purpose of this paper is to look at some of the factors in the current education system
that some of the proposed reforms aim to change. To get the best measure of the effect on the
quality of education, I look at how these variables impact a state’s average score on the SAT. The
independent variables used in this paper are the relative strength of teachers unions, average class
size, enrollment per district, the cost of living adjusted average starting teacher salary, and the
percent of people with a bachelor’s degree, all measured at the state-level.
II Sample
The sample I will use in this study is public school data from 20 states in the US5
. The reasoning
behind the selection of these states will be explained in the following section.
III Dependent Variable
The dependent variable in this study is the average SAT scores by state for the year 2013.
The SAT is an aptitude test that is designed to asses a student’s readiness for college. I will use this
measure as a proxy for student achievement because standardized scores are perceived as better
measures than other measures whose criteria vary by district or state (such as grade point average or
graduation rates). The SAT is also one of the most recognized and widely used tests for college
entrance and has been used since 19266
.
The test is divided into three sections, and scores for each section are out of 800 possible
points. The total score is calculated as the sum of the three scores. However, some universities take
4 Uncommon Schools, Frequently Asked Questions About Public, Charter Schools
5 Public school data was chosen because private schools have more freedom to exercise their own standards for the
variables used in this study.
6 The College Board: About the SAT
4. Page | 4
the highest score for each section that the student has taken in their lifetime. This means that a
student’s score of one complete test may not be the score colleges use for acceptance. To control
for this, I have elected to run each score in its own regression. I also chose to look at state-level
scores because the average scores vary widely across the country and many educational decisions are
made by state and local governments rather than by the federal government.
The data on SAT scores was collected from the Commonwealth Foundation of
Pennsylvania7
. I chose this source because the data was collected at the state-level, and the
participation rate by state is included. The participation rate is of particular importance because even
though the SAT is one of the most commonly used standardized tests, is not the only test that
universities use as a basis for acceptance. This means that there are many college-bound students
who do not take the SAT, and the state-by-state participation rate varies significantly.
A large difference in the SAT participation rate across the states could create a potential
problem with the results of this study. When a higher amount of students take the exam, there are
more lower-ability students taking the exam, which drives the average score for the state down.
Therefore, states with lower participation rates will have higher average SAT scores. To get the best
distribution of states with students taking the exam, I chose the 20 states with participation rates
from 25% to 75%.
IV Independent Variables
Union Membership (Union)
Though private sector union membership is falling, teachers unions are some of the most
powerful organizations in all of American politics. Unions are formed to promote teacher benefits,
7 The Commonwealth Foundation: SAT Scores by State 2013
5. Page | 5
but the political reach of these organizations extends far beyond educational lobbying by supporting
many special interest groups that are not education-oriented. The two strongest unions are the
National Education Association and the American Federation of Teachers, which account for over
$600 million combined receipts, $70 million in political activities and lobbying, over 4 million
members, and more than $92 million in contributions, gifts, and grants8
. Many supporters of
education reform believe teachers unions specifically lobby against reform legislation to protect bad
teachers and keep union membership high. My hypothesis on this variable is that a higher union
strength will negatively affect average SAT scores due to inefficiencies and the protection of
underperforming teachers.
The variable for Union Strength is measured as the relative strength of union power in the
50 states and Washington DC. This data is gathered from a three year study conducted by the
Thomas B. Fordham Institute9
. In the study, they look at the involvement of unions in over three
dozen union characteristics, including membership, involvement in politics, scope of policies, state
politics, and perceived influence to determine how powerful unions are in each state. In the
Fordham report, the strongest state union is given a value of 51, the second strongest a value of 50,
and so on to a value of 1. Although only 20 states were used in this paper, I kept the original ranking
from the study rather than reassigning the values from 1-20 for two reasons. The first was that
Union strength was relatively evenly distributed in the sample used for my regressions10
. The second
reason was that reassigning the values on a 1-20 scale would not accurately reflect the disparity of
power the strongest unions have compared to the weakest unions.
8 Teachers Union Exposed: Union Profiles
9 Thomas B. Fordham Institute: How Strong Are U.S. Teacher Unions? A State-By-State Comparison
10 The mean value (located on Figure 1) is 27.4, with the 5 strongest unions and 4 of the top 5 weakest unions
represented in the sample.
6. Page | 6
Average Class Size (ACS)
Average class size was chosen because it has been a popular topic for union lobbying and
impacts both students and teachers. This data is obtained from the American Legislative Exchange
Council’s (ALEC) Report Card on American Education, with data reported for 201011
. Though the
SAT data is for 2013, I chose the ALEC report card because the report itself is one of the most
comprehensive reviews of American education and has data for all 50 states. Additionally, the
Fordham Institute study of 2012 covers 3 years of prior data to determine their union strength rating
scale, and 2010 falls within their study timeframe.
The logic of supporting a smaller average class size is that a smaller student to teacher ratio
will increase teacher interaction and therefore student performance. Smaller classes are also easier
environments to teach and are part of increasing teacher benefits. Because of the inherent positive
impacts associated with smaller class sizes for the teacher and the student, this variable will be
measured using a one-tailed test. I therefore hypothesize that states with smaller average class sizes
have higher average SAT scores.
Enrollment per District (EpD)
Enrollment per district seeks to capture the efficiency of each school district. Districts with
higher enrollments have more students and fewer resources. With larger districts, school faculty and
parents have less of a voice on policy issues and the best interests of certain groups may be left out.
However, it may be possible that a larger district creates an economy of scale by cutting down on
some of the administrative costs, leaving more money to go to teachers and students. Taking both
of these factors into account, I believe that the diluted voice a teacher or parent will outweigh the
11 NEA: Rankings and Estimates Report: Rankings of the States 2012 and Estimates of School Statistics 2013
7. Page | 7
effects of any efficiency gains created with larger districts. Thus, I predict that a higher enrollment
per district will adversely affect a state’s average SAT score.
This data is defined by taking the total enrollment for each state in 2011 and dividing it by
the total number of school districts for each state in 2011. Enrollment and district data were
collected from the National Educational Association’s Rankings and Estimates Report12
. I chose this
report because it fell in the time frame of the study and is only a year later than the previous variable
that was concerned with enrollment figures. Though the variables are intended to describe two
different phenomena, I ran a correlation on enrollment per district and average class size to combat
any concerns for multicolinearity. The correlation returned a value of 0.005388, so both of the
variables’ presence should not interfere with the results of the regression.
Cost of Living Adjusted Average Starting Teacher Salary (Tpay)
Teacher salary level is one of the biggest points of contention among educational lobbyists
and proponents of reform. Public school teacher salaries are relatively low in the United States when
compared to other careers that require similar educational attainment, driving many people away
from becoming a teacher. Intuitively, higher salaries should make teachers generally happier and
perform their jobs better. In the United States however, most public school teacher salaries are
based on years of experience and the highest degree the teacher attained, not on the performance of
their students.
Because salaries are not based on student achievement, average salary level for all teachers
would not be an ideal measure to relate to SAT scores since there is no economic incentive for
better student performance. However, I have elected to use starting salary because theoretically
teachers will want to maximize their starting salaries since they will get paid more as their career
12 National Education Association: 2011-2012 Average Starting Teacher Salaries by State
8. Page | 8
progresses. This means districts with higher starting salaries can attract more teachers, and should be
able to hire the best applicants. Therefore, I predict that as teacher salary increases, SAT scores
increase as well.
Because the cost of living varies from state to state, I divided the teacher salary by the state’s
cost of living index. Data on the average teacher salary starting pay for teachers across the country is
collected from the National Education Association13
for 2013 and the cost of living is gathered from
Missouri Economic Research and Information Center14
for Q2 of 2014.
Percent of People with a Bachelor’s Degree (PBD)
The percent of people with a bachelor’s degree was chosen as a proxy for the role parents
have on student success. Though education reform doesn’t have any control over the amount of
people that currently have a bachelor’s degree or higher, this variable was included because parent
involvement is a key indicator of student success. Parents with advanced degrees tend to have higher
paying jobs, giving their children access to more resources and mobility to purchase houses in more
desirable school districts. These parents could also provide students with an additional resource for
understanding schoolwork and going through school with the expectation of going to college.
This variable will be measured using a one-tail test as well because of the inherent positive
benefits of highly educated parents. The data was collected from the US Census’s 2012 Statistical
Abstract.15
I predict that as the percentage of people with a bachelor’s degree increases, the average
SAT score will also increase.
13 National Education Association: 2011-2012 Average Starting Teacher Salaries by State
14 Missouri Economic Research and Information Center: Cost of Living Data Series Second Quarter 2014
15 United States Census Bureau: The 2012 Statistical Abstract: Educational Attainment: Table 233
9. Page | 9
V Results
Union Strength (Union)
This variable was insignificant in all three regressions, with p-values of 0.6733, 0.9996, and
0.6806 for Math, Reading, and Writing, respectively. Therefore, the strength of a teachers union in a
state does not affect the average SAT score. Additionally, due to the variable’s insignificance, the
coefficient and impact are also inconsequential.
Average Class Size (ACS)
This variable was also insignificant in all three regressions, with one-tail p-values of 0.2855,
0.3206, and 0.4884. This result shows that the average class size in a state does not affect the average
SAT score, and that its impact and sign on the coefficient can be ignored.
Enrollment per District (EpD)
As predicted, the coefficient of enrollment per district has a negative sign with marginally
significant p-values for Math (at the 10% level) and highly significant p-values (at the 1% level) for
Reading and Writing. Referring to Figure 2 for the amount of the variable’s impact, a one standard
deviation increase in enrollment per district causes SAT scores to decrease by 6.01 points on Math
scores, 10.02 points on Reading scores, and 9.62 points on Writing scores. This confirms the original
hypothesis that a lower enrollment per district leads to a higher state-level average SAT score.
Cost of Living Adjusted Average Starting Teacher Salary (Tpay)
The cost of living adjusted salary proved significant (at the 5% level) for Math and Reading
and highly significant for Writing. Though the variable was significant, it did not have the coefficient
10. Page | 10
I had anticipated. A one standard deviation increase salary leads to a decrease of 7.47 points on
Math scores, 9.39 points on Reading scores, and 8.22 points on Writing scores.
Percent of People with a Bachelor’s Degree (PBD)
The percent of people with a bachelor’s degree also proved marginally significant for Math
and Reading and highly significant for Writing. This variable also had the predicted positive
coefficient, with a one standard deviation increase leading to an increase of 4.46 points for Math
scores, 5.46 points on Reading scores, and 8.04 points on Writing scores.
VI Conclusion
The research presented in this paper addresses economic factors that affect student
performance using state-level average SAT scores on Math, Reading, and Writing as a proxy for
student achievement. Each section of the SAT was run in its own regression to control for any
effects of aggregate scoring. Of the five variables tested in this paper, enrollment per district, cost of
living adjusted average starting teacher salary, and percent of people with a bachelor’s degree proved
to be significant with similar impacts on SAT scores.
Enrollment per district had the predicted negative coefficient, confirming the hypothesis that
smaller relative representation in school districts overpowers any positive gains from economies of
scale in larger districts. Though charter schools and private school vouchers seek to lower the
enrollment in school districts, increasing the number of districts is not a widespread campaign for
reform. I believe that this is because of the large range and standard deviation among states, and
more districts may only be beneficial in certain states. Based on the results, the two states in this
sample that would benefit most from more school district would be Florida and Hawaii. Florida has
11. Page | 11
over 2.6 million students enrolled in public schools and only 67 school districts16
. Hawaii has over
177,000 students and only 1 school district that encompasses all eight major islands, making
representation in district meetings much more difficult and costly than other states.
While I have noted some problems with the coefficient on this variable, the results for the
cost of living adjusted average teacher starting salary could be caused by more than purely economic
phenomena. It is possible that the best teachers are simply not motivated by money, and chose their
career without giving much consideration to differences in income across districts and states. This
would also account for the possibility of some teachers going to poorer performing districts because
they are purely incentivized by the opportunity to help underachieving students succeed over a
higher salary. These results are unclear to whether the sign on this coefficient would be positive if
there were a different method for teacher compensation, or if the best teachers are indifferent to
their salaries regardless of how they are determined.
The significance of the percent of people with a bachelor’s degree demonstrates that higher
educated states have higher performing students. However, since the variable measures the entire
population of the state and not only the parents, there may be some room for interpretation on the
true impact on SAT scores.
Unfortunately, with the lack of a nation-wide uniform standardized achievement test, there is
no proxy available that perfectly assesses student performance. However, the results of this study are
able to support the claims that more school districts may be beneficial for certain states, teachers
respond differently to their current compensation than expected, and that more educated states have
higher performing students.
16 A comparable state in the size of enrollment would be New York, which has 695 school districts.
13. Page | 13
Figure 2: Variable Impact
A variable’s impact is calculated by multiplying its Standard Deviation by its Regression
Coefficient. A variable’s impact is defined as the change on the average SAT score by a 1 standard
deviation increase in a significant independent variable.
Math Impact Reading Impact Writing Impact
Union 1.455827 Union -0.00148 Union 1.1017477
ACS 3.355743 ACS 2.915263 ACS 1.6668106
EpD -6.0146 EpD -10.0229 EpD -9.615793
Tpay -7.47117 Tpay -9.38995 Tpay -8.223388
PBD 4.461549 PBD 5.455162 PBD 8.0407849
