The Price of Higher Education: An Econometrics Analysis

Shub Gurung

Dr. Kim Craft

Introduction to Econometrics

8 December 2012

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Table of Contents

I. IntroductionII. Theoretical MethodIII. Empirical ModelIV. DataV. ResultsVI. ConclusionVII. AppendicesVIII. Bibliography

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I. Introduction

Every American household eventually has to go through one particular dilemma sooner

or later. That dilemma concerns higher education. This is a concern primarily because of how

much higher education costs. Every year, we are seeing a trend of growing tuition in any given

higher education institution whether it is a community college or an ivy league school. It is

indeed a very crucial dilemma because the affect higher education has one one’s life. Only about

25% of Americans go to college in any given year, which could be a shock to many as the United

States is one of the wealthiest industrial countries. However, this percentage does make sense

once you know the mammoth sum it takes to attend any given higher education institute, unless

one has an innate gift, the rest of the young men and women are left digging deep inside their

own pockets. In many cases this burden is left to the parents.

Then there is another issue that one will be faced with after graduation; the huge amounts

of debt. So is it all worth it in the end? Many young Americans enter college for financial

security for the future. Higher education could also be considered to be a long term investment

for the future. According to a study done by the LA Times, an average college student makes

84% more than a high school graduate over their lifetime. That number was 75% back in 1999

(College graduates). Tuition rates are sky rocketing, it is seemingly getting more and more

important to attend a higher education degree in order to avoid a bleak future. So once the

decision is made to attend college, deciding whether to attend a private school or public school

can be another hurdle. Generally, private schools tend to be a lot pricier than public schools. The

purpose of this study is to find out what variables contribute to high tuition costs.

II. Theoretical Model

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It is vital to understand that higher education institutions operate in a very unique market. It is

also important to understand that price is not the sole determinant to its unique supply and

demand model. One of the most important explanatory variables is how well the student’s

abilities match up to his or her potential institution. In other words, elite schools like Harvard are

less likely to consider a high school senior with a GPA lower than a 3.5. In a Mercedes car

dealership, one will not find potential buyers that belong to the lower income bracket. In the

same way universities and colleges are able to weed out potential students or potential buyers for

their service. This is truly a unique market to say the least. These institutes clearly have

particular buyers in mind. Also, there seems to be a vast difference in products amongst the

various institutes. No one institute is identical to the next. This difference is largely caused by

classroom sizes, the size of the school and by rankings. In addition, it is also important to know

whether a school is public or private. Public and private schools have very different goals in

mind and the way they operate is very different. Public schools are partially funded by the

government whereas private schools largely count on their respective endowments.

It has already been established that higher education institutes operate in a very different

model and another feature that is unique is the product itself. These institutes are supplying a

product that is intangible, on top of that there is no guarantee that product will work after

purchasing it. After purchasing higher education, there is no guarantee of success, however time

and again studies have shown that college graduates earn a substantially larger sum of money

over a lifetime than their high school graduate counterparts. This is mainly due to the fact that

there is some sort of warranty that comes along with this unique product. This is how one

institute is able to differentiate itself from the rest. If one particular institute is known to give out

larger warrantees or guarantees than the others, then they have the power to raise tuition. Buyers

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are in reality paying for how good the warranty is. This is the same reason why an institute like

Salt Lake community college does have the power to raise their prices, because they give

potential customers less warranty than say Bringham Young University. Likewise, buyers too do

not mind paying more if there is a larger warranty. This is one of the primary reasons as to why

there is such a variation amongst tuitions.

The concept of warranty of a college ties us to another important variable. That variable

is how prestigious the school is. Potential buyers believe that the pricier the school, the better the

education they will receive in return. Prestigious schools are known for providing a far superior

education than most of the other suppliers in the market. For this matter, buyers are willing to

pay the extra money to purchase a quality product. Prestige of an institution can often times be

examined on the yearly lists of Forbes publishes each year. If a school is ranked higher, it is

almost the case that the price will be higher as well. However, prestige of a school alone does not

determine the tuition, there are numerous of other variables that are as equally as important. If

one important variable is missing then the overall result will be skewed.

Another indicator or a variable is the acceptance rate of the college. In general, if the

acceptance rate is smaller, we understand this be to be a superior school. Hence, as we have

discussed above, a superior school must mean a raise in tuition compared to its closest

competitors. Besides the acceptance rates of schools, entrance exam scores are as equally as

important. A school with a higher ACT score will usually indicate that is a good school, hence

raising the tuition of that school. Along with entrance exam standards, how small a classroom

can also determine the price of the product.

The general concept is that if the student to faculty ratio is smaller, teachers are more able

to focus on each student’s needs. This is why small Liberal Arts colleges are preferred to large

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state schools by many students and parents alike. The conception is that in small liberal arts

schools, teachers know students by their names and are readily available to cater to their needs.

Whereas in a bigger state school the general assumption is that a professor might be in a hall

with a microphone teaching to 400 hundred students. Eventually the more attention a student

gets from faculty, the more likely he or she is likely to succeed is the general idea. People are

willing to spend extra to receive extra attention from faculty. This helps raise the tuition as well.

Lastly, the size of the student body should also have a hand in determining the size of the tuition.

A school with a large student population will require more facilities and services than others.

This will drive the price up.

There are of course numerous other variables that determine overall tuition costs of a

given institution but the ones that I have mentioned above will provide the best basis for

investigation. I will use regression to analyze these variables I think will be statistically

significant in determining private and public college tuitions. I have randomly selected a sample

of 50 colleges from across the United States (25 are public and 25 are private).

III. Empirical Model

The following is the stochastic model:

Ytuition= ß0+ß1(acceptance rate)+ß2 (act)+ß3(log.popn.)+ß4(student/faculty) +ß5(ranking)+E

Key:

Tuition=Annual Cost of attending a 4 year institution (for public schools, in-state tuition was used)

Acceptance Rate=the percentage of applicants the college or university grants acceptance

ACT=the average ACT scores at the institution

Log.Popn= The total size of the student body logged

Student/Faculty =the number of students per faculty member ratio

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Ranking= Rank of institution based on the 2012 Forbes List

E=stochastic error term with normal assumptions

(Expected Signs):

The first variable acceptance rate coefficient is expected to be inversely related to tuition.

Acceptance rate is how hard it is to get into a certain school. In turn, acceptance rate has a

positive correlation with the prestige of the school. The more prestigious a school is, the more

costly it will be. A school will be pricier if the acceptance rate is lower.

The coefficient of the average ACT score should be positive. Much like acceptance rate, the

average ACT score often times defines a school’s prestige level. This is a method a school uses

to weed out its potential buyers; it can then select a pool of students that match the caliber of the

school. If the school has a higher average ACT score, then it is most likely that the school’s

tuition will be higher. Unlike acceptance rate, the average ACT score and tuition will be positive

related.

The total student body population coefficient or log.popn coefficient is bound to have a

positive relationship with tuition as well. The higher the student body population, the higher the

tuition should be the case. This is mainly because more students require a lot more facilities and

services. For example a bigger school might need two cafeterias and two gyms. This will cause

the tuition to rise. The total student body population is logged for the functional form. It is a rule

of thumb to log populations in such regression models.

The coefficient for faculty to student ratio is going to be negative. If the ratio is lower, then

by logic the school will have to hire more faculty members. His will in turn raise the price of

tuition. In most small liberal arts schools, the ratio of faculty to students is often very small as

shown in the data. This is a very positive advertisement tool, this will drive tuition rates.

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Finally, the ranking coefficient should have an inverse relationship with tuition. If an

institution has a rank lower in number, then it should mean that it has more prestige. This in turn,

will mean that the tuition will have a higher tuition. The rankings were taken from the yearly

Forbes rankings for American colleges and universities.

IV. Data

For this regression project, I collected a sample of 50 random colleges and universities from

across America. The sample of 50 random universities and colleges is equally divided between

private and public schools. The purpose of this project is also to see what variables might be

responsible for raising the tuition in private schools. I obtained the data from College Board

website which is primarily designed for students who are looking to go to college. The results of

the analysis can be seen in the following regression model (Table 1.)

Table 1

Summary of Fit

Regression Statistics

Multiple R0.91117202

4

R Square0.83023445

8Adjusted R Square

0.810024274

Standard Error7302.63506

2Observations 48

Parameter Estimators

CoefficientsStandard

Error t Stat P-value

Intercept(104080.947

8) 18224.74028 5.7109701531.03E-

06

Accep. Rate(8766.88991

1) 7886.512211(1.11163080

4) 0.27262

ACT 135.3168528 475.6752798 0.284473166 0.77744

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6

Log Popn(6323.18816

5) 1529.694836(4.13362718

9)0.00016

7Student/Faculty Ratio

(1308.104782) 431.9262321

(3.028537479) 0.00419

Ranking (9.28323473) 11.05316925(0.83987085

7)0.40573

6*numbers in brackets denotes negative coefficient

V. Results

Estimated Equation:

Tuition-hat= -104080.94-8766.88 Acceptance Rate+135.31 ACT

(t-ratio=5.71) (t-ratio=-1.11) (t-ratio=.272)

-6323.18 Log Popn- 1308.10 Student/Faculty -9.28 Rankings

(t-ratio=-4.13) (t-ratio=-3.02) (t-ratio=-.839)

In this regression model, I obtained an adjusted R Square of .81. This means that 81% of

the total variation in tuition costs was explained by the variables of acceptance rate, Average

ACT score, Total Student Body Population (logged), Student to faculty ratio and lastly rankings.

Though I did obtain a high adjusted R Square, it does not fully explain the model. We can also

know the quality of the model by the F-test, in the regression, the value was 41.08 .The f-test

value is greater than the critical F value. This tells us that there is no issue with

heteroskedasticity. The F-Test is a good measure of the overall fit of regression because it

performs a joint significance test that involves all the explanatory variables ceterus perebus.

After looking at the joint significance of the variables, we can further look at individual

significance of the each variable by investigating their p values and t-stat values. In this

regression model coefficients of student/faculty ratio and Logged Student Body Population were

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the only two variables that turned out to be statistically significant with all else equal in a 5%

confidence level. This was the case because both of those variables had coefficient values that

had a t-stat value greater than 2 and a p value that was less than. 05.

The coefficients of the variables each tell us the relationship it has with tuition. For each

percent increase in acceptance rate, tuition cost will decrease roughly by $8766. An increase in

the average ACT by one point will increase the tuition by $135.31. An increase in one student

(logged) will decrease the tuition by $6323 (Which does not make sense logically). Each

additional faculty per student will drop the tuition by $1308. Lastly, an increase in one place

(meaning lower in number) in rankings will increase the tuition by roughly $9.28.

After finding out that only two out of the five variables were statistically significant, I

suspect the remaining three to be multicollinear. Multicollinearity happens when two or more

explanatory variables are strongly related, that the end results are skewed. I suspect that this was

the case because the three variables that were not statistically significant were variables that

strongly related to prestige. This correlation could have caused greater variance in the Y hat line.

This would eventually mean bigger standard error.

VI. Conclusion

We knew that the market in which higher institutions operate in are very unique from

everything else. However, we can still apply the basic economic supply and demand principle.

The purpose was to test the five variables that I thought would be significant in determining the

tuition of an institution. However, out of the 5 only 2 came out to be statistically significant. I am

positive that the other three variables did were not statistically significant due to the fact that they

were highly multicollinear. In fact, the three variables that were not statistically significant were

variables that were directly related to prestige. This tells us that all three of them had too much of

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a strong connection. I could have also used different measurements to determine the tuition rate,

variables such as endowment, financial aid percentage and so on. I could have omitted some

variables that were important in explaining the overall cost of tuition. We also found out that the

statistically significant coefficient of variables Average ACT score and student to faculty ratio

could be determinants of what makes private schools more expensive than their public school

counterparts.

VII. Appendices

School TuitionAccep. Rate

ACT

Log Popn

Student/Faculty Ratio

Ranking

Amherst $44,610 0.13 32 7.49 8 13

Boston College $43,878 0.32 30.5 9.11 13 26

Brown $43,716 0.17 31 8.76 9 19

Bryant U. (RI) $35,940 0.63 24 8.11 16 137

Bryn Mawr (PA) $42,246 0.47 28 7.18 8 52

Bucknell $45,378 0.36 24 8.18 11 56

Dartmouth $45,042 0.1 32 8.34 8 34

Depauw (IN) $38,750 0.58 25 7.76 10 79

Emory $42,980 0.27 32 8.61 7 46

Grinnel College $41,004 0.51 30 7.43 9 63

Ithaca $37,000 0.67 30 8.74 12 333

Kenyon $44,420 0.38 30 7.41 10 39

Lafayette (PA) $42,980 0.4 28.5 7.82 11 49

Lehigh $42,220 0.33 29.5 8.49 9 108

M.I.T. $42,050 0.1 33.5 8.39 7 11

Northwestern $43,779 0.18 32.5 9.16 7 22

Notre Dame $42,971 0.24 33 9.04 13 12

NYU $43,204 0.32 30.5 10.01 12 97

Oberlin (OH) $44,905 0.3 30 7.99 10 75

Penn $43,566 0.12 32 9.19 6 17

Pomona (CA) $41,438 0.13 31 7.38 8 9

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Skidmore $44,020 0.42 28 7.90 9 84

Vassar $46,270 0.23 31.5 7.78 8 20

Univ. of Mississippi $6,282 0.79 24 9.64 19 270

Univ. of Florida $6,282 0.43 27.5 10.39 20 80

Univ. of Alabama $9,200 0.44 25.5 10.17 19 274

Texas A&M Univ. $8,506 0.64 15 10.59 21 149

Univ. of Kansas $9,678 0.93 25 9.86 20 308

San Diego State $7,076 0.33 24 10.18 22 355Univ. of Texas

(austin)$9,792 0.47

2810.56 18

104

Univ. of Georgia $9,842 0.63 27 10.18 18 125

Arizona State Univ. $9,724 0.89 23 10.98 24 305

Univ. of Tennessee $9,092 0.7 26 9.96 15 365

Georgia Tech. $10,098 0.51 30 9.54 17 135

U. of North Carolina $7,694 0.31 29.5 9.82 14 47

Temple Univ. $13,596 0.63 23 10.23 15 480

Univ. of Arizona $10,035 0.69 24 10.33 24 272

Univ. of Virginia $12,006 0.33 30 9.67 16 36

Ohio State Univ. $10,037 0.63 28 10.67 19 188

Penn State Univ. $16,444 0.54 29 10.57 17 184

Univ. of Washington $12,428 0.58 26.5 10.28 13 87

Purdue Univ. $9,900 0.68 26 10.33 14 195

Univ. of Oregon $9,310 0.73 27 9.93 20 210Univ. of Illinois

(urbana)$14,522 0.68

2810.38 18

86

UCLA (berkely) $12,874 0.22 30 10.16 17 50

Univ. of Cincinnati $10,784 0.65 24 10.04 18 507

Univ. of Utah $7,139 0.83 24 10.10 14 161Southern Utah

University$5,576 0.72

22.58.88 20

550

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Works Cited

College Board.< www.collegeboard.com>

"College graduates earn 84% more than high school grads, study says." Money and Co.. Los Angeles Times, 05 2011. Web. Web. 10 Dec. 2012.

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Works Cited

http://latimesblogs.latimes.com/money_co/2011/08/college-gradutates-pay.html

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