Introduction

As any parent knows, tuition continues to increase at institutions of higher learning around the country every year. As colleges increase their prices, they must take into consideration what amenities students are willing to expend on, thus maximizing the net tuition of the college. One such amenity, is a diverse student body, which many schools have taken particular strides to insure. In the wake of the controversy surrounding affirmative action and similar programs undertaken to by colleges to create diversity, an important question arises. Do students of these colleges actually demand diversity? If the answer is yes, then racial diversification practices should be continued not only because they provide a social good, but also because they provide increased economic profits for schools.

If a student demands diversity, then they will be willing to pay more to attend a college that meets this demand. Thus, we would be expected that those colleges with the greatest amount of diversity (as defined by the percentage of Latino, Black, Asian and Native American students), will have a higher net tuition then those with less diversity. In order to identify this demand, we will be using data from (number) liberal arts colleges to ascertain the determinants of net tuition revenue. What we have found, however, is that increased percentages of minorities seems to have a negative impact of net tuition revenue.

While this can be interpreted to mean that students to do demand diversity, it is out belief that they do, despite these results. What is likely to have caused these results is the fact that minorities generally require more financial assistance to attend these colleges. Thus, as a school has a higher minority population, they will have a lower net tuition revenue. This is not, however, a totally accurate depiction of what students demand.

Literature Review

There is a fairly extensive body of economic literature about the effect of tuition and fees on the matriculation rates of a college. While this does not pertain directly to our study, much of the factors taken into consideration are similar. One such paper is, "Tuition and Enrollment Yield at Selective Liberal Arts Colleges" by Jeffery Parker and Jeffery Summers. In their study, they found that increasing tuition and fees has a substantial impact on decreasing demand for a college. In conducting this study, Summer and Parker used data from 85 liberal arts colleges over a three year period. They then separated applicants into three categories according to financial need. They measure demand for a college by the number of accepted students who matriculate at that college. They also control for quality of the college, as Measured by US News rankings, as well as for financial aid. Finally, they included variables such as SAT scores and endowment to control for the quality of the school. Their final conclusions were that an increase in tuition and fees deters both aid and non-aid from enrolling at a college. Furthermore, schools that are ranked high as well as those that have a great deal of non-tuition revenue (endowments) have an easier time getting students to enroll. They also found that liberal arts colleges are not very good substitutes for one another.

Another journal article, "The Effects of the Financial Aid Package on the Choice of a Selective College" measures the effect of financial aid on attendance at Occidental College in California. They found that "Tuition costs definitely affect the enrollment decisions of financial aid applicants, as does the amount of scholarships. Loans and work-study opportunities play a much less important role, *ceteris paribus*." (Moore, Studenmund, and Slobko p.319) While I am sure that this study has some useful implications, I think that it could be more useful if it was a cross college comparison such as other studies have done. Mostly, this would be useful because it would be possible to examine the effect of tuition on enrollment of one college compared to that of other colleges.

The journal article most similar to ours is entitled, "Tuition and US Private College Characteristics: The Hedonic Approach," by Jon D. Harford and Richard D. Marcus. In this study, they make an attempt to identify the determinants of net tuition revenue though data from a cross-section of 780 private colleges. One variable in the study was BLACK, the percentage of black students at the college, which was found to be significant and negative. "if blacks compromise 10% more of the student body, then the expected tuition declines by roughly $70 to $90." The study found that those schools with a greater number of desirable characteristics, such as more library books, greater number of faculty, higher SAT scores, etc. have higher net tuition. While our study is similar to this study, in that we are trying to determine the effect of diversity on net tuition revenue, there are two key differences. First, we test the effect of tuition on not only Black students, but also on Hispanic, Asian, International, and Native American students. Second, rather then include variables on SATs, volumes of books, student/faculty rations and the like, we are instead including a Tier variable (based on US News rankings) which takes into account all of these factors.

Model

For our model, we had three different measures of the financial situation of a college: Endowment per student, endowment income per student, and the student faculty ratio. The student/faculty ratio is a measure of financial well being because the more faculty that a school is able to hire, the better they must be financially, as they must have the means to pay for additional faculty salaries. Thus, the lower a schools student/faculty ratio, the better off a school is financially. These three measures, however, are highly correlated with one another and can not be used within the same model. Therefor, we have created three different sets of models (with eight models within each set), each of which uses a different measure of financial well being.

For the ranking of the college, we used to US News and World Report, which divides liberal arts colleges into four tiers of rankings. Tier 1 is composed of the top 40 liberal arts schools, tier two of schools ranked 41 to 80, and so fourth. Though our data consists of rankings from the years of 1984 to 1994, we used the ranks issued in 1995. We did this for two reasons. First, the rankings began after 1984, our first observations. Furthermore, the rank of a school is fairly stable. Being so, it is rare that a school moves from one tier to another within the course of a few years.

As a measure of diversity, we used a racial break up of fall enrolment figures. There were two obstacles that we ran into at this point. First, because it is generally the case that minority students need a greater deal of financial aid assistance, an increase in the percentage of minority students could decrease net tuition revenues as a result of the large amounts the college would have to expend on aid on these students. While this would be perceived at meaning that there is no demand for diversity, it would not necessarily be the case. The second problem is that it may be the case that the minority percentage is determined endogenously, with the level of net tuition revenue affecting the number of minorities. In order to deal with this problem, we have the option of either using a two-stage least squares model or a lagged minority percentage variable. The problem with using a two-stage least squares variable, however, is that there is a great deal of difficulty in finding an appropriate instrument that is correlated with minority percentage but not with net tuition revenue. The use of a lagged minority variable is best in this case, as it is unlikely that current net tuition had any effect on the percentage of minorities four years ago. Finally, to correct for the issue of financial aid to minority students, we split up domestic minorities from international students. The logic behind this is that many schools do not provide financial aid to international students. Since it was not clear to us which affects actually take place we estimated models using the lagged and un-lagged version as well as splitting up the domestic from international and keeping them together.

The other characteristics are numerous and more difficult to measure. For instance the Hillary Effect, which significantly increased demand for women’s colleges and the net tuition revenue of these colleges in the early 90’s. In an attempt to minimize the error and capture some of these random effects we used a partial fixed effects model, putting in a dummy variable for each year. In addition, we controlled for the region of the college since where the school is located often affects of the demand for the school. Other factors, such as library, SATs, and the high school GPA of admits are all taken into consideration in the ranking of the schools by US News. Our hypothesis is that diversity of students, like any other favorable characteristic, will have a positive impact on the net tuition revenue of a college.

Methodology/Data

In order to test whether or not diversity effects net tuition revenue, we used a panel data set of private liberal arts colleges classifies are "LA1" by the Carnegie Classification System. We obtained this data from the Integrated Post-secondary Education Data System (IPEDS) database, and got data from 1984 through 1994. We began by going through the data and discarding any college that had fall enrollment levels below 800 in 1984. We also eliminated historically black colleges such as Spellman and Moorehouse. Lastly, any college that was missing a significant amount of data was also removed from our data set. The only addition that we made to our data was the US News and World rankings for 1995.

The main variables where the endowment, endowment income, minority percentage, domestic minority percentage, international minority percentage, tier 1 through tier 4 dummy variables, the regional dummy variables, and the individual year dummy variables. The variables where constructed as follows:

**Log net tuition** = log [(tuition — scholarships) / fall enrollment]

**Log endowment per student** = log (endowment / fall enrollment)

Log endowment income per student = log (endowment income / fall enrollment)

**Minority percentage** = [(fall enrollment of international students + fall enrollment of Black students + fall enrollment of Native American students + fall enrollment of Asian students + fall enrollment of Hispanic students) / total fall enrollment]

**Domestic percentage** = [(fall enrollment of Black students + fall enrollment of Native American students + fall enrollment of Asian students + fall enrollment of Hispanic students) / total fall enrollment]

**International percentage** = fall enrollment of international students / total fall enrollment

For a complete listing of the variables and their means and standard deviations see Table 1.

We used a partial fixed effect model to control for the variation from year to year that often skews OLS results in panel data models. We implemented a dummy variable for all the years in the data set. We did not estimate a full fixed effects model because there were not enough single school observations to warrant using a dummy variable to control for individual school characteristics. However, after estimating only a few variations of this model it was clear that multicollinarity was a large problem. After running a correlation test we found that the student faculty ratio was highly correlated with the other measures of financial status (endowment per student and endowment income). Therefore, we decided that the ration had to be used without those other. Yes, when we ran the regression using only the ration and the diversity variable, the total minority percentage had a negative effect. There was a great deal of multicolliniarity between the minority percentage and the student ratio. In addition we had put in a sticker price variable that measured the actually sticker price of a school. However, we found this to be highly correlated with both financial status variables and the minority percentage and therefore dropped it from the model.

Results and Analysis

The results obtained from the regressions vary drastically depending on what measure of financial status is used and what model is used. Model 1 contains the measure of financial status and the total minority percentage variable. For the case of endowment per student, the coefficients and t-values are in Table 2. This model has an F-value of 249.99 and is significant at the 99% level. This strongly indicates that as a whole the model has good explanatory power. Both variables are significant at the 99% level, indicating that they significantly effect net tuition revenue. These results indicate that if endowment per student increases by 1- percent then net tuition revenue per student increases by .178%. Similarly, for every 1% increase in the total minority percentage, net tuition per student rises by .897%. Hence, looking at these results, there is strong evidence that increasing diversity increases net tuition revenue. The adjusted R-squared for Model 1 is .3609, meaning that this model explains 36.09% of net tuition revenue.

When Model 1 is ran using the endowment income per student (Table 3) the F-value is 173.38 and is significant at the 99% level. In addition, both variables are again highly significant. Endowment income per student is significant at the 99% level and for every 1% increase in endowment income per student, net tuition increases by .154%. Total minority percentage is also significant at the 99% level with a coefficient of 1.057. Meaning that for every 1% increase in the total minority percentage, net tuition revenue increases by 1.06%. The adjusted R-squared for this model is .2729 which is slightly lower than the R-squared using endowment per student, indicating that endowment explains more of net tuition revenue than endowment income does.

When Model 1 is ran using the student faculty ratio, the results drastically differ. The results are in Table 4. The F-value does not change much and indicates that the model continues to have good explanatory power. The student faculty ratio variable is significant at the 99% level and has a coefficient of 14.43; meaning, that when the student faculty ratio increases by 1, net tuition revenue per student increases by 14.4%. While this effect may seem large, for the student faculty ratio to increase by 1, there has to be a huge increase the faculty size. The total minority percentage variable is significant at the 90% level, which is a significant drop from the significance it had using endowment and endowment income per student. However, it is still highly likely that there is a positive relationship between net tuition revenue and minority percentage. In this case, the coefficient is .349, indicating that for every 1% increase in the minority percentage there is a .349% increase in net tuition revenue per student. The adjusted R-squared for this model is .3018, which indicates that this model explains 30.18% of net tuition revenue per student.

Model 2 takes Model 1 and adds the tier variables, the region variables and the year variables. Controlling for these factors greatly changes the results. For the endowment per student case, the results are in Table 2. The F-value is 45.99 and is significant at the .01% level. Therefore, the model continues to have good explanatory power with these new variables added. The adjusted R-squared for this model is .5074, meaning that the model now explains 50.74% of net tuition revenue. This is a large increase from Model 1. In this model endowment per student continues to be significant at the .01% level, only this time for every 1% increase in endowment per student, net tuition revenue per student increases by .1176%. The total minority percentage variable in this model is no longer significant at either the 95% level or the 90% level. It is however significant at the 80% level. This means that there is a 20% chance that total minority percentage does not affect net tuition revenue. However, it is still likely that an increase in minority percentage increases net tuition revenue. The only tier variable that is significant is tier 1 and it is significant at the 97% level. The region variables all vary in their levels of significance. It is clear from these results that the location of the college affects the net tuition revenue. Two regions of interest are New England and West because a lot of liberal arts colleges are in New England and some of the highest-ranking colleges are in the West. Both New England and West are significant at the 99% level. For a college that is located in New England the net tuition revenue per student is .374% higher than a college located in the east and for a college located in the West the net tuition revenue per student is .392% higher than a college in the east. Only a few of the year variables are significant, indicating that there is variations in the net tuition revenue due to the year in 1984 and 1986 but not in any of the other years. All of the coefficients and the t-values can be seen in Table 2.

When Model 2 is ran using endowment income per student the F-value changes to 43.229 and remains significant at the 99% level. The endowment income per student variable remains highly significant but the effects of a 1% increase drops to .091% as opposed to the .1176% effect it had with endowment per student. The total minority percentage variable again was far from significant. In fact, using endowment income per student causes the probability to rise to 52% that total minority percentage does not affect net tuition revenue. The remainder of the variables has similar results to the results in the models with endowment per student. These coefficients and t-values can be seen in Table 3. The adjusted R-squared of this model is .4851, so the model still explains a good deal of the variation in net tuition revenue.

When the student faculty ratio is used in Model 2, almost every variable changes significantly, with the exception of the ratio variable. The student faculty ratio remains highly significant and the coefficient is similar to what it was in Model 1. However, the total minority percentage variable not only changes in significance but also the sign changes, indicating a negative relationship. Seeing that the sign was positive in every variation of the model aside from this one, and many the other variables that were previously insignificant became significant, we thought there must be multicollinearity. In a correlation test, we found that the student faculty ratio is highly correlated to the minority percentage and the tier dummies. Because of this correlation the significance of some of the variables changed as well as the signs. It is plausible that positive changes in the student faculty ratio are caused by a drop in the total enrollment of the college, which would in turn cause net tuition revenue to fall. This negative relationship may be getting picked up by the minority percentage variable and causing it to show a negative relationship. The adjusted R-squared of Model 2 using ratio is .5020 which is still fairly high and the F-value is still significant at the 99% level indicating that the model still has strong explanatory power.

Model 3 breaks up the minority variable into domestic minorities and international minorities. The only other variable that is included in this model is the financial variable. For the endowment per student case, the results can be found in Table 2. The results for the endowment income per student case see Table 3. Table 4 has the results for the ratio case.

Separating the domestic minorities from the international minorities did not change the other variables significantly. The endowment per student, endowment income per student and student faculty ratio variables all continue to be significant. The adjusted R-squared is relatively the same as when total minority percentage is used, which makes intuitive sense because nothing about the model has really changed. Separating the two parts of minority percentage made little difference. Both the domestic minority percentage and the international minority percentage were both highly significant in all of the Model 3’s, with the exception of the ratio model. When the ratio model is used, the domestic minority percentage is only significant at the 80% level but the international percentage is still significant at the 95% level.

In Model 4, the tier variables, region variables, and the year variables are added to Model 3. The results of this model are similar to the results obtained from Model 2. In fact, all of the variables have very similar results. In addition, the same multicollinearity problem arose in Model 4 when the ratio was used. Again here, the domestic minority variable had a less significant effect than the international minority variable. This could be due to the fact that international students often pay full tuition and therefore, contribute more to net tuition revenue than do domestic minorities. The results from Model 4 with the different measures of financial status can be seen in Tables 2, 3, and 4.

Models 5 through 8 are the same as Models 1-4 only using lagged minority percentage instead of current minority percentage. Using lagged minority percentage attempts to correct for the possibility that increased minorities brings down net tuition revenue because of the amount of aid they need. Although, given the results of models 1-4 this effect does not appear to be a problem because in almost all cases the relationship was positive. Given this, the reason for estimating models using the lagged percentage is because of the possibility that minority percentage may be partly endogenous.

The results of these models were significantly different then when the non-lagged version was used. In Models 5 and 7, which contain only the financial status variable and the diversity variable, the results were similar to what was found in Models 1 and 3. The financial measures were all significant at the 99% level. The coefficients on these variables were slightly higher than they were in Models 1 and 3 but overall there was not much difference. In Model 5, which has the lagged minority percentage, the minority percentage, the minority variable is significant at the 90% level. This significance is lower than the non-lagged minority percentage and this may be due to the fact that with the lag all the tuition contributions or subtractions that were present in the non-lagged minority variable. Using this, the lagged variable is better representing whether students demand diversity and as a result colleges can increase their net tuition by having a more diverse student body. Seeing that the variable is still significant at the 90% level, it is likely that there is this positive effect. The coefficient on lagged minority percentage is , indicating that for a 1% increase in minority percentage, net tuition revenue per student increases by . When the minority variable is broken up domestically and internationally, the significance level drops even further. In fact, domestic minority is insignificant in Model 7. Again, as in Model 3 international minority percentage is more significant than domestic minority percentage. The coefficient in Model 7 of lagged international minority percentage is…

In Models 6 and 8, the tier region and year variables are added. It is in these models that the minority variables become completely insignificant. In Model 6, the minority variable has a 99% likelihood of having no effect on net tuition revenue. This indicates that the minority makeup of the college 4 years ago has no effect of net tuition revenue. All the remainder of the variables was similar to the results that were found in Models 2 and 4. It was again the case that multicollinearity was present in the models containing the student faculty ratio, causing the results to show a significant negative relationship.

__Conclusion__

The significance of minority percentage on net tuition revenue per student was mixed between the models. There is evidence that there is a positive relationship but this evidence is weak and largely inconclusive. As more variables are added and the minority is broken up domestically and internationally the evidence of the relationship dissipates. Given this, we conclude that by increasing the minority make up of the student body, colleges receive very little benefit financially. While they may benefit if they increase the international minority significantly, this is most likely due to the fact that international students pay full tuition not because there is a demand for diversity from the student body. This is not to say, however, that students to not demand diversity. Rather, it is likely that the use of net tuition revenue to indicate the demand diversity is not accurate.