High tuition, financial aid, and cross-subsidization: do needy students really benefit?

• Author: Rose, David C.

Our policy is total Robin Hood - we put our tuition up as high as possible and then put most of the extra money into financial aid. [Eamon M. Kelly, president of Tulane University, 19871.](1)

1. Introduction

   One way to make a college education widely accessible is to charge low tuition. Yet many college administrators argue that a policy of charging high tuition while generously awarding financial aid can even further reduce the net price paid by needy students.(2) Since there is little doubt that this implicit form of cross-subsidization has benefited some students, this practice has been widely accepted by the public. To date, however, no one has investigated the actual impact of cross-subsidization on the net price paid by needy students.(3)

   The fact that this question has not been addressed is surprising since this form of cross-subsidization is observationally equivalent to ordinary price discrimination. Indeed, high tuition coupled with generous financial aid awards may simply reflect a policy of maximizing tuition revenues to pursue other objectives. How, then, can we be sure that institutions that claim they charge high tuition to subsidize needy students are in fact reducing their net price?

   In this paper we investigate whether the net price paid by the average needy student is negatively related to the degree in which institutions appear to inflate their tuition to engage in cross-subsidization. First we show that cross-subsidization can, under fairly general conditions, reduce the average net price paid by all needy students. Next we identify a necessary condition for concluding that cross-subsidization results in the average needy student paying a lower net price. We then test whether this condition is satisfied by examining the cross-sectional relationship between tuition and financial aid awards for 502 private institutions of higher learning. Finally, we compare some selected budget items of institutions that charge relatively high tuition to those that charge relatively low tuition to gain insight into what kinds of institutional objectives compete with the goal of maximizing accessibility.(4)

2. The Model

   Cross-Subsidization and Net Price for Needy Students

   Can institutions that charge inflated tuition actually reduce the net price paid by all needy students through cross-subsidization? This question can be addressed by way of an example. Let n be the total number of students attending a particular institution and let m be that institution's number of needy students. Now consider a tuition increase of one dollar that leaves both n and m unchanged.(5) All students must now pay an additional dollar to attend. Now suppose that each of the m needy students receives an additional dollar of financial aid to fully offset the tuition increase. In this case the net price paid by each needy student does not change but (n - m) dollars of additional tuition revenue is left over to be spent at the institution's discretion. If only one of these dollars is put into additional financial aid and divided among the needy students, then the tuition increase will actually reduce the net price paid by all needy students. Indeed, in this example average financial aid awards among needy students increased by the amount of the tuition increase ($1) plus 1/m even though the institution gains (n - m - 1) dollars of additional tuition revenue.

   Tuition, Institutional Financial Aid Awards, and Net Price

   In the example presented above we showed that institutions that can inflate their tuition can expropriate additional revenues from wealthy students to reduce the net price paid by all of their needy students. We now identify a necessary condition for concluding that such policies generally reduce the average net price paid by needy students.

   The financial aid award for any given student is determined by both the cost of attending a given institution and the student's ability to pay. We can characterize the relationship between tuition, ability to pay, and average financial aid awards with the following expression:

   [Mathematical Expression Omitted]

   where A is an institution's average financial aid award among all n full-time undergraduates, T is tuition, [P.sub.i] is the ith financial aid recipient's ability to pay, m is the number of needy students receiving institutional financial aid, and 0 [is less than or equal to] [THETA] [is less than or equal to] 1 is the average percentage of each financial aid recipient's need gap (T - [P.sub.i]) that is closed by institutional financial aid awards.(6) The student's ability to pay, [P.sub.i], is the institution's estimate of what the student can afford to spend on a college education. We assume that all institutions are in agreement as to the value of [P.sub.i] for any given student.(7)

   Let [T.sup.e] be the expected value of an institution's tuition given its observable characteristics. In other words, [T.sup.e] = E[T/X], where X is a vector of institutional characteristics that describe an institution. Now suppose an institution considers adopting tuition T > [T.sup.e] to engage in cross-subsidization. In such a case, how much larger must the average financial aid award be for the average net price paid by needy students to be reduced? A policy of charging T > [T.sup.e] implies that for every student (including the m needy ones) the cost of attending is now [DELTA T] = T - [T.sup.e] greater than when T = [T.sup.e]. Of course, if each of the m needy students receives less than [DELTA T] in additional financial aid, then it follows that the average net price paid by the m needy students will be greater than when T = [T.sup.e].

   Since [DELTA T] = T - [T.sup.e], equation (1) can now be rewritten as:

   [Mathematical Expression Omitted]

   which is equivalent to:

   [Mathematical Expression Omitted]

   where [THETA] = [THETA.sub.1] = [THETA.sub.2] = [THETA.sub.3]. An implicit assumption of this chain of equalities is that, for financial aid awards, there is no behavioral difference between tuition dollars up to [T.sup.e] and tuition dollars above [T.sup.e]. This, however, is antithetical to a policy of cross-subsidization since with such a policy the purpose of setting T > [T.sup.e] is to award financial aid to needy students at an accelerated rate, which is equivalent to observing that [THETA.sub.2] exceeds [THETA.sub.1].

   From the discussion above it should be clear that if the objective of charging T > [T.sup.e] is to make a college education more affordable for needy students, then financial aid awards for all needy students must be made at least [DELTA T] greater. Unfortunately, a direct test of this requires student-by-student data which is unavailable. This example does, however, have a straightforward...