Market power and price discrimination in the US market for higher education

• DOI: http://doi.org/10.1111/1756-2171.12267
• Author: Dennis Epple,Holger Sieg,Richard Romano,Sinan Sarpça,Melanie Zaber
• Date: 01 March 2019
• Published date: 01 March 2019

RAND Journal of Economics

Vol.50, No. 1, Spring 2019

pp. 201–225

Market power and price discrimination

in the US market for higher education

Dennis Epple∗

Richard Romano∗∗

Sinan Sarpc¸a∗∗∗

Holger Sieg‡

and

Melanie Zaber§

Weestimate an equilibrium model of private and state college competition that generates realistic

pricing patterns for private colleges using a large national data set from the National Post-

secondary Student Aid Study (NPSAS). Our analysis distinguishes between tuition variation that

reflects efficient pricing to students who generate beneficial peer externalities and variation that

reflects arguablyinefficient exercise of market power. Our findings indicate substantial exercise of

market power and, importantly, sizable variation in this power along the collegequality hierarchy

and among students with different characteristics. Finally, weconduct policy analysis to examine

the consequences of increased availability of quality public colleges in a state.

1. Introduction

The net tuition paid by students sitting in the same college classroom is often quite different,

varying by student characteristics such as ability, income, and minority status.1Some variation

in observed tuitions reflects efficient pricing to students that provide positive externalities to

their classmates. Other variation reflects arguably inefficient exercise of market power. The main

∗Carnegie Mellon University; epple@cmu.edu.

∗∗University of Florida; romanor@ufl.edu.

∗∗∗Ko c¸ University; ssar pca@ku.edu.tr.

‡University of Pennsylvania; holgers@econ.upenn.edu.

§RAND Corporation; mzaber@rand.org.

The authors thank two anonymous referees, Philipp Kircher,Charles Manski, Derek Neal, Cecilia Rouse, Marc Rysman,

PetraTodd, Ken Wolpin,for comments and discussions. We also thank the NSF for financial support (NSF SES-1355892).

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do

not necessarily reflect the views of the National Science Foundation or the National Center for Education Statistics.

1By net tuition, we mean tuition net of the student’s institutional financial aid. Weuse posted tuition to refer to the

amount paid by students that receive no institutional aid.

C2019, The RAND Corporation. 201

202 / THE RAND JOURNAL OF ECONOMICS

objective of this article is to quantify the magnitude of these different effects. To accomplish this

goal, we estimate an equilibrium model of privateand public college competition in which private

college pricing reflects a combination of exercise of market power and discounts to students who

provide valuablepeer externalities. The intuition for the latter is straightforward. Competition for

students who provide desirable peer externalities induces colleges to offer discounts (financial

aid) to attract higher-ability students and students who increase diversity. The exercise of market

power relies on a more subtle foundation. Idiosyncratic variation in student preferences permits

colleges to charge more to high-income households. Colleges do not observe an individual

student’s idiosyncratic preferences. They know that some members of the applicant pool will

have strong idiosyncratic preference for their school, and they know that high-income parents

will pay a premium to accommodate preferences of their children. Hence, colleges charge a

premium to high-income applicants, correctly anticipating that high-income applicants with high

idiosyncratic preference for the college will select into the college. Colleges then use these

additional revenues to enhance quality by cross-subsidizing low-incomehigh-ability students and

by increasing instructional expenditures.

Our empirical analysis builds on the model developed in Epple, Romano, Sarpca, and Sieg

(2017). Private colleges choose admission, tuition,and expenditure policies to maximize a quality

index, whereas state colleges choose admission policies and expenditure to maximize aggregate

achievement of their in-state students facing state-regulated tuitions.2Demand for colleges is

modelled using a discrete-choice random utility framework. The demand model accounts for

the fact that not all students are admitted to selective colleges. Both private and state colleges

optimally will use minimum-ability admission thresholds. Given these admission thresholds, we

can determine the set of colleges that are feasible for each student type.

The optimal financial aid or pricing policies of private schools have a number of interesting

properties. First, because private schools set a posted or maximum tuition, a minimum-ability

threshold that characterizes admission policies of private colleges arises. A certain fraction of

students do not obtain financial aid and pay this maximum tuition. These are students that are of

relatively lowability in the school and thus do not qualify for merit aid. Moreover,these students

must have income sufficiently high so that they are willing to pay the price maximum. Second,

for other students, net tuition can be expressed as a convex combination of “effective marginal

cost” and a markup on income.

Important differences distinguish this model from a standard oligopolistic pricing model.

First, effective marginal cost depends on the ability and minority status of a student. Pricing by

ability- or merit-based aid arises because high-ability students increase college quality through

peer and reputational effects. Discounts for minority students arise because they enhance diver-

sity.3Second, the markup term for a student does not depend on the overall market share of the

college, but on the market share conditional on observed student characteristics. We show that

these terms can differ by large margins among students, especially for highly selective colleges.

Hence, “local” or conditional market shares drive markups in the model, and not overall market

shares. Third, the markup is monotonically increasing in student or household income and arises

due to price discrimination. As a consequence, this model is sufficiently rich to generate the

qualitative features of tuition policies observed in the US market for higher education.

The main contribution of this article is that we derive and implement a new semiparametric

estimator for the parameters of the model. We can identify and estimate almost all parameters

of the model using a method of moments estimator that is based on the difference between the

observed and predicted price functions at private colleges. To implement this estimator, we need

a nonparametric plug-in estimator of the conditional market share for each student at the school

2The private college objective can be interpreted as a desire to maximize their reputation. The best objective to

attribute to colleges is an open question, and we discuss alternatives below.

3Our article is, therefore, also related to the recent literature that estimates empirical models of affirmative action.

Some recent work includes Bodoh-Creed and Hickman (2017), Kapor (2016), and Cestau, Epple, and Sieg (2017).

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The RAND Corporation 2019.