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                Dennis Epple

                 Prepared for
   Fiscal and Regulatory Competition
 60th Congress of the International Institute
              of Public Finance
      Milan, Italy, 23-26 August, 2004
Presentation Overview
   Framing the topic
      Some summary data

      Synopsis of Research on Colleges and Universities

   Research on College and University Competition
      Policy Issues

      Relevance outside US context?

      Model

      Empirical Evidence

   Open Research Issues

    US Colleges and Universities: Some Summary Data
    Approximately one third of US college-age students obtain a four-year
     undergraduate degree; 60% obtain some college education
    Students born outside the US comprise 11% of total college enrollment (two-
     and four-year institutions combined)
    There were 2,450 four-year colleges in the US in the year 2000
    All 50 states have public colleges or universities
       Many have multiple state universities and/or branch campuses

       Many states have multiple quality tiers

       Tuition is typically charged in public universities

       Government funding to public institutions is more than twice as large as
          tuition revenues they generate
       Average tuition in four-year public colleges ($4,281) was 20% of the
          average tuition in private colleges ($21,183) in 2002
       Enrollment in public colleges is 65% of total four-year college enrollment

Synopsis of Lines of Research
   Empirical Research on College Admission and Aid Policies, and Student
      Fuller, Manski, Wise (1982), Manski and Wise (1983)

      Kane and Spizman (1994)

      Bowen and Bok (1998),

      Kane (1998);
      Long (2002),

      Epple, Romano, Sieg (2003)

   Research on Changes Over Time in Extent of College Competition, Hoxby
    (1997, 2004)
   Peer effects in colleges, Betts and Morell (1992), Dale and Krueger (1998),
    Sacerdote (2001), Zimmerman (2000)
   Academic Labor Markets, Ehrenberg (2003, 2004 )
   Alumni Giving, Clotfelter (forthcoming)

Lines of Research Continued
   Dynamic General Equilibrium Model with Human Capital Formation,
    Heckman, Lochner, and Taber (1998)
   Borrowing Constraints, Intergenerational Mobility, and Public
    Financial Aid; Hanushek, Leung, Yilmaz (2004)
   Divergence of Interests between State Governments and State
    Universities, Groen and White, 2003.
   Pricing of Higher Education, Rothschild and White (1995)
   College Demographic Composition; Affirmative Action, Chan and
    Eyster (2003), Epple, Romano, Sieg (2002, 2004)
   Intra-college Resource Allocation and Incentives, Wilson (2002)
   Today’s Topic: Modeling and Empirical Analysis of Competition
    Among Colleges (Epple, Romano, Sieg, 2003, 2004)

Research summarized today is joint
 Richard Romano
 Holger Sieg

We Study:
   Tuition and Financial Aid Policies
   Spending on Instruction
   Variation in Quality Among Colleges
   Allocation of Students by Ability, Income and
    Other Characteristics Across Colleges
   Role of Endowments
   How do public and private universities differ?

Policy Issues :
   What is the Impact of Government Aid Targeted
    to Low Income Students?
      Increase college attendance by low income

       students, or
      Bid up college tuitions, or

      Increase colleges’ spending on instruction, or

      Increase grants given by colleges to students,
       leaving negligible impact on all above.

Policy Issues Continued…
   Impact of Policy with Respect to Diversity
      What is effect of college and university
       affirmative action efforts?
      What would be the effects of banning
       affirmative action?

Policy Issues Continued…
   What lessons does college competition have for
    predicting effects of school choice policies for
    primary and secondary education?
      Effects of public school choice policies

         Open enrollment vs Neighborhood schools

      Effects of Private school vouchers

         Effects on public schools

         Cream skimming?

         Impact of alternative voucher designs

Relevant Outside US Context?
   Our hope is yes…
   International Competition for Students
   Some key results are robust to differences in institutional arrangements
    and differences in objective functions
   Policy Applications
      Consequences of fostering development of private universities

      Government policy with respect to financial aid

      Public university policies and competition for students
           Tuition setting

           Criteria for Granting Financial Aid
           Selection/admission criteria

Our Approach
 Develop theory of college competition
 Conduct empirical testing of theory
 Develop parallel computational model
 Conduct policy analysis

Model Predicts:

 Dependence of admission and financial aid
  on student characteristics
    SAT scores

    Family income

    Racial/ethnic characteristics

 Variation of above across colleges

Model Also Yields Predictions
Regarding Market Competition and
Cross-College Variation:
 College quality hierarchy
 College expenditures
 College demographics
 Role of college endowments

Elements of Model
   Colleges seek to maximize a quality index
     Colleges can vary admission and aid as a
      function of student characteristics (SAT,
      income, race/ethnicity)
     Colleges choose instructional expenditures per
     Budget constraint: revenues from tuition,
      government subsidies, plus endowment income
      must cover costs

What determines college quality?
 Elements of quality in baseline model
    Instructional expenditure per student

    Admission test scores of student
     population (peer effects)
 Extended model incorporates college goals
  of achieving diversity in race and income

College “Technology” and Costs:
 Quality function q(,I)
    , peer average value of s in the college

    I, instructional expenditure per student

 Colleges Vary in Endowments, M
 Fixed Cost, F
 Variable “Custodial” Cost, V(k)

The Student Population
   Population of students/households follows
    bi-variate distribution, f(s,y), continuous in
    s and y
      s student aptitude (admission test score)

      y household income

Household Preferences:
 Households obtain utility from consumption
  of goods (household income net of tuition)
  and from quality of college attended by the
  student in the household: U=U(y-p, q(,I),s)
 We assume income elasticity of demand for
  college quality is positive
 The non-college option is “free” and has
  quality q0

College Decision Problem
   College chooses
      (s,y): Fraction of type (s,y) to admit

      p(s,y): Price net of financial aid to type (s,y)

      I instructional expenditure per student

      k, Number of students in the college

   Each college takes each prospective student’s next-
    best alternative as given, implying reservation price
    for applicant (s,y): pR(q(I,),s,y)

College’s Objective function

Solution to college decision problem
   College admits only those students to whom it can
    charge price greater than effective marginal cost

Effective Marginal Cost Includes
Marginal Custodial Cost, Input Cost,
and Value of Student’s Peer

With even moderate competition
among colleges…
   Price to each student will be approximately equal
    to the student’s effective marginal cost (except in
    top college)
   Computational model implies that price is very
    close to marginal cost with even a modest number
    of colleges (e.g., a half dozen)
   Empirical analysis also implies price
    approximately equals effective marginal cost
   Hence, colleges have little “market power”

Additional Properties of Solution
 Colleges spend more than Pareto efficient
  amount on inputs because quality is valued
  per se
 Concern for peer quality leads colleges to
  operate below cost-minimizing scale—to
  avoid admitting marginal-ability applicants

Predictions of model
 Financial aid increases with measured
  student ability (e.g.,SAT scores)
 Cross-subsidization within colleges
    High-income, low-ability pay full tuition

    Low-income, high-ability receive tuition
     discounts (i.e. financial aid)

Predictions of Model Continued
 Strict hierarchy of college qualities same as
  ordering of endowments
 Stratification by income
 Stratification by ability
 Admissions exhibit “diagonal” stratification
  exhibited in following figure

Intuition/Robustness of Results
   Why does price vary with student aptitude?
      Robustness to alternative objective functions?

   Why a strict hierarchy?
   Robustness of hierarchy prediction:
      Suppose all colleges were public and all with
       same expenditure per student?
   Why diagonal stratification?
   Note: We have extended the model to incorporate
    price caps (colleges post maximum tuitions)
Empirical analysis exploits three
databases that we have merged:
   National Post-Secondary Student Aid Survey (NCES)
      Contains detailed data for a nationwide sample of
       college students (SAT, family income, college attended,
       financial aid received, college grades, etc.)
   Petersons Proprietary Database
      Contains detailed data for the universe of colleges and
       universities (enrollment, average SAT, average
       financial aid awarded, tuition, student/faculty ratio, etc)
   National Science Foundation Database
      Financial data for universe of colleges and universities
       (endowments, instructional expenditures, etc)

Evidence: College quality hierarchy

 Six equal-sized groups of colleges
 Grouped and ranked by SAT
 Summary Data in Table 1

     Descriptive Statistics for Private Colleges
Number                                                Non-                          Endowment
of         Mean    Mean     Gross     Institutional   Institutional   Expenditure   Income Per
Colleges   SAT     Income   Tuition   Aid             Aid             Per Student   Student

  200       851    47721     8982         2346           4231           4386           130

  162       975    50511     9900         2731           3490           4498           163

  154       997    54053    12402         4282           4861           5621           259

  115       1045   62787    13330         5099           3527           5719           420

  115       1139   63981    15588         7271           3865           9983           847

  77        1247   73616    19674         7611           4917          15947          4085

Diagonal stratification implies that the within-
college correlation of income and SAT will be
lower than the correlation in the overall
student population
   Correlation in overall college student population is
   Within-college correlation is significantly lower
    (.128), supporting prediction of diagonal
   Note: Similar finding using data for public and
    private high schools (Epple, Figlio, Romano,

Generalizations of Model
   Incorporate Preference for Racial and Income
   Quality function q(,I,, )
       average value of s in the college

      I instructional expenditure per student

       proportion non-white students in the college

       mean income in college relative to mean

       income in population (q decreasing in )

Effective Marginal Cost Includes
Marginal Custodial Cost,
Instructional Cost, and Value of
Student’s Peer Externalities
   Tuition Declines with s
   Tuition Lower for Minority Students (r=1)
   Higher Tuition for Higher-Income Students

Predictions of Extended Model
   Financial aid increases with measured student
    ability (e.g.,SAT scores)
   Financial aid decreases with income
   Cross-subsidization within colleges
      High-income, low-ability pay full tuition

      Low-income, high-ability receive tuition
   Financial aid greater for minority students,
    implying differing boundary loci (next slide)

Reduced-form Tests of Pricing
   Tobit analysis with college fixed effects (Results
    in 1995 dollars for mid-ranked schools.)
      Financial aid increases significantly with SAT
      Aid significantly higher for African American
       and Hispanic Students
      Financial aid higher for low incomes after
       controlling for pricing by SAT and minority
      Results are similar for public and private
Structural Econometric Model
 All predictions of model are imposed
 Parametric forms chosen for:
    College Quality function

    Achievement and utility functions

    Population Distribution of SAT and
    Cost function

Estimation of Structural Model
   Group colleges into six quality tiers
   Assume s, y, p (SAT, income, tuition net of aid)
    measured with error by econometrician
   Calculate the probability that student i with
    measured (si, yi) attends his/her chosen college
    and receives observed tuition net of aid, pi.
   Likelihood function is product of above
    probabilities for all students in the sample

Estimation of Structural Model
 Choose parameters for quality, utility, and
  cost functions and parameters for
  distributions of s, y, p.
 Solve model for equilibrium
 Calculate likelihood function
 Repeat above until parameters found that
  maximize the likelihood function

Estimation Results
   Structural estimates imply that there is substantial
    error of measurement in s, y, p.
   Estimates imply colleges highly competitive,
    prices differ negligibly from effective marginal
    costs in all quality tiers
   Estimates imply greater dependence of aid on
    SAT and on income than reduced form Tobit
    estimates—as one would expect in the presence of
    measurement error (next slide)
Estimated Shadow Prices From
Structural Model:
College Quality   Shadow Price   Shadow Price
      Tier         Of Ability     Of Income
      1              $39.25        $-0.144
      2             $43.50         $-0.179
      3             $47.43         $-0.183
      4             $50.64         $-0.187
      5             $54.13         $-0.193
      6             $59.77         $-0.197
Policy Analysis of Government Aid

 Suppose all non-institutional aid currently
  given to students with incomes above
  $80,000 is reallocated to poorer students
 Equilibria before and after policy change
  shown next

Equilibrium Impacts of Reallocating
Non-Institutional Aid
Tier   Mean SAT       Mean Income College Aid
       Before After   Before After    Before After
  1    1001   1005    58504   61715   1458    1381
  2    1040   1036    53967   52606   4335    4579
  3    1062   1063    58868   60041   5439    5471
  4    1083   1078    62592   60801   6700    7019
  5    1107   1102    66305   63132   9010    9480
  6    1141   1135    74132   69004   10787   11553
The Research Frontier
   Model differences between public and private
   Model asymmetric information—students have
    private idiosyncratic preferences for different
    colleges (Our current research focus)
   Model dynamics including, especially, giving by
    alumni and other factors giving rise to changes in
    endowments over time


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