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Trang 3HARVARD UNIVERSITY
Graduate School of Arts and Sciences
THESIS ACCEPTANCE CERTIFICATE The undersigned, appointed by the
Division
Department Economics
Committee
have examined a thesis entitled
The Market for Higher Education: Ecdomic Analyses
of College Choice, Returns, and State Aid Policy presented by
Bridget Terry Long
candidate for the degree of Doctor of Philosophy and hereby certify that it is worthy of accept
Trang 5
The Market for Higher Education:
Economic Analyses of College Choice, Returns, and State Aid Policy A thesis presented
by
Bridget Terry Long
to
The Department of Economics in partial fulfillment of the requirements
Trang 6UMI Number: 9972364
Copyright 2000 by Long, Bridget Terry All rights reserved
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Trang 8Abstract
The Market for Higher Education:
Economic Analyses of College Choice, Returns, and State Aid Policy
Prof Caroline Hoxby Bridget Terry Long
Harvard University
This dissertation considers how college choices are made, how college financial
aid affects these decisions and is distributed, and why the benefits to higher education differ among the college-educated
The first paper examines the effect of state in-kind aid These subsidies allow public colleges to charge in-state students a discounted price, but the resulting price gap between public and private schools could have additional ramifications on the quality and sector of college choices First, I utilize a conditional logistic model to determine how college characteristics such as cost and quality affect choice and enrollment decisions Then, using the parameters of the model, I predict the choices students would make under different subsidy systems Students are predicted to choose state-subsidized colleges even if the gap in resources between public and private options is substantial thereby Suggesting that in-kind aid may negatively affect the quality of college investments in some states If a voucher system were instead enacted, half as many students would choose to attend public colleges
Trang 9subsidies that students would receive in different states and compare them to their families’ state tax liabilities Although higher-income individuals are found to receive the largest subsidies, the benefit they receive net taxes is often below what is enjoyed on average by lower-income students
The final paper, joint with Caroline Hoxby, examines the growing income
inequality among the college-educated by quantifying the roles of three possible sources The first source, or “extensive margin,” is the increasing demographic diversity of people
who attend college The second is an increasing return to aptitude The third, or
“intensive margin," combines the increasing self-segregation (on the basis of aptitude) of students among colleges and the increasing correlation between the average aptitude of a college's student body and its expenditure on education inputs We find that of the
Trang 10Acknowledgments Introduction Table of Contents The Effect of State Tuition Subsidies on Enrollment and College Choice Section I Section II Section II Section IV Section V Section VI Introduction Literature Review Framework and Model
Estimating the Determinants of College Choice and Enrollment Testing the Peltzman Hypothesis — The Effect on Quality Conclusions The Incidence of State In-Kind Subsidies to Higher Education Section I Section II Section II Section IV Introduction Estimating the Subsidies Received Results Conclusions
Explaining Rising Income and Wage Inequality among the College-Educated Joint with Caroline Hoxby Section I Section Section II Section IV Section V Section VI Section VII Section VIII Introduction
Background — Wage Inequality Measures from the CPS 1969-1996 The Combined-Surveys Data and Other Data
Descriptive Analysis of the Income and Wage Distributions Identifying the Intensive Margin
Parametric Decomposition of the Variance of Income and Wages Results
Trang 11Acknowledgments
First, and foremost, thank you Lord Almighty for the many blessings You have bestowed upon me Through You, all things are truly possible, and a way has been made out of no
way
The author gratefully acknowledges indispensable comments and support from Caroline Hoxby, Larry Katz, and Claudia Goldin Their time and effort was invaluable in helping
to form this work and develop me as an economist Additional thanks are given to Richard Murnane and Chris Foote Part of this research was supported by a grant from the American Educational Research Association which receives funds for its “AERA
Grants Program” from the National Center for Education Statistics, the Office of
Educational Research and Improvement (U.S Department of Education), and the
National Science Foundation under NSF Grant #RED-9452861 Opinions reflect those of the author and do no necessarily reflect those of the granting agencies
To my family and friends
Your love and unconditional support has continually sustained me Thank you for
teaching me to dream and then believing in my dreams completely To my Mother and Father
Your steadfast commitment to my education instilled in me its importance The
key you gave not only unlocked the door for me but inspired me to study how
education could also help others Second only to your love, it is the best gift you could have given
Finally, to Carl, my soulmate and best friend
You have been my rock and have shown me the light when things have appeared to be at their darkest I cannot express enough appreciation for the sacrifices you
have made to help me realize this dream Through your love, you have also taught me about the most important things in life, lessons that cannot be learned from
books Always and forever, I love you
“Our progress as a nation can be no swifter than our progress in education."
John Fitzgerald Kennedy
Trang 12Introduction
The return to a college education is substantial In 1997, individuals with only a
high school degree earned 29% less than those with an associate’s degree and 72% less than those with a bachelor’s degree.' This fact has encouraged the government to increase college accessibility Given the assumption that cost is an obstacle to
opportunity, various policies such as subsidized educational loans and grants have been implemented to reduce price barriers However, the largest support has come from state governments in the form of tuition subsidies In 1998, state governments gave over $52 billion to public institutions of higher education These appropriations have served to
reduce the tuition price for in-state students at public colleges.”
But this government involvement has left several questions First, the effect of State policy on student investment decisions is not fully understood Have these subsidies really increased access? Have they affected college decisions in other ways such as altering the quality of investments? There are also concerns about tax equity and the allocation of these state subsidies How are the tuition subsidies being distributed to
students, particularly by income level? How do the benefits received by students
compare to the tax liabilities of their families?
Moreover, when examining the long-term benefits of higher education, it is clear that the gains in income are not distributed evenly among students In fact, income
inequality has grown substantially among the college-educated during the last 30 years Why has there been such growth in the dispersion of incomes? What does this say about
! Calculated from the U.S Census Bureau, Current Population Reports
Trang 13the long-term repercussions of state in-kind subsidies if they do in fact alter college
decisions? This dissertation explores these three issues
In order to assess the effect of state subsidies on college decisions, the
determinants of college demand must first be considered How important is price and quality in college decisions? The first paper answers this question by developing a model
of college choice I then examine how state in-kind subsidies affect higher education
investments, particularly in terms of the quality and the sector of the school of choice
The second paper builds upon this model to examine the distribution of state subsidies
among students and analyzes the resulting tax incidence implications Finally, the third paper considers why income inequality has grown among the college-educated Its conclusions shed additional insight into how particular college choices could affect individuals in the long run
The Effect of State Tuition Subsidies on Enrollment and College Choice
The first paper examines the effect of a specific form of college financial aid — state in-kind subsidies which allow public colleges to charge in-state students a
discounted price While this aid may increase access to higher education, the resulting price gap between public and private schools could have additional ramifications on the quality, duration, and sector of college choices Depending upon the types of colleges a state decides to subsidize, a student could be induced to choose a school that is not a good
match or that has less resources than a private college they might otherwise attend In
Trang 14quality-adjusted human capital than they would if the grants were fungible and perhaps less than
they would in the absence of any aid (Peltzman, 1973) I test whether this is true using a
model of college choice, and then use the estimated parameters to predict individuals’ choices given different aid scenarios
My analysis is broken into several parts First, I analyze how state in-kind
subsidies affect which college an individual would choose by examining the influence of
cost while also accounting for concerns such as quality and location Although previous
work has had to rely upon state-aggregated variables, I utilize the conditional logistic model in order to take advantage of extensive match-specific information between
individuals and potential schools The second question I answer is whether the individual will choose to attend college at all Students who do not attend college in one state may
decide to do so in another given a different set of opportunities Therefore, I use a simple
logistic model to compare individuals who are similar in terms of family background and ability but who differed in the college enrollment decision due to the characteristics of
nearby schools and local labor market conditions The parameters of the model allow me
to predict the likelihood of attendance given the characteristics of the potential college
The net effect of the two-step choice model is that I can predict the colleges a student is most likely to attend and then whether the person will attend college at all
Using this methodology, I am able to simulate the effect of different subsidy systems on college decisions At one extreme, a state could offer highly competitive, subsidized,
public options like California does with UC Berkeley In contrast, a state may choose to
Trang 15me to answer whether students are being induced to choose lesser alternatives than they
would otherwise in terms of school expenditures and peer resources Finally, the paper
simulates how investment decisions would change if state aid were instead given in the
form of a voucher that could be applied to any within-state school
The results suggest that the level and distribution of state in-kind subsidies do substantially influence college investment decisions Students appear to choose state-
subsidized colleges even if the gap in resources between public and private options is
substantial If states instead awarded each individual with a voucher that could be
applied to any school, public or private, 54 percent fewer students are predicted to attend
a public college, and high-ability students would experience gains in college quality
The Incidence of State In-Kind Subsidies to Higher Education
The second paper of the dissertation questions how the financial benefits of state in-kind subsidies are distributed among students of different family income levels The allocation of state aid among individuals could have major implications on equity in the tax system As noted by Hansen and Weisbrod (1969), it is possible that middle- to upper-income college students enjoy the aid at the expense of poorer individuals since
low-income individuals are less likely to attend college but must still contribute to the
taxes which fund the state appropriations
The possible regressivity of state higher education subsidies has been a much-
debated topic but has yet to be resolved Although there is significant variation at the
Trang 16measures of subsidies and forego the detail needed for a clear answer The subsidy received by a student will depend on the level (four-year or two-year) and quality of the college attended, and enrollment patterns by income at these different types of schools must be taken into account in order to determine how state subsidies are truly distributed I use the methodology developed in the first paper to predict the choices and subsidies of a large sample of students under different state aid programs
Once estimating the subsidies received by students, the paper compares the benefits to the state income tax liabilities of their families The results suggest that the
distribution of state subsidies does differ significantly by income with high-income individuals receiving the largest subsidies However, when the benefit received by high- income individuals is compared to the tax liability of their families, seven of the ten states
were found to distribute subsidies in a progressive manner, and only in New York were
the net benefits of the higher-income groups larger than those of the lower-income groups Furthermore, in Nebraska and Massachusetts, there is some evidence that
income is redistributed in a progressive manner through state in-kind subsidies
Explaining Rising Income and Wage Inequality among the College-Educated
(joint with Caroline Hoxby)
Although the positive returns to a college education are well-documented, the
benefits of higher education are not evenly distributed among students During the last
two decades, the variance in the income of the college-educated has risen sharply The
Trang 17real terms from $13,275 in 1972 to $49,000 in 1995 (both in 1995 dollars) The final
paper of this dissertation, joint with Caroline Hoxby, attempts to quantify the roles of
several possible sources of this grown in inequality First, the variance in incomes could
be due to increased student diversity as the demographics of college students have changed over the last fifty years This first source is called the “extensive margin.” Second, we look at the changing return to aptitude over time Finally, we examine how changes in the market structure of college education have affected the way students are distributed among colleges Students tend to be more segregated by skill and there has been an increasing correlation between student body aptitude and school expenditures so that more able students tend to receive more college resources This is called the
“intensive margin.”
We decompose the increase in income dispersion by comparing the backgrounds and college experiences of males who were approximately age 32 at three different points of time: 1972, 1986, and 1992 For 1972, we use data from Occupational Changes in a
Generation; for 1986 the NLS72; and for 1995 the NLSY This data is matched to detailed information about each college’s student body, selectivity, expenditures, and
inputs using institutional surveys and other sources
First, we compare how real income has varied among these three groups of men
along different parts of the distribution For example, real incomes for men at the 90"
percentile have increased $15,000 in real terms from 1972 to 1995 However, men at the 10" percentile and below have realized real losses in income When grouping the men by
Trang 18by 13% from 1972 to 1995 while incomes for men at the least competitive schools grew
only by 5%
Our parametric analysis involves examining how our model changes when adding additional variables First, we estimate the model using only background variables, or things that would be attributed to the extensive margin Then, we added ability measures of the individual and the college attended Finally, we added variables to measure the intensive margin like college inputs and interactions between an individual’s aptitude and the standard deviation of college SAT scores Explanatory variables were added
sequentially in order to determine how the effects of background are affected by aptitude, and how the effect of aptitude is affected by college attributes Having estimated these equations, we do an analysis of the variance of earnings showing how much of the total
variance is explained by the model and how much is residual variance Finally, we use Oaxaca-type decompositions of the variance to attribute the growth in income inequality not only to changes in the variances of individual and school attributes (X, Z, and W) but to changes in the return to these attributes (8, 5, and y), and changes in the residual
We find that we can explain over half of the growth in inequality with observable demographics, measures of aptitude, and college attributes Of the growth that can be explained, about 1/4" is associated with the extensive margin, 1/3™ with an increased
return to measured aptitude, and 5/12" with the intensive margin If the intensive margin
Trang 19In conclusion, the third paper suggests that particular college choices are very important in determining the long-term returns of higher education Since state in-kind aid may influence college decisions (as shown in the first paper), it is important for
governments to take into consideration the conclusions of the final study If state
subsidies induce individuals to attend colleges with fewer resources, then they could have
long-term negative effects on the income levels realized by students These
considerations would also affect the incidence of state subsidies in terms of how the long-
Trang 20The Effect of State In-Kind Tuition Subsidies on College Enrollment and Choice
Section I: Introduction
State appropriations to public colleges make up the most significant higher
education aid policy in the United States, amounting to over $52 billion in 1998 In
comparison, the federal government spent only $15.4 billion for higher education financial assistance and training programs.' This in-kind aid serves as tuition subsidies allowing public institutions to charge in-state students a discounted price.” State
appropriations constitute nearly two-fifths of the total revenues received by public
schools while private institutions rely primarily on tuition revenue for support (nearly half of their total revenue) The difference in revenue source is apparent in the mean list
tuition prices of each sector In 1999, four-year private colleges charged an average of
$16,080 for tuition and fees while public colleges charged only $4,037.° After accounting for the fraction of the disparity attributable to differences in expenditures by sector, the price gap remains large and could affect whether individuals attend college and the
‘Sources: Center for Higher Education (data collected from state reports), and Digest of Education Statistics
? Although the list prices of colleges are generally below the actual cost of education at both public and
private schools, the amount of state support of public institutions seems to directly affect public tuition
levels Given budget constraints, state aid allows for a reduction in other sources of revenue at public
institutions, most notably tuition The correlation between the mean tuition cost of four-year public colleges
and the mean amount of state appropriations received by such schools was -0.68 from 1977 to 1997 (NCES
data) In practice, schools are generally discouraged by state legislatures from increasing the tuition above a certain percentage from year to year However, substantial increases have been allowed when state
appropriations have been reduced thereby implicitly linking the subsidy and tuition level
3 Amounts are for in-state students The figures are weighted by enrollment to reflect the charges incurred
Trang 21quality of their investments.* This paper examines the effect of state in-kind tuition subsidies along these dimensions of college choice
Governments have implemented several types of financial aid programs to reduce
postsecondary price barriers and the cost of capital for liquidity-constrained individuals
Fungible aid, such as federal educational loans and Pell grants, may be applied to any
school and thereby extends the budget constraint of a student In contrast, state in-kind aid is linked to specific colleges and only extends the budget constraint for particular choices This disturbs the cost tradeoffs between options as private tuition costs are expensive relative to those publicly subsidized Since colleges vary in the products and opportunities they offer, there may be important quality differences between any two
options and altering tradeoffs between schools could affect investment levels and educational returns Individuals may be propelled to choose schools that devote fewer resources to education production (expenditures) and have less competitive student
bodies (lower test scores).° Therefore, in-kind subsidies could induce individuals to invest in less quality-adjusted human capital than they would if the grants were fungible and perhaps less than they would in the absence of any aid Peltzman (1973) suggests that, contrary to the aims of the policy, the aggregate consumption of higher education
could fall
* Private four-year colleges spend on average $1,478 more per student on instructional expenditures,
academic support, and student services The gap is larger when also including scholarships, institutional support, operation and maintenance, research expenditures, public service expenditures, and transfers defined as total educational and general expenditures ($5,813) Source: 1995 IPEDS Calculated for non- specialized, baccalaureate-granting schools
5 Students are considered inputs as wells as outputs in educational production For example, students may generate peer effects on each other which could affect human capital production
Trang 22If state tuition subsidies encourage students to attend public rather than private
colleges, there could be implications on market efficiency In-kind aid may cause
students to favor colleges in the public sector This tendency, however, may give public
institutions unwarranted market power that could result in the reduction of their
incentives to provide quality education for a low cost Sonstelie (1982) argues that private schools are more efficient, and therefore, this redistribution of students to the
public sector would result in welfare cost The long-term return to postsecondary education may also be affected as trends suggest that school choice has become more
important in determining the realized gains to a college education.®
There are also concems as to whether aid irrespective of income is the best method to provide support In-kind subsidies may primarily help inframarginal students who are without need even when facing unsubsidized tuition costs In addition, many
question whether the method of financing state in-kind aid causes unintended
redistribution Although college attendance is primarily a middle-to-upper income activity, all income groups pay taxes, and therefore, the policy could be regressive
depending on the progressivity of state sales, income, and property taxes (Hansen and Weisbrod, 1969)
Finally, the insurance properties of state in-kind aid could either promote or
discourage efficient investment in human capital Since state aid is funded by income
taxes, individuals are not held fully responsible for the costs of higher education if they
® Variance in the income and wages among the college-educated has grown significantly during the last two
decades with graduates from schools with greater resources and selectivity reaping the largest returns Hoxby and Long (2000) argue this change is due to increasing college segregation on the basis of aptitude
Trang 23do not make a high salary Therefore, in-kind aid provides individuals with insurance against fluctuations in the value of their college education On the one hand, this may
increase investments in education because a person who cannot insure himself against
shocks to the value of his human capital (disabling accidents, for instance) will choose to
invest in less human capital On the other hand, the implicit insurance generates an
adverse selection problem in which the subsidies encourage college attendance among individuals who know that they have a low probability of earning enough later in life to fully “repay” the state for the cost of their education There may also be a moral hazard problem For example, a person might invest in a great deal of education but elect never to work and therefore not have to “repay” the state at all
This paper examines the two effects in-kind state tuition subsidies could have on postsecondary investments First, how much do in-kind subsidies affect the decisions of
whether to attend college and which school to choose? Second, do in-kind subsidies
actually cause college investments to decrease in quality as asserted by Peltzman? Are students being induced to choose lesser alternatives than they would otherwise in terms of school expenditures and peer resources? In summary, are discounted public options negatively distorting the investment decisions of individuals? In order to assess the impact of this aid on college investments, the paper will first estimate a model of college choice
By comparing their own characteristics with those of potential colleges,
individuals predict the potential returns to attending different schools They then elect
whether to enroll and what college to attend by choosing the option that maximizes their
Trang 24lifetime utility The college decision is therefore made up of two simultaneous problems The first goal of this paper is to estimate the “which college” decision ’
My model of college choice is designed to take advantage of the extensive match- specific information between potential students and colleges I estimate a conditional logistic regression model in which each individual’s match with 2,751 potential colleges
is examined Unlike previous work that has relied upon state-aggregate variables or greatly simplified the matching of students to colleges, this model uses far more
information Tuition costs are individual-specific depending on whether in-state or out- of-state tuition would be charged and also account for the Pell Grant a student could expect to receive There are also variables to measure the similarity of the student to prospective college peers and the distance of the college from the student Finally, school expenditures are included to assess the educational product offered by the college The
model predicts which college an individual would attend conditional on college
enrollment
The parameters of the model are identified because of considerable differences in
States’ in-kind subsidy programs For example, in 1995, state subsidy levels ranged from
$9,506 per student in Alaska to $2,312 per student in Vermont Figure 1 displays how
state aid is distributed among college students at public institutions Likewise, the resulting subsidized tuition costs differ greatly In 1995, state schools in Hawaii charged
7 While ordinarily a nested logit model would be used to estimate the two decisions simultaneously, the conditional logit model is too complex for a simple application of the theory and a two-step method is
Trang 25an average of only $979 per student while Vermont charged $8,351.2 However,
distinctions between state programs involve not just the average amount of the subsidy
but how the subsidies are distributed among schools of different expenditure levels,
degrees of competitiveness (student body aptitude), and types (two-year versus four-year) Several possible subsidy regimes exist At one extreme, a state could offer highly
competitive, subsidized, public options For example, the state of California supports UC Berkeley which boasts a median student body SAT of 1250 and student expenditures over
$12,000 per student (see Figure 2) In contrast, a state may only support schools with
average-ability students For example, Massachusetts does not offer any public schools
with a student body SAT median above 950 or student expenditures above $5,900 per student (see Figure 3).” The distribution of tuition subsidies within a state is important since over four-fifths of students attend colleges within their state of residence, and their Opportunities are therefore heavily dependent upon their state of residence
While the conditional logit regression model provides me with estimates to predict what school a student would choose given his circumstances, I must also
determine whether the student would enroll in college at all Students who do not attend college in one state may decide to do so in another given a different set of opportunities Therefore, I compare individuals who are similar in terms of family background and ability but who differed in the college enrollment decision I use the simple logit model with controls for the local labor market, individual characteristics, and the characteristics of the school to estimate the likelihood of enrollment given college choices
® Calculated per FTE student State appropriations exclude sums for research, agriculture, hospitals and
medical schools Source: Research Associates of Washington, State Profiles: Financing Public Higher
Education
Trang 26The two-step college choice model serves as a building block to assessing the impact of state in-kind support on the quality of college investments The parameters
estimated in the models allow me to predict the probability a student would choose a school given his opportunity set and the probability of attending that school at all Therefore, I am able to simulate the effect of different subsidy systems on college
decisions For example, the paper demonstrates what would happen if students were presented with the level and distribution of subsidies they would face in various states The “new” residence of the student is simulated by assigning revised measures of tuition
cost (in-state versus out-of-state charges) and distance as if the student lived in the state
Since the student bodies of each state differ, simple comparisons between the investments
made by each state’s students would be misleading However, this method wiil allow me to test Peltzman’s hypothesis While there may potentially be endogeneity between state policies and their populations, states with similar demographics pursue different policies providing the opportunity to do such a comparison Finally, the paper simulates how investment decisions would change if instead state aid was given in the form of a voucher that could be applied to any within-state public or private school
The data are from two main sources The National Education Longitudinal
Survey (NELS) is a study of 8" graders followed at two-year intervals since 1988 It contains extensive information on family background, high school performance, and
postsecondary educational choices The Integrated Postsecondary Education Data System (IPEDS) supplies information on the schools I use the 1992 data to capture college characteristics at the point when most NELS participants were 12" graders This
Trang 27
is supplemented with information from Barron’s Profile of American Colleges for
information about student body aptitude The results suggest that the level and
distribution of subsidies do influence college investment decisions Peltzman’s hypothesis is valid when in-kind subsidies are large even if the gap in quality between
public and private options is substantial Students do negatively adjust their investments
in response to the in-kind subsidies If states instead awarded each individual with a voucher that could be applied to any school, 54 percent fewer students are predicted to attend a public college, the net tuition price would fall, and high-ability students would
experience gains in student expenditures
Section II: Literature Review
Justifications for Aid to Education
Several justifications for the state support of higher education are rooted in
economic theory.'° First, capital markets for financing higher education are imperfect
Students are unable to use potential future earnings as collateral, and therefore, may not
be able to secure the funds to make their optimal investment in higher education In-kind tuition subsidies address this market imperfection by providing a long-term loan in which
the individual benefits as a student and repays the state in taxes over the rest of his life If in-kind subsidies allow individuals to attend college who optimally should but could not otherwise, they could move the economy to a more efficient equilibrium
!8 Poterba (1996) provides a good summary of several of these arguments
Trang 28State tuition subsidies could also induce society to invest at a more socially
optimal level The private considerations of an individual ignore the positive externalities education has on society and therefore may cause students to underinvest in education A policy that increases individual investments could therefore move the economy toward
the social optimum Aid to educational institutions may also be justified if colleges and
universities provide beneficial public goods such as products or information to the state Finally, the fact that public institutions are the providers of the subsidized product may make it easier for the state to monitor the product provided thereby reducing the
likelihood that the service rendered will be inadequate or below expectations This
avoids a fear associated with proprietary schools that suggests they do not actually provide the educational services that they claim
Concerns about In-Kind Subsidies
While economic theory suggests that state subsidies could remedy market imperfections, in-kind aid could also generate distortions Peltzman (1973) shows that in-kind subsidies may discourage students from investing in education beyond what is offered at public colleges Of particular concern are students who in the absence of subsidies would choose to invest in slightly more education than that of public colleges
If a sufficient number of people lower their investment in response to the in-kind
subsidies, aggregate educational investment could fall below the level it would be in a world without subsidies
Trang 29
options sit on the curve which has been drawn as linear for simplicity However, due to
the state subsidy, the price of a public college, for any given level of educational expenditures, is lower than that of a private school Public options allow students to invest in more human capital than is dictated by their original budget constraint and still consume the same amount of other goods Therefore, an individual’s budget constraint becomes “kinked” at the public options Individuals will tend to gravitate towards the
public options due to the increase in the consumption of other goods Although some
students may increase their investment in higher education to a public option that is
slightly above their previous choice, the concern of Peltzman is that students will adjust their investments downward in terms of expenditures and quality Since selective college
admissions policies limit the number of individuals who are able to increase their
investments, an overall negative effect on investment levels is feared with the
introduction of state in-kind aid
Figures 5a and 5b display examples of this for specific states In the California
example, aid to CSU Chico and UC Berkeley extends the budget constraint at their
points Meanwhile a student attending Scripps College (a private school) would not
receive such aid and is constrained to the original budget line The aid in fact makes UC
Berkeley less costly than Scripps College even though the former offers more educational
units or school resources in the production of human capital However, this is not true in
Massachusetts due to its distribution of subsidies The cost of augmenting the units of education offered at UMass Amherst to those provided by Tufts University (a private college) is extremely high as a student would forfeit the entire state subsidy In other
Trang 30words, the price of additional dollars of college expenditures is extremely high at the beginning of any interval not “covered” by in-kind subsidies
The reallocation of students from private to public colleges due to in-kind
subsidies may have efficiency implications if the public and private sectors differ in how
well they translate expenditures into human capital Sonstelie (1982) suggests that
private schools are more efficient since public schools have less incentive to reduce costs
This is because they may be able to derive market power from the fact that they do not have to compete directly with private schools that have similar expenditures, and there is not free entry into the market Public schools could abuse this capacity by offering a less
than competitive product per dollar spent Therefore, given a difference in efficiency by sector, a redistribution of students from the private to public sector could induce a welfare cost Sonstelie’s estimates based on data from California school districts in 1970 suggest
that private schools have lower costs than public schools for equivalent quality, and therefore, the welfare cost may be substantial for primary and secondary schools The relative efficiency of postsecondary institutions has not been adequately estimated in the literature to resolve this welfare-cost question for the higher education market
Finally, depending on the distribution of in-kind subsidies and format of state
taxes, an in-kind subsidy program could therefore be either regressive or progressive
This stems from the fact that college attendance is more common among students from higher income families who also pay more taxes Using California data, Hansen and
Weisbrod (1969) concluded that rich families got the largest subsidy since they were very
Trang 31However, this study is unlikely to be representative of all states since California has an in-
kind subsidy program that provides unusually generous subsidies to the types of colleges
often attended by the children of middle-to-upper income families In addition, since the
1960s, there have been significant changes in the market for higher education including the expansion of the community college system Detailed estimation of the lifetime taxes paid by different groups and the realized return to educational investments needs to be
taken into account for a more accurate conclusion These findings have sparked a rich
debate that has not yet been settled and will not be addressed in this present study
Estimates of the Effect of Price and Tuition Aid on Student Demand
Economists have utilized the demand framework to study how changes in the
price of higher education have affected individuals’ choices about college College
demand, or enrollment, will depend upon the cost of education, the prices of alternatives, and the tastes or preferences of the individual subject to a budget constraint Therefore,
investment in higher education should be negatively related to tuition costs, and public
tuition subsidies should increase the probability of enrollment
Early estimates of the effect of cost are based upon relating variation in aggregate data of college investment patterns to tuition and/or subsidy levels Campbell and Siegel
(1967) examine fluctuations in national rate of enrollment at four-year colleges from 1919 to 1964 Using national data by year, they estimate the elasticity of enrollment with
respect to real tuition price to be -0.44 when also controlling for real disposable income
per household.'' However, the aggregation of the data and resulting small sample size
'' The authors use data for only nine years of the period 1927-1963 due to incomplete tuition data
Trang 32(26 years) prevent the authors from making more reliable estimates and exploring issues
at the micro level State-level data are used as the level of observation in later studies Hopkins (1974) exploits state cross-sectional variation using 1963 data to analyze whether increases in public tuition levels dissuade individuals from enrolling in college
(discouragement effect) or causes them to attend a different type of college (substitution
effect) He incorporates student aid into the framework by defining net tuition per student as the state’s mean charges minus mean state scholarship aid After controlling for
education and income levels by state, the results translate into a demand elasticity of —
0.097 with respect to net public tuition when evaluated at the means In other words, the discouragement effect of an $1,000 increase (1992 dollars) in public tuition would cause
a ten percent drop in total college demand (from an enrollment rate of 37.7 percent to 34.0 percent) or nearly 58,000 fewer new students would have entered college that year.'? Some older students might also reconsider their enrollment decisions due to an increase in tuition costs so that the total number of those estimated to be potentially affected could be larger
Hopkins finds that the discouragement effect would also be accompanied by the
substitution of private college education for public college education His evidence
suggests that enrollments at private colleges increase when public tuitions rise and vice
versa However, Hopkins’ estimates of the size of the reallocation of students between
sectors are not statistically significant perhaps because he, like Campbell and Siegel, has
'? Calculations based off a first-time enrollment of 1,442,000 in 1965 Source: Statistical Abstract of the
U.S Figures are reported in 1992 dollars so as to make them comparable to the results of this study A
$1,000 change is equivalent to a $222 increase in 1963 dollars or doubling the mean tuition cost of public
Trang 33a small sample size More importantly, Hopkins acknowledges that policies that lower
public tuition levels would cause students to alter the sector of enrollment thereby
reducing the desired effect of increasing total enrollment.'?
Kane (1995) provides more recent estimates utilizing several data sources (the High School and Beyond, National Longitudinal Survey of Youth, and October Current Population Survey) and exploiting both between-state differences and within-state
changes in public tuition prices over time He finds that during the late 1970s and 1980s
states with higher public tuition levels had lower college entry rates, and within-state tuition increases led to lower enrollment rates Low-income students and those attending two-year colleges seemed to be most affected Kane’s estimates range from —0.10 to —
0.20 for a $1,000 increase (1992 dollars) in public two-year tuition levels and can be translated into an elasticity of demand of -0.20 Differences in four-year tuition levels
yield even smaller estimates as do within-state responses to tuition-level changes over time However, this work suffers from aggregation problems also prevalent in earlier the
studies
The Problems of Aggregation
College choice studies based upon cross-sectional variation in state-level tuition data are primarily identified by fixed differences between states These estimates could be misleading because it is difficult to distinguish the impact of tuition from any other characteristic of the state that has remained constant over time As Rouse (1994) cautions
with the interpretation of her own work using the same data as Kane, interpreting state
'? See Leslie and Brinkman (1988) for further discussion of early demand studies
Trang 34variation as a natural experiment for tuition changes has the problem that omitted state factors may be correlated with enrollment, subsidy level, and tuition For example, if unobserved state preferences for higher education cause a state to provide larger tuition subsidies, the unobserved preferences could be negatively correlated with the mean tuition level of the state The resulting parameter on tuition would be biased downward
This would suggest that the relationship between enrollment and tuition cost has been
underestimated using state cross-sectional data However, state income per capita may be
positively correlated with tuition levels This would result in the relationship between
enrollment and price being exaggerated in estimation
While state subsidy and tuition levels vary significantly by state, much of the heterogeneity in the market of higher education exists at a finer level Tuition levels and subsidy amounts differ greatly among different levels of schools within a state Public universities typically receive the largest subsidies, nearly the double the subsidy of public two-year colleges and on average ten percent more than that of public four-year colleges Tuition levels differ in similar manner by type of school with universities costing the
most and two-year colleges the least These differences also exist between four-year,
public universities In California, for example, each University of Califomia branch receives at least two and a half times the amount of state appropriations that a California State University site would receive In 1998, UC Davis received state appropriations that
Trang 35student Likewise, tuition costs vary That year UC Davis cost $4,230 while CSU
Fullerton charged only $1,927.'*
Cost is not the only variation that state-aggregation would mask State variation in
the number and quality of schools available to students is also substantial States like
California and Pennsylvania offer over thirty public, four-year institutions while states like Michigan and Virginia offer only fifteen In terms of student body aptitude, a proxy
for peer resources at the school, only Virginia and California offer public institutions
rated as most competitive
The distribution of cost, subsidies, and quality among schools within a state may be important to college decisions However, state-level aggregation masks much of this variation that could more clearly illustrate the determinants of enrollment For example, an above-average student in Massachusetts would have a very different opportunity set
than one from California (review Figures 2 and 3) College admissions test scores and high school grades will determine the level(s) of selectivity into which a student could expect to be accepted While a student from each state would face similar costs for a
private college (except for traveling costs), the resident of California would have cheap public options available to her that have student bodies with similar characteristics to her own The outlook for the student from Massachusetts would differ greatly As in many
other states, if he is a high-ability student, there are few public options for him No subsidized, public institutions exist within Massachusetts that have above-average
median student body SAT scores The resources devoted to students at each level of
'S Source on state appropriations: Center for Higher Education, Illinois State University Data collected
from state reports Source on enrollment and tuition costs: Peterson’s College Quest
Trang 36school also differ greatly between the states since schools with higher student body aptitude tend to have higher student expenditures.'*
Suppose that a student is deciding between schools in two states State A has many schools with median test scores that range from high to low State B instead has
only schools with average median test scores In state-aggregated data, the states would appear alike as their mean school quality level would be identical However, as described above, a student with an SAT of 1200 would have very different opportunities in each State If the student chose a school in State A that matched his characteristics, there
would be no way to distinguish in the data why In fact, if mean tuition levels differed by
State with State B having lower average costs, it would appear that higher tuition costs
increase the likelihood of attendance although unobserved school differences are really the motivating factor While the distribution of resources to different types, levels, and
qualities of schools within a state could affect college decisions, this would be masked using state-level variables Since ignoring this variation could bias estimation of the
parameters of college decision, college heterogeneity is a major source of identification problems in determining the effect of tuition subsidies
Section III: Framework and Model
This section explains how I attempt to account for heterogeneity in the college
market using a conditional logit choice model and a simple logistic enrollment model
Trang 37
Remaining concerns about the possible endogeneity of subsidy levels are also discussed Finally, data sources are outlined
Theoretical Framework
Assume an individual has J colleges from which to choose Each school, j, can be
characterized by a vector Y which is composed of measures of college cost, resources,
and location:
(1) Yj = {(P;, EX,, SB;, D, )
P; is the tuition price of school j School resources are divided into two parts: financial and peer resources They are measured by college expenditures, EX;, and student body
aptitude, SB;, and give a sense of the educational product received and possible peer effects Location is measured by D,, the distance in miles from the individual’s high school to the prospective college and is used as a proxy for geographic accessibility In this way, each college can be viewed as a package containing resources for a given price
and location From these characteristics, an individual can infer the ability of each school
to produce value-added human capital and consider the consumption goods the college
offers.'®
A vector X contains the individual’s attributes such as high school performance and family income The characteristics of the individual will affect his demand for education and his opportunity set For example, his prior performance and ability will
Trang 38affect his likelihood of being accepted by a highly-selective college as opposed to a junior college An individual’s background could also affect the acceptable tradeoffs he
perceives between schools For example, an individual may be more willing to sacrifice
school quality for a lower price if he is from a low-income family
Let the value of the „ college (characterized by the vector Y) to the i" decision maker be given by U(Yj, Xj) This value may partly depend on an interaction of the individual’s characteristics with those of the school For example, the cost of public school j for person i may be determined by residence — whether in-state versus out-of-
State tuition is charged While the costs of private colleges are not affected by residence, the discounted public colleges available to a student are limited geographically For example, the University of Illinois charges the same tuition to students from
Massachusetts and California but provides a special subsidy resulting in a lower price for someone from Iliinois This format produces an asymmetrical set of opportunities for
each student An individual’s characteristics could also affect the net cost of college since most institutional aid is dependent upon past achievement and family background
17
Utility may have random elements so that all individuals with X; are not assumed
have the same tastes:
(2) U (Yj, Xi) = U (Yj, Xj) + Eụ
Trang 39
That is, there are random deviations from the mean valuation U If we assume that the non-random part of utility is a linear function of individual and college characteristics we
get:
(3) U (Yj, Xi) = Zi Bi + ZjBo + ZijsBs + + Zi Bu + Sj
where f is a vector of parameters, Z,j are the variables that affect utility, and k is the total
number of variables Z may include variables that describe the elements of Y (i.e EX; and SB;), interact Y and X to form match-specific measures (i.e Pụ and Dị), or dummy
variables
Individuals compare the potential returns to attending different colleges along
with the option of not enrolling and entering the labor market directly The individual
then chooses the option that maximizes his lifetime utility subject to his budget constraint
as shown in (4)
(4) choose Y, iff U(¥;, Xi) = UCY;, Xi) Vk 4 j with Pas I
where J; is the budget constraint and is related to income
The college decision is therefore made up of two simultaneous choices The
individual must determine his best college option and concurrently decide whether to
attend college at all The first goal of this paper is to estimate the “which college”
"’ General aid, such as Pell Grants, will not affect this variable since it is just a shift in an individual’s
budget constraint
Trang 40decision I use the conditional logit regression model to predict which college an individual would attend conditional on college enrollment Second, I estimate the
“whether to attend question” using a simple logistic model comparing the group that did
not attend to similar individuals who did
Individuals who did not elect to attend college are not included in the college choice model for several reasons The reason stems from the fact that describing the “not
attend” option as an alternative with zero tuition cost, zero median test scores, and a distance of zero would bias parameter estimates For example, since some individuals
choose the option that had no cost as opposed to other options that did, the negative effect
of tuition price on college choice would be exaggerated In addition, the decision of whether to attend college is most likely nonlinear relative to choosing between different schools Therefore, estimates of the model including the “no college” group are unlikely to accurately describe both the college choice and whether to attend As a result, the group that did not attend college enters the analysis in a separate model to estimate the
decision of whether to attend
The College Choice Model
The above college choice framework emphasizes several points that must be addressed in the empirical model First, there is substantial heterogeneity among colleges