ARE PUBLIC SUBSIDIES TO - Am MIT spezialisierte KI-Forschung

ARE PUBLIC SUBSIDIES TO

HIGHER EDUCATION

REGRESSIVE?

William R. Johnson

Department of Economics

Universität von Virginia

P.O. Kasten 400182

Charlottesville, VA 22904

wjohnson@virginia.edu

Abstrakt
This article estimates the dollar amount of public higher
education subsidies received by U.S. youth and exam-
ines the distribution of subsidies and the taxes that
ﬁnance them across parental and student income lev-
els. Although youths from high-income families obtain
more beneﬁt from higher education subsidies, hoch-
income households pay sufﬁciently more in taxes that
the net effect of the spending and associated taxation is
distributionally neutral or mildly progressive. These re-
sults are robust to alternative assumptions and are con-
sistent with Hansen and Weisbrod’s earlier celebrated
ﬁndings for California, although not with the conclu-
sions often drawn from those ﬁndings.

288

C(cid:1) 2006 American Education Finance Association

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William R. Johnson

More than a quarter century ago, Hansen and Weisbrod stirred up a hornet’s
nest of controversy by claiming that public support for higher education could
well be regressive rather than progressive and could therefore lead to a more
unequal distribution of income.1 Their case rested on the empirical observa-
tion that the distribution of beneﬁts from higher education (in the California
System, which was the focus of their study) appeared to be more concentrated
among the upper-income households than did the associated tax burden. Der
debate sparked by the Hansen-Weisbrod thesis made it clear that the task of
assessing the distributional impact of public support for higher education is
complicated not only by the usual problem of data availability and the thorny
theoretical problem of tax incidence but also by disagreement about the appro-
priate measure of distributional impact for a policy that is both an inter- Und
an intragenerational transfer.

As Leslie and Brinkman’s (1988) survey reveals, a number of empirical
Studien, often for individual states, appeared in the years following the original
Hansen-Weisbrod analysis.2 However, interest in the redistributive aspect
of higher education ﬁnance seems to have waned in the 1980s and 1990s,
perhaps because of the seeming intractability of the question. Kane (1999,
P. 38) uses NPSAS (National Post-Secondary Student Aid Survey) data to
show that high-income youth receive roughly twice as large a subsidy as low-
income youth, but Kane’s analysis classiﬁes students only by parents’ current
income and does not consider either taxes paid or the student’s future income.
Longitudinal data from the National Longitudinal Survey of Youth (NLSY) gebraucht
here allows a more detailed tracing of the interrelationships between higher
education subsidies received by individuals, their own lifetime income, Und
their parents’ income. The data are used to estimate the distribution of higher
education subsidies received by young adults and the taxes that ﬁnance them
as a function of the various measures of their parents’ income. The subsidies
net of tax can also be related to the younger generation’s lifetime income, Die
dynastic income (parent and child) of the family, the parents’ education, Und
the young adult’s academic ability.

The ﬁrst part of the article sketches a theoretical framework. The second
part of the article describes the data and the calculation of the subsidy mea-
sures used in the empirical work. The third section looks at the distribution
of subsidies by various measures of parents’, student’s, and dynastic income.
My main ﬁnding is that while high-income households receive larger beneﬁts
on average than low-income households, the taxes they pay to ﬁnance those

Some of the important contributions at the time were Hansen and Weisbrod (1969), (1971), Hansen
(1970), Hartman (1972), and Pechman (1970), (1972).

2. An example is Moore 1978.

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289

HIGHER EDUCATION SUBSIDIES REGRESSIVE?

beneﬁts are even greater, so that beneﬁts net of taxes are not regressive—
low-income households receive positive net beneﬁts, while very-high-income
households receive negative net beneﬁts. Undeniably, the system would be
more progressive if beneﬁts were concentrated more on low-income house-
holds. This ﬁnding is robust to consideration of behavioral responses, liquidity
constraints, and externalities. Endlich, I reconcile my results with Hansen and
Weisbrod’s earlier ﬁndings for California.

1. A MODEL OF REDISTRIBUTION ACROSS DYNASTIC FAMILIES
As a simple starting point for the analysis, consider a dynastic family with
two generations each comprising a single person. The welfare of each family
depends on the consumption and leisure enjoyed by each generation. Jede
generation can trade leisure for goods at leisure’s real wage rate. The wage
rate for the parent in family i, w1i , is exogenous in this model, während die
wage for the second generation, w2i (ci ), depends on the family’s choice of
investment in college education, ci . The functions w2i (·) might differ across
families because of differences in children’s ability, location, or other fac-
tors. Investment in college is assumed to be non-negative, with variation cap-
turing both the extensive (Zeit) margin and the intensive (Qualität) margin.
The price per unit of college investment, pc , is relative to the consumption
good numeraire, as are wages. Endlich, each family is endowed with initial
Reichtum, Ii .

Government taxes the wage income of each generation at the respective
proportional rates of t1 and t2 and spends on public goods (assumed never to
affect the decisions modeled here) and college tuition subsidies. The subsidies
are discounts, at rate s, from the full cost of college, permitting parents to
purchase c units of investment in college for a cost of c · pc · (1 − s ). Der
government faces a long-run budget constraint and can borrow or lend at the
interest rate, R .

Each family’s indirect utility can be written as a function of the parameters

of its budget constraint:

V {Ii , w1i (1 − t1), w2i (·)(1 − t2), pc (1 − s )}

(1)

Underlying the function V are labor supply choices in each generation, A
college investment choice, and borrowing or saving.

The policy experiment is a balanced budget move from a vector of tax rates
and no tuition subsidy (t1, t2, 0) to another vector of tax rates and a subsidy rate
of s : (t1 + (cid:1)t1, t2 + (cid:1)t2, S ). The compensating variation measure of the effect

290

EDUCATION FINANCE AND POLICY

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William R. Johnson

of this policy change on family i, CV i , is the amount of money that restores
the household to its original level of well-being:

V {Ii , w1i (1 − t1), w2i (·)(1 − t2), pc (1 − s )}

= V {Ii + C Vi , w∗

1ich (1 − t1 − (cid:1)t1), w∗

2ich (·)(1 − t2 − (cid:1)t2), P

∗

C (1 − s )}

(2)

where the asterisks indicate the possibility that policy changes affect market
wage rates and the price of college education.

Redistribution without Behavioral Responses or Borrowing Constraints

Most of the empirical results presented in this article are estimates of the dis-
tribution of these compensating variations across families, computed under
the assumption that subsidies and taxes do not affect behavior and that house-
holds can borrow or lend at the government interest rate, R . The CV measure
of tax and subsidy policies in the zero-sum case will simply be the present
discounted value of the subsidy received by a family less the extra taxes paid
by both the parent’s and the child’s generation:

−C Vi = PDV [−(H1i · w1i ) · (cid:1)t1 − (w2i (ci ) · H2i ) · (cid:1)t2] + MwSt [ci · pc · s ]

(3)

In equation 3, H j i represents the exogenous labor supply of generation j in
family i, while ci is the amount of college chosen by family i. The differ-
ence between equations 2 Und 3 reﬂects the assumptions that wages and the
price of college are unaffected by the policy; that labor supply, hence earnings
and leisure, are unaffected by the policy; and that the absence of borrowing
constraints ensures that family utility is a function of leisure and discounted
Einkommen. Since leisure is unchanged, the effect of the policy is just the change
in discounted income. Market wages and prices will be unaffected because no
household changes its behavior.

The government budget constraint, that discounted tax revenue equals the
government’s discounted subsidy payments, implies that the sum of CV i over
all families is just zero. The total tax burden on all families is just the total cost
of the subsidy received by all families. To use the NLSY data set, which looks at
a sample of a subset of all families, namely those with children born between
1957 Und 1964, I need to assume that the subsidies received by this subset
of families are ﬁnanced by taxes imposed on the same subset. Das ist, if we
think of this subset of families as a cohort, I want to abstract from intercohort
redistribution and focus on intracohort redistribution.

To see that this necessary restriction is not unreasonable, imagine a steady-
state population consisting of many identical cohorts, born at different times,

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291

HIGHER EDUCATION SUBSIDIES REGRESSIVE?

each with the same lifetime distribution of earners and college subsidies. Seit
each cohort has the same distribution of earnings, taxes paid by each cohort are
identical. And since each cohort has the same distribution of college subsidies,
subsidies received by each cohort are identical. These assumptions imply that
the government budget constraint must be satisﬁed within each cohort; Das
Ist, the discounted taxes paid by a cohort must equal the discounted subsidy
received by a cohort. Mit anderen Worten, there can be no cross-cohort subsidy
when each cohort is identical.3 Given these assumptions, summing equation
3 over all parents in a particular birth cohort (sagen, parents of seventeen-year-
olds in 1980) yields an expression which is the present value of subsidies
received less the present value of additional tax revenues paid by that cohort.
By the government budget constraint, this must equal zero. Somit, the sum
of compensating variations within a cohort (and its progeny) is zero; losses
exactly offset gains within a cohort.

The fact that families can borrow or lend at the government interest rate
also implies that the Barro neutrality proposition holds here. It makes no
difference how the tax burden is spread across generations (within families)
because families can undo the effects of any particular government ﬁnancing
scheme. Darüber hinaus, the dynastic family model makes it clear that the appro-
priate measure of distribution effects is the extent to which the policy affects
the long-run welfare of families rather than the short-run income of particular
generations. Previous studies have attributed the beneﬁts of public universities
to the current annual income of parents of current students at such universi-
Krawatten, while the costs were assigned by the annual income of the taxpayers in
allgemein. Since parents of college-age children may be near their peak earning
Jahre, attributing the subsidy received by their children to that income may
overstate the extent to which these subsidies beneﬁt upper-income families.

To summarize, in the base case when no efﬁciency effects are allowed,
higher education policies are zero sum. These policies will be judged to be
progressive if higher income families as a group pay more in taxes attributable
to the policy than they receive in beneﬁts. All families who do not directly
partake of the beneﬁts will be worse off. By assuming a steady state with
identical cohorts, all redistribution occurs within a cohort, not across them.

Redistribution with Behavioral Responses and Borrowing Constraints

The above scenario will strike most readers as unrealistic because tuition
subsidies are intended to affect college-going behavior, overcoming borrowing
constraints or offsetting externalities. How should the gains and losses to

The same proposition holds even with growth in earnings over time and growth in the subsidy over
time as long as the growth rates are equal.

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EDUCATION FINANCE AND POLICY

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William R. Johnson

Price

pc(1-S)

Demand

C’

C (quantity)

Figur 1. Welfare Gain to Tuition Subsidy

particular households be accounted when behavior is affected by the tuition
subsidy? To tackle this question, consider ﬁrst the case in which the demand for
college responds to tuition subsidies but without the additional complication
of borrowing constraints or externalities. Figur 1 shows a downward-sloping
demand for units of higher education, denoted as c, as a function of the price
per unit faced by students and their families. The supply is assumed to be
inﬁnitely elastic. With no tuition subsidy, the price is pc and the amount
consumed is c ∗. When college is subsidized at the rate s , the net price to the
demander becomes pc (1 − s), and c rises by (cid:1)c = c (cid:2) − c ∗. The beneﬁt of the
subsidy to the family is the additional consumer surplus, or the shaded area
in ﬁgure 1, which is clearly less than the dollar cost of the subsidy, s · pc · c (cid:2). Wenn
we assume a constant elasticity of demand for college of η (in absolute value),
the beneﬁt of the tuition subsidy can be expressed as a function of η, S , Und
the dollar cost of the subsidy.4 To illustrate how the dollar cost of the subsidy

It is straightforward to show that the beneﬁt of the subsidy as a fraction of the dollar cost of the
subsidy is [(1 − s )η − (1 − s )]/S (1 − η).

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293

HIGHER EDUCATION SUBSIDIES REGRESSIVE?

Price

Pc + v

Pc (1-S) + v

pc(1-S)

True marginal
value

Demand

C’

C (quantity)

Figur 2. Welfare Gain to Tuition Subsidy with Borrowing Constraints

will be adjusted to account for behavioral response, when the subsidy rate, S ,
Ist .9, and the demand elasticity, η, Ist 0.15, the beneﬁt of the subsidy is about
80 percent of its dollar cost.

Suppose that subsidies are introduced to offset borrowing constraints.
How can we now measure the beneﬁts of tuition subsidies to households?
Consider ﬁgure 2, which depicts two curves—the true marginal value of higher
education to the family and student, and a lower curve, which represents the
actual demand for higher education as a function of the price faced by the
family. The effect of borrowing constraints is that the family does not purchase
education up to the point where the price equals its true marginal private value.
Somit, when the price is pc , Zum Beispiel, the household purchases only c ∗
Einheiten, leaving some potential gains unexploited.

It is convenient to parameterize the extent of borrowing constraints in
this ﬁgure by the parameter v, which is the vertical distance between the two
curves. Borrowing constraints cause a household that faces a price of p to act
as though it maximizes facing a price of p + v. In the ﬁgure, the household
facing a price of pc chooses an amount of education, c ∗, which is the amount
it would choose if it maximized net beneﬁts and faced a price of pc + v.

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EDUCATION FINANCE AND POLICY

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William R. Johnson

Now consider the effect of a subsidy at rate s . The net price falls to p(1 − s ),
and the household now chooses c (cid:2). The ﬁgure shows the case where the subsidy
is not sufﬁcient to completely offset the borrowing constraint, that is s · pc < v. The additional consumer welfare is shown by the shaded area, which is seen to be greater than the dollar cost of the subsidy.5 When v = 0, the beneﬁt expression reduces to the simpler formula derived above. To evaluate this expression, we need to know the extent to which actual sub- sidies offset the borrowing constraints. When the subsidy is optimal and just offsets the borrowing constraint so that students choose the optimal amount of education, s · pc = v, and the private beneﬁt now exceeds the dollar cost of the subsidy. To illustrate the size of the adjustment to dollar cost implied by borrowing constraints, with a subsidy rate of 90 percent and a demand elasticity of 0.15, the beneﬁt of an optimal subsidy will be 109 percent of its dollar cost. These results will allow us to adjust the dollar subsidies, which we can observe, to reﬂect changes in household welfare, using information about the size of the subsidy, the elasticity of demand, and assumptions about the size of borrowing constraints. However, to be consistent, I also need to adjust the dollar tax burdens to reﬂect the excess burden of the taxes used to ﬁnance the tuition subsidies, which can be done using estimates of the marginal welfare cost of taxation. 2. DATA AND MEASUREMENT OF SUBSIDY The NLSY Data Set The NLSY data set is a well-known panel data set, which has followed, since 1979, a group of young adults born between 1957 and 1964. Information on college attendance is quite complete, and the data include reasonably good adult earnings information, as this group was in its thirties at the time of the last wave of questioning (in 1996). The NLSY sample contains both a representative sample and additional oversamples of blacks, Hispanics, and low-income whites. All of the results in this article use only the representative sample. Computing the College Subsidy The ideal measure of the total higher education subsidy received by each NLSY sample member would be the sum, for all colleges and universities he 5. The ratio of beneﬁts to dollar cost are now equal to [(1 − (1 − s ) η ] + [(1 − s ) η − (1 − s )]/s (1 − η). v pc s l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / / 1 3 2 8 8 1 6 8 8 9 8 4 e d p 2 0 0 6 1 3 2 8 8 p d . . . . . f f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 295 HIGHER EDUCATION SUBSIDIES REGRESSIVE? or she attended, of the difference between the costs attributable to that person’s attendance and the student’s (or parent’s) payment of tuition and fees to the college or university. This would represent the net cost to others (outside the family) of that individual’s higher education. In the case of public higher education, the subsidy from the taxpayers is direct; in the case of private higher education institutions, the subsidy is derived from donors whose donations, and the return earned on the funds thereby endowed, enjoy favorable tax treatment. As a result, part of this private subsidy is actually an indirect public subsidy through the tax treatment of charitable donations and nonproﬁt private institutions. The measure actually used is derived from the HEGIS/IPEDS data on the ﬁnances of higher education institutions collected annually by the U.S. Department of Education. It compromises in the following ways with the ideal described above: (cid:1) The subsidy (costs of attendance less tuition and fees) is computed as student instructional costs and institutional ﬁnancial aid less total tuition and fees divided by total enrollment for the year and the higher educa- tion institution in question. Excluded from the subsidy calculation are capital costs, which are both difﬁcult to measure and, more important, problematic to attribute to current or past taxpayers or donors. Winston (1995) and Winston and Yen (1995) show that the neglect of capital costs understates subsidy amounts by approximately 25 percent, with modest variation across types of institutions. Applying a uniform understate- ment factor to the subsidy measure used here and assuming that all costs are paid by current taxpayers, yields distributional effects that are basically similar to those presented here. Hence I conclude that a thor- ough treatment of capital costs would probably not appreciably change the results. (cid:1) To simplify, the subsidy assigned an individual is that for the last un- dergraduate institution attended. Thus, if an individual attended X State University for one year, followed by attendance at Y State University for three years, I attribute to this person four years of receipt of the annual subsidy rate of Y State U. Consequently, no one will be recorded receiving both a public and a private subsidy. (cid:1) Postgraduate attendance is ignored. (cid:1) The subsidy for undergraduate attendance is limited to four years. If some- one attended for more than four years before receiving an undergraduate degree, that person is assumed to have received four years of subsidy, under the presumption that they received the equivalent of four years of subsidy spread over more calendar years. 296 EDUCATION FINANCE AND POLICY l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / / 1 3 2 8 8 1 6 8 8 9 8 4 e d p 2 0 0 6 1 3 2 8 8 p d . . . f . . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 William R. Johnson (cid:1) (cid:1) Individual receipt of ﬁnancial aid is not accounted for speciﬁcally in the subsidy computation because the NLSY has sketchy data on the amounts of ﬁnancial aid received. Each student is implicitly assigned average per student ﬁnancial aid for that institution. Since within each institution ﬁ- nancial aid is inversely related to family income, this simpliﬁcation reduces the apparent progressivity of the system. Individuals attending U.S. military academies are excluded from the anal- ysis because the subsidy as computed does not account for the substantial service obligation incurred by these students. Some of these data compromises are motivated by a desire to simplify the calculation of the subsidy; others are necessitated by the lack of information in the NLSY. 3. THE DISTRIBUTION OF SUBSIDIES ACROSS STUDENT AND PARENT CHARACTERISTICS Table 1 presents the basic facts of the distribution of higher education sub- sidies across NLSY panel members. Over half of the sample received some higher education subsidy; the mean subsidy received (conditional on receiv- ing a subsidy) was $8,129 in 1982 dollars. Public higher education institutions are attended more frequently than private, so a much higher fraction of the sample received public subsidies (recall that I am computing undergraduate subsidies only and am assigning all years attended to the last institution at- tended). Males and females receive roughly similar subsidies; males are less likely to attend but receive slightly higher subsidies when they do. Blacks and Hispanics overall are less likely to attend but receive roughly similar subsidies if they do. Subsidies and Current Parent Income For a subset of the NLSY sample, a measure of parent income when panel members were from sixteen to eighteen years old is available. Children of higher-income families receive greater public higher education subsidies than do children of lower-income families. Moving from the bottom income decile to the top, the fraction of youth receiving such subsidies rises from about one-quarter to about one-half, and the mean value of the subsidy, conditional on receiving one, doubles. Private subsidies are more dramatically concentrated among the children of higher income families, though some lower-income students receive con- siderable private subsidies. Private subsidies, which are ﬁnanced by donations past and present to private institutions, are also relevant to policy discussions l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / / 1 3 2 8 8 1 6 8 8 9 8 4 e d p 2 0 0 6 1 3 2 8 8 p d f . . . . . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 297 HIGHER EDUCATION SUBSIDIES REGRESSIVE? Table 1. Distribution of Subsidy to Higher Education across NLSY Sample Percent receiving subsidy 41.6% 41.1% 27.2% 26.9% Total sample Males: White Black Hispanic Females: White 43.9% Black Hispanic Total sample Males: White Black Hispanic 35.8% 32.5% 12.1% 11.2% 9.5% 8.5% Females: White 13.3% Black Hispanic Total sample Males: White Black Hispanic 10.0% 10.1% 53.7% 52.3% 36.7% 35.4% Females: White 57.2% Black Hispanic 45.8% 42.6% Distribution of Public Subsidy DISTRIBUTION OF SUBSIDY IF SUBSIDY > 0 (1982 DOLLARS) Mean Median 25th percentile 75th percentile 7,784 8,240 6,171 8,000 7,418 6,614 10,161 5,493 6,229 4,126 6,433 5,207 4,446 4,808 2,392 2,569 2,051 3,115 2,270 1,858 2,632 Distribution of Private Subsidy 9,324 8,848 15,373 7,237 9,532 6,114 4,693 4,673 8,591 6,516 4,815 2,516 14,234 12,256 1,771 1,849 2,099 4,456 1,618 1,354 4,108 Distribution of Total Subsidy 8,129 8,370 8,553 7,816 7,909 6,505 11,126 5,337 5,750 4,359 6,433 5,090 3,997 6,285 2,208 2,346 2,099 3,115 2,145 1,800 3,398 11,281 12,126 8,885 11,134 10,368 8,222 12,121 10,188 8,125 22,389 8,173 10,495 5,338 26,552 11,101 11,746 10,561 11,134 10,381 8,112 13,356 Notes: Based on cross-section portion of NLSY sample, excluding military academy graduates. Subsidy is difference between per student instructional expenses and average tuition and fees. because of the tax preferences given to charitable contributions, the earnings of endowment funds of private colleges and universities, and the real property of private colleges. The tax subsidy to private institutions will be included in some of the calculations to follow. These data allow a calculation of the net redistributive effect of higher edu- cation policy as measured by the taxes paid by parents and the subsidy received by their NLSY children. Let us consider ﬁrst only direct public subsidies (taxpayer support of public institutions) and assume that marginal changes in public expenditure on higher education are ﬁnanced with taxes that are proportional 298 EDUCATION FINANCE AND POLICY l D o w n o a d e d f r o m h t t p : / / Direkte . m i t . / F / e d u e d p a r t i c e – p d l f / / / / / 1 3 2 8 8 1 6 8 8 9 8 4 e d p 2 0 0 6 1 3 2 8 8 p d . F . . . . f by gu e s t o n 0 8 S e p e m b e r 2 0 2 3 William R. Johnson s r a l l o D 2 8 9 1 1,500 1,000 500 0 -500 -1,000 -1,500 -2,000 -2,500 -3,000 1 2 3 4 5 6 7 8 9 10 Net Direct Public Subsidy Net Direct and Indirect Public Subsidy l D o w n o a d e d f r o m h t t p : / / Direkte . m i t . Deciles of Parents’ Annual Income Figure 3. Net Public Subsidy per Child by Parents’ Annual Income to income. Public higher education subsidies are ﬁnanced largely by state gov- ernments, who rely on income taxes and sales taxes for revenue. Fullerton and Rogers (1993) ﬁnd that state income taxes are progressive, while state sales taxes are regressive. Overall proportionality is probably not a terribly inaccurate assumption. Since the average public subsidy is almost exactly 10 percent of average parents’ income, a proportional income tax of 10 percent would ﬁnance the entire public higher education subsidy. The overall pattern is shown by the light gray bars in ﬁgure 3. Families in income deciles 1, 2, 3, 5, 6, 7, Und 8 receive more in subsidy than they pay in tax, while families in the remain- ing income deciles (4, 9, Und 10) pay more than they receive. Since decile 4 pays only slightly more than it receives, the overall redistributive effect of the policy would appear to be progressive. The top two deciles pay more in tax than they receive in subsidy, while the reverse is true in general for the bottom eight deciles. Natürlich, there is also redistribution within in- come deciles, with some families at all income levels beneﬁting directly from higher education subsidies and others paying taxes but not receiving beneﬁts. The darker bars in ﬁgure 3 add the additional indirect tax subsidy to private institutions to the direct tax subsidy for public institutions. I approximate the net tax subsidy to private institutions as 40 percent of each dollar spent. The three principal tax preferences are deductibility of charitable donations, the exclusion of endowment earnings from taxation, and the exemption of real / / f e d u e d p a r t i c e – p d l f / / / / / 1 3 2 8 8 1 6 8 8 9 8 4 e d p 2 0 0 6 1 3 2 8 8 p d . . . F . . f by gu e s t o n 0 8 S e p e m b e r 2 0 2 3 299 HIGHER EDUCATION SUBSIDIES REGRESSIVE? property from property taxation. The ﬁrst preference alone would imply a subsidy equal to the donor’s marginal tax rate, td . The second implies that a dollar donation to an endowment buys a perpetuity of r dollars a year, while if the endowment interest were taxed at the rate tr and the original donation were not deductible, the annual income stream endowed by a dollar gift would be r (1 − td )(1 − tr ). Setting td = .28 (a common marginal income tax rate) and tr = .35 (the corporate income tax rate), each dollar of nonproﬁt endowment earnings is subsidized by 53.2 cents of tax reduction. Somit, 40 percent is a conservative estimate of the subsidy to private institutions, at least when donations are used to fund endowments. The overall pattern of progressivity is not greatly affected by the addition of the indirect public subsidy of private institutions. Approximating the Distribution of Net Beneﬁts by Parents’ Permanent Income For several reasons, the estimates shown in ﬁgure 3 might seriously misrep- resent the redistributive effect of public higher education subsidies. In what follows, I attempt to address some of these issues. Distribution of Children versus Distribution of Parents Since the sampling frame of the NLSY is designed to replicate the children’s generation, not the parent’s generation, parents with many children are over- represented and parents with few children are underrepresented. If high- income parents have more children than low-income parents, the calculations above will overstate progressivity by understating the beneﬁts received by high-income parents relative to low-income parents. This ﬂaw can be partially corrected by using information on the number of siblings of each NLSY re- spondent and weighting the beneﬁts received by each parent by the total size of the family. The expected value of beneﬁts received by a family with n chil- dren is just n times the expected per child beneﬁt. The actual beneﬁt received by the NLSY child is an unbiased estimate of the family’s per child beneﬁt. Zum Beispiel, a two-child family in which one child, the NLSY panel member, is observed receiving a $5,000 public subsidy, would be estimated as having
received $10,000 in public higher education subsidies. This is only a partial correction because families with no children are completely unrepresented in the NLSY. The failure to include adults who never have children overstates pro- gressivity only if such adults have lower incomes than the median observed household. Jedoch, data from the June 2000 Current Population Survey show that across all household income levels, roughly the same fraction of women, 35–44 years old, are childless. This implies that the income distri- bution of childless women is roughly the same as the income distribution 300 EDUCATION FINANCE AND POLICY l D o w n o a d e d f r o m h t t p : / / Direkte . m i t . F / / e d u e d p a r t i c e – p d l f / / / / / 1 3 2 8 8 1 6 8 8 9 8 4 e d p 2 0 0 6 1 3 2 8 8 p d . F . . . . f by gu e s t o n 0 8 S e p e m b e r 2 0 2 3 William R. Johnson of women with children, so the omission of childless households does not obviously bias the estimated progressivity of tuition subsidies. Life-Cycle Income Patterns The parent’s annual income when the child is age seventeen misrepresents the family’s permanent income because of well-known patterns of earnings and income over the life cycle. Parents of seventeen-year-olds may be close to their peak earning years, and it is well known that life-cycle earnings growth is greater for highly educated workers. The dispersion of the annual income of parents at that stage of life cycle would overstate the dispersion of life- time income and could misrepresent the progressivity of higher education subsidies. I deal with this issue by linking each family’s annual income to the es- timated life-cycle earnings patterns estimated by Murphy and Welch (1990). This amounts to assuming that each household’s income proﬁle follows the average pattern for households with that household’s characteristics. Using a 3 percent real discount rate, the present discounted value of these life-cycle income proﬁles can be computed. Adjusting Lifetime Income for Transitory Effects As is well known, transitory ﬂuctuations in income imply that the dispersion of current income overstates the dispersion of permanent income. This could bias the apparent progressivity of subsidies upward because taxes are assumed to be proportional to lifetime income. If annual income, or even lifetime income pegged to annual income, overstates permanent income for upper- income households, then too much tax would be imputed to these households while too little is imputed to low-income households, whose actual lifetime income will be understated by annual income. To adjust for transitory effects, I use estimates by Gottschalk and Mofﬁtt (1994) of the relative variances of transitory and permanent earnings by edu- cation level to form a weighted average of predicted permanent income and the family’s actual transitory income. Konkret, suppose that the income of household i in year t, Yit , is a linear function of observables, Xit , plus a permanent family ﬁxed effect, µi , and a transitory shock, eit Yit = β Xit + µi + eit . (4) Let the weighting factor, w, be the share of transitory variance in the total error variance: w = var(e)/[var(e) + var(µ)]. (5) l D o w n o a d e d von h t t p : / / Direkte . m i t . / F / e d u e d p a r t i c e – p d l f / / / / / 1 3 2 8 8 1 6 8 8 9 8 4 e d p 2 0 0 6 1 3 2 8 8 p d . F . . . . f by gu e s t o n 0 8 S e p e m b e r 2 0 2 3 301 HIGHER EDUCATION SUBSIDIES REGRESSIVE? The proposed estimator of β Xit + µi is then (1 − w)Yit + wb Xit (6) where b is the estimate of β from an OLS cross section regression of equation 4. If all variance is transitory, w = 1, and the estimator of permanent income is the prediction of the cross-section regression (no need to worry about unobserved heterogeneity). If all the variance is permanent heterogeneity, Jedoch, then w = 0 and the estimator is observed income of the household. “Adjusted lifetime income” takes the value computed by equation 6 and adjusts by the same Murphy-Welch proﬁles described above to estimate discounted lifetime income. The results of these additional adjustments are shown in table 2 and the ﬁrst four columns of table 3. As table 2 zeigt an, adjusting for transitory vari- ance compresses the income distribution. Since taxes are again assumed to be proportional to lifetime income, this reduces the share of total taxes paid by the upper deciles of the income distribution, but not enough to reverse the progressive pattern of the policy as shown by ﬁgure 4. In order to assess the sta- tistical properties of the pattern depicted in ﬁgure 4, table 3 presents regression estimates of the adjusted income decile pattern of net subsidies. In column 1, I regress net direct subsidy only on income decile dummies, omitting the lowest decile. Most of the higher deciles receive smaller net subsidies than does the bottom decile, with the top two deciles receiving signiﬁcantly less subsidy, both in an economic sense and in a statistical sense. Column 2 of table 3 estimates the same relation with three covariates—the child’s AFQT score, the parent’s combined years of education, and a dummy variable for black. Because parents’ education and AFQT are strong predictors of college attendance and are posi- tively correlated with parents’ income, their addition to the equation makes the net subsidy received by high-income families on the basis of their income alone even more negative. The positive coefﬁcient on black in this regression may be surprising, but it reﬂects the fact that black students are more likely to attend college than white students, holding constant family income and academic skill. As in the previous ﬁgures, the concept of the direct and indirect pub- lic subsidy adds the implicit public subsidy of private institutions and the taxes which pay for that subsidy to the direct public subsidy already dis- cussed. Results using this subsidy concept are shown as the dark bars in ﬁgure 4 and the regression results in columns 3 Und 4 of table 3. The results conﬁrm the progressive nature of higher education subsi- stirbt. 302 EDUCATION FINANCE AND POLICY l D o w n o a d e d f r o m h t t p : / / Direkte . m i t . / F / e d u e d p a r t i c e – p d l f / / / / / 1 3 2 8 8 1 6 8 8 9 8 4 e d p 2 0 0 6 1 3 2 8 8 p d f . . . . . f by gu e s t o n 0 8 S e p e m b e r 2 0 2 3 William R. Johnson 1 2 3 4 5 6 7 8 9 10 0 N e t D ir e c t P u b lic S u b s id y N e t D ir e c t a n d In d ir e c t P u b lic S u b s id y 3,0 0 0 2,0 0 0 1,0 0 0 0 s r a l l o D 2 8 9 1 -1,0 0 0 -2,0 0 0 -3,0 0 0 -4,0 0 0 -5,0 0 0 -6,0 0 0 D e c ile s o f A d ju s t e d L if e t im e In c o m e Figure 4. Net Public Subsidy per Household by Parents’ Adjusted Lifetime Income Table 2. Distribution of Total Subsidy by Parents’ Lifetime Income (Adjusted for Transitory Changes) PUBLIC SUBSIDY PRIVATE SUBSIDY TOTAL SUBSIDY Decile Mean lifetime income (1982$)

Percent
receiving

Mean
value

Percent
receiving

Mean
value

Percent
receiving

Mean
value

Alle

179,507

235,938

270,614

298,638

326,360

358,179

392,700

431,047

488,049

625,440

360,427

34.7

27.6

41.2

36.0

46.8

55.2

52.2

54.5

48.3

40.3

7,562

5.4

1,187

38.1

5,779

11.7

1,961

36.7

9,082

8.9

5,591

52.3

7,856

13.4

7,727

46.7

11,738

8.1

2,493

55.0

15,346

10.1

2,635

62.8

12,946

13.9

1,814

59.4

18,228

14.5

2,625

73.7

16,643

12.3

3,838

69.1

19,045

30.7

11,061

79.6

12,301

11.7

3,706

53.7

8,749

7,740

14,673

15,583

14,231

17,981

14,760

20,853

20,481

30,106

16,007

Notiz: Lifetime income is adjusted by averaging lifetime income with predicted income from a re-
gression of lifetime income on parent characteristics (Ausbildung, Wettrennen, location, Beruf) mit
weights equal to the relative permanent and transitory variances, as a fraction of total variance, von
education level (Gottschalk and Mofﬁtt 1994).

Distributions by Dynastic Income

The presence of data in the NLSY on both parent’s income and child’s income
as a young adult allows an approximation of dynastic income, or the discounted
sum of parent’s and child’s lifetime income. The child’s lifetime income is
estimated by applying the Murphy-Welch trajectories and the Mofﬁtt-
Gottschalk variance decompositions to the latest three observations on the

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304

EDUCATION FINANCE AND POLICY

William R. Johnson

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Net Direct Public Subsidy
Net Direct and Indirect Public Subsidy

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Deciles of Dynastic Income

Figur 5. Net Public Subsidy by Dynastic Income (Parent and Child)

child’s income as an adult. As was the case with adjusted lifetime income,
while high-income dynasties enjoy greater public subsidies than lower-income
dynasties, the distribution of mean subsidies is not as unequal as the distribu-
tion of mean dynastic income. Private subsidies are more focused on the very
top decile but are also substantial for low-income dynasties. Figur 5 displays
the net subsidy calculations, when taxes are assumed to be proportional to
dynastic income. Here the top decile appears to be, on net, subsidizing the col-
lege expenses of the lower nine deciles, but curiously the ninth decile receives
the greatest positive subsidy. The regression results in columns 5–8 of table 3
conﬁrm that the top decile’s net subsidy is large and signiﬁcantly negative,
while the ninth’s is strongly positive.

Distributions by Child’s Lifetime Income

Another distributional perspective argues that the parent’s income is irrele-
vant. Since the child is the beneﬁciary of the subsidy, the appropriate distribu-
tional analysis compares net subsidies received across the distribution of the
child’s lifetime income. The tax burden for the subsidy is then assigned to the
child’s lifetime income. One could imagine the costs of educating the child’s
cohort being ﬁnanced by borrowing, with the debt repaid by levying taxes in
the future on the income of that cohort. Figur 6 displays the distributional
pattern of subsidies by deciles of child’s lifetime income. Clearly, the pattern
of mild progressivity exhibited by other income measures is preserved here.

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305

HIGHER EDUCATION SUBSIDIES REGRESSIVE?

10,000

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Net Direct and Indirect Public Subsidy

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Deciles of Student Income

Figur 6. Net Public Subsidy by Student’s Lifetime Income

Distributions by Parent’s Education

The distribution of subsidies by parents’ education is also of interest. Par-
ents’ education may be a rough proxy for the household’s permanent income,
and data on it are available for many more NLSY panel members than on
parents’ income.6 Public subsidies are highly skewed toward the children of
well-educated parents. The income of the top decile in the distribution of par-
ents’ education is only twice the income of the bottom, but the children of the
top decile receive four times the direct public subsidy and thirty-two times the
private subsidy obtained by the children of the bottom decile.

The net redistributive effect of direct and indirect subsidies across deciles
of parents’ education favors highly educated parents, again assuming propor-
tional taxation of parents’ adjusted lifetime income. Evidently parents’ edu-
cation has such a strong effect on children’s college attendance (and quality
of college) that the children of highly educated parents receive more subsidy
than their parents pay in taxes. So even if higher education subsidies do not
redistribute from the poor to the rich, they do redistribute from the less ed-
ucated to the more educated. The contrast between the results for parents’
education and parents’ income make clear that while income and education
are correlated, the correlation is far from perfect.

6. Data on parents’ income were available only for the younger members of the sample, who had not

reached the age of eighteen when the panel began.

306

EDUCATION FINANCE AND POLICY

William R. Johnson

Caveats

No matter which deﬁnition of income is used, or whether the focus is par-
ents’ or students’ income, the implication of the results above is that the net
redistributive effect of public subsidies for higher education is either distribu-
tionally neutral or mildly progressive. Andererseits, the subsidy strongly
redistributes toward the families with well-educated parents. The reason for
the progressivity is that while subsidies are larger for higher income families,
a proportional tax system means that taxes are even higher. While we are used
to thinking of beneﬁts as regressively distributed if high-income households
receive more beneﬁt than low-income households, the net impact of a policy
is the difference between beneﬁts and costs. Hence an equal payment to all
households ﬁnanced by proportional taxes is progressive.

It is worth recapitulating some of the limitations and biases of the pro-
cedure. Progressivity is probably understated because the subsidy measure
does not include the intra-institutional distributional effect of ﬁnancial aid,
which is undoubtedly progressive. Stattdessen, because my subsidy measure is
computed as per student costs less tuition receipt, ﬁnancial aid is in effect
allocated equally to all students.

The simplifying assumption of a proportional tax system has been adopted.
This may not be a reasonable assumption for marginal changes in tax revenue,
even if it characterizes the overall tax systems of many states. Georgia’s HOPE
scholarships are ﬁnanced by a state lottery that is not close to a proportional
tax. One could compute exactly how regressive a state tax system would have
to be to push the net redistributive effect into regressivity. To illustrate, im
case of the parent’s lifetime income, the tax system would have to impose tax
rates three times as high on the bottom two deciles as on the top two deciles in
order to make the net subsidy distributionally neutral. Fullerton and Rogers
(1993, P. 174) ﬁnd that while sales and excise taxes are regressive, the ratio of
the effective tax rate faced by the bottom 20 percent of the population to the
rate faced by the top 20 percent is on the order of 1:2, nowhere near the degree
of regressivity needed to reverse the conclusions above.

Behavioral Responses

How robust are these results when behavioral responses are considered?
Tisch 4 presents results using the adjusted lifetime parental income mea-
sure of the ﬁrst column of table 3. To adjust for behavioral responses, we need
to estimate the shaded areas in ﬁgures 1 Und 2 and that requires an estimate of
the subsidy rate, S , and the demand elasticity, η. Winston, Carbone, and Lewis
(1998) estimate the subsidy rate for public higher education institutions in the
mid-1980s at about 90 Prozent, so I use s = 0.9. For the elasticity of demand

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307

HIGHER EDUCATION SUBSIDIES REGRESSIVE?

Tisch 4. Robustness of Net Subsidy to Behavioral Responses

Income Decile

(1)

(2)

(3)

(4)

(5)

Subsidy Response

Tax Response

Borrowing Constraints

with Optimal Subsidy

2,410

−423

718

−595

−692

2,125

2,217

197

−1,999

−3,958

823

−1,859

−1,212

−2,481

−2,766

−740

−928

−2,837

−5,062

−7,775

1,581

−1,564

−622

−2,099

−2,351

294

190

−2,049

−4,597

−7,414

−5

−3,000

−2,553

−3,986

−4,424

−2,573

−2,955

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−7,660

2,216

−989

150

−1,344

−1,522

−2,571

−2,955

−5,083

−7,660

−11,232

−11,323

Notes: Income measure is adjusted lifetime family income. Elasticity of demand = .15, subsidy
rate = .9, marginal welfare cost of taxation = .15. For column (5), borrowing constraints are
assumed to affect only the bottom ﬁve deciles.

for higher education with respect to net tuition, I rely on two sources that yield
similar estimates. Leslie and Brinkman (1988, P. 132) present a meta-analysis
of demand studies from which they conclude that the enrollment rate falls by
.7 percentage point for each additional $100 in net tuition. Using this response, along with information about enrollment rates and tuition in the mid-1980s, I conclude that η = .13. Kane (1999, P. 114) estimates an enrollment effect of 5 percentage points per $1,000 in tuition in the early 1990s, was impliziert
an η = .15. Endlich, a consensus estimate of the marginal welfare cost of taxa-
tion in the 1980s based on work of Ballard, Shoven, and Whalley (1985) Und
Browning (1987) Ist 15 Prozent, implying that a dollar of tax revenue imposes a
burden of $1.15. These three parameter values underlie the results in table 4. The ﬁrst column of table 4 reproduces the net subsidy results underly- ing the ﬁrst column of table 3. This is a zero-sum case with no behavioral responses to taxes or subsidies. The second column shows the effect of be- havioral response to subsidies with no borrowing constraints; here the value of the subsidy is .8 of its dollar cost, so the sum of net subsidies is negative, but the effect is still progressive, with the lowest decile gaining and the high- est income deciles losing. Column 3 shows just the effect of tax distortions, while column 4 considers both subsidy and tax distortions. Endlich, column 5 assumes that the subsidy exactly offsets borrowing constraints that face the bottom ﬁve deciles of the income distribution. While this is a case that would 308 EDUCATION FINANCE AND POLICY l D o w n o a d e d f r o m h t t p : / / Direkte . m i t . F / / e d u e d p a r t i c e – p d l f / / / / / 1 3 2 8 8 1 6 8 8 9 8 4 e d p 2 0 0 6 1 3 2 8 8 p d . . F . . . f by gu e s t o n 0 8 S e p e m b e r 2 0 2 3 William R. Johnson seem to be most favorable to ﬁnding progressivity of subsidies, the bottom ﬁve deciles actually lose on net because what they gain from the subsidies is more than matched by their loss from the taxation that ﬁnances those subsidies. Trotzdem, the effect of the policy is progressive in the sense that the highest deciles lose the most in percentage terms. 4. COMPARISON WITH HANSEN AND WEISBROD Can these results be reconciled with the famous study by Hansen and Weisbrod (1969) that found the California higher education system to be regressive? Perhaps no reconciliation is needed. Hansen and Weisbrod stud- ied one state, Kalifornien, in the 1960s, while this study encompasses the entire nation and looks at students who attended college primarily in the 1980s. It is also possible, though implausible, that California’s system is regressive while other states’ systems are progressive. It is also possible that the progressivity of the entire system rose between the 1960s and the 1980s. But a simpler reconciliation is possible if we ask the same questions of the data in this study that Hansen and Weisbrod did of their data. The limitations of the data available to Hansen and Weisbrod led them to analyze the problem in the following way. They divided the population of California families into four groups, corresponding to the level of higher education institution attended by the family’s child. Some families have no children in the university system, some have children in junior college, some in state colleges, and some with children in University of California (UC) campuses. These four groups represent an ascending order of gross subsidy, as UC students receive more subsidy per year and spend more years in college than junior college students. What Hansen and Weisbrod showed was that, comparing these four groups of parents, gross subsidy was positively related to both mean household income and to net subsidy. Das ist, the parents of the UC students have both the highest family incomes of the four groups and receive the greatest net subsidy, when their tax burdens are accounted for. Families with no students in the system have the lowest incomes and, Natürlich, receive negative net subsidies since they enjoy no direct beneﬁt and must pay taxes to support the system. These empirical patterns led Hansen and Weisbrod to conclude, “On the whole, the effect of these subsidies is to promote greater rather than less inequality among people of various social and economic backgrounds, by making available substantial subsidies that lower-income families are either not eligible for or cannot make use of ” (1969, P. 191). Tisch 5 describes an exercise parallel to Hansen and Weisbrod’s using this study’s data. Households are arrayed by level of gross public subsidy. Decile 10 corresponds to those households receiving the most gross subsidy; they have l D o w n o a d e d f r o m h t t p : / / Direkte . m i t . F / / e d u e d p a r t i c e – p d l f / / / / / 1 3 2 8 8 1 6 8 8 9 8 4 e d p 2 0 0 6 1 3 2 8 8 p d . . . . F . f by gu e s t o n 0 8 S e p e m b e r 2 0 2 3 309 HIGHER EDUCATION SUBSIDIES REGRESSIVE? Tisch 5. Family Income and Net Subsidy by Gross Subsidy Level Deciles of Gross Subsidy Annual Family Income Net Subsidy Gross Subsidy 1–5 6 7 8 9 10 30,694 34,208 32,228 33,888 34,048 40,341 −3,124 −2,685 −1,492 754 5,029 0 838 1,722 4,127 8,603 13,262 17,740 the highest mean incomes and receive the greatest net subsidies. The bottom ﬁve deciles are lumped together, as they are families who receive no direct subsidy because their NLSY child did not attend a public institution. If one looked only at table 5, one might conclude, as Hansen and Weisbrod did, that the system is regressive. Jedoch, as we know, the same data generated the progressive patterns revealed in ﬁgures 3 durch 6. It may appear paradoxical that net subsidy and income can both be pos- itively correlated with gross subsidy, as table 5 zeigt an, yet net subsidy and income are negatively correlated with each other. A simple numerical example shows how this can happen. Suppose half the families have high incomes of $10,000, while the other half have low incomes of $2,000. Suppose that if a child goes to college, the gross subsidy is $6,000; the alternative is not going
to college, where the gross subsidy is 0. Proportional taxes on income are
levied to ﬁnance the system, Und 30 percent of high-income families’ children
go to college, while only 20 percent of low-income children go to college. In
this economy, the average household income of children who go to college
Ist $6,800, compared with only $5,733 for non-college-goers. The average net
subsidy received by college goers is $4,300, compared with −$1,433 for non-
college goers. Noch, average net subsidy received by high-income households
is −$700, compared with +$700 received by low-income households.7 The
key is the 70 percent of high-income households who pay substantial taxes yet
have no children receiving subsidies.

Since the overall redistributive effect of a policy is revealed by the pattern
of net subsidy across income levels, one could conclude that Hansen and
Weisbrod got the numbers right but drew an incorrect conclusion of regres-
sivity from their evidence.

This basic pattern holds for a wide range of assumptions about the income distribution and the
proportion of children from each income level going to college, as long as high-income children are
more likely to go to college.

310

EDUCATION FINANCE AND POLICY

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William R. Johnson

5. FINAL COMPLICATIONS: CHANGES IN PRICES AND EXTERNALITIES
Changes in Prices

The recent work of Heckman, Lochner, and Taber (1999) has emphasized the
effect of subsidies in changing market prices. Bei diesem Modell, two important
prices that could be altered by tuition subsidies are the price of college, pc , Und
the second generation’s wage function, which could become ﬂatter as the real
wage of the less educated rose and the real wage of the more educated fell.
Such a change in relative wages would augment the progressivity of a tuition
subsidy policy.8 The price of college might also rise as input suppliers such
as college professors earn greater rents. This price change would likely reduce
progressivity if faculty have higher incomes than the families of their students.
Jedoch, in 2000–2001, the average faculty salary at four-year institutions was
around $59,000, while the median family income of freshmen at four-year institutions was reported to be roughly $64,000.9 Hence there is no strong
evidence that students’ parents are poorer than faculty, although the salary
ﬁgure is not family income.

Externalities

If college educations for some confer beneﬁts on others, a complete reckoning
of distributional effects should include these externalities, both real and ﬁscal.
A ﬁscal externality arises because those who are induced by subsidy to acquire
college educations will, on average, pay more tax and receive fewer transfer pay-
gen. A real externality occurs if the pretax incomes of non-college-educated
workers rise when more workers attend college. Externalities of either vari-
ety, in the absence of other complications to the basic model, make a tuition
subsidy a positive-sum policy and alter the pattern of net beneﬁts by income
Klasse.

Reasonable assumptions about the nature of externalities lead straight-
forwardly to the conclusion that externalities will reinforce the progressive
distributional effects found in the basic model. Hier, a policy is called pro-
gressive if the relative inequality of income is reduced by the policy, das ist,
if the policy raises the income of low-income households by a greater per-
centage than it raises the income of high-income households. A policy could
reduce relative inequality, daher, while still raising the dollar gap between
the incomes of rich and poor. To make the point requires some algebra. In-
dexing income deciles by k, let Bk, Tk, and Nk denote respectively the average

Johnson (1984) provides a particularly compelling version of this argument.

8.
9. Chronicle of Higher Education 2001: 23, 27. The median freshman family income was found by

interpolating a uniform distribution between $60,000 Und $75,000.

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311

HIGHER EDUCATION SUBSIDIES REGRESSIVE?

beneﬁt received by households who receive positive direct beneﬁts, the average
tax paid per household, and the fraction of households who receive positive
beneﬁts. With this notation, the average net beneﬁt received by households in
income decile k is just the difference between beneﬁts received and taxes paid,
orNk · Bk − Tk. As we have seen, these net beneﬁts in the simple model have
been positive for low-income deciles and negative for the very highest income
deciles.

To account for the distributional impact of externalities, we need a rea-
sonable and simple way to allocate externalities across households. Fiscal
externalities—higher future tax revenue attributable to the policy—reduce the
incremental lifetime tax revenue needed to ﬁnance the policy. Let us simply as-
sume that the tax reduction attributable to the ﬁscal externality is the same frac-
tion, e, of each household’s incremental tax burden in the simple model.10 The
net beneﬁt received by income decile k is now equal to Nk · Bk − Tk + e · Tk.
If e = 0, we are back in the simple model without externalities. If e = 1, Die
tuition subsidy is self-ﬁnancing—it generates enough incremental tax revenue
to pay for itself. In the self-ﬁnancing case, nonbeneﬁciary taxpayers invest in
the college educations of others and will earn the market rate of return on that
investment in the form of higher net taxes paid by the direct beneﬁciaries of
subsidies. Note that when e = 1, the distribution of net beneﬁts is the same
as the distribution of gross beneﬁts, since there is no extra tax required to
ﬁnance the policy. As table 2 zeigt an, gross beneﬁts are absolutely higher, but a
smaller percentage of income, for high-income deciles. daher, when exter-
nalities are so large that e = 1, tuition subsidies reduce the relative inequality
of income. Since we have already shown that when e = 0 and we are back
in the simple model without externalities, tuition subsidies reduce relative
income inequality, any value of e between 0 Und 1 will also reduce relative
inequality.11

What if the externalities are not ﬁscal externalities but real externalities rais-
ing the earnings of nonrecipients? Wieder, a reasonable and simple assumption
is that the real externality is the same proportion of every household’s income.
Using this assumption, we get the same result that we got above with ﬁscal
externalities. Suppose the real externality parameter is e ∗, so that a household
with income Y receives an externality beneﬁt of e ∗Y. Since incremental taxes
have assumed to be proportional, this gives the same pattern of beneﬁts as the

10. I am ignoring the timing of the future tax revenue. One could imagine the government borrowing
now to reduce current tax burdens, paying off the debt with the future tax revenue generated by the
additional college graduates.

11. This result is easy to show using the fact that the net beneﬁt for any value of e between 0 Und 1 Ist

just a weighted average of the net beneﬁts at e = 0 and net beneﬁts at e = 1.

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William R. Johnson

ﬁscal externality analysis, since T = tY and eT = etY = e ∗Y, where e ∗ = et and
t is the proportional tax rate. Somit, assuming ﬁscal externalities are propor-
tional to incremental taxes and assuming real externalities are proportional
to income yield the same distributional impact, which is to reduce relative
income inequality.

In most models of real externalities (see Acemoglu and Angrist 2000 oder
Moretti 2004), the wages of non-college-educated workers are increased more
by an increase in the number of college graduates than are the wages of college
graduates. This would suggest that e ∗ is higher for low-income deciles than for
high-income deciles, and the tuition subsidy would be even more progressive.

6. CONCLUSION
This article takes two approaches to the question of the distributional effect
of higher education subsidies. The ﬁrst approach neglects the resource al-
location effects of subsidies and the taxes levied to pay for them and treats
higher education policy as a zero-sum game. The costs and beneﬁts of pub-
lic subsidies can be allocated across various concepts of parent income and
parental education. In diesem Rahmen, higher education subsidies clearly re-
distribute toward households with highly educated parents. With respect to
redistribution by parental or student lifetime income, Jedoch, the evidence
for a range of alternative income concepts shows the effect subsidies net of
the taxes which ﬁnance them as mildly progressive or roughly distributionally
neutral. Although high-income families receive more in subsidies, they pay
sufﬁciently more in taxes that the net subsidies for high-income households
are negative, while those for low-income households are on average positive.
This basic result holds up even when we consider behavioral responses to
subsidies and taxes.

Since my conclusion conﬂicts with the results of Hansen and Weisbrod’s
justly famous 1969 Studie, I apply their methodology to my data and derive re-
sults parallel to their ﬁndings. A reasonable conclusion might be that Hansen
and Weisbrod’s results were incorrectly interpreted as implying the regres-
sivity of subsidies. Although those who receive higher education subsidies
are from families with higher-than-average incomes, and those families do
not pay in tax the cost of educating their children, it is still the case that all
high-income families considered together (including those with no children
receiving subsidies) are receiving negative net subsidies. Low-income fami-
Lügen, taken together, receive positive net subsidies. Higher education subsidies
beneﬁt upper-income households more than lower-income households, Aber
when the taxes that ﬁnance the subsidies are accounted for, the net effect is
somewhat progressive or at least not regressive.

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313

HIGHER EDUCATION SUBSIDIES REGRESSIVE?

The data for the results in this article pertain to college ﬁnances in the
1980S, leaving open the possibility that the distributional effect of the public
higher education ﬁnancing system has changed in the intervening two decades.
Zum Beispiel, the rise of merit aid (such as Georgia’s HOPE scholarships) Und
the decline of public university tuition subsidies would make the current
system less progressive than the one described here.

I appreciate helpful comments by William Becker, Charles Clotfelter, Ronald
Ehrenberg, Eric Hanushek, Tom Kane, John Siegfried, Steve Stern, Sarah Turner,
Gordon Winston, David Zimmerman, anonymous referees, and workshop participants
at Colorado State University, the University of Maryland, the University of Virginia,
and the University of Wisconsin. Neil Seftor and Jessica Howell provided valuable
assistance. Financial support from the Andrew W. Mellon Foundation to the Virginia
Project on the Economics of Higher Education is gratefully acknowledged.

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