Capital Market Failure, Adverse Selection and Equity Financing of Higher Education

TI 2005-037/3
Tinbergen Institute Discussion Paper
Capital Market Failure, Adverse
Selection and Equity Financing of
Higher Education

Bas Jacobs1
Sweder J.G. van Wijnbergen2
1 European University Institute, University of Amsterdam, and Tinbergen Institute,
2 University of Amsterdam, Tinbergen Institute, and CEPR.

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CAPITAL MARKET FAILURE, ADVERSE SELECTION
AND EQUITY FINANCING OF HIGHER EDUCATION*

Bas Jacobs‡
European University Institute, University of Amsterdam,
and Tinbergen Institute (b.jacobs@uva.nl)

Sweder J.G. van Wijnbergen
University of Amsterdam, Tinbergen
Institute and CEPR (svw.heas@planet.nl)

March, 2005

Abstract: We apply theories of capital market failure to analyze
optimal financing of risky higher education. In the market solution,
students can only finance their education through debt. There is
underinvestment in human capital, because some students with socially
profitable investments in human capital will not invest in education
due to adverse selection problems in debt markets and because
insurance markets for human capital related risk are absent. Legal
limitations on the use of human capital in financial contracts cause this
underinvestment; without them private markets would optimally
finance these risky investments through equity rather than debt and
supply income insurance. The government, however, can circumvent
this problem and implement equity and insurance contracts through the
tax system using a graduate tax. This paper shows that public equity
financing of education coupled to provision of some income insurance
is the optimal way to finance education when private markets fail due
to adverse selection. We show that education subsidies to restore
market inefficiencies are sub-optimal.

Key words: human capital, capital market imperfections, credit
rationing, financing risky investment, optimal education
finance, graduate taxes, education subsidies.
JEL-codes: H21, H24, H52, H81, I22, I28, J24

* Comments by Lans Bovenberg, Amber Davis, Casper van Ewijk, Joeri Gorter, Rick
van der Ploeg and seminar participants of the University of Amsterdam, the CPB
Netherlands Bureau for Economic Policy Analysis and the CEPR Economics of
Education Conference, May 11-12 2001, Bergen, Norway are gratefully
acknowledged. Bas Jacobs thanks the NWO Priority Program ‘Scholar’ financed by
the Dutch Organization for Sciences for financial support.
‡ Corresponding author: Department of Economics, University of Amsterdam,
Roetersstraat 11, 1018 WB Amsterdam, the Netherlands. Phone: +31 – 20 – 525
5088, Fax: +31 – 20 – 525 4310.

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“Investment in professional training will not necessarily be pushed to
the margin because earning power is seldom explicitly treated as an
asset to be capitalized and sold to others by the issuance of “stock”.
[…] If individuals sold “stock” in themselves, i.e., obligated
themselves to pay a fixed proportion of future earnings, investors could
“diversify” their holdings and balance capital appreciations against
capital losses.” Friedman and Kuznets (1945, p.90)


1 Introduction

In most countries of the world, higher education is heavily subsidized by the
government. Apart from merit motives and the presumed presence of externalities of
education1, the main argument in favor of these subsidies is that the government
should guarantee accessibility of higher education. Capital markets can fail to deliver
a sufficient supply of funds to graduates to finance their education. And, students are
generally averse to invest in risky education while incurring debt.2 Failures of capital
and insurance hamper access especially for students from lower socio-economic
backgrounds. Education subsidies indeed avoid financial market failures by reducing
the need for students to borrow and thereby reducing the risks of debt financed
investments in education. The question that remains to be answered is however
whether education subsidies are the most efficient means to warrant access to higher
education.
Economists have often advocated more efficient forms of education finance
such as income contingent loans or graduate taxes. The idea is that both capital and
insurance market failures will be directly addressed by providing the funds to study
and by (partially) insuring students’ income risks without using education subsidies,
see Nerlove (1972, 1975), Barr (1991, 1993), Chapman (1997), van Wijnbergen
(1997), Oosterbeek (1998), and García-Peñalosa and Wälde (2000). Friedman and
Kuznets (1945) and Friedman (1962) argue that graduates should be allowed to issue
equity to finance their investments in human capital. Except for García-Peñalosa and
Wälde (2000), none of these studies has yet applied formal analysis to the problem of
optimal financing of education and to the solutions proposed. And García-Peñalosa
and Wälde (2000) do not pay attention to the underlying micro-economic causes of

1 Positive externalities may indeed justify at least some education subsidies. Although,
Moretti (2004) finds empirical evidence favoring external effects of education, others
are more skeptical, see for example Heckman and Klenow (1998), Acemoglu and
Angrist (2000), Krueger and Lindahl (2002), amongst others.
2 The importance of capital market failures is still a matter of empirical controversy.
Some argue that capital markets are highly imperfect based on the significant and
positive association between socioeconomic status and enrollment in (higher)
education, see e.g. Haveman and Wolfe (1995). On the other hand, this relation may
be due to unobserved characteristics such as parental education and abilities. After
instrumenting for this, Shea (2000) finds weak evidence for the unimportance of
credit constraints. Cameron and Taber (2000), Cameron and Heckman (2001) and
Carneiro and Heckman (2002) argue that credit constraints are not really important
empirically. Plug and Vijverberg (2005), on the other hand, find strong evidence for
the importance of capital market failures while correcting for unobserved
characteristics using adopted children as a natural experiment.

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market failures. But any discussion of optimality is incomplete if the underlying
causes of the market failure that gives rise to intervention to begin with, are not
explicitly incorporated in the analysis.
Some might argue that moral hazard effects explain the absence of properly
working capital markets for financing education and the absence of insurance for
human capital risks.3 Students and graduates may not exert enough effort to study and
work after graduation. As banks and insurance companies are not able to monitor
student’s and graduate’s efforts, they are afraid that students will hit and run when
they apply for a loan, or students might become lethargic during and after graduation
because they are insured against failure outcomes. Although moral hazard is certainly
an issue to be taken into consideration in the design of public intervention, we also
think that moral hazard is not the main problem explaining the capital market failures
blocking efficient financing mechanisms for private education, for two reasons.

First, and most importantly, moral hazard effects would result in
overinvestment in human capital, since the high return investments cross-subsidize the
low return investments in those circumstances.4 Aggregate overinvestment in human
capital is however not a good description of reality, because the returns to in particular
higher education are very high and for example easily approach the returns to equity.5
We therefore think that underinvestment in education is a more likely possibility,
certainly in the absence of government intervention. Consequently, moral hazard is
not the dominant information problem in the market. Second, moral hazard in
financial markers will encourage the poorer students to overinvest in education at the
expense of the richer ones, since the latter will loose more in the case of default.
Hence, moral hazard cannot explain the well documented overrepresentation of the
well-to-do in higher education.
In this paper we argue that adverse selection in educational debt markets in
combination with the impossibility for private parties to write equity and insurance
contracts covering returns on human capital explain why and how governments
should intervene in the financing of higher education. Adverse selection in debt
markets leads to under-investment because some students with socially profitable
investments will not invest or will not get credit (credit rationing). Banks may not
increase the interest rate to meet excess demand for credit because this results in large
shifts in the overall riskiness of students applying for a loan because the low-risk
students drop out of the credit market, see e.g. Stiglitz and Weiss (1981), Mankiw
(1986), and Hellman and Stiglitz (2000).6 Risk averse individuals further require a
risk premium on their investments. Hence, if these income risks cannot be insured
under-investment is exacerbated, cf. Eaton and Rosen (1980). We show that an equity

3 See for example De Meza (2000) for this line of reasoning in the context of small
firms and Judd (2000) in the context of insuring human capital risks.
4 Bernanke and Gertler (1990) and Hoff and Lyon (1995) modify De Meza and Webb
(1987, 1990) by adding additional costs for investors to verify their type. These may
result in under-investment of some investors which are socially desirable, but these
models all display overinvestment at the aggregate level.
5 See for example Card (1999) and Harmon et al. (2003).
6 Asymmetric information may also play a role in the insurance market. Individual
earnings capacities and abilities are generally well known before income insurance
contracts can be written so that adverse selection occurs and the ‘good risks’ separate
themselves from the ‘bad risks’ and the market for insurance contracts may break
down, cf. Rothshield and Stiglitz (1976), and Sinn (1995).

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participation model as proposed by Friedman and Kuznetz (1945), Friedman (1962)
and García-Peñalosa and Wälde (2000) is indeed the optimal way of financing higher
education in the presence of adverse selection in capital markets and the absence of
insurance markets to insure human capital risks. In practice, this solution boils down
to a graduate tax for the financing of higher education. Our analysis builds on the
credit rationing literature pioneered by Stiglitz and Weiss (1981).
We also contribute to the literature on adverse selection in credit markets and
credit rationing by allowing for risk averse students. Stiglitz and Weiss (1981),
Mankiw (1986) and De Meza and Webb (1987), and others have generally analyzed
risk neutral investors. However, risk aversion of students is a real life phenomenon
and we show that the introduction of risk aversion has non-trivial consequences.
Credit rationing is less likely to occur, and may even disappear when students are
sufficiently risk averse. The intuition is that high-risk students also require a large
risk-premium on their investments. When banks increase interest rates, positive
selection effects may become dominant over adverse selection effects if high-risk
students drop out of the credit market first because they require a larger risk premium
on their investments.7
Furthermore, we show that debt financing of higher education is not optimal
and that students would prefer equity financing where it available. However, legal
problems prevent the execution of both equity and insurance contracts by the private
sector in the case of education financing. The reason for this is that the use of human
capital as collateral or claiming its proceeds as dividends is impossible because
slavery and indentured labor are outlawed in all civil societies. This effectively
precludes financial contracts that are contingent upon the returns of human capital
investment. Therefore, only debt finance is provided in markets, credit is rationed, and
under-investment prevails – also due to risk aversion. For the case of risk neutral
investors Cho (1986) and De Meza and Webb (1987) have shown that equity contracts
are indeed optimal in the Stiglitz and Weiss (1981) model. Loosely speaking, a bank
offering a debt contract only attracts the high-risk students, while an equity contract
attracts only the low-risk students (i.e. investors with low-risk projects). Therefore,
only equity contracts are offered. However, with risk averse students, this is less
obvious. If the positive selection effect of higher interest rates always dominates the
adverse selection effect due to limited liability, one might expect that debt contracts
and not equity contracts are the equilibrium contracts, because debt contracts then
attract the low-risk students. We show that this does not happen and an equity contract
is always preferred to a debt contract no matter how risky the students are. The reason
is that equity contracts offer more income insurance than debt contracts and avoid
distortionary redistributions of incomes from low to high-risk students. As a
consequence, the underinvestment problem is mitigated. Students with low-risk
investments will now invest in higher education while they would under-invest with
debt financing. And, more students with risky education enroll because they are better
protected against failure outcomes.
Government intervention in financing education is warranted, because only
the government can implement equity contracts. The crucial distinction between
private parties and the government is that the government can monitor and enforce
claims on all returns from human capital through the tax system, as it already does
through the regular income tax. Equity participation by the government comes down

7 De Meza (2000, p.F21) also speculates that this may occur but does not refer to
work showing this formally.

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to allowing students to finance education in exchange for a claim on part of the
students’ future incomes through a tax on the returns of the investment, i.e. a graduate
tax. Also, we show that introducing a graduate tax is in general not sufficient to
attain the optimal level of investment in human capital, since risk aversion of
graduates implies that they still under-invest. Although both equity and debt financing
feature income insurance, not all income risks are eliminated, so that some under-
investment due to risk aversion remains. Therefore, additional income insurance is
welfare improving. The government may restore social efficiency by reducing income
risks through a higher graduate tax.
We show that education subsidies are at most second-best instruments to
restore social efficiency in investment in human capital. We find that efficiency in
investment in human capital can only be restored by giving very large education
subsidies (on educational costs or interest costs), because education subsidies do not
insure income risks. An equity participation scheme will be far more effective to give
the high risk students incentives to invest in human capital, because of the associated
income insurance. An unfortunate by-product of subsidized higher education is also
that it implies reverse redistribution. The incidence of subsidies falls on the average
tax payer, whereas the benefits accrue to the most talented, and hence generally better
paid. Additionally, a disproportional number of graduates belong to the most wealthy
families. Hence, equity financing of education avoids this perverse redistribution of
incomes, since in principle no subsidies are needed.
Finally, we present some calculations on the likely consequences of
introducing a graduate tax in the Netherlands. We show that in a graduate tax system
payment uncertainties are significantly reduced compared to a loan system and
substantial savings on government outlays could be achieved with only modest tax
rates. The setup of the paper is as follows. In section 2 we present the model and
analyze the role of capital market imperfections and risk on decisions to invest in
learning. Optimal finance of education is analyzed in section 3. In section 4 we
discuss sub-optimal ways of financing education. Section 5 presents some calculations
of a graduate tax system using Dutch data. In section 6 we discuss the consequences
of moral hazard for our results and Section 7 concludes.

2 Investment in human capital with capital and insurance market imperfections

2.1 Students
The benchmark model is the simplest possible model with capital and insurance
market imperfections. We extend Stiglitz and Weiss (1981) by allowing for risk
averse investors. Consider a mass of graduates with index i, of unit measure. Each
graduate decides whether to enroll in higher education which requires an investment
of K. K can be thought of as tuition costs and foregone earnings. The return to the
investment in human capital is random. We only consider two-outcome projects and
denote the return under the successful outcome R s,
f
i , and Ri if the investment in human
capital fails. We assume without loss of generality that R fi = Rf for all i. Expected
returns are the same for all graduates:

(1)
R ? R =
+ ?
=
?
i
pi Rsi
1
(
p )R f
i
const.
i,


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where pi in [0,1] is the probability of a success for graduate i. We say that graduate i is
riskier than graduate j if pi < pj.8 9
All graduates have identical initial wealth Wi = W which is assumed
insufficient to cover all costs of education: W < K. Therefore, additional finance is
required.
We make the following important ‘non-slavery’ assumption. Private financial
contracts between students and financial institutions cannot be made contingent upon
the returns Ri of the investment in human capital. Only debt finance is therefore
allowed, since a debt contract (r, B), that specifies the principal B and interest rate r, is
independent of the returns of the investment. Furthermore, income insurance is
impossible since this would also require contracts dependent on the return to human
capital. If graduates decide to invest in education they borrow B = K - W at interest
rate r. If the investment in education fails, banks receive the failure return Rf. If
education is successful, banks receive principal plus interest. We assume that R si > (1
+ r)B > Rf always holds. Graduates have limited liability, therefore the return i for
graduate i is given by:

(2)
? ?
? +
.
i
ma [
x Ri
1
(
r)B, 0]

Graduates are risk averse, with a standard expected utility function EU( i) with U(0) =
0, U' > 0, U' < 0, U' ' 0. We also impose Inada type conditions on U: lim 0 U'( i)
= , lim
U'( i) = 0. Graduates are willing to invest in risky education financed
with debt as long as:

(3)
EU (? =
? +
?
+ ?
),
i )
piU (Rsi
1
(
r)B) U ( 1
(
)W )

where is the safe real return on non-human investments (savings).
Expected utility is either monotonically increasing in pi or non-monotonic;
first increasing, then reaching a maximum and finally decreasing in pi. To see this,
differentiate (3) while substituting (1):

dEU (? i )
(4)
= U ( s
R
r B
U R
r B R
R

i ? 1
( + ) ) ?
(' si ? 1
( + ) )( si ? f ) <
dpi

U (Rs ? +
?
? +
? +
.
i
1
(
r)B) U ('Rsi
1
(
r)B)(Rsi
1
(
r)B)

The last line equals zero for risk neutral investors and is positive for risk averse
investors. The sign of (4) is therefore strictly negative for risk neutral investors. The
sign of (4) however cannot be determined in general. We know that the second line is
always positive for any concave utility function. Therefore, the first line may be either

8 Generally speaking one cannot say that graduate i has higher risk than graduate j if
pi < pj because the variance of returns first increases and then decreases with pi
because the returns are bi-modally distributed. However, with mean returns restricted
to be equal across all i, it is easily shown that the variance decreases with pi.
9 There is no systematic macroeconomic risk and all risks are idiosyncratic. In the
empirical application below we argue why this is a reasonable benchmark in the case
of higher education.

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positive or negative, since R s
s
i – Rf > Ri – (1 + r)B. Whether (4) will be positive or not
depends on the size of (1 + r)B – Rf and marginal utility of income U' (which is lowest
for low-risk investors). If borrowing costs are large compared to the returns (small R si
– (1 + r)B), returns in the bad outcome relatively low (high R si – Rf), then (4) may be
negative, and vice versa. Therefore, (4) is will be typically negative for low-risk
investors with relatively small risk aversion due to relatively safe investments and
who have a large marginal utility of income since they have relatively high borrowing
costs relative to the returns.
We can sketch the graph of EU(pi); cf. Figures 1 and 2 below. We know that
EU(0) = 0, and EU(1) = U(R – (1 + r)B) > 0. The graph of EU(pi) either always
increases monotonically, or first increases and then decreases to reach EU(1). The
intuition for the shape of EU(pi) can be understood most easily by also plotting
U(E i), which denotes utility from the certainty equivalent and corresponds to the
case where there is perfect income insurance. This line also corresponds to the Stiglitz
and Weiss (1981) case with risk neutral investors. As we move along the horizontal
axis from pi = 1 to pi = 0 (from right to left), we know that investments become more
risky. If graduates could eliminate income risks so as to obtain the certainty
equivalent of income, the utility (of expected income) would increase for graduates
with lower pi. Equation (4) is always negative for risk neutral graduates (U linear),
since only the limited liability effect allows the high risk graduates to shift the
downside risks to banks.
However, if graduates are risk averse, expected utility is lower than the utility
of expected income. Expected utility may initially increase if pi is lowered due to the
positive effect of having limited liability. This limited liability effect is more
important when risk aversion is small, incomes in the bad state of nature are lower (Rf
lower) or if interest rates are higher so that debt costs are higher ((1 + r)B larger),
since then the welfare gain of being able to shift default costs to banks increases.
Eventually, however, expected utility must become decreasing if pi decreases, because
risk aversion becomes dominant in lowering expected utility. This is because the
'utility cost’ of being risk averse increases ‘quadratically’ with lower pi, whereas the
utility benefit of having limited liability only increases ‘linearly’ with decreasing pi.
For example, if utility features constant relative risk aversion (CRRA), (EU( i)
= p
s
i (Ri – (1 + r)B )1 - /(1 – )), then (4) may be always positive (low interest rate,
high return in bad outcome) for risk averse graduates, i.e. when 0 < < 1, see Figure
1. Stronger risk aversion (higher ) decreases the slope of the EU line. We plotted the
case in which the interest rate is higher (r = 1.5) in Figure 2. Hence, for high pi the
positive effect of limited liability dominates the negative risk aversion effect on risk
taking, so that EU( i) is first increasing and then decreasing as pi falls.


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Figure 1 - Investment decision with debt financing and with high and low risk aversion (Rf = .5,
R = 3, W = .6, B = 1, = 0, r = .5).
5
4.5
4
3.5
3
EU(Pi) CRRA = .5
U(EPi) CRRA = .5
2.5
EU(Pi) CRRA = .75
U((1+rho)W)
2
1.5
1
0.5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
probability of succes
Risk aversion may have important consequences for the equilibrium of the model. For
the marginal graduate, i.e. the graduate who is indifferent between investing in
education or putting money in the bank, (3) holds with equality. The success
probability at which a student is marginally indifferent between investing and staying
out, pm, may decline or increase if banks increase interest rates depending on whether
(4) > 0. This follows from totally differentiating pmU((R - Rf)/pm – (1 + r)B - Rf)) =
U((1 + )W):

dp
p U
B
m
m
(.
')
(5)
=
.
dr
U (.) ?U (.
')( s
f
R ? R
m
)

Consequently, dpm/dr > 0 when (5) > 0 and vice versa. In the limiting case where
graduates are risk neutral, pm = (R – Rf – (1 + )W)/((1 + r)B – Rf), and therefore,
dpm/dr < 0 for risk neutral graduates.


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