Educational and Wage Risk : Social Insurance Versus Quality of Education

Abstract

In this model of education, where individuals are exposed both to educational risk and to wage risk within the skilled sector, successful graduation depends both on individual effort to study and on public resources. We show that insuring the present risks is a dichotomic task: Wage risk is diversified ex post among the skilled by graduate taxation and skill-specific tuition fees. Educational risk of failure and inequality between skilled and unskilled workers are mitigated ex ante by enhancing the quality of education. The necessary expenditures are optimally financed by regressive tuition fees and the net revenue from the graduate tax.

Full text

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Educational and Wage Risk:
Social Insurance vs. Quality of Education



DIRK SCHINDLER
BENJAMIN WEIGERT


CESIFO WORKING PAPER NO. 2513
CATEGORY 1: PUBLIC FINANCE
DECEMBER 2008

PRESENTED AT CESIFO AREA CONFERENCE ON PUBLIC SECTOR ECONOMICS, APRIL 2008




An electronic version of the paper may be downloaded
• from the SSRN website: www.SSRN.com
• from the RePEc website: www.RePEc.org
• from the CESifo website: Twww.CESifo-group.org/wpT

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CESifo Working Paper No. 2513



Educational and Wage Risk:
Social Insurance vs. Quality of Education


Abstract

In this model of education, where individuals are exposed both to educational risk and to
wage risk within the skilled sector, successful graduation depends both on individual effort to
study and on public resources. We show that insuring the present risks is a dichotomic task:
Wage risk is diversified ex post among the skilled by graduate taxation and skill-specific
tuition fees. Educational risk of failure and inequality between skilled and unskilled workers
are mitigated ex ante by enhancing the quality of education. The necessary expenditures are
optimally financed by regressive tuition fees and the net revenue from the graduate tax.
JEL Code: H21, I2, J2.
Keywords: human capital investment, educational risk, wage risk, learning effort, graduate
taxation, regressive tuition fees.






Dirk Schindler
University of Konstanz
Fach D 133
78457 Konstanz
Germany
Dirk.Schindler@uni-konstanz.de



December 19, 2008
The paper has profited from discussion with Bas Jacobs and Stefan Zink and from valuable
suggestions by participants of the CESifo Area Conference on Public Sector Economics in
Munich and the IIPF-meeting in Maastricht.

Benjamin Weigert
Justus-Liebig-University Giessen
Department of Economics
Licher Strasse 66
Germany – 35394 Giessen
benjamin.weigert@wirtschaft.uni-giessen.de

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1Introduction
This paper deals with educational and wage risks and characterizes optimal edu-
cational and tax policies to mitigate the effects of wage inequality and skill-biased
technological change. Optimal educational policies thereby include regressive (ex
ante) tuition fees and graduate taxation as well as public real investment in order
to foster the quality of educational institutions (e.g., universities).
At least in the last 20 years, one observes an increasing wage inequality in
nearby all developed countries. On the one hand, the wage gap between skilled
and unskilled workers is rising and on the other hand there are wage differen-
tials across industries within the skilled sector. These trends in wages are mainly
driven by ongoing globalization of the world economy and by skill-biased tech-
nological change.1Jacobs (2004) forecasts the wage gap between skilled and
unskilled wages to be widening even more, due to a higher growth rate in skilled
labor demand relative to skilled labor supply. Skill-biased technological progress
does, however, not only harm unskilled workers, it also affects the utilization and
depreciation of human capital in different industries in different ways (see, e.g.,
Wildasin, 2000). This leads to wage uncertainty in the skilled sector and fits to
the Mincer (1974)-view of education and human capital investment increasing
risk. The results by Mincer (1974) are renewed and backed, e.g., by Carneiro
et al. (2003), examining high-school and college graduates and showing the over-
whelming part of variance in returns to education to be unpredictable by students
at the time of investment.
Taken together, these wage inequalities correspond to educational risk (risk of
failure to enter the skilled sector) and to wage risk within the skilled sector, be-
cause ex ante it is uncertain which kind of employment one will find. The main
difference between these kinds of risk is that for educational risk households and
the government determine the probability distribution endogenously by choosing
learning effort and educational quality. Hence, ex ante insurance by increasing the
success probability (i.e., the quality of education) is possible. This fits to regard-
ing the education system as a ‘filter technology’ producing ex post heterogeneity
1See, e.g., Krugman (1995) and Katz and Autor (1999). Another reason for observed wage
inequality is seen in increasing educational wage differentials.
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and calling for redistribution, even if the playing field is level by full access to
education, i.e., if households are homogenous ex ante or if there is equality of
opportunities in case of ex ante heterogeneity, see Konrad (2004). For wage risk
instead, only the ex post exposure to risk can be affected, but the entry probabil-
ity for each state of nature is exogenous. In a risk- and inequality-averse society,
these two kinds of risk do not only cause inefficient investment in education,2but
also give raise to redistributive motives between winners and looser. As private
insurance markets seem not to work (see Sinn, 1996) due to, e.g., adverse selec-
tion – the good risks are opting out – and legal limitations (students are too young
for writing binding contracts), this calls for governmental intervention.
However, what can be done? Is it sufficient to increase population’s acquire-
ment of higher education and human capital, as proposed by the EU ‘Lisbon-
agenda’ (EU-Council, 2005)? How should this be financed? What happens, if
risk of failure and of ending up as unskilled worker is weighed against wage risk
of skilled workers? Are ex post income transfers another, a better or an additional
way of insurance?
We show that the welfare maximizing governmental revenue policy is char-
acterized by (i) a graduate tax on skilled earned income, (ii) a general lump-sum
tax, which can be seen as general tuition fees paid by all households and (iii)
by skilled-specific tuition fees, turning most likely into education subsidies to
successful students and creating, consequently, a regressive structure of ‘front-
loaded’ tuition fees. A general labor tax is not used. Unskilled workers are net tax
payers and tax revenue is spent on investments to enhance the quality of educa-
tion in order to increase the success probability in educational investment for all
households. This provides ex ante insurance and mitigates distortions in learning
effort, created by taxation.
These results are derived in a two-period model, where the individuals first
decide on their learning effort. This determines their success probability in higher
education. At the end of the first period, success risk in education and an industry-
specific productivity shock in the skilled sector realize. The latter shock can be
seen as technological change, affecting utilization of human capital differently
2See Levhari and Weiss (1974), who are the first in analyzing these topics, but also Kodde
(1986, 1988).
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across industries. At the beginning of the second period, the individuals observe
in which sector respectively in which industry within the skilled sector they will
be employed and choose their sector-contingent labor supply. The benevolent
government can use a proportional wage tax on all incomes, a graduate tax (being
paid only by skilled workers) and skill-specific tuition fees in order to finance
both a general lump-sum transfer and public funding of the education system.
Public educational spending is assumed to increase the success probability by
enhancing the quality in the educational sector and therefore by enhancing the
‘filter technology.’
The proceeding is as follows: In the next section, we provide a short overview
on related literature. The model is presented in section 3. Then, we characterize
optimal household behavior in section 4 and describe public policy in section 5. In
section 6, finally, optimal usage of tax instruments and optimal public investment
are derived. Section 7 concludes.
2Relationship to the Literature
There is some literature on optimal tax policy in case of risky human capital in-
vestment and wage uncertainty. This paper combines and extends two strands:
First, there are models focusing on (pure) wage risk (within one sector), second
there are models dealing with success risk in education and the wage differential
between a skilled and an unskilled sector.
It is well known from the seminal paper series by Eaton and Rosen (1980a,b)
that it is optimal to implement a distorting wage tax, because the insurance pro-
videdwill outweigh the excessburden, if wageincome is subject to (idiosyncratic)
risk. Hamilton (1987) confirms this result and extends their model for capital
income taxation as indirect education policy. He argues that remaining underin-
vestment in education is inefficient and calls for education subsidies. In a related
setting, Anderberg and Andersson (2003) show that education itself can have an
insurance effect, if the government centrally decides on educational investment
and that it should be overprovided in this case, because this increases both welfare
and tax revenue.
Other recent papers, dealing with risky human capital formation and risky
3