Student loans: When is risk sharing desirable?

• Author: Itzhak Zilcha,Bernhard Eckwert
• DOI: http://doi.org/10.1111/ijet.12126
• Published date: 01 June 2017
• Date: 01 June 2017

doi: 10.1111/ijet.12126

Student loans: When is risk sharing desirable?

Bernhard Eckwert∗and Itzhak Zilcha†

In higher education, pure credit market funding leads to underinvestment due to insufficient

risk pooling, while pure income-contingent loan funding leads to overinvestment. We analyze

whether funding diversity – a market structure in whichcredit markets coexist alongside income-

contingent loan funding – might restore efficiency of the educational investment process. In

the absence of government intervention, we find that funding diversity improves pooling of

individual income risks and, under some condition, leads to higher social welfare than pure

credit marketfunding . Ifcombined w ith a policy that restricts accessto higher education, funding

diversity even achieves full investment efficiency and strictly dominates credit marketfunding .

Key wor ds higher education, funding diversity, human capital formation.

JEL classification D31, H31, I22.

Accepted 14 October 2015

1 Introduction

Higher education financing faces two main problems which may lead to underinvestment in skilled

human capital formation. The first problem is due to the peculiarities of human capital which

prevent this form of capital from being used as loan collateral. As a consequence, banks arereluctant

to provide higher education loans (see, for example, Galor and Zeira 1993). The second problem

is caused by imperfections in the market for risk bearing. Investment in higher education is risky

because students are at least partially ignorant about their abilities and, hence, about the returns on

their investments. Yet, financial markets are unlikely to provide adequate pooling or diversification

of these risks due to the existence of moral hazard incentives in an agent’s acquisition of human

capital and in his performance in the labor market.

As a possible response to these market failuresthe creation of income-contingent loan-repayment

programs has been suggested (Friedman 1962; Nerlove 1975; Chapman 2006). Income-contingent

loans have the special characteristic that the terms of repayment depend on the borrowers’ future

incomes: individuals with higher incomes have higher repayment obligations. Such loan contracts

not only allow students to pool (part of) their future income risks but can also be used to transfer

risks on investment in human capital from borrowersand lenders to third parties. Yet, while income-

contingent loans may ease credit constraints and improve risk allocation, they often also imply

significant cross-subsidization between subgroups of students with different future income prospects

which may lead to excessive investment in higher education. In fact, students with poor income

∗Bielefeld University,Bielefeld, Germany. Email: beckwert@wiwi.uni-bielefeld.de

†TelAviv University and College of Management Academic Studies, Israel.

Financial support from the Pinhas Sapir Center for Development, Tel Aviv University, is gratefully acknowledged. We

especially wish to acknowledge receiving helpful suggestions from an anonymous referee.

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International Journal of Economic Theory

Risk sharing and student loans Bernhard Eckwert and Itzhak Zilcha

prospects are more likely to take out education loans under such a scheme than students with

good income prospects and, hence, the human capital formation process is characterized by adverse

selection (Eckwert and Zilcha 2010, 2012).

Typically, none of these schemes exists in isolation. Our paper therefore concentrates upon the

implications of funding diversity: we study the implications of credit funding and income-contingent

loans funding when these two schemes coexist and compete against each other for higher education

finance. For this purpose, we set up a theoretical framework in which individuals live for two

periods. In the “youth” period, agents obtain education and in the “working” period they generate

incomes based on their human capital and skills. At birth, each individual is randomly endowed with

some innate ability which becomes fully known only in the working period. Following compulsory

schooling in the youth period, each individual receivesa (publicly observed) signal which is correlated

to his/her true innate ability. The decision whether to acquire higher education after compulsory

schooling depends on the financing options available to the agent and on the information conveyed

by the signal.

We consider two financing regimes. Under the first regime, the government guarantees access

to credit markets for all students who attend higher education. Under the second regime, which is

the main focus of our study, income-contingent education finance coexists with competitive credit

markets. We find that pure credit market funding leads to underinvestment in higher education.

By contrast, funding diversity leads to overinvestment due to adverse selection. Nevertheless, un-

der some condition, funding diversity dominates pure credit market funding in terms of social

welfare.

Funding diversity in higher education is plagued by adverse selection in two respects. First,

the cross-subsidization within the income-contingent loans program entices students with negative

expected net returns on their investments to participate in the program. This misallocation of

educational investment raises the financing costs for all participants, because the program is not

subsidized by the government and, hence, must break even in equilibrium. Second, the elevated

financing costs within the program provide incentives for students with good income prospects to

shun the program and turn to the credit market for funding. This effect pushes the financing costs

within the program even higher.

The fact that funding diversity alone does not remedy the misallocation of educational invest-

ment suggests a role for government policy. This policy would restrict access to higher education to

individuals with non-negative expected net returns on their investments, given the signals attained

after compulsory schooling. We find that such policy, if combined with funding diversity in higher

education, is quite appropriate as it restores efficiency of the educational investment process and, at

the same time, mitigates the adverse selection problem within the income-contingentloans program.

Moreover,under a p olicy of restricted access, funding diversity always leads to higher social welfare

compared to pure credit market funding.

Our work is related to the theoretical literature that analyzes imperfections in financing modes

of higher education. One of the earlier contributions is Loury (1981) who analyzes imperfections in

the form of exogenous borrowing constraints for education funding. Since then, a number of papers

have integrated similar constraints into more extended equilibrium models of higher education. For

example, De Gregorio and Kim (2000) and De Fraja (2002) develop models in which students from

better-off households are less affected by borrowing constraints, which leads to an elitist education

provision in equilibrium. Using a Kehoe and Levine (1993) framework, Andolfatto and Gervais

(2006) and de la Croix and Michel (2007) analyze the role of endogenous liquidity constraints for

educational decisions and human capital formation.

218 International Journal of Economic Theory 13 (2017) 217–231 © IAET