Theory fails to predict clearly whether a greater public investment in the higher education system effectively decreases the inequality between the educational attainment of rich and poor students. It is assumed that a rich student enrolled at a university receives a monetary transfer from his parents and allocates it between private consumption and investment in private education. When private and public educational investments are substituted, it is found that a further public investment narrows the educational gap. This result is due to the behavior of rich households. Once public investment has increased, rich students and their parents reduce private investments and monetary transfer, respectively; this allows the education of the poor student to increase more than the education of the rich one. This result also holds under weak complementarity.

Empirical and theoretical evidence confirms that children whose parents are characterized by high levels of income and human capital are more likely to be enrolled in universities and achieve better higher education. Higher education inequality has been largely confirmed in several countries. However, there are many doubts about the existence of a policy for equality. This paper shows that an increasing public investment in the higher education system may be an effective policy to reduce the educational gap between students from high and low income households. We develop a theoretical model in which the educational attainment of the child depends on public investment, pre-university human capital and investment in private education. Public investment in education is to be interpreted in general sense as public expenditure. Private investment includes time and private goods which increase the individual human capital. In our setting, pre-university human capital represents what Heckman (1995), and Carneiro and Heckman (2002 and 2003) call cognitive ability, which is the scholastic aptitude of the students arisen from the joint effect of parental education and income. They find that high income and well-educated parents are able to develop a better scholastic aptitude in their children by assisting and directing their studies and sending them to better pre-university institutes. Our main result is that a higher public investment may unambiguously narrow the educational gap under substitutability and weak complementarity between private and public investment.

Becker and Tommes (1986), and Nordblom (2003) represent two polar examples analyzing this issuethe former assumes substitutability whereas the latter complementarity. However, defining which private investments are complements or substitutes to the public one is not as obvious as it seemsboth complementarity and substitutability seem plausible in the higher education accumulation. Substitutability, for instance, is more reasonable when the level of public investment is low. In this case, the educational achievement may depend only on the private investments.

Public Finance journal, Public Investment, Educational Process, Decision Makers, Labor Market, Human Capital Production, Empirical Observations, Private Investments, Public Schooling, Policy Implications.