Should educational policies be regressive?

In this paper, we show that when the government is able to transfer wealth between generations, regressive policies are no longer optimal. The optimal educational policy can be decentralized through appropriate Pigouvian taxes and credit provision, is not regressive, and provides equality of opportunities in education (in the sense of irrelevance of parental income for the amount of education). Moreover, in the presence of default, the optimal policy can be implemented through income-contingent payments.