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Education expansion may lead to ‘over-education’, where the social connections of parents may exert more significant influence on the return to education of children. With the assumption of a positive correlation between return on human capital and parental income in the presence of over-education, we show that: (i) the expansion of education may cause horizontal inequity in education opportunities and inefficiency in human capital accumulation; (ii) the positive correlation between return on human capital and parental income causes a more persistent intergenerational immobility; (iii) an expansion of education (especially higher education) leads to more persistent intergenerational immobility.