We seek to quantify the role of education as a mechanism through which family background affects economic outcomes. To this end, we generalise mediation analysis to allow for multidimensional treatments. This improves the validity of mediation analysis for our application, in which family background is exogenous and multidimensional. Our approach allows the mediating role of education to vary across background characteristics, whilst also estimating its overall mediating effect. We estimate that educational attainment explains 21%–37% of the family background effect on hourly earnings in Australia, and only 13%–19% of the effect on wealth. We argue that these estimates are likely upward-biased. Therefore the link between family background and economic outcomes operates mostly through other mechanisms.