We seek to quantify the role of education as a mechanism through which family background affects earnings. To this end, we propose a generalisation of statistical 'mediation analysis'. In our approach, the treatment and mediator can be multidimensional. This allows us to directly and flexibly account for a range of background characteristics which affect child earnings through the pathway of education and through other mechanisms. The results suggest that educational attainment explains 24%-39% of the overall family background effect on earnings in Australia. The mediating role of education seems to be larger for Australia than for the UK.