Postgraduate degree holders experience lower cyclical wage variation than those with undergraduate degrees. Moreover, postgraduates have more specific human capital than undergraduates. Using an equilibrium search model with long-term contracts and imperfect monitoring of worker effort, this paper attributes the cyclicality of the postgraduate-undergraduate wage gap to the differences in specific capital. Imperfect monitoring creates a moral hazard problem that requires firms to pay efficiency wages. More specific capital leads to lower mobility, thereby alleviating the moral hazard and improving risk-sharing. Estimates reveal that specific capital explains the differences both in labour turnover and in wage cyclicality across education groups.