This paper develops a labour market model with on-the-job search, match-specific pro-

ductivity draws and an endogenous irreversible schooling decision. The choice of schooling

is modeled as an optimal stopping problem which gives rise to the equilibrium heterogeneity

of workers with respect to the formal education. The optimal schooling decision is charac-

terized by the reservation productivity of students which is a monotonic function of time.

Moreover, this reservation productivity is lower in expansions when job-to-job mobility is

more intensive. Therefore, the model is compatible with the empirical evidence that expan-

sions have a positive effect on the probability of a school dropout. The schooling density

is downward-sloping and the equilibrium wage distribution is right-skewed with a unique

interior mode. This means that the majority of workers earn wages in the middle range of

the earnings distribution. At the same time there is a small proportion of employees in the

beginning of their career with wages in the left tail of the earnings distribution and a small

proportion of high-skilled workers earning wages in the right tail of the distribution.