Hours and Participation with Job Assignment Frictions

We consider a competitive equilibrium matching model where technological progress is embodied in new jobs. Jobs are slowly created over time and in equilibrium there is dispersion in job technologies. Workers can be employed in at most one job. They decide on whether to participate in the labor market and on how many hours to work when assigned to a job. This endogenously generates inequality in wages and in labor supply. When the pace of technological progress accelerates differences in job technologies widen and the technology gap with respect to the frontier increases more in worse jobs. As a result, the balance of income and substitution effects on labor supply is asymmetric across jobs and it becomes optimal to work longer hours in the top jobs and work less hours in the worst ones. With a fixed cost of labor supply this implies that the participation rate falls as workers work less often in order to avoid the worst jobs, and they supply longer hours on average when employed. This model can explain the simultaneous fall in labor force participation and the increase in working hours experienced by US male workers since the mid 70s in a context of raising wage inequality. In addition, it can ex- plain the differences across education groups. In the data, less educated workers see both participation and hours fall. Our model predicts assortative matching, and hence, less educated individuals have access to the worst jobs in the economy, those that worsen the most with the increase in the speed of embodied technical change. Hence, for these workers the returns on market work fall disproportionately and they reduce labor supply in both margins