Offshoring tasks, yet creating jobs?

We show that in a Ricardo-Viner-type trade model with unemployment due to search and matching the productivity effect of offshoring emphasized by Grossman & Rossi-Hansberg (2008) emerges as a vehicle of job creation. Improvements in the technology of offshoring causes job losses at the extensive margin where ever more tasks are performed abroad, but it also causes job creation from cost-savings associated with enhanced trade in tasks. We identify conditions under which job creation dominates job destruction. We also show that employment may follow a non-monotonic pattern of adjustment to successive improvements in the technology of offshoring.