According to a recent paper (pdf):
The study found that offshoring tends to increase productivity and reduce costs, which can prompt firms to expand domestic hiring enough to offset the jobs lost to workers overseas. "Offshoring has no effect on native employment in the aggregate," the authors said. "While offshore workers compete directly with natives, their employment generates productivity gains that ‘increase the size of the pie,’ leading to an overall neutral impact on native employment."
The Dish 