Runjuan Liu and Daniel Trefler estimate the impact of U.S. offshore outsourcing with the Chinese and Indians, and U.S. service inshoring (U.S. sales of services abroad) to them, on U.S. labor markets (Much Ado About Nothing: American Jobs and the Rise of Service Outsourcing to China and India). Overall, "We precisely estimate small positive effects of inshoring and smaller negative effects of offshore outsourcing. The net effect is positive." However, the effects tend to be negative for the less educated or less skilled.
But, we're talking about small impacts. From the abstract:
To illustrate how small the effects are, suppose that over the next nine years all of inshoring and offshore outsourcing grew at rates experienced during 1996-2005 in business, professional and technical services i.e., in segments where China and India have been particularly strong. Then workers in occupations that are exposed to inshoring and offshore outsourcing (1) would switch 4-digit occupations 2 percent less often, (2) would spend 0.1 percent less time unemployed, and (3) would earn 1.5 percent more. These are not annual changes – they are changes over nine years – and are thus best described as small positive effects.