Economists differ over how much outsourcing will change the American job market in the future, but there is little evidence that trade has been a major cause of job loss or even wage stagnation so far. As Robert Z. Lawrence of the Peterson Institute for International Economics wrote in a recent study: “The recent increase in U.S. inequality ... has little to do with global forces that might especially affect unskilled workers — namely, immigration and expanded trade with developing countries.”
The Peterson Institute study Brooks cites does not focus on the trade deficit.
The trade deficit is associated with a substantial decline (several million) in the number of manufacturing workers employed in the U.S., as we discuss in Trading Away Our Future. The decline in manufacturing employment due to the trade deficit has effects that extend well beyond the manufacturing sector. In particular, unemployed manufacturing workers (and those who choose not to pursue a manufacturing career) compete with those in other sectors of the economy.
Would eliminating the trade deficit end economic inequality? No. Would it make a difference? Probably. It would bring manufacturing employment back towards its 1965-1995 historical range of about 17 million workers. It would make a difference. (http://www.epi.org/content.cfm/bp171)