United States-China relations continue to surface as an issue on the campaign trail, particularly in battleground states like Ohio where manufacturing is a major force in the local economy. Now both President Obama and Mitt Romney are running television commercials that trade accusations over who is softer on China, and who is more to blame for sending American jobs there.

The Romney campaign ad states: “Under Obama we’ve lost over half a million manufacturing jobs, and for the first time China is beating us. Seven times Obama could have stopped China’s cheating. Seven times he refused.” Then it cuts to Mr. Romney, who declares, “It’s time to stand up to the cheaters and make sure we protect jobs for the American people.”

The announcer concludes, “Barack Obama: failing to stop cheating, failing American workers.”

The Obama campaign ad, released a day after the Romney one first appeared, opens on an incredulous note. “Mitt Romney tough on China?” an announcer asks. “Romney’s companies were called pioneers in shipping U.S. manufacturing jobs overseas. He invested in firms that specialized in relocating jobs to low-wage countries like China. Even today part of Romney’s fortune is invested in China. Romney’s never stood up to China. All he’s done is send them our jobs.”

Who is right? Mr. Romney’s first claim — that more than half a million manufacturing jobs have disappeared since Mr. Obama took office — is supported by data from the Bureau of Labor Statistics, which show manufacturing employment at 12.5 million in January 2009 and put it at just under 12 million as of August, a net loss because of job cuts during the recession.