China is one of six topics on the agenda for Monday night’s presidential foreign policy debate. But the subject is likely to get outsize attention because it’s the only one on the list that directly relates to voters’ overwhelming concern: the domestic economy.

In the last debate, the word “China” came up nearly two dozen times as the candidates competed to sound tough on the fast-rising Asian economic power.

“On Day One, I’ll declare China a currency manipulator,” Republican candidate Mitt Romney says in stump speeches in Ohio and other industrial states, part of a pledge to “crack down” on tactics that he says improperly draw away U.S. technology, ideas and jobs.

And President Obama has been hammering Romney’s investments in China through the private-equity firm Bain Capital, a record that he says belies the Republican candidate’s severe-sounding approach. “Governor, you’re the last person who is going to get tough on China,” Obama said in the CNN-sponsored televised debate last week.

In contrast, Obama emphasizes his supposedly more rigorous approach. “We have brought more trade cases against China in one term than the previous administration did in two,” he says.

Despite the heated rhetoric, an examination of the record of the two candidates shows that both are centrists on trade with a reluctance to dramatically change the trajectory of U.S.-China relations.

Obama has talked tough on China before, but his record in office does not impress advocates of a crackdown.

In the 2008 presidential campaign Obama vowed, as Romney does today, to adopt a hard line on Chinese currency manipulation. But once in office, he never did, preferring a negotiated response that he says has been effective.

“That’s a weak point for Obama. He should have been more active,” said Thea Lee, chief international economist at the AFL-CIO.

Others concerned about offshore job migration recall that Obama also pledged in 2008 to cut tax incentives for companies moving jobs overseas but did not reach the goal.

“After being elected, Obama had a big majority in both chambers [of Congress] and huge public opinion approval, yet he didn’t get it done,” said Ron Hira, a professor at the Rochester Institute of Technology who tracks the movement of U.S. jobs offshore.

Romney has experience with investment in China and other countries, but he doesn’t talk about it much on the stump. As the Obama campaign has frequently noted, Bain Capital has had a stake in companies engaged in some of the very practices Romney now decries.

Romney’s relationship with China is complicated. But it is perhaps brought into sharpest relief by looking back to 1998, when several Bain Capital entities under his control made a passive investment in a Chinese manufacturing firm, Global Tech Appliances.

During the 1990s, Global Tech was manufacturing bread-makers and other kitchen appliances for Sunbeam, an American company that had begun laying off North American factory workers.

An early 1998 prospectus from Global Tech described six-day-a-week production at its plants in China and noted the growing international trend toward outsourcing. The prospectus said that well-equipped Chinese factories “along with the use of inexpensive labor enables the Company to efficiently produce” goods for brand-name manufacturers in the West that are “increasingly outsourcing product development and manufacturing.”

In addition to performing jobs for U.S. appliance manufacturers, Global Tech had by early 1998 become the subject of a lawsuit filed in U.S. federal district court alleging that the firm had engaged in patent infringement as it expanded its product line, a complaint later affirmed by the U.S. Supreme Court.

Bain never owned Global Tech outright, but it did invest passively, eventually controlling more than 10 percent of the company’s stock.

After the Boston Globe reported on Bain’s investment last month, the Chinese firm’s treatment of workers was decried by an international labor group and by the Obama campaign, which claimed in broadcast ads that Global Tech paid its workers “next to nothing . . . in sweatshop conditions.”

Romney hasn’t publicly addressed the charge. But in past statements, he described a trip to China during which he visited a factory manufacturing bread-makers and other appliances, which in many ways matches the description of Global Tech’s facility operating in 1998. Romney came away from his trip impressed with the discipline of the young female workers at the plant and discussed his impressions briefly in a recent book and in a 1998 seminar in Boston hosted by the University of Massachusetts.

“I went to a factory of 5,000 workers making breadmakers and mixers,” Romney says, according to a transcript of the seminar. “And 5,000 Chinese, all graduated from high school, 18 to 24 years old, were working, working, working, as hard as they could, at rates of roughly 50 cents an hour. They cared about their jobs; they wouldn’t even look up as we walked by.”

In his book “No Apology,” Romney describes returning to Boston after touring an appliance factory in China and then visiting an unnamed competing American factory.

“If productivity were solely a measure of how fast and how hard people work, you’d have to conclude that Chinese workers are highly productive perhaps even more productive than our own,” Romney wrote in the 2010 book. “But in fact the American workforce is more productive, much more productive. The reason is because workforce productivity is a measure of the value of the goods and services produced by a worker not just how fast or intently they work.”

He speculates that American productivity may occur because U.S. workers have greater skill, experience and the chance to work with advanced equipment.

For his part, Obama, acknowledged in the last debate that “there are some jobs that are not going to come back, because they’re low-wage, low-skill jobs.” He emphasizes investment in “advanced manufacturing” and education to make the United States a leader.

Romney made a point in the last debate of highlighting Obama’s own pension investments. The president brushed away the comment with a joke about the size of Romney’s pension. But the Republican point was no joke. Obama’s retirement accounts hold stock in American firms, such as Apple, that rely on low-cost Chinese labor.

Investment in Global Tech drew the interest not only of Bain Capital, but also of leading institutional investors, including, for a couple of years, the country’s largest public pension fund, Calpers. It provides retirement income for California’s public employees.

Alice Crites contributed to this report.