Washington (CNN Business) President Donald Trump, who since the beginning of his political career has promised to stem the flow of jobs overseas, says his trade wars are doing just that.

"Big Steel is opening and renovating plants all over the country. Auto companies are pouring into the US, including BMW, which just announced a major new plant. The USA. is booming!," the President tweeted this week.

Is that really true?

Well, maybe. But it's hard to tell definitively, because it turns out that offshoring — and "reshoring," as the opposite effect of bringing jobs back into a country is known — is extremely difficult to measure with any precision.

The answer matters as Democrats line up to oppose Trump's newly signed replacement for the North American Free Trade Agreement — and as he engages in a slow dance with Chinese leader Xi Jinping as well as European leaders over an array of trade issues at the G20 summit in Argentina.

What we do know: Manufacturing has been rebounding ever since the depths of the recession, with employment going from 11.5 million jobs in 2010 to nearly 12.8 million today. That happened for a number of reasons, including the rise of oil and gas fracking providing cheap energy and a glut of unemployed people willing to accept lower-wage jobs. Employers also face more risk in long global supply chains, and have shifted to a "just-in-time" manufacturing strategy that allows distributors to respond quickly to changing customer needs if their factories are on American soil.

Yet we also know that the trade balance in goods — the difference between what we import and what we export — has continued to widen under the Trump administration, reaching $77.2 billion in October, up from $67.7 billion at the beginning of his term and the second largest gap ever. That means American consumers and companies are buying more stuff from abroad that could be made in the US, such as automobiles

"It's still a two-way street," says Scott Paul, president of the Alliance for American Manufacturing, which is backed by the United Steelworkers union and manufacturers. "We still have manufacturing that is leaving the US, but you also see some reshoring."

There is one source of data that measures offshoring explicitly: Trade Adjustment Assistance, a federal subsidy that since 1975 has been available to workers who lose jobs when companies move work overseas or simply cut production due to competition from cheaper imports. Use of the program spiked during the recession, and then receded to more normal levels.

That's still not a perfect yardstick, however, since it's also influenced by how generous funding for the program is and how willing states are to certify applications. It's not very useful for real-time measurement, since application data is posted with a delay. Moreover, it misses the more gradual drift of production to other countries.

Sometimes it's easy to tell when a job has been offshored, like when furnace and air-conditioner maker Carrier said in 2016 it would move all the work in an Indiana plant to Mexico — a plan infamously, if only partially, reversed by Trump as president-elect.

But General Motors said this week it would shut down five North American plants, plus three others elsewhere in the world, as it shrinks its sedan business in favor of light trucks and SUVs.

Other companies have similarly cited changing demand patterns. For example, United Technologies is currently winding down operations at its aerospace plant in Chula Vista, California that it bought in 2012, which will result in the loss of more than 300 jobs. The company says that the aircraft components that had been made there since the 1950s simply weren't selling anymore.

"We haven't found anything that's feasible in that location," says Stacey MacNeil, vice president of communications for UTC Aerospace Systems, the division that operates the plant.

The union that represents those workers says it's hard to believe that a plant that once employed more than 10,000 workers could shrink to almost nothing over the course of three decades, while Mexico's aerospace industry boomed.

"Companies do this all the time," says Owen Herrnstadt, chief of staff at the International Association of Machinists. "They outsource work, invest elsewhere, leave some work on programs that are ending—and then shut down saying the program ended, instead of investing in the US plant in the first place, which could keep US workers employed on new programs."

And as part of its effort to pull jobs back to the US through an overhaul of NAFTA, American negotiators persuaded Mexico to accept a provision that would require that at least 40% of imported vehicles to be made by workers who earn more than $16 an hour. That might ease the wage differential that makes it so appealing for automakers to move production south of the border, but would prove very difficult to enforce.

"I would think that on the Mexican side they're thinking 'this is going to be so hard to implement that we're not giving that much up,'" says Gordon Hanson, an economics professor at the University of California-San Diego.

So far, from the Mexican side of the border, it doesn't look like offshoring has slowed down. Eduardo Saavedra is vice president for business development at the Offshore Group, which provides contract manufacturing in Mexico for mostly US-based clients, and says that business has only continued to increase under the Trump administration.

"Among our clients, we haven't met with people who are concerned with the rhetoric coming from the White House," Saavedra says.

And of course, there's another factor: American companies have to react to other countries' retaliatory tariffs, too.

In a survey of 800 manufacturers conducted in mid-October by IHS Markit, respondents on average said that the new US tariffs and escalating trade war would make them slightly more likely to move production overseas over the next two years. The exceptions? Metal goods and mechanical engineering firms.

Now, there is some evidence that increased offshore activity by US multinational companies can actually raise net employment in America — but only slightly, and with lots of job disruption along the way.

That's why the labor-backed worker advocacy group Good Jobs Nation has been pushing Trump to lean on large federal contractors like United Technologies and Boeing by dinging them in the procurement process if they manufacture outside the US.

Manufacturing experts say that in many cases manufacturers go overseas simply because they can't find enough workers to fill the jobs they have. Data from the Bureau of Labor Statistics shows that there were a record high 506,000 manufacturing jobs open in the U.S. in August.

"From an employer's perspective, there is a huge shortage of labor," says Scott Jacobs, executive director of the Great Lakes Trade Adjustment Assistance Center, which assists firms that have been hurt by imports. "One of the things that would really help manufacturers is an even greater focus on trying to provide communities with assistance to really help colleges or companies themselves develop training programs."

to locate production outside the US. And although the tax cut package passed last year reduced the U.S. corporate rate significantly, it also created loopholes that reduced taxes on offshore income even more, giving companies new incentivesto locate production outside the US.

Sen. Sherrod Brown would Those tax cuts could have been conditioned on retaining jobs in the U.S., says Susan Helper, an economist at Case Western Reserve University who served as chief economist at the Commerce Department under President Barack Obama. A bill introduced by Ohio DemocraticSen. Sherrod Brown would take away the offshore tax loophole for car companies that cut jobs in the U.S. as they expand overseas.

"We just gave these companies a blank check, a corporate tax break that could have been used for all kinds of other things," Helper says. "Why are we letting them do this?"