President Trump's trade war with China won't bring back the jobs lost from the trade deficit with China, according to Robert Scott, a senior economist at the left-leaning Economic Policy Institute, whose work Trump cited on the campaign trail and during his presidency.

Why it matters: Here's an example of the trade debate's complexity. Some economists who agree with Trump that unfair trade has hurt U.S. workers don't think his tariff response will reverse the damage.

U.S. jobs have been impacted, Scott says in a new report, because "imports from China have soared while exports to China have increased much less.” In some regions of the U.S., the manufacturing sector is not growing as much as it could “if new factories were opening and existing plants were hiring more workers,” thanks to more production of goods in China, not the U.S.

• China has to stop weakening the yuan, which makes Chinese exports less expensive for U.S. consumers, Scott told Axios. (In a recent report, the Treasury Department did not call out China as a currency manipulator, despite Trump's repeated accusations.)

Trump campaigned on the promise to bring manufacturing jobs back. Considering jobs in this sector have been on the upswing, he may claim some success. But Scott told Axios that tariffs, which could potentially raise costs for factories, won't be the reason for total revival of the industry.

The other side: Mark Perry, a scholar at conservative think tank American Enterprise Institute, says factory jobs have been declining since the 1940s, way before China entered the WTO, and technology is to blame, not trade.

• "Those factory jobs ain’t ever comin’ back, no matter what Trump does," Perry said.

Go deeper:

• Inside Trump's China bet
• The forever trade war