President Trump boasts that his “America First” trade and economic policies are bringing well-paid manufacturing jobs back to America. That’s probably his biggest “deliverable” to Trump voters. But is this claim true?

Trump won the presidency partly because he voiced the anger of American workers about lost jobs and stagnant wages. But in the process, he fundamentally misled the country by claiming that trade is the major cause of job losses, and that renegotiating trade agreements would save the middle class.

What Trump is offering is a palliative that has raised false hopes. He implies that a few good trade deals will refurbish the Rust Belt and restore the good old days of manufacturing. It won’t happen, and to pretend otherwise is a hoax.

Trump campaigned on a false argument that global trade was taking away American jobs. So he killed the Trans-Pacific Partnership his first week in office and is now demanding changes in NAFTA and other trade agreements. He has dressed up a few announcements from jittery U.S. corporations to argue that doomed manufacturing plants are being saved and that jobs are “already starting to pour back.”

Stephen K. Bannon, Trump’s chief strategist, has inflated this economic nationalism into a full-blown ideology that posits a battle between workers who are being hurt by globalization and an elite that benefits. Referencing the TPP at last week’s Conservative Political Action Conference, Bannon said that Trump “got us out of a trade deal and let our sovereignty come back to ourselves.”

But the numbers show that Trump and Bannon are fighting the wrong battle. Manufacturing employment has indeed declined in America over the past decade, but the major reason is automation, not trade. Robots, not foreign workers, are taking most of the disappearing American jobs. Rather than helping displaced blue-collar workers, Trump’s promises of restoring lost jobs could leave them unprepared for the much bigger wave of automation and job loss that’s ahead.

The most persuasive numbers were gathered in 2015 by Michael J. Hicks and Srikant Devaraj at Ball State University. They showed that manufacturing has actually experienced something of a revival in the United States. Despite the Great Recession, manufacturing grew by 17.6 percent, or about 2.2 percent a year, from 2006 to 2013. That was only slightly slower than the overall economy.

But even as manufacturing output was growing, jobs were shrinking. The decade from 2000 to 2010 saw “the largest decline in manufacturing employment in U.S. history,” the Ball State economists concluded. What killed those jobs? For the most part, it wasn’t trade, but productivity gains from automation. Over the decade, the report notes, productivity gains accounted for 87.8 percent of lost manufacturing jobs, while trade was responsible for just 13.4 percent.

Robotics allows manufacturers to create more output with fewer people. That’s not a conspiracy imposed by Bannon’s global elite. It’s simply a fact of economic life and progress. And it’s not just blue-collar workers who are suffering. Smarter machines kill jobs in finance, law and, yes, even journalism.

To see how Trump is mislabeling the causes of workers’ anger, take a look at job losses in various industries. In motor-vehicle manufacturing, 85.5 percent of job losses came from productivity gains; in steel and other primary metals, 76.7 percent; in paper products, 93.2 percent; in textiles, 97.6 percent.

Trump proposes that we “buy American.” But in a world of globalized supply chains, what is an American car? Does a Toyota Camry made in Kentucky count? Is a Ford F-150 assembled in Kansas City American even if some of its parts were made in Mexico? The interdependence of global manufacturing is part of why Ford and Toyota stay healthy and profitable, for workers and shareholders both. How does Trump propose to unthread this subtly woven quilt?

Trump wants to deliver on his campaign promises. Good for him. But by misidentifying the source of the Rust Belt’s woes, he is doing his supporters a double disservice. He’s giving them false hope that jobs replaced by machines will be reclaimed by people. Alas, economic history doesn’t move in reverse. Perhaps worse, Trump is giving people reasons to avoid the job retraining that would prepare them for the next tsunami of automation, which consultants predict could destroy more than half of all current jobs.

What will Trump say then to the workers in Michigan, Ohio and West Virginia who believed in him — who thought the old jobs were coming back — and are savaged in the next round of job losses?

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