“That’s definitely a conservative estimate,” Mr. Florence said. “It’s very hard to measure how it affects employers, but if we could, it would be in addition to what we see here.”

The effect is seen not just in the applicants eliminated based on drug screening, but in those deterred from even applying. In congressional testimony this month, the Federal Reserve chairwoman, Janet L. Yellen, linked increased opioid abuse to declining participation in the labor force among prime-age workers.

The Fed’s regular Beige Book surveys of economic activity across the country in April, May and July all noted the inability of employers to find workers able to pass drug screenings.

“It’s not just a matter of labor participation; there is also a lot of collateral economic damage,” said Alan B. Krueger, a Princeton economist who wrote a widely discussed paper on the subject last year.

Were it not for the drug issue, said Mr. Krueger, who served as chairman of the Council of Economic Advisers under President Barack Obama, workers trapped in low-wage jobs might be able to secure better-paying, skilled blue-collar positions and a toehold in the middle class.

“This hasn’t gotten as much attention as the participation issue, but we could potentially match perhaps 10 percent of the population in better jobs,” he said. “That could have a positive, cascading effect on wages.”

Plants like Mr. Sherwin’s can help provide that ladder. But workplace considerations — not social conservatism or imposition of traditional mores — make employee drug use an issue.