In a Democratic debate in September, Mr. Sanders differed with Joe Biden in saying wages would rise if employers were no longer involved with health benefits. Many Americans are skeptical; in a Kaiser Family Foundation poll, 63 percent said their wages would stay the same if their employers’ health costs fell.

Some studies in economics support the theory that employers trade off health insurance premiums for wages almost dollar for dollar. A study in the Southern Economics Journal examined salary and benefits data from the New York Department of Education in the 1970s. Controlling for confounding factors like teaching experience, education, school budget and other benefits, the study found that a dollar increase in the value of health benefits was associated with an 83-cent reduction in salary on average.

But other studies of public-sector employees find little to no evidence of a comparable trade-off between wages and health insurance premiums. One, in the Journal of Health Economics and based on data from over 6,000 school districts, found that a dollar increase in benefits was associated with a reduction in wages and salaries of only 15 cents.

Another from the same journal, in which the Harvard health economist Michael Chernew is a co-author, used national surveys of public-sector workers and employers’ data and produced similar findings.

Why might premium and wage changes not perfectly offset each other in public-sector jobs? One possibility is unionization, which is more likely in the public than in the private sector. Unionized workers are better able to bargain for higher compensation than individual workers, who are more easily let go and replaced with others. Negotiated contracts could end up with health insurance benefits increasing without offsetting reductions in salary.

“One reason unionized public-sector workers may be unwilling to fully pay for premium increases with reduced wages is that the higher premiums reflect things they do not fully value,” Mr. Chernew said. “For example, workers may not be willing to sacrifice already low wages for higher health care prices that don’t reflect better health care.”

So much for the public sector; what about the private one? Here, many studies suggest closer to a one-to-one trade-off between workplace health insurance premiums and wages. Some of these studies focus on specific benefits, like maternity care, or on different populations, like those with obesity, finding that their higher costs to employers are offset by lower wages.