Will cheaper health insurance really raise wages? The evidence is thin.

Economists believe something that on its face sounds absolutely bizarre to a normal human being: Obamacare's tax on expensive health insurance will give Americans a pay raise.

Here's the argument: Economic theory predicts that companies have a set amount they're willing to pay a worker, given her specific talents and skills. Under this theory, companies are agnostic to whether they spend that money on a salary, a health plan, maybe a gym subsidy, or even a free puppy. What's important is attracting the best workers, and companies will use that money however is necessary in order to get those workers and keep them happy.

"Employers are thinking, 'What wage do I have to pay to get a worker?'" says Katherine Baicker, a health economist at Harvard University. "They're indifferent if a dollar goes to health insurance or wages or nice office space."

Obamacare slaps a 40 percent tax on the most expensive health plans — this is the much-maligned Cadillac tax. The argument for the Cadillac tax is it will cut health costs: Employers will choose cheaper insurance plans to stick beneath the Cadillac tax threshold, and then they'll move the money they would have spent on insurance over to wages. The result: America's health care spending falls, and its paychecks swell. No wonder economists love it.

But why wouldn't companies just pocket the money instead? To understand the answer better, I interviewed a half-dozen labor economists who have studied this exact question — and read more than a dozen studies on the issue.

A close review of the evidence reveals something discomfiting: Economists have convincing arguments about why, in theory, the Cadillac tax should raise wages. But when it comes to actual data — real-life examples that show the wage-premium trade-off is happening — evidence is sparse. One 1999 summary of the research put it this way: "The typical estimates [of the wage-premium trade-off] are either wrong-signed, insignificant, or both."

Or, as a paper published this year stated bluntly: "Many studies fail to find any relationship."

Still, economists remain confident in the theory and chalk up the relatively weak evidence to poor data and the difficulty of designing studies that can isolate the relationship between wages and premiums. They argue that even though the data is poor, employers would have to raise wages if they cut health care spending — otherwise, their competitors would do so and steal their best talent.

"Economists have strongly held views on this because there isn't a good theory about why the trade-off wouldn't happen," says Darren Lubotsky, an economist at the University of Illinois Chicago whose research focuses on this issue. "But the hard part has been demonstrating the trade-off empirically. And it's proven hard to get consistent estimates of something close to a dollar-for-dollar trade-off."

The economic theory on this point is strong. The actual proof from the real world is sparse.

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Economists have spent more than two decades trying to tease out the relationship between wages and premiums, often with little success.

There isn't much public data available on individual workers' health premiums and wages. And even when there is, there are dozens of other factors that can influence how quickly the two grow.

To work around this, researchers study moments when health premiums changed and look at what happened to wages afterward. They've looked at everything from mandated maternity benefits to increased malpractice payouts to try to see how higher health insurance premiums affect wages. And they have found a relationship — the problem is it seems to vary by quite a lot.

Economists Alan Krueger and Jon Gruber co-authored one of the first papers to show this trade-off in 1991. They looked at what happened when states required companies to create workers' compensation programs that provide cash benefits to employees injured on the job. They found that "a substantial portion of the cost of providing workers' compensation benefits is shifted to employees in the form of lower wages."

Economists have spent decades trying to tease out the relationship between wages and health care

More recent research has also confirmed a trade-off, although it has typically shown an amount that is smaller than dollar-for-dollar. In other words: They show that a dollar increase in health benefits does not appear to depress wages by a full dollar.

One 2006 study found that a 10 percent increase in premiums correlated with a 2.3 percent reduction in wages. One 2013 paper used a national data set to estimate that each dollar increase in health insurance premiums translates into a 52-cent decrease in wages. Another study, published this year, looked at salary and insurance data from more than 600 school districts in Illinois. It showed that for each dollar increase in health premiums, teachers lost 17 cents from their take-home pay.

What's missing from the research: a study showing lower premiums increase wages

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But all this research runs in the wrong direction. The argument around the Cadillac tax isn't about whether high health premiums depress wages. It's about the opposite question: whether lowering health insurance costs will boost wages for Americans — or if companies will just pocket the difference.

And, worryingly, there are no studies that of that dynamic. Zero.

The economists I spoke with, however, were untroubled by this gap in the research. For one, it's just a harder situation to study: Health insurance premiums pretty much always go up. Insurance regulators never bar companies from covering certain treatments that would drive down insurance costs.

There is some data showing that in the 1990s, wages grew faster as health premiums grew slower. But economists like Gruber — who does believe the wage-premium trade-off works both way — readily admit that's not robust enough evidence to make the case.

"We have suggestive evidence that it's true, and if you draw a graph, there's a negative correspondence, particularly in the mid-1990s," says Gruber. "But at the same time, it's way too broad to draw any conclusions."

But Gruber and the other economists I spoke with didn't find this absence especially troubling. They argue that if the wage-premium relationship works in one direction, there's no good reason to expect it not to exist in the reverse.

"There's no economic reason to think it wouldn't be symmetric," says Gruber. "If it's really true that firms could just say, 'I'm going to keep it,' then why aren't they already paying lower wages?"

Harvard's Baicker suggests imagining an extreme example, where a company cuts their health plan entirely and doesn't do anything to compensate with a raise for workers. In that situation, its easy to understand why workers would start looking for a job elsewhere.

"If an employer could have gotten away without paying as much compensation as they already do, they would be doing that already," she says.

The government would still take a cut of any wage bump

Even if economic theory plays out as predicted — and all premium dollars cut get transferred over to wages — workers still would lose money.

That's because right now, employers don't get taxed for the money they put into insurance plans. But they do get taxed for the money they spend on wages. So a dollar spent on health insurance buys more than a dollar spent on wages.

Workers would be getting post-tax dollars as their new replacement wages. For some people this is still valuable. If you're a young worker who uses little health care, for example, you might be totally fine with receiving 60 to 70 cents of your health insurance dollar as cash compensation.

But if you're an older worker with more complex health conditions to manage, this is a lousy deal. All of a sudden, the exact same amount of money from your employer can't buy the same amount of medical care that it used to.

There are other ways Americans could lose, too

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The theory outlined above assumes a competitive labor market — one in which workers really could go take a job elsewhere if their benefits got slashed without a compensating pay raise.

And there are places and people in the economy for whom this is probably real life; they're in-demand talent who have their pick of jobs. Their companies have to fight to keep them employed.

But then there are other workers who might not have their pick of jobs. Their choices might be between employment and unemployment. And in those markets, it does seem plausible that companies could use a health benefit cut as a moment to reevaluate wages. The Cadillac tax could force management to think about whether they really do need to plow that money back into wages, or if they might be able to get by spending less.

"When the economy is pretty slack, anything that pushes down benefit contributions could take a very long time to show as wages," says Josh Bivens of the Economic Policy Institute. "That failure to differentiate when the labor market is slack versus competitive is probably one reason why empirical studies are less robust than you think."

Even if the Cadillac tax does cause a pay increase, it probably won't feel like a raise at all

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Most of us know what happens when we get a raise: There's an immediate bump to our salary. It's obvious that we're getting paid more than we used to.

If economists are right, any pay increases from the Cadillac tax probably won't work like that. Wage increases generally take a few years to cycle into the economy, as workers switch jobs and new graduates come into the workforce. It is unlikely to resemble a lump-sum increase to a given worker's wages, the type of salary increase that we're typically use to.

Not everyone will feel the wage bump equally, either. Workers tend to place different values on their health insurance policy. Namely, people who use their health insurance may get more value from it than the dollar amount they actually pay for the policy. They might use tens of thousands of dollars' worth of health care while paying a fraction of that in premiums.

"As a profession, I think economists believe the wage increases filter through the economy, but for any one individual employee it might not feel like that," Baicker says.

To that person, even if she did get the full value of her health plan returned as higher wages, it would still feel like a crummy deal. Before, she would have been able to buy an unlimited amount of health care with a $10,000 or so plan. In the extreme example where that plan disappears entirely — or a less extreme example, where the deductible inches upward — she'd be able to purchase less with the exact same dollars.

"There will be a transition period, and that will surely create winners and losers," Baicker says. "Who ends up happy will not be straightforward."