The U.S. Supreme Court will hear oral arguments on Monday in a case that’s being billed as a potentially devastating blow to organized labor in the U.S. In Janus v. American Federation of State, County and Municipal Employees, Council 31, the justices will decide whether laws in 22 states and the District of Columbia that allow public-sector unions to charge nonmembers fees for collective-bargaining activities violate the employees’ free-speech rights.

Supporters of the fees — including many Democrats, who receive funding from the labor movement — warn that such a decision could decimate unions’ economic power and hurt workers as a result, while anti-union forces on the right say that these fears are overblown. But we don’t really know what would happen in the long term if those fees were struck down, because the research doesn’t paint a clear picture either way.

Economic theory does suggest an answer. For many economists, these fees — known as “agency” fees or “fair share” fees — are a necessary solution to a classic economic dilemma known as “free ridership.” The thinking goes that because unions are required to advocate on behalf of all workers, not just their members, there’s no reason for individual workers to pay for a benefit they could get for free. And if enough workers stopped paying dues, according to this reasoning, the unions would shrink, causing problems for the workers they support. But we can’t always tell if the theory matches up with what happens in the real world. In the case of union fees, that’s largely because there’s no straightforward method that will allow the direct effects of the change to be observed.

Unionization rates are generally lower across the board in states that have scrapped contribution requirements for public- and private-sector unions, known as “right-to-work” states. But critics of the fees say that doesn’t mean that ending the mandatory fees is directly responsible for the decline of unions — or that some loss of union membership can justify restrictions on workers’ free-speech rights. They argue that public-sector unions will survive in the absence of mandatory payments since they still exist in right-to-work states and that the unions can retain a significant percentage of the workforce as members even without requiring all workers to pay fees.

The issue of free ridership was also at play 40 years ago, when the Supreme Court ruled in Abood v. Detroit Board of Education that the fees were constitutional for public-sector unions. Although it wasn’t the central issue in that case, the court said the fees “counteract” free riding. Today’s justices are divided on how heavily to weigh this concern: In previous cases involving public-sector dues, Justice Samuel Alito, a conservative, wrote that free-rider arguments are “generally insufficient to overcome First Amendment objections,” while Justice Elena Kagan, a liberal, argued that “endemic free-riding” continues to provide justification for requiring payments from non-members.

In this case, the justices are being asked to overturn the precedent set in Abood, and it seems likely that they will. Critics of the unions say the problem isn’t free riders — it’s “forced riders” like plaintiff Mark Janus.

“Are you really receiving a benefit when you’re being required to pay to support a view that you disagree with?” said Robert Alt, president of the Buckeye Institute, a right-leaning think tank in Ohio. He argued that even though unions may see an initial loss in revenue, they can attract membership and stay influential in ways that don’t involve a forced payment.

But Richard Freeman, an economist at Harvard University, said that if Janus prevails, he expects significant numbers of public-sector employees to “bail out” over time and leave the unions with less revenue and workers with less support. “The unions might not disappear, but their power will be really diminished,” he said. That’s worrying, he said, because without strong unions, workers could see a decline in benefits and wages.

It’s difficult to figure out which workers are forced riders and which are free riders — and it’s also challenging to determine what the impact of removing agency fees would actually be. To make their arguments, both sides in the case being heard Monday are drawing on a natural experiment that has been going on in the states for years — by comparing right-to-work and non-right-to-work states and by examining the results of states changing their policies on union fees. As with many natural experiments, though, disentangling the effects of a single policy difference from the myriad forces affecting something like wage growth can be nearly impossible.

Since 2012, six states have enacted “right-to-work” legislation that prohibits employment contracts from requiring union dues as a condition of employment. Twenty-two additional states have similar but less recent laws, while 22 states do not have right-to-work laws.

Individual studies have produced what seem like decisive answers to the question of what happens when the agency-fee requirement is removed — but taken together, they don’t present a coherent narrative. Part of the problem is that when economists design studies to address this question, controlling for all the right factors is difficult. Right-to-work policies, for starters, exist alongside other pro-business policies, and disentangling whether a loss in, say, manufacturing jobs is related to the decline of the unions or something like competition from abroad is tricky.

A 2011 study from the left-leaning Economic Policy Institute examined differences between right-to-work states and states without right-to-work policies, controlling for the demographic and job characteristics of workers, as well as state-level economic conditions and differences in the cost of living. That study found that wages in right-to-work states are 3.2 percent lower than wages in non-right-to-work states. A 2007 study by a professor at Hofstra University found, similarly, that employment and wages were lower in right-to-work states.

But another study, which controlled for economic conditions at the time the states adopted right-to-work, found that right-to-work laws were associated with higher wages in most cases. And other research has found that employment may be higher in right-to-work states, at least in some sectors. There may also be some variation by industry and worker demographics: For example, an examination of right-to-work laws in the Midwest found that they decreased wages for workers with two- or four-year college degrees, but had little to no impact for workers with graduate degrees or only high school degrees.

A review of the empirical evidence surrounding right-to-work laws conducted by the Congressional Research Service in 2014 concluded that “even the most sophisticated studies are unable to fully isolate the effects” of different agency-fee policies.

There is a general consensus among experts and advocates — including some opponents of the required payments — that if agency fees are struck down, public-sector unions will probably lose members and face diminished revenues in the short term. But some economists believe unions may be able to adapt and innovate in response, from changing how they negotiate agreements to the broader employment services they provide.

“It seems like the unions might have to morph into a new kind of organization,” Freeman said. “There’s no doubt they’ll be weakened in the short term. The question is whether they’ll be able to come back from that and continue offering substantial benefits to workers.”