The nation's unemployment rate is at a 49-year low and wages are finally rising after years of stagnation. But President Trump is handling the tight labor market by restricting immigration laws, not loosening them as previous administrations have done.

He's effectively conducting an economic experiment: Will the problem of a tight labor market solve itself by forcing wages higher or will the lack of new workers hobble that growth?

The unemployment rate in May fell to 3.8 percent, the lowest it has been since 1969. Average hourly wages have risen by 2.7 percent, or 71 cents over the past year. In June, Costco reported that it would set its minimum opening wage at $14 an hour, a $1 boost for an entry-level position.

Employers are literally starved for workers, says William Dunkelberg, chief economist for the National Federation of Independent Business, the main trade group for small business. “We’re doing things like being less strict on drug testing and investing even more in training to make unqualified people a little less unqualified,” Dunkelberg told the Washington Examiner.

The labor shortage is creating problems because without workers, work isn’t getting done. “The biggest complaint and largest shortage we have now among our members is in construction. It's pretty clear we would be building houses a lot faster and prices wouldn't be rising so fast if we could hire more workers … You can get all of the supplies you need. You just cannot get the people to paste them together.”

The solution to tight labor markets in the past has been to import more workers by easing up on immigration rules. The Trump administration has a different view, though. It doesn't view a tight labor market as a problem. It views it as a solution to the problem of stagnant wages because it forces employers to pay more to attract workers. Bringing in more immigrants just eases pressure on employers to do that.

“There are a lot of Americans out there who would love to work if the price is right and the job is right,” White House economic adviser Larry Kudlow told CNBC after the Department of Labor released the jobs report on June 1.

“President Trump recognizes that low-skilled immigration harms our economy and above all, it harms American workers,” the White House said this year.

To that end, the administration has stepped up border arrests and has attempted to crack down on "sanctuary cities" that don't alert federal authorities to illegal immigrants.

It is tightening legal immigration, too, moving to put the H-1B high-tech visa program for foreign workers under stricter requirements and oversight and limiting the ability of visa holders' spouses to work. It also put the H-2B visa program for temporary, non-agricultural workers under a lottery system for the first time. But after complaints from industries that rely on those workers and were shut out, the administration opened an extra 15,000 visas so they can fill empty jobs.

The administration’s immigration policies are not the reason for the tight labor market, though. The number of immigrants coming to the U.S. hasn't declined much since Trump took office, despite all of the hand-wringing about the issue, argues Steven Camarota, director of research for the Center for Immigration Studies, which favors restrictive policies.

The number of foreign-born people in the work force is 25.8 million, according to Census data, up 1.3 million from two years ago, Camarota notes. The number of native-born people in the workforce is 69.4 million, up 1.2 million over the same two-year period, indicating that the tight labor market is gobbling up every worker it can find. So the non-native workforce grew by about 5 percent, while the native-born one grew by a little less than 2 percent.

At the same time, the labor participation rate for native-born workers is 70 percent, still below its pre-2007 recession level of just under 74 percent. “The bottom line is that something very odd is going on in the U.S. labor market and I don’t think it is fair to say that there just aren’t any workers available. It is very hard to account for what is happening … It may be that there just hasn’t been enough wage increases to draw workers in,” Camarota said.

Ali Noorani, executive director of the National Immigration Forum, which favors open policies, argues the tightness of the labor market is being caused by economic growth outpacing the growth of the workforce, noting that baby boomers are now retiring. "It is the diminishing size of the workforce that explains the tight labor market," he said.

Dunkelberg offers a different theory: The remaining idle workers are the most difficult cases. Employers complain that the workers have poor social skills, bad work histories or unrealistic salary demands.

Other economists say Trump's policies are having an effect. Immigration normally would be increasing under the current conditions, says Madeline Zavodny, economics professor at the University of North Florida in Jacksonville. Immigrants historically have flocked to the U.S. when unemployment rates are low.

“It appears unauthorized immigration hasn’t resumed its pre-recession levels, probably because of tougher border and interior enforcement combined with a stronger Mexican economy and changing demographics there,” Zavodny said.

The question is where the economy goes from here. There isn’t much precedent for a situation where the market is this tight and additional workers are not coming in. Federal Reserve Bank of Dallas President Robert Kaplan has warned that limiting "sensible immigration" would slow economic growth.

“We need to come to grips with immigration reform in order to supplement labor force growth in the U.S.,” he said in April.

“If we want to maintain this growth, much less increase it, we are going to have to figure out a way to grow our workforce. Unfortunately, this administration would rather see our workforce continue to shrink," Noorani said.

It's not as though immigrants don't have other options, Noorani adds. They can immigrate to other countries such as Canada or Europe, or not even move. Many Mexicans are staying in their home country now that its economy is improving.

But allowing more immigrants won’t necessarily solve the jobs problem, Dunkelberg said, since the need for workers is just that big. But it will help. “It’s not clear that opening the border would get you the labor that you need. … but certainly the labor supply is an issue and immigration is a part of that.”