Do immigrants take jobs from Americans and lower their wages by working for less?

The answer, according to a report published on Wednesday by the National Academies of Sciences, Engineering and Medicine, is NO, immigrants do not take American jobs — but with some caveats.

The question is at the heart of the furious debate over immigration that has divided the country and polarized the presidential race. Many American workers, struggling to recover from the recession, have said they feel squeezed out by immigrants.

Donald J. Trump, the Republican nominee, has called for a crackdown on illegal immigrants, saying they “compete directly against vulnerable American workers.” He promises to cut back legal immigration with new controls he says would “boost wages and ensure open jobs are offered to American workers first.”

Hillary Clinton, his Democratic rival, takes an upbeat view, saying immigrants contribute to the economy whether they are here legally or not, by providing labor for American employers and opening businesses that create jobs for Americans rather than taking them.

The report assembles research from 14 leading economists, demographers and other scholars, including some, like Marta Tienda of Princeton, who write favorably about the impacts of immigration and others who are skeptical of its benefits, like George J. Borjas, a Harvard economist. Here’s what the report says:

• “We found little to no negative effects on overall wages and employment of native-born workers in the longer term,” said Francine D. Blau, an economics professor at Cornell University who led the group that produced the 550-page report.

• Some immigrants who arrived in earlier generations, but were still in the same low-wage labor markets as foreigners just coming to the country, earned less and had more trouble finding jobs because of the competition with newer arrivals.

• Teenagers who did not finish high school also saw their hours of work reduced by immigrants, although not their ability to find jobs. Professor Blau said economists had found many reasons that young people who drop out of high school struggle to find work. “There is no indication immigration is the major factor,” she said.

• High-skilled immigrants, especially in technology and science, who have come in larger numbers in recent years, had a significant “positive impact” on Americans with skills, and also on working-class Americans. They spurred innovation, helping to create jobs.

“The prospects for long-run economic growth in the United States would be considerably dimmed without the contributions of high-skilled immigrants,” the report said. It did not focus on American technology workers, many of whom have been displaced from their jobs in recent years by immigrants on temporary visas.

The report asked another question Americans are debating: Do immigrants burden government budgets?

That answer is “more mixed,” Professor Blau said.

• The first generation of newcomers generally cost governments more than they contribute in taxes, with most of the costs falling on state and local governments, mainly because of the expense of educating the children of immigrant families.

For those governments, total annual costs for first-generation immigrants are about $57 billion. But by the second generation in those families, immigrants, with improved education and taxpaying ability, become a benefit to government coffers, adding about $30 billion a year. By the third generation, immigrant families contribute about $223 billion a year to government finances.

• In the last two decades, the number of immigrants in the country increased 70 percent to about 43 million people; they are now 13 percent of the population. One in every four Americans is either an immigrant or the child of one. And since 2001, about one million immigrants have come legally to the United States each year.

The report called immigration “integral to the nation’s economic growth” because immigrants bring new ideas and add to an American labor force that would be shrinking without them, helping ensure continued growth into the future.