One of the reasons lower-income workers have taken such a hit over the past few decades is because of illegal immigration. But how much of a hit is a matter of great debate among economists.

Harvard immigration specialist George Borjas finds that during the 1980s and 1990s, low-skilled immigration reduced the wages of U.S. born high-school dropouts by about 10%.

His Harvard colleague and sometimes academic collaborator, Lawrence Katz, is more sanguine about the impact.

Increased immigration has been “at most a small contributor to rising inequality among pre-existing U.S. residents and to poor income growth for low and moderate-income people,” said Mr. Katz, a labor economist. Technological change, educational deficiencies, global trade and the decline of unions had a greater effect, he said.

The debate over the economic effect of immigration comes down to whether migrants—illegal or not—“substitute” for workers or “complement” them. If a Mexican construction worker competes for a job that a U.S. worker could reasonably do, that substitution essentially increases the supply of workers. That can drive up unemployment and drive down wages for natives. On the other hand, cheaper construction workers complement higher-paid managers by lowering company costs. That makes the firm better able to win new bids and, in theory, hire more workers, immigrants and natives alike.

Mr. Borjas, the Harvard economist, has been among the most prolific academics arguing that the substitution effect handicaps U.S. workers, especially those without a high school diploma, because illegal immigrants tend to be less educated. In a 2015 paper, examining the effects of a big surge in Cuban low-skilled immigration to Miami in 1980—the so-called Mariel boatlift—he found that wages of Miami high school dropouts fell sharply, as did the wages of those dropouts compared with high-school graduates.

But University of California, Berkeley, economist David Card earlier examined the Marielitos, as they were called, and didn’t find any significant drop in native wages.

Mr. Borjas says Mr. Card didn’t dig deep enough into the data to isolate the effects on high school dropouts, a charge Mr. Card rejects. “The sample I analyzed was reasonable and representative,” he said, in a debate that continues.

Some economists focus on immigrants not simply as competitors for native workers, but as generators of economic activity who start companies, and buy goods and services. If the number of low-skilled Mexican immigrants were to drop by half because of tougher border enforcement, the unemployment rate among unskilled natives would increase, calculate economists Giovanni Peri of the University of California, Davis, and Andri Chassamboulli of the University of Cyprus, because the U.S. economy would take an overall hit. The wages of native unskilled workers, however, would rise because of reduced competition.

Many of the studies on the effects of immigration were completed when illegal immigration was steadily increasing, and economists were trying to assess the effect of greater competition on low-end jobs. Illegal immigration reached its peak of 12.2 million in 2007 and fell by one million immigrants in 2012, according to the Pew Research Center in Washington, D.C.

That should change the economic effects of immigration because fewer immigrants should give natives more running room. But the example of Arizona, where the number of undocumented immigrants has fallen 40% since 2007—the subject of a front-page story in The Wall Street Journal—shows that isn’t always the case. While wages have risen in some immigrant-heavy industries such as construction, landscaping and farm work, there’s scant evidence that employment has increased for natives.

A study by Moody’s Analytics for The Wall Street Journal of the effects of the exodus in Arizona finds that natives and legal Hispanic immigrants have gotten less than 10% of the jobs vacated by immigrants, in part because the recession reduced job prospects for all workers. Looking strictly at the years 2008 to 2009, the years of steepest decline in unauthorized immigration, economists Sarah Bohn, Magnus Lofstrom of the Public Policy Institute of California and Steven Raphael of the University of California, Berkeley, find that employment among low-skilled natives and legal immigrants dropped.

Mark Zandi, Moody’s chief economist, called the lessons of Arizona “sobering.” Not only are the lives of undocumented immigrants turned upside down, he said, the exodus “reduces employment and output more broadly, as business activity is disrupted and lost spending by the undocumented hurts businesses that sell everything from groceries and homes to them.”

Related reading:

The Thorny Economics of Illegal Immigration

Which Party Really Benefits From More Immigrants?

New Evidence on Immigrants and Jobs

U.S. Begins Immigration Crackdown on Central Americans

Mexican Immigration to U.S. Reverses

How an Immigration Downturn Has Contributed to the Construction-Worker Shortage

China Passes Mexico as the Top Source of New U.S. Immigrants