After Arizona passed a series of tough anti-immigration laws, Rob Knorr couldn’t find enough Mexican field hands to pick his jalapeño peppers. He sharply reduced his acreage and invested $2 million developing a machine to remove pepper stems. His goal was to cut the number of laborers he needed by 90% and to hire higher-paid U.S. machinists instead.

“We used to have many migrant families. They aren’t coming back,” says Mr. Knorr, who owns RK Farms LLC, an hour’s drive from Phoenix.

Few issues in the presidential campaign are more explosive than whether and how much to crack down on illegal immigration, which some Republican candidates in particular blame for America’s economic woes. Arizona is a test case of what happens to an economy when such migrants leave, and it illustrates the economic tensions fueling the immigration debate.

Immigrants Push Down Wages for Low-Income Workers—But How Much?
Economists of opposing political views agree the state’s economy took a hit when large numbers of illegal immigrants left for Mexico and other border states, following a broad crackdown. But they also say the reduced competition for low-skilled jobs was a boon for some native-born construction and agricultural workers who got jobs or raises, and that the departures also saved the state money on education and health care. Whether those gains are worth the economic pain is the crux of the debate.

Gordon Hanson, a University of California at San Diego economist who has studied the issue for the nonpartisan Council on Foreign Relations, has detailed how large-scale immigration undermines wages for low-skilled workers. In Arizona’s case, he thinks the state is paying an economic price for its decision. “As the U.S. economy continues to recover, the Arizona economy will be weighed down by slower growth and by less export production in traditional industries” such as