In the spring and summer of 1980, some 125,000 Cuban refugees sailed from the port town of Mariel on fishing boats and pleasure craft toward the U.S., many destined to settle in Miami.

Nearly four decades later, that exodus is at the center of an unresolved, sometimes bitter argument among economists, hinging on a basic question: When foreigners come to the U.S., does their presence drive down the wages of native workers? The long-running dispute has gained new relevance as the Trump administration tries to implement and enforce...