U.S. employment figures contain a mystery that has left many economists scratching their heads: How is the country generating so many jobs even while the unemployment rate has drifted up?

The emerging consensus: a surge in immigration. It not only explains inconsistencies in the jobs data but suggests the economy can keep adding plenty of jobs without overheating. That in turn would let the Federal Reserve still consider interest-rate cuts.

The Labor Department’s Bureau of Labor Statistics bases its monthly employment figures on two surveys. One survey of about 119,000 businesses and government agencies, called the establishment survey, is the main source for determining how many jobs the U.S. added each month. The other, a rotating survey of about 60,000 households, is used to calculate the unemployment rate and includes a separate employment estimate.

Data in the two surveys never precisely match, even after accounting for differences in the types of employment they cover—the establishment survey doesn’t include farmworkers, for example. But recently, the differences between the two have become extreme.