More: There is the case of Greece, where the government faked deficit numbers for years, contributing to a debilitating debt crisis that required multiple rounds of bailouts. The country then criminally prosecuted the head of the statistical agency when he insisted on reporting the true figures, further eroding the country's international standing.

There is the case of China, where earlier this century the local authorities manipulated data to hit growth targets mandated by Beijing, forcing analysts and policymakers to turn to alternative measures to gauge the state of the country's economy.

Perhaps most famously, there is the case of Argentina, which in the 2000s and 2010s systematically understated inflation figures to such a degree that the international community eventually stopped relying on the government's data. That loss of faith drove up the country's borrowing costs, worsening a debt crisis that ultimately led to it defaulting on its international obligations.

It is too soon to know whether the United States is on a similar path. But economists and other experts said that Mr. Trump's decision on Friday to fire Erika McEntarfer, the Senate-confirmed head of the Bureau of Labor Statistics, was a troubling step in that direction.

Janet L. Yellen, the former Treasury secretary and chair of the Federal Reserve, said the firing was not what is expected from the most advanced economy in the world.

"This is the kind of thing you would only expect to see in a banana republic," Ms. Yellen said.