Staffing shortfalls have forced the BLS to stop collecting prices in Lincoln, Neb.; Provo, Utah; and Buffalo, N.Y. In the rest of the country, the bureau is also missing an average of about 15% of the price data it usually collects, it said last week.

Markets appear unfazed by Trump's shocking move to fire the BLS chief. Stronger rate-cut odds and solid earnings are helping investors look past the news.

The Bureau of Labor Statistics uses surveys to collect economic data including employment counts, wages and inflation.