“They rely more heavily on Residency 1 Year Ago,” Mr. Salvo said in an interview, referring to a data point that indicates how many people are moving, and where.

The way the bureau relies on this information, Mr. Salvo said, “hits the city very hard,” because it “lowered the number of international migrants coming to New York City,” which in turn affects how the federal government directs its resources.

Of the 8.4 million population estimate for New York City, Mr. Salvo said, “we think the number is a bit low.” He said the figure was probably closer to 8.5 million people.

Mr. Salvo also cautioned against doing year-to-year comparisons of the bureau’s estimated figures because, he said somewhat diplomatically, “the methods do not justify what we associate with precision.”

Nicole Gelinas, a financial analyst with the Manhattan Institute, took the Census Bureau’s figure with some hesitancy, but said overcrowding and “infrastructure capacity” could lower the quality of life for people here. And that, over time, could propel some of them to move.

Andrew A. Beveridge, a sociology professor at Queens College, questioned the bureau’s methodology but said of the city’s population size, “I think there is probably some truth to it.” The reason? “The rents are off the charts.”