When a Census Bureau report last week announced a record increase in the typical American household's annual income last year, the good news came with a caveat. The growth had been limited to towns and cities, the data showed, and there was no statistically detectable change in rural areas.

Some observers argued that the report demonstrated why Republican presidential nominee Donald Trump's narrative of American economic decline was succeeding in rural areas of the country. Although the country was prospering overall, the data seemed to reveal that some areas of the country were not.

"Census figures confirmed, however, that much of the economic growth in 2015 was concentrated in large cities, not the rural areas where most of Trump’s support is located," Don Lee wrote in the Los Angeles Times.

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On Monday, though, the Census Bureau announced it was removing that finding from its report. Data on rural incomes from 2014 were "not comparable" to the data from last year, according to a statement from the bureau, because of a change in the geographic definition of rural areas.

"It is, in essence, a retraction," said Arloc Sherman, a researcher at the liberal Center on Budget and Policy Priorities. He said that the census had apparently made "an honest mistake."

The flawed estimates were based on the bureau's Current Population Survey, one of several surveys conducted regularly by the bureau. The problem resulted from how, as the population grows and Americans move from one part of the country to another, the bureau must adjust the boundaries that define metropolitan areas. These adjustments, carried out every decade, altered the map for the Current Population Survey last year.

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The changes in the boundaries moved almost 6 million people into metropolitan areas. These adjustments rendered meaningless the estimated change in rural incomes from one year to the next, according to the statement.

"The U.S. Census Bureau is removing the statistical comparisons between 2014 and 2015," the statement read.

Instead, the statement directs readers to the American Community Survey — a separate survey, also conducted by the bureau, that is designed to provide accurate information about smaller geographic areas. Unlike the boundaries for the Current Population Survey, those used for the American Community Survey were not adjusted in a major way last year.

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The data from the American Community Survey shows that average household incomes in metropolitan areas increased by 3.6 percent last year. In rural areas, incomes increased 3.4 percent, according to an analysis by Sherman and a colleague.

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These figures suggest that economic progress last year was more or less evenly shared between rural and urban areas, in contrast to the results from the Current Population Survey, which suggested that these improvements were concentrated in cities.

On the other hand, these figures suggest a more modest increase in incomes overall. The Current Population Survey had indicated a 5.2 percent average increase in household incomes nationally — the greatest annual increase in five decades of data recorded by the Census Bureau — and a 7.3 percent increase in metropolitan areas. These apparently impressive gains dominated headlines last week in media coverage of the new data.

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News reports typically focus on the overall figures from the Current Population Survey, because of the two surveys, it is the one designed to provide information about national trends. The American Community Survey, by contrast, is focused on data at the local level. Both surveys, however, include national averages in household incomes, and sometimes the results can diverge.

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This past year, the less optimistic figures from the American Community Survey may be a better guide to overall economic conditions, said Gary Burtless, an economist at the Brookings Institution. As evidence, he points to a divergence between the census surveys and yet a third source of federal data on the economy: the Bureau of Economic Analysis.

This data, based largely on individual firms' tax records, is regarded as more reliable, though it only reveals broad, national trends. The data suggests less of an economic gain nationally: The gross domestic product grew by 2.4 percent last year, according to the agency. (This figure is not directly comparable to the Census Bureau's numbers, which are medians that represent the typical household's income and could be affected not only by growth in the economy but also by inequality.)

"Yes, there was a major improvement in average incomes in the United States in 2015, no doubt about it," Burtless said. Yet the rosy numbers from the Current Population Survey showed "an even bigger jump" than he believed was plausible.

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On the other hand, Burtless also argues that the Current Population Survey has been too pessimistic about income growth nationally in the recent past, and that the abrupt gains the survey reported last year might best be seen as a correction for previous errors.

The estimates from the two federal agencies have yielded similar results for decades, but they have diverged recently. Burtless argues that based on the data from the Bureau of Economic Analysis, the Census Bureau's reporting has failed to convey substantial improvements in the national economy since 2004.

The Current Population Survey may have had flaws last year, reporting too great of an increase in the country as a whole and no increase at all in rural areas. Nonetheless, taking other sources of data into account, it does look like things are getting better for ordinary American households.

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