For five years, the United States economy has been expanding at a steady clip, the stock market soaring, the headlines filled with talk of recovery. Yet public opinion polling shows most Americans still think the economy is pretty miserable.

What might account for the paradox? New data from a research firm offers a simple, frustrating answer: Middle-class American families’ income is lower now, when adjusted for inflation, than when the recovery began half a decade ago.

Sentier Research, a firm led by former census officials, used census data to tabulate an estimate of the median household income — how much is earned by families at the exact middle of the nation’s income distribution. In June 2014, it found in a report issued Wednesday, the median household income was $53,891, down from $55,589 in inflation-adjusted dollars when the economic expansion began in June 2009.

The economic paradox isn’t much of a paradox at all in this light: The purchasing power of the typical American family is 3.1 percent lower now than it was five years ago. No wonder people are unhappy about the economy! The benefits of rising levels of economic activity have simply not accrued to middle-income wage earners.

Other measures of Americans’ income that rely on averages paint a sunnier picture. For example, inflation-adjusted per-person disposable personal income is up 4.2 percent from mid-2009 to mid-2014. But averages like that can be distorted by strong income gains among the wealthiest, so looking at the median income can give a better sense of economic conditions faced by the majority of Americans. And by that measure, the gloomy news actually goes back even beyond the disappointing recovery of the last five years.

Sentier’s estimates of median household income, which are broadly consistent with the Census Bureau’s annual estimates, remain lower than they were in January 2000, when the data series began. The middle-income American family is worse off, in other words, than it was 14 years ago.

One more negative twist: The researchers broke down the shift in median income by type of family. And the steepest declines, with median income off 10.4 percent in the last five years, is in families with three or more children. It is large families that are seeing incomes fall off most sharply.

But there is some good news, too. If you look not at the entire five years of the current expansion, but only the last three, there has been improvement. June 2014 household incomes were up 3.8 percent in inflation-adjusted terms from June 2011.

“The recovery has been very slow,” said Gordon W. Green, an author of the report and a former census official. “Income didn’t start to turn around until the summer of 2011. The problem is that income dropped so sharply during the first two years that even though we started to rebound in the summer of 2011, by the time we get to the present, we’re still not where we were when the recovery started. But it is encouraging that income has turned around.”

The Census Bureau’s data on median income is more reliable than Sentier’s estimates, but it comes out once a year and with long delays (the 2013 number isn’t due until next month). The researchers behind the new numbers crunch data in the bureau’s Current Population Survey to arrive at an estimate of median income that is available monthly and with a much shorter delay.

So for a sense of when incomes are starting to accelerate for ordinary Americans — and thus when the official recovery feels like a broadly shared recovery — keep an eye on their data.

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