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.