But in some expensive sections of the country, many families with income levels near the $250,000 cutoff insist that they have more in common with middle-class Americans than millionaires or billionaires.

“You take a couple in Westchester County, a police officer with a lot of overtime and a principal at a public school,” said Vincent R. Cervone, a certified public accountant in New York City. “They’re grateful to be working. They aren’t in danger of eviction or starving. But the cost of the average house is $500,000  five times the national average. Taxes are higher than the rest of the country. If they have a couple of children in college, can you call them rich? Not by any common-sense standard.”

The dispute over what income level qualifies as rich is caused, in part, by the tendency of people to gauge their own wealth by comparing themselves to those closest to them. A study released this month by two Princeton University professors found that in most of the country, people feel comfortably middle class if they earn $70,000. But in New York City, the figure was $165,000. The median income in New York City is $55,980, according to the Census Bureau.

J. Bradford DeLong, an economics professor at the University of California, Berkeley, said many of the top earners in the United States did not consider themselves rich because they compared themselves to the statistically small segment of the people who earned more than them, rather than the much larger segment who made less.

“It is pathetic and embarrassing that somebody with five times the median household income, someone in the top 2 or 3 percent of the population, thinks of himself as just another ‘average Joe,’ ” said Professor DeLong, who was a deputy assistant secretary of the Treasury Department in the Clinton administration. “Why don’t you ask someone who makes $40,000 or $50,000 a year if they have a lot in common with a family making $250,000?”

The fact that families making $250,000 are sometimes being invoked in the same terms as billionaires is a symptom of one of the paradoxes of the American tax system: at the same time that wealth has become far more concentrated in recent decades, the tax code has become far less precise in differentiating levels of affluence.