A total of 38 million households, including 25.5 million that are middle-class, live paycheck to paycheck, meaning they have no cash savings, according to a new study by three academic economists.That amounts to about one-third of total households, CBS Marketwatch reports. Among the middle class households, many own homes and have retirement accounts, but they have no savings that they can tap immediately, according to the study by Greg Kaplan of Princeton University, Giovanni Violante of New York University and Justin Weidner of Princeton University and presented by the Brookings Institution.The middle-class households have a median income of $41,000. "We don't expect them to be living paycheck to paycheck," Kaplan told CNNMoney. Families with income of $51,000 and higher aren't living paycheck to paycheck, the study finds.So why do those in the middle class who are living paycheck to paycheck put their savings in homes and retirement accounts rather than in more liquid assets, such as stock and bonds?It might be that they expect bigger returns on their homes and retirement investments, Kaplan said.Joseph Cohen, a sociologist at Queens College in New York City, has an interesting take on middle-class spending. “America is a place where luxuries are cheap and necessities costly," he told The Washington Post. "A big-screen TV costs much less than it does in Europe, but healthcare will sink you. . . . A medical event, an auto repair or a temporary job loss can exert a large shock."