As the U.S. economy continues to rebound from the worst slowdown since the Great Depression, one downside is how rising rents are putting the squeeze on consumers, with Millennials especially hard hit.

Economists surveyed by Zillow expect rents to continue climbing for at least the next two years. Zumper, another rental listings site, sees rent increases outpacing inflation as developers of multifamily housing developments ratcheted up their activity in June to the highest level since 1988.

"Real estate development should catch up to demand 2-3 years from now given the cyclical nature of the market," wrote Devin O'Brien, Zumper's head of strategic marketing, in an email to CBS MoneyWatch. He added that the market overall is becoming "much more landlord-focused" overall.

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The timing couldn't be worse for Millennials, workers roughly aged 22 to 34. As Zillow noted, they pay on average 30 percent of their income for rent, up from 23 percent for similarly aged Americans in 1979.

Finding properties, though, that meet that income criteria can be difficult. Zillow found that only 8 percent of rental properties in the Miami market listed on its site that could be considered" affordable" under that widely held definition. Los Angeles was the next least affordable market with 12.7 percent of Zillow's listing meeting the benchmark, followed by New York City with 20.4 percent.

Other researchers have come to similar conclusions. Data from New York University's Furman Center for Real Estate and Urban Policy found that the supply of affordable housing has failed to keep pace with demand in 11 of the largest U.S. cities.

"With the exception of Dallas and Houston, the average renter in each metropolitan area could not afford the majority of recently available rental units in their city," according to NYU. "The cities were even less affordable to low-income renters, who could afford no more than 11 percent of recently available units in the most affordable cities.

Rental conditions vary widely. San Francisco rents have surged 12.9 percent for the past year, hitting a median $3,500 per month for a one-bedroom unit, the highest of any market Zumper tracks. Rent controls in the Bay Area, whose economy is booming thanks to its proximity to Silicon Valley, is supposed to keep housing affordable.

At the opposite end of the spectrum, a one-bedroom apartment in Detroit can be rented for $500, a decrease of 11.5 percent during the same time, according to Zumper.

Rents are on the rise for many reasons, including a preference among Millennials to rent instead of buy and the continuing difficulty many consumers have in securing a mortgage even as the Federal Reserve continues to keep interest rates artificially low.

The ramifications of this trend in rents are profound. According to Census Bureau data, the share of 18-to-34-year-olds living with a parent increased from 28 percent in 2007 to 31 percent in 2014 . Not surprisingly, the homeownership rates among these consumers fell to 34.6 percent in the first quarter from the same time in 2009.

In an effort to encourage these consumers to purchase homes, Fannie Mae and Freddie Mac are offering mortgages for buyers putting down just 3 percent of a home's value. Despite some experts' predictions of a housing boom because of demand led by Millennials, it has yet to occur.