Renters across America's biggest cities are finding it more expensive to keep a roof over their heads.

From 2006 to 2013, the population of renters grew in all 11 of the largest U.S. cities, and the median rent grew faster than inflation in almost all of them, according to a new study by the NYU Furman Center and Capital One (see chart at bottom).

"While renters constituted a majority of the population of just five of these cities in 2006, by 2013 that number had increased to nine cities," the report states.

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Philadelphia saw the biggest increase in the number of renters, marking a 28 percent rise from 2006. The 10 other biggest cities all saw increases, including 25 percent in Miami and 22 percent each in Boston, Washington, D.C., and San Francisco.

That surge stems in part from the housing bubble. Housing developers frantically put up buildings in the years immediately preceding the 2008 crash and, after credit dried up following the collapse, rented out units they were unable to sell. But demand for rental property in many cities has outstripped supply, driving down vacancy rates and driving up housing costs.

"[B]esides making apartment searches more unpleasant and stressful, having more people trying to rent fewer available units often has another result: higher rents," the report states.

Renters who moved recently are getting squeezed the most in all 11 cities cited in the study. In Atlanta, for example, people who moved within the past five years paid a median rent of $996, compared with $820 for tenants who have been in place for longer. The gap was even wider in Boston, where more recent renters paid a median of $1,400, versus $840 for longer-term residents.

Rising rents coincide with another post-recession trend making it hard for many Americans to afford a home: stagnant wage growth. Average hourly earnings are on pace to rise an annualized 2..2 percent, barely keeping up with inflation.

The rental situation isn't unique to the big cities. A report released earlier this month by the National Association of Realtors (NAR) found more than 90 percent of U.S. metropolitan areas saw declining homeownership rates between 2010 and 2013.

"Unfortunately, due to an underperforming labor market, insufficient housing supply and overly stringent underwriting standards since the recession, homeownership has plunged to a rate not seen in over two decades. As a result, the country has become more unequal as the number of homeowners has fallen while the number of renters has significantly risen." Lawrence Yun, NAR's chief economist, said in a statement in releasing the trade group's report.