In the aftermath of the nation’s housing-market collapse and recession, more than 500 midsize and large cities have seen a rise in the share of homes that are rented rather than owned, according to a USA TODAY analysis of Census data. Almost 4 million homes have been lost to foreclosures in the past five years, turning many former owner-occupied homes into rentals. The shift to rental housing is potentially long-lasting and portends changes for neighborhood stability and how people build wealth, economists say.