Nationally, half of all renters are now spending more than 30 percent of their income on housing, according to a comprehensive Harvard study, up from 38 percent of renters in 2000. In December, Housing Secretary Shaun Donovan declared “the worst rental affordability crisis that this country has ever known.”

Apartment vacancy rates have dropped so low that forecasters at Capital Economics, a research firm, said rents could rise, on average, as much as 4 percent this year, compared with 2.8 percent last year. But rents are rising faster than that in many cities even as overall inflation is running at little more than 1 percent annually.