In the years seeing Cambridge housing voucher recipients with homes in the city drop to 77 percent from 93 percent, the density of renters has also dropped in various neighborhoods — and overall, according to this Cambridge Housing Authority graphic.

Even with coveted federal subsidies to help with rent, an increasing number of low-income tenants are moving outside the city, many because of skyrocketing Cambridge rents, housing officials and activists say.

Between 2004 and 2008, the number of Cambridge Section 8 subsidy holders who rent elsewhere rose to 588 from 185, the Cambridge Housing Authority says. Another statistic mirrors the trend: In 2004, 93 percent of Section 8 tenants with a certificate from Cambridge lived in the city, dropping to 77 percent in 2008.

The authority administers the program for any CHA tenant who lives within the Interstate 495 corridor, and those outside the city live in 31 communities as far away as Burlington, Salem and Rockport, according to the authority’s deputy executive director, Michael Johnston. The top five are Boston, Somerville, Medford, Malden and Everett.

The research by a Massachusetts Institute of Technology graduate student interning at the authority leaves some questions unanswered. No one interviewed tenants, some of whom could have been living outside the city already when they got a Section 8 voucher. And there are no figures for years since 2008.

Still, “the main argument [for the trend] at least in our minds is the rent costs” in Cambridge, said Carolina Lucey, senior program manager and head of the authority’s Policy and Technology Lab, which oversees research. Another “academic view,” she said, “is that people move to places where there are opportunity neighborhoods” — meaning simply a place that offers opportunity such as good schools, good restaurants and so on.

But “in our view Cambridge is an opportunity neighborhood,” Lucey said. She said the authority hopes to update the figures and gather information on why tenants chose to live elsewhere — if the agency can arrange another academic partnership.

Tenant advocates have no doubt it’s rent levels in Cambridge forcing poor people out even when they get federal aid.

“One of the things I do is I try to help people [with subsidies] who are looking in Cambridge … the people I’ve dealt with really want to live in Cambridge,” said Kathy Watkins, a board member of the Alliance of Cambridge Tenants and a Section 8 tenant. “It’s very difficult.”

Fewer, with less proportionately

Funding has shrunk for the popular program, forcing Cambridge and many other communities to stop accepting applications. About 4,700 households — almost 12,000 people — are on the authority’s waiting list.

On the surface, it would seem tenants that get Section 8 benefits wouldn’t be affected by market rent levels. Tenants pay roughly 30 percent of their income for rent and the federal or state government pays the rest. The catch is that the government caps the rent it will subsidize; federal officials set a “fair market rent” for each apartment size every year, and Section 8 recipients must find an apartment for that rent or less.

In Cambridge, unlike in many parts of the country, the market rate for apartments keeps rising, stretching the distance from fair market rents.

Authority officials said they’re aware of the Cambridge rental market and have made exceptions. For example, the authority sets its own “fair market rent” as much as 20 percent higher than the federal limit and will go even higher in special cases such as to help disabled tenants. It also allows some tenants to pay more than 30 percent of their income for rent on a case-by-case basis.

Last year the city’s Section 8 rent cap ranged from $1,220 for a studio to $2,191 for a four-bedroom apartment. The authority allowed 164 apartments to rent for substantially more than the federal limit; this year the number increased to 222 apartments.

There are no definitive market rent statistics for Cambridge. Lucey said researchers looked at figures from Zillow, the real estate research service. On its website, Zillow reports the median rent in Cambridge (the point at which half the rents were higher and half lower) at $2,239 in June 2011 and $2,524 in June this year.

U.S. Census Bureau figures, based on questionnaires and interviews with a sample of residents, show the median rent in Cambridge was $962 in 2000, but the agency changed its collection method for that statistic so more recent figures are less reliable. For example, the median rent in Cambridge from 2006 to 2010 was $1,448, but that figure could be off by plus or minus $29, according to the bureau.

Watkins, the tenant activist, says it’s clear what’s happening. “When I moved here in 1985 it was a great place to be with all sorts of interesting people [of all income levels],” she said. “Now it seems like it’s the very poor or the very wealthy.”

Proponents of development and “smart growth” argue that higher density and more housing in the city will reduce rents by increasing the supply.

“That doesn’t work in Cambridge,” Watkins said.

“There’s a finite amount of space and an insatiable hunger from people who want to live here,” she said. “They’ve been building and building, and the rents keep going up.”