Affordability and Austin aren’t necessarily synonymous, especially when it comes to housing.

The city’s seen an unprecedented level of growth over recent years, much of that due to the oft-maligned cohort known as millennials, of which, according to a Fannie Mae survey, Austin has the largest concentration in the U.S. at 27 percent.

Austin’s not alone. More and more millennials are flocking to urban cores in cities across North America, and one researcher from the University of Waterloo in Ontario, Canada, chose to investigate housing, labor and lifestyle issues surrounding millennials in Austin, and other cities, with a survey called "Generationed City."

The study examines the so-called “youthification” of cities: the migration of youth to urban cores where they rent, rather than own, their housing. Moos says he chose Austin as a case study city because of its boom in population and popularity over the past few years. New York, Calgary and Toronto are also case study cities.

In 2013, nearly half (just over 47 percent) of Austin renters were paying more than $1,000 in monthly rent – compared to 34.6 percent in 2010. And Austin’s housing prices, and home sales, set records in February, March and April this year, according to the Austin Board of Realtors. But, more than half of homes purchased lie outside the Austin city limits.

Moos wants to see whether that migration is a passing trend or if millennials will buck the Baby Boomer and Gen-X trends of eventually fleeing the city to buy homes in the suburbs. However, the survey covers anyone between the ages of 18 and 40, which means it does include some Gen-X'ers as well.

“What I’ve found is that those areas are staying young over time,” he says. “So, young people are moving in and then move back out, and then more young people move into those same neighborhoods.”

Moos says the migrations often accompany a rise in property values, but that they don't explicitly qualify as gentrification, as some young people moving into the neighborhoods may work part-time or contract jobs. The cost of high rent in desirable neighborhoods, in conjunction with lower wages and other factors, can offset wages, limit millennials' spending power and reduce housing sales.

“If you’re only on contract, then you’re not sure how much income you’re going to have [in] two or three months when your contract ends,” Moos says. “You might just be renting, [rather] than if you had a full-time job, when you know how much income you’re going to have down the road.”

City of Austin Demographer Ryan Robinson says Austin’s seen this trend firsthand. He says that the city’s core has been “hollowed out" of families with children, but adds that younger Austinites have a penchant for urban living.

“A lot of folks, and I’m one of them, are sort of looking to millennials to maybe turn this around,” he says. “Millennials have a well-demonstrated preference for central city, urban living. And, so, a lot of us are kind of banking on those households, those millennial households, to stay within the central city, but to start to have kids.”

Robinson says that Austin’s abundance of millennials is a powerful selling point for companies looking to relocate here, but that Austin-based companies aren’t necessarily creating entry-level jobs that many millennials are seeking, which is causing an affordability gap that’s exacerbated by higher rents.

“That collapse in affordability is being driven primarily by skyrocketing housing prices — not just for sale stock, but also rental stock," he says. “In really simple terms, even though we’ve got this giant population of millennials, they are having a tougher and tougher time affording to live in the central city, which is clearly their preference.”

Moos says, once completed, he hopes the study and survey data will provide policy suggestions to cities like Austin.

You can take the “Generationed City” survey online here.