This generation still believes in the American dream.

More than half (57%) of Generation Z renters are confident that they will own their own home, slightly more than millennials at 55%, according to a new report by real-estate firm Zillow released Wednesday. “Many of them say their concept of homeownership is not any different from their parents’ generation,” said Jeremy Wacksman. chief marketing officer at Zillow. (Generation Z generally includes people born in the late 1990s and early 2000s, though precise definitions vary.)

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Of course, most Generation Z-ers are a long way away from being able to afford a home: 55% of this cohort earns less than $25,000 annually, according to the study. And those who do rent typically aren’t finding luxurious accommodations. Unsurprisingly, 82% of Generation Z renters live with someone else, making them twice as likely to have a roommate or to live with family as renters from all generations. And almost half live in a space with less than 1,000 square feet.

But this isn’t the first study to suggest Generation Z are optimistic about home ownership, perhaps because they weren’t old enough to experience the Great Recession. Some 97% of Generation Z believe that they will own a home in the future and 82% indicate that homeownership is the most important factor in achieving the American Dream, according to this report by the National Association of Realtors. (The association obviously has a vested interest in young Americans buying homes.)

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There’s been a lack of inventory in the U.S. housing market, helping to push up prices. Nearly three-quarters of existing homeowners over the age of 55 said their current home fits their needs, according to data from Realtor.com. That’s forced many millennial home owners to stay in smaller homes — contributing to the 17% year-over-year decline in the supply of starter homes, per Realtor.com. (Realtor.com is operated by News Corp subsidiary Move Inc., and MarketWatch is a unit of Dow Jones, which is also a subsidiary of News Corp.)

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Generation Z, like their older millennial cohorts, will likely face an extremely competitive rental market. There are millions of Generation X households that have gone back to renting after experiencing foreclosures during the property market crash. That means more renters are staying renters throughout their 40s and 50s rather than becoming home buyers. “Generation Z’s first rental experience is probably more competitive than with any other generation,” Wacksman said.

On the upside, members of Generation Z is faster at searching for housing, thanks in no small part to their familiarity with technology. One-third of these renters spend less than one month finding a place to live, as compared with roughly one-quarter of all renters. Additionally, members of Gen Z submit 3.1 applications on average when searching for a rental, as compared with 2.6 for millennials, 2.4 for Gen Xers and 2.2 for baby boomers.

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These Generation-Z tendencies could prove useful when they transition to home buying in earnest. Many first-time home buyers, especially millennials, are surprised to discover that most people won’t make a successful offer on a home in their first, second or even third go-around, Wacksman said. “They’re just willing to submit more, and they move faster,” he said. “That may lead them toward competing better in the market.”