Lennar CEO: Housing market improving, but …

Recent housing data suggest the market is improving, but the gains are a "pretty low slope," Lennar CEO Stuart Miller said Wednesday.

"For the average American across the country … it's really tough to buy a home. Homes are in short supply and we haven't seen production come back," Miller said on CNBC's "Squawk Box."

Homebuilder sentiment in May dropped 2 points month-over-month to 54, the National Association of Home Builders said May 18. Still, home prices in 20 metro cities rose 5 percent year-over-year in March, according to S&P/Case-Shiller's 20-City Composite

Miller made his remarks ahead of the release of weekly U.S. mortgage applications data, which showed the number of applications fell 7.6 percent from the week ending May 29.

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He added the market's slow recovery can be attributed to a number of factors, including the reluctance of Generation Y from buying houses.

"The millennials have not jumped into the market as first-time buyers," he said. "Historically, it's always been an axiom of our business that when 20-year-olds move back home, it takes six to 12 months for everyone to realize it's a bad idea. This time around, that's not the case."

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