NEW YORK (CNNMoney) -- College is more expensive now than ever, but there's still a compelling reason to go: it's a fast track to the American Dream.

You're much more likely to own a home by age 33 if you went to college, according to a New York Federal Reserve report released Monday.

That's still true for those who have student loans, and it even holds for those who didn't finish their degrees.

Of course, it will be harder to save for a down payment if you're in debt. More than 55% of those who have a bachelor's degree and don't have students loans own a home by 33, compared to about 52% of those who took on debt.

But less than one-third of people who didn't go to college at all are homeowners at the same age, according to the data

"The message here is go to school and finish school. And even if you have student debt, you'll be in better shape than if you didn't go," said New York Fed President William Dudley at a press briefing.

It's clear that going to college is a pathway to upward income mobility. The data also show that home ownership rates are higher for those who go to college regardless of whether their parents were upper-, middle-, or lower-class.

But college still costs a lot. The average student leaves school with $34,000 in debt, up nearly 70% from 10 years ago, the report said.

"The number of families that can actually make the payments without doing any borrowing is just declining against the relative cost," said Andrew Haughwout, Senior Vice President of the New York Fed's Research and Statistics Group.

New York Fed officials blamed the rising cost of college at least in part on the reduction in state spending on higher education.

Not only are students borrowing more, more students are borrowing. Total student debt has ballooned to $1.3 trillion, surpassing total credit card debt and auto loans.

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