While student loan debt does play a role in the low homeownership rates among millennials, it does not fully explain why this generation is slow to purchase a home, according to Freddie Mac's monthly Insight & Outlook for September released Wednesday.

Some housing experts expected the homeownership rate, which has been decreasing since 2004, to get a much-needed boost as millennials entered the housing market. However, there have been no results on this end and the homeownership rate has continued to fall.

One explanation that most seem to point to is student loan debt, the report says. Freddie Mac questions if student loan debt and the decline in the millennial homeownership rate are directly related.

"While we can’t answer that question definitively, there are some tantalizing clues in the data," the report said. "Note that student loan debt alone can’t explain the low homeownership rate among millennials. After all, the homeownership rate in this cohort has dropped 5 to 6 percentage points for student loan borrowers and non-borrowers alike."

"The low homeownership rate among Millennials is still something of a puzzle—it cannot be explained solely by the increase in student loan debt."

Freddie Mac's data showed student debt tripled over the past 10 years, reaching $1.2 trillion in the fourth quarter of 2014. Although student debt increased for all age groups, the balances are focused among those under 30 years old and those between 30 and 39 years old.

Pre-crisis homeownership rates of 27-to-30-year-olds with student loans, with at least some college education, were 2 to 3 percent higher than homeownership rates of those with no student loans. This gap started to close during the recession and changed direction in 2011. The homeownership rate of borrowers was about one percentage point lower than the rate of non-borrowers by 2014.

Freddie Mac separated student loan borrowers into three groups for how they approach homeownership and mortgage lending:

Successful investors: Borrowers who completed their degrees and found that their post-college earnings are matching their expectations. Unless they are challenged to accumulate a down payment, student loan debt is not a significant deterrent to purchasing their first home. However, they may be delaying for other reasons;

Disappointed earners: Graduates of four-year institutions whose return on their education investment is less-than-expected. They may not be able to find a job in their field and their wage income is lower than originally anticipated. Some of these borrowers took highly-specialized instruction in fields that deteriorated during their period of studies (for example, petroleum engineers graduating now). Their relatively low earnings and student debt burden may hinder homeownership for this group.

At-risk borrowers: These are the borrowers identified by Looney and Yannelis in their analysis of the Department of Education data. Many of these borrowers are from less affluent groups. They may be economically worse off than before they started school—they have no improvement in their job prospects but they have significant student debts to repay. Delinquency and default on their student loans has hurt their credit scores

"The low homeownership rate among millennials is still something of a puzzle—it cannot be explained solely by the increase in student loan debt," said Sean Becketti, chief economist, Freddie Mac. "However student debt plays a role —higher balances are associated with a lower probability of homeownership at every level of college and graduate education. And recent data has confirmed that not all student debt is created equal."