NEW YORK ( MainStreet) — Rising student loan debt is a probable risk that might slow down a strong economic recovery, New York Federal Reserve Bank President William Dudley said Wednesday.

"It's a prospective risk that we need to analyze further," Dudley told reporters at a press conference at the New York Fed. "The fact is that the student loan burden is climbing pretty sharply, and the fact is that it cannot be discharged."

Real wages have been sluggish to rise, increasing the burden of paying back student loans for college borrowers.

"It is true that real wages for college graduates maybe leveling off, " said Jaison Abel, a senior economist at the New York Fed.

An estimated 40% of households headed by someone younger than 35 hold student debt from investing in their higher education, according to the Pew Research Center.

A recent New York Fed report on household debt released earlier this month found the outstanding loan balances on credit reports for student loans increased to a staggering $1.02 trillion as of September - a $33 billion dollar increase from June. Student loan delinquency is also on the rise with 11.8% of borrowers more than 90 days past due.

"One thing you see in aggregate debt data is a very rapid rise in student loan debt over the last few years, and this is something that potentially has real implications for economic performance going forward." Dudley said.

Most college students still find it challenging to find a first-time job opportunity in the current labor market. Unemployment rates have only dipped down by 2.75 percentage points over the last four years to 7.3% from its initial peak in October 2009 when unemployment soared to 10%.

"We find that it's a little hard in this environment for college students to get their first job out of college," the New York Fed chief said.

Dudley noted payroll growth has not been strong enough relative to the growth of the overall economy, although there are nascent signs that the labor market shows signs of improvement based on the most recent jobs report.

The latest data show the economy added an average of 200,000 jobs each month for the last three months -- a stronger pace after slowing to 150,000 in July.

Federal Reserve Chair Ben Bernanke remarked the U.S. labor market was "an awful amount slack" earlier this November at a panel at the International Monetary Fund, but he dismissed concerns on unpaid student loans.

"To the extent that there's a lot of student loan debt held by people not working, it's obviously a drag on recovery," he said. "I don't see it as a source of financial crisis per se, simply because it is primarily the asset of the federal government. What it could be, ultimately, is another fiscal cost."