More than three years after the onset of the recession, administrators say Yale’s budget has still not fully recovered.

In a letter to faculty today, University President Richard Levin and Provost Peter Salovey said that although the University endowment rose by 21.9 percent in the fiscal year that ended June 30, a rise in spending is expected to outpace an increase in revenue for the 2012-’13 academic year. This anticipated gap will require administrators to make budget cuts — but not the “across-the-board cost reductions” experienced in recent years.

“This year’s budget process will close the Fiscal Year 2013 gap, and give us time to reflect on the future priorities for the University and the best approach for funding them,” Levin and Salovey said. “Over the coming months, and extending into next fall, we will be working with deans, directors, faculty, and staff to identify the most important priorities for the future and how we might find the resources to advance them.”

Salovey and Levin said budget cuts have reduced the $350 million budget gap that followed the roughly 25 percent investment loss in fiscal year 2009. But revenue is only expected to increase by 2.6 percent next year because of the endowment’s spending rule while expenses are anticipated to grow by 6 percent.