After a flirtation with thrift after the recession, young Americans have stopped saving.

Adults under age 35—the so-called millennial generation—currently have a savings rate of negative 2%, meaning they are burning through their assets or going into debt, according to Moody’s Analytics. That compares with a positive savings rate of about 3% for those age 35 to 44, 6% for those 45 to 54, and 13% for those 55 and older.

The...