Economists expect the low U.S. unemployment rate to go even lower over the next year, reaching levels not seen in a half-century.

Private-sector economic forecasters surveyed in recent days by The Wall Street Journal on average saw the jobless rate—4% in June after touching 3.8% in May—falling to 3.7% by the end of 2018 and 3.6% by mid-2019.

“Right...