For now, the Fed is "clearly on hold," Hatzius said Friday in a "Squawk on the Street" interview. However, he added, "The economy is still doing pretty well. We're still growing above trend, [but] not as much as we were in the middle of last year."
The Fed opted not to raise rates from a range between 2.25 percent and 2.5 percent during its policy meeting this week, and pledged that future moves would be approached patiently. After the fourth Fed rate hike of 2018 in December, Chairman Jerome Powell did leave the door open to other options in 2019, emphasizing "data dependency." However, at the time, the Fed projected two more rate increases this year.
In reaction, stocks surged Wednesday, with the Dow Jones Industrial Average closing above 25,000 for the first time since Dec. 4. The Dow closed just below the flat-line Thursday but rose Friday on a better-than-expected jobs report for the month of January.
With all of January in the books, the Dow rose about 7 percent, its best monthly performances since October 2015. However, after the rout in the final three months of 2018, the Dow was still 7 percent below its all-time intraday highs in early October before Powell touched off concerns about an aggressive rate-hike policy. He later walked back that notion. But uncertainty persisted.
Now, there is a growing chorus, including Art Cashin of UBS and Guggenheim's Scott Minerd, saying the Fed "is done raising rates and maybe will even cut rates" in 2019.
With the latest Fed comments, markets have definitely taken their rate hike estimates down, Hatzius said. "We no longer look for quarterly hikes. We still think one hike in 2019 but it's a very different outlook at this point"
Former Atlanta Fed President Dennis Lockhart also expects the Fed to hike at least once this year. He told CNBC on Thursday, central bankers will likely be on hold until midyear before they'll have to re-evaluate inflation data and decide whether to hike.