New York City's population fell by 800,000 in the 1970s.
From 1980 to 1990, New York City's population climbed rose from 7.1 to 7.4 million.
From 1990 to 2000, New York City's population climbed from 7.4 million to 8 million.
Giuliani did prevent it from sliding back into the abyss after Dinkins, but the major turnaround after the sharpest population decline is attributed to Ed Koch.
If we are going to be precise ...
Annual figures on population indicate that New York City's population reached bottom in 1991.
Matching this with mayors, the decline occured during Mayor Koch's 12-year tenure (1978-1989) as mayor, and was "discovered" during Mayor Dinkins' 4-year tenure (1990-1993). New Yorker, therefore, associate the decline with Mayor Dinkins. This may not be entirely fair. Plus, New Yorkers love Mayor Koch, and conveniently attribute the atrophy of their formerly and now once again great city to his 1-term successor.