To add some more concrete numbers, in 2015 there were 14,357 units completed in New York. Permits were issued for 56,528 units. (Only 20,000 permits were issued in 2014. They were down 65% in Q1 2016.)
For a city of over 8 million people, I would expect 50,000 units/year to be the sustainable level. 20,000/year seems quite low.
http://www.nycrgb.org/downloads/research/pdf_reports/16HSR.p...
The reason for this is new buildings have to follow modern regulations which drops the usable square footage of properties considerably (for example, having the building X feet back from the street etc). In Manhattan where every square foot counts this is of course unacceptable. Old buildings are grandfathered into older, less restrictive, regulations.
https://www.nytimes.com/interactive/2016/05/19/upshot/forty-...
There's also opportunities to upgrade old industrial space to residential, no net loss in housing.