This would make sense if the population growth was increasing but at a slower rate. But, the population is actively declining. Somehow, 5.3% of people went from having housing to leaving, so I don’t think housing is the only story here.
And rent control exacerbates it, as you have literally over a million people that are a "locked into" their below-market rate units and can never leave because they'll never find anything that cheap elsewhere, regardless of whether they still need that much space. My great aunt for example is 101 years old and lives in a 3 bedroom apartment in Queens. 50 years ago there were 4 people living in that apartment (including her husband and her kids, all now dead).
Plus there's the issue of renovations/demolitions that remove units and replace them with a smaller number of more expensive units.
No, that's not how normal distributions work. Among the 5.3%, some significant portion of those left empty housing units in their wake. They weren't all 3rd roommates that left.
Yes, when your rent goes up 10-20% YoY and you simultaneously lose some or all of your income, you tend to leave.
A lot of people left NYC in the last few years because they could not afford it, with housing being both the main expense and also the one that has increased the most in the last few years.
It's also possible for supply of housing to reduce simultaneously. Say if there was a change in rental laws that strongly incentivized landlords to pull units from the market?[0]
[0] https://reason.com/2019/06/17/new-yorks-progressive-backed-r...
Somewhat ironically, you have people choosing to stay single and not have kids, which gives them more money to spend on themselves for more room, which eats up housing and drives up prices.