[sumtechguy]

The theory is rent control tends to reduce the desire for building more units. Not unfounded as who would build more and you ability to move with the market is hindered. Thus creating in a weird way more scarcity. If there is one that can drive prices up very nicely, its scarcity.

[Detrytus]

Not only that, it also creates an incentive for renters to hold on to units they do not need anymore, because if they forego the lease then the next renter will get much higher rent (and so will they, at their new place). So they keep it, just in case.