I did some reading, and while the long term trend is an increase in rents historically, rent control doesn’t reduce investment. The best study I could find is that it cases less movement of people (they tend to stay put longer) and more owner-renter situations. It also seems to lead to increased gentrification.

I’m undecided if I think it’s a good idea or not. While it seems true that over the long term, rent control appears to increase rents. I wasn’t able to find really solid studies, however, and it’s very hard to compare prices in different locations, etc.