https://www.cato.org/publications/research-briefs-economic-p...
Pretty much the only study I’m aware of that took the issue head-on, from the Cato institute.
They found that rent control greatly benefits recipients, that rents increase diffusely citywide (about 5%), and that the overall positive and negative impacts were roughly equally balanced (~$3Bn over 17 years). The net is slightly positive, in fact.
In other words, rent control pretty much does what’s printed on the tin: helps certain renters a lot, hurts others a tiny amount, averages out to zero net impact. Here’s the TL;DR:
”On net, incumbent San Francisco residents appear to come out ahead, but this is at the great expense of welfare losses from future inhabitants.”
You can certainly debate the desirability of that outcome, but it’s exactly as advertised.