Here's the latest: "... while rent control prevents displacement of incumbent renters in the short run, the lost rental housing supply likely drove up market rents in the long run, ultimately undermining the goals of the law." https://web.stanford.edu/~diamondr/DMQ.pdf

Previously: "Rent control policies generally lead to higher rents in the uncontrolled market, with rents some-times substantially higher than would be expected without rent control (i.e., between 10 to 25 percent higher). Over time, if rent control does not apply to new construction, there is some evidence that the impact on uncontrolled rents diminishes." https://www.nmhc.org/globalassets/knowledge-library/rent-con...

It also follows from supply and demand. Owners are more likely to sell rather than rent out their places, and tenants are more likely to stay in their below-market rent units, both of which reduces supply for new (i.e. market-rate) tenants.