And for some hard data, here's a meta-study on the subject: https://www.sciencedirect.com/science/article/pii/S105113772...

> [A]ccording to the studies examined here, as a rule, rent control leads to higher rents for uncontrolled dwellings. The imposition of rent ceilings amplifies the shortage of housing. Therefore, the waiting queues become longer and would-be tenants must spend more time looking for a dwelling. If they are impatient or have no place to stay (e.g., in the houses of their friends or relatives) while looking for their own dwelling, they turn to the segment that is not subject to regulations. The demand for unregulated housing increases and so do the rents.