It doesn't, but I have a gut feeling that it may impact the prices for new rents in some unexpected ways. For example, people who are living in a rent controlle

It doesn't, but I have a gut feeling that it may impact the prices for new rents in some unexpected ways. For example, people who are living in a rent controlled place may be less likely to leave, this may impact the supply/demand ratio (relatively to the total) and affect the market. Also the apartment owners are aware of the rent control law and so they may try to increase the initial price to try to compensate for it.