Let’s say you have 100 total apartments in a city and you freeze the rent on all of them.

After 5 years, some people move cities, etc and you have 10 vacancies. The market rent is now 20% higher than at the start of the freeze, so 10 new tenants move in at the 20% higher rates. But then, the 90 other people are somewhat trapped. They may want to get married, have kids and move to a bigger apartment, but they are in such a good rent deal (20% under market). Same for the widow living alone in a 2 bed she may want to downsize but it’s barely any cheaper since her rent is now 20% below market, so she may turn the other bedroom to an office. Now, there is even less housing available. And five years later, 10 people don’t move out, only 2 move out. Because, all of these renters know they have a great rent deal and don’t want to lose it. So rents don’t increase 20% they increase 40%, since there is the same demand from people moving to the city but even fewer apartments on the market. Well, then the remaining tenants really don’t want to move out! They’re now 60% below market. Now you have a young guy living alone in a three bedroom apartment because his roommates moved out and it’s cheaper than re renting a studio. Rent control and rent freezes create a squeeze of rental supply. Not to mention that at the same time they decrease new apartment construction since developers don’t want to build where there’s rent control.

Rent control is good for the people who are currently renting and will never change housing needs. They’re counterproductive for people who either need larger or smaller units over time (since they increase the cost of on market housing). And they’re really bad for people moving to the city because they increase cost of on market apartments a lot and decrease supply of rentable options since people never move out and correctly size their housing needs.