Curiously, some places (notably San Francisco) in the United States have the opposite system: rents are unregulated for the first few decades of a building's life, and then annual increases are capped after that. This ensures that the older housing stays affordable for the people who live in it, but it allows prices to rise for new construction, which should in principle increase the amount of housing that gets built. In theory buildings should generate most of their value in the early part of their life when they're more desirable.
This system isn't always managed as well as it could be — subsidized unit requirements are layered on top of that, and in St. Paul the payoff period is only thirty years, which has made some developers balk. The political factions often imagine all investors as good or bad instead of as a force that can be managed to achieve desired social outcomes.