Emily Badger at the Atlantic Cities writes a balanced piece on the debate surrounding height restrictions in cities. On the one hand, we have density being a quality that provides positive externalities for cities by itself and should be encouraged, while on the other you have the negative effects of density such as loss of sight lines, possible increases in congestion, and increased use of city services.
One thing she throws in somewhat casually however, is that this increased density may raise rents. I've previously written about this fallacy in a different context, but this is a purer example of how this kind of thinking can be damaging. Densification has both positive and negative externalities, and these deserve to be compared to come up with a more coherent plan on how to maximize density while minimizing the negative side effects if may lead to. Rising rents simply isn't one of these negatives.
The problem is rising rents and densification are definitely correlated in most practical cases, and wouldn't be in a purely theoretical context. Instead of densification causing rising rents however, they are both caused by an exogenous increase in demand. Whenever you have restricted development (which is pretty much the only type of development that can happen in a city), an exogenous increase in demand will lead to a pent up need to increase supply. Because development is limited and supply is not able to catch up with demand, prices will rise.
When you compare this to more stagnant areas which have no increase in demand, and therefore will have no invasive development and no increasing prices, one can erroneously think that the development in the more popular area is what caused the high prices.
This sort of dynamic can be dangerous because it feeds into itself. The more restrictions in place, the more pronounced this effect will be. This means that the cities that are more predisposed to restrict development will seemingly be proved right more than those with more lax restrictions.
I'd even go farther with this line of reasoning. I'd argue that restrictions on development could increase the other negative effects of density. A developer without restrictions might be more able to make their property more desirable than others; they'd add some public space, or build more aesthetically pleasing buildings. If a developer is constrained, they'd be more focused on squeezing in as many units as allowed by law, perhaps at the expense of those more aesthetic effects. This only adds to the feedback loop, and the city will be again be prompted to restrict development further.
The only way out of this is to realize this connection simply does not exist, and to try to completely divorce housing prices from arguments about densification. Despite what evidence may suggest, prices are still driven down by increases in supply. While I personally believe there should be less restrictions on development, there are still valid arguments to be made on the pro-restrictions side. Rising rents simply isn't one of them.