You can read lots of articles about the crisis of housing affordability in desirable cities. There's a huge debate about what to do, but it looks to me like it comes down to one question: what happens if you let developers build more housing?

Everyone pretty much agrees that permits to build additional housing result in building high-end housing. There are far fewer units of every type desired than available so there is plenty of demand for luxury units, and those give the most profit per square foot, so that's what developers are going to want to build if given the chance. The question is, what happens to the rest of the market?

Here opinions diverge sharply. One view is that building luxury units does nothing to help the poor or middle class because they can't afford to live in them, and may even give higher rents for other buildings because they're now next to fancy luxury towers. The other view is that the rich people moving into the luxury units are moving out of somewhere else, opening those units up for other people. This gives you "filtering," a process of reverse gentrification where apartments that were occupied by rich people are now occupied by somewhat less rich people, and on down the chain, slightly lowering rents for everyone along the way.

If you have the former view, you might require developers to build affordable housing, some number of units set aside at below market rate. Or perhaps you mandate smaller units with fewer amenities, decreasing their market price that way, and making room for more people on a given amount of land. Or you protest new housing developments, because they're catering to rich people instead of solving the real problem. But if you have the latter view then these restrictions are actively harmful: you want developers free to build as much housing as they think is profitable, and rules like "30% affordable" bring down the threshold of profitability enough that many fewer units will get built. You want to get out of the way of developers, find places our current permiting process is overly restrictive, and just get lots of new housing units built quickly.

Can we look at what does happen to the rest of the market when new high-end units are built? It's a tricky problem, because what we care about isn't "did rents go down after building more?" but "did building more give us lower rents than we would have had otherwise?". There's lots of theorizing (Aaron 1973, Smith-Heimer 1990) and some analysis of rents by building age (Rosenthal 2013), but what else can we do to answer this question?

(The filtering idea makes sense to me, but it's a complicated economic argument which could easily be missing something important about how the market actually works.)