Birthrate doesn’t matter, population does. [Population continues to grow.](https://fred.stlouisfed.org/series/POPTOTUSA647NWDB)
In addition, as people get richer, they want more space to live in ([houses have gotten significantly bigger](https://www.newser.com/story/225645/average-size-of-us-homes-decade-by-decade.html)), and they want more space to themselves ([number of people per household is going down over time)](https://www.statista.com/statistics/183648/average-size-of-households-in-the-us/). Both of which means the same amount of housing houses fewer people.
Couple those demographic trends with changes in the laws around homebuilding, which have made it harder and more expensive to build lots of new homes (zoning and building codes really took off in the latter half of the 20th century), means that demand has skyrocketed while supply has not been able to keep up.
Hence, the housing crisis.
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