Is There a Housing Shortage or Not?

The housing shortage in the US is a perennially popular topic of conversation for the urbanist crowd (which online includes basically everyone.) The basic argument is that housing starts collapsed after the financial crisis and have never truly recovered. This, combined with restrictions on building that limit the supply of housing in many cities (San Francisco and New York are almost always the culprits here), has left America with a housing deficit that's driving up housing costs.