Academics argue there isn't a housing shortage as much as a problem with income and the mix of housing available

 -- "Housing Prices Are Too High. Building More Homes Won’t Solve the Problem," Barron's

A longer-term perspective, however, shows that America isn’t suffering from a housing shortage. Housing production has lagged behind household growth since 2010, but this doesn’t account for the massive overhang of housing produced in the previous decade. Fueled by the housing bubble of 2000-07, 160 homes were added to the stock for every 100 households formed during the aughts, our analysis of Census Bureau data shows. This level of production created a huge surplus of housing, which has yet to be fully absorbed. 

Put differently, from 2000-21, the nation grew by 18.5 million households. To maintain an adequate inventory of vacant housing, which historically would be 9.3% of the total, the housing stock needed to expand by 20.2 million units. Instead, it grew by 23.7 million housing units, producing a surplus of 3.5 million units. 

... The belief that there is a housing shortage is correctly motivated by concern over the housing-affordability problems that confront so many households. But census data show that these housing-affordability problems largely reflect a mismatch between household incomes and housing prices. 

Here, prices refer to housing prices in the market as a whole, not just the prices of new-to-the-market homes, which fluctuate widely with the pace of housing production. Housing-affordability problems for the population as a whole aren’t related to housing shortages or low vacancy rates. Rather, they are driven by high overall housing prices and low household incomes.