Yes, not enough housing can bid up prices. But as we’ve been saying for years, you can’t have gentrification without a gentry class. In other words, housing prices, in part, are expensive because the gentry class is able to afford those prices (while housing becomes increasingly unaffordable even for the upper-middle class).
Thanks to Il Trumpe, we have a small natural experiment that supports this idea. In his tax bill, only the first $10,000 of state and local taxes (‘SALT’) are deductible. While Republicans did this largely to fuck over states that actually spend money to improve the lives of their citizens, it also meant less money in the pockets of the well-to-do. You’ll never guess what happened next (boldface mine):
In Westchester County, where a typical property tax bill for a single family home is more than $17,000, the average sales price declined 7.6% between the first quarter of 2018 and the same quarter this year. Sales prices for luxury homes (average price $2 million) plummeted 22% during the same period, according to appraiser Miller Samuel Inc. and brokerage Douglas Elliman Real Estate.
Even though it’s not discussed that much, a more progressive tax code–with more brackets that start increasing at lower amounts*–would lower housing prices.
*This is why Krugman’s insistence that the bulk of economic problems can be laid at the feet of the 0.1 percent or higher rings false. They do cause a lot of damage, but so do the 0.1-10% percentiles.