As you say "parts of the country", in my mind it's not merely a house building problem it's a location of jobs problem. Detroit has 1000s of empty big houses, but no one wants to live there as there aren't enough jobs as there used to be. Perhaps one policy should be relocation of jobs, spread them around, might be cheaper than building 1000s of homes.
Its similar in the UK, lot's of jobs in London causing housing shortage in South East UK but lots of empty homes up North where there are fewer jobs.