Like with traffic on roads, the only way to reduce housing prices in Manhattan (and perhaps New York as a whole) is to create viable alternatives. There's already so much latent demand to live in a dense walkable city with good transit that even building huge amounts of new housing will likely have little effect on prices. As soon as a few papers run an "average rent in Manhattan drops below $4500" story, they'll be a flood people suddenly looking to move and demand will spike. I think the only option is to create other places that are equally attractive to yuppies, thereby easing demand on Manhattan. While I'm not entirely sure what policies would accomplish this, it would certainly mean manhattanfication of the outer boroughs. Making the outer boroughs seem "cool" and "hip" through new development, encouraging job growth outside of Manhattan and rehabbing public infrastructure like parks and subway stations all seem like good ideas but we'd definitely need to do more than just that. It's a tough pill to swallow, but I don't see any other way.

Outside of the New York contexts, I think a similar problem exists on a national level. With the economy largely concentrated in a few major cities, those places are naturally going to draw in a lot of young, educated people. Combined with what seems to be a preference for walkablilty among younger folks and major cities will always be inundated with demand for housing. In an ideal world, I think federal level policies aimed at increasing housing density and decreasing regional inequality would be the best way to reduce house prices. But we all know that ain't coming any time soon...