Would 4 percent mortgages get capitalized into house prices?

I don't know--and neither does anyone else.

I am in the middle of a project with Chris Redfearn and Stuart Gabriel that looks precisely at this issue. Our finding is that capitalization varies a lot by time and place. The coasts are different from the middle of the country; the period before 1997 is different from the period after. When we do rolling regressions across time to attempt to identify capitalization effects, we get very unstable coefficients.

This is not to say borrower relief is a bad idea--I have come around to the view that we need to do it (although I would like to see clawbacks). But let's not kid ourselves--we have no good model to predict the effectiveness of any policy right now.