How much did interest rates matter for the housing boom?

Both theory and data suggest that lower real rates cannot account for more than one-fifth of the boom in house prices.

That's from Edward Glaeser, Joshua Gottlieb, and Joseph Gyourko; here is more.  Here is some of the theory:

If people expect to move in the future, low interest rates today will not lead them to bid up prices so much now because they realise they might have to sell later at a lower price when rates are higher. The option to prepay also weakens the link between current interest rates and house prices for the same reason. Rates also should have little or no impact on prices in elastically supplied markets as shown in Glaeser et al. (2008).

Finally, if people are credit-constrained, lower rates today need not lead to higher prices. After all, if the marginal buyer cannot take advantage of those lower rates, they should not affect the buyer’s valuation of a home. Taken together, we show that these factors can reduce the predicted impact of interest rates on home prices by about two-thirds, bringing it down to 6 or 8 from previous conclusions of around 20.