The sensitivity of housing demand to mortgage rates and available leverage is key to understanding the effect of monetary and macroprudential policies on the housing market. However, since there is generally no exogenous variation in these variables that is independent of confounding factors (such as economic conditions or household characteristics), it is difficult to cleanly estimate these sensitivities empirically. We circumvent these issues by designing a survey in which respondents are asked for their maximum willingness to pay (WTP) for a home comparable to their current one, under different financing scenarios. We vary down payment constraints, mortgage rates, and non-housing wealth. We find that a relaxation of down payment constraints, or an exogenous increase in non-housing wealth, has large effects on WTP, especially for relatively poorer and more credit-constrained borrowers. On the other hand, changing the mortgage rate by 2 percentage points only changes WTP by about 5 percent on average. These findings have implications for theoretical models of house price determination, as well as for policy.