In this paper we seek to understand the role of financial constraints in the housing market and their effectiveness as a macroprudential policy tool aimed at cooling a housing boom. We exploit a natural experiment arising from the 2012 Canadian law change that restricts access to mortgage insurance (MI) whenever the purchase price of the home is 1 million Canadian dollars or more. Our empirical approach is motivated by a directed search model that features auction mechanisms and financially constrained bidders. We model the introduction of the Canadian MI regulation of 2012 as a tightening of the financial constraint faced by a subset of prospective buyers. This prompts some sellers to reduce their asking price in order to elicit bids from both constrained and unconstrained buyers. Competition between bidders intensifies, which dampens the impact of the policy on sales prices. Using transaction data from the Toronto housing market, we employ a distribution regression approach combined with a regression discontinuity design to test the model's predictions. We find that the limitation of MI causes a 1.05 percent increase in the annual growth of houses listed just under 1M and a 0.33 percent increase in the annual growth of houses sold just below 1M. In addition, the policy causes a sharp rise in the incidence of both shorter-than-average listing times and sales above asking in the under 1M segment, consistent with the model's predictions. Overall, our analysis points to the importance of strategic and equilibrium considerations in assessing the effectiveness of macroprudential policies.