The presence of incumbent homeowners creates a friction in housing markets, as incumbents may wait to match with a buyer for their current home before buying their next home.  Exploiting a shock to housing demand caused by the 2015 surprise cut in Federal Housing Administration mortgage insurance premiums, we find that homeowners buy their next home sooner when the probability of their current home selling increases.  This effect is especially pronounced in cold housing markets, in which homes take a long time to sell.  We build and calibrate a model of the joint buyer-seller decision that explains these findings as a result of homeowners avoiding the cost of owning two homes simultaneously.  Simulations of the model demonstrate that stimulus to home buying generates a substantial multiplier effect in cold housing markets by freeing up owners attempting to sell their current home, allowing them to re-enter the market as buyers.