We identify the causal effect of house prices on mortgage demand and supply in Switzerland by exploiting exogenous shocks to immigration and thereby to house prices. Detailed micro data allow us to observe multiple offers for each mortgage request. We find a 1% increase in house prices to raise the requested mortgage amount by 0.52%. Due to positive feedback effects, the entire partial correlation is 0.78%. While we find higher house prices to increase mortgage demand, they induce banks to make fewer offers and charge higher rates, especially later in the boom and especially for highly leveraged households.