We introduce a methodology to estimate the households' marginal willingness to pay for housing characteristics in regulated housing markets, where houses and households are matched using queueing time. For the Amsterdam Metropolitan area, the households' marginal willingness to pay for the market value of public housing, so the value when sold in the private market, is estimated. We find that the annual marginal willingness to pay for the market value is close to the annual capitalisation rate applicable to investments in housing. We provide evidence of random, and therefore inefficient, matching between households and public houses with long queueing times.