We propose a new non-parametric approach to estimate the production function for housing. Our estimation treats output as a latent variable and relies on the first-order condition for profit maximisation by competitive house builders. For parcels of a given size, we compute housing by summing across the marginal products of non-land inputs. In turn, differences in non-land inputs are caused by differences in land prices that reflect differences in the demand for housing across locations. We implement our methodology on recently-built single-family homes in France. We find that the production function for housing is reasonably well, though not perfectly, approximated by a Cobb-Douglas function and close to constant returns. After correcting for differences in user costs between different inputs, we obtain a share of non-land inputs of about 80\% in the production of housing.