We propose a new nonparametric 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 maximization with respect to non-land inputs by competitive house builders. For parcels of a given size, we compute housing by summing across the marginal products of non-land inputs. 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 newly-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 land and non-land inputs and taking care of some estimation concerns, we estimate an elasticity of housing production with respect to non-land inputs of about 0.80.
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