The Production Function for Housing : Evidence from France

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 maximisation with respect to nonland inputs by competitive house builders. For parcels of a given size, we compute housing by summing across the marginal products of nonland inputs. Differences in nonland 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 CobbDouglas function and close to constant returns after correcting for differences in user costs between land and nonland inputs and taking care of some estimation concerns. We estimate an elasticity of housing production with respect to nonland inputs of about 0.80