A Semi-Nonparametric Approach to Estimating ProductionFunctions When Output Prices are Unobserved

There exists significant dispersion in output prices between firms in many industries. As a consequence the value of output is not necessarily a good measure of the quantity of output. Estimation of production functions for these types of goods is thus challenging if quantities and prices of output are not separately observed by the econometrician. This paper provides a new semi-nonparametric approach for estimating production functions which treats quantity and prices for output as latent variables. To illustrate the usefulness of the techniques we consider an application that focuses on estimating production functions for housing. The empirical analysis is based on a comprehensive database of recently built properties in Allegheny county. We find that the new methods proposed in this paper work well in the application and provide reasonable estimates for the supply of housing per unit of land and the housing production function