Reconstructing Disaggregate Production Functions

This paper demonstrates a method for reconstructing flexible form production functions using minimal disaggregated data sets. The policy focus of our approach puts emphasis on the ability of the model to reproduce the existing production system and predict the disaggregate outcomes of policy changes. We combine Positive Mathematical Programming (PMP) with Generalized Maximum Entropy (GME) estimation to capture the individual heterogeneity of the local production environment, and allow the reconstructed production function to precisely replicate the input usage and outputs produced in the base year. Since we can generate demand, supply and substitution elasticities from the reconstructed model we can represent a wide range of policy responses. The empirical application used in this paper is a production model of California's irrigated crop sector that was constructed to measure the economic effect of environmental policy changes to irrigation water supplies, as part of a joint State and Federal program termed CalFed. We demonstrate that the disaggregate regional models give greater predictive precision, when compared with the model reconstructed on the aggregate data, and that they show a significant variation in the calculated regional elasticities of input demand and output response. From this, we conclude that any gains from aggregation - namely the reduction of small sample bias of the parameter estimates - would be swamped by the distortion of production response to policy changes, given the heterogeneity of the regions and the resultant bias.