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.

本文给出了一种利用最小分解数据集重构柔性生产函数的方法。我们方法的政策重点强调模型再现现有生产系统和预测政策变化的非综合结果的能力。我们结合正数学规划(PMP)和广义最大熵(GME)估计来捕获本地生产环境的个体异质性，并允许重建的生产函数精确地复制基准年的投入使用和产出。由于我们可以从重建的模型中产生需求、供应和替代弹性，我们可以代表广泛的政策反应。本文中使用的实证应用是一个加州灌溉作物部门的生产模型，该模型是为了衡量环境政策变化对灌溉用水供应的经济影响而构建的，是一个名为CalFed的州和联邦联合项目的一部分。我们证明，与在综合数据上重建的模型相比，非集计区域模型提供了更大的预测精度，而且它们显示了计算的输入需求和输出响应的区域弹性的显著变化。由此，我们得出结论，考虑到地区的异质性和由此产生的偏差，从综合中获得的任何收益——即参数估计的小样本偏差的减少——都将被对政策变化的生产反应的扭曲所淹没。