A Revealed Preference Approach to Identification and Inference in Producer-Consumer Models

This article provides a new identification result for a large class of models in which consumers participate in production. I show that consumer preferences are necessary and sufficient to identify production functions through cross-equation restrictions implied by first-order conditions. In addition, I derive a nonparametric revealed preference characterization of the class of models that exhausts its empirical implications. Finally, I use a novel and easy-to-apply inference method that is valid under partial identification. This method can be used to statistically test the model, can deal with any type of latent variables (e.g., measurement error), and can be combined with standard exclusion restrictions. Using data on shopping expenditures and shopping intensity from the NielsenIQ Homescan Dataset, I show that a doubling of shopping intensity decreases prices paid by about 15%. At the same time, I find that search costs are significant, hence, largely diminishing benefits of price search.

本文针对消费者参与生产的一大类模型给出了全新的识别结果。笔者证明，消费者偏好可通过一阶条件（first-order conditions）所蕴含的跨方程约束（cross-equation restrictions），成为识别生产函数的充要条件。此外，本文推导了该类模型的非参数显示偏好（nonparametric revealed preference）刻画，穷尽其全部经验涵义。最后，本文采用一种新颖且易于应用的推断方法，该方法在部分识别（partial identification）框架下依然有效。该方法可用于对模型进行统计检验，能够处理任意类型的潜变量（latent variables，例如测量误差（measurement error)），并可与标准排他性约束（exclusion restrictions）相结合。借助尼尔森IQ家庭扫描数据集（NielsenIQ Homescan Dataset）中的购物支出与购物强度数据，本文发现，购物强度每提升一倍，消费者所支付的价格约下降15%。与此同时，本文还发现搜索成本显著存在，进而大幅抵消了价格搜索所能带来的收益。