Identification and Estimation of Production Functions for Multiproduct Firms

This paper studies the identification property and estimation of a multiproduct firm model with firm-product production functions and firm-product level productivity. We characterize a set of moment conditions using the multiproduct firm’s first-order conditions and the productivity’s evolution process. We first show that the production functions are nonparametrically non-identified without observing the input allocations. For parametric production functions, we formally prove that the Cobb-Douglas production functions are point identified under mild conditions and the standard GMM method can be applied. For more general parametric production functions, we propose using the partial identification method. We provide Monte Carlo evidence suggesting that the CES production functions are partially identified. Applying our method to a sample of grain manufacturing firms, we find that the production functions for single-product and multiproduct firms are different for the same product