Production Function Estimation for Multi-Product Firms

Abstract

We study a stylized model of multi-product firms with firm-product level heterogeneity in Hicks-neutral production technology. The productivity process allows flexible correlation between the production efficiency of different products. We characterize the empirical content and show that the scale and location of the production function are non-parametrically non-identified without observing the allocation of inputs and exogenous input price variations. Based on the model’s empirical content, we develop an estimation strategy for any parametric family of production functions. For general production functions, we argue this procedure is subject to unclear identification and heavy computation. In the case of Cobb-Douglas production function, we show the optimal input allocation rules can be solved in closed form and the corresponding moment conditions identify the production functions. Monte Carlo evidence shows that our identification strategy performs well. We then apply our methodology to a sample of agricultural goods manufacturing firms and show that multi-product firms’ production technologies differ from single-product firms even for the same product. We also ∗We thank comments and suggestions from Paul Grieco, Daniel Grodzicki, Marc Henry, Karl Schurter, and other seminar participants at the Industrial Organization Brownbag at Penn State University. Two authors contribute equally to this paper.