On the Non-Identification of Revenue Production Functions

Production functions are potentially misspecified when revenue is used as a proxy for output. I formalize and strengthen this common knowledge by showing that neither the production function nor Hicks-neutral productivity can be identified with such a revenue proxy. This result obtains when relaxing the standard assumptions used in the literature to allow for imperfect competition. It holds for a large class of production functions, including all commonly used parametric forms. Among the prevalent approaches to address this issue, only those that impose assumptions on the underlying demand system can possibly identify the production function.