On the non-identification of revenue production functions

It is well‑known that production functions are potentially misspecified when revenue is used as a proxy for output. In this paper, I formalise and strengthen this common knowledge by showing that neither the production function nor Hicks‑neutral productivity can be identified when revenue is used as a proxy for physical output. This result holds under the standard assumptions used in the literature for a large class of production functions, including all commonly used parametric forms. Among the prevalent approaches to address this issue, I show that only those which impose assumptions on the underlying demand system can possibly identify the production function