On the non-identification of revenue production functions

Staff working papers set out research in progress by our staff, with the aim of encouraging comments and debate.
Published on 17 February 2023

Staff Working Paper No. 1,015

By David Van Dijcke

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.

On the non-identification of revenue production functions