On the Non-Identification of Revenue Production Functions

TL;DR

This paper demonstrates that using revenue as a proxy for output in production functions leads to non-identification of the true production function and productivity, especially under imperfect competition, unless additional demand assumptions are imposed.

Contribution

It formally proves the non-identification problem of production functions when revenue proxies are used under relaxed assumptions, highlighting the need for demand-based assumptions for identification.

Findings

Revenue-based proxies do not identify production functions under imperfect competition.

Most common parametric production functions are affected by this non-identification issue.

Only demand system assumptions can potentially achieve identification.

Abstract

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.