We discuss the limitations of using unit quantity data to measure output in the estimation of production functions. We introduce a simple model, the quality-equivalent Cournot model, where revenue or deflated revenue is the preferable measure of output as it allows consistent estimation of output elasticities and markups. In contrast, because reported units are not comparable across firms, relying on quantity data for productivity analysis or to generate output elasticities used in the production approach to markup estimation may be problematic.
Ackerberg et al. (Fri,) studied this question.