Nonparametric Identification of Production Function, Total Factor Productivity, and Markup from Revenue Data

TL;DR

This paper develops a nonparametric method to identify production functions, total factor productivity, and markups using revenue data alone, under general demand and imperfect competition conditions.

Contribution

It introduces a novel nonparametric identification approach that derives key economic quantities solely from revenue data, without requiring output quantity observations.

Findings

Successfully identifies production functions, TFP, and markups from revenue data.

Provides constructive methods for identifying demand systems and consumer utility.

Applicable under broad demand and market competition assumptions.

Abstract

Commonly used methods of production function and markup estimation assume that a firm's output quantity can be observed as data, but typical datasets contain only revenue, not output quantity. We examine the nonparametric identification of production function and markup from revenue data when a firm faces a general nonparametri demand function under imperfect competition. Under standard assumptions, we provide the constructive nonparametric identification of various firm-level objects: gross production function, total factor productivity, price markups over marginal costs, output prices, output quantities, a demand system, and a representative consumer's utility function.