Identification and Estimation of Production Function and Consumer Demand Function under Monopolistic Competition from Revenue Data

TL;DR

This paper demonstrates that key economic functions like production and demand can be identified nonparametrically from revenue data alone in monopolistic competition, enabling welfare analysis without output quantity data.

Contribution

It provides the first nonparametric identification of production and consumer demand functions from revenue data without output quantities, under certain demand restrictions.

Findings

Nonparametric identification of production and demand functions from revenue data.

A semiparametric estimator performs well in simulations and real data.

Market power reduces welfare by 3-6% in Chilean manufacturing industries.

Abstract

We establish nonparametric identification of production functions, total factor productivity (TFP), price markups, and firms' output prices and quantities, as well as consumer demand, using firm-level revenue data, without observing output quantity, in a monopolistically competitive environment with a fully nonparametric demand system. This result overturns the widely held view -- formalized by Bond, Hashemi, Kaplan, and Zoch (2021) -- that output elasticities and markups are not nonparametrically identifiable from revenue data without quantity information. Under the additional restriction that demand satisfies the homothetic single-aggregator (HSA) structure of Matsuyama and Ushchev (2017), we further nonparametrically identify the representative consumer's utility function from firm-level revenue data. This new identification result enables counterfactual welfare analysis without parametric assumptions on preferences. We propose a semiparametric estimator that is feasible for standard firm-level datasets under a Cobb--Douglas production specification. Monte Carlo simulations show that the estimator performs well, while treating revenue as output induces substantial bias. Applying the estimator to Chilean manufacturing data, we reject the CES specification in favor of HSA, and find that market power reduces welfare by approximately 3%--6% of industry revenue in the three largest manufacturing industries in 1996.