🤖 AI Summary
This study addresses the challenge of structural identification in monopolistically competitive markets where only firm-level revenue is observed and output quantities are unobserved. It achieves, for the first time, fully nonparametric identification of the production function, total factor productivity, price markups, and consumer demand. Methodologically, the paper combines a Cobb-Douglas production technology with the Matsuyama–Ushchev homogeneous single-aggregate (HSA) demand system to develop a semiparametric estimator suitable for standard firm panel data. Theoretically, it overturns the prevailing conclusion that output elasticities and markups cannot be identified from revenue alone. Monte Carlo simulations confirm the estimator’s finite-sample performance, and an application to Chilean manufacturing rejects the constant elasticity of substitution (CES) demand assumption in favor of the HSA structure, revealing welfare losses from market power amounting to approximately 3%–6% of industry revenue in three major sectors in 1996.
📝 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.