Prices, Profits, Proxies, and Production

TL;DR

This paper develops a nonparametric framework to identify and bound production and profit functions for heterogeneous firms using latent quantities and prices, extending classical duality results to complex settings.

Contribution

It introduces a method to identify firm production sets and profits without directly observing prices or quantities, accommodating heterogeneity and endogeneity.

Findings

Provides a way to estimate production sets from profit data.

Extends duality theory to discrete heterogeneity and latent prices.

Shows convergence of nonparametric estimators to true production sets.

Abstract

This paper studies nonparametric identification and counterfactual bounds for heterogeneous firms that can be ranked in terms of productivity. Our approach works when quantities and prices are latent, rendering standard approaches inapplicable. Instead, we require observation of profits or other optimizing-values such as costs or revenues, and either prices or price proxies of flexibly chosen variables. We extend classical duality results for price-taking firms to a setup with discrete heterogeneity, endogeneity, and limited variation in possibly latent prices. Finally, we show that convergence results for nonparametric estimators may be directly converted to convergence results for production sets.