We study identification of multi-output production possibilities sets for heterogeneous firms that can be ranked in terms of productivity. Our setup applies with price-taking, profit-maximizing firms. We require observation of profits  and either prices or proxies for prices. We characterize the identified set for production sets and provide conditions that ensure point identification of production sets. Our results extend classical duality results for the deterministic firm problem to a setup with rich heterogeneity, and with potentially limited variation in prices. We  show that existing convergence results for quantile estimators may be directly converted to convergence results for production sets  .
This paper studies nonparametric identification and counterfactual bounds for heterogeneous firms that can be ranked in terms of productivity. We require observation of profits or other optimizing-values such as costs or revenues, and either prices or attributes that determine prices. We extend classical duality results for price-taking firms to a setup with rich heterogeneity, and with limited variation in prices. We characterize the identified set for production sets, and provide conditions that ensure point identification. We present a general computationally-feasible framework for sharp counterfactual bounds, such as bounds on quantities at a counterfactual price. We show that existing convergence results for quantile estimators may be directly converted to convergence results for production sets , which facilitates statistical inference .
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We study identification of multi-output production possibilities sets
This paper studies nonparametric identification and counterfactual bounds
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Our setup applies with price-taking, profit-maximizing firms.
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or other optimizing-values such as costs or revenues,
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proxies for
attributes that determine
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characterize the identified set for production sets and provide conditions that ensure point identification of production sets. Our results
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the deterministic firm problem
price-taking firms
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potentially
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characterize the identified set for production sets, and provide conditions that ensure point identification. We present a general computationally-feasible framework for sharp counterfactual bounds, such as bounds on quantities at a counterfactual price. We
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, which facilitates statistical inference