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 .
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 .
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We
Our approach works when quantities and prices are latent rendering standard approaches inapplicable. Instead, we
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attributes that determine prices
price proxies of flexibly chosen variables
R
rich heterogeneity, and with
discrete heterogeneity, endogeneity, and
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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
possibly latent prices. Finally, we show that
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quantile
nonparametric
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, which facilitates statistical inference