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Production Function Estimation with Unobserved Input Price Dispersion

We propose a method to consistently estimate production functions in the presence of input price dispersion when intermediate input quantities are not observed. We find that the traditional approach to dealing with unobserved input quantities—using deflated expenditure as a proxy—substantially biases the production estimates. In contrast, our method controls for heterogeneous input prices by exploiting the first-order conditions of the firm's profit maximization problem and consistently recovers the production function parameters. Using our preferred method, we provide empirical evidence of significant input price dispersion and even wider productivity dispersion than is estimated using proxy methods.