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Production Function Estimation without Invertibility: Imperfectly Competitive Environments and Demand Shocks

Author

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  • Doraszelski, Ulrich
  • Li, Lixiong

Abstract

We advance the proxy variable approach to production function estimation. We show that the invertibility assumption at its heart is testable. We characterize what goes wrong if invertibility fails and what can still be done. We show that rethinking how the estimation procedure is implemented either eliminates or mitigates the bias that arises if invertibility fails. In particular, a simple change to the first step of the estimation procedure provides a first-order bias correction for the GMM estimator in the second step. Furthermore, a modification of the moment condition in the second step ensures Neyman orthogonality and enhances efficiency and robustness by rendering the asymptotic distribution of the GMM estimator invariant to estimation noise from the first step.

Suggested Citation

  • Doraszelski, Ulrich & Li, Lixiong, 2025. "Production Function Estimation without Invertibility: Imperfectly Competitive Environments and Demand Shocks," CEPR Discussion Papers 20373, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:20373
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    File URL: https://cepr.org/publications/DP20373
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    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • L10 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - General
    • O3 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights

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