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A Generalized Control Function Approach to Production Function Estimation

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  • Ulrich Doraszelski
  • Lixiong Li

Abstract

We develop a generalized control function approach to production function estimation. Our approach accommodates settings in which productivity evolves jointly with other unobservable factors such as latent demand shocks and the invertibility assumption underpinning the traditional proxy variable approach fails. We provide conditions under which the output elasticity of the variable input -- and hence the markup -- is nonparametrically point-identified. A Neyman orthogonal moment condition ensures oracle efficiency of our GMM estimator. A Monte Carlo exercise shows a large bias for the traditional approach that decreases rapidly and nearly vanishes for our generalized control function approach.

Suggested Citation

  • Ulrich Doraszelski & Lixiong Li, 2025. "A Generalized Control Function Approach to Production Function Estimation," Papers 2511.21578, arXiv.org, revised Dec 2025.
    • Handle: RePEc:arx:papers:2511.21578
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    File URL: http://arxiv.org/pdf/2511.21578
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    References listed on IDEAS

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    1. Ulrich Doraszelski & Li Lixiong, 2025. "Production Function Estimation without Invertibility: Imperfectly Competitive Environments and Demand Shocks," NBER Working Papers 33939, National Bureau of Economic Research, Inc.
    2. Ulrich Doraszelski & Lixiong Li, 2025. "Production Function Estimation without Invertibility: Imperfectly Competitive Environments and Demand Shocks," Papers 2506.13520, arXiv.org, revised Jul 2025.
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