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Clustering for Multi-Dimensional Heterogeneity with an Application to Production Function Estimation

Author

Listed:
  • Xu Cheng

    (University of Pennsylvania)

  • Frank Schorfheide

    (University of Pennsylvania)

  • Peng Shao

    (Boston University)

Abstract

This paper studies the estimation of multi-dimensional heterogeneous parameters in a nonlinear panel data model with endogeneity. These heterogeneous parameters are modeled with group patterns. Through estimating multiple memberships for each unit, the proposed method is robust to sparse interactions; in other words, certain combinations of unobserved features are less common compared to other combinations. We estimate the memberships along with the group-specific and common parameters in a nonlinear GMM framework and derive their large sample properties. Finally, we apply this approach to the estimation of production function and re-evaluate the trajectory of the aggregate markup.

Suggested Citation

  • Xu Cheng & Frank Schorfheide & Peng Shao, 2023. "Clustering for Multi-Dimensional Heterogeneity with an Application to Production Function Estimation," PIER Working Paper Archive 23-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    • Handle: RePEc:pen:papers:23-016
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    File URL: https://economics.sas.upenn.edu/system/files/working-papers/23-0016%20PIER%20Paper%20Submission.pdf
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    More about this item

    Keywords

    Clustering; GMM; K-mean; Panel Data; Production Function Estimation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • D22 - Microeconomics - - Production and Organizations - - - Firm Behavior: Empirical Analysis
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production

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