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Estimating production functions with control functions when capital is measured with error

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  • Kim, Kyoo il
  • Petrin, Amil
  • Song, Suyong

Abstract

We revisit the production function estimators of Olley and Pakes (1996) and Levinsohn and Petrin (2003). They use control functions to address the simultaneous determination of inputs and productivity. Both assume that input demand is a monotonic function of productivity holding capital constant and then invert this function to condition on productivity during estimation. If the observed capital variable is measured with error, input demand will not generally be monotonic in the productivity shock holding observed capital constant. We develop consistent estimators of production function parameters in the face of this measurement error. Our identification and estimation results combine the nonlinear measurement error literature with Wooldridge’s (2009) joint estimation method to construct a proxy for productivity that addresses simultaneity. Our approach directly extends to the case where other inputs like intermediates or labor are observed with error.

Suggested Citation

  • Kim, Kyoo il & Petrin, Amil & Song, Suyong, 2016. "Estimating production functions with control functions when capital is measured with error," Journal of Econometrics, Elsevier, vol. 190(2), pages 267-279.
  • Handle: RePEc:eee:econom:v:190:y:2016:i:2:p:267-279
    DOI: 10.1016/j.jeconom.2015.06.016
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    1. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    2. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    3. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
    4. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    5. Ackerberg, Daniel & Caves, Kevin & Frazer, Garth, 2006. "Structural identification of production functions," MPRA Paper 38349, University Library of Munich, Germany.
    6. Olley, G Steven & Pakes, Ariel, 1996. "The Dynamics of Productivity in the Telecommunications Equipment Industry," Econometrica, Econometric Society, vol. 64(6), pages 1263-1297, November.
    7. Hu, Yingyao & Huang, Guofang & Sasaki, Yuya, 2020. "Estimating production functions with robustness against errors in the proxy variables," Journal of Econometrics, Elsevier, vol. 215(2), pages 375-398.
    8. Andrews, Donald W.K., 2017. "Examples of L2-complete and boundedly-complete distributions," Journal of Econometrics, Elsevier, vol. 199(2), pages 213-220.
    9. Song, Suyong, 2015. "Semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors," Journal of Econometrics, Elsevier, vol. 185(1), pages 95-109.
    10. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    11. Joel L. Horowitz, 2006. "Testing a Parametric Model Against a Nonparametric Alternative with Identification Through Instrumental Variables," Econometrica, Econometric Society, vol. 74(2), pages 521-538, March.
    12. Ulrich Doraszelski & Jordi Jaumandreu, 2013. "R&D and Productivity: Estimating Endogenous Productivity," Review of Economic Studies, Oxford University Press, vol. 80(4), pages 1338-1383.
    13. James Levinsohn & Amil Petrin, 2003. "Estimating Production Functions Using Inputs to Control for Unobservables," Review of Economic Studies, Oxford University Press, vol. 70(2), pages 317-341.
    14. Wooldridge, Jeffrey M., 2009. "On estimating firm-level production functions using proxy variables to control for unobservables," Economics Letters, Elsevier, vol. 104(3), pages 112-114, September.
    15. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
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    5. Hu, Yingyao & Huang, Guofang & Sasaki, Yuya, 2020. "Estimating production functions with robustness against errors in the proxy variables," Journal of Econometrics, Elsevier, vol. 215(2), pages 375-398.
    6. Fu, Shihe & Xu, Xiaocong & Zhang, Junfu, 2021. "Land conversion across cities in China," Regional Science and Urban Economics, Elsevier, vol. 87(C).
    7. Abito, Jose Miguel, 2019. "Estimating Production Functions with Fixed Effects," MPRA Paper 97825, University Library of Munich, Germany.
    8. De loecker, Jan & Collard-Wexler, Allan, 2016. "Production Function Estimation with Measurement Error in Inputs," CEPR Discussion Papers 11399, C.E.P.R. Discussion Papers.
    9. Josh Martin & Rebecca Riley, 2023. "Productivity measurement - Reassessing the production function from micro to macro," Working Papers 033, The Productivity Institute.
    10. Allan Collard-Wexler & Jan De Loecker, 2016. "Production Function Estimation and Capital Measurement Error," NBER Working Papers 22437, National Bureau of Economic Research, Inc.
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    More about this item

    Keywords

    Production function; Unobserved productivity; Measurement error; Nonparametric estimation; Control variate;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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