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

Kyoo Il Kim, Amil Petrin, Suyong Song

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)267-279
Number of pages13
JournalJournal of Econometrics
Issue number2
StatePublished - Feb 1 2016

Bibliographical note

Funding Information:
We thank Jinyong Hahn, Bruce Hansen, Yingyao Hu, Arthur Lewbel, Rosa Matzkin, and other seminar participants at UCLA, NSF-NBER CEME conference at Cornell University, 2013 North American Summer Meeting of Econometric Society at USC, IO conference at University of Tokyo, European Meeting of Econometric Society at Gothenburg, Midwest Econometrics Group at Bloomington for many helpful comments. Suyong Song gratefully acknowledges research grant from Yoshio Niho Excellence Fund . All errors are our own.

Publisher Copyright:
© 2015 Elsevier B.V.


  • Control variate
  • Measurement error
  • Nonparametric estimation
  • Production function
  • Unobserved productivity

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