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Location Properties of Point Estimators in Linear Instrumental Variables and Related Models

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  • Keisuke Hirano
  • Jack R. Porter

Abstract

We examine statistical models, including the workhorse linear instrumental variables model, in which the mapping from the reduced form distribution to the structural parameters of interest is singular. The singularity of this mapping implies certain fundamental restrictions on the finite sample properties of point estimators: they cannot be unbiased, quantile-unbiased, or translation equivariant. The nonexistence of unbiased estimators does not rule out bias reduction of standard estimators, but implies that the bias-variance tradeoff cannot be avoided and needs to be considered carefully. The results can also be extended to weak instrument asymptotics by using the limits of experiments framework.

Suggested Citation

  • Keisuke Hirano & Jack R. Porter, 2015. "Location Properties of Point Estimators in Linear Instrumental Variables and Related Models," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 720-733, December.
    • Handle: RePEc:taf:emetrv:v:34:y:2015:i:6-10:p:720-733
    DOI: 10.1080/07474938.2014.956573
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    4. David M. Kaplan, 2019. "Unbiased Estimation as a Public Good," Working Papers 1911, Department of Economics, University of Missouri.
    5. Karthik Rajkumar, 2019. "Ridge regularization for Mean Squared Error Reduction in Regression with Weak Instruments," Papers 1904.08580, arXiv.org.
    6. Tetsuya Kaji, 2021. "Theory of Weak Identification in Semiparametric Models," Econometrica, Econometric Society, vol. 89(2), pages 733-763, March.

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