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

Keisuke Hirano, Jack R. Porter

Research output: Contribution to journalArticle

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)720-733
Number of pages14
JournalEconometric Reviews
Issue number6-10
Publication statusPublished - May 22 2015



  • Bias correction
  • Finite sample properties
  • Instrumental variables
  • Weak instruments

ASJC Scopus subject areas

  • Economics and Econometrics

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