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Higher order approximations of IV statistics that indicate their properties under weak or many instruments


  • Frank Kleibergen


We show that the higher order biases of instrumental variable statistics in the strong instrument case indicate the degeneracy of the first order asymptotic distributions of these statistics under weak or many instrument asymptotics. We express the higher order approximations using an estimator of the concentration parameter that is independent of the product of the instruments and the structural errors. The expressions of the higher order approximations of IV statistics whose first order asymptotic distributions are robust to instrument quality remain unaltered under weak and strong instruments. The higher order expressions of IV statistics whose first order asymptotic distributions depend on instrument quality also depend on that

Suggested Citation

  • Frank Kleibergen, 2004. "Higher order approximations of IV statistics that indicate their properties under weak or many instruments," Econometric Society 2004 North American Winter Meetings 199, Econometric Society.
  • Handle: RePEc:ecm:nawm04:199

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    More about this item


    weak and many instruments; higher order approximation;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General


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