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On Optimal Inference in the Linear IV Model




This paper considers tests and confidence sets (CS�s) concerning the coefficient on the endogenous variable in the linear IV regression model with homoskedastic normal errors and one right-hand side endogenous variable. The paper derives a finite-sample lower bound function for the probability that a CS constructed using a two-sided invariant similar test has infinite length and shows numerically that the conditional likelihood ratio (CLR) CS of Moreira (2003) is not always "very close," say .005 or less, to this lower bound function. This implies that the CLR test is not always very close to the two-sided asymptotically-efficient (AE) power envelope for invariant similar tests of Andrews, Moreira, and Stock (2006) (AMS). On the other hand, the paper establishes the finite-sample optimality of the CLR test when the correlation between the structural and reduced-form errors, or between the two reduced-form errors, goes to 1 or -1 and other parameters are held constant, where optimality means achievement of the two-sided AE power envelope of AMS. These results cover the full range of (non-zero) IV strength. The paper investigates in detail scenarios in which the CLR test is not on the two-sided AE power envelope of AMS. Also, theory and numerical results indicate that the CLR test is close to having greatest average power, where the average is over a grid of concentration parameter values and over pairs alternative hypothesis values of the parameter of interest, uniformly over pairs of alternative hypothesis values and uniformly over the correlation between the structural and reduced-form errors. Here, "close" means .015 or less for k=20, where k denotes the number of IV�s, and .025 or less for 0

Suggested Citation

  • Donald W.K. Andrews & Vadim Marmer & Zhengfei Yu, 2017. "On Optimal Inference in the Linear IV Model," Cowles Foundation Discussion Papers 2073R, Cowles Foundation for Research in Economics, Yale University, revised Feb 2018.
  • Handle: RePEc:cwl:cwldpp:2073r
    Note: Includes Supplimental Material

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    Cited by:

    1. Tetsuya Kaji, 2019. "Theory of Weak Identification in Semiparametric Models," Papers 1908.10478,, revised Aug 2020.
    2. Kiviet, Jan, 2019. "Instrument-free inference under confined regressor endogeneity; derivations and applications," MPRA Paper 96839, University Library of Munich, Germany.
    3. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    4. Donald W. K. Andrews & Patrik Guggenberger, 2015. "Identification- and Singularity-Robust Inference for Moment Condition," Cowles Foundation Discussion Papers 1978, Cowles Foundation for Research in Economics, Yale University.
    5. Patrik Guggenberge & Frank Kleibergen & Sophocles Mavroeidis, 2021. "A Powerful Subvector Anderson Rubin Test in Linear Instrumental Variables Regression with Conditional Heteroskedasticity," Economics Series Working Papers 960, University of Oxford, Department of Economics.
    6. Olatunji Abdul Shobande & Mobolaji Daniel Akinbomi, 2020. "Competition dynamics in Nigerian aviation industry: a game theoretic approach," Future Business Journal, Springer, vol. 6(1), pages 1-8, December.
    7. Horowitz, Joel L., 2021. "Bounding the difference between true and nominal rejection probabilities in tests of hypotheses about instrumental variables models," Journal of Econometrics, Elsevier, vol. 222(2), pages 1057-1082.

    More about this item


    Conditional likelihood ratio test; Confidence interval; Infinite length; Linear instrumental variables; Optimal test; Weighted average power; Similar test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation


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