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A conditional linear combination test with many weak instruments

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  • Lim, Dennis
  • Wang, Wenjie
  • Zhang, Yichong

Abstract

We consider a linear combination of jackknife Anderson-Rubin (AR), jackknife Lagrangian multiplier (LM), and orthogonalized jackknife LM tests for inference in IV regressions with many weak instruments and heteroskedasticity. Following I.Andrews (2016), we choose the weights in the linear combination based on a decision-theoretic rule that is adaptive to the identification strength. Under both weak and strong identifications, the proposed test controls asymptotic size and is admissible among certain class of tests. Under strong identification, our linear combination test has optimal power against local alternatives among the class of invariant or unbiased tests which are constructed based on jackknife AR and LM tests. Simulations and an empirical application to Angrist and Krueger’s (1991) dataset confirm the good power properties of our test.

Suggested Citation

  • Lim, Dennis & Wang, Wenjie & Zhang, Yichong, 2024. "A conditional linear combination test with many weak instruments," Journal of Econometrics, Elsevier, vol. 238(2).
  • Handle: RePEc:eee:econom:v:238:y:2024:i:2:s0304407623003184
    DOI: 10.1016/j.jeconom.2023.105602
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    More about this item

    Keywords

    Many instruments; Power; Size; Weak identification;
    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
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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