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Structural Inference from Reduced Forms with Many Instruments

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Abstract

This paper develops exact finite sample and asymptotic distributions for structural equation tests based on partially restricted reduced form estimates. Particular attention is given to models with large numbers of instruments, wherein the use of partially restricted reduced form estimates is shown to be especially advantageous in statistical testing even in cases of uniformly weak instruments and reduced forms. Comparisons are made with methods based on unrestricted reduced forms, and numerical computations showing finite sample performance of the tests are reported. Some new results are obtained on inequalities between noncentral chi-squared distributions with different degrees of freedom that assist in analytic power comparisons.

Suggested Citation

  • Wayne Yuan Gao & Peter C.B. Phillips, 2016. "Structural Inference from Reduced Forms with Many Instruments," Cowles Foundation Discussion Papers 2062, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2062
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    Cited by:

    1. is not listed on IDEAS
    2. Max-Sebastian Dovì & Anders Bredahl Kock & Sophocles Mavroeidis, 2024. "A Ridge-Regularized Jackknifed Anderson-Rubin Test," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 1083-1094, July.
    3. Peter C. B. Phillips, 2022. "An Econometrician amongst Statisticians: T. W. Anderson," Cowles Foundation Discussion Papers 2333, Cowles Foundation for Research in Economics, Yale University.
    4. Eleonora Brandimarti, 2025. "Self-Selection, University Courses and Returns to Advanced Degrees," Papers 2511.09260, arXiv.org.
    5. Christopher L. Skeels & Frank Windmeijer, 2018. "On the Stock–Yogo Tables," Econometrics, MDPI, vol. 6(4), pages 1-23, November.

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    Keywords

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    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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