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Identification- and many instrument-robust inference via invariant moment conditions

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  • Tom Boot
  • Johannes W. Ligtenberg

Abstract

Identification-robust hypothesis tests are commonly based on the continuous updating objective function or its score. When the number of moment conditions grows proportionally with the sample size, the large-dimensional weighting matrix prohibits the use of conventional asymptotic approximations and the behavior of these tests remains unknown. We show that the structure of the weighting matrix opens up an alternative route to asymptotic results when, under the null hypothesis, the distribution of the moment conditions is reflection invariant. In a heteroskedastic linear instrumental variables model, we then establish asymptotic normality of conventional tests statistics under many instrument sequences. A key result is that the additional terms that appear in the variance are negative. Revisiting a study on the elasticity of substitution between immigrant and native workers where the number of instruments is over a quarter of the sample size, the many instrument-robust approximation indeed leads to substantially narrower confidence intervals.

Suggested Citation

  • Tom Boot & Johannes W. Ligtenberg, 2023. "Identification- and many instrument-robust inference via invariant moment conditions," Papers 2303.07822, arXiv.org, revised Sep 2023.
    • Handle: RePEc:arx:papers:2303.07822
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    References listed on IDEAS

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    Cited by:

    1. Johannes W. Ligtenberg, 2023. "Inference in IV models with clustered dependence, many instruments and weak identification," Papers 2306.08559, arXiv.org, revised Mar 2024.

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