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Instrument Validity for Heterogeneous Causal Effects

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  • Zhenting Sun

Abstract

This paper provides a general framework for testing instrument validity in heterogeneous causal effect models. The generalization includes the cases where the treatment can be multivalued ordered or unordered. Based on a series of testable implications, we propose a nonparametric test which is proved to be asymptotically size controlled and consistent. Compared to the tests in the literature, our test can be applied in more general settings and may achieve power improvement. Refutation of instrument validity by the test helps detect invalid instruments that may yield implausible results on causal effects. Evidence that the test performs well on finite samples is provided via simulations. We revisit the empirical study on return to schooling to demonstrate application of the proposed test in practice. An extended continuous mapping theorem and an extended delta method, which may be of independent interest, are provided to establish the asymptotic distribution of the test statistic under null.

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  • Zhenting Sun, 2020. "Instrument Validity for Heterogeneous Causal Effects," Papers 2009.01995, arXiv.org, revised Oct 2023.
    • Handle: RePEc:arx:papers:2009.01995
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    References listed on IDEAS

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    1. Toru Kitagawa, 2015. "A Test for Instrument Validity," Econometrica, Econometric Society, vol. 83(5), pages 2043-2063, September.
    2. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, January.
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    Cited by:

    1. Hongyi Jiang & Zhenting Sun & Shiyun Hu, 2023. "A Nonparametric Test of $m$th-degree Inverse Stochastic Dominance," Papers 2306.12271, arXiv.org, revised Jul 2023.
    2. Thomas Carr & Toru Kitagawa, 2021. "Testing Instrument Validity with Covariates," Papers 2112.08092, arXiv.org, revised Sep 2023.
    3. Hongyi Jiang & Zhenting Sun, 2023. "Testing Partial Instrument Monotonicity," Papers 2308.08390, arXiv.org, revised Aug 2023.
    4. Jiang, Hongyi & Sun, Zhenting, 2023. "Testing partial instrument monotonicity," Economics Letters, Elsevier, vol. 233(C).
    5. Soonwoo Kwon & Jonathan Roth, 2024. "Testing Mechanisms," Papers 2404.11739, arXiv.org.
    6. Zhenting Sun & Kaspar Wuthrich, 2022. "Pairwise Valid Instruments," Papers 2203.08050, arXiv.org, revised Jan 2024.

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