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A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates

Author

Listed:
  • Qingliang Fan
  • Zijian Guo
  • Ziwei Mei
Abstract
This paper proposes an overidentifying restriction test for high-dimensional linear instrumental variable models. The novelty of the proposed test is that it allows the number of covariates and instruments to be larger than the sample size. The test is scale-invariant and is robust to heteroskedastic errors. To construct the final test statistic, we first introduce a test based on the maximum norm of multiple parameters that could be high-dimensional. The theoretical power based on the maximum norm is higher than that in the modified Cragg-Donald test (Koles\'{a}r, 2018), the only existing test allowing for large-dimensional covariates. Second, following the principle of power enhancement (Fan et al., 2015), we introduce the power-enhanced test, with an asymptotically zero component used to enhance the power to detect some extreme alternatives with many locally invalid instruments. Finally, an empirical example of the trade and economic growth nexus demonstrates the usefulness of the proposed test.

Suggested Citation

  • Qingliang Fan & Zijian Guo & Ziwei Mei, 2022. "A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates," Papers 2205.00171, arXiv.org, revised May 2024.
    • Handle: RePEc:arx:papers:2205.00171
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    References listed on IDEAS

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    1. Qingliang Fan & Zijian Guo & Ziwei Mei & Cun-Hui Zhang, 2023. "Inference for Nonlinear Endogenous Treatment Effects Accounting for High-Dimensional Covariate Complexity," Papers 2310.08063, arXiv.org, revised Jun 2024.

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