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Testing overidentifying restrictions on high-dimensional instruments and covariates

Author

Listed:
  • Hongwei Shi

    (Beijing Normal University)

  • Xinyu Zhang

    (Beijing Normal University)

  • Xu Guo

    (Beijing Normal University)

  • Baihua He

    (University of Science and Technology of China)

  • Chenyang Wang

    (Beijing Technology and Business University)

Abstract

The validity of instruments plays a crucial role in addressing endogenous treatment effects and instruments that violate the exclusion restriction are invalid. This paper concerns the overidentifying restrictions test for evaluating the validity of instruments in the high-dimensional instrumental variable model. We confront the challenge of high dimensionality by introducing a new testing procedure based on U-statistic. Our procedure allows the number of instruments and covariates to be in exponential order of the sample size. Under some mild conditions, we establish the asymptotic normality of the proposed test statistic under the null and local alternative hypotheses. The effectiveness of the proposed method is clearly supported by simulations and its application to a real dataset on trade and economic growth.

Suggested Citation

  • Hongwei Shi & Xinyu Zhang & Xu Guo & Baihua He & Chenyang Wang, 2025. "Testing overidentifying restrictions on high-dimensional instruments and covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(2), pages 331-352, April.
    • Handle: RePEc:spr:aistmt:v:77:y:2025:i:2:d:10.1007_s10463-024-00918-5
    DOI: 10.1007/s10463-024-00918-5
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