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Testing Under Weak Identification With Conditional Moment Restrictions

Author

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  • Jun, Sung Jae
  • Pinkse, Joris

Abstract

We propose a semiparametric test for the value of coefficients in models with conditional moment restrictions that has correct size regardless of identification strength. The test is in essence an Anderson-Rubin (AR) test using nonparametrically estimated instruments to which we apply a standard error correction. We show that the test is (1) always size-correct, (2) consistent when identification is not too weak, and (3) asymptotically equivalent to an infeasible AR test when identification is sufficiently strong. We moreover prove that under homoskedasticity and strong identification our test has a limiting noncentral chi-square distribution under a sequence of local alternatives, where the noncentrality parameter is given by a quadratic form of the inverse of the semiparametric efficiency bound.

Suggested Citation

  • Jun, Sung Jae & Pinkse, Joris, 2012. "Testing Under Weak Identification With Conditional Moment Restrictions," Econometric Theory, Cambridge University Press, vol. 28(6), pages 1229-1282, December.
  • Handle: RePEc:cup:etheor:v:28:y:2012:i:06:p:1229-1282_00
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    Cited by:

    1. Zhipeng Liao & Xiaoxia Shi, 2020. "A nondegenerate Vuong test and post selection confidence intervals for semi/nonparametric models," Quantitative Economics, Econometric Society, vol. 11(3), pages 983-1017, July.
    2. Jinho Choi & Juan Carlos Escanciano & Junjie Guo, 2022. "Generalized band spectrum estimation with an application to the New Keynesian Phillips curve," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 1055-1078, August.
    3. Bertille Antoine & Pascal Lavergne, 2020. "Identification-Robust Nonparametric Interference in a Linear IV Model," Discussion Papers dp20-03, Department of Economics, Simon Fraser University.
    4. Wang, Wenju & Wang, Qiao, 2019. "Consistent specification test for partially linear models with the k-nearest-neighbor method," Economics Letters, Elsevier, vol. 177(C), pages 89-93.
    5. Kohtaro Hitomi & Masamune Iwasawa & Yoshihiko Nishiyama, 2022. "Optimal minimax rates against nonsmooth alternatives [Optimal testing for additivity in multiple nonparametric regression]," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 322-339.
    6. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    7. Kohtaro Hitomi & Masamune Iwasawa & Yoshihiko Nishiyama, 2018. "Rate Optimal Specification Test When the Number of Instruments is Large," KIER Working Papers 986, Kyoto University, Institute of Economic Research.
    8. Antoine, Bertille & Lavergne, Pascal, 2014. "Conditional moment models under semi-strong identification," Journal of Econometrics, Elsevier, vol. 182(1), pages 59-69.
    9. Rachida Ouysse, 2014. "On the performance of block-bootstrap continuously updated GMM for a class of non-linear conditional moment models," Computational Statistics, Springer, vol. 29(1), pages 233-261, February.
    10. Xu, Ruonan, 2021. "On the instrument functional form with a binary endogenous explanatory variable," Economics Letters, Elsevier, vol. 206(C).
    11. Li, Hongjun & Li, Qi & Liu, Ruixuan, 2016. "Consistent model specification tests based on k-nearest-neighbor estimation method," Journal of Econometrics, Elsevier, vol. 194(1), pages 187-202.
    12. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.

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