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Uniform Validity of the Subset Anderson-Rubin Test under Heteroskedasticity and Nonlinearity

Author

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  • Atsushi Inoue
  • `Oscar Jord`a
  • Guido M. Kuersteiner

Abstract

We consider the Anderson-Rubin (AR) statistic for a general set of nonlinear moment restrictions. The statistic is based on the criterion function of the continuous updating estimator (CUE) for a subset of parameters not constrained under the Null. We treat the data distribution nonparametrically with parametric moment restrictions imposed under the Null. We show that subset tests and confidence intervals based on the AR statistic are uniformly valid over a wide range of distributions that include moment restrictions with general forms of heteroskedasticity. We show that the AR based tests have correct asymptotic size when parameters are unidentified, partially identified, weakly or strongly identified. We obtain these results by constructing an upper bound that is using a novel perturbation and regularization approach applied to the first order conditions of the CUE. Our theory applies to both cross-sections and time series data and does not assume stationarity in time series settings or homogeneity in cross-sectional settings.

Suggested Citation

  • Atsushi Inoue & `Oscar Jord`a & Guido M. Kuersteiner, 2025. "Uniform Validity of the Subset Anderson-Rubin Test under Heteroskedasticity and Nonlinearity," Papers 2507.01167, arXiv.org.
    • Handle: RePEc:arx:papers:2507.01167
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    References listed on IDEAS

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    1. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, September.
    2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    3. Donald W.K. Andrews, 2017. "Identification-Robust Subvector Inference," Cowles Foundation Discussion Papers 2105, Cowles Foundation for Research in Economics, Yale University, revised Sep 2017.
    4. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
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