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Uniform Inference in Panel Autoregression

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Abstract

This paper considers estimation and inference concerning the autoregressive coefficient (") in a panel autoregression for which the degree of persistence in the time dimension is unknown. The main objective is to construct confidence intervals for " that are asymptotically valid, having asymptotic coverage probability at least that of the nominal level uniformly over the parameter space. It is shown that a properly normalized statistic based on the Anderson-Hsiao IV procedure, which we call the M statistic, is uniformly convergent and can be inverted to obtain asymptotically valid interval estimates. In the unit root case confidence intervals based on this procedure are unsatisfactorily wide and uninformative. To sharpen the intervals a new procedure is developed using information from unit root pretests to select alternative confidence intervals. Two sequential tests are used to assess how close " is to unity and to correspondingly tailor intervals near the unit root region. When " is close to unity, the width of these intervals shrinks to zero at a faster rate than that of the confidence interval based on the M statistic. Only when both tests reject the unit root hypothesis does the construction revert to the M statistic intervals, whose width has the optimal N^{-1/2}T^{-1/2} rate of shrinkage when the underlying process is stable. The asymptotic properties of this pretest-based procedure show that it produces confidence intervals with at least the prescribed coverage probability in large samples. Simulations confirm that the proposed interval estimation methods perform well in finite samples and are easy to implement in practice. A supplement to the paper provides an extensive set of new results on the asymptotic behavior of panel IV estimators in weak instrument settings.

Suggested Citation

  • John Chao & Peter C.B. Phillips, 2017. "Uniform Inference in Panel Autoregression,"Cowles Foundation Discussion Papers 2071, Cowles Foundation for Research in Economics, Yale University.
    • Handle:RePEc:cwl:cwldpp:2071
    Note: Includes supplemental material
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    File URL:https://cowles.yale.edu/sites/default/files/files/pub/d20/d2071-a.pdf
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    References listed on IDEAS

    as
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    Cited by:

    1. Chengwang Liao & Ziwei Mei & Zhentao Shi, 2024. "Nickell Meets Stambaugh: A Tale of Two Biases in Panel Predictive Regressions,"Papers 2410.09825, arXiv.org.
    2. Khalaf, Lynda & Saunders, Charles J., 2020."Monte Carlo two-stage indirect inference (2SIF) for autoregressive panels,"Journal of Econometrics, Elsevier, vol. 218(2), pages 419-434.
    3. In Choi & Sanghyun Jung, 2021."Cross-sectional quasi-maximum likelihood and bias-corrected pooled least squares estimators for short dynamic panels,"Empirical Economics, Springer, vol. 60(1), pages 177-203, January.

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    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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