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Uniform Inference in Panel Autoregression

325 Pages Posted: 18 Jan 2017  

John C. Chao

University of Maryland

Peter C. B. Phillips

Yale University - Cowles Foundation; University of Auckland; University of Southampton; Singapore Management University - School of Economics

Date Written: January 6, 2017


This paper considers estimation and inference concerning the autoregressive coefficient (ρ) 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 ρ 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 ρ is to unity and to correspondingly tailor intervals near the unit root region. When ρ 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.

Keywords: Confidence interval, Dynamic panel data models, panel IV, pooled OLS, Pretesting, Uniform inference

JEL Classification: C230, C360

Suggested Citation

Chao, John C. and Phillips, Peter C. B., Uniform Inference in Panel Autoregression (January 6, 2017). Cowles Foundation Discussion Paper No. 2071. Available at SSRN: or

John C. Chao

University of Maryland ( email )

Department of Economics
College Park, MD 20742
United States
301-405-1579 (Phone)
301-408-3542 (Fax)

Peter C. B. Phillips (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
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203-432-5429 (Fax)

University of Auckland ( email )

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New Zealand
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University of Southampton

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Singapore Management University - School of Economics

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